Streamflow Data Assimilation for the Retrieval of Soil Moisture Initial States Christoph Rüdiger Supervisors: Jeffrey Walker, Jetse Kalma, Garry Willgoose

Streamflow Data Streamflow Data Assimilation Assimilation

for the Retrieval of for the Retrieval of Soil Moisture Initial StatesSoil Moisture Initial States

Christoph RüdigerChristoph Rüdiger

Supervisors:Supervisors:Jeffrey Walker, Jetse Kalma, Garry Jeffrey Walker, Jetse Kalma, Garry

WillgooseWillgoose

Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005

Objective OneObjective One

““We shall require a substantially We shall require a substantially

new manner of thinking, new manner of thinking,

if mankind is to survive.”if mankind is to survive.”

- Albert Einstein (1879 – 1955)- Albert Einstein (1879 – 1955)


Objective TwoObjective Two

Drought MonitoringDrought Monitoring

Flood PredictionFlood Prediction

Irrigation PoliciesIrrigation Policies

Weather ForecastingWeather Forecasting


Importance of Soil MoistureImportance of Soil Moisture

Koster et al., JHM 2000


State of the ArtState of the Art• In-situ ObservationsIn-situ Observations

+ Detailed measurements of soil moisture+ Detailed measurements of soil moisture+ Good representation of vertical profile+ Good representation of vertical profile+ High temporal resolution+ High temporal resolution– Short correlation lengthShort correlation length– Accessibility of sites requiredAccessibility of sites required– Manpower requiredManpower required

• Hydrological ModelsHydrological Models+ High spatial and temporal resolutions+ High spatial and temporal resolutions– Insufficient knowledge of soil and atmospheric Insufficient knowledge of soil and atmospheric

physicsphysics– Errors through forcing dataErrors through forcing data


State of the ArtState of the Art- Remote Sensing - - Remote Sensing -

Koster et al., JHM 2000


MethodologyMethodology

• Hydrological modelling with a semi-Hydrological modelling with a semi-distributed land surface modeldistributed land surface model

• Variational-type assimilation of Variational-type assimilation of streamflow into the land surface modelstreamflow into the land surface model

• Multiple synthetic studies to understand Multiple synthetic studies to understand the performance and requirements of the performance and requirements of the assimilation schemethe assimilation scheme

• Real data studyReal data study


Hydrological Model – Hydrological Model – Catchment Land Surface ModelCatchment Land Surface Model• Explicit treatment Explicit treatment

of lumped of lumped moisture storesmoisture stores

• All moisture All moisture stores are stores are interlinkedinterlinked

• Implicit Implicit treatment of treatment of surface variability surface variability through the CTIthrough the CTI

Koster et al., 2000


Internal routingInternal routing

Travel time TpiVelocity weight v-1

Unit Hydrograph for Catchment

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 4 5 6 7 8

Hours

Co

ntr

ibu

tin

g F

rac.

of

To

tal

Are

a [1

/h]


Field RequirementsField Requirements

• Ground ObservationsGround Observations– Climate DataClimate Data– Streamflow ObservationsStreamflow Observations– Soil Moisture ObservationsSoil Moisture Observations

• Remote SensingRemote Sensing– Satellite Remote Sensing (AMSR-E)Satellite Remote Sensing (AMSR-E)


Field SiteField Site


Remote SensingRemote Sensing


What is Variational Data What is Variational Data Assimilation?Assimilation?

model outp

ut

time


Data Assimilation SchemeData Assimilation Scheme

• NLFIT – Nonlinear Bayesian RegressionNLFIT – Nonlinear Bayesian Regression(Kuczera, 1982)(Kuczera, 1982)

• Minimising the objective function Minimising the objective function (least square error)(least square error)

• Change of initial conditions to find Change of initial conditions to find optimumoptimum

• No linearisation of model neededNo linearisation of model needed• Conservation of water balanceConservation of water balance


Case StudiesCase Studies

• Synthetic Data StudySynthetic Data Study– Single Sub-CatchmentSingle Sub-Catchment– 3 Nested Sub-Catchments3 Nested Sub-Catchments– Full CatchmentFull Catchment

• Real Data StudyReal Data Study– Full CatchmentFull Catchment


Synthetic StudySynthetic Study• ““True”True”

– Data from different locationsData from different locations– Homogeneous distribution of forcing data Homogeneous distribution of forcing data

• Wet biasWet bias– precipitation +20%, radiation -30%precipitation +20%, radiation -30%

• Dry biasDry bias– precipitation -20%, radiation +30%precipitation -20%, radiation +30%

• Random noiseRandom noise• Optimal length of assimilation windowOptimal length of assimilation window• (Model Parameterisation)(Model Parameterisation)


