Estimating Soil Moisture Profile Dynamics From NearSurface Soil Moisture Measurements and Standard M

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Estimating Soil Moisture Profile Dynamics From
Near-Surface Soil Moisture Measurements and
Standard Meteorological Data

• Jeffrey Walker

Department of Civil, Surveying and Environmental
Engineering The University of Newcastle AUSTRALIA
Supervisor Co-Supervisor
Garry Willgoose Jetse Kalma
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Importance of Soil Moisture

• Meteorology
• Evapotranspiration - partitioning of available
  energy into sensible and latent heat exchange
• Hydrology
• Rainfall Runoff - infiltration rate water supply
• Agriculture
• Crop Yield - pre-planting moisture irrigation
  scheduling insects diseases de-nitrification
• Sediment Transport - runoff producing zones
• Climate Studies

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Background to Soil Moisture
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Research Objective

• Develop a methodology for making improved
  estimates of the soil moisture profile dynamics
• Efforts focussed on
• Identification of an appropriate soil moisture
  profile estimation algorithm
• Remote Sensing for surface soil moisture -
  volume scattering
• Observation depth f(frequency, moisture,
  look angle, polarisation)
• Assessment of assimilation techniques
• Importance of increased observation depth
• Effect of satellite repeat time
• Computational efficiency - moisture
  model/assimilation
• Collection of an appropriate data set for
  algorithm evaluation
• Proving the usefulness of near-surface soil
  moisture data

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Seminar Outline

• Identification of an appropriate methodology for
  estimation soil moisture profile dynamics
• Near-surface soil moisture measurement
• One-dimensional desktop study
• Model development
• Simplified soil moisture model
• Simplified covariance estimation
• Field applications
• One-dimensional
• Three-dimensional
• Conclusions and Future direction

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Literature Review

• Regression Approach
• Uses typical data and land use - location
  specific
• Knowledge Based Approach
• Uses a-priori knowledge on the hydrological
  behaviour of soils
• Inversion Approach
• Mainly applied to passive microwave
• Water Balance Approach
• Uses a water balance model with surface
  observations as input

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Water Balance Approach

• Updated 2-layer model by direct insertion of
  observations - Jackson et al. (1981), Ottle and
  Vidal-Madjar (1994)
• Fixed head boundary condition on 1D Richards eq.
  - Bernard et al. (1981), Prevot et al. (1984),
  Bruckler and Witono (1989)
• Updated 1D Richards equation with Kalman filter -
  Entekhabi et al. (1994)
• Updated 2-layer basin average model with Kalman
  filter - Georgakakos and Baumer (1996)
• Updated 3-layer TOPLATS model with direct
  insertion statistical correction Newtonian
  nudging (Kalman filter) and statistical
  interpolation - Houser et al. (1998)

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Soil Moisture Profile Estimation Algorithm

• Initialisation Phase
• Use a knowledge-based approach
• Lapse rate Hydraulic equilibrium Root density
  Field capacity Residual soil moisture
• Dynamic Phase (Water Balance Model)
• Forecast soil moisture with meteorological data
• Update soil moisture forecast with observations
• Direct insertion approach
• Dirichlet boundary condition
• Kalman filter approach

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Data Assimilation

• Direct-Insertion

• Kalman-Filtering

Observation Depth
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The (Extended) Kalman-Filter

• Forecasting Equations
• States Xn1 An Xn Un
• Covariances ?n1 An ? n AnT Q
• Observation equation
• Z H X V

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Active or Passive?

• Passive
• Measures the naturally emitted radiation from the
  earth - Brightness Temperature
• Resolution - 10s km ? 100 km (applicable to
  GCMs)
• Active
• Sends out a signal and measures the return -
  Backscattering Coefficient
• More confused by roughness, topography and
  vegetation
• Resolution - 10s m (applicable to partial area
  hydrology and agriculture)

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The Modified IEM

• Modified reflectivities
• Dielectric profile
• m 12 gives varying profile to depth 3mm
• Radar observation depth 1/10 ? 1/4 of the
  wavelength

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Radar Observation Depth
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Evol /Esur ?

