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Topsoil Structure Influencing Soil Water Retrieval by Microwave Radiometry

K. Schneeberger, M. Schwank,* Ch. Stamm, P. de Rosnay, Ch. Matzler, and H. Fluhler

ABSTRACT Remote sensing makes use of electromagnetic energythat is reflected and emitted by the earth’s surface. AMany remote sensing applications, including those of future spacemicrowave radiometer measures the emission from themissions, require accurate knowledge of the influence of topsoil struc-

ture on the water content as measured using L-band radiometry. We land surface at wavelengths ranging from about 1 to 30 cm.report on field-measured L-band (1.4 GHz) microwave emission from The observed radiation is proportional to the ther-a bare soil. Of special interest in this work is the procedure used to modynamic temperature of the surface and the emis-transform remotely sensed data to soil water content and its compara- sivity (Rayleigh-Jeans approximation of Planck’s Law).bility with time domain reflectometer (TDR) in situ measurements. Microwave emissivity strongly depends on the water con-Surface roughness of the soil was characterized on a millimeter scale tent because of the large contrast between the dielectricusing an optical measurement technique. Different models for inter-

constant of water (about 80 at 1.4 GHz) and dry soilpreting the microwave signals in terms of the water content were in-(3–5). L-band measurements (1.4 GHz, � � 21 cm) arevestigated. The agreement between in situ water contents and surfacemost suitable for estimating soil water content, mainlywater contents estimated with radiometry data using the Fresnel equa-because they have a rather deep penetration depth com-tion was found to be poor. A coherent layer model, with and without

considering roughness effects, was tested to compare radiometrically pared with measurements at shorter wavelengths (Burkemeasured and modeled soil reflectivities. The correspondence remained et al., 1979; Jackson and Schmugge, 1989) and becauseunsatisfactory, even when we considered a dielectric gradient fitted they are less influenced by vegetation cover. However,to the TDR profiles and surface roughness represented by a scattering L-band measurements are still restricted to the topsoilmodel. We developed a new air-to-soil transition model, which in- (Jackson, 1993). Microwave radiometry is an indirectcludes dielectric mixing effects due to small-scale surface structures. method of measuring the surface water content. SeveralThis model considerably improved agreement between measured and

steps are necessary to convert the measured signal intomodeled results. We conclude that small-scale structures of the topsoilwater content. This multistep procedure and the rele-cannot be neglected in interpreting L-band measurements.vant model assumptions are discussed below.

Several large-scale experiments (on the order of oneto several hectares or square kilometers) have beenSoil water content is a key variable for estimat-performed to study the microwave emission from natu-ing water and energy fluxes at the earth surface. Itral soils (Schmugge et al., 1992; Jackson et al., 1995,strongly controls infiltration processes and therefore the1999). Due to spatial variability of the calibration mea-hydrologic fate of precipitation reaching the soil sur-surements, water content measurements in the footprintface. The water content is also a critical factor determin-area are difficult to validate at such scales. The experi-ing the amount of actual evaporation, thus affecting alsomental data used in our study were obtained at the plotthe feedback loop from soil to atmosphere. Because ofscale. While this is not a typical scale for remote sensingits importance to many hydrological questions, consider-applications, it does allow for more reliable ground truthable effort has gone into the development of measure-data. This is an important prerequisite for testing thement techniques to determine the soil water contentassumptions of various interpretation approaches. Theat larger scales (Kerr et al., 2001). Passive microwavemost common evaluation procedure is the use of a co-remote sensing is one of the most promising approachesherent model based on brightness temperatures normal-(Njoku and Kong, 1977; Schmugge, 1985; Jackson, 1993)ized by the topsoil temperature and an empirical correc-since (i) the atmosphere is almost transparent at micro-tion of the surface roughness according to models suchwave frequencies, which allows all-weather measure-as those proposed by (Choudhury et al., 1979) or (Wig-ments; (ii) microwave radiation penetrates plant cano-neron et al., 2001).pies; and (iii) the measurements are independent of

We investigate the influence of the model choice onsolar radiation, which enables one to make day andthe estimated water content based on radiometer data.night observations.We discuss the comparability of such estimates with thosemeasured in situ using TDR probes. Based on experi-

K. Schneeberger, formerly at Institute of Terrestrial Ecology, ETH mental evidence, we develop a new model that considersZurich, Grabenstrasse 11a, 8952 Schlieren, Switzerland; M. Schwank the influence of small scale roughness on the L-bandand H. Fluhler, Institute of Terrestrial Ecology, ETH Zurich, Graben- signal.strasse 11a, 8952 Schlieren, Switzerland; Ch. Stamm, EAWAG, Ueb-

On lateral scales smaller than a certain fraction of oneerlandstrasse 13, 8600 Duebendorf, Switzerland; P. de Rosnay, Centrewavelength (typically one-half), the radiative electromag-d’Etudes Spatiales et de la Biosphere (CESBIO) 18 av. Edouard Belin,

bpi 2801, 31401 Toulouse Cedex 4, France; Ch. Matzler, Institute of netic fields cannot follow the fine structure of the me-Applied Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Swit- dium (which is also the reason for the cut off of wavezerland. Received 6 June 2004. Special Section: Hydrogeophysics. propagation in wave guides whose width is less than*Corresponding author (mike.schwank@env.ethz.ch).

