1. Background Information Examples of Data Assimilation
Session H42A - Poster 0344
Land Data Assimilation: A Possible Centerpiece of CUAHSI Modeling Activities?
Dennis McLaughlin
Department of Civil and Environmental Engineering
Massachusetts Institute of Technology
Cambridge, MA
Eric Wood
Department of Civil Engineering
Princeton University
Princeton, NJ
W. James Shuttleworth
Department of Hydrology and Water Resources
University of Arizona
Tucson, AZ
Paul Houser
NASA Goddard Space Flight Center
Code 974
Greenbelt, MD
Dennis Lettenmaier
Department of Civil and Environmental Engineering
University of Washington
Seattle, WA
Data assimilation seeks to characterize the true state of an environmental system by combining information from measurements, models, and other sources.
Typical measurements for hydrologic/earth science applications include:
Ground-based hydrologic and geological measurements (stream flow, soil moisture, soil properties, canopy properties, etc.)
Ground-based meteorological measurements (precipitation, air temperature, humidity, wind speed, etc.)
Remotely-sensed measurements (usually electromagnetic) which are sensitive to hydrologically relevant variables (e.g. water vapor, soil moisture, etc.)
Mathematical models used for data assimilation:
Models of the physical system of interest.
Models of the measurement process.
Probabilistic descriptions of uncertain model inputs and measurement errors.
A description based on combined information should be better than one obtained from either measurements or model alone.
Data Assimilation Methods:
Direct Insertion, Updating, or Dynamic Initialization
Newtonian Nudging
Optimal of Statistical Interpolation
Kalman Filtering
Variational Approaches – Adjoint
(Background information is taken from McLaughlin, 2001.)
Types of Measurement Errors:
Introduction
Background Information
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Large-scale trend described by model
True value
Measurement
Instrument Error
Scale-related Error
The Consortium of Universities to Advance Hydrologic Science, Inc. (CUAHSI) and the U.S. Global Change Research Program (USGCRP) both identify data assimilation as a target research area for the advancement of the hydrologic sciences. Hornberger et al. (2001) states, "Development must continue on data assimilation methods for weather and climate prediction. They have led to remarkable progress in estimating global water and energy fluxes. Applying the same techniques to hydrology (e.g., McLaughlin, 1995) or biogeochemistry can yield quantitative data for variables that have heretofore been unavailable.”
Data assimilation refers broadly to methods that incorporate observations into a (generally deterministic) dynamical model, to produce improved predictions or nowcasts at the time of assimilation, and subsequent improved (future) forecasts. Data assimilation is widely used in weather forecasting to ingest disparate observations at irregular spatial and temporal intervals to produce better model initial conditions, and hence improved forecast accuracy. It is also being used increasingly in oceanographic and climate models. Its use in land surface modeling is relatively new, but it shows promise for improving hydrologic predictions by incorporating soil moisture, snow, surface temperature, and other remotely sensed and in situ observations. Data assimilation has proven valuable also as a diagnostic tool for evaluation of model error sources and for evaluation of optimal observation strategies.
Types of Assimilation Problems:
Temporal Aspects:
Interpolation: no time-dependence, characterize system only at time t=ti
Use for interpolation of spatial data (e.g. kriging)
Smoothing: characterize system over time interval t to ti
Use for reanalysis of historic data
Filtering/forecasting: characterize system over time interval t to ti
Use for real-time forecasting
Spatial Aspects:
t=ti
When models are discretized over time/space there are two sources of output measurement error:
Instrument errors (measurement device does not perfectly record variable it is meant to measure).
Scale-related errors (variable measured by device is not at the same time/space scale as corresponding model variable)
The data assimilation algorithm uses specified information about input fluctuations and measurement errors to combine model predictions and measurements. t t2 t1 ti ti t2 t1 t
Downscaling: Characterize system at scales smaller than output measurement resolution
Measurement States
Upscaling: Characterize system at scales larger than output measurement resolution
Measurements State
Time-varying input (e.g. precip)
State
(e.g. soil
moist.)
