Dennis McLaughlin, Parsons Lab', Civil

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Dennis McLaughlin, Parsons Lab., Civil
Environmental Engineering, MIT Dara Entekhabi,
Parsons Lab., Civil Environmental Engineering,
MIT Rolf Reichle, NASA Goddard Space Flight Center

• Problem context - Mapping continental-scale soil
  moisture from satellite passive microwave
  measurements. Problem is spatially distributed,
  nonlinear, and has many degrees of freedom
  O(106). Available models of hydrologic system
  and measurement process are highly uncertain.
• Variational data assimilation
• Results from a synthetic experiment (OSSE)

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Soil Moisture
Soil moisture is important because it controls
the partitioning of water and energy fluxes at
the land surface. This effects runoff (flooding),
vegetation, chemical cycles (e.g. carbon and
nitrogen), and climate.
Soil moisture varies greatly over time and space.
Measurements are sparse and apply only over very
small scales.
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Microwave Measurement of Soil Moisture
L-band (1.4 GHz) microwave emissivity is
sensitive to soil saturation in upper 5 cm.
Brightness temperature decreases for wetter
soils. Objective is to map soil moisture in real
time by combining microwave meas. and other data
with model predictions (data assimilation).
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Relevant Time and Space Scales
Plan View Estimation pixels (small) Microwave
pixels (large)
Vertical Section Soil layers differ in
thickness Note large horizontal-to-vertical scale
disparity
For problems of continental scale we have 105
est. pixels, 105 meas, 106 states,
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State equations are derived from mass and energy
conservation Soil moisture is governed by a 1D
(vertical) nonlinear diffusion eq (PDE). Soil
temperature and canopy moisture are linear ODEs.
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The Estimation (Data Assimilation) Problem
Suppose we are given a vector Zi z1, ..., zi
of all meas. taken through ti. Ideally, we wish
to derive the posterior density py(t) Zi at
any time t . . . . . In practice, we must settle
for partial information about this density

• Some options
• Variational Approaches
• Derive mode of py(t) Zi . Good for smoothing
  problems (t lt ti) . Requires adjoint model,
  limited capabilities for handling model error
  (process noise), does not give info. about
  accuracy of state ests.
• Extended Kalman Filtering
• Uses Gaussian assumption to approximate
  conditional mean and covariance of py(t) Zi.
  Good for filtering/forecasting problems (t ? ti
  ). Requires computation and storage of very
  large covariance matrices. Tends to be unstable.
  Provides some info. about estimation accuracy.

Is there a more efficient and complete way to
characterize py(t) Zi ?
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Operating System Simulation Experiment (OSSE)
OSSE generates synthetic measurements which are
then processed by the data assimilation
algorithm. These measurements reflect the effect
of random model and measurement errors.
Performance can be measured in terms of
estimation error.
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Synthetic experiment uses real soil, landcover,
and precipitation data from SGP97 (Oklahoma).
Radiobrightness measurements are generated from
our land surface and radiative transfer models,
with space/time correlated model error (process
noise) and measurement error added.
SGP97 study area, showing principal inputs to
data assimilation algorithm
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Variational algorithm performs well even without
precipitation information. In this case, soil
moisture is inferred only from microwave
measurements.
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1. Developed and tested an efficient variational
smoothing algorithm based on an indirect
representer solution technique. Method is able
to accommodate time-dependent model errors. 2.
Developed and applied an approach for assessing
accuracy of soil moisture and temperature
estimates (computation of radiobrightness
prediction error variances). 3. Used
variational method to study soil moisture mission
design issues, including spatial
resolution/downscaling, length of smoothing
interval, and effects of precipitation
withholding. 4. Developed and tested an
ensemble Kalman filter (EnKF) which is able to
handle highly nonlinear models. 5. Compared the
performance of the variational and EnKF
approaches.
Publications Reichle, R. H., 2000 Variational
Assimilation of Remote Sensing Data for Land
Surface Hydrologic Applications, PhD
dissertation, Massachusetts Institute of
Technology, Dept. of Civil and Environmental
Engineering, Cambridge, MA 02139, USA. Reichle,
R., D. Entekhabi, and D. McLaughlin, Downscaling
of Radiobrightness Measurements for Soil Moisture
Estimation A Four-Dimensional Variational Data
Assimilation Approach, Water Resources Research,
in press. Reichle, R., D. McLaughlin, and D.
Entekhabi, Variational data assimilation of
microwave radiobrightnes observations for land
surface hydrologic applications, IEEE
Transactions on Geoscience and Remote Sensing, in
press. Reichle, R., McLaughlin, D., and D.
Entekhabi, Hydrologic data assimilation with the
ensemble Kalman filter, Monthly Weather Review,
in press.