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SPECIAL SECTION: HYDROGEOPHYSICS

Topsoil Structure Influencing Soil Water Retrieval by Microwave Radiometry

^a Institute of Terrestrial Ecology, ETH Zurich, Grabenstrasse 11a, 8952 Schlieren, Switzerland
^b Institute of Terrestrial Ecology, ETH Zurich, Grabenstrasse 11a, 8952 Schlieren, Switzerland
^c EAWAG, Ueberlandstrasse 13, 8600 Duebendorf, Switzerland
^d Centre d'Etudes Spatiales et de la Biosphere (CESBIO) 18 av. Edouard Belin, bpi 2801, 31401 Toulouse Cedex 4, France
^e Institute of Applied Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
^* Corresponding author (mike.schwank{at}env.ethz.ch)

Received 6 June 2004.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS CONCLUSIONS REFERENCES

 
Many remote sensing applications, including those of future space missions, require accurate knowledge of the influence of topsoil structure on the water content as measured using L-band radiometry. We report on field-measured L-band (1.4 GHz) microwave emission from a bare soil. Of special interest in this work is the procedure used to transform remotely sensed data to soil water content and its comparability with time domain reflectometer (TDR) in situ measurements. Surface roughness of the soil was characterized on a millimeter scale using an optical measurement technique. Different models for interpreting the microwave signals in terms of the water content were investigated. The agreement between in situ water contents and surface water contents estimated with radiometry data using the Fresnel equation was found to be poor. A coherent layer model, with and without considering roughness effects, was tested to compare radiometrically measured and modeled soil reflectivities. The correspondence remained unsatisfactory, even when we considered a dielectric gradient fitted to the TDR profiles and surface roughness represented by a scattering model. We developed a new air-to-soil transition model, which includes dielectric mixing effects due to small-scale surface structures. This model considerably improved agreement between measured and modeled results. We conclude that small-scale structures of the topsoil cannot be neglected in interpreting L-band measurements.

Abbreviations: DSM, digital surface model • TDR, time-domain reflectometer

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS CONCLUSIONS REFERENCES

 
SOIL WATER CONTENT is a key variable for estimating water and energy fluxes at the earth surface. It strongly controls infiltration processes and therefore the hydrologic fate of precipitation reaching the soil surface. The water content is also a critical factor determining the amount of actual evaporation, thus affecting also the feedback loop from soil to atmosphere. Because of its importance to many hydrological questions, considerable effort has gone into the development of measurement techniques to determine the soil water content at larger scales (Kerr et al., 2001). Passive microwave remote sensing is one of the most promising approaches (Njoku and Kong, 1977; Schmugge, 1985; Jackson, 1993) since (i) the atmosphere is almost transparent at microwave frequencies, which allows all-weather measurements; (ii) microwave radiation penetrates plant canopies; and (iii) the measurements are independent of solar radiation, which enables one to make day and night observations.

Remote sensing makes use of electromagnetic energy that is reflected and emitted by the earth's surface. A microwave radiometer measures the emission from the land surface at wavelengths ranging from about 1 to 30 cm. The observed radiation is proportional to the thermodynamic temperature of the surface and the emissivity (Rayleigh-Jeans approximation of Planck's Law). Microwave emissivity strongly depends on the water content because of the large contrast between the dielectric constant of water (about 80 at 1.4 GHz) and dry soil (3–5). L-band measurements (1.4 GHz, = 21 cm) are most suitable for estimating soil water content, mainly because they have a rather deep penetration depth compared with measurements at shorter wavelengths (Burke et al., 1979; Jackson and Schmugge, 1989) and because they are less influenced by vegetation cover. However, L-band measurements are still restricted to the topsoil (Jackson, 1993). Microwave radiometry is an indirect method of measuring the surface water content. Several steps are necessary to convert the measured signal into water content. This multistep procedure and the relevant model assumptions are discussed below.