half of one wavelength). Electrostatic near fields have toPublished in Vadose Zone Journal 3:1169–1179 (2004).© Soil Science Society of America Abbreviations: DSM, digital surface model; TDR, time-domain reflec-

tometer.677 S. Segoe Rd., Madison, WI 53711 USA

1169

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1170 VADOSE ZONE J., VOL. 3, NOVEMBER 2004

berger and Willneff, 2003). The photographs were taken ran-adapt locally to the medium to fulfill the boundary con-domly at different locations within the footprint area. A digitalditions. However, these fields do not radiate. They onlysurface model (DSM) was calculated using the commercialinfluence the manner of propagation, and are best takensoftware package SOCET SET (LH Systems, Leica Geosys-into account by means of an effective dielectric constant.tems GIS & Mapping, Atlanta, GA). Four 30 by 30 cm2 imagesThis issue is the main ingredient of dielectric mixingwere taken with a still video camera Nikon Coolpix 990 andmodels such as Eq. [10] to be discussed later, and the used for generating the DSM. To facilitate simultaneous ad-motivation for developing the new model. justment, a common reference system was defined, using analuminum frame with reference marks. The marks with coded

MATERIALS AND METHODS targets allow automated orientation and calibration of thecamera and the generation to corrected images, which wereThe database we used consists of radiometric measurementsimported into a digital photogrammetric workstation for gen-conducted during a field experiment in summer 2002. In thiserating the DSM. This procedure allows quick and precisesection we briefly describe the measurement techniques. Asampling of elevation data. The procedure permits the surfacemore detailed description of the experiment and instrumentsto be defined not only in terms of distinct deviation transects,was reported in Schneeberger et al. (2004) and Matzler et al.

(2003). but also by a complete three-dimensional reproduction at aresolution of 1 mm (Fig. 1).

Remote Sensing SystemTHEORYWe used a Dicke radiometer (ELBARA) operating at L-band

(1.4 GHz). The radiometer was equipped with a dual-polarized In this section we describe the sequence of steps for inter-conical horn antenna with a 3-dB beamwidth of 12�, and sym-preting the radiometric signal to obtain the surface watermetrical and identical beams. For sensing the emitted electro-content as sketched in Fig. 2. The description of the newlymagnetic radiation of the site, the center of gravity of thedeveloped air-to-soil transition model is described. This modelradiometer was mounted 6.7 m above the soil surface on awas successfully used to improve the consistency between thetower directed at an observation angle of � � 55� relative toin situ and remotely sensed data. We present a sensitivitythe vertical direction. This setup resulted in an elliptic foot-analysis of the reconstructed soil reflectance in terms of theprint of approximately 9 � 8 m2.water content profile within the topsoil.The radiometer was calibrated with internal hot and cold

loads (at temperatures Thot � 338 K and Tcold � 278 K) ac-cording to Microwave Radiometry

T Bi,p � �i(U i,p � u i

cold) � Tcold [1] A microwave radiometer measures a voltage that is trans-lated into a brightness temperature TB using a calibrationwithfunction (Eq. [1]). This brightness temperature TB is relatedto the soil emissivity E via�i �

Thot � Tcold

u ihot � u i

cold TB � ETsoil � (1 � E)Tsky [2]where T B

i,p is the brightness temperature for polarization pwhere Tsoil is the thermodynamic temperature of the soil and(� vertical or horizontal) detected on channel i (� 1 or 2);Tsky the radiation temperature of the sky background. Assum-u i

hot and u icold are the measured calibration voltages correspond-

ing that the observed scene is in thermodynamic equilibrium,ing to the internal calibration targets, and U i,p is the measuredthe emissivity E is related to the soil reflectivity R by Kirch-voltage when the radiometer is pointed onto the scene ofhoff’s Law, R � 1 � E.observation. The calibration function itself is system specific

As was shown by Delahaye et al. (2002), the stable sky back-and has to be defined for each radiometer. In this experiment,the calibration using the internal targets at temperatures Thot ground temperatures Tsky measured with a radiometer pointingand Tcold was performed before each measurement. Sky bright- away from the Milky Way is expected to be about 6 K. There-ness temperature was additionally measured periodically to fore, the last term of Eq. [2] can be neglected, since the back-check the stability of the remote sensing system. ground temperature reflected by the soil surface will contrib-

ute little to TB.In Situ Soil Water Content and Temperature For accurate calculation of the emissivity, the soil tempera-

ture profile T(z) should be integrated over the temperature sens-Soil water contents were measured in situ with horizontallying depth. According to Ulaby et al. (1986) the sensing depthinstalled two-rod TDR probes. These probes and soil tempera-is of the order of 20 to 40 cm at 1 GHz, depending on theture sensors were placed horizontally at five depths (2, 7, 15,water content of the soil. Mathematically the resulting effec-25, and 45 cm) in three replicates along the main target areative temperature Tsoil is expressed as follows (Chanzy et al.,of the L-band radiometer. The reliability of the TDR measure-1997):ments 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 Tsoil �

1cos(�) �

∞

0T(z)(z)exp�� B(z)

cos(�) �dz [3]of the experiment. The linear correlation coefficient betweenthe TDR measurements and the gravimetric soil water content

in whichwas 0.94, which indicates good reliability of the TDR mea-surements. B(z) � �

z

0(z)dz

Measuring Soil Surface Roughness where � is the radiometric observation angle and B(z) thetotal attenuation from depth z to the soil surface. The attenua-To map the microrelief, the soil surface was photographed

and the images were photogrammetrically interpreted (Schnee- tion coefficient can be approximated by

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www.vadosezonejournal.org 1171

Fig. 1. Photograph of the soil surface with the reference frame (left) and derived digital surface model (DSM) (right). Bright gray values indicatehigh elevations, and dark values low elevations.

