Prospects for river discharge Prospects for river discharge estimation through assimilation of estimation through assimilation of

remotely sensed altimetry: The remotely sensed altimetry: The WatER satellite missionWatER satellite mission

Kostas Andreadis

UW Land Surface Hydrology Group Seminar14 June 2006

Summary

● Water Elevation Recovery (WatER) proposed satellite mission

● Motivation and scope of this study● Methodology and experimental design● Results and Problems ● Future work

Importance of water measurements

● Poor knowledge of spatial and temporal dynamics of surface water discharge and storage globally

● In-situ measurements not sufficient Inadequate global coverage Essentially provide an 1-D view of flow

dynamics, especially in basins with extensive floodplains and wetlands

Still valuable, but do not answer key science questions

What measurements do we need? Fundamentally different from in-situ

measurements● Water surface elevation (h)● Temporal changes in water surface (∂h/∂t)● Water surface slope (∂h/∂x)● Inundated area Spaceborne measurements can be a

viable option for providing this type of measurements on a global scale

Current spaceborne approaches● Area : visible band (MODIS,

Landsat) and SAR imagery● Elevation : profiling altimetry

(TOPEX) and imaging (SRTM) methods

● ∂h/∂t : repeat altimeter measurements or SAR

● ∂h/∂x : derived from elevation SRTM or altimeter measurements

● Discharge : several methods, mostly problematic

Problems with existing sensors● Poor spatial resolution (GRACE and all

profiling altimeters)● Conventional radar and lidar altimeters

are nadir viewing, missing water bodies between orbital tracks

● Poor temporal resolution associated with SRTM and repeat-pass SAR

● Canopy and cloud cover problems for optical sensors

Required spatial and temporal sampling resolutions

● In summary, an interferometric altimeter (120 Km swath) covers nearly all global rivers and lakes

● Whereas, a profiling instrument would miss ~30% of rivers and ~70% of lakes (16-day cycle)

WatER instrumentation

● Two Ka-band antennae

● 200 MHz bandwidth

● Spatial resolution 10-70 m

● Overpass frequency ~7 days (mid-latitudes)

Ka-band Radar Interferometer (KaRIN)

What about discharge?● Impractical to measure discharge from

space● LeFavour and Alsdorf (2005) used

Manning's equation to estimate discharge from SRTM data

● Data assimilation of remotely sensed hydraulic measurements (h, ∂h/∂t, ∂h/∂x) into a hydrodynamics model, to indirectly estimate discharge

Scope of this study

● Create a baseline simulation of discharge and water surface elevation

● Generate synthetic WatER measurements using an instrument simulator

● Assimilate those into a hydrodynamic model and compare with the baseline simulation

● Proof-of-concept application

● Ohio River basin

● Small upstream reach

● Reach length ~50 km

Study domain

Clark (2006)

Experimental design

Hydrodynamic model● LISFLOOD-FP, a raster-based inundation

model● Based on a 1-D kinematic wave equation

representation of channel flow, and 2-D flood spreading model for floodplain flow

● Assumes rectangular, wide channel● Requires high resolution topographic data● Overbank flow modeled using Manning's

equation● Spatially uniform or variable Manning's

coefficient

Ensemble Kalman filter● Monte Carlo approach

to the traditional Kalman filter

● Ensemble representation of error covariances● State vector containing water depth and discharge, but only former directly observable

● Discharge updated based on developed covariances with water depth

Baseline and Open-loop simulations

● Spatial resolution of 270 m, and 20 sec temporal resolution

● Baseline or “truth” simulation● Nominal precipitation forcing VIC to

provide lateral inflows and upstream boundary conditions

● Open-loop simulation● Perturbed precipitation forcing VIC to

provide lateral inflows and upstream boundary conditions, and perturbed initial depths

Satellite measurement simulation● NASA JPL instrument

simulator● Provides “virtual”

observations from LISFLOOD-FP water stage

● 50 m spatial resolution● ~8 day overpass

frequency● Essentially

Virtual_obs=Truth+Error22 April 1995

Measurement errors● Spatially uncorrelated● Normally distributed, N(0, 20 cm)● Standard deviation of 20 cm for the

aggregated pixel scale (270 m)

Goteti et al. (submitted)

Problems...● Using the standard EnKF algorithm,

neither depth or discharge seemed to get updated correctly

Problems...● When the state dimension (or number of

observations) is much larger than the ensemble size, the problem becomes rank deficient

● Solution with pseudo-inverse and several approximations can lead to instabilities

● But, if we assume that the observation errors are uncorrelated, we can solve the KF equation sequentially (in batches)

● Rank increases, and results should be the same as if we had solved for the entire state matrix

Water Depth Update● Spatial snapshot (24 May 1995) of water

depth simulations (shown as WSL)

Truth Open loop Filter

Discharge Update● Spatial snapshot of discharge simulations

right after an assimilation step (24 May 1995)

Truth Open loop Filter

Water depth and discharge time series

● Time series at a specific point● Water depth (left) and discharge (x-

direction) (right)

Spatially averaged RMSE time series of water depth

● Dashed lines show times of updates

● Results from one representative ensemble member

Spatial maps of time-averaged RMSE

Open loop Filter

● Largest impact on the floodplain● Assimilation had relatively smaller effect on water

depth in the channel

Sensitivity to measurement error

● N(0,0.2) gave best overall results

● But other errors (s=0.1 and s=0.3) gave equally good results

RM

SE

(m)

6-hr Timestep

20 cm

10 cm

30 cm

Conclusions

● Using a sequential EnKF, water depth gets updated properly

● But discharge still has problems, producing implausible values

● Measurement error assumptions do not affect filter performance (at least for water depth recovery)

Future Work

● Avoid using a pseudo-inverse and revert to the “standard” seqEnKF

● Perhaps, use Manning's equation as the observation operator for model discharge

● Explore model errors in other parameters (e.g. Manning's n, channel width)

● Application on a more topographically complex basin

Questions?