Several large-scale experiments (on the order of one to several hectares or square kilometers) have been performed to study the microwave emission from natural soils (Schmugge et al., 1992; Jackson et al., 1995, 1999). Due to spatial variability of the calibration measurements, water content measurements in the footprint area are difficult to validate at such scales. The experimental data used in our study were obtained at the plot scale. While this is not a typical scale for remote sensing applications, it does allow for more reliable ground truth data. This is an important prerequisite for testing the assumptions of various interpretation approaches. The most common evaluation procedure is the use of a coherent model based on brightness temperatures normalized by the topsoil temperature and an empirical correction of the surface roughness according to models such as those proposed by (Choudhury et al., 1979) or (Wigneron et al., 2001).

We investigate the influence of the model choice on the estimated water content based on radiometer data. We discuss the comparability of such estimates with those measured in situ using TDR probes. Based on experimental evidence, we develop a new model that considers the influence of small scale roughness on the L-band signal.

On lateral scales smaller than a certain fraction of one wavelength (typically one-half), the radiative electromagnetic fields cannot follow the fine structure of the medium (which is also the reason for the cut off of wave propagation in wave guides whose width is less than half of one wavelength). Electrostatic near fields have to adapt locally to the medium to fulfill the boundary conditions. However, these fields do not radiate. They only influence the manner of propagation, and are best taken into account by means of an effective dielectric constant. This issue is the main ingredient of dielectric mixing models such as Eq. [10] to be discussed later, and the motivation for developing the new model.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS CONCLUSIONS REFERENCES

 
The database we used consists of radiometric measurements conducted during a field experiment in summer 2002. In this section we briefly describe the measurement techniques. A more detailed description of the experiment and instruments was reported in Schneeberger et al. (2004) and Mätzler et al. (2003).

Remote Sensing System
We used a Dicke radiometer (ELBARA) operating at L-band (1.4 GHz). The radiometer was equipped with a dual-polarized conical horn antenna with a 3-dB beamwidth of 12°, and symmetrical and identical beams. For sensing the emitted electromagnetic radiation of the site, the center of gravity of the radiometer was mounted 6.7 m above the soil surface on a tower directed at an observation angle of = 55° relative to the vertical direction. This setup resulted in an elliptic footprint of approximately 9 x 8 m².

The radiometer was calibrated with internal hot and cold loads (at temperatures T_hot = 338 K and T_cold = 278 K) according to

[1]

with

where T_B^i,p is the brightness temperature for polarization p (= vertical or horizontal) detected on channel i (= 1 or 2); uⁱ_hot and uⁱ_cold are the measured calibration voltages corresponding to the internal calibration targets, and U^i,p is the measured voltage when the radiometer is pointed onto the scene of observation. The calibration function itself is system specific and has to be defined for each radiometer. In this experiment, the calibration using the internal targets at temperatures T_hot and T_cold was performed before each measurement. Sky brightness temperature was additionally measured periodically to check the stability of the remote sensing system.

In Situ Soil Water Content and Temperature
Soil water contents were measured in situ with horizontally installed two-rod TDR probes. These probes and soil temperature sensors were placed horizontally at five depths (2, 7, 15, 25, and 45 cm) in three replicates along the main target area of the L-band radiometer. The reliability of the TDR measurements was tested by taking soil cores to determine the water content gravimetrically at depths of 0 to 3 and 3 to 10 cm. This sampling scheme was repeated 15 times during the 48 d of the experiment. The linear correlation coefficient between the TDR measurements and the gravimetric soil water content was 0.94, which indicates good reliability of the TDR measurements.

Measuring Soil Surface Roughness
To map the microrelief, the soil surface was photographed and the images were photogrammetrically interpreted (Schneeberger and Willneff, 2003). The photographs were taken randomly at different locations within the footprint area. A digital surface model (DSM) was calculated using the commercial software package SOCET SET (LH Systems, Leica Geosystems GIS & Mapping, Atlanta, GA). Four 30 by 30 cm² images were taken with a still video camera Nikon Coolpix 990 and used for generating the DSM. To facilitate simultaneous adjustment, a common reference system was defined, using an aluminum frame with reference marks. The marks with coded targets allow automated orientation and calibration of the camera and the generation to corrected images, which were imported into a digital photogrammetric workstation for generating the DSM. This procedure allows quick and precise sampling of elevation data. The procedure permits the surface to be defined not only in terms of distinct deviation transects, but also by a complete three-dimensional reproduction at a resolution of 1 mm (Fig. 1) .