(z) � 4�

�

ε″(z)

2√ε(z)[4]

where � is the wavelength and ε(z) and ε″(z) are the realand imaginary parts of the soil dielectric constant. Choudhuryet al. (1982) proved the following approximation:

Tsoil � T45cm � (T2cm � T45cm)C [5]

where T2cm and T45cm are the soil temperatures measured atthe 2- and 45-cm depth, respectively, and C is a fitting param-eter, which we assumed to be 0.5 in our experiment (Schnee-berger et al., 2004). In this study we use approximation Eq. [5]to calculate the effective soil temperature Tsoil. The resultingrelative error of the emissivity E � TB/Tsoil due to this approxi-mation is minor and the consequences for the radiometricallydetermined soil water content are therefore negligible. How-ever, using the approximation given by Eq. [5] leads to anunderestimation of the temporal dynamics of Tsoil and thus toan overestimation of the daily variations of the radiometricallydetermined soil reflectivities Rradio.

In the simplest model, the soil reflectivity R is a functionof the angle of observation �, and polarization h (horizontal)or v (vertical). The reflectivity is related to the dielectric con-stant εsoil by the Fresnel equations (Ulaby et al., 1981):

Rh(�) � �cos� � √εsoil � sin2�

cos� � √εsoil � sin2��2

[6]

Rv(�) � �εsoil cos� � √εsoil � sin2�

εsoil cos� � √εsoil � sin2��2

[7]

These equations are only valid for a homogeneous soil witha smooth surface. These assumptions are hardly ever metunder natural conditions. The models described in the follow-ing section account for the heterogeneities in the surface layer.Fig. 2. Schematic diagram of water content estimation from a passive

Converting dielectric constant into water content requiresmicrowave signal. State variables are shown within rectanglethe use of a dielectric mixing model (Wang and Schmugge, 1980;frames. Several models (elliptic frames) used to evaluate the radio-

metric signal. Model references are given in the bibliography. Dobson et al., 1985; Roth et al., 1990). These models require

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1172 VADOSE ZONE J., VOL. 3, NOVEMBER 2004

texture and porosity as additional inputs. The frequently usedmixing formula of Topp et al. (1980) is an empirical relation-ship between the dielectric constant of the soil and its watercontent, which depends also on soil temperature. However,Ferre et al. (1996) showed that this relation is in accordancewith the CRIM mixing model. Here we used the model ofWang and Schmugge, (1980). The dielectric constant of waterwas corrected for temperature effects according to Cole andCole (1941).

As already mentioned, we intend to compare water contentsmeasured in situ with remotely sensed data. Since soil reflectiv-ity is strongly related to water content and less influenced bythe temperature profile, we decided to perform the compari-son between remote sensing data and the in situ data by meansof soil reflectivity. Therefore the radiometrically determinedsoil reflectivity Rradio is compared with the reflectivity, which

Fig. 3. Flowchart used for calculating the reflectivities Rt from the inis calculated using a stratified soil model based on dielectricsitu measured profiles �i,t and Ti,t. (Subscript i refers to layer i and tprofiles derived from the in situ measurements. We addition-to time; εh, t

app is defined by Eq. [10]; �2, t is the water content at 2 cm;ally include the influence of surface soil structure.h is the roughness parameter.)

Dielectric Gradients within the Soil Topsoil StructureEmission, and therefore reflectivity, depends on the dielec- Surface roughness is known to influence radiometric mea-

tric properties of the topsoil. The microwave emission from surements (e.g., Choudhury et al., 1979), possibly due to scat-the soil for a given dielectric profile may be predicted using tering or volume effects. Several experiments have been con-a model that incorporates coherent or noncoherent radiation. ducted to study the scattering influence of surface roughnessA noncoherent model (Burke et al., 1979) incorporates only on microwave emission (Wang et al., 1983; Mo and Schmugge,the amplitudes of the emitted intensities, whereas a coherent 1987; Paloscia et al., 1993; Wigneron et al., 2001). They allmodel is based on the propagation of electric fields, including showed an increase in the measured emission and a decreasetheir phase relations (Njoku and Kong, 1977; Wilheit, 1978). in the reflectivity with increasing surface roughness. This isBoth types of models discretize the soil into a finite number due to an increase in surface area that interfaces with theof homogeneous soil layers. Radiative transfer through these atmosphere and thus transmits the up-welling energy. Shi et al.layers is then calculated for layer thicknesses smaller than one- (2002) showed that the influence of surface roughness dependstenth of the observation wavelength. A comparison of these two on the polarization as well as on incidence angle. In contrasttypes of models revealed a generally deeper soil water content to earlier studies they found that the emission from a roughsampling depth for the coherent models (Schmugge and Choud- surface at vertical polarization decreases compared with thathury, 1981). from a smooth surface.