• Addressed through error analysis of
  backscattering equation
• 2 change in mc ? 0.15 - 1 dB, wet ? dry
• Radar calibration ? 1 - 2 dB
• 1.5 dB ? 0.17

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Application of the Models
rms 25 mm correlation length 60 mm incidence
angle 23o moisture content ? 9 v/v
vv polarisation
hh polarisation
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1D Desktop Study

• 1D soil moisture and heat transfer

• Moisture Equation
• Matric Head form of Richards eq.
• Assumes
• Isothermal conditions (decoupled from
  temperature)
• Vapour flux is negligible
• Temperature Equation
• Function of soil moisture
• Assumes
• Effect from differential heat of wetting is
  negligible
• Effect from vapour flux is negligible

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Temperature Dependence
Low Soil Moisture (5)

• Microwave remote sensing is a function of
  dielectric constant
• High Soil Moisture (40)

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Synthetic Data
Initial conditions Boundary conditions
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Direct-Insertion Every Hour

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Kalman-Filter Update Every Hour

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Kalman-Filter Update Every 5 Days
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Quasi Profile Observations

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Kalman-Filter Update Every 5 Days

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Volumetric Moisture Transformation
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Summary of Results

• Continuous Dirichlet boundary condition
• Moisture 5 - 8 days Temperature gt20 days

• 10 cm update depth
• Required Dirichlet boundary condition for 1 hour
• Required Dirichlet boundary condition for 24
  hours
• Moisture Transformation

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A Simplified Moisture Model

• Computationally efficient ?-based model
• Capillary rise during drying events
• Gravity drainage during wetting events
• Lateral redistribution
• No assumption of water table
• Amenable to the Kalman-filter
• Buckingham Darcy Equation
• q K???K
• Approximate Buckingham Darcy Equation
• q K?VDFK
• where VDF Vertical Distribution Factor

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Vertical Distribution Factor

• Special cases
• Uniform Infiltration Exfiltration
• Proposed VDF

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Model Comparison

• Exfiltration (0.5 cm/day)
• Infiltration (10 mm/hr)

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Kalman-Filter Update Every 5 Days
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KF Modification for 3D Modelling

• Implicit Scheme
• ?1n1 Xn1 ?1n1 ?2n Xn ?2n
• State Forecasting
• Xn1 An Xn Un
• where An ?1n1-1 ?2n
• Un ?1n1-1 ?2n ?1n1
• Covariance Forecasting
• ?n1 An ? n AnT Q

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KF Modification for 3D Modelling

• Covariance Forecast
• Auto-regressive smooth of ?1 and ?2
• ?1n1 ? ?1n (1 ? ) ?1n1
• Estimate correlations from
• ? A?AT where A ?1-1 ?2
• Reduce ? to correlation matrix
• ?i,j e? where

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Correlation Estimate
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Modified Kalman-Filter Application
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Field Application
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Meteorological Station
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1D Model Calibration/Evaluation
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1D Profile Retrieval - 1/5 Days
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3D Model Calibration
3D Model Evaluation
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3D Profile Retrieval

• All observations
• Single Observation

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Summary of Results
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Conclusions

• Radar observation depth model has been developed
  which gives results comparable to those suggested
  in literature
• Modified IEM backscattering model has been
  developed to infer the soil moisture profile over
  the observation depth
• Computationally efficient spatially distributed
  soil moisture forecasting model has been
  developed
• Computationally efficient method for forecasting
  of the model covariances has been developed

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Conclusions

• Require an assimilation scheme with the
  characteristics of the Kalman-filter (ie. a
  scheme which can potentially alter the entire
  profile)
• Require as linear forecasting model as possible
  to ensure stable updating with the Kalman-filter
  (ie. ?-based model rather than a ?-based model)
• Updating of model is only as good as the models
  representation of the soil physics
• Usefulness of near-surface soil moisture
  observations for improving the soil moisture
  estimation has been verified

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Future Direction

• Addition of a root sink term to the simplified
  soil moisture forecasting model
• Improved specification of the forecast system
  state variances
• Application of the soil moisture profile
  estimation algorithm with remote sensing
  observations, published soils and elevation data,
  and routinely collected met data
• Use point measurements to interpret the
  near-surface soil moisture observations for
  applying observations to the entire profile - may
  alleviate the decoupling problem