peer review only - homogenisation · peer review only on the reliability ... complete list of...

Peer Review O

nly

On the reliability of Brazilian rainfall data for climate

studies

Journal: International Journal of Climatology

Manuscript ID: JOC-09-0074

Wiley - Manuscript type: Research Article

Date Submitted by the Author:

24-Feb-2009

Complete List of Authors: Sugahara, Shigetoshi; UNESP, Instituto de Pesquisas Meteorológicas da Rocha, Rosmeri; Universidade de São Paulo, de Ciências Atmosféricas Silveira, Reinaldo; Instituto Tecnológico SIMEPAR

Keywords: daily rainfall series, inhomogeneity, change-point, climate change problem, remote climate influence, multiple-breaks linear regression model, Brazil

http://mc.manuscriptcentral.com/joc

International Journal of Climatology - For peer review only

Peer Review O

nly

1

On the reliability of Brazilian rainfall data for climate studies

Shigetoshi Sugahara*

Instituto de Pesquisas Meteorológicas e Programa de Pós-Graduação da Faculdade de Ciências,

UNESP/Bauru, São Paulo, Brazil.

Rosmeri Porfirio da Rocha

Departamento de Ciências Atmosféricas, Universidade de São Paulo, São Paulo, Brazil

Reinaldo Silveira

Instituto Tecnológico SIMEPAR

Centro Politécnico da UFPR, Curitiba, Brazil

* Corresponding author address: Shigetoshi Sugahara, Instituto de Pesquisas Meteorológicas,

UNESP/Bauru, Av. Luis Edmundo Carrijo Coube 14-01, Bauru, SP, 17033-360 Brazil

Telephone: +55(14)3103-6030

Fax number: +55(14) 3203-3649

E-mail: [email protected]

Page 1 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

2

ABSTRACT

A set of 887 historical daily rainfall series of Brazil from different climates were assessed for

inhomogeneity. These series have at least 30 years in length. The work was undertaken assuming that

all stations are potentially inhomogeneous, regarding raw data. Various statistical techniques were

applied to track down inhomogeneity including multiple breaks linear regression model with supF test,

the Anderson-Darling distribution test, the proportion test, and the Mann-Kendall trend test, among

others. The examined quantities in the annual time scale were number of dry days, median of daily

amounts, and total annual. The outcomes of these tests indicated the presence of various types of

homogeneity problem in the majority of series. Many of them can be attributed to bad observing

routine, among which are the reporting of only significant amount or zero neglecting small amounts,

during one or more sub-periods of record, the reporting of missing observations as zero, and multi-day

accumulation. These homogeneity problems might be observed all across the country, regardless source

of data. The number of series classified as homogeneous is disappointingly small, only 11 out of the

total number (or 1.2%), when 5% significance level is adopted as critical level in all homogeneity tests.

This number certainly could hinder achievement of many climate studies, particularly those in which

the involved climate signal is weak and spatially complex, as that associated with El Niño-Southern

Oscillation (ENSO) and long-term climatic trend.

Key words: daily rainfall series; rain-gauge; inhomogeneity; change-point, climate change problem;

remote climate influence; multiple-breaks linear regression model; Brazil.

Page 2 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

3

1. Introduction

The need for reliable climate series is growing rapidly. In fact, they are essential to any climate studies

and many recent studies of quality assessment of instrumental climate records have been motivated by

IPCC report (2001), which calls attention to the need for quantitative reconstruction of past climate

change. It is well known that a climate time series could only be regarded reliable if it is homogeneous,

i.e., if their variations were caused only by variation of weather and climate (Conrad and Pollak, 1950).

Unfortunately, most long-term climate series are contaminated by spurious variations due to non-

climatic factors, among which are changes in instruments, observing routines, local environment,

instrument exposure, and station relocation (e.g. Karl and Williams, 1987; Peterson et al., 1998;

Alexandersson, 1986; Alexandersson and Moberg, 1997; Hansen-Bauer and Førland, 1994;

DeGaetano, 2006; Easterling and Peterson, 1995; Vincent, 1998; Wijngaard et al., 2003; Auer et al.,

2005; Davey and Pielke, 2005; Klok and Klein Tank, 2008). All these factors can introduce bias into

the climate statistics in some degree, which in turn might lead to misinterpretations or doubtful

conclusions about the evolution of climate and of the climate itself (e.g. Hansen-Bauer and Førland,

1994; Peterson et al., 1998; Tuomenvirta, 2001; Caussinus and Mestre, 2004; Wijngaard et al., 2003;

Davey and Pielke, 2005; Rust et al., 2008; Sherhood et al., 2008).

The homogeneity assessment is by no means a trivial exercise. In general, various statistical

tools need to be considered (e.g. Tuomenvirta, 2001; Auer et al., 2005) due to a variety of homogeneity

problems that have to be addressed. Moreover, in the homogeneity work it is necessary to consider that

the effectiveness of a particular tool may depend on the testing variable, climate, stations density, etc.

(e.g. Lavery et al., 1992; Hansen-Bauer and Førland, 1994; Peterson et al., 1998; Tuomenvirta, 2001;

Wijngaard et al., 2003; Klok and Klein Tank, 2008). A station history metadata would be useful for

this task if it brings information that can help identify potential inhomogeneities, though it rarely occurs,

as reported by many authors of various nations (e.g. Klein Tank, 2008; Auer et al., 2005; Wijngaard et

Page 3 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

4

al., 2003). An important aspect of inhomogeneity assessment is that no homogeneity work is definitive.

A good example of it is given by Viney and Bates (2004), for the Australian daily rainfall dataset, in

which an error caused by multi-day accumulation, particularly that involving weekends (Saturday-

Sunday), was found even within a data set deemed to be highly reliable after Lavery et al. (1992) and

Haylock and Nicholls (2000).

The sudden jump also called change- or break- point is one of the most common type of

inhomogeneity encountered in the climatic series. This can be caused for example by the relocation of

the station or change in observing practices (e.g. Alexandersson, 1986; Peterson et al., 1998; Wijngaard

et al., 2003; Klok and Klein Tank, 2008). Statistically, such series is broken down into segments with

observations following the same statistical properties within each segment. To the knowledge of

present authors, in the works involving rainfall over Brazil this problem has not received due attention,

with rare exceptions as in Xavier et al. (1996), and Sugahara et al. (2008). But these works are

restricted to few stations of Sao Paulo state, in the Southeastern portion of Brazil. In other works, a

possible presence of it has been disregarded tacit or explicitly, even those in which only homogeneous

data should be used, such as climate variability studies.

Not always the inhomoneity appears as abrupt variations. Instead, in some cases it appears as

slow variations as an effect of the environmental change around the station (e.g. Peterson et al. 1998).

But regardless of type of homogeneity, what is important to consider is that, as stated by Auer et al.

(2005), in general all climate series exceeding a few decades are contaminated by non-climatic

information.

When the testing variable is precipitation, an additional problem that can emerge is related to

the reporting of missing day as day of no precipitation (see e.g. Lavery et al., 1994; Viney and Bates,

Page 4 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

5

2004; Liebmann and Allured, 2005; Higgins et al., 2006). Particularly, with respect to the South

American daily rainfall dataset, Liebmann and Allured (2005) have called attention to this problem. An

obvious effect of this is that it leads to biased estimates of both dry and wet spell length, which are an

important local climatic characteristic for agricultural and water resources purpose, and recently has

been regarded in the climate change analysis.

The present work aims to perform homogeneity analysis of long-term daily observations of

rainfall across Brazil territory. Following Auer et al. (2005), the work is carried out under the

assumption that all series are potentially inhomogeneous, even those which were used in many

previous works.

The remaining of this work is organized as follows. Section 2 describes the dataset gathered for

this work. The possible types of inhomogeneity that are expected to be encountered are discussed in

Section 3. In Section 4 we describe methods for detection of inhomogeneity. In Section 5 we present

the results, and considering that some regions have attracted more attention than other, we seek to

present the results for each state separately, with the hope that they may be useful for future research.

Section 6 presents the concluding remarks.

2. Data

The raw data daily rainfall series checked on this work are from 887 rain-gauges stations which began

reporting daily amount since 1970 or before and extended at least up to 1997. The minimum length of

30 years and completeness of records were required in the selection process. One record having more

than four consecutive missing years was discarded. A year with more than 15 missing days, which may

also include negative amount, was considered as missing.

Page 5 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

6

The elected stations cover a substantial portion of Brazil with different climates. The sources of

data are: DAEE (Departamento de Águas e Energia Elétrica do Estado de São Paulo), ANA (Agência

Nacional de Águas), ANEEL (Agência Nacional de Energia Elétrica), FUNCEME (Fundação

Cearense de Meteorologia e Recursos Hídricos), SUDENE (Superintendência do Desenvolvimento do

Nordeste), DNOCS (Departamento de Obras contra Secas). The dataset of DAEE are only for São

Paulo State and available to the public and it can be downloaded from http://www.sigrh.sp.gov.br/cgi-

bin/bdhm.exe/plu. The dataset for other regions of Brazil are also public available from

http://hidroweb.ana.gov.br/. The list of 887 stations is presented in Appendix, where for the sake of

economy of space only station identity (ID) code is shown, but it is sufficient to access the data from

aforementioned Web sites, including geographic position, name, and altitude. From this list the readers

or users may see which stations were assessed for homogeneity and also perform their own

homogeneity analysis. We are conscious that no homogeneity assessment is definite.

The elected stations are distributed across 21 states as shown in Figure 1a. The map with

geographic location of each station is depicted in Figure 1b. As one may see both the density and the

number of stations are highly variable. The São Paulo state, in Southeast (SEB), is favored by a high

density network with 385 stations of DAEE, but some areas as of the Northeast are poorly covered, and

for Amazon Basin no station was elected, since unfortunately many stations in those regions stopped to

collect rainfall data before 1997 or their data had not been updated in the time of this work. The rainfall

series from the institutions which impose data policy restriction or those not easily available for public

accessibility are not regarded in this work.

