improvedrainfallpredictionthroughnonlinearautoregressive...

Research ArticleImproved Rainfall Prediction through Nonlinear AutoregressiveNetwork with Exogenous Variables A Case Study in Andes HighMountain Region

Mario Pentildea12 Angel Vazquez-Patintildeo34 Darıo Zhintildea5 Martin Montenegro5

and Alex Aviles 5

1Direccion de Investigacion (DIUC) Universidad de Cuenca Campus Central Av 12 de Abril sn y Loja 010203Cuenca Ecuador2Departamento de Quımica Aplicada y Sistemas de Produccion Facultad de Ciencias Quımicas Universidad de CuencaCampus Central Av 12 de Abril Sn y Loja 010203 Cuenca Ecuador3Facultad de Ingenierıa Universidad de Cuenca Av 12 de Abril Sn y Loja 010203 Cuenca Ecuador4Departamento de Ingenierıa Civil Universidad de Cuenca Av 12 de Abril Sn y Loja 010203 Cuenca Ecuador5Carrera de Ingenierıa Ambiental Facultad de Ciencias Quımicas Universidad de Cuenca Campus CentralAv 12 de Abril Sn y Loja 010203 Cuenca Ecuador

Correspondence should be addressed to Alex Aviles alexavilesucuencaeduec

Received 3 December 2019 Revised 4 July 2020 Accepted 1 September 2020 Published 17 September 2020

Academic Editor Roberto Coscarelli

Copyright copy 2020 Mario Pentildea et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Precipitation is the most relevant element in the hydrological cycle and vital for the biosphere However when extreme pre-cipitation events occur the consequences could be devastating for humans (droughts or floods) An accurate prediction ofprecipitation helps decision-makers to develop adequate mitigation plans In this study linear and nonlinear models with laggedpredictors and the implementation of a nonlinear autoregressive model with exogenous variables (NARX) network were used topredict monthly rainfall in Labrado and Chirimachay meteorological stations To define a suitable model ridge regression lassorandom forest (RF) support vector machine (SVM) and NARX network were used Although the results were ldquounsatisfactoryrdquowith the linear models the specific direct influences of variables such as Nintildeo 1 + 2 Sahel rainfall hurricane activity North PacificOscillation and the same delayed rainfall signal were identified RF and SVM also demonstrated poor performance However RFhad a better fit than linear models and SVM has a better fit than RF models Instead the NARX model was trained using severalarchitectures to identify an optimal one for the best prediction twelve months ahead As an overall evaluation the NARX modelshowed ldquogoodrdquo results for Labrado and ldquosatisfactoryrdquo results for Chirimachay +e predictions yielded by NARX models for thefirst six months ahead were entirely accurate +is study highlighted the strengths of NARX networks in the prediction of chaoticand nonlinear signals such as rainfall in regions that obey complex processes +e results would serve to make short-term plansand give support to decision-makers in the management of water resources

1 Introduction

Precipitation is one of the main components in the hy-drological cycle [1 2] It is one of the most importantvariables associated with atmospheric circulation in mete-orological studies [3] Moreover it is the main source ofrecharge in water balance studies from local to regionalscales [4] However its forecast has become a significant

challenge owing to the complexity of the atmosphericprocesses that produce rainfall [5] +is reality is evident inhigh mountain regions [6] with high time-space variabilitylike the Andes mountain range In particular the wateroriginating from the Andean high mountains is used fordiverse purposes (eg human consumption agriculturelivestock grazing industry and recreation) in downstreamcities [7ndash9] (eg Merida in Venezuela Bogota in Colombia

HindawiAdvances in MeteorologyVolume 2020 Article ID 1828319 17 pageshttpsdoiorg10115520201828319

and Quito in Ecuador) An accurate prediction of precipi-tation (temporal and spatial) can help decision-makers toassess in advance both flood and drought situations [10 11]and it could support extreme hydrological management anddiminish the impacts on the population

In different studies a variety of methods have been usedto forecast rainfall Some of them have shown accurateresults like the multiple linear regression and k-nearest-neighbors methods as in [12 13] Other approaches haveused the outputs of global climate models to improve theseasonal and subseasonal forecasting [14ndash16] and theprobabilistic forecasts for uncertainty quantification[17ndash19] Other studies have applied artificial intelligenceapproach for rainfall prediction such as artificial neuralnetworks (ANNs) [5 10ndash12 20ndash24] support vector machine(SVM) [12 13 24 25] logistic regression [26] and randomforest [27 28] Also other studies have investigated theoptimum selection of predictors to improve forecast accu-racy [29] NARX model is a novel approach for many ap-plications of prediction of environmental variables forexample water level of wetland systems [30] groundwaterlevels [31ndash33] urban drainage framework [34] stream flowand inflow to reservoirs [35 36] water level in urban flood[37ndash39] and rainfall forecasting [40 41]

+e unpredictable and chaotic nature of the rainfallbehavior makes its prediction a critical challenge+eNARXmodel is suitable for dealing with time series with suchcharacteristics [42] since the output value of a variable is anonlinear function of the past values of the same variableand other exogenous variables Nonlinear mapping isconvenient in chaotic environments and it is superior toconventional autoregressive models It is also superior toANN since NARX uses its memory to make predictionsNARX presents an improvement opportunity due to itsperformance in the prediction of time series that has aseasonal component

In Andean countries like Ecuador some of themethods mentioned above have also been used to predictprecipitation For example in [43] continuous transferfunction models were used to predict rainfall on the coastsof Ecuador Also Mendoza et al [44] used sea surfacetemperature (SST) as a predictor and canonical correla-tion as a method to predict rainfall in the coast and Andesof Ecuador +ese studies highlight the complex rela-tionship between predictors and rainfall in the AndesHowever new methods like NARX could be applied in theEcuadorian Andes to improve the performance of pre-cipitation forecasting

+is study first explores the performance of the mostcommonly used linear models for the rainfall forecast Itthen compares them with nonlinear models to verify theirperformance in a mountain basin located in the south ofEcuador Finally NARX models are used to forecast rainfallseveral steps ahead +e results obtained can have a sig-nificant impact on mountain systems because they could beused to obtain improved performance in high mountainareas

2 Materials and Methods

21 Study Area +e study area is composed of the highmountain subbasins Tomebamba and Machangara locatedin the Andean southern Ecuador (Figure 1) +e two sub-basins are essential to supply water to the city of Cuencaconsidered the third most important in Ecuador [45]Moreover the two subbasins belong to the Paute hydro-graphic system which together with others provide waterto generate energy +e subbasins altitude varies between2440 and 4400masl which in turn allows finding a greatvariety of vegetation For example in high areas there arepatches of Polylepis reticulata tussock grasses ground ro-settes cushion plants and ground rosettes while in the lowareas there are agricultural land pastures as well as urbanzones [9 46 47]

Two meteorological stations are taken into account forthe analysis Labrado and Chirimachay +ese are locatedin the upper parts of the two subbasins at 3300masl(Figure 1) According to Celleri et al [48] there are twotypes of precipitation within the study area bimodal type I inthe lower parts of the subbasins and bimodal type II in themiddle and upper zones Both regimes have two peaks ofprecipitation during April and October however the bi-modal type II regimen presents a less dry season from Juneto August (Figure 2)

22 Precipitation Data Rainfall data from Labrado (sub-basin of Machangara) and Chirimachay (subbasin ofTomebamba) stations were provided by the EcuadorianNational Institute of Meteorology and Hydrology(INAMHI httpwwwserviciometeorologicogobec) +estudy period is 1964ndash2015 Table 1 shows a statisticalsummary of the rainfall data

23Climatic Indices +e 27 climatic indices listed next wereused in the study +e Atlantic Meridional Mode (AMM)SST Index [49] Atlantic Multidecadal Oscillation (AMO)[50] Antarctic Oscillation (AO) [51] Bivariate ENSO Timeseries (BEST) [52] Caribbean Index (CAR) [53] hurricaneactivity (HURR) [54] Multivariate ENSO Index (MEI) [55]North Atlantic Oscillation (NAO) [56] Nintildeo 1 + 2 Nintildeo 3Nintildeo 34 and Nintildeo 4 [57] North Pacific Oscillation (NP)[58] North Tropical Atlantic SST Index (NTA) [53] Oce-anic Nintildeo Index (ONI) [59] Pacific Decadal Oscillation(PDO) [60] Pacific North American Index (PNA) [61]Quasibiennial Oscillation (QBO) [62] Sahel rainfall(SAHELRAIN) [63] Southern Oscillation Index (SOI) [64]solar flux [65] Tropical Northern Atlantic Index (TNA)[66] Trans-Nintildeo Index (TNI) [67] Tropical Southern At-lantic Index (TSA) [68] western hemisphere warm pool(WHWP) [69] Western Pacific Index (WP) [70] and globalmean landocean temperature (GMSST) [71 72] Time seriesof these indices are available in httpswwwesrlnoaagovpsddataclimateindiceslist