Single Catchment Synthetic Single Catchment Synthetic StudyStudy


Control Experiments – One Control Experiments – One MonthMonth


Control Experiment – One Control Experiment – One YearYear


Streamflow AssimilationStreamflow Assimilation


One Year Assimilation One Year Assimilation WindowWindow

RMSERMSE SurfaceSurface Root ZoneRoot Zone ProfileProfile StreamfloStreamfloww

AnnuaAnnuall

0.126 (0.137)

0.061 (0.077)

0.056 (0.070)

21.41 (26.01)

MonthlMonthlyy

0.095 (0.077)

0.026 (0.031)

0.025 (0.031)

15.66 (18.57)

ControControll

0.156 (0.179)

0.095 (0.122)

0.086 (0.112)

28.66 (36.29)


First Lessons LearntFirst Lessons Learnt

• Using the water balance allows for the Using the water balance allows for the improved retrieval of initial soil moisture improved retrieval of initial soil moisture statesstates

• Retrieval of Retrieval of surfacesurface soil moisture is difficult soil moisture is difficult• Biased data leads to a gap between the Biased data leads to a gap between the

observed and modelled variables observed and modelled variables assimilation windows should be shortassimilation windows should be short

• High correlation between the three prognostic High correlation between the three prognostic variables variables in future only one state retrieval in future only one state retrieval necessary necessary

• Reaching extremes (model thresholds) erases Reaching extremes (model thresholds) erases memory of the assimilation memory of the assimilation

timetime

dis

charg

ed

isch

arg

e


Surface Soil Moisture Surface Soil Moisture AssimilationAssimilation


Joint AssimilationJoint Assimilation

RMSERMSE SurfaceSurface Root Root ZoneZone ProfileProfile StreamfloStreamflo

ww

TrueTrue0.0120.184

0.0010.160

0.0010.146

0.05563.83

Wet Wet BiasBias

0.0550.200

0.0250.183

0.0220.168

32.1195.04

Dry Dry BiasBias

0.1000.168

0.0650.139

0.0600.128

1.66129.34

RandoRandomm

ErrorsErrors

0.0290.096

0.0020.062

0.0020.057

14.1335.63


More Lessons LearntMore Lessons Learnt

• Surface soil moisture assimilation can lead Surface soil moisture assimilation can lead to a good retrieval of soil moistureto a good retrieval of soil moisture

• However, surface soil moisture does not However, surface soil moisture does not care about magnitude of streamflowcare about magnitude of streamflow

• In the joint assimilation changes in In the joint assimilation changes in streamflow have more impactstreamflow have more impact

j

j

m

j qqLSE2

ˆ j

j

m

j

r

qqnLSE2

2ˆ

1


Results from Single Catchment Results from Single Catchment StudyStudy

• PositivesPositives::– Streamflow carries sufficient information about Streamflow carries sufficient information about

upstream soil moistureupstream soil moisture– Only few iterations neededOnly few iterations needed– Surface soil moisture can be used with this Surface soil moisture can be used with this

modelmodel– Length of assimilation window important (Seo et Length of assimilation window important (Seo et

al., 2003)al., 2003)

• NegativesNegatives::– Some problems retrieving surface soil moistureSome problems retrieving surface soil moisture– Biased data cause problemsBiased data cause problems


3 Nested Catchments Study3 Nested Catchments Study

• Assimilation of 1 Observation OnlyAssimilation of 1 Observation Only– StreamflowStreamflow– Surface Soil MoistureSurface Soil Moisture

• Assimilation of 2 Different Assimilation of 2 Different ObservationsObservations– Streamflow from Catchment 4Streamflow from Catchment 4– Surface Soil Moisture from Catchment 3Surface Soil Moisture from Catchment 3

22

33

44



Catchment 3 Catchment 4



Catchment 3 Catchment 4


Results from 3 Catchment Results from 3 Catchment StudyStudy

• One streamflow observation at the One streamflow observation at the lowest catchment is sufficient to find lowest catchment is sufficient to find optimumoptimum

• Surface soil moisture assimilation Surface soil moisture assimilation alone is not adequate, as no alone is not adequate, as no upstream feedback availableupstream feedback available

• Joint assimilation combines the Joint assimilation combines the positive effects of both techniquespositive effects of both techniques


Full Catchment StudyFull Catchment Study

• Study for all CatchmentsStudy for all Catchments• Three ApproachesThree Approaches

– One observation at catchment outletOne observation at catchment outlet– 8 streamflow observations8 streamflow observations– Mixed observations (streamflow and Mixed observations (streamflow and

surface soil moisture) from different surface soil moisture) from different catchmentscatchments

