1. Integrating hydrogeodetic data and models: towards an assimilative framework Jürgen Kusche, Annette Eicker, Maike Schumacher Bonn University With input from Petra Döll, Hannes Müller-Schmied (Frankfurt University) IGCP Workshop, October 29/30, 2012, Johannesburg 1

2. Hydrologic modelling and geodetic data (hundreds of papers) Model of global freshwater system dynamics Input fields Parameters Validation Output fields Data 2

3. What we now should do Model of global freshwater system dynamics Output fields Input fields Parameters Calibration Data Assimilation 3

4. Challenges Model of global freshwater system dynamics Output fields Scenario inputs Parameters Climate model scenario Data New sensors Understanding the present state of the global freshwater system –Freshwater as a ressource –Memory function for climate –Being able to reliably simulate future evolution Challenges –Global scale: data problem –Limited representation of physics / conceptual realism in the models –Being able to assess the potential of new and future sensors, data sets, models 4

5. Working Hypothesis (I) During the past years (e.g. SPP 1257) we have –established methods for validating models with time variable gravity (GRACE, SG), deformation (GPS), river/lake level from radar altimetry, … –found that global HMs are poor at simulating some very important fields (e.g. long-term evolution of groundwater storage, annual phase in some region) –proven beyond doubt that geodetic data* improves over HMs at some time/spatial scales (whereas HMs are better at others) –seen a number of attempts towards model calibration –Understood that integration into hydrological models is useful – we need to develop a multidisciplinary framework. But we are still missing the methods for this integration! * Geodetic data is different from precipitation/land coverage/cloud data etc. in that it does not „drive“ the models – but this is fuzzy, anything that the model predicts can be used for C/DA (snow coverage) 5

6. Calibration Approach (CA) Model –Physical or conceptional relations, involving some „parameter“ –Initial conditions –Forcing data Calibration against observed data: improve estimates of one or more, possibly poorly known model parameters –Leads to exact model solution (single „calibrated run“) closest to the data - physical relations will not be violated –If the model is bad, distance to observed data can be big –In Data Assimilation called „Parameter Estimation“ Cost function measures –Distance between data and model-simulated data, plus –Distance between parameter and a-priori parameter (possibly implicit through ensemble sampling) 6

7. Werth and Güntner (2009, 2010) WGHM with ECMWF/GPCC forcing Select 6-8 most relevant parameters per basin (based on sensitivity analysis / MC simulation) Calibration data: GRACE TWS basin average + monthly mean runoff Cost function with 2 objectives (TWS and runoff misfit), Nash-Sutcliffe coefficient MC optimization,  -NSGAII algorithm for ensemble generation (Kollat and Reed) Pareto solution „…multi-objective improvement of the model states is obtained for most of the river basins, with mean error reductions up to 110 km 3 /month for discharge and up to 24 mm of a water mass equivalent column…“ 7

8. Werth and Güntner (2009, 2010) Calibration reaches to all storage compartments 8

9. Getirana (2010) MGB-IPH model for Amazon basin Select 8 most relevant parameters based on sensitivity analysis Calibration data: ENVISAT altimetry (CTOH GDRs, ICE-1), local gauge data Different cost functions with 1-2 objectives (Nash-Sutcliffe for anomalies, tangent and coefficient of regression) MC optimization (MOCUM-UA for ensemble generation) Pareto solution „…results demonstrate the potential of spatial altimetry for the automatic calibration of hydrological models in poorly gauged basins…“ 9

10. Getirana (2010) Obs: observed IGP: Initial guess parameters (open loop run) Otm: Calibrated 10

11. Data Assimilation Approach (DA) State estimation means: find model state that in some weighted metrics best fits model relations (incl. forcing, initial conditions), and observed data Cannot lead to physically consistent model solution since usually the problem is overdetermined Cost function measures –Distance between data and model-simulated data, plus –Distance between model estimate and simulated model state Most general: combination (C/DA) Calibration parameter as subset of state vector 11

12. Zaitchik, Rodell, Reichle (2008), Li et al. (2012) Catchment LSM, works on topographically defined „catchments“ (avg. area 4000 km 2 ), Mississippi, Europe, … Meteo forcing data: from GLDAS data base Calibration data: GRACE basin average for sub-basins, (over-) simplified error covariance Validation data: Observed groundwater, river discharge EnKF for near-realtime, EnKS (iterative application) for optimal reanalysis, Ensemble: 20 members Special scheme for temporally disaggregating monthly GRACE data No explicit parameter calibration ? State error covariance: includes propagated perturbations in precipitation,radiation forcing and prognostic variables „…assimilation estimates of groundwater variability exhibit enhanced skill with respect to measured groundwater in all four subbasins“ 12

13. Zaitchik, Rodell, Reichle (2008) CLSM open loop CLSM with GRACE-DA 13

14. Working Hypothesis (II) Why do we want to integrate models and data ? As a prerequisite for prediction –develop best physically/conceptual consistent model, „best“ in the sense that it best predicts relevant fields – but can be tested only against observed data  Calibration Understanding the present state (with all interactions, feedbacks, …), for science and management –Develop most realistic description of fields (groundwater, fluxes, soild mosture, human consumption, …) –Vertical disaggregation and horizontal downscaling of GRACE data –NRT for monitoring ? –Geodesy: de-alisiasing for GRACE/GRACE-FO  Data assimilation 14

15. Variational Assimilation (3D/4DVAR) Minimization of cost function (deterministic approach) or 4DVAR considers exact observation timing within analysis interval Model covariance required, no explicit computation of the covariance of updated model Iterative solution (steepest descend, CG, …) requires re- computation of the gradient, gradient requires integration of the adjoint model operator H + 15

