Assimilating remotely sensed snow observations into a macroscale hydrologic model

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Assimilating remotely sensed snow observations
into a macroscale hydrologic model

• Konstantinos M. Andreadis
• MSE Defense
• Advisor Dennis P. Lettenmaier

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Overview

• Background
• Methods
• Implementation
• Results and Discussion
• Conclusions

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Importance of Snow

• Snow plays key role in hydrologic cycle
• As much as 90 of annual streamflow is snowmelt
  driven in the western US
• In situ observations are unable to capture
  temporal and spatial variability of snow
  processes
• Large-scale observation strategies focus on
  remote sensing

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Remote Sensing of Snow Cover

• Contrast in reflectance between snow-covered and
  snow-free areas
• Visible wavelength sensors have been used
  operationally since 1966 (NOAA POES and GOES
  satellites)

• Cloud-free conditions are required
• Insufficient spatial and spectral resolution
• Lack of any information about water storage

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Remote Sensing of SWE

• Depth and water equivalent directly affect
  microwave emissions from snow surfaces
• Passive microwave sensors have been used to map
  SWE globally (SSMR and SSM/I)

• Coarse spatial resolution (25 km)
• Changing snowpack conditions affect microwave
  signal
• Wet snow prohibits retrieval of any parameter

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Model-based Approaches

• Additional information about snow properties may
  be gained from land surface hydrologic models

• Uncertainties in forcing data and model
  parameters
• Nonlinearities and scaling issues in processes
  modeled

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Motivation

• Data assimilation offers the framework to
• optimally combine models and remote sensing
  observations
• account for the limitations of both

• Availability of improved remotely sensed data
  products (MODIS, AMSR-E) increases the potential
  for snow data assimilation

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Study Objective

• Evaluate the performance of a system that
  assimilates MODIS Snow Cover Extent (SCE) and
  AMSR-E Snow Water Equivalent (SWE) data into the
  Variable Infiltration Capacity (VIC) model, using
  an ensemble Kalman Filter (enKF)

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Data Assimilation Background

• Successful applications in meteorology and
  oceanography
• Data assimilation techniques
• Variational Assimilation (3-D or 4-D)
• Kalman filter variants

• Soil moisture estimation by assimilating
  brightness temperature observations (most
  applications)
• Snow data assimilation (few applications)
• Direct insertion and statistical interpolation
• Extended Kalman filter (Sun et al. 2004)

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The Kalman Filter
System model
Propagation of error covariance information is
computationally expensive
Observation
yt-1
Time
tk
tk1
tk-1
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The Ensemble Kalman Filter
Propagation Step
Propagation Step
Analysis Step
yfi,t1
yi,t-1
Time
tk
tk1
tk-1
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VIC Model Description

• Solves energy and water balance over grid cells
• Subgrid variability in soil moisture,
  precipitation, topography and vegetation
• Baseflow is a nonlinear function
• Separate scheme for routing streamflow

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VIC Snow Model

• Two layer energy and mass balance model
• Surface layer simulates energy exchanges with the
  atmosphere
• Pack layer acts as storage and simulates deeper
  snowpacks

• Snow interception and densification
• Snow areal extent is represented indirectly

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Experimental Design

• VIC simulation without assimilation designated
  Prior estimate
• Assimilation of MODIS SCE data for October 1999
  to June 2003
• Assimilation of AMSR-E SWE data for October 2003
  to April 2004

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Snake River Basin

• Major tributary of the Columbia River
• Snow accumulation and ablation exert strong
  controls over streamflow

• Mean annual precipitation ranges from 350 to 1500
  mm
• High streamflows occur during spring snowmelt

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Model Implementation

• VIC run in water balance mode, at a spatial
  resolution of 1/8o and daily time step
• Meteorological inputs include daily
  precipitation, maximum and minimum air
  temperature and wind speed
• VIC solves each grid cell separately model
  state vector dimension is relatively small
  can be solved for in smaller ensemble space
  25 ensemble members
• Ensemble is generated by treating forcing
  variables as stochastic terms

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Ensemble Generation

• Log-normally precipitation values are generated

• Minimum and maximum daily air temperature are
  perturbed with Gaussian random fields

• Spatially correlated Gaussian random fields with
  exponential correlation function

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MODIS Snow Cover Data

• MODerate resolution Imaging Spectroradiometer
• Snow mapping based on two indices (NDSI and NDVI)
  and cloud/thermal mask
• Product MD10A1 available since February 18 2000
  at a 500 m spatial resolution
• Validation studies (Maurer et al. 2003, Cline and
  Barnett 2003) have found misclassification errors
  of 10 to 20
• Image registering with DEM provided fractional
  snow coverage map of model elevation bands
• Cloud threshold of 20