View larger version (92K): [in this window] [in a new window]   Fig. 1. Photograph of the soil surface with the reference frame (left) and derived digital surface model (DSM) (right). Bright gray values indicate high elevations, and dark values low elevations.

	THEORY

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS CONCLUSIONS REFERENCES

View larger version (28K): [in this window] [in a new window]   Fig. 2. Schematic diagram of water content estimation from a passive microwave signal. State variables are shown within rectangle frames. Several models (elliptic frames) used to evaluate the radiometric signal. Model references are given in the bibliography.

[2]

where T_soil is the thermodynamic temperature of the soil and T_sky the radiation temperature of the sky background. Assuming that the observed scene is in thermodynamic equilibrium, the emissivity E is related to the soil reflectivity R by Kirchhoff's Law, R = 1 – E.

As was shown by Delahaye et al. (2002), the stable sky background temperatures T_sky measured with a radiometer pointing away from the Milky Way is expected to be about 6 K. Therefore, the last term of Eq. [2] can be neglected, since the background temperature reflected by the soil surface will contribute little to T_B.

For accurate calculation of the emissivity, the soil temperature profile T(z) should be integrated over the temperature sensing depth. According to Ulaby et al. (1986) the sensing depth is of the order of 20 to 40 cm at 1 GHz, depending on the water content of the soil. Mathematically the resulting effective temperature T_soil is expressed as follows (Chanzy et al., 1997):

[3]

in which

where is the radiometric observation angle and B(z) the total attenuation from depth z to the soil surface. The attenuation coefficient can be approximated by

[4]

where is the wavelength and '(z) and ''(z) are the real and imaginary parts of the soil dielectric constant. Choudhury et al. (1982) proved the following approximation:

[5]

where T_2cm and T_45cm are the soil temperatures measured at the 2- and 45-cm depth, respectively, and C is a fitting parameter, which we assumed to be 0.5 in our experiment (Schneeberger et al., 2004). In this study we use approximation Eq. [5] to calculate the effective soil temperature T_soil. The resulting relative error of the emissivity E = T_B/T_soil due to this approximation is minor and the consequences for the radiometrically determined soil water content are therefore negligible. However, using the approximation given by Eq. [5] leads to an underestimation of the temporal dynamics of T_soil and thus to an overestimation of the daily variations of the radiometrically determined soil reflectivities R_radio.

In the simplest model, the soil reflectivity R is a function of the angle of observation , and polarization h (horizontal) or v (vertical). The reflectivity is related to the dielectric constant ^soil by the Fresnel equations (Ulaby et al., 1981):

[6]

[7]

These equations are only valid for a homogeneous soil with a smooth surface. These assumptions are hardly ever met under natural conditions. The models described in the following section account for the heterogeneities in the surface layer.

Converting dielectric constant into water content requires the use of a dielectric mixing model (Wang and Schmugge, 1980; Dobson et al., 1985; Roth et al., 1990). These models require texture and porosity as additional inputs. The frequently used mixing formula of Topp et al. (1980) is an empirical relationship between the dielectric constant of the soil and its water content, which depends also on soil temperature. However, Ferré et al. (1996) showed that this relation is in accordance with the CRIM mixing model. Here we used the model of Wang and Schmugge, (1980). The dielectric constant of water was corrected for temperature effects according to Cole and Cole (1941).

As already mentioned, we intend to compare water contents measured in situ with remotely sensed data. Since soil reflectivity is strongly related to water content and less influenced by the temperature profile, we decided to perform the comparison between remote sensing data and the in situ data by means of soil reflectivity. Therefore the radiometrically determined soil reflectivity R_radio is compared with the reflectivity, which is calculated using a stratified soil model based on dielectric profiles derived from the in situ measurements. We additionally include the influence of surface soil structure.

