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

2. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Objective One “We shall require a substantially new manner of thinking, if mankind is to survive.” - Albert Einstein (1879 – 1955)

3. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Objective Two Drought Monitoring Flood Prediction Irrigation Policies Weather Forecasting

4. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Importance of Soil Moisture Koster et al., JHM 2000

5. Christoph Rüdiger Final PGrad Seminar 22 September 2005 State of the Art In-situ ObservationsIn-situ Observations + Detailed measurements of soil moisture + Good representation of vertical profile + High temporal resolution –Short correlation length –Accessibility of sites required –Manpower required Hydrological ModelsHydrological Models + High spatial and temporal resolutions –Insufficient knowledge of soil and atmospheric physics –Errors through forcing data

6. Christoph Rüdiger Final PGrad Seminar 22 September 2005 State of the Art - Remote Sensing - Koster et al., JHM 2000

7. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Methodology Hydrological modelling with a semi-distributed land surface modelHydrological modelling with a semi-distributed land surface model Variational-type assimilation of streamflow into the land surface modelVariational-type assimilation of streamflow into the land surface model Multiple synthetic studies to understand the performance and requirements of the assimilation schemeMultiple synthetic studies to understand the performance and requirements of the assimilation scheme Real data studyReal data study

8. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Hydrological Model – Catchment Land Surface Model Explicit treatment of lumped moisture storesExplicit treatment of lumped moisture stores All moisture stores are interlinkedAll moisture stores are interlinked Implicit treatment of surface variability through the CTIImplicit treatment of surface variability through the CTI Koster et al., 2000

9. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Internal routing Travel time T pi Velocity weight v -1

10. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Field Requirements Ground ObservationsGround Observations –Climate Data –Streamflow Observations –Soil Moisture Observations Remote SensingRemote Sensing –Satellite Remote Sensing (AMSR-E)

11. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Field Site

12. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Remote Sensing

13. Christoph Rüdiger Final PGrad Seminar 22 September 2005 What is Variational Data Assimilation? model output time

14. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Data Assimilation Scheme NLFIT – Nonlinear Bayesian Regression (Kuczera, 1982)NLFIT – Nonlinear Bayesian Regression (Kuczera, 1982) Minimising the objective function (least square error)Minimising the objective function (least square error) Change of initial conditions to find optimumChange of initial conditions to find optimum No linearisation of model neededNo linearisation of model needed Conservation of water balanceConservation of water balance

15. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Case Studies Synthetic Data StudySynthetic Data Study –Single Sub-Catchment –3 Nested Sub-Catchments –Full Catchment Real Data StudyReal Data Study –Full Catchment

16. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Synthetic Study “True”“True” –Data from different locations –Homogeneous distribution of forcing data Wet biasWet bias –precipitation +20%, radiation -30% Dry biasDry bias –precipitation -20%, radiation +30% Random noiseRandom noise Optimal length of assimilation windowOptimal length of assimilation window (Model Parameterisation)(Model Parameterisation)

17. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Single Catchment Synthetic Study

18. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Control Experiments – One Month

19. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Control Experiment – One Year

20. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Streamflow Assimilation

21. Christoph Rüdiger Final PGrad Seminar 22 September 2005 One Year Assimilation Window RMSESurface Root Zone ProfileStreamflowAnnual0.126 (0.137)0.061 (0.077)0.056 (0.070)21.41 (26.01) Monthly0.095 (0.077)0.026 (0.031)0.025 (0.031)15.66 (18.57) Control0.156 (0.179)0.095 (0.122)0.086 (0.112)28.66 (36.29)

22. Christoph Rüdiger Final PGrad Seminar 22 September 2005 First Lessons Learnt Using the water balance allows for the improved retrieval of initial soil moisture statesUsing the water balance allows for the improved retrieval of initial soil moisture states Retrieval of surface soil moisture is difficultRetrieval of surface soil moisture is difficult Biased data leads to a gap between the observed and modelled variables  assimilation windows should be shortBiased data leads to a gap between the observed and modelled variables  assimilation windows should be short High correlation between the three prognostic variables  in future only one state retrieval necessaryHigh correlation between the three prognostic variables  in future only one state retrieval necessary Reaching extremes (model thresholds) erases memory of the assimilationReaching extremes (model thresholds) erases memory of the assimilation time discharge

23. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Surface Soil Moisture Assimilation

24. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Joint Assimilation RMSESurface Root Zone ProfileStreamflowTrue 0.012 0.184 0.001 0.160 0.001 0.146 0.055 63.83 Wet Bias 0.055 0.200 0.025 0.183 0.022 0.168 32.11 95.04 Dry Bias 0.100 0.168 0.065 0.139 0.060 0.128 1.661 29.34 Random Errors 0.029 0.096 0.002 0.062 0.002 0.057 14.13 35.63

25. Christoph Rüdiger Final PGrad Seminar 22 September 2005 More Lessons Learnt Surface soil moisture assimilation can lead to a good retrieval of soil moistureSurface soil moisture assimilation can lead to a good retrieval of soil moisture However, surface soil moisture does not care about magnitude of streamflowHowever, surface soil moisture does not care about magnitude of streamflow In the joint assimilation changes in streamflow have more impactIn the joint assimilation changes in streamflow have more impact

26. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Results from Single Catchment Study Positives:Positives: –Streamflow carries sufficient information about upstream soil moisture –Only few iterations needed –Surface soil moisture can be used with this model –Length of assimilation window important (Seo et al., 2003) Negatives:Negatives: –Some problems retrieving surface soil moisture –Biased data cause problems

27. Christoph Rüdiger Final PGrad Seminar 22 September 2005 3 Nested Catchments Study Assimilation of 1 Observation OnlyAssimilation of 1 Observation Only –Streamflow –Surface Soil Moisture Assimilation of 2 Different ObservationsAssimilation of 2 Different Observations –Streamflow from Catchment 4 –Surface Soil Moisture from Catchment 3 2 3 4

28. Christoph Rüdiger Final PGrad Seminar 22 September 2005 3 Nested Catchments Study Catchment 3Catchment 4

29. Christoph Rüdiger Final PGrad Seminar 22 September 2005 3 Nested Catchments Study Catchment 3Catchment 4

30. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Results from 3 Catchment Study One streamflow observation at the lowest catchment is sufficient to find optimumOne streamflow observation at the lowest catchment is sufficient to find optimum Surface soil moisture assimilation alone is not adequate, as no upstream feedback availableSurface soil moisture assimilation alone is not adequate, as no upstream feedback available Joint assimilation combines the positive effects of both techniquesJoint assimilation combines the positive effects of both techniques

31. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Full Catchment Study Study for all CatchmentsStudy for all Catchments Three ApproachesThree Approaches –One observation at catchment outlet –8 streamflow observations –Mixed observations (streamflow and surface soil moisture) from different catchments 2 3 4 5 6 7 1 8

32. Christoph Rüdiger Final PGrad Seminar 22 September 2005 One Observation – Soil Moisture c1c2c3c4c5c6c7c8 True0.1820.2290.2290.1590.2290.229 0.159 0.1590.179 Guess0.2630.3070.3320.2840.3280.3300.2780.268 NLFIT0.1490.2680.3060.3000.2470.2700.2130.179 Std dev 0.131 10 -3 0.229 10 -1 0.229 10 -2 0.204 0.208 10 -2 0.252 10 -2 0.239 10 -1 0.302 10 -2

33. Christoph Rüdiger Final PGrad Seminar 22 September 2005 One Observation – Soil Moisture c1c2c3c4c5c6c7c8 True0.1820.2290.2290.1590.2290.229 0.159 0.1590.179 Guess0.2630.3070.3320.2840.3280.3300.2780.268 NLFIT0.1490.2680.3060.3000.2470.2700.2130.179 Std dev 0.131 10 -3 0.229 10 -1 0.229 10 -2 0.204 0.208 10 -2 0.252 10 -2 0.239 10 -1 0.302 10 -2 Streamflow RMSE Guess118.1NLFIT8.024

34. Christoph Rüdiger Final PGrad Seminar 22 September 2005 One Observation generated runoff r = f(  1,  2 )p +  precipitation 1 1+21+2

35. Christoph Rüdiger Final PGrad Seminar 22 September 2005 8 Streamflow Observations Guess Iter. 1 Iter. 2 Iter. 3 Iter. 4 Iter. 5 FinalTrue c10.26364.1169.8550.2272.85 …... 0.1680.182 c20.30714.79 0.244 0.403 XXX0.2440.229 c30.332154.397.7186.5738.46 …... 0.2310.229 c40.284195163.0159.8109.4 …... 0.1640.159 c50.328 0.230.0025 XXXX0.2300.229 c60.33029.6936.13 0.236 0.45 XX0.2360.229 c70.27836.0739.0216.04 17.0 1.19 X0.1700.159 c80.26868.15107.3309.6220.3 …... 0.1820.179

36. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Mixed Observations Surface SM Streamflow Assimilation sm3, sm5, sm6 fix c1, c2, c4, c7, c8 ro1, ro4, ro6, ro8 Check residual variance Check standard deviation Catchments fixed

37. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Real Study Best forcing dataBest forcing data New parameters for routing model neededNew parameters for routing model needed CLSM heavily overestimates runoffCLSM heavily overestimates runoff

38. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Conclusions Streamflow Data Assimilation is a viable tool for the retrieval of catchment soil moistureStreamflow Data Assimilation is a viable tool for the retrieval of catchment soil moisture Simple sub-catchment structures only need small number of observationsSimple sub-catchment structures only need small number of observations Not many events needed for good fitNot many events needed for good fit Assimilation window should be short, with preferably at least one eventAssimilation window should be short, with preferably at least one event …. (cont’d)

39. Christoph Rüdiger Final PGrad Seminar 22 September 2005 Conclusion (cont’d) Biased forcing data introduce errors into water balance, which create positive or negative sinksBiased forcing data introduce errors into water balance, which create positive or negative sinks Model constraints may interfere with retrieval of initial statesModel constraints may interfere with retrieval of initial states Joint assimilation of different observations and magnitudes is possible when least squares products are scaled with the residual varianceJoint assimilation of different observations and magnitudes is possible when least squares products are scaled with the residual variance

40. Christoph Rüdiger Final PGrad Seminar 22 September 2005 and now ….??? © Bill Watterson, 1995