The gauge-only precipitation gridded analyses of daily rainfall data covering South America,

for horizontal resolution of 1o and 2.5o, are now provided by NOAA-CIRES Climate Diagnostic Center

(CDC) (Liebmann and Allured, 2005), benefiting scientific community worldwide. Specifically for

Page 6 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

http://www.sigrh.sp.gov.br/cgi-bin/bdhm.exe/plu

http://www.sigrh.sp.gov.br/cgi-bin/bdhm.exe/plu

http://hidroweb.ana.gov.br/

Peer Review O

nly

7

Brazil, a new version of the NOAA-Climate Prediction Center historical gauge-only precipitation

gridded daily precipitation analysis, for the horizontal resolution of 1o x 1o, with improved rain-gauge

station coverage was recently presented by Silva et al. (2007). Because of our screening process,

stations used here are considerably smaller in number and density than considered in those analyses.

3. Some possible types of inhomogeneity expected to be encountered in rainfall data of Brazil

The reporting of missing observation as zero is recognized as one of the most serious problems

to be dealt with in the homogeneity analysis of the daily rainfall series (Higgins et al., 2000, Liebmann

and Allured, 2005). This flaw handling of missing observations has been identified even in the other

places of the globe like Australia (Lavery et al., 1992; Viney and Bates, 2004) and United States

(Higgins et al., 2000), where good observing practice is better established than in the countries like

Brazil.

According to the undocumented historical information kindly provided by the

DAEE hydrologist Dr. Sergio de Toledo (2008, personnel communication), this practice has been quite

common over time, particularly in some DAEE stations and even more on weekends, at least for the

periods before 1969-1970 and after mid-1980s. This implies that for some stations the data would be

reliable only for the period between 1971 and before mid-1980s. We are also told about the existence

of multi-day accumulation problem for some stations, either for not having observer at the station,

especially at the weekends, or forgetting the reading of the instrument by the observer. Even though

this historical information is not as precise as we wanted, it suggests what types of homogeneity

problem might be addressed. Therefore, it would not be surprising to find, for the DAEE rainfall series,

discontinuity in number of dry days, larger proportion of zero precipitation for weekends, and

distribution of daily amount varying with days of week, in addition to most commonly identified

problems of homogeneity, as those related for instance to the station relocation and changes of

Page 7 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

8

surrounding. For the stations outside Sao Paulo state, for which no information about stations history

was available at the time of this work, we assume they are potentially inhomogeneous with all possible

problems of homogeneity expected for DAEE stations.

4) Method

a) testing variables

The variables considered in the homogeneity analysis are normalized annual number of dry

days (NACZP), annual median of daily amount ( 50q ), and total annual. The latter is used only in the

final stage, after isolating more homogenous series. A dry day is defined as that day with zero

precipitation. In the construction of NACZP and 50q series, a missing year was interpolated using bi-

cubic spline.

b) Detection of abrupt and gradual change

Among various techniques presented in the literature for detection of abrupt change (e.g.

Carlstein, 1988; Guan, 2004; Alexandersson, 1986; Alexandersson and Moberg, 1997; Wang, 2003;

Caussinus and Mestre, 2004; Perreault et al., 2000a) we adopted that proposed by Bai and Perron (1998,

2003), henceforth BP, which has been firmly established in the statistical literature (see e.g. Granger

and Hyung, 1999). The method has the flexibility of fitting multiple breaks linear regression model to a

time series, enabling the access of the occurrence of various “regime change” over time, in terms of

mean. The break-points, i.e., where occurs change in the regression coefficients or model structure, are

treated explicitly as unknown variables to be estimated from the data as such way that the method is

suitable when no metadata information is available about them. The method can be applied for a wide

range of conditions. For example, serial correlation, different distributions for the errors across each

Page 8 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

9

segment between breaks and heteroskedacity are allowed. The strategy for estimating the change-points

is based on ordinary least square (OLS) and the residual sum of squares (RSS). The dynamic

programming algorithm, based on principle of optimality (e.g. Belmann, 1957), is used to evaluate all

potential change-points (Bai and Perron, 2003). For a series of record length T , this algorithm requires

at most least-squares operations of order )T(O 2 for any number of breaks m , or )1m( + regimes,

while standard procedure requires least squares operations of order )T(O m . From a computational

point of view, this is an important feature mainly when a large number of series have to be analyzed as

in the present work. The complete theoretical insights and mathematical formulation of the method are

given in the above referred papers, and also in more recent paper by Perron (2005). In the

meteorological literature, some authors (e.g. Wang 2003, 2008) have put effort for the development of

regression-based method for change-point problem whose central idea is similar to that of BP. Let y

be an annual series of some quantity. One change-point at year ct is defined whether the time average

of y over a number of years before ct would differ significantly from the time average after the same

year. As a way for assessing whether there exist evidence for such a change-point or not, we tested if

the data support the hypothesis that there is no structural change, against an alternative that the

structure changed over time. In this work, we choose, among various, the supF test which has been

deeply discussed by Andrews (1993), whose performance is well-evaluated, outperforming for example

in some situations methods based on information criteria such as Bayesian or Akaike Information

Criteria, which had been proposed by Yao (1988). In the supF test, the F statistic is computed for all

potential change points. The null hypothesis of no structural change is hence rejected if some value of

F exceed a specified limit corresponding to a particular significance levelα . The p -value for the test

can be obtained based on Hansen (1997).

For the present work, because of station sparsely for most regions, the BP method there seems

to be more suitable than the widely used approach proposed by Alexanderson (1986) called standard

Page 9 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

10

normal homogeneity test (SNHT), a likelihood ratio test which relies on so-called reference series

supposedly homogeneous based on neighboring station. In the case of rainfall climate series from

Brazilian rain-gauge network another problem for utilizing this approach is that there is practically no

information about homogeneity. The ineffectiveness of SNHT, for areas where lack good neighboring

stations, has been pointed out by many authors (e.g. Vincent, 1998; Hansen-Bauer and Forland, 1994;

Peterson et al., 1998; Wijngaard et al., 2003), and it has been one of the reasons for adopting

alternative approaches in various countries. In the present work, as in Lavery et al. (1992) and many

others, we restrict homogeneity assessment to absolute tests, i.e., focusing on each station without

accounting for neighboring stations. This approach has been adopted for example by Trenberth and

Paolino (1980) for detecting inhomogeneities in the Northern Hemisphere sea-level pressure data.

We compared the ability of BP method with that of developed in the Bayesian framework, by

means of Monte Carlo simulation study, to ensure that the result of change-point analysis is method-

independent as much as possible. From a number of Bayesian approaches for change-point problem

available in the literature (see e.g. Menzefricke, 1981; Hsu, 1984; Smith, 1975; Elliot and Shope, 2003),

we chose the one that is based on so-called product partition model (PPM) introduced by Hartigan

(1990) and Barry and Hartigan (1992,1993). Further references for PPM method are Crowley (1997)

and Quintana and Iglesias (2003). The BP and PPM approaches are completely independent in the

sense that there is no theoretical bridge between them. In Meteorology, Bayesian approach and its

variations to change-point problem have been used by some authors. Elsner et al. (2004) used them for

detecting shifts in the annual hurricane rates in North Atlantic and coastal area of the US, Chu and

Zhao (2004) for identifying change-points in the Tropical cyclone activity. In hydrology, Perreault

(1999) and Perreault et al. (2000b) used Bayesian method for detecting sudden change in a sequence

of energy inflows modeled by normally distributed random variables. Like BP, PPM is suitable for

detecting unknown change-points because they are treated as a random variable. Figure 2 illustrates the

Page 10 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

11

outcomes of these methods applied for a simulated Gaussian series of length 45 with mean µ and

standard deviation σ , for which five breaks were imposed at ct =5, 15, 25, 30, 40, with shifts σ3 ,

σ3− , σ3− , σ3 , σ3− , respectively. The series has mean 0.7 and standard deviation 0.07, resembling

a typical NACZP series. For example, at Nova Palmira, in Rio Grande do Sul state, one of the stations

considered by Ropelewski and Bell (2008), the average and standard deviation of NACZP series are

0.70 and 0.067, respectively. The length 45 corresponds approximately to overall mean for all 887

rainfall series. Note in Figure 2 that all the breaks were correctly identified by BP method, in terms of

both number and location. The value of supF is significant at the 510− level. A good dating of the

breaks is also given by PPM method, considering that the main peaks in the posterior probability of

change-points coincides with location of imposed breaks. Further, a good agreement between OLS

linear fitting and posterior mean obtained by PPM method is notable, even though the latter is rather

noisy. An inherent difficulty of using PPM is the interpretation of the posterior probability of change

point without an overall visual inspection of outcomes, as in Figure 2. This is a disadvantage of the

PPM especially when many series are involved in the work, and it was an important reason for

preferring BP method in the present work, despite of the similarity of their outcomes as seen above. It

is worth mentioning that the underlying notion of break in homogeneity is better described by

segmentation with constant mean level given by BP method than noisy PPM posterior mean. The

similarity in the capacity of the break detection and dating of the breaks of the two methods was also

observed in Monte Carlo study with 4000 simulated series (not shown). We noted in two methods that

their capacity of detecting breaks diminish with reduction of shift amplitude and when distance

between breaks diminished, as occur with other methods as for example SNHT. An important feature

of both methods is that bias toward detecting breaks where actually there is not is satisfactorily small.

Page 11 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

12

For detecting gradual change we used Mann-Kendall rank correlation (see e.g. Hipel and

McLeod, 2005). This analysis was carried out after applying other tests and with those series isolated as

being more homogeneous.