Dielectric Gradients within the Soil
Emission, and therefore reflectivity, depends on the dielectric properties of the topsoil. The microwave emission from the soil for a given dielectric profile may be predicted using a model that incorporates coherent or noncoherent radiation. A noncoherent model (Burke et al., 1979) incorporates only the amplitudes of the emitted intensities, whereas a coherent model is based on the propagation of electric fields, including their phase relations (Njoku and Kong, 1977; Wilheit, 1978). Both types of models discretize the soil into a finite number of homogeneous soil layers. Radiative transfer through these layers is then calculated for layer thicknesses smaller than one-tenth of the observation wavelength. A comparison of these two types of models revealed a generally deeper soil water content sampling depth for the coherent models (Schmugge and Choudhury, 1981).

We used a coherent model based on a matrix formulation of the boundary conditions at the layer surfaces derived from Maxwell's equations (Bass et al., 1995). The output of this algorithm is the reflectivity, and the expected inputs are two vectors containing the thickness and the dielectric constants of the layers, wavelength, polarization, and incidence angle of the radiation. The dielectric profiles used in the model were based on in situ measured TDR and temperature profiles _i,t and T_i,t. These in situ data were fitted with a third-order polynomial and then back-transformed to obtain the discrete profiles _t(z) and T_t(z) at a uniform resolution of 1 mm, which is <1% of the relevant L-band wavelength. Below we discuss several extrapolation approaches between the uppermost TDR probe at z = 2 cm and the footprint surface at z = 0 cm, and the influence of this extrapolation on the resulting soil reflectivity R_t.

The calculated reflectivities R_t based on the in situ measured water content and temperature profiles _t(z) and T_t(z) will be compared with corresponding soil reflectivities R_radio observed with the radiometer. Figure 3 illustrates the flowchart for calculating R_t from the in situ measured profiles _i,t and T_i,t. The dielectric profile ^soil_t(t) was calculated with the mixing model of Wang and Schmugge (1980) together with the model of Cole and Cole (1941) for calculating the dielectric constant of pure water.

View larger version (22K): [in this window] [in a new window]   Fig. 3. Flowchart used for calculating the reflectivities Rt from the in situ measured profiles i,t and Ti,t. (Subscript i refers to layer i and t to time; h,tapp is defined by Eq. [10]; 2,t is the water content at 2 cm; h is the roughness parameter.)

Topsoil Structure
Surface roughness is known to influence radiometric measurements (e.g., Choudhury et al., 1979), possibly due to scattering or volume effects. Several experiments have been conducted to study the scattering influence of surface roughness on microwave emission (Wang et al., 1983; Mo and Schmugge, 1987; Paloscia et al., 1993; Wigneron et al., 2001). They all showed an increase in the measured emission and a decrease in the reflectivity with increasing surface roughness. This is due to an increase in surface area that interfaces with the atmosphere and thus transmits the up-welling energy. Shi et al. (2002) showed that the influence of surface roughness depends on the polarization as well as on incidence angle. In contrast to earlier studies they found that the emission from a rough surface at vertical polarization decreases compared with that from a smooth surface.

Ulaby et al. (1982) proposed using the Fraunhofer criterion to define whether a surface is smooth or rough for electromagnetic waves of wavelength relative to the standard deviation of surface heights:

[8]

Unfortunately, the Fraunhofer criterion only refers to the amplitude of the roughness but ignores its lateral dimension, which becomes relevant at the limit of the resolution of the radiometric observation. To account for the fact that lateral structures smaller than the observation wavelength ( < 21 cm at L-band) are not resolved, we developed a new model that considers the small-scale structure of the topsoil as an isotropic dielectric mixture of bulk soil and air. This approach leads to a description of roughness in terms of a continuous transition of the dielectric properties of air to those of bulk soil. This concept was first proposed by Hüppi (1987). This new model, denoted as the air-to-soil transition model, is described in Air-to-Soil Transition Model below.