2 Advances in Meteorology

2deg40

prime0Prime

S

79deg10prime0PrimeW 79deg5prime0PrimeW 79deg0prime0PrimeW


0deg45

prime0Prime

N1deg

16prime0Prime

S3deg

17prime0Prime

S

3deg17

prime0Prime

S1deg

16prime0Prime

S0deg

45prime0Prime

N

2deg45

prime0Prime

S2deg

50prime0Prime

S2deg

55prime0Prime

S

2deg40

prime0Prime

S2deg

45prime0Prime

S2deg

50prime0Prime

S2deg

55prime0Prime

S

81deg11prime0PrimeW 79deg10prime0PrimeW 77deg9prime0PrimeW 75deg8prime0PrimeW

81deg11prime0PrimeW 79deg10prime0PrimeW79deg0prime0PrimeW 78deg30prime0PrimeW

79deg0prime0PrimeW 78deg30prime0PrimeW

2deg30

prime0Prime

S

2deg30

prime0Prime

S3deg

0prime0Prime

S

3deg0prime0Prime

S


0 25 5 10kilometers

N

LabradoChirimachay

4400

2440

Altitude (masl)

Figure 1 Location of the study area made up of the subbasins Machangara and Tomebamba

2 3 8754 61 1210 1190

40

80

120

160

mm

(mon

th)

(a)

2 3 8754 61 1210 1190

40

80

120

160

mm

(mon

th)

(b)

Figure 2 Seasonality of rainfall in (a) Labrado and (b) Chirimachay stations

Advances in Meteorology 3

24 Linear Models

241 Linear Model +e linear model predicts a quantitativeoutput y based on a single predictor x assuming that a linearrelationship between them exists +e following equationdescribes this linear relationship

y β0 + β1x + ε (1)

where β0 is the bias (offset) β1 is the coefficient (slope) ofvariable x and ε is the error or random noise

242 Multivariate Linear Model In general the multivar-iate linear model supposes that p distinct predictors areavailable and the output is a weighted linear combination ofthe set X of predictor variables x +e formula of themultivariate linear model is as follows

y β0 + β1x1 + β2x2 middot middot middot βpxp + ε (2)

where xj represents the jth predictor and βj represents themagnitude of the relationship between the jth predictor andthe output y +e absolute value of the coefficients βj definesthe degree of influence of the predictor over the output [73]

243 Linear Model Regularization and Selection As theavailability of variables increases the probability of fallinginto overfitting also increases [74] Overfitting is an errorthat occurs when a model fits too closely to a limited set ofdata points decreasing the predictive power of the model Toprevent this drawback commonly ridge and lasso regres-sions are used as regularization techniques [73] +e ob-jective of applying these techniques is to obtainparsimonious models In the multivariate linear model theadjustment of the parameters is made by minimizing thecost function (residual sum square RSS) through the least-squares +e RRS formula is shown as follows

RSS 1113944n

i1yi minus β0 minus 1113944

p

j1βjxij

⎛⎝ ⎞⎠

2

(3)

where n is the number of samples in the dataset and xij is thevalue of the ith sample in the jth predictor Ridge regressionaggregates a penalty term to the cost function which is equalto the sum of squares of the magnitude of the coefficients Asa result this method keeps all the predictors with the lowestcoefficient magnitudes In the lasso regression approach thepenalty term is equal to the sum of the magnitude of theabsolute coefficient and some values even can become zero+is is the reason why Lasso is considered as a feature

selection method Ridge regression and lasso minimize thequantity depicted on the following equations respectively

RSS + 1113944p

j1βj2 (4)

RSS + λ1113944p

j1 βj

11138681113868111386811138681113868

11138681113868111386811138681113868 (5)

where λge 0 is a tuning parameter +e impact of regulari-zation over the estimated coefficient is controlled through λthat accompanies the penalty term In an extreme case whenλ 0 the penalty term does not cause any effect Converselyas λ⟶infin the incidence of the regularization penalty in-creases [73]

244 Training and Testing Datasets +e data of the 27synoptic climatic indices were lagged 12months with respectto rainfall data +is decision is due to a practical matter Topredict 12 months of rain information on exogenous var-iables from the previous 24 to 12 months is necessary Fromthat the information was lagged from 1 to 24 months sothere were 675 time series used as predictors correspondingto the climatic indices To incorporate the sense of autor-egression in linear models the same rainfall signal was usedas a predictor in the models that considered lagged exog-enous predictors Although some predictors were correlatedwith each other (eg Spearman index of 094 between TNAand NTA) none were omitted +is is because only perfectlycorrelated signals (ie genuinely redundant) do not provideadditional information [75]+e original dataset was dividedinto two subsets the first one from January 1964 to De-cember 2014 and the second one from January 2015 toDecember 2015 +e Minmax normalization process wasapplied to the first subset which produced parameters tonormalize the second subset as well +e first subset wasrandomly divided into a subset to train models (80 to findthe best coefficients) and a subset to test (20 to assess themodel) Applying this approach fifty multivariate linearmodels to estimate the rainfall were fitted namely twenty-five for each method (ridge and lasso) one with no lags and24 with lags ranging from 1 to 24 lags +e algorithm used todefine the best value of λ and fit the models was cross-validation [73]

25 RandomForest Random forest (RF) [76] is based on theidea of boosting the prediction of a model using an assemblyof decision trees [77] results Each random tree is based onan independent random vector of sample values with thesame distribution RF has become popular in hydrologicaland climatic applications (eg [27 28]) due to its highperformance efficient training in big datasets and high

Table 1 Statistical summary of stations rainfall data

Station Standard deviation Maximum Minimum Mean Skewness KurtosisLabrado 4565 28730 1280 10406 068 346Chirimachay 5733 49030 190 11190 179 975


dimensions and the estimation of the importance of thedifferent features that represent the instances

Several hyperparameters can be optimized in the con-struction of the model based on random forest From themdifferent values for the number of decision trees its max-imum depth and the number of features used in the con-struction of the trees were explored in a grid search 6-foldcross-validation [78] fashion For this 85 of data were usedas a training subset For testing the performance of theresulting model the remaining independent 15 was usedFinally the model was used for the prediction of rainfall in2015 in the two study stations

26 Support Vector Machines Support vector machine(SVM) [79] raises the dimensionality of the data to a vectorspace where it is possible to construct a linear regressionmodel +e linear regression is performed based on repre-sentative data points that make up a so-called support vector+e representation of the data in a high dimension is doneusing kernel functions Here the Gaussian radial basisfunction (RBF) was used Two hyperparameters must beoptimized for the regularization (parameter C) and thespread of influence of the support vector (parametergamma)

+e optimization of the hyperparameters was done in thesame way as with RF ie 85 of data for training and 6-foldcross-validation and 15 for testing +e resulting modelwas used for predicting the rainfall in 2015 in the two studystations Many studies in climate and meteorology have usedSVM [12 13 24 25] and RF in prediction so we use themhere as a baseline to compare the performance of NARX

27 Recurrent Neural Nets with Exogenous Inputs NARXModel +e nonlinear autoregressive network with exoge-nous inputs (NARX) is a dynamic recurrent neural network(RNN) with feedback connections that enclose severallayers of the network ie the output is considered as anotherinput of the network Figure 3 depicts the NARX modelarchitecture

Its memory ability is useful for the prediction of non-linear time series Besides unlike classic artificial neuralnetworks NARX gains degrees of freedom by incorporatingvaluable information from exogenous inputs [32] +ere aretwo different architectures of NARX the series-parallelarchitecture (called open-loop) and the parallel architecture(called close-loop) presented by the following equationsrespectively

1113954y(t + 1) F y(t) y(t minus 1) y t minus ny1113872 11138731113872

X(t + 1) X(t) X t minus nx( 11138571113857(6)

1113954y(t + 1) F 1113954y(t) 1113954y(t minus 1) 1113954y t minus ny1113872 11138731113872

X(t + 1) X(t) X t minus nx( 11138571113857(7)

where F(middot) is the mapping function and 1113954y(t + 1) is thepredicted output of NARX for the time t + 1 determined atthe instant t +e terms y(t) y(t minus 1) y(t minus ny) are the

true past values of the time series also known as the groundtruth and 1113954y(t) 1113954y(t minus 1) 1113954y(t minus ny) is the past predictedoutputs generated by the NARX +e true values of exog-enous inputs are X(t + 1) X(t) X(t minus nx) +e num-bers of input delays and output delays are defined by nx andny respectively

+e series-parallel architecture is used in the trainingprocess because the real output is available leading to aconventional feed-forward representation while the parallelarchitecture can make predictions based on feeding back theestimated output instead of accurate output

+e mapping function F(middot) (which is initially un-known) is fitted as the training process progresses +emultilayer perceptron (MLP) architecture is used torepresent this approximation since it is a robust structurecapable of learning any kind of continuous nonlinearmapping A classic MLP contains three basic layers inputhidden and output layers Moreover it has elements suchas neurons activation functions and connectionsweights As the number of hidden neurons increases themodel can approach more complex functions Howeverthe selection of the number of these hidden neuronsdepends on the addressed case study In general just onehidden layer with neurons ranging from [05p 2p] iscommonly used [80] +e sigmoid-linear transfer functioncombination can provide an efficient mathematical rep-resentation of the output as a function of the input signal[32]