All the computations were carried out using R software environment for statistical computing

and graphics (R Development Core Team 2008).

c) Distribution test for daily amounts

After identifying discontinuity either in NACZP or 50q , we tested for the difference in the

distribution of daily amounts between one segment and another determined by the change-points. This

is equivalent of verifying whether these segments are stochastically different, i.e., in a broader sense

than just testing for difference in the mean or median, and may help see whether, for example, the

observer had the habit of reporting only significant amount in some sub-period. The null hypothesis of

interest is that the samples of daily amounts for different segments come from the same (unknown)

population. Therefore, a series with m breaks involves 2/)1m(m + hypothesis testing, regarding

pairwise comparisons. We adopted two statistical methods to carry out this analysis, namely

Kolmogorov-Smirnov (KS) test and Anderson-Darling (AD) test, again for ensuring that different

methods lead to the same conclusion, as far as possible. The KS and AD tests adopted here are from the

recent development by Abadie (2002) and Scholz and Stephens (1987), respectively, with a significant

improvement that permits to be used safely even to the samples containing tied values, commonly

present in instrumental data due to rounding. The procedure proposed by Abadie (2002) is a bootstrap

version of classic KS test. In the present work this method was implemented with 1000 replications.

The KS method is designed for testing two samples at a time, while AD method can be used for testing

simultaneously more than two samples. But for a consistent comparison, the latter was also used for

Page 12 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

13

pairwise comparison. Thus, we isolated statistically more significant outcomes from

2/)1m(m + possible tests for each series with m break-points. We also used KS and AD tests for

examining the homogeneity problem related to accumulation, i.e., checking for the difference in the

distribution of daily amount among different days of week.

d) Proportion test

The difference in the proportion of zero precipitation among days of week was checked by

using Pearson chi-squared test (e.g. Siegel, 1975). As aforementioned, this difference is expected in

some rainfall records, at least for stations located in Sao Paulo state. The null hypothesis of interest is

that the proportions of zero precipitation in a daily series are the same for all days of week, such that a

series exhibiting a significant difference should be considered inhomogeneous, as physically there is no

plausible explanation for it.

5. Results

a) Discontinuity in the NACZP series

Table 1 shows, for each state, the number of NACZP series exhibiting one or more

discontinuity ( bN ), and those among bN series rejected by the supF test, )(N Fsup α , at the five

significance levels α =0.20, 0.15, 0.10, 0.05, 0.01. This kind of homogeneity problem was detected in

the majority of stations (730 out of 887 or 82.2% of total) and all across the country, not only for

DAEE stations in Sao Paulo state, for which this problem was already expected according to historical

information (section 3). For some states the percentage of stations exhibiting this problem is impressive.

If the significance level 0.05 was taken as a critical level for rejection of null hypothesis that a rainfall

Page 13 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

14

series is homogeneous, for the states like Mato Grosso, Sao Paulo, Paraná and Rio Grande do Sul,

respectively 85.7%, 83.6%, 78% and 72% of their rainfall series would be classified as inhomogeneous.

The situation is not much better for Ceará, Sergipe, Bahia, Rio de Janeiro and Santa Catarina, with

more than 60% of station rejected at this significance level. For some states as Paraíba, which has only

two stations, none of them could be considered homogeneous at this significance level. A similar

situation is encountered for Pará.

In Sao Paulo state, 350 out of 385 (91% of total number) stations exhibit at least one

discontinuity in NACZP series ( bN in Table 1). Of these 350, 150 stations exhibit break for the years

1969, 1970 or 1971, and for 97% of these cases the shift is negative and statistically significant at the

level 0.01. This result was expected because the practice of reporting missing days as days of no

precipitation was reduced from 1969-1971 in some stations, as aforementioned (section 3). Figure 3

reveals this as the first sharp increases in the cumulative sum of annual counts of stations exhibiting

break. Other major increase of inhomogeneity series is depicted in this analysis for 1983, which is also

in agreement with the historical information about DAEE stations (section 3).

For Sao Paulo state, Figure 4 shows the spatial distribution of the stations exhibiting change-

point for the years 1969, 1970 or 1971 (filled circles) and those which do not (open circles). The lack

of spatial coherence does not support the speculation exercise by attributing, for instance, the detected

change-points as trigger of regional climate change. The spatial coherence is not observed for change-

point in 1983 and 1990 (not shown).

Figure 5 shows examples of NACZP series revealing discontinuity. The calculated supF statistic

for all these series trespasses the limit of the 0.01 level. The median of the distribution of daily amounts

for each segment (or sub-period) is also shown. Since it is multi-year based median we denote it as

Page 14 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

15

50Q to differentiate from the single year median 50q . Our aim to show 50Q is to call attention to the fact

that it is systematically larger (lower) for the sub-period with larger (lower) number of dry days, which

is exactly contrary to that would be expected climatologically. This bias is certainly a result of bad

observing practice, particularly in that cases in which the observers reported only significant amounts

or zero during some period(s). For examining this feature regarding all bN stations (Table 1), we

constructed a scatter diagram as shown in Figure 6a, where 50Q and mean NACZP (mNACZP)

correspond to each sub-period. Similar diagrams with respect to higher quantiles, 95Q (95% quantile)

and 99Q (99% quantile) are shown in Figures 6b-6c. The Kendall rank correlations between mNACZP

and 50Q , 95Q , and 99Q are 0.59, 0.42 and 0.29, with p-values practically zero, indicating the presence

of a significant bias in the distribution of daily amounts. A high quantile as 95Q are often regarded as

reference value in climate-change problem, in particular, for assessing long-term trend in the frequency

and intensity of extreme events (see e.g. Haylock et al., 2006; Dufek and Ambrizzi, 2008; Sugahara et

al., 2008). But if this quantile was computed using series as those identified here with homogeneity

problem, certainly it will lead to a doubtful result, unless the magnitude of actual change is

substantially larger than an artificially introduced change.

In the climate series broken down into segments, such as those shown in Figure 5, it is difficult

to discover which one of sub-periods of the data are credible without rely upon other sources of

precipitation measurements as satellites and radars (see e.g. Higgins et al., 2000). Unfortunately, the

satellite data are available only for the period after 1970s, and weather radars data are not a solution for

Brazil mainly due to poor spatial and temporal coverage. A sub-period with lower mNACZP not

necessarily is the period with reliable data. It may simply be revealing that during this period the

improper reporting of zero precipitation was practiced with less frequency. The most important point to

be highlighted here, however, is that there is no reasonable explanation for this relation, since, on the

Page 15 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

16

average, for a sub-period with lower mNACZP characterizing wetter climate we expect more intense

daily amount, and not the contrary as we found here.

b) Changes in distribution of daily amount related with change-points in NACZP series.

All bN series exhibiting discontinuity in NACZP series were examined if the distribution of

daily amounts changed from one segment to another, in a significant manner. As an illustrative

example let us consider Figure 7, which shows, for the station 00440023, the changes in empirical

cumulative distribution of daily amounts related with three break-points in NACZP series over the

period of records 1912-2007 (see Figure 5a), defining four segments 1912-1930, 1931-1963, 1964-

1977, and 1978-2007. It is important to note that the difference in the distributions of daily amounts

between the sub-periods 1912-1930 and 1978-2007 is relatively small for lower daily amount as

reflected for example in median (see Figure 5a), but it increases for larger amounts approximately from

80% quantile, making the two sub-periods stochastically different at the 0.01 level, according to both

KS and AD tests. It well illustrates how important is the comparison of the distributions of different

segments for further ascertaining on the inhomogeneity. By comparing only the median, for instance,

the presence of this inhomogeneity would not have been detected, since as stated above the difference

in the distributions is manifested only in higher quantile.

Figure 8 shows the result of the KS and AD tests for bN stations. The plotted p-values show

that both tests lead to the same conclusion in practically all the cases. It can be noted that for majority

of bN stations, a break in NACZP series is related to highly significant change (small p-value) in the

distribution of daily amounts. An important practical implication of it is that when homogeneity

adjustment is performed these changes have to be inevitably taken into account, which seems to be an

Page 16 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

17

extremely complex task. Table 2 shows for each state the results of the AD test. As result for KS test is

practically the same, it is not shown. The summary regarding all stations are also presented.

c) Different counts of zero precipitation for different days of week

The missing of observations at the weekend as previously mentioned was relatively common by

the observers of the DAEE stations in Sao Paulo State, at least during some period of records. In such

case, the accumulated Monday’s readings comprised 2-3 days accumulation and Saturday and Sunday

were simply reported as days of no precipitation.

Even though the information about possible presence of similar problem is restricted only to the

rainfall series of Sao Paulo State, we attempted to ascertain the inhomogeneity in which the count of

zero varies as function of day of week regarding all stations. The result shows the presence of this

physically inconceivable inhomogeneity in many stations all across country. In fact, we expect the

same proportion of zero precipitation for every day of the week, except by some difference due to

sampling fluctuation. The stations exhibiting larger number of zero particularly for weekend are

highlighted in Figure 9a. Note that in some regions the proportion of stations presenting such feature is

quite impressive, such as for states of Sao Paulo (65%), Ceará (75%), Pernambuco (75%), Paraná

(82%), Santa Catarina (82%), and Rio Grande do Sul (66%). For some stations we found larger

proportion of zero precipitation for the days of week but not for weekend, for example Thursday, as in

the case of station 00440023 discussed before. The counts of stations exhibiting the largest number of

zero daily precipitation apportioned by day of week is shown in Figure 9b, regarding all the 887

stations. The feature captured in this figure is more than sufficient for showing that the Brazilian

historical rainfall data must be used very carefully.