Surface Scattering Models
If we consider the roughness of the soil as a scattering effect, several physical (Tsang and Kong, 2001; Fung, 1994; Ulaby et al., 1986) or empirical models (Choudhury et al., 1979; Mo and Schmugge, 1987; Wegmüller and Mätzler, 1999; Wigneron et al., 2001; Shi et al., 2002) can be used to calculate the reflectivity. We selected the model of Shi et al. (2002), who developed a parameterized surface reflectivity model using data simulated with the integral equation method for a wide range of surface roughness and soil water content conditions. In this way, they overcame the problems of earlier models, which are only valid either for restricted surface types in the case of physically based models (Laguerre et al., 1994) or only for the experimental conditions under which they have been tested.

The surface reflectivity is composed of a coherent, R_p^coh, and noncoherent term R_p^non. Both depend on polarization p and are parameterized by , the correlation length l, and . The reflectivity of a rough surface R_p^r is then given by

[9]

where r_p is the Fresnel reflectivity at polarization p, is the incidence angle, k is the wavenumber, and A_p and B_p are roughness parameters that depend on p, , , l, and the type of correlation function (Shi et al., 2002).

Air-to-Soil Transition Model
Since surface scattering models are not capable of describing the effect of small-scale soil roughness (small relative to the horizontal wavelength of the soil features) on the L-band radiation we propose an alternative roughness model denoted as the air-to-soil transition model. This model makes use of the fact that most of the dielectric structures in the topsoil are smaller than the observation wavelength and, in addition, below the Bragg limit. They are therefore laterally not resolved at L-band observation. As a consequence, the structured topsoil appears as a transition layer of thickness h with volume fraction v_h^soil of soil material, which increases with depth. We describe this transition layer with a depth-dependent two-phase mixing model considering the two phases, air and soil material (Fig. 4) . In this way, mixing effects caused by the unresolved, loose arrangement of topsoil structures like cracks, stones, organic debris, and topographic features are included. As depicted in Fig. 4, a more specific interpretation of the transition layer thickness h is the peak-to-peak roughness of the soil surface. In this figure h is the distance between the deepest depression and the highest peak at the surface in an area corresponding to the resolution limit of the radiometer observation. At the L-band this area is of the order of A = 21 by 21 cm². The interpretation of h being the peak-to-peak roughness is applicable with the assumption that the proportional air-to-soil transition is dominated by topographical effects. Furthermore, horizontal inhomogeneities in the soil material due to horizontal components of fluxes are not considered.

View larger version (26K): [in this window] [in a new window]   Fig. 4. Illustration of the principles implemented in the air-to-soil transition model. Sh(z*) is the surface height distribution and vhsoil(z*) the cumulated value corresponding to the volume fraction of the soil material; z = 0 is the average surface height of a soil area A of the order by ; z* = 0 and z* = h refer to the highest peak and the lowest depression within A. The TDR and temperature probes are located at depths of 2 and 7 cm. tsoil(z*) is the dielectric constant of the bulk soil material (including soil water), and h,tapp(z*) is the apparent dielectric constant of the two-phase (air, soil material) transition layer of thickness h.

[10]

which reduces to the refractive mixing model used by Birchak et al. (1974) if the exponent ß equals 0.5.

The transition layer thickness h is interpreted as the topographic roughness parameter; the depth dependence of the volume fraction v_h^soil is consequently related to the height distribution S_h(z*) of the surface. This becomes obvious when v_h^soil is understood to be the cumulative probability density of S_h(z*):

[11]

The depth variable z* (defined to be zero at the highest peak) is related to depth z by z* = z + h/2. In this study we parameterize S_h(z*) with a normalized quadratic function of z* comprising h as the roughness parameter (Fig. 4):

[12]

The integral of S_h(z*) over depth z* and hence v_h^soil is zero above the highest soil peak (z* < 0) and approaches unity below the deepest soil depression at z* > h (Fig. 4):

[13]

Since v_h^soil depends on the roughness parameter h, the dielectric profile _h,t^app also depends on h. Therefore, we need a relation between h and the photogrammetrically determined standard deviation _opt of the surface height within an area on the order of 21 by 21 cm²:

[14]

in which the left side is the probability of finding a surface height within ± around the average surface height at z* = h/2 for the quadratic height distribution S_h(z*) given by Eq. [12]. This integral is evaluated and equated to the corresponding ±* probability for the Gaussian distribution with standard deviation * centered around . This relates the roughness parameter h to the standard deviation of the surface height:

[15]

From the profiles _h,t^app (Eq. [10]) we calculated soil reflectivities R_t incorporating the soil roughness, as discussed below. The effect of the extrapolation applied to the in situ measurements _i,t (Fig. 3) on the resulting soil reflectivities R_t is discussed in the following.