Measurement system
Hydrologic system
Random fluctuations
Output
(e.g. radiobrightness)
Random error
Random fluctuations
Time-invariant input (e.g. sat. hydr. cond.)
Data assimilation algorithm
Means and covariances of true inputs and output measurement errors
Estimated states and outputs
Example 1: Ts Assimilation Results
Surface temperature has very little memory or inertia, so without a continuous correction, it tends drift toward the control case quickly.
(Houser et al., 2001)
Examples of Data Assimilation
Summary
Progress in hydrologic data assimilation (potentially applicable to soil moisture and temperature, groundwater, snowpack, groundwater, and streamflow prediction) has lagged behind its atmospheric and ocean counterparts and must be accelerated. CUASHI is considering a major initiative in this area. Some progress has already been made in improving hydrologic predictions using data assimilation methods, as illustrated by the above three examples. Another potential benefit of data assimilation – unrealized as yet in hydrology – is its value in diagnostic studies, and subsequent improvement of model physical representations. Global and regional reanalysis is a powerful tool that has been used by the atmospheric sciences community, but to date its value has not been exploited in hydrology, even though several well-known reanalyses do estimate land surface variables over global grids. One possible area where CUASHI could help lead future developments in the hydrologic sciences is to encourage the development of reanalysis products that are more relevant to land surface processes, and to foster their use to improve hydrologic prediction tools. 
Example 2: Real-Time Rainfall Estimation Problem Set-Up
Objective: Characterize areally averaged 15 minute and hourly rainfall in each pixel of a regular grid (pixels ~ 10 km2). (McLaughlin, 2001) Ground radar pattern
Scattered Met. Stations
Instantaneous Satellite Estimation pixels Antennae Footprint
Example 3: Soil Moisture Assimilation
Objective: Combine Southern Great Plains 1997 (SGP’97) experimental data with the TOPLATS model output to predict soil moisture at a site in the Arkansas-Red River Basin. (Crow et al., 2001)
Microwave Measurements: L-band (1.4 GHz) microwave emissivity is sensitive to soil saturation in upper 5 cm. Brightness temperature decreases for wetter soils.
Sensitivity of microwave brightness temperature to soil moisture (SGP’97)
SSM/I 19 GHz
ESTAR 1.4 GHz
Soil moisture
In this problem we need to:
Downscale satellite measurements (i.e. estimate rainfall at a finer spatial scale than the satellite radiobrightness measurements).
Upscale radar measurements (i.e. estimate rainfall at a coarser spatial scale than the radar measurement pixels)
Assimilate (or incorporate) all measurements into the NWP model (so that estimates derived from the model reflect measurements)
Account for:
Subpixel variability
Model errors
Measurement errors
All of this needs to be done in a systematic framework!
Observation
Assimilation with
Bias Correction
Assimilation
No Assimilation
References
Crow, W.T., E.F. Wood. The assimilatioin of remotely sensed soil brightness temperature imagery into a land surface model using Ensemble Kalman filtering: A case study based on ESTAR measurements during SGP (in preparation)
Hornberger, G.M., J.D. Aber, J. Bahr, R.C. Bales, K. Beven, E. Foufoula-Georgiou, G. Katul, J.L. Kinter III, R.D. Koster, D.P. Lettenmaier, D. McKnight, K. Miller, K. Mitchell, J.O. Roads, B.R. Scanlon, and E. Smith. A Plan for a New Science Initiative on the Global Water Cycle. US Global Change Research Program, Wahington, DC, 2001.
Houser, P.R., J.D. Radakovich, A. daSilva, and M.G. Bosilovich: Surface temperature assimilation and diurnal bias correction (in preparation)
McLaughlin, D. Recent developments in hydrologic data assimilation. Rev. of Geophys, Supplement: , 1995.
McLaughlin, D. Lecture Material from the Summer School on Hydrologic Assimilation with Remotely Sensed Measurements. Universita degli Studio di Perugia, July 16-20, 2001.
This poster was assembled by Jennifer Adam, University of Washington graduate research assistant, from material provided by the authors. Her efforts are gratefully acknowledged.