Page 17 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

18

Figure 10 shows, for three stations, the plot of normalized number of dry days for whole

period apportioned by day of week (left), along with the plot of two NACZP series (right)

corresponding to days of week with the largest and lowest proportion of zero precipitation. The p-value

for the proportion test, as presented in the legend, considers only days with the largest and the lowest

proportions, and the null hypothesis is that the proportions of zero for these days are the same. For the

three cases, we can note that the difference in the proportions is highly significant. The results for all

887 stations are shown in Table 3.

d) Break in 50q series

The choice of median as testing variable in the homogeneity analysis offers some advantage

over other quantities such as the total annual or the annual average due to its resistance to outliers (e.g.

Wilks, 1995). For a given station, a break in a series of 50q may have been caused by station relocation,

change in instruments, etc. as already mentioned, but not necessarily due to the same factor that caused

break in homogeneity of NACZP series. For example, a break in 50q series may be caused only by

change in the instrument and this does not necessarily cause a break in NACZP series. The opposite

may also occur, i.e., a break in NACZP series not necessarily implies on breaks in median series. For

example, the daily amount may have been collected in such irregular way, without respecting any rules,

that only NACZP would reveal presence of breaks, as for this quantity the rainfall amount (>0) does

not matter.

The result of change-point analysis of the 50q series is presented in Table 4. Regarding all

N stations, the number ( *bN ) of stations exhibiting discontinuity in the 50q series is larger than that for

time series of NACZP, 87% for the former against 82% for the latter, probably due to larger magnitude

Page 18 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

19

of shift in 50q series than that in NACZP series. For instance, the number of 50q series rejected by supF

test at the 0.01 significance level, )01.0(N*b , is 595, against 537 for NACZP series. Furthermore, we

noted that 91.5% of stations presenting break-point(s) in NACZP also reveal break-points(s) in 50q ,

while in 85.5% of 50q with break(s) present also break(s) in NACZP series. Interestingly, Mato Grosso,

São Paulo and Rio Grande do Sul show larger number of series with break(s) in NACZP than for 50q .

Figure 11 shows examples of inhomogeneous 50q series, for different regions of Brazil. The null

hypothesis of no structural change for these series is rejected at the 0.01 significance level.

e) Change in distribution of daily amount related to change-points in q50 series

The presence of a break in 50q series already indicates change in the distribution of daily

amount from one sub-period to another sub-period, but we can give a support to it or confirm the result

of change-point analysis, in a more statistically meaningful way, by means of KS and AD tests as done

earlier in Section 5b. Thus the 2/)1m(m + null hypotheses that the samples of daily amounts for

m different segments of each 50q series come from the same population were tested, isolating among

these tests the most significant outcomes. The result for all *bN series indicated that 769 of them

(99.6%) are rejected at the 0.01 significance level, and all of them at the 0.05 significance level, giving

an important support to the change-point analysis (see Table 5 for more detail).

f) Accumulation problem

We showed earlier that for many stations the number of zero precipitation varies significantly

with the day of week. We attempted to verify the presence of similar behaviour in the daily amounts

that would be probably detected whether, for example, a gauge was often unread in some specific day

Page 19 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

20

of week and accumulating rainfall over more than one day. For the cases in which the gauge was not

read at the weekends, Monday readings might be on errors or biased. Figure 12a shows one example in

which 50% quantile for Sunday and Monday is larger than that for other days of week, mainly when

compared to that for Tuesday. The station is C5-050, whose behavior of the NACZP series was shown

in Figures 10c-d. The large 50% quantile for Sunday may have been caused by the observer who

reported only when it rains significantly or zero, neglecting small rainfall amount. It is consistent with

the lowest number of wet days for this day (Figure 12b). For Monday which also has large 50%

quantile, a possible reason is the accumulation over weekend, since it exhibits the largest frequency of

wet days (Figure 12b). Figure 12c compares 50q series for Sunday and Tuesday. Note that the

difference is relatively small only between mid-1970s and mid-1980s coinciding with the period in

which had more reliable observation according to station history (section 3). For some years, for

example 1950, the discrepancy is so large that leads us to suspect that the observer either reported only

extreme cases or guessed values.

We addressed this question of improper accumulation testing for difference in the distribution

of daily amount among days of week using AD test. The null hypothesis in this case is that the

distributions of daily amounts are equal for every day of week, except by sampling fluctuations. The

result is shown in Table 6. In this analysis we consider that the improper rainfall accumulations not

necessarily are related to the weekend, and among all possible comparison only the most significant

result was considered.

g) Non climatic trend and overall evaluation of the tests

Before testing a possible presence of nonclimatic trend, an evaluation of all tests considered so

far is made in this section. The trend test is applied only to those series classified as homogeneous,

Page 20 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

21

according to the previous tests. Thus, for isolating such series, we reject any series if it presents one of

following conditions:

(i) NACZP series exhibit at least one break at the significance level α of supF test (Section 5a),

(ii) NAZCP series exhibit at least one break (Section 5a), and AD test (or KS test) indicates that the

difference in the distribution of daily amount between different segments of NACZP series is

statistically significant at the level α (Section 5b),

(iii) the proportion test indicates the difference in the number of dry days among different days of week

significant at the level α (Section 5c),

(iv) at least one break is detected in the 50q series at the significance level α of supF (Section 5d),

(v) at least one break is detected in the 50q series and AD test (or KS test) indicates that the difference

in the distribution of the daily amounts among different segments of the 50q is significant at the level

α (Section 5e),

(vi) the AD test indicates that the distribution of daily amounts for one day of week is different from

that for any other day at the level α (Section 5f).

In the conditions (ii) and (v) the significance level for supF is not taking into account, but only for AD

test.

Table 7 presents a summary of this joint assessment of homogeneity, where )(Nac α is the

number of stations which did not present none of the above conditions with respect to the significance

levelα .

A difficulty in statistic-based homogeneity assessment is the choice of significance level to

decide which series should be rejected or not. It is especially true when metadata are not available to

help identify potential non-homogeneity or for confirming the results of statistical analysis. As

aforementioned, the metadata with the stations history available for the present work is only for a very

restricted area collected through an interview, and far from completeness and precision such that its

Page 21 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

22

usefulness is quite limited. However, it is important to consider that some statistical feature, such larger

number of dry days for some particular day of week, must be attributed only to bad observing practices,

since no physical process can be associated with it. In this case, a metadata is totally dispensable, and

certainly this type of information would not have been reported by observers. Another case that can

discards the metadata information is that related with positive correlation between average number of

dry days and the median of daily amounts within the segments determined by break points. This

relation can not be attributed to any physical process either. Such problems suggest that the choice of a

critical level, as for example 0.05, appears to be more appropriate than less stringent critical level 0.01,

which is used for example in the homogeneity analysis of European daily temperature and precipitation

series (Wijngaard et al., 2003). Thus, a record would be regarded as useful if it exhibits no

inhomogeneity at the 0.05 significance level, in the applied tests.

In the trend assessment, as above mentioned, we considered only those stations which passed in

all previous tests at the 0.05 level, and considering as testing variables, the total annual as well as the

previously considered NACZP and 50q . With the respect to the total annual, the presence of break was

examined before trend analysis. To calculate total annual, a daily amount trespassing the limit defined

by (see e.g. González-Rouco et al., 2001) IQR3QP 75out += was considered as an outlier. The

75Q stands for 75% quantile of daily amount (>0) computed for each day of year regarding all records

and IQR is interquartilic range, defined as 2575 QQ − . A procedure to estimate p-quantile for each day

of year is described in Sugahara et al. (2008). The daily amounts over outP were substituted by this limit.

It was found that among 16 stations in Table 7 that passed at the significance level 0.05, five

stations exhibit at least one break in their total annual at the 0.05 significance level, reducing the

number of homogeneous (or useful) stations to 11, which are listed in Table 8. Their geographical

positions are shown in Figure 13. Of these 11 stations, three stations exhibit trend significant at the 0.05

significance level, one of them in NACZP and two other in total annual. Before using these series in

Page 22 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

23

climate studies, further analysis is necessary to verify the origin of these trends, whether they were

caused for example by sheltering effect associated with buildings, trees, etc.

6. Concluding remarks

Raw data of historical daily rainfall series for 887 stations belonging to different climate regions

of Brazil were assessed for homogeneity, statistically. In principle this dataset is useful for climate

studies, regarding the series length and completeness. But, unfortunately, our result shows that most

series are infected by some type of non-climatic variation, most of them due to the bad observing

practices, as flaw handling of missing observations and multi-day accumulation, among others. These

problems were identified all across country. If the 0.05 significance level was taken as critical level for

all the applied tests, only 11 series may be considered homogeneous, corresponding to 1.2% of total

number of stations.

The poor spatial station coverage given by these stations (Figure 13), certainly poses difficulties

in various climate studies. For example, if ascertaining the statistical significance of the influence of

ENSO phenomenon on rainfall over Brazil or any other in which spatial coherence is an important

aspect of the problem. The gridded analysis of daily rainfall for Brazil such as provided by CDC

(Liebmann and Allured, 2005) and CPC (Silva et al., 2007) as well as those for monthly precipitation

provided by Chen et al. (2002), would not be an alternative for overcoming the problem of insufficient

data coverage, since both analyses rely on the rain-gauge data from the same sources considered in the

present work.

The result of the present work also call attention to the need for recalculation of each currently

used 1961-1990 period standard climatic normal for precipitation, which relied on inhomogeneous

Page 23 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

24

series. This is important for example to give credibility of climate monitoring. Obviously, for this

purpose, as well as for climate studies in general, a scheme for continuous data quality monitoring also

should be implemented by institutions elected for maintaining the network of observations. Needless to

say that homogeneity-adjustment of inhomogeneous series is also crucial for verification and validation

of climate models performance. With respect to the climate-trend and climate variability studies, since

they are sensitive to both inhomogeneity and homogeneity-adjustment the inhomogeneous series

should be discarded, if one intends reliable results.

