An algorithm is developed to solve the inverse problem for the retrieval of the soil moisture and temperature profiles based on remotely sensed observations of multispectral irradiance. A model of coherent wave radiative transfer and a model of coupled heat and moisture diffusion in porous media are combined in order to estimate the liquid volumetric water content and temperature profiles in a soil column using low-frequency passive microwave and infrared emitted radiation observations and without the use of empirical relations. The central purpose of this mainly theoretical paper is to pose the inverse problem and present the physics-based algorithm as the solution. The algorithm is tested on a basic synthetic example in order to ascertain that the retrieval is feasible. Additional work in the future is necessary and planned in order to test the algorithm with field observations, extend it to include vegetation, and refine it for detail in the specification of heterogeneity in soil types and boundary conditions. >

Solving the inverse problem for soil moisture and temperature profiles by sequential assimilation of multifrequency remotely sensed observations

A computer model of the upper soil and lower atmosphere boundary layer has been developed for use with remotely sensed data. It includes both energy and moisture balances, and it uses a predictor/corrector integrator with an automatically changing time step; these two components make the model both stable and efficient. It is driven by surface heat and moisture fluxes computed from standard meteorological data. Remotely sensed surface temperature and soil moisture can be compared to model estimates for calibration. The model has been tested using 44 hours of data from a bare soil site. Using daily maximum surface temperatures for calibration, estimated hourly surface temperatures agreed with measurements to better than 1 K. The results are insensitive to the soil heat capacity and most sensitive to the thermal conductivity and aerodynamic roughness. By varying these within physically reasonable limits, bounds on daily evaporation of 3.2 mm and 3.8 mm were estimated.

A soil and atmospheric boundary layer model for evapotranspiration and soil moisture studies

The significance of the soil surface moisture (θs) with respect to daily bare soil evaporation (Ed) is analyzed using data from numerical simulations. This was performed by running a mechanistic model of heat and water flows in the soil. The mechanistic model was calibrated and validated on three different soils with contrasted hydraulic properties. Results show that θs does not allow an accurate estimate of the ratio of Ed to the daily potential evaporation (Epd). Added variables such as Epd and the wind velocity are necessary to improve the prediction of the Ed/Epd ratio. In a second attempt, a simple model of Ed is proposed. It is based on three empirical parameters and required the measurement of θs obtained at midday, Epd, and the daily wind velocity. For a given soil, a single set of the three parameters allows an accurate estimate of Ed under soil moisture and climatic conditions encountered through the year in temperate areas.

Significance of soil surface moisture with respect to daily bare soil evaporation

A freeze indicator (FI), based on a low 37-GHz radiobrightness and a low 10.7, 18, and 37-GHz radiobrightness spectral gradient, has been used to classify frozen surfaces in the northern Great Plains. By modeling the radiometer beampatterns as Gaussian, freeze/thaw boundaries can be located at the (fine) resolution of the 37-GHz channel. The performance of the freeze indicator, and subsequent boundary location estimate, depends on the accuracy of the boundary decision criteria. It is shown that decision criteria based on clustering and unsupervised classification yield good performance. A simple algorithm for registering coarse-resolution FI boundaries to equivalent boundaries in fine-resolution 37-GHz radiobrightness images is also presented. >

Radiobrightness decision criteria for freeze/thaw boundaries

Microwave brightness temperature measurements were made over three different bare soils at frequencies of 5 GHz (X = 6 cm) and 1.67 GHz (X = 18 cm) to compare differences in penetration depth according to texture, soil moisture, and wavelength. The soil plots were wetted, and circularly polarized microwave measurements were made during the dry-down cycle. Soil profile temperature and profile moisture content were monitored continuously for the duration of the experiment. Laboratory analyses of soil physical properties such as texture and bulk density were conducted to aid theoretical calculations of the soil dielectric constants. Laboratory measurements of the soil dielectric constants were also made. Two commonly used soil dielectric models were compared. Theoretical values of soil dielectric constant were calculated with the Dobson model and the Wang-Schmugge model, and both compared reasonably well with laboratory measurements and also to values reported in the literature. Calculated soil emissivities derived from the field measurements also compared well with emissivities calculated from both the modeled dielectrics and those measured in the laboratory. Emissivities were compared with the average soil moisture for surface profiles of varying thickness. It was found that the observed effective penetration depth appeared to exceed the theoretically defined values.

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Comparison of soil moisture penetration depths for several bare soils at two microwave frequencies and implications for remote sensing

This simulation study evaluates the response of a 21-cm radiometer, measuring the radiation emitted by a bare soil, to varying accumulations of rain. We show that correlations between the decrease in emissivity after a rain storm and the total accumulation depend strongly on the physical characteristics of the soil which affect its capacity to hold water. These are primarily soil texture and pre-rain soil moisture. A method is also discussed which would use the numerical models with remotely sensed microwave brightness and surface physical temperatures, along with conventional weather data, to estimate the total accumulation.

Correlating Rainfall with Remotely Sensed Microwave Radiation Using Physically Based Models

A computer program that simulates the flow of heat and moisture in soils is described The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator Simulations of heat and moisture flow under actual field conditions were also performed Ground truth data were used for the boundary conditions and soil transport properties The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved

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P. J. Camillo

Papers

Correlating Rainfall with Remotely Sensed Microwave Radiation Using Physically Based Models

A computer program for the simulation of heat and moisture flow in soils