Effect of the Extrapolation Approach within the Topsoil
The dielectric depth profiles _t^soil in the soil phase were derived from the in situ measured profiles _i,t and T_i,t by interpolation and extrapolation, and by applying the models of Wang and Schmugge (1980) and Cole and Cole (1941) (Fig. 3). Between the uppermost TDR probe at z = 2 cm (corresponding to z* = 2 cm + h/2) and the footprint height at z = 0 cm (corresponding to z* = h/2) the _i,t profiles were extrapolated to obtain the _t profiles having a depth resolution of 1 mm (Fig. 4). As illustrated in the insets of Fig. 5a and 5b , the shape of the _t profiles between the footprint height and the highest local peak (h/2 > z* > 0) were assumed to be constant, having the extrapolated value at the footprint height. We expect that the chosen extrapolation affects the dielectric profile in the topsoil and thus the resulting calculated soil reflectance R_t. To estimate the influence of this assumed water content extrapolation on the calculated reflectivity R_t, we made model calculations with a variety of water content extrapolations within the top 2 cm of the soil. For this purpose two typical water content profiles _wet and _dry as measured with the TDR probes during wet (Day of Year 157) and dry conditions (Day of Year 173) were examined. These representative profiles were constructed by averaging the measurements at the individual depths over one day. Under wet conditions, the TDR water content at 2 cm depth was 0.26 m³ m^–3 and under dry conditions 0.16 m³ m^–3. For the profiles _wet and _dry we calculated corresponding soil reflectivities R_wet(h) and R_dry(h) for the roughness parameter range 0 h 80 mm and for two different water content extrapolations (Fig. 5a and 5b).

View larger version (15K): [in this window] [in a new window]   Fig. 5. Influence of the thickness h of the air-to-soil transition zone on the soil reflectivity for different assumptions about the shape of the water content profiles in 0 z 20 mm (dotted and dashed lines of the insets). The calculations were performed for typical water content profiles (a) dry and (b) wet as observed under dry and wet conditions (Fig. 10). For comparison, the radiometrically observed soil reflectivities Rradio, dry and Rradio, wet are also indicated. The relationship between the height variance and the transition zone thickness h is given by Eq. [15].

View larger version (30K): [in this window] [in a new window]   Fig. 10. (a) Reflectivities measured with the L-band radiometer at horizontal polarization (black thick line) compared with reflectivities Rt calculated by using the air-to-soil transition model considering a water content dependent transition zone of thickness h(2,t) (thick gray line). The gray dotted line indicates reflectivities calculated during period 1 if the transition zone dependence h(2,t) from period 2 is used, and reflectivities during period 2 calculated using h(2,t) from period 1. (b) Water content 2,t measured with the TDR 2 cm below the soil surface. The data section labeled as wet condition and dry condition refers to the discussion in the section Effect of the Extrapolation Approach within the Topsoil.

For the wet conditions, the lack of in situ measured soil profile data in the 2-cm surface layer was alleviated assuming either a constant water content above 2 cm or a fully saturated soil surface (dashed and dotted profile of the inset of Fig. 5b). As above, the constant water content in the top 2 cm was chosen to be equal to that measured with the uppermost TDR probe, while the extrapolation to the fully saturated surface was realized by using a quadratic function having the same gradient at 2 cm as the fitted _wet(z) profile.

For dry and wet conditions, the calculated reflectivities R_wet(h) and R_dry(h) decreased by increasing the transition zone thickness h. For dry conditions and h > 40 mm the soil reflectivities R_dry(h) became almost indistinguishable for the two water content extrapolation approaches. This means, that the shape of the water content distribution in the topsoil is obscured by the increasing soil roughness. This tendency is also observed during wet conditions, but less distinct.

