Department of Civil, Surveying and Environmental Engineering The University of Newcastle AUSTRALIA Supervisor:Co-Supervisor: Supervisor:Co-Supervisor: Garry WillgooseJetse Kalma Garry WillgooseJetse Kalma Estimating Soil Moisture Profile Dynamics From Near-Surface Soil Moisture Measurements and Standard Meteorological Data Jeffrey Walker

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

Background to Soil Moisture Remote Sensing Satellite Surface Soil Moisture Soil Moisture Sensors Logger Soil Moisture Model [q, D ( ), ( )]   f     s (z)

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

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

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

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)

Soil Moisture Profile Estimation Algorithm  Initialisation Phase Use a knowledge-based approach â 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 â Direct insertion approach â Dirichlet boundary condition â Kalman filter approach

Data Assimilation  Direct-Insertion  Kalman-Filtering Observation Depth

The (Extended) Kalman-Filter  Forecasting Equations States: X n+1 = A n X n + U n Covariances:  n+1 = A n  n A n T + Q  Observation equation Z = H X + V

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

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

Radar Observation Depth

E vol /E sur = ?  Addressed through error analysis of backscattering equation  2% change in mc  dB, wet  dry  Radar calibration  dB  1.5 dB  0.17

Application of the Models vv polarisation hh polarisation rms = 25 mm correlation length = 60 mm incidence angle = 23 o moisture content  9% v/v

1D Desktop Study  1D soil moisture and heat transfer  Moisture Equation Matric Head form of Richard’s eq. Assumes: â Isothermal conditions (decoupled from temperature) â Vapour flux is negligible  Temperature Equation Function of soil moisture Assumes: â Effect from differential heat of wetting is negligible â Effect from vapour flux is negligible

Temperature Dependence Low Soil Moisture (5%) Microwave remote sensing is a function of dielectric constant High Soil Moisture (40%)

Synthetic Data Initial conditions Boundary conditions

Direct-Insertion Every Hour

Kalman-Filter Update Every Hour

Kalman-Filter Update Every 5 Days

Quasi Profile Observations

Kalman-Filter Update Every 5 Days

Volumetric Moisture Transformation

Summary of Results  Continuous Dirichlet boundary condition  Moisture daysTemperature >20 days  10 cm update depth  Required Dirichlet boundary condition for 1 hour  Required Dirichlet boundary condition for 24 hours ] Moisture Transformation

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  VDF+K where VDF = Vertical Distribution Factor

Vertical Distribution Factor  Special cases Uniform Infiltration Exfiltration  Proposed VDF

Model Comparison  Exfiltration (0.5 cm/day)  Infiltration (10 mm/hr)

Kalman-Filter Update Every 5 Days

KF Modification for 3D Modelling  Implicit Scheme  1 n+1 X n+1 +  1 n+1 =  2 n X n +  2 n  State Forecasting X n+1 = A n X n + U n where A n = [  1 n+1 ] -1 [  2 n ] U n = [  1 n+1 ] -1 [  2 n –  1 n+1 ]  Covariance Forecasting  n+1 = A n  n A n T + Q

KF Modification for 3D Modelling  Covariance Forecast Auto-regressive smooth of  1 and  2  1 n+1 =   1 n + (1 –  )  1 n+1 Estimate correlations from:  = A  A T where A = [  1 ] -1 [  2 ] Reduce  to correlation matrix  i,j = e  where

Correlation Estimate

Modified Kalman-Filter Application

Field Application

Meteorological Station

1D Model Calibration/Evaluation

1D Profile Retrieval - 1/5 Days

3D Model Calibration 3D Model Evaluation

3D Profile Retrieval  All observations  Single Observation

Summary of Results

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

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

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