We used a coherent model based on a matrix formulation Ulaby et al. (1982) proposed using the Fraunhofer criterionof the boundary conditions at the layer surfaces derived from to define whether a surface is smooth or rough for electromag-Maxwell’s equations (Bass et al., 1995). The output of this al- netic waves of wavelength � relative to the standard deviationgorithm is the reflectivity, and the expected inputs are two � of surface heights:vectors containing the thickness and the dielectric constantsof the layers, wavelength, polarization, and incidence angle �

�

32cos�[8]

of the radiation. The dielectric profiles used in the model werebased on in situ measured TDR and temperature profiles

Unfortunately, the Fraunhofer criterion only refers to the�i,t and Ti,t. These in situ data were fitted with a third-orderamplitude of the roughness but ignores its lateral dimension,polynomial and then back-transformed to obtain the discretewhich becomes relevant at the limit of the resolution of theprofiles �t(z) and Tt(z) at a uniform resolution of 1 mm, whichradiometric observation. To account for the fact that lateralis 1% of the relevant L-band wavelength. Below we discussstructures smaller than the observation wavelength (� 21 cmseveral extrapolation approaches between the uppermostat L-band) are not resolved, we developed a new model thatTDR probe at z � 2 cm and the footprint surface at z � 0 cm,considers the small-scale structure of the topsoil as an isotropicand the influence of this extrapolation on the resulting soildielectric mixture of bulk soil and air. This approach leads toreflectivity Rt. a description of roughness in terms of a continuous transitionThe calculated reflectivities Rt based on the in situ measuredof the dielectric properties of air to those of bulk soil. Thiswater content and temperature profiles �t(z) and Tt(z) will be concept was first proposed by Huppi (1987). This new model,compared with corresponding soil reflectivities Rradio observed denoted as the air-to-soil transition model, is described in Air-with the radiometer. Figure 3 illustrates the flowchart for to-Soil Transition Model below.calculating Rt from the in situ measured profiles �i,t and Ti,t.

The dielectric profile ε soilt (t) was calculated with the mixing

Surface Scattering Modelsmodel of Wang and Schmugge (1980) together with the modelof Cole and Cole (1941) for calculating the dielectric constant If we consider the roughness of the soil as a scatteringof pure water. effect, several physical (Tsang and Kong, 2001; Fung, 1994;

In a first comparison, the calculated reflectivities Rt are Ulaby et al., 1986) or empirical models (Choudhury et al.,compared with Rradio. In a second comparison, Rt is calculated 1979; Mo and Schmugge, 1987; Wegmuller and Matzler, 1999;from the dielectric profiles εh, t

app. They are based on ε soilt modified Wigneron et al., 2001; Shi et al., 2002) can be used to calculate

by the air-to-soil transition model used to incorporate the soil the reflectivity. We selected the model of Shi et al. (2002),who developed a parameterized surface reflectivity model us-roughness with the roughness parameter h.

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www.vadosezonejournal.org 1173

Fig. 4. Illustration of the principles implemented in the air-to-soil transition model. Sh(z*) is the surface height distribution and v hsoil(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 atdepths of 2 and 7 cm. ε t

soil(z*) is the dielectric constant of the bulk soil material (including soil water), and εh, tapp(z*) is the apparent dielectric

constant of the two-phase (air, soil material) transition layer of thickness h.

ing data simulated with the integral equation method for a more, horizontal inhomogeneities in the soil material due tohorizontal components of fluxes are not considered.wide range of surface roughness and soil water content condi-

tions. In this way, they overcame the problems of earlier mod- The apparent dielectric profile εh,tapp(z*) relevant for the L-band

emission of the soil as observed at time t is described using aels, which are only valid either for restricted surface types inthe case of physically based models (Laguerre et al., 1994) or dielectric two-phase mixing model (Sihvola, 1999) for the air

and soil phases. Inserting the dielectric constant εair of the aironly for the experimental conditions under which they havebeen tested. phase and the dielectric constants ε t

soil(z*) of the soil phase aslocally measured at time t together with their correspondingThe surface reflectivity is composed of a coherent, Rp

coh, andnoncoherent term R p

non. Both depend on polarization p and volume fractions 1 � v hsoil(z*) and v h

soil(z*) into the mixing for-mula yieldsare parameterized by �, the correlation length l, and �. The

reflectivity of a rough surface R pr is then given by

ε apph,t (z*) � ��1 � v soil

h (z*)�ε�air � v soil

h (z*)ε soilt (z*)�1/�

[10]R r

p � Rcohp � R non

p � rp exp��(2k� cos �)2� � Apr Bpp [9]which reduces to the refractive mixing model used by Birchak

where rp is the Fresnel reflectivity at polarization p, � is the et al. (1974) if the exponent � equals 0.5.incidence angle, k is the wavenumber, and Ap and Bp are rough- The transition layer thickness h is interpreted as the topo-ness parameters that depend on p, �, �, l, and the type of graphic roughness parameter; the depth dependence of thecorrelation function (Shi et al., 2002). volume fraction v h

soil (z*) is consequently related to the heightdistribution Sh(z*) of the surface. This becomes obvious whenv h

soil (z*) is understood to be the cumulative probability densityAir-to-Soil Transition Modelof Sh(z*):Since surface scattering models are not capable of describ-

ing the effect of small-scale soil roughness (small relative to v hsoil (z*) � �

z*

0Sh(z)dz [11]

the horizontal wavelength of the soil features) on the L-bandradiation we propose an alternative roughness model denoted The depth variable z* (defined to be zero at the highest peak)as the air-to-soil transition model. This model makes use of the is related to depth z by z* � z � h/2. In this study we param-fact that most of the dielectric structures in the topsoil are eterize Sh(z*) with a normalized quadratic function of z* com-smaller than the observation wavelength � and, in addition, prising h as the roughness parameter (Fig. 4):below the Bragg limit. They are therefore laterally not resolvedat L-band observation. As a consequence, the structured top-soil appears as a transition layer of thickness h with volume Sh(z*) � �

6z*2

h3�

6z*h2

for 0 � z* � h

0 for z* 0 and z* � hfraction vh

soil of soil material, which increases with depth. We de- [12]scribe this transition layer with a depth-dependent two-phasemixing model considering the two phases, air and soil material The integral of Sh(z*) over depth z* and hence v h

soil(z*) is(Fig. 4). In this way, mixing effects caused by the unresolved, zero above the highest soil peak (z* 0) and approachesloose arrangement of topsoil structures like cracks, stones, unity below the deepest soil depression at z* � h (Fig. 4):organic debris, and topographic features are included. As de-picted in Fig. 4, a more specific interpretation of the transitionlayer thickness h is the peak-to-peak roughness of the soil sur-face. In this figure h is the distance between the deepest de- v soil

h (z*) � 0 z* 03z*2

h2�

2z*3

h30 � z* � h

1 z* � h

[13]pression and the highest peak at the surface in an area corre-sponding 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 Since v h

soil(z*) depends on the roughness parameter h, the di-electric profile ε h,t

app(z*) also depends on h. Therefore, we needapplicable with the assumption that the proportional air-to-soil transition is dominated by topographical effects. Further- a relation between h and the photogrammetrically determined

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1174 VADOSE ZONE J., VOL. 3, NOVEMBER 2004

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 watercontent 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].

standard deviation �opt of the surface height within an area the soil. For this purpose two typical water content profiles �wet

on the order of 21 by 21 cm2: and �dry as measured with the TDR probes during wet (Day ofYear 157) and dry conditions (Day of Year 173) were examined.

�h/2��

h/2��Sh(z*)dz* � These representative profiles were constructed by averaging

the measurements at the individual depths over one day. Underwet conditions, the TDR water content at 2 cm depth was 0.261

�*√2��

���*

���*exp���(z* � �)2/2�*2�dz* � 0.6827 [14]

m3 m�3 and under dry conditions 0.16 m3 m�3. For the profiles�wet and �dry we calculated corresponding soil reflectivities Rwet(h)

in which the left side is the probability of finding a surface and Rdry(h) for the roughness parameter range 0 � h � 80 mmheight within �� around the average surface height at z* � and for two different water content extrapolations (Fig. 5ah/2 for the quadratic height distribution Sh(z*) given by Eq. and 5b).[12]. This integral is evaluated and equated to the correspond- In the case of dry conditions, the lack of in situ measureding ��* probability for the Gaussian distribution with stan- soil profile data within the top 2 cm was alleviated by assumingdard deviation �* centered around �. This relates the rough- two extreme profiles as illustrated in the inset of Fig. 5a: a con-ness parameter h to the standard deviation � of the surface stant water content (dashed profile) and an extrapolation toheight: a fully desiccated soil surface (dotted profile). The constant

water content at 0 � z � 2 cm depth was assumed to be equal�(h) � 2.479h [15]to that measured at the 2-cm depth. The extrapolation to the

From the profiles ε h,tapp(z*) (Eq. [10]) we calculated soil re- desiccated surface was realized by means of a quadratic func-

flectivities Rt incorporating the soil roughness, as discussed be- tion having the same gradient at the 2-cm depth as the fittedlow. The effect of the extrapolation applied to the in situ mea- �dry(z) profile.surements �i,t (Fig. 3) on the resulting soil reflectivities Rt is For the wet conditions, the lack of in situ measured soil pro-discussed in the following. file data in the 2-cm surface layer was alleviated assuming either

a constant water content above 2 cm or a fully saturated soilEffect of the Extrapolation Approach within the Topsoil surface (dashed and dotted profile of the inset of Fig. 5b). As

above, the constant water content in the top 2 cm was chosenThe dielectric depth profiles ε tsoil in the soil phase were de-

to be equal to that measured with the uppermost TDR probe,rived from the in situ measured profiles �i,t and Ti,t by interpola-while the extrapolation to the fully saturated surface was real-tion and extrapolation, and by applying the models of Wangized by using a quadratic function having the same gradientand Schmugge (1980) and Cole and Cole (1941) (Fig. 3). Be-at 2 cm as the fitted �wet(z) profile.tween the uppermost TDR probe at z � 2 cm (corresponding

For dry and wet conditions, the calculated reflectivitiesto z* � 2 cm � h/2) and the footprint height at z � 0 cm (cor-Rwet(h) and Rdry(h) decreased by increasing the transition zoneresponding to z* � h/2) the �i,t profiles were extrapolated tothickness h. For dry conditions and h � 40 mm the soil reflec-obtain the �t profiles having a depth resolution of 1 mm (Fig. 4).tivities Rdry(h) became almost indistinguishable for the twoAs illustrated in the insets of Fig. 5a and 5b, the shape of thewater content extrapolation approaches. This means, that the�t profiles between the footprint height and the highest localshape of the water content distribution in the topsoil is ob-peak (h/2 � z* � 0) were assumed to be constant, having thescured by the increasing soil roughness. This tendency is alsoextrapolated value at the footprint height. We expect that theobserved during wet conditions, but less distinct.chosen extrapolation affects the dielectric profile in the topsoil