Especially for Brazilian rain-gauge based climate series, for which were encountered serious

problems of homogeneity, the procedures regarded in the present work could be considered as the first

stage of any climate study based on data, as for guaranty of a minimum credibility, regardless data

sources and period of interest. Although a large number of stations were not accessed for homogeneity

due to our selection procedure, we suspect, on grounds of the present results, that many of them would

be likely infected by the similar inhomogeneities.

Acknowledgments

The authors would like to thank Dr. Sergio Cirne de Toledo for valuable historical information about

DAEE stations, and to the ANA and DAEE for providing their rainfall dataset. The research of the

first and third authors was partially supported by Brazilian Financial Support Agency (FINEP) under

contracts #01.06.1120.00 and #01.06.1126.00. The first author thanks to Marcos Antonio Antunes de

Oliveira for his assistance in the computational work.

Page 24 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

25

APPENDIX – List of 887 stations considered in this study for inhomogeneity assessment.

00147002 00241002 00338001 00338008 00338009 00338016 00339004 00340014 00340015 00340018 00340020 00340023 00341000 00341001 00342002 00342005 00342006 00438002 00438015 00438019 00438022 00438035 00439018 00439019 00440004 00440005 00440023 00441002 00441005 00442010 00444001 00538003 00538007 00538008 00538009 00538010 00539005 00539037 00540020 00541008 00541009 00542003 00542007 00542008 00542010 00542012 00635013 00637010 00638007 00638013 00638044 00639009 00639015 00639029 00639030 00640002 00640019 00641000 00641003 00641004 00641006 00642001 00642008 00642010 00644003 00735036 00735050 00735067 00737006 00738003 00739038 00740001 00740002 00740009 00740011 00741001 00741005 00741009 00742000 00742004 00742006 00742007 00743000 00743002 00743004 00743005 00744000 00836043 00838000 00838002 00839009 00839014 00840015 00843002 00848003 00935001 00936031 00936045 00936051 00936052 00937005 00937022 00940018 00942000 00948000 01036003 01036005 01036009 01037007 01037009 01037036 01137001 01137027 01140000 01140010 01141008 01143010 01144005 01238000 01238010 01238042 01241017 01244011 01339027 01339041 01340003 01340015 01343017 01344008 01346000 01346002 01347000 01347001 01348000 01348001 01439002 01439006 01439014 01439043 01439044 01440001 01441002 01443001 01444000 01444001 01444004 01444017 01447001 01447002 01448000 01448001 01457001 01539002 01539006 01539008 01539010 01540003 01543002 01544012 01547001 01548003 01549002 01549003 01556005 01640000 01641001 01642002 01645000 01645002 01645005 01651000 01653002 01655002 01743002 01744010 01753000 01754000 01756000 01840000 01840004 01840015 01841010 01842004 01842005 01842007 01842008 01844001 01846003 01846007 01847001 01847003 01847010 01849000 01940000 01940001 01940005 01940006 01940007 01940009 01940010 01940012 01940013 01940016 01940020 01940022 01940023 01941000 01941003 01941004 01941005 01941006 01941008 01941009 01941010 01941011 01941012 01942002 01942006 01943001 01943004 01943007 01943008 01943010 01943023 01943025 01943027 01943035 01944004 01944021 01944024 01946004 01946005 01946007 01946022 01947001 01947006 01949002 01949006 02040001 02040003 02040005 02040007 02040009 02040011 02040012 02040017 02040018 02040020 02041000 02041001 02041002 02041003 02041008 02041010 02041011 02041013 02041014 02041017 02041018 02041019 02041020 02041021 02041023 02042008 02042010 02042014 02042015 02042016 02042017 02042027 02043009 02043011 02043014 02043025 02043026 02043027 02044009 02044027 02045004 02045005 02046011 02140000 02141006 02141007 02141014 02141015 02141016 02141017 02142000 02142002 02142007 02142008 02142015 02142022 02142058 02143001 02143003 02143005 02143006 02143008 02143009 02143011 02143016 02143018 02143019 02143020 02143022 02144001 02144002 02144003 02144004 02144005 02144006 02144007 02144009 02144018 02144020 02144021 02144024 02144025 02145001 02145007 02145009 02145017 02145021 02145023 02145024 02146028 02146029 02147054 02241001 02241002 02241003 02242001 02242002 02242003

Page 25 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

26

02242004 02242005 02242007 02242008 02242010 02242011 02242012 02242013 02242014 02242016 02242017 02242018 02242020 02242021 02242024 02242025 02242026 02242027 02242028 02242029 02243003 02243004 02243005 02243010 02243011 02243012 02243013 02243015 02243016 02244030 02244031 02244033 02244034 02244036 02244037 02244038 02244039 02244041 02244042 02244044 02244045 02244047 02244057 02244065 02244068 02244071 02244097 02244099 02244101 02244106 02245065 02245074 02245077 02245080 02245085 02245086 02246047 02349033 02350002 02350010 02453013 02454001 02548000 02548001 02548003 02549000 02549001 02549004 02549017 02550001 02550003 02550005 02551000 02551001 02551004 02552000 02552001 02552002 02554002 02649002 02649003 02649004 02649006 02649007 02649008 02649009 02649010 02649012 02649013 02649016 02649017 02649018 02650006 02651000 02651003 02651004 02748001 02748003 02749000 02749001 02749003 02749005 02749006 02749007 02749012 02749013 02749015 02749031 02750007 02750008 02750009 02750010 02750012 02751006 02751007 02752006 02753004 02753006 02754001 02755001 02848000 02849000 02849002 02849004 02849005 02849008 02850009 02851003 02851021 02851022 02851024 02853003 02853010 02853014 02854003 02854005 02854006 02855001 02855002 02855005 02951010 02951022 02951027 02951028 02952003 02953008 02954001 02954004 02954005 02954007 02955002 02955007 02956006 02956007 03052011 03152002 03152005 03152008 03152016 03153007 03153008 03252006 03252008 03253001 03253003 03253004 B4-002 B4-003 B4-005 B4-012 B4-015 B4-018 B4-021 B4-026 B4-029 B4-032 B4-040 B4-053 B5-003 B5-004 B5-005 B5-009 B5-012 B5-015 B5-020 B5-024 B5-028 B5-029 B5-034 B5-035 B5-036 B5-040 B5-050 B6-001 B6-003 B6-007 B6-008 B6-009 B6-010 B6-020 B6-022 B6-030 B6-033 B6-034 B6-036 B6-037 B6-039 B6-047 B6-048 B7-005 B7-006 B7-008 B7-011 B7-012 B7-013 B7-014 B7-016 B7-036 B7-038 B8-001 B8-002 B8-004 B8-011 B8-012 B8-016 C3-030 C3-031 C3-034 C3-040 C4-019 C4-021 C4-029 C4-032 C4-033 C4-040 C4-041 C4-043 C4-052 C4-054 C4-069 C4-071 C4-072 C4-075 C4-077 C4-079 C4-085 C4-086 C4-087 C4-088 C4-091 C4-092 C4-093 C5-009 C5-011 C5-016 C5-017 C5-018 C5-020 C5-024 C5-027 C5-028 C5-035 C5-040 C5-041 C5-042 C5-048 C5-050 C5-055 C5-056 C5-073 C5-074 C5-082 C5-084 C5-092 C5-104 C6-002 C6-003 C6-008 C6-023 C6-036 C6-041 C6-050 C6-051 C6-056 C6-066 C6-071 C6-078 C6-085 C6-086 C6-088 C7-001 C7-003 C7-004 C7-008 C7-009 C7-010 C7-011 C7-012 C7-023 C7-034 C7-036 C7-043 C7-045 C7-046 C7-062 C7-075 C7-079 C8-004 C8-008 C8-009 C8-014 C8-018 C8-030 C8-042 C8-043 D1-005 D1-006 D1-020 D2-009 D2-013 D2-015 D2-020 D2-028 D2-029 D2-031 D2-035 D2-037 D2-041 D2-060 D2-065 D2-068 D2-070 D2-072 D2-075 D2-077 D2-078 D2-080 D2-084 D3-002 D3-003 D3-014 D3-015 D3-018 D3-022 D3-023 D3-027 D3-042 D3-046 D3-052

Page 26 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

27

D3-054 D4-004 D4-012 D4-016 D4-027 D4-029 D4-030 D4-032 D4-034 D4-035 D4-036 D4-037 D4-043 D4-044 D4-046 D4-047 D4-052 D4-059 D4-060 D4-061 D4-064 D4-068 D4-082 D4-087 D4-088 D4-094 D5-003 D5-006 D5-008 D5-019 D5-023 D5-029 D5-035 D5-039 D5-044 D5-047 D5-053 D5-076 D6-005 D6-006 D6-011 D6-018 D6-020 D6-021 D6-025 D6-035 D6-040 D6-041 D6-059 D6-083 D6-084 D6-089 D7-020 D7-031 D7-032 D7-033 D7-036 D7-043 D7-053 D8-004 D8-006 D8-008 D8-040 D8-041 D8-047 D9-001 D9-002 D9-003 D9-004 D9-014 E1-005 E2-002 E2-008 E2-009 E2-022 E2-024 E2-028 E2-034 E2-036 E2-045 E2-046 E2-048 E2-049 E2-054 E2-055 E2-057 E2-092 E2-098 E2-099 E2-102 E2-106 E2-110 E2-112 E2-113 E2-116 E3-002 E3-006 E3-010 E3-015 E3-022 E3-027 E3-034 E3-035 E3-040 E3-041 E3-042 E3-047 E3-050 E3-052 E3-054 E3-067 E3-074 E3-082 E3-085 E3-091 E3-097 E3-099 E3-106 E3-108 E3-109 E4-010 E4-015 E4-018 E4-019 E4-020 E4-026 E4-028 E4-030 E4-032 E4-036 E4-037 E4-046 E4-047 E4-049 E4-050 E4-053 E4-055 E5-001 E5-014 E5-015 E5-017 E5-019 E5-027 E5-030 E5-032 E5-045 E5-051 E5-069 E6-002 E6-003 E6-006 E6-007 E6-008 E6-021 E6-022 E6-030 E6-032 F3-005 F4-001 F4-004 F4-006 F4-007 F4-011 F4-012 F4-014 F4-016 F4-018 F4-019 F4-021 F4-022 F4-025 F4-027 F4-028 F4-029 F4-030 F4-031 F4-034 F4-035 F4-036 F4-037 F4-040 F4-043 F4-048 F5-005 F5-007 F5-008 F5-010 F5-011 F5-012 F5-014 F5-017 F5-019 F5-020 F5-021 F5-022 F5-023 F5-027 F5-031 F5-032 F5-033 F5-035 F5-041

References

Abadie A. 2002. Bootstrap tests for distributional treatment effects in instrumental variable models.

