integrating hydrogeodetic data and models: towards an assimilative framework jürgen kusche, annette...

Integrating hydrogeodetic data and models: towards an assimilative

framework

Jürgen Kusche, Annette Eicker, Maike SchumacherBonn University

With input from Petra Döll, Hannes Müller-Schmied (Frankfurt University)

IGCP Workshop, October 29/30, 2012, Johannesburg 1

Hydrologic modelling and geodetic data (hundreds of papers)

Model of global freshwater system

dynamics

Input fields

Parameters

Validation Output fields

Data

2

What we now should do


dynamics

Output fields

Input fields

Parameters

Calibration Data

Assimilation3

Challenges


dynamics

Output fields

Scenario inputs

Parameters

Climate model scenario

DataNew sensors

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

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

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

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 km3/month for discharge and up to 24 mm of a water mass equivalent column…“ 7

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

8

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

Getirana (2010)Obs: observedIGP: Initial guess parameters (open loop run)Otm: Calibrated

10

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

Zaitchik, Rodell, Reichle (2008), Li et al. (2012)

• Catchment LSM, works on topographically defined „catchments“ (avg. area 4000 km2), 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

Zaitchik, Rodell, Reichle (2008)

CLSM open loop

CLSM with GRACE-DA

13

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

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

Adjoint OperatorH+=G+F+

• F+ adjoint of Jacobian of F, propagated back from t to t0• 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

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

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

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 consistencyCal

+ physically consistent solution- does not provide update model covariance- performance depends on ensemble size, efficient for >2 parameter?- no state adjustment 19

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

k k kl A xobservations (GRACE)

llΣwith

Kalman filter

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Kalman Filter

Total water storage(grid)

1 1k k k

x B xprediction (model):

xxΣwith

Full covariance matrix(grid)

GRACE monthly solutions

• ITG-Grace2010• spherical harm. Nmax=60• full covariance matrix

0.5°x0.5° grid

27 calibration parameters+

CANOPYSNOWSOILLAKE (local)WETLAND (local)LAKE (global)WETLAND (global)RESERVOIRRIVERGROUNDWATER

10 compartments:

21

Ensemble runs of WGHM

22

1 1k k k

x B xsample 1

1 1k k k

x B x

1 1k k k

x B x

…

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

Tiii

iixx xxxx

N)()(

1

1

Σvariances and correlations of storages and parameters

variation within given boundaries

22


23

1 1k k k

x B xsample 1

1 1k k k

x B x

1 1k k k

x B x

…

sample 2

sample N


variances and correlations of storages and parameters

analysis of:• model sensitivities• correlation structures


30 WGHM model runs by variation of individual parameters(basin averages)


ensemble mean

Tiii

iixx xxxx

N)()(

1

1

Σ

variation within given boundaries

23

24river

wetland

total water storage

wat

er

hei

ght

[mm

]

date [MJD]

Ensemble: perturbing 5 parameters in WGHM

groundwatersnow soil

standard run

Model predictions: basin averages Mississippi, year 2008

24

25river

wetland

total water storage

wat

er

hei

ght

[mm

]

date [MJD]


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

1 1k k k

x B xsample 1

1 1k k k

x B x

1 1k k k

x B x

…

sample 2

sample N





ensemble mean

Tiii

iixx xxxx

N)()(

1

1

Σ

26


27

1 1k k k

x B xsample 1

1 1k k k

x B x

1 1k k k

x B x

…

sample 2

sample N



next slide:gridded standard deviationsafter one year



ensemble mean

Tiii

iixx xxxx

N)()(

1

1

Σ

27

28


riverwetland

5 parameters

water height [mm]

Standard deviations of model storages after one year( from 30 ensemble runs)

28

29


riverwetland

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

Contribution of observations

30

( ) x x K l AxKalman 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

1T T xx xx llΣ A AΣ A Σ

gain matrix K

30


31


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


model prediction


gain matrix K How much contribute all GRACE TWS grid cell to the basin average of each storage compartment?

Apply averaging operator:

( ) Mx Mx MK l Ax

basin averagefor each compartment

contribution of each GRACE cell observation to basin average

sum of weights

32

Contribution of GRACE to basin average

33

one year

33

Contribution of GRACE to basin average

34

one year

Contribution of GRACE varies between compartments and this ratio changes in time

34

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)

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integrating hydrogeodetic data and models: towards an assimilative framework jürgen kusche, annette...

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