For dry conditions, the radiometrically measured soil re-and thus the resulting calculated soil reflectance Rt. To estimateflectivity Rradio,dry � 0.32 is reproduced by the model calculationthe influence of this assumed water content extrapolation onRdry(h) with h ≈ 40 mm, independently of the chosen extrapola-the calculated reflectivity Rt, we made model calculations with

a variety of water content extrapolations within the top 2 cm of tion (Fig. 5a). For wet conditions, the radiometrically mea-

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sured reflectivity Rradio,wet � 0.55 is reproduced for the range12 h 26 mm depending up on the assumed extrapolationof the water content profile above the uppermost TDR probe(Fig. 5b). This analysis shows that soil reflectivities Rradio canbe explained when the soil roughness is represented by theair-to-soil transition model. In other words, the radiometricreflectivities cannot be explained only by assuming a reason-able topsoil water content profile.

If the water content profiles are not measurable, numericalsimulations of the water flow can be used to define the watercontent gradients near the surface. However, the potential ofmodel calculations should not be overestimated. Most conven-tional models used for water flow only treat isothermal liquidflow in incompressible porous media. These assumptions aregenerally not valid at or near the soil surface. For example, thevapor flux is important under the drying conditions. This re-quires a two-phase (liquid and gaseous phase) model to accountfor vapor transfer and liquid flow. The assumption of an isother- Fig. 6. Rainfall (gray line) and in situ measured water content (TDRmal process may also be inadequate. Instead, a model is needed at 2 cm, black line) during the experiment. The measurements werefor coupled flow and transport that includes the energy aspects segmented into three cycles following the precipitation periods.of phase transitions, and the incoming radiation as well. To quan- The times of the digital surface model (DSM) measurements aretify these processes a large number of parameters is needed also shown.for a porous medium that is usually ill-defined due to lack ofexperimental access. For instance, it is not immediately obvi-

the radiometer data are systematically lower, except forous how to measure a relatively simple quantity like pore vol-ume at a millimeter-scale resolution in an undisturbed field very wet conditions. This discrepancy is not surprisingsoil. For these reasons, we believe that modeling the drying for several reasons. For example, the radiometric deter-front in the very topsoil will result in large uncertainties. In mination of the water content yields a value horizontallyour opinion it seems more advantageous to study the possible

averaged over the footprint area, whereas the TDR probeseffects of the gradient in the water content in the topsoil byare local values representing a narrow volume near themodeling various scenarios covering a range of plausible dis-metal rods (Baker and Lascano, 1989; Ferre et al., 1998).tributions.As will be discussed, the radiometer is more surfacesensitive than the TDR probes buried at the 2-cm depth.RESULTS By assuming a homogeneous soil profile and a smooth

In this section we interpret the radiation measured surface as in the Fresnel approach, we neglected the nat-with the L-band radiometer and its relation to the in situ ural soil heterogeneities (Fig. 1). These factors explainmeasured data. Below we discuss the transformation of the significantly lower radiometrically monitored waterthe radiometric signals to volumetric water contents. We contents compared with the TDR measurements. The dis-follow thereby the simplest path through the evaluation crepancies were especially pronounced during the dry-scheme of Fig. 2, as described in Microwave Radiometry ing phase.above. In this case the soil is assumed to be a homoge-neous dielectric with a smooth surface.

We then replace the concept of constant dielectric soilproperties with a layered dielectric medium. The coher-ent layer model is then used to calculate reflectivitiesexpected for the in situ measured properties. The calcu-lated reflectivities will be compared with the radiometerreflectivity measurements. We also discuss alternative ap-proaches for constructing the dielectric profile based onavailable TDR data and surface structures and the cor-responding changes in the resulting reflectivities.

Fresnel Reconstruction of Water ContentDuring the experiment several precipitation events

with subsequent drying were observed (Fig. 6). The mea-sured brightness temperature and the calculated emissiv-ity closely followed this weather pattern. Figure 7 showswater contents obtained using the Fresnel equation rela-

Fig. 7. Comparison between volumetric water contents measured intive to the water contents measured in situ with TDRsitu with TDR at the 2-cm depth and those calculated based onprobes at the 2-cm depth. the Fresnel equations (Eq. [6] and [7]) using the ELBARA (1.4

In comparison with the water contents determined GHz) radiometer data. For the calculations the soil profile and thesurface were assumed to be smooth.with the TDR probes, the water contents calculated from

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1176 VADOSE ZONE J., VOL. 3, NOVEMBER 2004

Table 1. Optically measured standard deviation �opt of height andhorizontal correlation length l of the soil surface at three stagesof the experiment. Ah, Av, Bh, and Bv were calculated ac-cording to Shi et al. (2002) for a Gaussian correlation functionand used to account for the roughness effect on the soil reflec-tivity according to Eq. [9]. The �opt values are of the sameorder as the corresponding standard deviations �� used in theair-to-soil transition model.