22

33

44

5566

77

11

88


One Observation – Soil One Observation – Soil MoistureMoisture

c1c1 c2c2 c3c3 c4c4 c5c5 c6c6 c7c7 c8c8

TrueTrue 0.180.1822

0.220.2299

0.220.2299

0.150.1599

0.220.2299

0.220.2299

0.150.15

99

0.170.1799

GuessGuess 0.260.2633

0.300.3077

0.330.3322

0.280.2844

0.320.3288

0.330.3300

0.270.2788

0.260.2688

NLFITNLFIT 0.140.1499

0.260.2688

0.300.3066

0.300.3000

0.240.2477

0.270.2700

0.210.2133

0.170.1799

Std devStd dev0.130.13

111010-3-3

0.220.2299

10 10-1-1

0.220.2299

10 10-2-2

0.200.2044

0.200.2088

10 10-2-2

0.250.2522

10 10-2-2

0.230.2399

10 10-1-1

0.300.3022

10 10-2-2


One Observation – Soil One Observation – Soil MoistureMoisture

c1c1 c2c2 c3c3 c4c4 c5c5 c6c6 c7c7 c8c8

TrueTrue 0.180.1822

0.220.2299

0.220.2299

0.150.1599

0.220.2299

0.220.2299

0.150.15

99

0.170.1799

GuessGuess 0.260.2633

0.300.3077

0.330.3322

0.280.2844

0.320.3288

0.330.3300

0.270.2788

0.260.2688


0.260.2688

0.300.3066

0.300.3000

0.240.2477

0.270.2700

0.210.2133

0.170.1799

Std devStd dev0.130.13

111010-3-3

0.220.2299

10 10-1-1

0.220.2299

10 10-2-2

0.200.2044

0.200.2088

10 10-2-2

0.250.2522

10 10-2-2

0.230.2399

10 10-1-1

0.300.3022

10 10-2-2

StreamflStreamflowow

RMSERMSE

GuesGuesss

118.118.11



One ObservationOne Observationgenera

ted

run

off

r = f(1,2)p +

precipitation

1

1+2


8 Streamflow Observations8 Streamflow ObservationsGues

s Iter. 1Iter. 1 Iter. 2Iter. 2 Iter. 3Iter. 3 Iter. 4Iter. 4 Iter. 5Iter. 5 Final True

cc11

0.263 64.1164.11 69.8569.85 50.2250.22 72.8572.85 … … ...... 0.168 0.182

cc22

0.307 14.7914.79 0.2440.2440.4030.403 XX XX XX 0.244 0.229

cc33

0.332 154.3154.3 97.7197.71 86.5786.57 38.4638.46 … … ...... 0.231 0.229

cc44

0.284 195195 163.0163.0 159.8159.8 109.4109.4 … … ...... 0.164 0.159

cc55

0.328 0.2300.230.0025.0025 XX XX XX XX 0.230 0.229

cc66

0.330 29.6929.69 36.1336.13 0.2360.2360.450.45 XX XX 0.236 0.229

cc77

0.278 36.0736.07 39.0239.02 16.0416.04 17.017.01.191.19 XX 0.170 0.159

cc88

0.268 68.1568.15 107.3107.3 309.6309.6 220.3220.3 … … ...... 0.182 0.179


Mixed ObservationsMixed Observations

Surface Surface SMSM

StreamflowStreamflow

AssimilationAssimilation

sm3, sm5, sm6sm3, sm5, sm6

fixfix

c1, c2, c4, c7, c8c1, c2, c4, c7, c8ro1, ro4, ro6, ro8ro1, ro4, ro6, ro8

Check residual Check residual variancevarianceCheck standard Check standard deviationdeviation

Catchments fixedCatchments fixed

Catchments fixedCatchments fixed


Real StudyReal Study

• Best forcing dataBest forcing data• New parameters for routing model New parameters for routing model

neededneeded• CLSM heavily overestimates runoffCLSM heavily overestimates runoff


ConclusionsConclusions

• Streamflow Data Assimilation is a viable Streamflow Data Assimilation is a viable tool for the retrieval of catchment soil tool for the retrieval of catchment soil moisturemoisture

• Simple sub-catchment structures only Simple sub-catchment structures only need small number of observationsneed small number of observations

• Not many events needed for good fitNot many events needed for good fit• Assimilation window should be short, Assimilation window should be short,

with preferably at least one eventwith preferably at least one event

……. (cont’d). (cont’d)


Conclusion (cont’d)Conclusion (cont’d)

• Biased forcing data introduce errors Biased forcing data introduce errors into water balance, which create into water balance, which create positive or negative sinkspositive or negative sinks

• Model constraints may interfere with Model constraints may interfere with retrieval of initial statesretrieval of initial states

• Joint assimilation of different Joint assimilation of different observations and magnitudes is observations and magnitudes is possible when least squares products possible when least squares products are scaled with the residual varianceare scaled with the residual variance


and now ….???and now ….???

© Bill Watterson, 1995

Documents

Streamflow Data Assimilation for the Retrieval of Soil Moisture Initial States Christoph Rüdiger Supervisors: Jeffrey Walker, Jetse Kalma, Garry Willgoose