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)
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Objective TwoObjective Two
Drought MonitoringDrought Monitoring
Flood PredictionFlood Prediction
Irrigation PoliciesIrrigation Policies
Weather ForecastingWeather Forecasting
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Importance of Soil MoistureImportance of Soil Moisture
Koster et al., JHM 2000
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
State of the ArtState of the Art- Remote Sensing - - Remote Sensing -
Koster et al., JHM 2000
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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]
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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)
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Field SiteField Site
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Remote SensingRemote Sensing
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
What is Variational Data What is Variational Data Assimilation?Assimilation?
model outp
ut
time
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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)
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Single Catchment Synthetic Single Catchment Synthetic StudyStudy
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Control Experiments – One Control Experiments – One MonthMonth
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Control Experiment – One Control Experiment – One YearYear
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Streamflow AssimilationStreamflow Assimilation
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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)
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
Surface Soil Moisture Surface Soil Moisture AssimilationAssimilation
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
3 Nested Catchments Study3 Nested Catchments Study
Catchment 3 Catchment 4
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
3 Nested Catchments Study3 Nested Catchments Study
Catchment 3 Catchment 4
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
StreamflStreamflowow
RMSERMSE
GuesGuesss
118.118.11
NLFITNLFIT 8.0248.024
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
One ObservationOne Observationgenera
ted
run
off
r = f(1,2)p +
precipitation
1
1+2
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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)
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
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
Christoph RüdigerChristoph RüdigerFinal PGrad Seminar 22 September 2005Final PGrad Seminar 22 September 2005
and now ….???and now ….???
© Bill Watterson, 1995