For dry conditions, the radiometrically measured soil reflectivity R_radio,dry = 0.32 is reproduced by the model calculation R_dry(h) with h 40 mm, independently of the chosen extrapolation (Fig. 5a). For wet conditions, the radiometrically measured reflectivity R_radio,wet = 0.55 is reproduced for the range 12 < h < 26 mm depending up on the assumed extrapolation of the water content profile above the uppermost TDR probe (Fig. 5b). This analysis shows that soil reflectivities R_radio can be explained when the soil roughness is represented by the air-to-soil transition model. In other words, the radiometric reflectivities cannot be explained only by assuming a reasonable topsoil water content profile.

If the water content profiles are not measurable, numerical simulations of the water flow can be used to define the water content gradients near the surface. However, the potential of model calculations should not be overestimated. Most conventional models used for water flow only treat isothermal liquid flow in incompressible porous media. These assumptions are generally not valid at or near the soil surface. For example, the vapor flux is important under the drying conditions. This requires a two-phase (liquid and gaseous phase) model to account for vapor transfer and liquid flow. The assumption of an isothermal process may also be inadequate. Instead, a model is needed for coupled flow and transport that includes the energy aspects of phase transitions, and the incoming radiation as well. To quantify these processes a large number of parameters is needed for a porous medium that is usually ill-defined due to lack of experimental access. For instance, it is not immediately obvious how to measure a relatively simple quantity like pore volume at a millimeter-scale resolution in an undisturbed field soil. For these reasons, we believe that modeling the drying front in the very topsoil will result in large uncertainties. In our opinion it seems more advantageous to study the possible effects of the gradient in the water content in the topsoil by modeling various scenarios covering a range of plausible distributions.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS CONCLUSIONS REFERENCES

 
In this section we interpret the radiation measured with the L-band radiometer and its relation to the in situ measured data. Below we discuss the transformation of the radiometric signals to volumetric water contents. We follow thereby the simplest path through the evaluation scheme of Fig. 2, as described in Microwave Radiometry above. In this case the soil is assumed to be a homogeneous dielectric with a smooth surface.

We then replace the concept of constant dielectric soil properties with a layered dielectric medium. The coherent layer model is then used to calculate reflectivities expected for the in situ measured properties. The calculated reflectivities will be compared with the radiometer reflectivity measurements. We also discuss alternative approaches for constructing the dielectric profile based on available TDR data and surface structures and the corresponding changes in the resulting reflectivities.

Fresnel Reconstruction of Water Content
During the experiment several precipitation events with subsequent drying were observed (Fig. 6) . The measured brightness temperature and the calculated emissivity closely followed this weather pattern. Figure 7 shows water contents obtained using the Fresnel equation relative to the water contents measured in situ with TDR probes at the 2-cm depth.

View larger version (27K): [in this window] [in a new window]   Fig. 6. Rainfall (gray line) and in situ measured water content (TDR at 2 cm, black line) during the experiment. The measurements were segmented into three cycles following the precipitation periods. The times of the digital surface model (DSM) measurements are also shown.

View larger version (43K): [in this window] [in a new window]   Fig. 7. Comparison between volumetric water contents measured in situ with TDR at the 2-cm depth and those calculated based on the Fresnel equations (Eq. [6] and [7]) using the ELBARA (1.4 GHz) radiometer data. For the calculations the soil profile and the surface were assumed to be smooth.

Reflectivity from TDR Water Content Profiles Using a Coherent Layer Model
Without Considering Top Surface Structure
Next, we analyze the need for a more sophisticated model for the interpretation of the microwave signal. For this purpose, the measured reflectivities R_radio are compared with the results R_t obtained with a coherent model considering a horizontally stratified near-surface soil structure, and verified independently by means of optical in situ measurements.

