benefits and drawbacks of using data assimilation for hydrological modelling in karstic regions....

Benefits and drawbacks of using data assimilation for hydrological modelling in karstic regions.

Recent work on the Lez catchment in Southern France

IAHS General Assembly in Göteborg - July 2013

Mathieu COUSTAU, Elizabeth HARADER, Valérie BORRELL ESTUPINA, Sophie RICCI, Olivier THUAL, Christophe BOUVIER, Andrea PIACENTINI

Made possible by a collaboration

Montpellier, September 2005

Session : Testing simulation and forecasting models in non-stationary conditions

1

Environmental context The Mediterranean region is subject to violent rainfall producing devastating flash floods. These

flash floods are responsible for numerous deaths and expensive material damages.

How to improve forecast of these floods ?

Scientific issue Hydrological models are helpful to understand and to forecast these floods. However The

physical processes involved are not well represented.The precipitation used to force models is not accurately measured, nor is it stationary, and it should be be corrected in order to reduce model uncertainty. Model parameters require some level of adaptation to better represent catchment behaviour.

How to deal with the limited performance of the hydrological models linked to the heterogeneity or non stationary of the observed data between the calibration and validation steps ?

Methodological difficultyData assimilation is an innovative method that allows to correct the model parameters as well

as the forcing input to the model (precipitation) when discharge observations are available. As a result, the capacity of the model to cope with non stationary conditions is improved.

Which data assimilation strategy should be implemented in order to improve flash flood forecatsing ?

General Context & Issues

2Intro Study Case Model Correction Results Conclusion

Project Work Packages : - The observation tasks - The model work package- The vulnerability study- The climate changes and

pumping scenarii impacts

*Gestion Multi Usages : Multiple-Use Management

Sources: Dörflinger and

al., 2008

Context & Issues : The Lez GMU* project


A 4-year project focused on the karstic water resource and active

management

Regional water

agencyDepartmental administration

Private company

Research labs

Main objective discussed in this presentation : How to improve flash flood forecasting using data assimilation?

• Small catchment • 114 km2

• Short lag times, 2-5h • Vineyards, scrubland, forest (poor urban cover)• From 34 m asl to 700 m

• Karstic formations• spring = resurgence of a 380 km2 karstic aquifer• karst covered with soil or karst outcrops

• Extreme rainfall events (mesoscale convective systems ) • The spring has been exploited for more than 100 years for water needs of the population• The Mediterranean region is prone to flash flooding events due to intense rainfalls.

Sources: Nuissier and al., 2008;

Dörflinger and al., 2008; Kong A Siou

and al., 2011; Coustau, 2008

The Lez catchment


Rain and Floods studied after 1994

• 4 Rain Gauges within the surface catchment, measurements at an hourly time step

• Weather radar over the region with different correcting algorithms (Hydram, Calamar) with a temporal resolution of 5 minutes

• Around 20 raingauges available in the region with a daily time step

• 1 streamflow gauge at the outlet (Peak discharge : 40 to 467 m3/s)

• 21 flood eventsSmall floods and false alarms are

not considered.


The data Base

Event Rain Intensity

mean (mm/h)

Runoff coefficient

Spring Peak

discharge (m3/s)

Outelt peak

discharge (m3/s)

Oct 2001 10.4 0.33 24 238

Sep 2002 8 0.34 8 103

Dec 2002 4.6 0.97 20 373

Sep 2003 10.9 0.14 3 91

Dec 2003 7.3 0.70 28 423

Sep 2005 10.8 0.36 - 467

• Nîmes radar• S band • indirect measure

• Resolution• 1 km• 5 minutes

Indirect measurements are subject to large errors depending on the reflectivity.

The difference between corrected radar rainfall and rain from gauges can be high.

Corrections : Mean Field Bias (MFB) to correct radar rainfall with discharge data.

Data Assimilation to correct radar rainfall with discharge data.


Weather Radar : benefits & challenges

RiN1

GiN1

MFB

Conceptual reservoir model = SCS loss function adaptated for

karstic watershed

7 7Intro Study Case Model Correction Results Conclusion

The Hydrological Model

Loss Function : modified SCS

S

p(t)

min(1,w/S) * ds * S(t)

(1-min(1,w/S)) * ds * S(t)

ds * S(t)

p(t) – r(t)

S(t)

r(t) = C(t) * p(t)

S0

sol + karst

Sources: Borrell and al. 2008, Coustau and al. 2010

• 2 parameters : w and ds• S (initial condition) : the potential storage depth must be calibrated

IRD, HSM

• Lag and route transfer function : with 2 parameters (Vo and Ko)

•Parsimonious Model•Robustness evaluated by cross

calibration•Model performance evaluated

through the Nash criterion.

