Soil Moisture Data Assimilation in the SHEELS Land Surface Model

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Soil Moisture Data Assimilation in the SHEELS
Land Surface Model

• Clay Blankenship
• USRA
• Special thanks to Bill Crosson, Jon Case

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Overview

• Data assimilation and retrieval background
• 1dvar, 3dvar, and Kalman Filters
• Soil Moisture Data Assimilation
• SHEELS LSM
• AMSR-E data
• Results
• Some results from profile retrievals with MIRS

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Data Assimilation (and Variational Retrievals)
Given observations y and background state xb,
estimate most likely state x taking into
account errors in both xb and y.  
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Retrieved-Bkgd State
Obs-Calc Obs
x geophysical state xb background (a priori)
of state y observations H(x) forward operator
converting x into observation space Pb
background error covariance R obsforward model
error covariance

• In data assimilation you are using observations
  to improve a model. In profile retrievals you
  always have some assumed background state (maybe
  climatology).

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Retrieval and Data Assimilation Applications
Profile Retrieval (1d) Soil Moisture (1d) NWP (3d or 4d)
Model Variable Column vector of T, q, hydrometeors Column vector of soil q and T 3D (or 4D) grid of T, q, u, v, clouds
Observations TB from satellite instrument(s) TB or retrieved near-surface water content TB from multiple satellites, raobs, surface obs, etc.
Typical size of state vector 500 (or 5 to 15 in EOF space) 5-20 106 to 108
Typical size of observation vector 5-20 1-3 up to 106
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Data Assimilation (and Variational Retrievals)
Given observations y and background state xb,
estimate most likely state x taking into
account errors in both xb and y.   To
maximixe this probability, minimize -2 times its
log
Bkgd Error Cov
OF Error Cov


Retrieved-Bkgd Atmosphere
Obs-Calc TB
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DA Solution
Minimizing the cost function Given initial
guess xxb, linearize and solve for new estimate
of x. Skipping the math, the solution can be
expressed as  The Gain represents a weighted
average of bk and ob errors The Jacobian K
relates the y terms to x terms and can include
interpolation, averaging or integration, radiative
transfer, etc.
Bkgd Gain
Innovation
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Data Assimilation Methods
1DVar/3DVar 4DVar Kalman Filter Ensemble Kalman Filter
Background Error Covariance Matrix (normally fixed) Defined at t0. Flow dependent based on model adjoint. Computed based on linearized model dynamics. Estimated from ensemble covariance
Gain Calculation
Equivalent to KF with fixed Gaussian background errors Equivalent to EnKF assuming perfect model, Gaussian bk error Most general method in terms of error covariance Most general method in terms of error covariance
Applies innovations at proper time
Hybrid methods use ensemble spread to define
background covariance in 3dvar.
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Soil Moisture Data Assimilation in the SHEELS
Land Surface Model
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SHEELS
SHEELS Simulator for Hydrology and Energy
Exchange at the Land Surface

• Distributed land surface hydrology model
  provides soil state(T,q), fluxes of energy and
  moisture
• Heritage 1980s Biosphere-Atmosphere Transfer
  Scheme (BATS)
• Can run off-line or coupled with meteorological
  model
• Flexible vertical layer configuration designed
  to facilitate microwave data assimilation
• Described in Martinez et al. (2001), Crosson et
  al. (2002)

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SHEELS Input
SHEELS Input

• Required static variables
• Soil type (STATSGO) Landcover (U of Md)
• Saturated hydraulic conductivity Canopy height
• Saturated matric potential Fractional vegetation
  cover
• Soil wilting point Minimum stomatal resistance
• Soil porosity Root depth
• Reflectance properties
• Seasonal
• Leaf area index Topography (GTOPO30)
• Surface elevation and slope
• Time-dependent input (forcing)
• Wind speed (NLDAS)
• Air temperature
• Relative humidity
• Atmospheric pressure
• Downwelling solar radiation
• Downwelling longwave radiation