L-band

Cycle Day of Year �opt �� l Ah Av Bh Bv

mm cm1 141.5–153.5 8.2 7.8 2.27 0.0665 0.0709 1.3606 0.49002 156.4–169.5 6.0 3.3 2.30 0.0365 0.0404 1.3711 0.49633 171.3–188.3 9.4 2.27 0.0858 0.0901 1.3570 0.4880

three times during the experiment, as indicated in Fig. 6.Although Table 1 did not show much difference in thesurface characteristics, a comparison of horizontal andFig. 8. Comparison of reflectivities Rradio measured with the L-bandvertical reflectivities indicates some change in the sur-radiometer ELBARA (thick black line) at horizontal (upper graph)

and vertical (lower graph) polarization with reflectivities calculated face characteristics (Fig. 9). The surface was roughestusing the Fresnel equations (Eq. [6] and [7]) based on water con- during the first cycle, which included the first rainfalltents measured in situ by TDR at the 2-cm depth (thin black line), event followed by a draining and drying period. The datathe coherent radiative transfer model (Rt, thick dark-gray line),

for the following two cycles indicated some smoothing ofand the same model but introducing a roughness correction to thethe surface. During the second cycle the observationscoherent reflectivities according to Shi et al. (2002) (thick light-

gray line). were even below the theoretical curve for a perfectlysmooth surface. This may have been due to rain splash–induced silting of the soil surface, which could haveReflectivity from TDR Water Content Profileschanged the porosity of the bulk soil and thus the condi-Using a Coherent Layer Modeltions for the calculated Fresnel curves. In the third cycle

Without Considering Top Surface Structure the surface was locally roughened due to the manual re-moval of sparse vegetation. Overall the reflectivity dataNext, we analyze the need for a more sophisticatedwere close to the function expected for a perfectly smoothmodel for the interpretation of the microwave signal.surface, which is supported by the Fraunhofer criterionFor this purpose, the measured reflectivities Rradio are com-(Eq. [8]). Results are also consistent with the surfacepared with the results Rt obtained with a coherent modelroughness correction model of Shi et al. (2002) as ap-considering a horizontally stratified near-surface soilplied to the calculated reflectivities Rt using the mea-structure, and verified independently by means of opti-sured surface characteristics of Table 1 (Fig. 8). Fig-cal in situ measurements.ure 8 shows the radiometrically measured reflectivities.Figure 8 shows the comparison between radiometri-They are plotted together with the calculated reflectivi-cally measured reflectivities Rradio and reflectivities R cal-ties using the Fresnel approach and a coherent approachculated with different models. The fit to the radiometer

data is slightly improved when the layer model basedon the TDR profiles is used instead of the Fresnel modelbased on the water content at a depth of 2 cm. Both stilloverestimate the measured reflectivity. The reflectivitiesRt were calculated for a layered profile generated fromonly five TDR measurements, with the measurementclosest to the soil surface being at z � 2 cm. Therefore,the water content estimates in the uppermost surfacelayers, which dominate the reflectivities, are most suspect.Furthermore, the topsoil structure in this case was notconsidered in the calculated reflectivity. As a next step,the reflectivity Rt calculated using the layer model is mod-ified to include the surface scattering effect describedwith the roughness model of Shi et al. (2002).

Including Surface Scattering

The value of the standard deviation � of surface heightsFig. 9. Reflectivities measured with ELBARA at horizontal vs. verti-was estimated with the DSM data to quantify the influ-

cal polarization. The solid line represents the values expected forence of surface scattering with the roughness model of a perfectly (Lambertian) rough surface, whereas the dash-dottedShi et al. (2002). The optical roughness measurements line holds for a perfectly smooth surface. Symbols refer to the

three cycles as specified in Fig. 6.yielding the surface height deviations �opt were repeated

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Fig. 10. (a) Reflectivities measured with the L-band radiometer athorizontal polarization (black thick line) compared with reflectivi-ties Rt calculated by using the air-to-soil transition model consider- Fig. 11. Dependence of the roughness parameter h on the volumetricing a water content dependent transition zone of thickness h(�2,t) water content �2,t measured at the 2-cm depth for the two periods(thick gray line). The gray dotted line indicates reflectivities calcu- �1 and �2 (solid lines). The dashed lines show h values for �1 andlated during period �1 if the transition zone dependence h(�2,t) from �2 averaged over the measured water content range. The calculatedperiod �2 is used, and reflectivities during period �2 calculated using � corresponding to h during �1 or �2 are indicated on the righth(�2,t) from period �1. (b) Water content �2,t measured with the axis. These values are of the same order as the optically measuredTDR 2 cm below the soil surface. The data section labeled as wet values �opt shown in Table 1.condition and dry condition refers to the discussion in the sectionEffect of the Extrapolation Approach within the Topsoil.

