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?