mapping surface roughness and soil moisture using … surface roughness and soil moisture using...

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nt 112 (2008) 391–402www.elsevier.com/locate/rse

Remote Sensing of Environme

Mapping surface roughness and soil moisture using multi-angle radarimagery without ancillary data

M.M. Rahman a,⁎, M.S. Moran a, D.P. Thoma a, R. Bryant a, C.D. Holifield Collins a,T. Jackson b, B.J. Orr c, M. Tischler d

a USDA ARS Southwest Watershed Research Center, Tucson, Arizona, USAb USDA-ARS Hydrology and Remote Sensing Laboratory, Washington DC, USA

c Office of Arid Land Studies, University of Arizona, Tucson, Arizona, USAd US Army Engineer Research and Development Center, Topographic Engineering Center, Alexandria, Virginia, USA

Received 4 April 2006; received in revised form 26 September 2006; accepted 31 October 2006

Abstract

The Integral Equation Model (IEM) is the most widely-used, physically based radar backscatter model for sparsely vegetated landscapes. Ingeneral, IEM quantifies the magnitude of backscattering as a function of moisture content and surface roughness, which are unknown, and theknown radar configurations. Estimating surface roughness or soil moisture by solving the IEM with two unknowns is a classic example of under-determination and is at the core of the problems associated with the use of radar imagery coupled with IEM-like models. This study offers asolution strategy to this problem by the use of multi-angle radar images, and thus provides estimates of roughness and soil moisture without theuse of ancillary field data. Results showed that radar images can provide estimates of surface soil moisture at the watershed scale with goodaccuracy. Results at the field scale were less accurate, likely due to the influence of image speckle. Results also showed that subsurface roughnesscaused by rock fragments in the study sites caused error in conventional applications of IEM based on field measurements, but was minimized byusing the multi-angle approach.© 2007 Published by Elsevier Inc.

Keywords: Soil moisture; Surface roughness; Radar; ENVISAT-ASAR; Integral Equation Model; Active microwave

1. Introduction

Information about the distribution of surface soil moisture(θS) is important for a number of applications ranging from themanagement of agriculture and natural resources to the scienceof understanding land–atmosphere interaction to determiningvehicle mobility. Images of radar backscatter from orbitingsensors have been used for mapping surface soil moisture(Moran et al., 2004). Retrieval of θS from radar backscatter (σ0)is often based on radar backscatter models, such as the IntegralEquation Model (IEM), which was developed for bare soil, butcan be used with sparse vegetation (Fung, 1994; Fung & Pan,

⁎ Corresponding author.E-mail address: [email protected] (M.M. Rahman).

0034-4257/$ - see front matter © 2007 Published by Elsevier Inc.doi:10.1016/j.rse.2006.10.026

1986; Fung et al., 1992). In general terms, IEM represents theradar backscatter of an image with known radar configurationsas a function (f) of θS and surface roughness, where

r0 ¼ f ðhRMS; LchSÞ: ð1ÞThe model characterizes surface roughness by the root mean

squared height (hRMS) variation of the surface at centimeterscale and the correlation length (Lc) of the same heightvariation. It is conventionally measured by a pin meter, andmore recently, by field-deployed laser scanners (both describedby Bryant et al. (2007)).

Recent studies have indicated that the magnitude of hRMS

and Lc are scale related (Le Toan et al., 1999) and highlydependent on the length of the transect (Bryant et al., 2007),when measured with a pin meter or laser scanner. This is trueespecially for the estimate of Lc (Bryant et al., 2007; Davidsonet al., 2000). The suggestions for optimum transect length vary

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http://dx.doi.org/10.1016/j.rse.2006.10.026

392 M.M. Rahman et al. / Remote Sensing of Environment 112 (2008) 391–402

from a couple of meters (Baghdadi et al., 2000) to hundreds ofmeters (Verhoest et al., 2000). Lc also depends on the type ofauto correlation function used in its estimation from field data(Baghdadi et al., 2004; Davidson et al., 2000). This implies thatconsistent roughness parameters may not be estimated usingfield data for use as an input to the IEM. Moreover, conductingfield measurement of roughness may become impractical andexpensive when large areas need to be covered.

In addition to the field measured roughness, the abundanceof rock fragments, if present in study locations, may influenceradar-perceived roughness. The radar signal penetrates a fewcentimeters below the ground and is likely to be affected bythe subsurface nature of roughness caused by rock fragmentsbelow the soil surface (Jackson et al., 1992). When the radarsignal penetrates a few centimeters below the ground surface,it experiences multiple bounce by the subsurface rockfragments, which may result in volume scattering. It is likelythat the radar-perceived roughness is a combination of surfaceand subsurface roughness. On the other hand, the pin metermeasures roughness at the top of the soil surface and is notdesigned to measure the roughness caused by the subsurfacerock fragments.