Journal of the American Statistical Association 97:284-292.

Alexandersson H. 1986. A homogeneity test applied to precipitation data. Journal of Climatology 6:

661-675.

Alexandersson H, Moberg A. 1997. Homogenization of Swedish temperature data. Part I: homogeneity

test for linear trends. International Journal of Climatology 17: 25-34.

Andrews DWK. 1993. Tests for parameter instability and structural change with unknown change

points. Econometrica 61: 821-856.

Page 27 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

28

Auer I, Bohm R, Jurkovic A, Orlik A, Putzmann R, Schoner W, Ungerbock M, Brunnetti M, Nanni T,

Maugeri M, Briffa K, Jones P, Efthymiadis D, Mestre O, Moisselin J, Begert M, Brazdil R,

Bochnicek O, Gegnar T, Gajic-Capka M, Zaninovic K, Majstorovic J, Szlai S, Szentimrey T,

Mercalli L. 2005. A new instrumental precipitation dataset for the greater alpine region for the

period 1800-2002. International Journal of Climatology 25: 139-166.

Bai J, Perron P. 1998. Estimating and Testing Linear Models With Multiple Structural Changes,

Econometrica, 66, 47-78.

Bai J, Perron P. 2003. Computation and Analysis of Multiple Structural Change Models, Journal of

Applied Econometrics, 18, 1-22.

Barry D, Hartigan JA. 1992. Product partition models for change point problems. The Annals of

Statistics 20:260-279.

Barry D, Hartigan JA. 1993. A Bayesian Analysis for Change Point Problems, Journal of The

American Statistical Association, 88:309-319.

Bellman RE. 1957. Dynamic Programming. Princeton University Press, Princeton, NJ. Republished

2003: Dover Publications, 366p. ISBN 0486428095

Carlstein E. 1988. Nonparametric changepoint estimation. Annals of Statistics 16: 188-197.

Caussinus H, Mestre O. 2004. Detection and correction of artificial shifts in climate series. Applied

Statistics 53: 405-425.

Chen M, Xie P, Janowiak JE. 2002. Global land precipitation: A 50-yr monthly analysis based on

gauge observations. Journal of Hydrometeorology 3: 249-266.

Page 28 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

29

Chu PS, Zhao X. 2004. Bayesian change-point analysis of Tropical cyclone activity: The Central North

Pacific case. Journal of Climate 17: 4893-4901.

Conrad V, Pollak C. 1950. Methods in Climatology, Harvard University Press, Cambridge, MA, 459pp.

Crowley EM. 1997. Product partition models for normal means. Journal of theAmerican Statistical

Association 92: 192-198.

Davey CA, Pielke RA. 2005. Microclimate exposures of surface-based weather stations. Implications

for the assessment of long-term temperature trends. Bulletin of American Meteorological

Society 86: 497-504.

DeGaetano AT. 2006. Attributes of several methods for detecting discontinuities in mean temperature

series. Journal of Climate 19: 838-853.

Dufek AS, Ambrizzi T. 2008. Precipitation variability in São Paulo State, Brazil. Theoretical and

Applied Climatology, 93: 167-178, DOI 10.1007/s00704.007-0348-7.

Easterling DR, Peterson TC. 1995. A new method for detecting undocumented discontinuities in

climatological time series. International Journal of Climatology 15: 369-377.

Elliott MR, Shope JT. 2003. Use of a Bayesian changepoint model to estimate effects of a graduated

driver’s licensing program. Journal of Data Science 1: 43-63.

Elsner JB, Niu X, Jagger TH. 2004. Detecting shifts in hurricane rates using a Markov Chain Monte

Carlo approach. Journal of Climate 17:2652-2666.

González-Rouco JF, Jiménez JL, Quesada V, Valero F. 2001. Quality control and homogeneity of

precipitation data in the Southwest of Europe. Journal of Climate 14: 964-978.

Page 29 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

30

Granger CW, Hyung N. 1999. Occasional structural breaks and long memory, University of California,

San Diego, Department of Economics, Discussion paper 99-14, June 1999. Available from

http://www.econ.ucsd.edu/papers/files/ucsd9914.pdf.

Guam Z. 2004. A semiparametric changepoint model. Biometrika 91: 849-862.

Hansen BE. 1997. Approximate asymptotic p values for structural-change test. Journal of Business &

Economic Statistics 15: 60-67.

Hansen-Bauer I, and Førland E. 1994. Homogeneizing long Norwegian precipitation series. Journal of

Climate 7:1001-1013.

Hartigan JA. 1990. Partition models. Communication in Statistics – Theory and Method 19:2745-2756.

Haylock M, Nicholls N. 2000. Trends in extreme rainfall indices for an updated high quality data set

for Australia, 1910-1998. International Journal of Climatology 20:1533-1541.

Haylock MR, Peterson TC, Alves LM, Ambrizzi T, Anunciação MT, Baez J, Barros VR, Berlato MA,

Bidegain M, Coronel G, Corradi V, Garcia J, Grimm AM, Karoly D, Marengo A, Marino MB,

Moncunill DF, Nechet D, Quintana J, Rebello E, Rusticucci M, Santos JL, Trebejo I, Vincent

LA. 2006. Trends in total and extreme South American rainfall in 1960-2000 and links with sea

surface temperature. Journal of Climate 19: 1490-1512.

Higgins RW, Shi W, Yarosh E, Joyce R. 2000. Improved United States Precipitation Quality Control

System and Analysis. NCEP/Climate Prediction Center Atlas 7, 40pp. Available from

http://www.cpc.ncep.noaa.gov/research_papers/ncep_cpc_atlas/7/index.html.

Page 30 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

http://www.econ.ucsd.edu/papers/files/ucsd9914.pdf

http://www.cpc.ncep.noaa.gov/research_papers/ncep_cpc_atlas/7/index.html

Peer Review O

nly

31

Hipel KW, McLeod AI. 2005. Time Series Modelling of Water Resources and Environmental Systems,

Available from www.stats.uwo.ca/faculty/aim/1994Book/.

Hsu DA. 1984. A Bayesian robust detection of shift in the risk structure of stock market returns.

Journal of the American Statistical Association 77: 407-416.

IPCC (Intergovernmental Panel on Climate Change) 2001. Climate Change 2001: The Scientific Basis.

Contribution of Working Group I to the Third Assessment Report of the IPCC. Ed. by J.T.

Houghton, Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell, and C.A.

Johnson. Cambridge University Press, Cambridge, UK.

Karl TR, Williams CN Jr. 1987. An approach to adjusting climatological time series for discontinuous

inhomogeneities. Journal of Climate and Applied Meteorology 26: 1744-1763.

Klok EJ, Klein Tank AMG. 2008. Updated and extended European dataset of daily climate

observations. International Journal of Climatology. DOI: 10.1002/joc.1779.

Lavery B, Kariko A, Nicholls N. 1992. A historical rainfall data set for Australia. Australian

Meteorological Magazine 40: 33-39.

Liebmann B, Allured D. 2005. Daily precipitation grids for South America. Bulletin of the American

Meteorological Society 86: 1567-1570.

Menzefricke U. (1981). A Bayesian analysis of a change in the precision of a sequence of independent

normal random variables at an unknown time point. Applied Statistics 30: 141-146.

Perreault L, Haché M, Slivitsky M, Bobée B. 1999. Detection of changes in precipitation and runoff

over eastern Canada and US using a Bayesian approach. Stochastic Environmental Research

and Risk Assessment 13: 201-216.

Page 31 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

32

Perreault L, Bernier J, Bobée B, Parent E. 2000a. Bayesian change-point analysis in

hydrometeorological time series. Part 1. The normal model revisited. Journal of Hydrology 235:

221-241.

Perreault L, Bernier J, Bobée B, Parent E. 2000b. Bayesian change-point analysis in

hydrometeorological time series. Parte 2. The normal model revisited. Journal of Hydrology

235: 242-263.

Perron P. 2005. Dealing with Structural Breaks, Boston University – Department of Economics –

Working Papers Series WP2005-017, Boston University – Department of Economics, available

from http://people.bu.edu/perron/papers/dealing.pdf

Peterson TC, Easterling DR, Karl TR, Groisman P, Nicholls N, Plummer N, Torok S, Auer I, Boehm R,

Gullet D, Vincent L, Heino R, Tuomenvirta H, Mestre O, Szentimrey T, Salinger J, Førland EJ,

Hanssen-Bauer I, Alexandersson H, Jones P, Parker D. 1998. Homogeneity adjustments of in

situ atmospheric climate data: A review. International Journal of Climatology 18: 1493-1517.

Quintana FA, Iglesias PL. 2003. Nonparametric Bayesian clustering andproduct partition models.

Journal of the Royal Statistical Society B 65: 557-574

R Development Core Team (2008). R: A language and environment for statistical computing. R

Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.