271 NARX Model Architecture In NARX models 27synoptic climate indices and the rainfall signal were used asinputs to the nets and rainfall was the output Again noneof the predictor was excluded To identify the optimumNARX architecture and due to the massive amount of netsetting allowed the standard trial-and-error method toselect the number of hidden nodes and lags number wasused +e input layer neurons depended on the number oflags used so architectures with 2 3 4 5 6 9 and 12 lagswere tested +e output layer had just one neuron +e nethad one hidden layer with 10 20 30 40 and 50 neurons+e neurons in the hidden layer used a sigmoid transferfunction whereas the output neuron used a linear transferfunction [32] During the training process the first subset israndomly dividing into a training sample a cross-valida-tion sample and a test sample (70 15 and 15 re-spectively) +e connections weights were initializedrandomly and they were tuned using the Lev-enbergndashMarquardt algorithm [80] which is one of the mostwidely used functions for time series network predictionand training [81] It is essential to mention that the trainingwas performed using the series-parallel architecture andthe test sample was evaluated with the architecture men-tioned above +e test sample is randomly selected so thesense of temporality is lost Once the NARX was fitted in aseries-parallel configuration it was converted to parallelarchitecture and the test close-loop (second subset) wasevaluated accordingly +is model can perform forecastingfor several time steps ahead hence the predicted outputs


(at previous steps) constitute a real-time series as well as thetest close-loop subset

28 Performance Measures

281 NashndashSutcliffe Efficiency Coefficient (NSE) +eNSE iswidely used to evaluate the performance of hydrologicalmodels NSE is even better than other metrics such as thecoefficient of determination However it is susceptible toextreme values since it makes a sum over the square values ofthe differences between the observed and the predictedvalues [82] +is index is defined by equation (5)

NSE 1 minus1113944

N

i1 Oi minus Pi( 11138572

1113944N

i1 Oi minus Oi( 11138572 (8)

where Oi and Pi are the observed and predicted values ineach period respectively and Oi is the average of the ob-served values

282 KlingndashGupta Efficiency (KGE) +e KGE is a perfor-mance measure based on three equally weighted compo-nents variability linear correlation and bias ratio betweenpredicted and observed data +is index is defined byequation (6)

KGE 1 minus

(α minus 1)2

+(cc minus 1)2

+(β minus 1)2

1113969

(9)

where a is the variability (the ratio between the standarddeviation of predicted over the observed values) cc is thelinear correlation between predicted and observed valuesand β is the division between the average of predicted overthe average of observed values

283 Determination of Bias Percentage (PBIAS) +e PBIASdetermines whether there is a tendency in the valuespredicted by the model (ie if these are higher or lowerthan the observed values) A positive PBIAS indicates thatthe model underestimates the predicted variable while anegative indicates that the variable is overestimating +eoptimal value is a PBIAS equal to zero+is index is definedas

PBIAS() 1113944

N

i1 Oi minus Pi( 1113857lowast 100

1113944N

i1Oi

(10)

284 Root Mean Square Error (RMSE) +e root meansquare error is the difference between forecasted values andthe observations +e RMSE is always positive and valuesclosed to zero indicate a perfect fit also RMSE is sensitive tooutliers +e RMSE is defined as

RMSE

1113944N

i1 Pi minus Oi( 11138572

N

1113971

(11)

where N is the length of the time seriesNSE KGE and PBIAS can classify the goodness of fit in

four categories [83 84] as shown in Table 2+ese metrics evaluate the goodness of fit of the models

in the training subset and the forecasting performance in thetesting subset

3 Results and Discussion

31 Multivariate Linear Model To obtain a multivariatelinear model for predicting rainfall for Labrado and

X (t + 1)

X (t ndash 1)

X (t ndash nx)

Y (t ndash ny)

Y (t ndash 1)

Y^ (t + 1)

Y (t)

X (t)

Input layer Hidden layer Output layer

Figure 3 Scheme of NARX models


Chirimachay dataset from January 1964 to December 2015is used Each of the fifty models was fitted with λ 10d withd minus2 minus19 minus18 99 10 +e fitted models ob-tained for each λ that produced the best performance wereselected NSE metric applied in training and testing sets withthe selected models for both ridge regression and lasso isdepicted in Figure 4

For both ridge regression and lasso a tendency is evi-dent As lags increase the NSE grows as well in the trainingset However for Labrado station (Figure 4(a)) the per-formance grows as lags increase to 18 where the perfor-mance in the test set fell +e models fitting the best for bothridge and lasso were obtained with around 16 lags In themodels with 16 lags the performance of both was the samewhile the fit was better for the ridge method Despite havingused regularization methods the overfitting raised frommodels that used 18 lags or more where it is clear that the fitincreases but the performance decreases In the Chir-imachay station (Figure 4(b)) the behavior was similar toLabrado +e best models for both ridge and lasso were witharound 18 lags In these models ridge was better than lassofor both fit and performance Again the overfitting problemraised from the model with 19 lags +e top five of thepredictors is shown in Appendix 1 +ese predictors wereranked by the absolute value of the βj in each fitted model

In Appendix 1 it can be seen that for Labrado stationthe predictor Nintildeo 1 + 2 lagged 1 period (Nintildeo 1 + 2_1)appears as the most influential index in linear models de-fined by the lasso method On the contrary for the ridgemethod Nintildeo 1 + 2 appears in the first six lagged modelshurricane activity lagged 7 periods (HURR_7) and becomethe most influential from seven to eleven lagged models andthe remainingmodels are influencing the same rainfall signalwith a lag of 12 months For the Chirimachay station Nintildeo1 + 2 was the most crucial variable because it always appearsas the first predictor of the model obtained by lassoMeanwhile for ridge regression the same rainfall (with a lagof one month) is the most influential predictor in modelsthat considered until eleven lags However from here(models with lags from twelve to twenty-four months) thesame rainfall with lags of 11 and 12 months became the mostimportant predictor Another essential predictor indexes areas follows North Pacific Oscillation lagged 1 period (NP_1)and Sahel rainfall lagged 3 or 5 periods (SAHELRAIN_3 andSAHELRAIN_5) which appears in the majority of themodels for both lasso and ridge regression model regardlessof the station It is worth noting that when we refer to thepredictors for example Nintildeo 1 + 2 lagged 1 period the truelag is 13 periods since we initially induced a lag of 12 periodsin the predictors with respect to the rainfall variable in theinitial database +is naturally does not apply to delayed

rainfall variables ENSO indexes have a strong influence onEcuadorian rainfall [43] +ey found that significant pre-dictors for rainfall come mainly from the tropical Pacific seasurface temperature especially from ENSO events +isstatement matches with our finding on the Nintildeo 1 + 2 andNorth Pacific Oscillation indexes Overall the models ob-tained for both Labrado and Chirimachay were ldquounsatis-factoryrdquo according to Table 2 thus implying the need tomove in nonlinear models to improve the performance

32 Random Forest Model +e RF model of 12 lags had thebest performance in Labrado station However the testingdisplays (Table 3) low values of NSE and KGE thus these areclassified as ldquoUnsatisfactoryrdquo On the contrary PBIAS isldquovery goodrdquo value and the RMSE is relatively high In thetest the close-loop values of NSE KGE and RMSE are badonly PBIAS is better relative to the test subset +e Chir-imachay station presents the better RF model with 12 lagssimilar to Labrado +us in the testing NSE and KGE showldquounsatisfactoryrdquo values and PBIAS is ldquovery goodrdquo In the testclose-loop subset the metrics NSE KGE and RMSE showlow performance and only PBIAS is ldquovery goodrdquo

+e RF models show poor results of forecasting (Fig-ure 5) thus NSE and KGE have low values and those areunsatisfactory +e model has difficulty in forecasting highand low extreme values the difference between observed andforecasting is more evident in January and July for bothstations in general RF shows a low forecasting performancealthough RF is better than LM

Also Chen et al [85] found RF performing better thanLM for drought forecasting However extreme events arenot accurate In concordance with [85] the RF models in thepeaks in rainfall are not accurate Rainfall in Labrado andChirimachay stations shows two high peaks in the year inApril and October (Figure 2) For this reason low values ofmonthly forecasting are observed in the wet and dry seasons

33 Support VectorMachineModel +e SVM model with 3lags presents a better performance for Labrado stationhowever for the test the statisticians are weak and the NSEand KGE show ldquounsatisfactoryrdquo values however PBIAS isldquovery goodrdquo and the RMSE is relatively high In the testclose-loop the metrics for evaluating the model worsenonly RMSE shows a little improvement +erefore thenumber of lags does not have a strong influence in themodel SVM models with 3 6 9 and 12 lags have verysimilar values of NSE KGE and PBIAS and the number oflags is not significantly different In the Chirimachay sta-tion the SVM model with 12 lags exhibits better perfor-mance However in the test subset the NSE and KGE

Table 2 Classification of the goodness of fit and performance

Goodness of fit NSE KGE PBIASVery good gt075 gt090 (minus10 10)Good (065 075] (075 09] (minus15 minus10] or [10 15)Satisfactory [050 065] [050 075] (minus25 minus15] or [15 25)Unsatisfactory lt050 lt050 lt minus25 or gt 25


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags

04

03

02

01

0

NSE

Ridge testingRidge training

Lasso testingLasso training

(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags



04

03

02

01

0

NSE

(b)

Figure 4 NSE metric for models obtained by ridge regression and lasso (a) Labrado (b) Chirimachay

Table 3 Results for RF models

Basin Lags Subset NSE KGE PBIAS RMSE

Labrado 12 Test (Ts) 024 021 minus275 3997Test close-loop 004 0 148 4041

Chirimachay 12 Test (Ts) 025 026 minus237 4718Test close-loop 009 006 61 3961

250

200

150

100

50

0

Fore

caste

d

250200150100500Observed

(a)