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Observation Operator

• We need a functional that relates SWE to SCE

Snow Depletion Curve (SDC)

• No linearization necessary
• Observation uncertainties influenced by errors in
  both MODIS retrievals and the observation
  operator
• We chose a normally distributed random error with
  zero mean and 10 std

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Snow Depletion Curve

• Developed by Anderson 1973, currently used at
  NWS

Adc snow depletion functional W areal SWE Wmax
max seasonal SWE SI 100 snow coverage
preset SWE value
Luce et al. 1999
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SDC Parameter Estimation

• Difficult to obtain direct observations of both
  SWE and SCE
• We used simulated open-loop SWE and MODIS data
• Separate SDC developed for 9 different classes.
  Based on elevation and land cover
• Parameter SI estimated by examining SCE time
  series
• Shape parameters estimated by fitting gamma
  distributions

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Validation Approach

• Surface observations are the only practical
  option for independent evaluation
• SNOTEL station network (NRCS)
• Daily measurements of SWE
• Located at relatively high elevations
• NOAA COOP station network
• Daily observations of snow depth
• Tend to be located at lower elevations

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Scale Issues

• Comparing point to areal estimates can be
  problematic
• One option is aggregating the data over larger
  temporal and spatial scales (e.g. seasonal or
  spatial averages)

• Express SWE values as percentiles of their
  respective climatologies
• 20 year record (1983-2003)

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MODIS Data Assimilation Results
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Snow Cover Extent

• Comparison of percentage agreement of SCE between
  MODIS and simulations
• Days included based on a 50 cloud threshold

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26 February 2001
6 March 2001
22 March 2001
5 April 2001
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Snow Cover Extent

• Comparison with station observations
• Stations having greater than 200 m elevation
  difference with the corresponding model grid,
  were screened (124 stations left, from 257
  originally)
• Percentage of pixels classified correctly over
  the entire simulation period (10/1999-6/2003)

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Snow Water Equivalent

• Mean peak seasonal SWE

Filter estimated peak SWE values are closer to
station values for 58 out of 66 available stations
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• SWE Percentile Relative Mean Squared Error (RMSE)
  for all available stations for each winter season
• enKF improved estimates for about half the
  stations
• However, performance was worse for the rest of
  the stations

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Snow Water Equivalent

• SWE mean differences from SNOTEL with time

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Snow Water Equivalent

• SWE mean RMSE variability with elevation and time

• Elevation zones are the same as those for the SDC
• March 1st was taken as the separating date
  between periods

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Snow Water Equivalent

• SWE and SCE time series at West Yellowstone
  SNOTEL station (2008 m, VIC RMSE 0.18 and enKF
  RMSE 0.25)

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Snow Water Equivalent

• SWE and SCE time series at Beaver Reservoir
  SNOTEL station (1545 m, VIC RMSE 0.25 and enKF
  RMSE 0.19)

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AMSR-E Data Assimilation Results
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AMSR-E SWE Data

• Advanced Microwave Scanning Radiometer
• Estimates SWE using a simple linear relationship
  with brightness temperature (37 GHz and 19 GHz)
• Official SWE dataset available since February
  2004
• We extended it, by using the same algorithm and
  brightness temperature datasets
• Preliminary validation studies showed RMSE errors
  of 100 mm, especially for deeper snowpacks
• Here, we chose a Gaussian random variable with
  zero mean and 15 std

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Snow Water Equivalent

• SWE Percentile RMSE as a function of maximum
  SNOTE SWE

enKF RMSE was improved for 31 out of 66
available stations
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Summary of Results

• The enKF is a flexible and computationally
  attractive solution
• Snow covered area was successfully updated by the
  filter
• SWE updated in consistent fashion
• Peak seasonal SWE estimation was improved
• MODIS assimilation improved RMSE during snowmelt
  period, but performance was degraded during snow
  accumulation
• Preliminary results from assimilating AMSR-E SWE
  data were consistent with other validation
  studies

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Limitations

• More accurate observation operator is required
  (e.g. use of independent SWE data to develop SDC)
• Non-continuity of SCE (0 to 1) Assimilation has
  no effect during full snow coverage
• Modeling of both background and observation
  errors
• Water balance errors imposed by temperature
  biases

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Future Research

• Assimilation of both MODIS and AMSR-E data
• Model bias correction using the enKF
• Use of the enKF for initialization of hydrologic
  forecasting schemes

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Questions?