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SHEELS Output
STATES Soil surface and canopy temperatures Soil
temperature Soil water/ice content Depth of
water on canopy Ponded water Snow temperature,
depth, and density FLUXES Surface latent and
sensible heat fluxes Ground heat flux Net
radiation flux Evapotranspiration
Infiltration Runoff
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Land Information System (LIS)
A modeling and data assimilation system with the
capability to run several different LSMs, from
GSFCs Hydrological Sciences Branch. It is very
customizable with the ability to swap out LSMs,
forcing datasets, etc. LSMS VIC, Noah,
CLM, Catchment,SiB2, Hyssib Base
Forcings ECMWF, GDAS, NLDAS...
Supplemental Forcings TRMM 3B42, Agrrad,
Cmap, Cmorph, Stg4... Parameters
Landcover, soils, greenness, albedo, LAI,
topography, tbot Data Assimilation
algorithm, observation, perturbation method
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Example Depth-Time Sections
NebraskaJAN-JUL 2003
Fractional soil moisture (waterice)
Soil Temperature
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SHEELS output time series
SHEELS output time series Volumetric soil
moisture, 1 Mar 2011 - 21 Apr 2011
0-10cm
Root zone
Total column (10m)
Salinas, California
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Precip, Soil Water, ET
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AMSR-E (Advanced Microwave Scanning Radiometer
for EOS)
NASA Aqua satellite with AMSR-E instrument

• AMSR-E
• Conically scanning passive microwave radiometer
  on NASA Aqua polar orbiter
• Measures polarized brightness temperatures at 6
  frequencies from 6.9 to 89.0 GHz
• We use the Level 3 retrieved soil moisture
  product (Njoku et al. 2003) resampled to a 25-km
  grid. (Obs twice daily.)
• Stated accuracy is .06 m3/m3. (Typical range is
  .05 to .40)
• Algorithm minimizes differences between the
  observed brightness temperatures and those
  generated using a forward radiative transfer
  model.
• Due to extensive radio frequency interference in
  the 6.9 GHZ channel, 10.7 and 18.7 GHz
  observations are used for soil moisture
  estimation.  

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Background and Observed Variables
q1
q2

• SHEELS state variables (x) include temperature
  and fractional water content in each of 14 layers
  
• 6 in the top 10 cm
• 6 root zone (up to 1.5m)
• 2 deep layers to 10m.

The observation (y) (retrieved soil moisture) is
the volumetric water content (cm3/cm3) near the
surface (exponentially weighted by depth) Mostly
top layer but must account for porosity to
convert from FWC to VWC Actually a retrieval or
estimate but in the context of data assimilation
its an observation.
q3
q4
q5
q6
q7
q8
q9
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Ensemble Kalman Filter in LIS

• The ensemble consists of N model state fields.
• The mean of the N ensemble states is used to
  define the state vector estimate.
• The spread of an ensemble of N model
  trajectories is used to estimate the error
  covariances. The full non-linear dynamic
  equations are used to propagate each ensemble
  member forward in time, thus determining the
  trajectories. This is in contrast to the
  traditional Kalman filter in which linearized
  model dynamics are used to propagate error
  covariances.
• When observations are available, each ensemble
  member is updated based on the difference between
  the observation and the model state, weighted by
  the Kalman gain (as in the EKF).
• Random error is added to the observation based on
  assumed noise characteristics this ensures that
  the variance of the updated ensemble matches the
  true estimation error covariances (Burgers et
  al., 1998, Mon. Wea. Rev.)
• Propagation of error covariance matrix is more
  stable than in the traditional Kalman filter,
  especially if there are strong non-linearities in
  the model.

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Domain
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Micronet Validation

• First validation attempt vs. ARS Micronet (Little
  Washita River, OK)
• Large bias and variability due to sampling error
  and soil properties
• Ran artificial experiments with 0.5x and 1.5x
  rain forcing, validated against Micronet and
  truth run.
• Large errors remain, but DA runs (dashed) tend to
  converge
• Square-wave error maybe due to day-night bias
  differences