Fore

caste

d

350

300

250

200

150

100

50

0350250 300200150100500

Observed

(b)

Figure 5 Continued


present very low ldquounsatisfactoryrdquo values only PBIAS isldquovery goodrdquo and RMSE is high +e test close-loop showsthat (Table 4) low values of NSE and KGE are ldquounsatis-factoryrdquo PBIAS is ldquovery goodrdquo and RMSE is relatively high+e SVM model for Labrado and Chirimachay are similarin other words in the test and test close-loop shows lowvalues than the test +ese values are poor and classified asldquounsatisfactoryrdquo also both models have ldquovery goodrdquo PBIASin test and test close-loop

Figure 6 shows SVM model forecasted vs observed data+emodel shows difficulty in forecasting rainfall peaks mainlyin January and September where significant discrepancies areobserved in both stations However the Chirimachay stationdisplays a lower performance Although SVM is one of mostaccurate rainfall prediction models [12] it failed to predictextreme rainfall [12] for this reason SVMdoes not show goodforecasting in Labrado and Chirimachay and both showsseveral low and high peaks in rainfall (Figure 6)

34 Recurrent Neural Nets with Exogenous Inputs (NARX)A different number of hidden neurons were evaluated for its ability togenerate accurate model outputs A hidden layer formed by 50 neuronswith sigmoid transfer function and a single output neuron with a linearfunctionprovidedthemosteffectivenetworkarchitectureFortheLabradostation3 lags in the inputwerenecessary toproduce thebestmodel and6lags for Chirimachay Table 5 shows the performance of the best models

According to Table 5 for Labrado basin the goodness offit (evaluated in train cross-validation and test samples) isldquosatisfactoryrdquo in accordance with coefficient NSE ldquogoodrdquo inagreement with KGE and ldquovery goodrdquo according to PBIASLikewise the performance (evaluated in the test close-loop)is ldquosatisfactoryrdquo for both NSE and KGE and ldquogoodrdquo for

PBIAS For the Chirimachay station the goodness of fit wasalso ldquosatisfactoryrdquo for both NSE and KGE and ldquovery goodrdquofollowing PBIAS Finally the performance was ldquosatisfactoryrdquoin agreement with NSE KGE and PBIAS As an overallevaluation the model fitted for Labrado was ldquogoodrdquo and themodel for Chirimachay was ldquosatisfactoryrdquo Figure 7 showsthe predicted versus real rainfall in the training subset forLabrado (a) and Chirimachay (b) Besides the predicted andreal rainfall in the test close-loop is presented as time series(c) for Labrado and (d) for Chirimachay

Figure 7 shows that for the training subset the modelreached a perfect fit for some data points (points over theline) but for other data points the predictions were weak(Figures 7(a) and 7(b)) Labrado station shows problemsmainly in peaks of rainfall where overestimation and un-derestimation are present (Figure 7(c)) On the contraryChirimachay station shows better forecasting than Labradoand the tendency is better captured from months 1 to 8 andfrom 9 to 12 it shows lousy forecasting (Figure 7(d))

In the test close-loop data points (second dataset) thepredictions were ldquovery goodrdquo for the first sixmonths and afterthat the performances decrease It makes sense because theforward predictions are based on predictions from previoussteps +erefore previous forecast errors affect subsequentpredictions All prediction models depend on long-term datafrom past time [81] +is is consistent with our study becauseit works with a long-time series of information and alsobecause the NARX models present good forecasts Howeverthe prediction quality decrease when the times ahead increase

+e overall results show a satisfactory performance of theNARX model However at a lower time scale and with localexogenous variables the NARX model has shown excellentperformance in other studies as well [40 41] Also some

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)

Figure 5 Comparison between predicted and observed values (a) observed vs forecasted subset for Labrado (b) observed vs forecastedChirimachay (c) forecasting for Labrado in 2015 (d) forecasting for Chirimachay in 2015


studies such as [81 86] show the suitable way of NARXmodel for getting good predictions on problems involvinglong-term dependencies Nevertheless these studies usefew predictors hence their performance could improveby including more exogenous variables like our study

+erefore NARX models are presented as a good alter-native for the prediction of some hydrometeorologicalvariables with various temporal scales because it takesadvantages of the information of relevant exogenousvariables

Table 4 Results for SVM models


Labrado 12 Test (Ts) 024 023 minus094 3985Test close-loop minus003 minus003 139 4185


250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)



Table 5 Results for NARX net models

Basin Model Subset NSE KGE PBIAS RMSE

Labrado 3 lags 50 hidden neurons

Train (Tr) 057 077 minus050 3120Cross-validation (Cv) 038 070 060 3083

Test (Ts) 054 077 minus300 3002Test close-loop 057 051 1230 4774

Chirimachay 6 lags 50 hidden neurons

Train (Tr) 052 075 260 4272Cross-validation (Cv) 053 072 minus520 4620

Test (Ts) 054 069 510 3669Test close-loop 061 061 2220 3676

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)

Figure 7 Comparison between predicted and observed values (a) training subset for Labrado (b) training subset for Chirimachay(c) forecasting for Labrado in 2015 (d) forecasting for Chirimachay in 2015


App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions

In this study linear and nonlinear approaches are evaluated forrainfall forecasting For the linear models the climatic indicesNintildeo 1+2 Sahel rainfall hurricane activity North PacificOscillation and the same delayed rainfall signal were the mostinfluential in the prediction of rainfall Even for models withpredictors with delays higher than or equal to 12 months thesame rainfall signal that delayed 12 months was the mostsignificant+us it shows the seasonality present in the rainfallsignal which expected similar measures for the same monthevery year However the linear models did not capture well therainfall dynamics and hence the evaluations were ldquounsatis-factoryrdquo Linear models reached the best performances withpredictors lagging around 16 or 18 periods plus an initial delayof 12 months between the predictors and the rainfall variable+e RF and SVM showed better forecasting than LM in bothstations but this model presents inaccuracy in low and highpeaks of rainfall +e SVM exhibits better performance thanRF nevertheless in general both display poor forecastingperformance in Labrado and Chirimachay

On the contrary the nonlinear autoregressive networkwith exogenous inputs was also evaluated Considering thatthe behavior of the rainfall is chaotic and highly nonlinearthe NARX networks had a better performance obtainingmodels considered ldquogoodrdquo for Labrado station and ldquosatis-factoryrdquo for Chirimachay station +e best NARX networkswere reported which had 50 neurons in the hidden layerand the delays were multiples of 3 periods (3 for Labrado and6 for Chirimachay) In the prediction of the 12 monthsahead the models almost always follow the real changes inthe rainfall signal For the first 6 months the models are veryaccurate in the prediction Nevertheless as we continue theprediction ahead the performance decreases

+e forecasting shows several problems for predictingpeaks this was more evident in the Labrado station +eseresults could be attributed to the complex behavior ofweather in Andean regions which has several external andlocal influences affecting the dynamic of rainfall processes+us the future challenges on rainfall prediction must focuson capturing these peaks and identify the triggers of theprecipitation events +ese improvements in rainfall pre-dictions are essential to generate plans for suitable decision-making in water resources management

Appendix

Predictors order

Data Availability

+e times series data of precipitation and climatic indices ofboth stations used to support the findings of this study areincluded within the supplementary information files

Disclosure

+e participation of AV-P is made in the context of hisdoctoral program in water resources offered by Universidad

de Cuenca EscuelaPolitecnicaNacional and UniversidadTecnica Particular de Loja

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors thank the INAMHI for the information pro-vided +is work was supported by the University of Cuencathrough its Research Department (DIUC) via the projectsldquoEvaluacion del Riesgo de sequıas en cuencas andinasreguladas influenciadas por la variabilidad climatica ycambio climaticordquo and ldquoEstudio de las condiciones clima-tologicas de America del Sur que producen las sequıas en elEcuador continentalrdquo

Supplementary Materials

+e files DB_Chirimachay_stationtxt and DB_Labrado_s-tationtxt are organized in the following way firstly thedates secondly the time series of the 27 climatic indices andthirdly the time series of the rain station (SupplementaryMaterials)

References

[1] E A B Eltahir and R L Bras ldquoPrecipitation recyclingrdquoReviews of Geophysics vol 34 no 3 pp 367ndash378 1996

[2] Q Sun C Miao Q Duan H Ashouri S Sorooshian andK L Hsu ldquoA review of global precipitation data sets datasources estimation and intercomparisonsrdquo Reviews of Geo-physics vol 56 no 1 pp 79ndash107 2018

[3] C Kidd and G Huffman ldquoGlobal precipitation measure-mentrdquo Meteorological Applications vol 18 no 3pp 334ndash353 2011

[4] M Xinggang J Wenxiong Z Guofeng et al ldquoStable isotopecomposition of precipitation at different elevations in themonsoon marginal zonerdquo Quaternary International vol 493pp 86ndash95 2018

[5] M N French W F Krajewski and Y R R CuykendallldquoRainfall forecasting in space and time using a neural net-workrdquo Journal of Hydrology vol 137 no 1ndash4 pp 1ndash31 1992

[6] C Daly D R Conklin and M H Unsworth ldquoLocal atmo-spheric decoupling in complex topography alters climatechange impactsrdquo International Journal of Climatology vol 30no 12 pp 1857ndash1864 2010

