Estimating Soil Moisture Profile Dynamics From NearSurface Soil

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: Garry Willgoose Co-Supervisor: Jetse Kalma

Importance of Soil Moisture · Meteorology n Evapotranspiration - partitioning of available energy into sensible and latent heat exchange · Hydrology n Rainfall Runoff - infiltration rate; water supply · Agriculture n n 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 Logger Soil Moisture Model (z) f [qs, D ( ), ( )] Soil Moisture Sensors

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 n n Simplified soil moisture model Simplified covariance estimation · Field applications n n One-dimensional Three-dimensional · Conclusions and Future direction

Literature Review · Regression Approach n Uses typical data and land use - location specific · Knowledge Based Approach n Uses a-priori knowledge on the hydrological behaviour of soils · Inversion Approach n Mainly applied to passive microwave · Water Balance Approach n 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 1 D Richards eq. Bernard et al. (1981), Prevot et al. (1984), Bruckler and Witono (1989) · Updated 1 D 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 n Use a knowledge-based approach Lapse rate; Hydraulic equilibrium; Root density; Field capacity; Residual soil moisture · Dynamic Phase (Water Balance Model) n Forecast soil moisture with meteorological data n Update soil moisture forecast with observations Direct insertion approach Dirichlet boundary condition Kalman filter approach

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

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

Active or Passive? · Passive n n Measures the naturally emitted radiation from the earth - Brightness Temperature Resolution - 10’s km 100 km (applicable to GCM’s) · Active n n n 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 3 mm · Radar observation depth 1/10 1/4 of the wavelength

Radar Observation Depth

Evol /Esur = ? · Addressed through error analysis of backscattering equation · 2% change in mc 0. 15 - 1 d. B, wet dry · Radar calibration 1 - 2 d. B · 1. 5 d. B 0. 17

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

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

Temperature Dependence Low Soil Moisture (5%) n 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 5 - 8 days Temperature >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 n n n 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 · Proposed VDF Infiltration Exfiltration

Model Comparison · Exfiltration (0. 5 cm/day) · Infiltration (10 mm/hr)

Kalman-Filter Update Every 5 Days

KF Modification for 3 D Modelling · Implicit Scheme 1 n+1 Xn+1 + 1 n+1 = 2 n Xn + 2 n · State Forecasting X n+1 n n =A X +U n n n+1 -1 n [ 2 ] n n+1 -1 n [ 2 – where A = [ 1 U = [ 1 ] ] · Covariance Forecasting n+1 n n n. T =A A +Q n+1 1 ]

KF Modification for 3 D Modelling · Covariance Forecast Auto-regressive smooth of 1 and 2 n+1 1 n = 1 + (1 – ) n+1 1 Estimate correlations from: = A AT where A = [ 1]-1 [ 2] Reduce to correlation matrix i, j = e where

Correlation Estimate

Modified Kalman-Filter Application

Field Application

Meteorological Station

1 D Model Calibration/Evaluation

1 D Profile Retrieval - 1/5 Days

3 D Model Calibration 3 D Model Evaluation

3 D 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 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 nearsurface soil moisture observations for applying observations to the entire profile - may alleviate the decoupling problem