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Bias Correction (CDF Matching)
AMSR-E Bias Correction
The dynamic range of AMSR-E observed soil
moisture is small relative to that of the
model. A correction (right) is applied to convert
the observation into a model-equivalent value. A
Cumulative Distribution Function (CDF)-matching
technique is used here. This is similar in
purpose to the bias corrections usually applied
to satellite observations in NWP models.
Simulations made without the proper correction
showed a pronounced dry bias.
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Landcover-dependent CDF Correction
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Impact of Land Use CDF CorrectionDifference in
fractional soil moisture immediately following
assimilation of AMSR-E data at 8 UTC on June 7,
2003 Land Use CDF minus Uniform CDF simulation.
The spatial pattern reflects the land use type
distribution and illustrates the impact of the
Land Use CDF correction on soil moisture data
assimilation.
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No Rain Experiment
22Z 24 Jun 2003 The data assimilation adds
soil water, particularly in the eastern part of
the domain and the Texas panhandle.
Truth Stage IV Precipitation Forcing
Control No Data Assimilation
Data Assimilation (Combined Bias Correction)
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False Rain Experiment
09Z 22 Jun 2003 The data assimilation is able
to reduce the water content from the false
rainfall in Kansas while increasing it in the
Texas panhandle.
Truth Stage IV Precipitation Forcing
Control No Data Assimilation
Data Assimilation (Combined Bias Correction)
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No Rain Experiment
Time series of top layer soil water in SE
Nebraska (point marked by diamond at left). The
3 DA runs are able to match the true run
closely throughout much of the experiment,
although they overestimate soil moisture from
about June 7-14.
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False Rain Experiment
Time series of top layer (1.6 cm) soil water
fraction from 5 runs (false rain scenario) in
Texas panhandle (100.5W, 35N). The DA run with
the combined bias correction (red line) shows
transitions that are less abrupt (reduced
amplitude) during data assimilation steps,
compared to the other DA runs (blue/green).
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Results (Statistics)
No Rain Run Control (No DA) Uniform BC Vegetation BC Combined BC
Bias -0.161 -0.042 -0.041 -0.042
Std. Dev. 0.128 0.130 0.129 0.130
RMS 0.206 0.137 0.136 0.137
Correlation (r2) 0.381 0.444 0.454 0.454
False Rain Run Control (No DA) Uniform BC Vegetation BC Combined BC
Bias -0.015 -0.013 -0.013 -0.014
Std. Dev. 0.171 0.149 0.148 0.148
RMS 0.172 0.150 0.149 0.149
Correlation (r2) 0.090 0.375 0.384 0.391
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Summary

• AMSR-E Soil Moisture Estimates assimilated into
  SHEELS LSM using EnKF
• Bias correction is necessary for good results.
• Must be regionally and seasonally appropriate.
• Landcover- and day/night-dependent corrections
  implemented.
• Day/night correction alleviates square wave
  pattern in biases
• With hiqh quality forcing data, validation vs.
  ground truth is difficult
• Variability of rainfall and soil properties
  within a FOV confound this.
• Could use anomaly correlations for verification
• DA improves modeled soil moisture in simulations
  with intentionally poor rain forcing
• Potentially of greatest use in areas without
  high-quality continuous rainfall data (radar,
  gauge networks).
• An advantage over microwave (polar orbiting)
  rainfall observations It can see the effects of
  rainfall after it happens (alleviates sampling
  issue)

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Possible Future Work

• Validation against ground stations by anomaly
  correlation
• Test impact on a coupled weather forecast model.
• Implement for SMOS and SMAP.
• AMSR-E .06 cm3/cm3
  accuracy
• SMOS (ESA, 2009) .04 cm3/cm3
• SMAP (NASA, 2014) .04 cm3/cm3

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1DVAR in MIRS
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Microwave Integrated Retrieval System (MIRS)

• NOAA STAR algorithm/software package
• 1DVAR physically-based retrieval algorithm based
  on OI theory
• Simultaneous retrieval of temperature, humidity,
  and hydrometeor profiles in EOF space
• Water vapor and hydrometeors are in logarithmic
  coordinates
• Assumes local linearity and gaussian pdf of state
  variable
• Applicable to any sensor combining imaging
  /sounding capabilities.
• Experimental products of cloud / precipitation
  liquid and ice have potential for refinement
  into contributions to GPM.
• Emissivity spectrum is part of the retrieved
  state vector enabling more direct response to
  precipitation over land.

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MIRS VariablesBackground3 EOFs
Graupel
Water Vapor
Cloud Liquid
Rain
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MIRS 1DVAR
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Intercomparison of AMSU and TRMM Rain Retrievals

• Retrievals from AMSU have consistently smaller
  Rain/Ice amounts compared to TMI
• Are these differences due to sensors or
  algorithms?
• Test whether improved first guess and
  background/covariance constraints can give more
  consistent results
• TRMM and GPM (will) have high resolution
  measurements but AMSUs are important for sampling

TS Lee (Sep 2, 2011)
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MIRS Experiments
Sep 2009 Study
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MIRS Results (Graupel and Rain)
W.Pac.
SE US
C. Africa

• More frequent large ice consistent with high
  lightning frequency over Africa.
• Strong convection, dry environment.

MIRS Graupel
MIRS Rain