[7] R Celleri and J Feyen ldquo+e hydrology of tropical andeanecosystems importance knowledge status and perspectivesrdquoMountain Research and Development vol 29 no 4pp 350ndash355 2009

[8] W Buytaert V Intildeiguez and B D Bievre ldquo+e effects ofafforestation and cultivation on water yield in the Andeanparamordquo Forest Ecology and Management vol 251 no 1-2pp 22ndash30 2007

[9] W Buytaert R Celleri B De Bievre et al ldquoHuman impact onthe hydrology of the Andean paramosrdquo Earth-Science Re-views vol 79 no 1-2 pp 53ndash72 2006

[10] A DDubey ldquoArtificial neural network models for rainfallprediction in pondicherryrdquo International Journal of ComputerApplications vol 120 no 3 pp 30ndash35 2015


[11] N Mishra H K Soni H K Soni S Sharma andA K Upadhyay ldquoDevelopment and analysis of artificialneural network models for rainfall prediction by using time-series datardquo International Journal of Intelligent Systems andApplications vol 10 no 1 pp 16ndash23 2018

[12] A M Bagirov and A Mahmood ldquoA comparative assessmentof models to predict monthly rainfall in Australiardquo WaterResources Management vol 32 no 5 pp 1777ndash1794 2018

[13] J-H Seo Y H Lee and Y-H Kim ldquoFeature selection for veryshort-term heavy rainfall prediction using evolutionarycomputationrdquo Advances in Meteorology vol 2014 pp 1ndash152014

[14] A Givati M Housh Y Levi D Paz I Carmona andE Becker ldquo+e advantage of using international multimodelensemble for seasonal precipitation forecast over IsraelrdquoAdvances in Meteorology vol 2017 pp 1ndash11 2017

[15] A Schepen T Zhao Q J Wang and D E Robertson ldquoABayesian modelling method for post-processing daily sub-seasonal to seasonal rainfall forecasts from global climatemodels and evaluation for 12 Australian catchmentsrdquo Hy-drology and Earth System Sciences vol 22 no 2 pp 1615ndash1628 2018

[16] A Schepen Q J Wang and D E Robertson ldquoSeasonalforecasts of Australian rainfall through calibration andbridging of coupled GCM outputsrdquoMonthly Weather Reviewvol 142 no 5 pp 1758ndash1770 2014

[17] S Khajehei and H Moradkhani ldquoTowards an improvedensemble precipitation forecast a probabilistic post-pro-cessing approachrdquo Journal of Hydrology vol 546 pp 476ndash489 2017

[18] A Moller A Lenkoski and T L +orarinsdottir ldquoMulti-variate probabilistic forecasting using ensemble Bayesianmodel averaging and copulasrdquo Quarterly Journal of the RoyalMeteorological Society vol 139 no 673 pp 982ndash991 2013

[19] A Schepen and Q J Wang ldquoEnsemble forecasts of monthlycatchment rainfall out to long lead times by post-processingcoupled general circulation model outputrdquo Journal of Hy-drology vol 519 pp 2920ndash2931 2014

[20] J Byakatonda B P Parida P K Kenabatho andD B Moalafhi ldquoPrediction of onset and cessation of australsummer rainfall and dry spell frequency analysis in semiaridBotswanardquo Jeoretical and Applied Climatology vol 135no 1-2 pp 101ndash117 2019

[21] M Dounia D Sabri and D Yassine ldquoRainfall-rain offmodeling using artificial neural networkrdquo APCBEE Procediavol 10 pp 251ndash256 2014

[22] H Mislan S Hardwinarto Y Sumaryono and M AipassaldquoRainfall monthly prediction based on artificial neural net-work a case study in tenggarong station East Kalimantan-Indonesiardquo Procedia Computer Science vol 59 pp 142ndash1512015

[23] V K Dabhi and S Chaudhary ldquoHybrid wavelet-postfix-GPmodel for rainfall prediction of anand region of IndiardquoAdvances in Artificial Intelligence vol 2014 pp 1ndash11 2014

[24] Z Chao F Pu Y Yin B Han and X Chen ldquoResearch onreal-time local rainfall prediction based on MEMS sensorsrdquoJournal of Sensors vol 2018 pp 1ndash9 2018

[25] C Cai J Wang and Z Li ldquoImproving TIGGE precipitationforecasts using an SVR ensemble approach in the huaihe riverbasinrdquo Advances in Meteorology vol 2018 pp 1ndash15 2018

[26] S-H Moon Y-H Kim Y H Lee and B-R Moon ldquoAp-plication of machine learning to an early warning system forvery short-term heavy rainfallrdquo Journal of Hydrology vol 568pp 1042ndash1054 2019

[27] M Min C Bai J Guo et al ldquoEstimating summertime pre-cipitation from himawari-8 and global forecast system basedon machine learningrdquo IEEE Transactions on Geoscience andRemote Sensing vol 57 no 5 pp 2557ndash2570 2019

[28] M Ali R Prasad Y Xiang and Z M Yaseen ldquoCompleteensemble empirical mode decomposition hybridized withrandom forest and kernel ridge regression model for monthlyrainfall forecastsrdquo Journal of Hydrology vol 58 Article ID124647 2020

[29] C Okonkwo ldquoAn advanced review of the relationships be-tween Sahel precipitation and climate indices a wavelet ap-proachrdquo International Journal of Atmospheric Sciencesvol 2014 pp 1ndash11 2014

[30] A Ali ldquoNonlinear multivariate rainfall-stage model for largewetland systemsrdquo Journal of Hydrology vol 374 no 3-4pp 338ndash350 2009

[31] F-J Chang L-C Chang C-W Huang and I-F KaoldquoPrediction of monthly regional groundwater levels throughhybrid soft-computing techniquesrdquo Journal of Hydrologyvol 541 pp 965ndash976 2016

[32] S M Guzman J O Paz and M L M Tagert ldquo+e use ofNARX neural networks to forecast daily groundwater levelsrdquoWater Resources Management vol 31 no 5 pp 1591ndash16032017

[33] A Wunsch T Liesch and S Broda ldquoForecasting ground-water levels using nonlinear autoregressive networks withexogenous input (NARX)rdquo Journal of Hydrology vol 567pp 743ndash758 2018

[34] F Previdi and M Lovera ldquoIdentification of parametrically-varying models for the rainfall-runoff relationship in urbandrainage networksrdquo IFAC Proceedings Volumes vol 42no 10 pp 1768ndash1773 2009

[35] B A Amisigo N van de Giesen C Rogers W E I Andahand J Friesen ldquoMonthly streamflow prediction in the voltabasin of west africa a SISO narmax polynomial modellingrdquoPhysics and Chemistry of the Earth Parts ABC vol 33 no 1-2 pp 141ndash150 2008

[36] M Ebrahim A Ahmadian and Y F Sadat ldquoGeoResJ hybriddarima-narx model for forecasting long-term daily inflow toDez reservoir using the North Atlantic oscillation (NAO) andrainfall datardquo GeoResJ vol 13 pp 9ndash16 2017

[37] F-J Chang P-A Chen Y-R Lu E Huang and K-Y ChangldquoReal-time multi-step-ahead water level forecasting by re-current neural networks for urban flood controlrdquo Journal ofHydrology vol 517 pp 836ndash846 2014

[38] H Kim H Keum and K Han ldquoReal-time urban inundationprediction combining hydraulic and probabilistic methodsrdquoWater vol 11 no 2 pp 293ndash318 2019

[39] T Nanda B Sahoo H Beria and C Chatterjee ldquoA wavelet-based non-linear autoregressive with exogenous inputs(WNARX) dynamic neural network model for real-time floodforecasting using satellite-based rainfall productsrdquo Journal ofHydrology vol 539 pp 57ndash73 2016

[40] P Benevides J Catalao and G Nico ldquoNeural network ap-proach to forecast hourly intense rainfall using GNSS pre-cipitable water vapor and meteorological sensorsrdquo RemoteSensing vol 11 no 8 p 966 2019

[41] Z Rahimi H Z Mohd Shafri and M Norman ldquoA GNSS-based weather forecasting approach using nonlinear autoregressive approach with exogenous input (NARX)rdquo Journalof Atmospheric and Solar-Terrestrial Physics vol 178pp 74ndash84 2018

[42] E Pisoni M Farina C Carnevale and Y L PiroddildquoForecasting peak air pollution levels using NARX modelsrdquo


Engineering Applications of Artificial Intelligence vol 22no 4-5 pp 593ndash602 2009

[43] L B de Guenni M Garcıa A G Muntildeoz et al ldquoPredictingmonthly precipitation along coastal Ecuador ENSO andtransfer function modelsrdquo Jeoretical and Applied Clima-tology vol 129 no 3-4 pp 1059ndash1073 2017

[44] D EMendoza E P Samaniego E A Pacheco VM Carrilloand y D R Ochoa-Tocachi ldquoStochastic rainfall forecasting forhigh tropical andean regionsrdquo 2017

[45] R Celleri L Campozano and y A Aviles ldquoIntegratedwaterresources management in an Andean mountain basinthecase of the Machaangara riverrdquo in Nexus OutlookAssessing Resource Use Challenges in the Water Energy andFood Nexus M Al-aidi and L Ribbe Eds pp 80ndash97 Re-search Gate Berlin Germany 2016

