How will storage change and discharge be estimated from SWOT? Michael Durand, Doug Alsdorf, Ernesto Rodríguez, Kostas Andreadis, Elizabeth Clark, Dennis Lettenmaier SWOT Workshop Monday 15 September 2008

Study area: The Ohio River basin Eleven Ohio tribs used Mainstem provides downstream b.c. for tribs USGS gages used for upstream b.c. Channel elevations from Hydro1k Study period:

Study area: The Ohio River basin Widths are extracted from Landsat imagery using RivWidth (Pavelsky and Smith) Widths are merged with Hydro1K, and input into LISFLOOD

Model sanity check Modeled discharge is compared with downstream gage discharge Basic temporal variations are captured

How well do steady flow and kinematic assumptions hold? If we can make these assumptions, then we can use simplified methods for performing a retrieval For most pixels, and most times, assumptions hold to within 1 % RMSE

Estimate depth from the WSE timeseries If steady flow and kinematic assumps hold, WSE can be interrogated to yield initial depth…. … IF there is adequate variability in the slope timeseries

Manning’s retrieval results Depth error propagates into discharge estimates Depth error is: –0.5 m or 100 % error (top) –5.0 m or 200 % error (bottom) Better depth estimation is certainly achievable: this is worst case!

Manning’s retrieval results The WSE signal provides excellent information about discharge variations despite poor depth estimates Depth error is: –0.5 m or 100 % error (top) –5.0 m or 200 % error (bottom)

Can we quantify how depth error propagates? Relative discharge:Absolute discharge: Error predicted from first-order Taylor series captures the major dynamics of the actual error Assume low slope variability for simplicity

Absolute versus relative discharge For relative flow (Q) For absolute flow (Q) Estimates of discharge variations will be more accurate than absolute discharge

Manning’s retrieval summary: What we’ve learned Discharge variations can be estimated accurately, even given poor depth estimates Depth is a key, limiting factor for discharge accuracy Kinematic assumption generally holds Steady flow assumption generally holds Model-predicted slope variability is low Future and ongoing work Improve depth estimation –Development of a width-to- depth algorithm –Incorporate morphology relationships in depth estimate –Investigate use of width variability to estimate initial depth –Investigate true slope timeseries variability –Investigate incorporation of other, prior information Characterize depth estimation error Develop global roughness coefficient database

Data assimilation shows promise for more accurate discharge estimates Goal: simultaneous estimation of discharge, depth, roughness Strategy: incorporate as much prior information in estimate as possible Method: Data assimilation provides a flexible framework for merging models and observations

The Ensemble Kalman Filter Initial State Forecast Analysis Member 1 Member 2 Observation Time t1t1 t2t2 t3t3 Spread in ensemble represents uncertainty in model inputs LISFLOOD hydrodynamic model used to forecast states States include discharge and depth

Observing System Simulation Experiment VIC hydrologic model used to provide boundary condition inflows True model simulation - used to generate SWOT observations Filter - ingests SWOT observations into the model Open loop simulation - does not benefit from observations

Study Area - upstream reach of Ohio River Ohio River near Martin’s Ferry 50 km long Upstream area ~ 60,000 km2

Water depth results TRUTH TRUTH – OPEN LOOP TRUTH – FILTER Water Depth maps for different simulations on 13 March 1995 (06:00) ‏

Discharge results Bias in open loop is corrected by the filter Accuracy is related to repeat-time More results: see Andreadis et al. (2007) in GRL

Depth, discharge, and roughness estimation Problem: simultaneous state and parameter (e.g., roughness) estimation Preliminary results show that roughness can be effectively recovered

Bathymetry estimation Prior True Posterior Prior Uncertainty Post. Uncertainty Durand et al., GRL, 2008, accepted

Thanks and acknowledgments Funding from NASA Ocean Surface Topography Science Team and Terrestrial Hydrology Programs Funding from Ohio State Climate Water Carbon Program Paul Bates ~ use of LISFLOOD model Judy Gardiner ~ parallelization of LISFLOOD model

How will storage change be estimated from SWOT? Straightforward calculation: –Area approximately constant –Variable area: more detailed analysis possible by developing an estimate of bathymetry over time Error and uncertainty analysis: –Currently focusing on temporal sampling issues

How will discharge be estimated from SWOT? Method 1: Manning’s retrieval algorithm –Instantaneous “snapshot” retrieval –Incorporates minimal ancillary information –Relatively less accurate, less computationally expensive Method 2: Data assimilation –Combination of hydrologic and hydrodynamic model, and SWOT observations –Incorporates much ancillary data –More accurate, more computationally expensive

Method 1: Manning’s retrieval algorithm Approximate discharge relationship as: Slope ( S ) and width ( w ) are SWOT observables Roughness coefficient ( n ) estimated via ancillary information Information about depth ( z ) can be derived from: –Upstream contributing area –Width observations –Slope timeseries variability Key Assumptions: -Rectanglar channel -Kinematic flow

SRTM heritage: Manning’s retrieval algorithm See LeFavour and Alsdorf, 2005, GRL for more details

Evaluation: Manning’s retrieval algorithm Motivation: how do we assess the accuracy of this approach with SWOT observations? Method: use a physically-based hydrodynamic model (LISFLOOD) which simulates the water level and discharge Evaluation: –Introduce realistic uncertainty in depth –Assume we have WSE observations –How accurately can we recover discharge predicted by hydrodynamic model?

LISFLOOD hydrodynamic model Inputs: –Boundary conditions (input flow) –Channel bathymetry –Floodplain DEM Outputs: –Water surface elevation –Channel discharge Diffusion wave solver:

Future directions Evaluate global computational cost of assimilation –Maybe we won’t need a retrieval algorithm at all? Use a “smoother” approach in order to account for potential temporal error persistence Evaluate the idea of using SWOT measurements to correct parameterizations and structural errors in hydrological models