Assimilation of Remotely-Sensed Surface Water Observations into a

Assimilation of Remotely-Sensed Surface Water Observations into a

Assimilation of Remotely-Sensed
Surface Water Observations into a
Raster-based Hydraulics Model
Elizabeth Clark1, Paul Bates2, Matthew Wilson3,
Delwyn Moller4, Ernesto Rodriguez4, Dennis
Lettenmaier1, Doug Alsdorf5
1.
2.
3.
4.
5.
University of Washington
University of Bristol
University of Exeter in Cornwall
Jet Propulsion Laboratory
Ohio State University
Purpose
• Globally, discharge measurements are
sparse and non-continuous
• Knowledge of global discharge aids in:
•
•
•
•
Closing the global water balance
Transboundary water management
Prediction of biogeochemical fluxes
Estimation of freshwater fluxes to the Arctic
• Satellite altimetry is able to estimate water
level of rivers, reservoirs, lakes, and wetlands
• We would like to extract discharge from water
level
Water Elevation Retrieval
• Ka-band SAR (synthetic
aperture radar) with two 50
km swaths
• Uses low incidence angle
(<4o) to increase the
brightness signal of water
relative to land
• Produces heights and coregistered imagery
• IS IT POSSIBLE TO OBTAIN
DISCHARGE FROM WATER
Image from Ernesto Rodriguez
LEVEL?
• Also see Doug Alsdorf’s talk tomorrow at
11:55 am Lido Room
Heritage: Estimation of
Streamflow from Water Level
• Stage-discharge relationships
derived for several locations in
Congo River basin (Coe and
Birkett, 2004)
• Regression models, generally
based on Manning’s equation
(Bjerklie et al., 2003)
Heritage: Hydrologic Data
Assimilation
• Soil moisture (e.g. Margulis et al.,
2002; Crow and Wood, 2003;
Reichle et al., 2002)
• Snow water equivalent (Andreadis
et al., in review; Durand and
Margulis, 2004)
Context: Virtual Mission
Conceptual Design
• Truth model:
• Hydrologic model to generate lateral inflows
and boundary conditions
• Hydrodynamic model to generate ‘true’ stage
• Measurements:
• Instrument simulator to add measurement
error
• Inversion problem:
• Now can we estimate the ‘true’ inflows from
the synthetic measurements?
Context: Virtual Mission
Hydrologic
Model (VIC)
Simulated
Streamflow
Hydraulics
Model
(LISFLOODFP)
Lateral
inflows and
boundary
conditions
Simulated Surface
Water Extent and
Elevation
Spatial and
Temporal Resolution
Tradeoffs
Measurement
Error
NASA/JPL
Instrument
Simulator
Simulated
Interferometric
Altimeter Swaths
“Truth”
Back Calculation
of Discharge
(Data Assimilation)
Inversion
Study Domain
• Ohio River flood
during 1996
• 14 km hydrologic
model resolution
• 270 m DEM for
hydraulics model
• 50 m simulated
satellite sampling
resolution
Model Inputs
• Discharge
(lateral inflows
and boundary
conditions)
generated by
VIC model
LISFLOOD-FP
1)
1-D finite difference
solutions of the full St.
Venant equations
2) 2-D finite difference and
finite element diffusion
wave representation of
floodplain flow
Qij=AijRij2/3Sij1/2/n,
i= upstream cell
j= downstream cell
n varies (channel vs. floodplain)
Simulated Truth
• Water depth
and discharge
from 19951998
• 20 s time step
• Output for
every ~11
hours
Observations
“True”
Error
80.6 km
Observed
39.2oN,
81.7oW•
38.5oN,
82.3oW
Water elevation (m)
Frequency
Repeat Cycle
34.9 to 35.1
16
Generated
by JPL
Instrument
Simulator
Error (m)
GHz
Mean Error
Days Std. Dev. Error
0
cm
10-15
cm
Data Assimilation: Ensemble Kalman
Filter
1. Boundary condition (BC) and lateral inflow
(LI) ensemble members represent
propagation through VIC model of input
errors from:
• Precipitation (Nijssen and Lettenmaier,
2003)
• Temperature (Andreadis, 2004)
2. LISFLOOD-FP propagates error from these
BCs and LIs
3. Observations synthesized to minimize model
errors versus normally-distributed
measurement errors
4. Water level and discharge (states) updated
Prospects for Data Assimilation
Schematic of
Ensemble Kalman
Filter
Perturbed
INPUTS
STATE
MEASUREMENTS
• Swaths of
remotely-sensed
water elevation with
known error
distribution
Filter incorporates
available
measurements to
minimize error
•Water depth
•Simulated
discharge
from VIC
•Manning’s n
•Spatially
distributed
discharge
Error is
introduced
into model
Model
propagates
error
2-D System
Model
Lisflood-FP
UPDATED
STATE
•Water depth
Kalman Filter
Analysis Step
•Spatially
distributed
discharge
OUTPUTS
•Estimated water depth
•Estimated discharge
•Associated error distributions
What will we learn from this
exercise?
• Feasibility of recovering discharge
with little to no in-situ data
• Evaluation of trade-offs between
acceptable error and spatial
resolution
• Will elevation recovery work for
streams of different sizes?
• How fast does the ability to recover
discharge degrade with spatial
resolution?
Conclusions
• Satellites have a great potential for
measuring the stage of inland waters.
• The use of data assimilation has been
effective in other hydrologic applications
and will likely play a role streamflow
estimation.
• Results of this exercise will show the
extent to which discharge can be
recovered from surface water
elevations.