[46] B C S Hansen D T Rodbell G O Seltzer B LeonK R Young and M Abbott ldquoLate-glacial and Holocenevegetational history from two sites in the western Cordillera ofSouthwestern Ecuadorrdquo Palaeogeography PalaeoclimatologyPalaeoecology vol 194 no 1ndash3 pp 79ndash108 2003

[47] V Vanacker G Govers S Barros J Poesen and J Deckersldquo+e effect of short-term socio-economic and demographicchange on landuse dynamics and its corresponding geo-morphic response with relation to water erosion in a tropicalmountainous catchment Ecuadorrdquo Landscape Ecologyvol 18 no 1 pp 1ndash15 2003

[48] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-timerainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[49] J C H Chiang and D J Vimont ldquoAnalogous pacific andatlantic meridional modes of tropical atmosphere-oceanvariabilityrdquo Journal of Climate vol 17 no 21 pp 4143ndash41582004

[50] D B Enfield A M Mestas-Nuntildeez and P J Trimble ldquo+eAtlantic Multidecadal Oscillation and its relation to rainfalland river flows in the continental USrdquo Geophysical ResearchLetters vol 28 no 10 pp 2077ndash2080 2001

[51] S Zhou A J Miller J Wang and J K Angell ldquoTrends ofNAO and AO and their associations with stratosphericprocessesrdquo Geophysical Research Letters vol 28 no 21pp 4107ndash4110 2001

[52] C A Smith and P D Sardeshmukh ldquo+e effect of ENSO onthe intraseasonal variance of surface temperatures in winterrdquoInternational Journal of Climatology vol 20 no 13pp 1543ndash1557 2000

[53] C Penland and L Matrosova ldquoPrediction of tropical atlanticsea surface temperatures using linear inverse modelingrdquoJournal of Climate vol 11 no 3 pp 483ndash496 1998

[54] G S Lehmiller T B Kimberlain and J B Elsner ldquoSeasonalprediction models for North Atlantic basin Hurricane loca-tionrdquoMonthly Weather Review vol 125 no 8 pp 1780ndash17911997

[55] K Wolter and M S Timlin ldquoEl NintildeoSouthern Oscillationbehaviour since 1871 as diagnosed in an extendedmultivariateENSO index (MEIext)rdquo International Journal of Climatologyvol 31 no 7 pp 1074ndash1087 2011

[56] A G Barnston and R E Livezey ldquoClassification seasonalityand persistence of low-frequency atmospheric circulationpatternsrdquo Monthly Weather Review vol 115 no 6pp 1083ndash1126 1987

[57] K TrenberthJeClimate Data Guide Nino SST Indices (Nino1 + 2 3 34 4 ONI and TNI) National Center for Atmo-spheric Research Boulder CO USA 2016

[58] J C Rogers ldquo+e North Pacific oscillationrdquo Journal of Cli-matology vol 1 no 1 pp 39ndash57 1981

[59] J-Y Yu H-Y Kao T Lee and S T Kim ldquoSubsurface OceanTemperature indices for central-pacific and eastern-pacifictypes of el Nintildeo and La nintildea eventsrdquo Jeoretical and AppliedClimatology vol 103 no 3-4 pp 337ndash344 2011

[60] N J Mantua and S R Hare ldquo+e Pacific decadal oscillationrdquoJournal of Oceanography vol 58 no 1 pp 35ndash44 2002

[61] R A Ebdon ldquoNotes on the wind flow at 50 mb in tropical andsub-tropical regions in January 1957 and January 1958rdquoQuarterly Journal of the Royal Meteorological Society vol 86no 370 pp 540ndash542 1960

[62] R J ReedW J Campbell L A Rasmussen and D G RogersldquoEvidence of a downward-propagating annual wind reversalin the equatorial stratosphererdquo Journal of Geophysical Re-search vol 66 no 3 pp 813ndash818 1961

[63] E S Nicholson A Review of Recent Studies on the RainfallRegime and Its Interannual Variability Vol 32306 EarthOcean and Atmospheric Sciences Department Florida StateUniversity Tallahassee FL USA 2013

[64] A J Troup ldquo+e southern oscillationrdquo Quarterly Journal ofthe Royal Meteorological Society vol 91 no 390 pp 490ndash5061965

[65] I Poole ldquoUnderstanding solar indicesrdquo Qst vol 200pp 38ndash40 2002

[66] D B Enfield A M Mestas-Nuntildeez D A Mayer and L Cid-Serrano ldquoHow ubiquitous is the dipole relationship in tropicalAtlantic sea surface temperaturesrdquo Journal of GeophysicalResearch Oceans vol 104 no C4 pp 7841ndash7848 1999

[67] K E Trenberth and D P Stepaniak ldquoIndices of el Nintildeoevolutionrdquo Journal of Climate vol 14 no 8 pp 1697ndash17012001

[68] B Rajagopalan Y Kushnir and Y M Tourre ldquoObserveddecadal midlatitude and tropical Atlantic climate variabilityrdquoGeophysical Research Letters vol 25 no 21 pp 3967ndash39701998

[69] C Wang and D B Enfield ldquo+e tropical western Hemispherewarm poolrdquo Geophysical Research Letters vol 28 no 8pp 1635ndash1638 2001

[70] J M Wallace and D S Gutzler ldquoTeleconnections in thegeopotential height field during the northern HemispherewinterrdquoMonthlyWeather Review vol 109 no 4 pp 784ndash8121981

[71] J Hansen R Ruedy J Glascoe and M Sato ldquoGISS analysis ofsurface temperature changerdquo Journal of Geophysical ResearchAtmospheres vol 104 no D24 pp 30997ndash31022 1999

[72] J Hansen M Sato and K Lo ldquoGlobal surface temperaturechangerdquo Global Pipeline Monthly vol 5 no 2 pp 1ndash29 2009

[73] G James D Witten T Hastie and Y R Tibshirani AnIntroduction to Statistical Learning Vol 7 Springer BerlinGermany 2000

[74] G Chandrashekar and F Sahin ldquoA survey on feature selectionmethodsrdquo Computers amp Electrical Engineering vol 40 no 1pp 16ndash28 2014

[75] I Guyon and A Elisseeff ldquoAn introduction to variable andfeature selectionrdquo Journal of Machine Learning Researchvol 3 pp 1157ndash1182 2003

[76] L Breiman ldquoRandom forestsrdquo Machine Learning vol 45no 1 pp 5ndash32 2001

[77] J R Quinlan ldquoInduction of decision treesrdquo MachineLearning vol 1 no 1 pp 81ndash106 1986

[78] M Kubat ldquoA simple machinendashlearning taskrdquo in An Intro-duction to Machine Learning M Kubatpp 1ndash18 SpringerInternational Publishing Cham Switzerland 2017


[79] V N Vapnik ldquoDirect methods in statistical learning theoryrdquoin +e Nature of Statistical Learning +eory V N VapnikEd pp 225ndash265 Springer New York NY USA 2000

[80] H B Demuth M H Beale O De Jess and Y M T HaganNeural Network Design Martin Hagan Stillwater OK USA2014

[81] T Lin B G Horne P Tino and C L Giles ldquoLearning long-term dependencies in NARX recurrent neural networksrdquoIEEE Transactions Neural Networks vol 7 pp 1329ndash13381996 httpsieeexploreieeeorgabstractdocument548162

[82] D R Legates and G J McCabe ldquoEvaluating the use ofldquogoodness-of-fitrdquo Measures in hydrologic and hydroclimaticmodel validationrdquo Water Resources Research vol 35 no 1pp 233ndash241 1999

[83] D N Moriasi J G Arnold M W Van Liew R L BingnerR D Harmel and T L Veith ldquoModel evaluation guidelinesfor systematic quantification of accuracy in watershed sim-ulationsrdquo Transactions of the American Society of Agriculturaland Biological Engineers vol 50 no 3 pp 885ndash900 2007

[84] K Abbaspour S Raghavan S A Vaghefi M Faramarzi andY L Chen Integrated Soil and Water Management SelectedPapers from 2016 International SWAT Conference MDPIBasel Switzerland 2017

[85] J Chen M Li and y W Wang ldquoStatistical uncertainty es-timation using random forests and its application to droughtforecastrdquo Mathematical Problems in Engineering vol 2012Article ID 915053 2012

[86] H T Siegelmann B G Horne and y C L Giles ldquoCom-putational capabilities of recurrent NARX neural networksrdquoIEEE Transactions on Systems Man and Cybernetics Part B(Cybernetics) vol 27 no 2 pp 208ndash215 1997


and Quito in Ecuador) An accurate prediction of precipi-tation (temporal and spatial) can help decision-makers toassess in advance both flood and drought situations [10 11]and it could support extreme hydrological management anddiminish the impacts on the population

In different studies a variety of methods have been usedto forecast rainfall Some of them have shown accurateresults like the multiple linear regression and k-nearest-neighbors methods as in [12 13] Other approaches haveused the outputs of global climate models to improve theseasonal and subseasonal forecasting [14ndash16] and theprobabilistic forecasts for uncertainty quantification[17ndash19] Other studies have applied artificial intelligenceapproach for rainfall prediction such as artificial neuralnetworks (ANNs) [5 10ndash12 20ndash24] support vector machine(SVM) [12 13 24 25] logistic regression [26] and randomforest [27 28] Also other studies have investigated theoptimum selection of predictors to improve forecast accu-racy [29] NARX model is a novel approach for many ap-plications of prediction of environmental variables forexample water level of wetland systems [30] groundwaterlevels [31ndash33] urban drainage framework [34] stream flowand inflow to reservoirs [35 36] water level in urban flood[37ndash39] and rainfall forecasting [40 41]