Figure 8 shows the comparison between radiometrically measured reflectivities R_radio and reflectivities R calculated with different models. The fit to the radiometer data is slightly improved when the layer model based on the TDR profiles is used instead of the Fresnel model based on the water content at a depth of 2 cm. Both still overestimate the measured reflectivity. The reflectivities R_t were calculated for a layered profile generated from only five TDR measurements, with the measurement closest to the soil surface being at z = 2 cm. Therefore, the water content estimates in the uppermost surface layers, which dominate the reflectivities, are most suspect. Furthermore, the topsoil structure in this case was not considered in the calculated reflectivity. As a next step, the reflectivity R_t calculated using the layer model is modified to include the surface scattering effect described with the roughness model of Shi et al. (2002).

View larger version (44K): [in this window] [in a new window]   Fig. 8. Comparison of reflectivities Rradio measured with the L-band radiometer ELBARA (thick black line) at horizontal (upper graph) and vertical (lower graph) polarization with reflectivities calculated using the Fresnel equations (Eq. [6] and [7]) based on water contents measured in situ by TDR at the 2-cm depth (thin black line), the coherent radiative transfer model (Rt, thick dark-gray line), and the same model but introducing a roughness correction to the coherent reflectivities according to Shi et al. (2002) (thick light-gray line).

View this table: [in this window] [in a new window]   Table 1. Optically measured standard deviation opt of height and horizontal correlation length l of the soil surface at three stages of the experiment. Ah, Av, Bh, and Bv were calculated according to Shi et al. (2002) for a Gaussian correlation function and used to account for the roughness effect on the soil reflectivity according to Eq. [9]. The opt values are of the same order as the corresponding standard deviations used in the air-to-soil transition model.

View larger version (22K): [in this window] [in a new window]   Fig. 9. Reflectivities measured with ELBARA at horizontal vs. vertical polarization. The solid line represents the values expected for a perfectly (Lambertian) rough surface, whereas the dash-dotted line holds for a perfectly smooth surface. Symbols refer to the three cycles as specified in Fig. 6.

View larger version (26K): [in this window] [in a new window]   Fig. 11. Dependence of the roughness parameter h on the volumetric water content 2,t measured at the 2-cm depth for the two periods 1 and 2 (solid lines). The dashed lines show h values for 1 and 2 averaged over the measured water content range. The calculated corresponding to h during 1 or 2 are indicated on the right axis. These values are of the same order as the optically measured values opt shown in Table 1.

1

Model Comparison
Table 2 shows the mean deviation between reflectivity R_radio measured with the radiometer and the reflectivity R_t calculated with the different models over the whole observation period. As can be seen, the stepwise refinement of the models leads to smaller deviations between measured and modeled reflectivities. The deviation was largest using the simple Fresnel approach described. The coherent model led to only a small improvement. Introducing the surface scattering model of Shi et al. (2002), enhanced the horizontal polarization but worsened the agreement at vertical polarization. Finally, the air-to-soil transition model improved the correspondence significantly.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS CONCLUSIONS REFERENCES

By extrapolating the dielectric profiles derived from the in situ measurements to the soil surface, and assuming an air-to-soil transition zone, we improved the consistency between the radiometer reflectivity data and the modeled soil reflectivity considerably. The necessity of considering roughness effects by applying the air-to-soil transition model was demonstrated. From this we concluded that small-scale surface structures are relevant in the analysis of L-band observations. Unfortunately, the uppermost soil layers are difficult to characterize by conventional methods. To understand the nature of soil emission in more detail, the near surface boundary layer should be more precisely examined and parameterized at high spatial resolution.

	ACKNOWLEDGMENTS

 
The radiometer used in this study was designed and constructed at the Institute of Applied Physics, University of Bern. Special thanks are due to Daniel Weber and Max Wüthrich. The digital surface models were derived with the help of Jochen Willneff from the Institute of Geodesy and Photogrammetry ETH Zurich. Success of the demanding field experiment was largely due to Jörg Leuenberger, Hannes Wydler and Hanspi Läser from the Institute of Terrestrial Ecology, ETH Zurich. This work has been supported by a science grant from the Swiss Federal Institute of Technology (ETH) Zurich.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS CONCLUSIONS REFERENCES

 

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