Ropelewski CF, Bell MA. 2008. Shifts in the statistics of daily rainfall in South America conditional on

ENSO phase. Journal of Climate 21: 849-865.

Rust HW, Mestre O, Venema VKC. 2008. Fewer jumps, less memory: homogenized temperature

records and long memory. Journal of Geophysics Research 113, D19110,

doi:10.1029/2008JD009919.

Page 32 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

33

Scholz FW, Stephens MA. 1987. K-sample Anderson-Darling tests. Journal of the American Statistical

Association 82: 918-924.

Sherwood SC, Titchner HA, Thorne PW, McCarthy MP. 2008. How do we tell which estimates of past climate

change are correct?. International Journal of Climatology, DOI: 10.1002/joc.1825.

Siegel S. 1975. Estatística não-paramétrica para as ciências do comportamento. Editora McGraw-Hill do Brasil,

São Paulo, 350p. In Portuguese.

Silva VB, Kousky VE, Shi W, Higgins RW. 2007. An improved gridded historical daily precipitation

analysis for Brazil. Journal of Hydrometeorology 8: 847-861.

Smith AFM. 1975. A Bayesian approach to inference about a change-point in a sequence of random

variables. Biometrika 62: 407-416.

Sugahara S, da Rocha RP, Silveira R. 2008. Non-stationary frequency analysis of extreme daily rainfall

in São Paulo, Brazil. International Journal of Climatology, DOI: 10.1002/joc.1760.

Trenberth KE, Paolino Jr. DA. 1980. The northern hemisphere sea-level pressure data set: trends, errors

and discontinuities. Monthly Weather Review 108: 855-872.

Tuomenvirta H. 2001. Homogeneity adjustments of temperature and precipitation series – Finnish and

Nordic data. International Journal of Climatology 21: 495-506.

Vincent LA. 1998. A technique for the identification of inhomogeneities in Canadian temperature

series. Journal of Climate 11: 1094-1104.

Viney NR, Bates BC. 2004. It never rains on Sunday: The prevalence and implications of untagged

multi-day rainfall accumulations in the Australian high quality data set. International Journal of

Climatology 24: 1171-1192.

Page 33 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

34

Wang XL. 2003. Comments on “detection of undocumented changepoints: A revision of the two-phase

regression model”. Journal of Climate 16: 3383-3385.

Wang XL. 2008. Penalized Maximal F test for Detecting Undocumented Mean Shift without Trend

Change. Jour. Atmos. Ocean Tech 25: 368-384.

Wijngaard JB, Klein Tank AMG, Können GP. 2003. Homogeneity of 20th century European daily

temperature and precipitation series. International Journal of Climatology 23: 679-692.

Wilks DS. 1995. Statistical methods in the Atmospheric Sciences. Academic Press, San Diego,

California, ISBN 0-12-751965-3, 468.

Xavier AFS, Xavier TMZ, Silva Dias MAF, Toledo JRC. 1996. Qualidade dos dados diários de chuva

no Estado de São Paulo. Revista Brasileira de Recursos Hídricos 12:71-87. In Portuguese.

Yao Y-C. 1988. Estimating the number of change-points via Schwarz’ Criterion. Statistics and

Probability Letters 6: 181-189.

Page 34 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

35

FIGURE CAPTIONS

Fig. 1 – (a) Map of Brazil with 21 states: PA (Pará), MA (Maranhão), PI (Piauí), CE (Ceará), RN (Rio

Grande do Norte), PB (Paraiba), PE (Pernambuco), AL (Alagoas), SE (Sergipe), TO (Tocantins), BA

(Bahia), MT (Mato Grosso), GO (Goiás), MG (Minas Gerais), ES (Espírito Santo), RJ (Rio de Janeiro),

SP (São Paulo), PR (Paraná), SC (Santa Catarina), and RS (Rio Grande do Sul). The respective counts

of stations are indicated in parenthesis. (b) Map with locations of 887 stations selected for this work.

Fig. 2. Example of change-point analysis by BP (top) and PPM (bottom) methods. The simulated

Gaussian series NACZP of length 45 have 7.0=µµµµ and 07.0=σσσσ . The breaks (arrows) are imposed at

the points ct equal to 5, 15, 25, 30, and 40, with the respective amplitudes σσσσ0.3 , σσσσ0.3− , σσσσ0.3− , σσσσ0.3

and σσσσ0.3 . On the top, the continuous lines represent linear fitting regarding breaks; dotted lines

represent linear fitting under null hypothesis of no break, and dashed lines give the posterior mean. On

the bottom, are shown posterior probability of the break point.

Figure 3 – (top) Cumulative sum of the number of stations exhibiting break for each year, from 1941 to

2001. The three sharp increases are marked with vertical line. (bottom) The total number of stations.

Fig. 4 – Stations in Sao Paulo state which exhibit change-point in the NACZP series for the years 1969,

1970 or 1971 (filled circles, otherwise open circles).

Fig. 5 – Examples of NACZP series (open circle) exhibiting change-points (vertical dashed line). The

number displayed above each segment corresponds to the 50Q (in mm). The station ID, latitude and

longitude are shown on top of each panel.

Page 35 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

36

Fig. 6 – Scatter diagram for mNACZP versus (a) 50Q , (b) 95Q , and (c) 99Q , regarding all detected

segments in bN (Table 1) rainfall series.

Fig. 7 – Empirical cumulative distribution (ECDF) of daily amount for the four sub-periods (see legend)

defined by change-points in 1930, 1963, and 1977.

Fig. 8 – Result for bN rainfall series of the KS and AD tests, evaluating the difference in the

distribution of daily amounts among sub-periods defined by change-points in the NACZP series.

Fig. 9 – (a) 501 stations (out of 887) that reported zero precipitation on Saturday or Sunday (filled

circles) more than at other days of week. (b) Counts of stations exhibiting the largest number of zero

precipitation apportioned by days of week.

Fig. 10- Left: NACZP for whole period. Right: NACZP for two days of week exhibiting largest

(continuous line) and lowest (open circle) NACZP for whole period.

Fig. 11 – Examples of 50q series (open circle) exhibiting change-points (vertical dashed line). The

station ID, latitude, longitude and state are shown on top of each panel. The value above each segment

corresponds to the mNACZP.

Figure 12- Plots for station C5-050 of whole period (a) 50Q , (b) normalized count of wet days

(precipitation>0) apportioned by day of week, and (c) 50q series for Sunday and Tuesday.

Figure 13 – Geographical distribution of 11 stations that passed in all homogeneity tests at the 0.05

significance level (filled circle).

Page 36 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

1

Fig. 1 - (a) Map of Brazil with 21 states: PA (Pará), MA (Maranhão), PI (Piauí), CE (Ceará), RN (Rio

Grande do Norte), PB (Paraíba), PE (Pernambuco), AL (Alagoas), SE (Sergipe), TO (Tocantins), BA (Bahia),

MT (Mato Grosso), GO (Goiás), MG (Minas Gerais), ES (Espírito Santo), RJ (Rio de Janeiro), SP (São

Paulo), PR (Paraná), SC (Santa Catarina), and RS (Rio Grande do Sul). The respective counts of stations are

indicated in parenthesis. (b) Map with locations of 887 stations selected for this work.

(a)

Page 37 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

2

Fig. 2 - Example of change-point analysis by BP (top) and PPM (bottom) methods. The simulated Gaussian

series NACZP of length 45 have 7.0=µµµµ and 07.0=σσσσ . The breaks (arrows) are imposed at the points

ct equal to 5, 15, 25, 30, and 40, with the respective amplitudes σσσσ0.3 , σσσσ0.3− , σσσσ0.3− , σσσσ0.3 and σσσσ0.3 . On

the top, the continuous lines represent linear fitting regarding breaks; dotted lines represent linear fitting

under null hypothesis of no break, and dashed lines give the posterior mean. On the bottom, are shown

posterior probability of the break point.

Page 38 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

3

Figure 3 – (top) Cumulative sum of the number of stations exhibiting break for each year, from 1941 to 2001.

The three sharp increases are marked with vertical line. (bottom) The total number of stations.

Page 39 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

4

Fig. 4 – Stations in Sao Paulo state which exhibit change-point in the NACZP series for the years 1969, 1970

or 1971 (filled circles, otherwise open circles).

Page 40 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

5

Page 41 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

6

Fig. 5 – Examples of NACZP series (open circle) exhibiting change-points (vertical dashed line). The

number displayed above each segment corresponds to the 50Q (in mm). The station ID, latitude and longitude

are shown on top of each panel.

Page 42 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

7

Fig. 6 – Scatter diagram for mNACZP versus (a) 50Q , (b) 95Q , and (c) 99Q , regarding all detected segments

in bN (Table 1) rainfall series.

Page 43 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

8

Fig. 7 – Empirical cumulative distribution (ECDF) of daily amount for the four sub-periods (see legend)

defined by change-points in 1930, 1963, and 1977.

Figure 8 – Result for bN rainfall series of the KS and AD tests, evaluating the difference in the distribution of

daily amounts among sub-periods defined by change-points in the NACZP series.

Page 44 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

9

Fig. 9 – (a) 501 stations (out of 887) that reported zero precipitation on Saturday or Sunday (filled circles)

more than at other days of week. (b) Counts of stations exhibiting the largest number of zero precipitation

apportioned by days of week.

Page 45 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

10

Fig. 10- Left: NACZP for whole period. Right: NACZP for two days of week exhibiting largest (continuous

line) and lowest (open circle) NACZP for whole period.

Page 46 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

11

Fig. 11 – Examples of 50q series (open circle) exhibiting change-points (vertical dashed line). The station ID,

latitude, longitude and state are shown on top of each panel. The value above each segment corresponds to

the mNACZP.