+e unpredictable and chaotic nature of the rainfallbehavior makes its prediction a critical challenge+eNARXmodel is suitable for dealing with time series with suchcharacteristics [42] since the output value of a variable is anonlinear function of the past values of the same variableand other exogenous variables Nonlinear mapping isconvenient in chaotic environments and it is superior toconventional autoregressive models It is also superior toANN since NARX uses its memory to make predictionsNARX presents an improvement opportunity due to itsperformance in the prediction of time series that has aseasonal component

In Andean countries like Ecuador some of themethods mentioned above have also been used to predictprecipitation For example in [43] continuous transferfunction models were used to predict rainfall on the coastsof Ecuador Also Mendoza et al [44] used sea surfacetemperature (SST) as a predictor and canonical correla-tion as a method to predict rainfall in the coast and Andesof Ecuador +ese studies highlight the complex rela-tionship between predictors and rainfall in the AndesHowever new methods like NARX could be applied in theEcuadorian Andes to improve the performance of pre-cipitation forecasting

+is study first explores the performance of the mostcommonly used linear models for the rainfall forecast Itthen compares them with nonlinear models to verify theirperformance in a mountain basin located in the south ofEcuador Finally NARX models are used to forecast rainfallseveral steps ahead +e results obtained can have a sig-nificant impact on mountain systems because they could beused to obtain improved performance in high mountainareas

2 Materials and Methods

21 Study Area +e study area is composed of the highmountain subbasins Tomebamba and Machangara locatedin the Andean southern Ecuador (Figure 1) +e two sub-basins are essential to supply water to the city of Cuencaconsidered the third most important in Ecuador [45]Moreover the two subbasins belong to the Paute hydro-graphic system which together with others provide waterto generate energy +e subbasins altitude varies between2440 and 4400masl which in turn allows finding a greatvariety of vegetation For example in high areas there arepatches of Polylepis reticulata tussock grasses ground ro-settes cushion plants and ground rosettes while in the lowareas there are agricultural land pastures as well as urbanzones [9 46 47]

Two meteorological stations are taken into account forthe analysis Labrado and Chirimachay +ese are locatedin the upper parts of the two subbasins at 3300masl(Figure 1) According to Celleri et al [48] there are twotypes of precipitation within the study area bimodal type I inthe lower parts of the subbasins and bimodal type II in themiddle and upper zones Both regimes have two peaks ofprecipitation during April and October however the bi-modal type II regimen presents a less dry season from Juneto August (Figure 2)

22 Precipitation Data Rainfall data from Labrado (sub-basin of Machangara) and Chirimachay (subbasin ofTomebamba) stations were provided by the EcuadorianNational Institute of Meteorology and Hydrology(INAMHI httpwwwserviciometeorologicogobec) +estudy period is 1964ndash2015 Table 1 shows a statisticalsummary of the rainfall data

23Climatic Indices +e 27 climatic indices listed next wereused in the study +e Atlantic Meridional Mode (AMM)SST Index [49] Atlantic Multidecadal Oscillation (AMO)[50] Antarctic Oscillation (AO) [51] Bivariate ENSO Timeseries (BEST) [52] Caribbean Index (CAR) [53] hurricaneactivity (HURR) [54] Multivariate ENSO Index (MEI) [55]North Atlantic Oscillation (NAO) [56] Nintildeo 1 + 2 Nintildeo 3Nintildeo 34 and Nintildeo 4 [57] North Pacific Oscillation (NP)[58] North Tropical Atlantic SST Index (NTA) [53] Oce-anic Nintildeo Index (ONI) [59] Pacific Decadal Oscillation(PDO) [60] Pacific North American Index (PNA) [61]Quasibiennial Oscillation (QBO) [62] Sahel rainfall(SAHELRAIN) [63] Southern Oscillation Index (SOI) [64]solar flux [65] Tropical Northern Atlantic Index (TNA)[66] Trans-Nintildeo Index (TNI) [67] Tropical Southern At-lantic Index (TSA) [68] western hemisphere warm pool(WHWP) [69] Western Pacific Index (WP) [70] and globalmean landocean temperature (GMSST) [71 72] Time seriesof these indices are available in httpswwwesrlnoaagovpsddataclimateindiceslist


2deg40

prime0Prime

S



0deg45

prime0Prime

N1deg

16prime0Prime

S3deg

17prime0Prime

S

3deg17

prime0Prime

S1deg

16prime0Prime

S0deg

45prime0Prime

N

2deg45

prime0Prime

S2deg

50prime0Prime

S2deg

55prime0Prime

S

2deg40

prime0Prime

S2deg

45prime0Prime

S2deg

50prime0Prime

S2deg

55prime0Prime

S




2deg30

prime0Prime

S

2deg30

prime0Prime

S3deg

0prime0Prime

S

3deg0prime0Prime

S


0 25 5 10kilometers

N

LabradoChirimachay

4400

2440

Altitude (masl)


2 3 8754 61 1210 1190

40

80

120

160

mm

(mon

th)

(a)

2 3 8754 61 1210 1190

40

80

120

160

mm

(mon

th)

(b)



24 Linear Models


y β0 + β1x + ε (1)






RSS 1113944n


p

j1βjxij

⎛⎝ ⎞⎠

2

(3)



RSS + 1113944p

j1βj2 (4)

RSS + λ1113944p

j1 βj

11138681113868111386811138681113868

11138681113868111386811138681113868 (5)














X(t + 1) X(t) X t minus nx( 11138571113857(6)


X(t + 1) X(t) X t minus nx( 11138571113857(7)










NSE 1 minus1113944

N


1113944N

i1 Oi minus Oi( 11138572 (8)



KGE 1 minus

(α minus 1)2

+(cc minus 1)2

+(β minus 1)2

1113969

(9)



PBIAS() 1113944

N


1113944N

i1Oi

(10)


RMSE

1113944N


N

1113971

(11)






X (t + 1)

X (t ndash 1)

X (t ndash nx)

Y (t ndash ny)

Y (t ndash 1)

Y^ (t + 1)

Y (t)

X (t)















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags

04

03

02

01

0

NSE



(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags



04

03

02

01

0

NSE

(b)






250

200

150

100

50

0

Fore

caste

d

250200150100500Observed

(a)

Fore

caste

d

350

300

250

200

150

100

50

0350250 300200150100500

Observed

(b)

Figure 5 Continued










200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)









250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




























































































2deg40

prime0Prime

S



0deg45

prime0Prime

N1deg

16prime0Prime

S3deg

17prime0Prime

S

3deg17

prime0Prime

S1deg

16prime0Prime

S0deg

45prime0Prime

N

2deg45

prime0Prime

S2deg

50prime0Prime

S2deg

55prime0Prime

S

2deg40

prime0Prime

S2deg

45prime0Prime

S2deg

50prime0Prime

S2deg

55prime0Prime

S




2deg30

prime0Prime

S

2deg30

prime0Prime

S3deg

0prime0Prime

S

3deg0prime0Prime

S


0 25 5 10kilometers

N

LabradoChirimachay

4400

2440

Altitude (masl)


2 3 8754 61 1210 1190

40

80

120

160

mm

(mon

th)

(a)

2 3 8754 61 1210 1190

40

80

120

160

mm

(mon

th)

(b)



24 Linear Models


y β0 + β1x + ε (1)






RSS 1113944n


p

j1βjxij

⎛⎝ ⎞⎠

2

(3)



RSS + 1113944p

j1βj2 (4)

RSS + λ1113944p

j1 βj

11138681113868111386811138681113868

11138681113868111386811138681113868 (5)














X(t + 1) X(t) X t minus nx( 11138571113857(6)


X(t + 1) X(t) X t minus nx( 11138571113857(7)










NSE 1 minus1113944

N


1113944N

i1 Oi minus Oi( 11138572 (8)



KGE 1 minus

(α minus 1)2

+(cc minus 1)2

+(β minus 1)2

1113969

(9)



PBIAS() 1113944

N


1113944N

i1Oi

(10)


RMSE

1113944N


N

1113971

(11)






X (t + 1)

X (t ndash 1)

X (t ndash nx)

Y (t ndash ny)

Y (t ndash 1)

Y^ (t + 1)

Y (t)

X (t)















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags

04

03

02

01

0

NSE



(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags



04

03

02

01

0

NSE

(b)






250

200

150

100

50

0

Fore

caste

d

250200150100500Observed

(a)

Fore

caste

d

350

300

250

200

150

100

50

0350250 300200150100500

Observed

(b)

Figure 5 Continued










200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)









250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




























































































24 Linear Models


y β0 + β1x + ε (1)






RSS 1113944n


p

j1βjxij

⎛⎝ ⎞⎠

2

(3)



RSS + 1113944p

j1βj2 (4)

RSS + λ1113944p

j1 βj

11138681113868111386811138681113868

11138681113868111386811138681113868 (5)














X(t + 1) X(t) X t minus nx( 11138571113857(6)