8

Sources: Borrell and al. 2008, Coustau and al. 2010


The Hydrological Model

Transfer Function : Lag & Route

t0 t

R

Rainfall on the watershed

lag (V0)

diffusion (K0)

Qm

Tm

t0 t0 + Tm t

Transfered rainfall at the outlet

2

2

)(

)(1

obsobs

obssim

QQ

QQNash

The model can be initialized with piezometric levels or the soil humidity. The mix of rain gauges and radar rainfall corrected with MFB considerably improve the performance of the model (in particular the initial estimation). We loose quality in forcast-like mode due to uncertainty in the S estimation. The use of the MFB => no forecast-like runs ! The results in re-analysis mode are improved over the forecast mode.


Analysis and forecast-like runs 7 different piezometric stations to

establish the initial correlation : 0,63 < R2 < 0,81

The SIM parameter to establish the initial correlation : R2 = 0.67

Satisfactory quality for the false forecast-like runs (Nash > 0.7 for

9 events)

HYDROLOGICAL MODEL

State Variable Parameters

S , Vo

Rrain(t)

Qb(t)

Q(t)

t

Observations

Qo(t)

Assimilation :

Extended Kalman Filter

234

Qb(t) : background run

Qo(t) : observationsQa(t) : analysis run

correction1

Qa(t)

Data Assimilation

Correction on the observed radar rainfall

tRrain 4

A sensitivity analysis highligthed the most influence parameters : S and Rainfall

Kalman gain:K = BHT(HBHT+R)-1

Update: xa = xb - K(yo – H(xb))

x control vectorH, H observation operatoryo observation vectorxb background xa analysisB background error cov. matrixR observation error cov. matrix

11

A Simplified Extended Kalman Filter (updated BLUE)

*OpenPALM is a coupling software developped at CERAFCS.


Data Assimilation to correct S with discharge data

Observations

Background (S = 160 mm)

Analysis : Iteration 1 (S = 140 mm)

Analysis : Iteration 5 (S = 131 mm)

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Improvement in the forecast-like mode when correcting initial S value with Data Assimilation :


Data Assimilation to correct S with discharge data

(ERDP)

Improvement

Corrected parameter by DA

obs

obsbbRDP Qp

QpQpE

bRDPaRDPRDP EEE )(

Calculated for the Background and Analyse

The correction of S improves the peak flow in re-analysis mode and in forecast-like mode.

In reanalysis mode :• initialise S using known hydrograph• and create background hydrograph α =1 (pink)• then assimilate to find multiplier, α and calculate analysis (green)

Rain

fall

(mm

)


Data Assimilation to correct radar rain with discharge data

Q(m3/s)

In forecast-like mode :• use the piezometric level to estimate S• and create background hydrograph α =1 (pink)• then assimilate the first observed discharges to find multiplier, α and calculate analysis (green)

Uncertainty in forecast is increased by : • Parameterisation of S with piezometry • Reduced assimilation window,peak not included • Variability of the rainfall error (α constant )

Forecats-like runs

Average NS = 0.50


Results of the forecast mode

Direct runs with radar rainfall not corrected

ref Average NS = 0.05

Re-analysis runs 96% Average NS = 0.70

Forecast-like runs 61% Average NS = 0.50

Harader and al. 2012

Evaluation of the results: • iterate for each episode (1997-2008)• calculate performance criteria:

Peak Height (PH)Nash-Sutcliffe criterion (NS)

The correction of precipitation produced by weather radar in re-analysis conditions improved simulation quality.

General objective : to propose an appropriate methodology for a flood forecasting model under changing conditions to improve its efficiency

15Thank you for your attention.

Conclusions & Perspectives

Different rainfall measurements

Temporal variability of initial condition

Different flood intensities

The conceptual hydrological model does not guarantee the quality of flood simulations with intensities not observed in the data base used for calibration.

The data assimilation loop helps to improve flash flood simulation on re-analysis settings, whatever the flood intensities are.

The data assimilation loop opens new perspectives in forecast-like settings.

Work in progress : Improving algorithms in order to

correct radar rainfall before forcing the model Work on other karstic watersheds

Data Assimilation of discharge at the beginning of the flood

initial condition rainfall

Planned work with data assimilation : Multiple windows for correcting rainfall Considering both rain gauges and radar rain in the corrected fields

benefits and drawbacks of using data assimilation for hydrological modelling in karstic regions....

Documents

lez catchment

model precipitation

model parameters

devastating flash floods

model uncertainty

flash flood forecasting

flood eventssmall floods

mediterranean region