For all these reasons, measurement of distributed surfaceroughness has been a barrier for regional application and wideuse of microwave technology for surface soil moisture sensing.It would be beneficial to develop a surface roughness mappingsystem based solely on satellite data and a radar backscattermodel, eliminating the need for field measurements altogether.In such a situation, an operational soil moisture assessmentsystem based on a radar backscatter model would be practical.Furthermore, maps of surface roughness may have potentialusefulness based on their own merit. The availability of image-based roughness maps may provoke future applications toerosion prediction, surface runoff modeling and soil moistureestimation from passive microwave imagery.

Many components of research needed to develop an image-based approach have already been published and can becompiled to develop a method for mapping of roughness andsoil moisture. Zribi and Dechambre (2002) indicated aninteresting property of IEM that may have great use. Theyfound that the difference in backscatter (Δσ0) generated by theIEM model with two different incidence angles, keeping allother parameters constant, is in proportion to roughness only.It was found that Δσ0 is proportional to the ratio of hRMS andLc, which was referred to as the z-index and defined as hRMS

2 /Lc. Z-index is computed by Zribi and Dechambre (2002),where

h2RMS=Lc ¼ gðDr0Þ: ð2Þ

This equation is generally valid when the difference inincidence angles is large and surface moisture conditions remainunchanged. Here, ‘g’ is a function, the specific form of whichcan be estimated using IEM simulated data. This formulationprovides a foundation for mapping of surface roughness usingradar imagery with two incidence angles. However, theformulation does not provide an explicit solution of hRMS and

Lc, which are needed as inputs to IEM for the retrieval of surfacesoil moisture from radar imagery.

As a complement to the work by Zribi et al., Rahman et al.(2007) expressed the relation between hRMS and Lc usingsimple equations based on IEM theory. Then, using a radarimage obtained with relatively dry surface condition (θS on theorder of 0.03 m3 m−3), they showed that it was possible toderive both hRMS and Lc from the measurement of radarbackscatter. That is, the effect of θS on the σ0 of a radar signalmeasured in the dry season (σdry

0 ) is very low and this wasneglected altogether without making significant error. IEMsimulation indicates that 0.03 m3 m−3 deviations in the soilmoisture may cause error up to 1 db (Rahman et al., 2007),when the moisture condition is low. Considering the statedabsolute accuracy of the radar sensor is approximately 1 dB(Staples & Branson, 1998), this error may be acceptable. Thegeneral form of the equation was written as

r0dry ¼ hðhRMSLcÞ: ð3Þ

This equation holds over certain incidence angle ranges,usually 30 to 50°. The specific form of the equation wasestimated using IEM simulated data for certain radar config-urations (Rahman et al., 2007).

Substituting terms between Eqs. (2) and (3) it should bepossible to solve for two roughness parameters, hRMS and Lc,explicitly, where

Lc ¼ xðDr0; r0dryÞ; andhRMS ¼ wðDr0; r0dryÞ: g ð4Þ

Here, ω and ψ are two functions determined by substitutionof terms. The resulting roughness maps then can be used toparameterize IEM for producing surface soil moisture map.

As evident in this formulation, a maximum of three radarimages are needed for roughness mapping. These include twoimages with different incidence angles to determine Δσ0 andone image with dry ground condition to measure σdry

0 . Theimage requirements can be reduced to two if the images attwo incidence angles are available for dry surface conditions.In this case, one of them can be used for extracting σdry

0 andboth can be used to extract Δσ0. The images required forcomputing Δσ0 can be acquired with either dry or wetsurface conditions. However, the moisture content of theground surface has to remain unchanged during acquisitionof these two images, since Δσ0 is modeled as a function ofroughness only (Eq. (2)). Moreover, the roughness itself hasto remain unchanged during acquisition of all images, sincethe goal is to solve for the roughness parameters fromimages.

In spite of these limitations, data from currently orbitingradar sensors can be used to resolve Eq. (4) and determine bothhRMS and Lc for IEM parameterization. In the second step, thevalues of hRMS and Lc can be substituted in Eq. (1) andexpressed as

r0wet ¼ kðDr0; r0dry; hSÞ; ð5Þ

393M.M. Rahman et al. / Remote Sensing of Environment 112 (2008) 391–402

where the subscript “wet” in σwet0 is used to distinguish it from

backscatter of a dry surface (σdry0 ), as defined earlier. Eq. (5)

then can be inverted for solving surface soil moisture, where

hS ¼ λ�1ðDr0; r0dry; r0wetÞ: ð6Þ

Here, Δσ0 and σdry0 are functions of roughness parameters,

such as Δσ0(hRMS, Lc) and σdry0 (hRMS, Lc), which in turn

implies that θS is modeled in Eq. (6) as function of roughnessand σwet

0 . In the presence of integrals and Fourier transform inthe ‘λ’ function of IEM, it is difficult, though not impossible, toget an inverse. This difficulty can be overcome by anapproximation of Eq. (6) with a polynomial of required order.IEM simulated data can be used for this purpose.