X(t + 1) X(t) X t minus nx( 11138571113857(7)










NSE 1 minus1113944

N


1113944N

i1 Oi minus Oi( 11138572 (8)



KGE 1 minus

(α minus 1)2

+(cc minus 1)2

+(β minus 1)2

1113969

(9)



PBIAS() 1113944

N


1113944N

i1Oi

(10)


RMSE

1113944N


N

1113971

(11)






X (t + 1)

X (t ndash 1)

X (t ndash nx)

Y (t ndash ny)

Y (t ndash 1)

Y^ (t + 1)

Y (t)

X (t)















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags

04

03

02

01

0

NSE



(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags



04

03

02

01

0

NSE

(b)






250

200

150

100

50

0

Fore

caste

d

250200150100500Observed

(a)

Fore

caste

d

350

300

250

200

150

100

50

0350250 300200150100500

Observed

(b)

Figure 5 Continued










200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)









250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References



































































































X(t + 1) X(t) X t minus nx( 11138571113857(6)


X(t + 1) X(t) X t minus nx( 11138571113857(7)










NSE 1 minus1113944

N


1113944N

i1 Oi minus Oi( 11138572 (8)



KGE 1 minus

(α minus 1)2

+(cc minus 1)2

+(β minus 1)2

1113969

(9)



PBIAS() 1113944

N


1113944N

i1Oi

(10)


RMSE

1113944N


N

1113971

(11)






X (t + 1)

X (t ndash 1)

X (t ndash nx)

Y (t ndash ny)

Y (t ndash 1)

Y^ (t + 1)

Y (t)

X (t)















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags

04

03

02

01

0

NSE



(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags



04

03

02

01

0

NSE

(b)






250

200

150

100

50

0

Fore

caste

d

250200150100500Observed

(a)

Fore

caste

d

350

300

250

200

150

100

50

0350250 300200150100500

Observed

(b)

Figure 5 Continued










200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)









250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References































































































NSE 1 minus1113944

N


1113944N

i1 Oi minus Oi( 11138572 (8)



KGE 1 minus

(α minus 1)2

+(cc minus 1)2

+(β minus 1)2

1113969

(9)



PBIAS() 1113944

N


1113944N

i1Oi

(10)


RMSE

1113944N


N

1113971

(11)






X (t + 1)

X (t ndash 1)

X (t ndash nx)

Y (t ndash ny)

Y (t ndash 1)

Y^ (t + 1)

Y (t)

X (t)















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags

04

03

02

01

0

NSE



(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags



04

03

02

01

0

NSE

(b)






250

200

150

100

50

0

Fore

caste

d

250200150100500Observed

(a)

Fore

caste

d

350

300

250

200

150

100

50

0350250 300200150100500

Observed

(b)

Figure 5 Continued










200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)









250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References







































































































0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags

04

03

02

01

0

NSE



(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Lags



04

03

02

01

0

NSE

(b)






250

200

150

100

50

0

Fore

caste

d

250200150100500Observed

(a)

Fore

caste

d

350

300

250

200

150

100

50

0350250 300200150100500

Observed

(b)

Figure 5 Continued










200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)









250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




































































































200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

200

150

100

50

0

Rain

fall

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)









250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References


































































































250200150100500Observed

250

200

150

100

50

0

Fore

caste

d

(a)

350250 300200150100500Observed

Fore

caste

d

350

300

250

200

150

100

50

0

(b)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(c)

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

200

150

100

50

0

Rain

fall

(d)











450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




































































































450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(a)

450

300

150

0

Fore

caste

d

0 100 200 300 400 500Observed

TrTsCv

(b)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(c)

Rain

fall

200

150

100

50

0

ndash50

ForecastedObserved

1 2 3 4 5 6 7 8 9 10 11 12Months

(d)



App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




























































































App

end

ix

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L0Ridge

Nintildeo1+2

Nintildeo3

ONI

WP

HURR

Nintildeo1+2

Nintildeo3

SOLA

RTN

ITS

ALasso

Nintildeo3

Nintildeo1+2

ONI

WP

NTA

Nintildeo3

Nintildeo1+2

ONI

SOLA

RTN

I

L1Ridge

Nintildeo1+2_1

NP_

1ONI

HURR

_1Ra

infall_

1Ra

infall_

1Nintildeo1+2_1

NP_

1HURR

_1TS

A_1

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1TS

A_1

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1TS

A_1

L2Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Nintildeo1+2_2

HURR

_1Ra

infall_

1NP_

1Nintildeo1+2_1

HURR

_1NAO_2

Lasso

Nintildeo1+2_1

NP_

1HURR

_1Ra

infall_

1GMSST_

2Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1NAO_2

L3Ridge

Nintildeo1+2_1

NP_

1Ra

infall_

1Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

3Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

NP_

1Ra

infall_

1HURR

_1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1NAO_2

Rainfall_

3

L4Ridge

NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Rainfall_

1Nintildeo1+2_4

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_1Ra

infall_

3

L5Ridge

Nintildeo1+2_1

Rainfall_

1Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

1Ra

infall_

3NP_

1Nintildeo1+2_1

NAO_2

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3NAO_2

L6Ridge

Nintildeo1+2_1

Rainfall_

3Ra

infall_

1SA

HEL

RAIN

_3NP_

1Ra

infall_

1Ra

infall_

6Nintildeo1+2_1

Rainfall_

3NP_

1Lasso

Nintildeo1+2_1

Nintildeo1+2_5

Rainfall_

3Ra

infall_

1Nintildeo4_5

Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

6Ra

infall_

3

L7Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

Rainfall_

3NP_

1Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Nintildeo1+2_1

Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

3

L8Ridge

HURR

_7Nintildeo1+2_1

Rainfall_

1NP_

1Ra

infall_

3Ra

infall_

1HURR

_7Ra

infall_

3Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L9Ridge

HURR

_7SA

HEL

RAIN

_3Ra

infall_

3Ra

infall_

1NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Ra

infall_

8Ra

infall_

3Lasso

Nintildeo1+2_1

Nintildeo1+2_5

HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_7NP_

1Ra

infall_

8

L10

Ridge

HURR

_7Ra

infall_

1Nintildeo1+2_1

SAHEL

RAIN

_3NP_

1Ra

infall_

1HURR

_7Ra

infall_

6Nintildeo1+2_1

Rainfall_

3Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

1Ra

infall_

3BE

ST_9

Nintildeo1+2_1

Rainfall_

1NP_

1HURR

_7Ra

infall_

8

L11

Ridge

HURR

_7Ra

infall_

3SA

HEL

RAIN

_3Ra

infall_

1NP_

1Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Ra

infall_

8Lasso

Nintildeo1+2_1

HURR

_7Ra

infall_

3Ra

infall_

1SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

11HURR

_7NP_

1

L12

Ridge

Rainfall_

12HURR

_7Ra

infall_

3SA

HEL

RAIN

_3NP_

1Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7SO

I_11

Rainfall_

3Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L13

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1SA

HEL

RAIN

_3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L14

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Ra

infall_

1Ra

infall_

1Ra

infall_

12Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3SO

I_11

Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L15

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11HURR

_7

L16

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3SA

HEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7Ra

infall_

3Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L17

Ridge

Rainfall_

12HURR

_7NP_

1Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Ra

infall_

1Ra

infall_

11HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Rainfall_

12HURR

_7NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1

L18

Ridge

Rainfall_

12HURR

_7Ra

infall_

3NP_

1Nintildeo1+2_1

Rainfall_

12Ra

infall_

11Ra

infall_

1HURR

_7Ra

infall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1Ra

infall_

12Ra

infall_

11NP_

1


Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




























































































Tabl

eC

ontin

ued

Labrado

Chirimachay

Lags

Mod

el1

23

45

12

34

5

L19

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7SA

HEL

RAIN

_5Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Nintildeo1+2_18

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

NP_

1Ra

infall_

12

L20

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

12Ra

infall_

11Ra

infall_

1HURR

_19

Rainfall_

17Lasso

Nintildeo1+2_18

Nintildeo1+2_1

Rainfall_

12NP_

1Ra

infall_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

12Ra

infall_

11

L21

Ridge

Rainfall_

12Ra

infall_

3HURR

_7SA

HEL

RAIN

_3HURR

_19

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12NP_

1HURR

_7Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12

L22

Ridge

Rainfall_

12Ra

infall_

3HURR

_7HURR

_19

SAHEL

RAIN

_3Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

12Nintildeo1+2_18

NP_

1Ra

infall_

3Nintildeo1+2_1

Rainfall_

1HURR

_19

Nintildeo3_16

NP_

1

L23

Ridge

Rainfall_

3Ra

infall_

12SA

HEL

RAIN

_3HURR

_7AO_14

Rainfall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1Ra

infall_

11Ra

infall_

12HURR

_19

L24

Ridge

Rainfall_

3SA

HEL

RAIN

_3Ra

infall_

12AO_14

SAHEL

RAIN

_5Ra

infall_

11Ra

infall_

12Ra

infall_

1HURR

_19

Rainfall_

6Lasso

Nintildeo1+2_1

Rainfall_

3Ra

infall_

12Nintildeo1+2_18

NP_

1Nintildeo1+2_1

Rainfall_

1HURR

_19

Rainfall_

11Ra

infall_

12


4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




























































































4 Conclusions




Appendix

Predictors order

Data Availability


Disclosure





Acknowledgments




References




























































































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