Page 47 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

12

Fig. 12- Plots for station C5-050 of whole period (a) 50Q , (b) normalized count of wet days (precipitation>0)

apportioned by day of week, and (c) 50q series for Sunday and Tuesday.

Page 48 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

13

Fig. 13 – Geographical distribution of 11 stations that passed in all homogeneity tests at the 0.05 significance

level (filled circle).

Page 49 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

Table 1 – Result for the supF test applied to the NACZP series. N is total number of

stations, bN is number of stations with at least one change point, and )(N Fsup α is number

of stations among bN stations rejected by supF test at the significance level α .

states N bN )20.0(N Fsup )15.0(N Fsup )10.0(N Fsup )05.0(N Fsup )01.0(N Fsup

PA 1 1 1 1 1 1 1

MA 3 2 1 0 0 0 0

CE 40 29 27 27 25 25 24

RN 3 1 1 1 0 0 0

PB 2 2 2 2 2 2 2

PE 8 6 5 5 4 4 2

AL 10 8 7 7 6 6 4

SE 4 4 4 4 4 3 3

PI 38 28 21 21 18 17 12

TO 2 1 1 1 1 1 1

MT 7 6 6 6 6 6 5

GO 16 8 7 7 7 6 3

BA 30 25 22 22 21 20 12

MG 122 85 79 76 73 64 48

ES 50 31 27 26 26 23 23

RJ 57 41 38 38 37 36 32

SP 385 350 345 342 336 322 294

PR 28 25 22 22 22 22 20

SC 35 34 30 28 27 23 19

RS 46 43 39 39 37 34 32

ALL 887 730 685 675 653 615 537

Page 50 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

Table 2 – Same as Table 1, but for the AD test, with respect to the difference in the

distribution of daily amounts among the segments determined by breaks in NACZP series.

)(NAD α is count of stations among those bN rejected by the AD test at the significance

level α . The results for α =0.15, 0.20 are not shown because they are practically same as

those for α =0.10.

states N bN )10.0(NAD )05.0(NAD )01.0(NAD

PA 1 1 1 1 1

MA 3 2 2 2 2

CE 40 29 29 29 27

RN 3 1 1 1 1

PB 2 2 2 2 2

PE 8 6 6 6 6

AL 10 8 8 8 8

SE 4 4 3 3 3

PI 38 28 28 28 25

TO 2 1 1 1 1

MT 7 6 6 6 6

GO 16 8 8 8 6

BA 30 25 25 25 25

MG 122 85 85 85 84

ES 50 31 31 30 30

RJ 57 41 40 40 40

SP 385 350 348 347 344

PR 28 25 25 25 25

SC 35 34 31 31 30

RS 46 43 41 41 41

ALL 887 730 721 719 706

Page 51 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

Table 3 – Same as Table 1, but for the proportion test evaluating difference in number of

zero precipitation among the days of week. )(NP α is count of stations among N stations

rejected by the test at the significance level α .

states N )20.0(NP )15.0(NP )10.0(NP )05.0(NP )01.0(NP

PA 1 1 0 0 0 0

MA 3 2 3 3 3 1

CE 40 36 21 18 11 1

RN 3 3 1 1 0 0

PB 2 2 1 1 1 0

PE 8 5 2 1 0 0

AL 10 8 5 4 1 1

SE 4 2 2 2 2 1

PI 38 27 15 12 6 1

TO 2 1 1 1 0 0

MT 7 5 5 5 2 1

GO 16 8 8 7 6 1

BA 30 22 11 9 5 3

MG 122 87 68 44 26 14

ES 50 46 23 16 10 5

RJ 57 46 39 28 19 3

SP 385 325 305 268 206 94

PR 28 27 23 23 18 9

SC 35 32 29 27 20 6

RS 46 40 35 30 20 8

ALL 887 718 651 552 399 161

Page 52 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

Table 4 – Same as Table 1, but for supF test applied to 50q series. *bN is the number of

stations with at least one change point, and )(N*

Fsup α is the number of stations rejected by

supF test at the significance level α .

States N *bN )20.0(N

*Fsup )15.0(N

*Fsup )10.0(N

*Fsup )05.0(N

*Fsup )01.0(N

*Fsup

PA 1 1 1 1 1 1 1

MA 3 2 2 2 1 1 1

CE 40 33 32 32 32 31 28

RN 3 3 3 2 2 1 1

PB 2 2 2 2 2 2 2

PE 8 7 6 6 5 5 4

AL 10 8 8 7 7 7 6

SE 4 4 4 4 4 4 4

PI 38 35 31 30 28 23 19

TO 2 1 1 1 1 1 0

MT 7 5 4 4 4 4 3

GO 16 13 13 13 13 9 7

BA 30 28 25 25 23 23 19

MG 122 105 97 95 94 85 74

ES 50 40 40 39 38 36 28

RJ 57 49 47 47 47 47 40

SP 385 342 327 325 321 311 279

PR 28 27 26 26 26 23 22

SC 35 28 28 28 28 28 27

RS 46 39 35 35 33 33 30

ALL 887 772 732 724 710 675 595

Page 53 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly


distribution of daily amounts among the segments determined by breaks in 50q series.

)(N*AD α is the number of stations among *

bN rejected by AD test at the significance level

α .

States N *bN )20.0(N*

AD )15.0(N*AD )10.0(N*

AD )05.0(N*AD )01.0(N*

AD

PA 1 1 1 1 1 1 1

MA 3 2 2 2 2 2 2

CE 40 33 33 33 33 33 33

RN 3 3 3 3 3 3 3

PB 2 2 2 2 2 2 2

PE 8 7 7 7 7 7 7

AL 10 8 8 8 8 8 8

SE 4 4 4 4 4 4 4

PI 38 35 35 35 35 35 35

TO 2 1 1 1 1 1 1

MT 7 5 5 5 5 5 5

GO 16 13 13 13 13 13 13

BA 30 28 28 28 28 28 28

MG 122 105 105 94 94 85 74

ES 50 40 40 40 40 40 40

RJ 57 49 49 49 49 49 49

SP 385 342 342 342 342 342 339

PR 28 27 27 27 27 27 27

SC 35 28 28 28 28 28 28

RS 46 39 39 39 39 39 39

ALL 887 772 772 772 772 772 769

Page 54 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly


distribution of daily amounts between one day of week and another.

)(N **AD α is the number of stations rejected by AD test at the significance level α .

states N )20.0(N**

b )15.0(N**

b )10.0(N**

b )05.0(N**

b )01.0(N**

b

PA 1 0 0 0 0 0

MA 3 0 0 0 0 0

CE 40 26 24 20 15 5

RN 3 0 0 0 0 0

PB 2 0 0 0 0 0

PE 8 3 3 2 0 0

AL 10 7 4 3 2 0

SE 4 0 0 0 0 0

PI 38 28 24 19 10 5

TO 2 1 1 1 0 0

MT 7 0 0 0 0 0

GO 16 4 3 1 1 0

BA 30 6 4 3 3 0

MG 122 14 9 3 0 0

ES 50 10 9 7 5 1

RJ 57 9 8 7 4 0

SP 385 268 239 193 138 60

PR 28 8 6 5 4 0

SC 35 11 10 7 3 0

RS 46 9 9 5 2 1

ALL 887 404 353 276 187 72

Page 55 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

Table 7 – Same as Table 1, but for combined tests. )(Nac α is the number of stations which

passed in all tests with respect to the significance level α , before trend test and change-

points analysis for total annual amount.

States N )10.0(Nac )05.0(Nac )01.0(Nac

PA 1 0 0 0

MA 3 0 0 1

CE 40 0 1 1

RN 3 0 0 0

PB 2 0 0 0

PE 8 1 0 0

AL 10 0 0 0

SE 4 0 0 0

PI 38 0 1 1

TO 2 0 0 0

MT 7 0 0 0

GO 16 0 0 1

BA 30 0 0 0

MG 122 3 6 11

ES 50 0 1 5

RJ 57 1 1 3

SP 385 0 4 11

PR 28 0 1 1

SC 35 0 0 0

RS 46 0 1 4

ALL 887 4 16 39

Page 56 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Peer Review O

nly

Table 8- List of 11 stations which passed in homogeneity tests at the 0.05 significance level,

and the Mann-Kendall rank correlation τ for trend analysis, where asterisk indicates that

τ is significant at the 0.05 level.

τ no. station name (state) lat.

(degree

South)

long.

(degree

West)

period

Total

annual

NACZP 50q

1 C4-077 Mococa (SP) 21.63 47.01 1961-97 0.0788 0.255*

0.0583

2 C5-028 Jaboticabal

(SP)

21.33 48.31 1964-03 0.0752 0.0692 0.129

3 C6-086 Avanhandava

(SP)

21.45 49.95 1968-00 0.0236 0.0579 0.0147

4 02549017 São José dos

Pinhais (PR)

25.51 49.15 1965-97 0.0903 0.192 0.0379

5 02242010 Manuel

Ribeiro (RJ)

22.90 42.71 1968-05 0.234*

0.075 0.0313

6 01940013 Colatina (ES) 19.23 40.59 1969-05 0.0386 0.109 0.0634

7 00340018 Ibiapina (CE) 3.91 40.88 1912-06 0.0488 0.0014 0.072

8 01444001 Montalvania

(MG)

14.41 44.48 1966-02 0.0161 0.0658 0.063

9 01943027 São Gonçalo

do Rio Baixo

(MG)

19.86 43.36 1954-05 0.0333 0.0223 0.0123

10 02142000 Astolfo

Dutra (MG)

21.30 42.85 1942-05 0.196*

0.148 0.0382

11 00641006 Monsenhor

Hipólito (PI)

6.98 41.11 1963-00 0.0728 0.0359 0.0333

Page 57 of 57



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

peer review only - homogenisation · peer review only on the reliability ... complete list of...

Documents