16. Adjoint Operator H + =G + F + F + adjoint of Jacobian of F, propagated back from t to t 0 G + adjoint of Jacobian of G, transforms observed misfit from data space to model space Gradient of cost function provided by backward integration of adjoint model Adjoint model –Analytical derivation –Step-by-step –Automatic generation: adjoint compilers (Giering et al.) 16

17. EnKF/S KF: update of state vector and parameter Ensemble approach: Conditional pdfs for predicted states approximated by a finite set of model trajectories Propagation of model covariance Update constructed in the space spanned by the ensemble. 17

18. EnKF/S Using future observation for optimal solution: EnKS The update is constructed in the space spanned by the ensemble. So, how big should be the ensemble? How should we initialize the ensemble in order to optimally „explore“ the model space? Though the EnKF involves full nonlinear model propagation and observation equations, it is based on 2nd-order statistics Technical issues –Data perturbation approach or square-root approach, for getting the statistics right –Use assimilative framework (e.g. PDAF, Nerger)? 18

19. Comparison VAR vs. EnKF vs. „conventional“ calibration Comparison papers VAR/EnKF all from the meteo (can we tranform their findings to our problem?) or math communities VAR + physically consistent solution within analysis interval - requires adjoint model - does not provide update model covariance EnKF/KS + no adjoint model required + easy to implement + provides update model covariance - performance depends on ensemble size - possible loss of physical consistency Cal + physically consistent solution - does not provide update model covariance - performance depends on ensemble size, efficient for >2 parameter? - no state adjustment 19

20. 20 WaterGap hydrological model (WGHM), 0,5deg calibration and assimilation: EnKF Data: GRACE and river discharge full spatial resolution, full error covariance current status testing sensitivity studies assessing impact of GRACE next run the C/DA model climate input errors include river discharge Eicker et al, U Bonn/U Frankfurt 20

21. observations (GRACE) with Kalman filter 21 Kalman Filter Total water storage (grid) prediction (model): with Full covariance matrix (grid) GRACE monthly solutions ITG-Grace2010 spherical harm. N max =60 full covariance matrix 0.5°x0.5° grid 27 calibration parameters + CANOPY SNOW SOIL LAKE (local) WETLAND (local) LAKE (global) WETLAND (global) RESERVOIR RIVER GROUNDWATER 10 compartments: 21

22. Ensemble runs of WGHM 22 sample 1 … sample 2 sample N state vector x: 10 compartments per grid cell 27 calibration parameters analysis of: model sensitivities correlation structures Test case: Mississippi, year 2008 empirical ensemble covariance matrix ensemble mean variances and correlations of storages and parameters variation within given boundaries 22

23. Ensemble runs of WGHM 23 sample 1 … sample 2 sample N state vector x: 10 compartments per grid cell 27 calibration parameters variances and correlations of storages and parameters analysis of: model sensitivities correlation structures Test case: Mississippi, year 2008 30 WGHM model runs by variation of individual parameters (basin averages) empirical ensemble covariance matrix ensemble mean variation within given boundaries 23

24. 24 river wetland total water storage water height [mm] date [MJD] Ensemble: perturbing 5 parameters in WGHM groundwater snow soil standard run Model predictions: basin averages Mississippi, year 2008 24

25. 25 river wetland total water storage water height [mm] date [MJD] groundwater snow soil standard run Model predictions: basin averages Mississippi, year 2008 Model sensitivity of storage compartments to different (sets of) parameters Ensemble: perturbing 5 parameters in WGHM 25

26. Ensemble runs of WGHM 26 sample 1 … sample 2 sample N state vector x: 10 compartments per grid cell 27 calibration parameters variances and correlations of storages and parameters Test case: Mississippi, year 2008 empirical ensemble covariance matrix ensemble mean 26

27. Ensemble runs of WGHM 27 sample 1 … sample 2 sample N state vector x: 10 compartments per grid cell 27 calibration parameters variances and correlations of storages and parameters next slide: gridded standard deviations after one year Test case: Mississippi, year 2008 empirical ensemble covariance matrix ensemble mean 27

28. 28 groundwatersnowsoilriverwetland 5 parameters water height [mm] Standard deviations of model storages after one year ( from 30 ensemble runs) 28

29. 29 groundwatersnowsoilriverwetland 5 parameters water height [mm] Standard deviations of model storages after one year ( from 30 ensemble runs) Varying spatial distribution of model uncertainties in different compartments 29

30. Contribution of observations 30 Kalman filter: update observations model prediction How much contributes one GRACE TWS grid cell to the individual storage compartments of each individual cell? groundwater snow wetlands gain matrix K 30

31. Contribution of observations 31 Kalman filter: update observations model prediction How much contributes one GRACE TWS grid cell to the individual storage compartments of each individual cell? groundwater snow wetlands gain matrix K Disaggregation of GRACE information into storage compartments and grid cells seems possible 31

32. Contribution of observations 32 Kalman filter: update observations model prediction gain matrix K How much contribute all GRACE TWS grid cell to the basin average of each storage compartment? Apply averaging operator: basin average for each compartment contribution of each GRACE cell observation to basin average sum of weights 32

33. Contribution of GRACE to basin average 33 one year 33

34. Contribution of GRACE to basin average 34 one year Contribution of GRACE varies between compartments and this ratio changes in time 34

35. Key questions Key questions that need to be answered –How should we use the new types of data (GRACE, altimetric level, …) cf. new IAG WG Land hydrology from gravimetry –What components of modeling can be improved through C/DA –How will we characterize model noise and forcing data noise –How will we deal with systematic model and forcing data errors –How can we test data-integrated modeling –How far can we improve understanding of the present state of the freshwater system –How far can we improve simulations –Can we formulate recommendations for upcoming and future systems (e.g. see current discussion on Sentinel-3 SAR/LRM coverage inland/oceans) 35