a good fit to the measured reflectivities, the optimalwith and without considering the scattering effects intro- dependence h(�2,t) of the transition layer thickness fromduced by model of Shi et al. (2002). For the L-band the water content �2,t at the 2-cm depth was determineddata the correction due to the roughness is minimal empirically (Fig. 11). However, the decrease in the trans-since for this wavelength the surface is supposed to be ition zone thickness h with increasing water contentsmooth (Eq. [8]) with respect to scattering. The effect could be interpreted also as a temporary reduction inof surface roughness is different for the two polariza- the soil roughness under wet conditions. Local pondingtions, as stated by Shi et al. (2002). While roughness due to rainfall may appear and disappear dependingreduces the reflectivity at horizontal polarization rela- on the precipitation and infiltration rates. The pondingtive to the reflectivity of a smooth surface, the same effect was visually observed under wet conditions; thus,roughness increases the reflectivity at vertical polariza- it is very plausible that the soil roughness decreasedtion. This effect also diminishes the difference between under wet conditions.horizontal and vertical polarization, which can be seen The data plotted in Fig. 10b show that the measuredat the beginning of the experiment (Fig. 7). Hence, devi- water content �2,t at z � 2 cm varied between 0.18 andations between the two polarizations may be attributed 0.34 m3 m�3. The radiometric and modeled data agreedat least in part to surface scattering. well for the entire observation period when the param-

eter function h(�2,t) (solid lines in Fig. 11) for the twoIncluding the Air-to-Soil Transition Model periods �1 (Day of Year 155 corresponding to Cycle 1)

and �2 (Day of Year � 155) was adapted accordingly.As discussed above, the radiometrically measured re-The two functions for h(�2,t) and the corresponding val-flectivities did not satisfactorily match those calculatedues averaged over the measured range of �2,t are plottedbased on the in situ profiles, even when scattering duein Fig. 11. Results indicate that the radiometric datato surface roughness was considered. In the followingmeasured during the second period �2 agree better withwe use the air-to-soil transition model. In Fig. 10a thethe modeled values when we assume a transition zoneL-band reflectivity measured for horizontal polarizationh smaller than that in period �1. Physically, this may(thick black line) is plotted together with modeled re-reflect surface leveling during rainfall (Fig. 6 and 9),flectivities (thick gray line). The modeled reflectivitieswhich would justify the use of a reduced transition zonewere based on dielectric profiles ε t

soil from the in situthickness h. Furthermore, the decrease in soil roughnessTDR measurements, corrected according to the air-to-with time agreed with the DSM data observed at thesoil transition model and resulting in the εh

app profilesbeginning of the experiment and at the end of period �2(Fig. 3). As seen in Fig. 5, the minimum and maximum(Table 1). Scaled values of the peak-to-peak roughness hradiometric reflectivities Rradio,dry and Rradio,wet were repro-to the standard deviation � according to Eq. [15] areduced by the model, either for a limited range of halso indicated in Fig. 11 (right axis). For the first periodor by making restrictive assumptions concerning the�1 this yields ��1 � 7.8 mm, which is in excellent agree-extrapolation of the water content profile within thement with the DSM �opt data for this period (Table 1).topsoil. For the data fit presented in Fig. 10a, the waterDirect comparisons of the � values have to be consid-content profiles were chosen to be constant within theered with caution. The DSM measurements representtop 2 cm of the soil (dashed profile extrapolations in

Fig. 5a and 5b). Using this assumption and aiming at local conditions on a scale of 30 by 30 cm2, whereas the

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1178 VADOSE ZONE J., VOL. 3, NOVEMBER 2004

Table 2. Mean deviation between reflectivity measured with the ing an air-to-soil transition zone, we improved the con-ELBARA radiometer at horizontal and vertical polarizations sistency between the radiometer reflectivity data and theand the reflectivity calculated with the different model ap-

modeled soil reflectivity considerably. The necessity ofproaches over the entire observation period.considering roughness effects by applying the air-to-soil

Fresnel Coherent Shi et al. (2002) Air-to-soil transition transition model was demonstrated. From this we con-Horizontal 0.103 0.089 0.079 0.029 cluded that small-scale surface structures are relevant inVertical 0.041 0.033 0.045 – the analysis of L-band observations. Unfortunately, the

uppermost soil layers are difficult to characterize byair-to-soil transition model considers structures aver- conventional methods. To understand the nature of soilaged over the entire elliptic footprint area of approx- emission in more detail, the near surface boundary layerimately 9 by 8 m2. Although the optically measured should be more precisely examined and parameterizeddatabase is clearly insufficient for justifying the changes at high spatial resolution.in h or � in time, it shows that these values are of asimilar order of magnitude. ACKNOWLEDGMENTS

The radiometer used in this study was designed and con-Model Comparison structed at the Institute of Applied Physics, University of Bern.Special thanks are due to Daniel Weber and Max Wuthrich.Table 2 shows the mean deviation between reflectivityThe digital surface models were derived with the help of JochenRradio measured with the radiometer and the reflectivityWillneff from the Institute of Geodesy and PhotogrammetryRt calculated with the different models over the wholeETH Zurich. Success of the demanding field experiment wasobservation period. As can be seen, the stepwise refine- largely due to Jorg Leuenberger, Hannes Wydler and Hanspi

ment of the models leads to smaller deviations between Laser from the Institute of Terrestrial Ecology, ETH Zurich.measured and modeled reflectivities. The deviation was This work has been supported by a science grant from thelargest using the simple Fresnel approach described. The Swiss Federal Institute of Technology (ETH) Zurich.coherent model led to only a small improvement. Intro-ducing the surface scattering model of Shi et al. (2002), REFERENCESenhanced the horizontal polarization but worsened the Baker, J., and R. Lascano. 1989. The spatial sensitivity of time-domainagreement at vertical polarization. Finally, the air-to- reflectometry. Soil Sci. 147:378–384.

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