Since the solution of all parameters, such as hRMS, Lc and θS,can be obtained through simultaneous use of images asdescribed above, pixel-by-pixel computation can be implemen-ted to derive the outputs in the form of maps.

The specific objectives of this study are as follows:

1) Implement the method outlined above for mapping charac-teristic parameters of surface roughness by the use of twoEnvisat ASAR images (June 9 and June 15, 2004) obtainedunder dry surface conditions;

2) Compare image-based measurements of hRMS and Lc withconventional pin meter measurements for 13 sites in thesemiarid Walnut Gulch Experimental Watershed (WGEW)near Tucson, Arizona;

3) Use the resulting roughness map to parameterize IEM formapping soil moisture from two more Envisat ASAR images(July 14 and August 2, 2004) of WGEW under relatively wetground condition; and

4) Validate the resultant surface soil moisture maps with fieldmeasurements of the same 13 sites during the overpass ofEnvisat on July 14 and August 2, 2004.

2. Materials and methods

To achieve research objectives, a study was conducted inArizona in 2004, where a range of radar remote sensing data,and field collected roughness and soil moisture data was used.The IEM model approximated by simple functions were appliedto the radar data for estimation of soil moisture and surface

Table 1Sensor configuration of radar imagery used in this study

Envisat ASAR

Image data June 9, 2004 June15, 2004Purpose Roughness mapping Roughness mappPixel resolution 12.5 m 12.5 mUsed polarization VV VVImage swath IS6 IS2Incidence angle 41.08° 24.8°Frequency C-band (5.3 GHz) C-band (5.3 GHWavelength 5.6 cm 5.6 cmTime of overpass 10:16 am 10:27 am

roughness, which were then compared with the field collecteddata.

2.1. Study site

This field study was conducted in the 150 km2 Walnut GulchExperimental Watershed (WGEW) operated by United StatesDepartment of Agriculture, Agriculture Research Service(USDA-ARS). The watershed is located in the Sonoran desert,State of Arizona, near the US–Mexico border. The watershed hasa semi-arid climate in which the average annual rainfall is330 mm. It is characterized by rolling hills ranging in elevationfrom 1220 to 1960 m and the major soil type is sandy loam withrock fragment fractions on the order of 47% by volume withinthe top few centimeters of the soil surface (USDA–NRCS,2002). The watershed has sparse vegetation, consisting mainly ofdesert grass and shrub. There are many ephemeral streams andchannels running across the watershed with no perennial watersupply or source. The watershed is instrumented with precipi-tation gages, meteorological stations, soil moisture sensors andflumes for hydrologic experimentations (Renard et al., 1993).

2.2. Satellite data processing

Four Envisat ASAR images were used in this study; thespecific type of the product is Alternating Polarization EllipsoidGeocoded, which is described in the ASAR product handbook(ESA, 2002). Some of the features of the images used foranalysis in this study are given in Table 1.

The image digital numbers (DN) are in units of amplitudeand were converted to backscatter values (σ0) following theASAR product handbook. The computation of σ0 was

r0 ¼ hA2iK

sina; ð7Þ

where σ0 is the radar backscatter in power [m2/m2], A is thepixel intensity in amplitude values, K is the external calibrationconstant [m2/m2] and α is the distributed incidence angle. Theexternal calibration constant and distributed incidence angles ofa particular image are found by performing header analysisusing ‘BEST’ software (www.envisat.esa.int). The backscatteris converted from power to decibel unit (dB) for the use in the

July 14, 2004 August 2, 2004ing Soil moisture mapping Soil moisture mapping

12.5 m 12.5 mVV VVIS6 IS541.08° 37.39°

z) C-band (5.3 GHz) C-band (5.3 GHz)5.6 cm 5.6 cm10:16 am 10:19 am

http://www.envisat.esa.int


analysis. Power to decibel conversion is a logarithmic con-version, where

r0ðdBÞ ¼ 10½log ðr0Þ�: ð8ÞThe ASAR images acquired on June 9 and June 15, 2004

were coincident with dry surface conditions and were used forthe roughness mapping. The two images were selected so thatthe difference in incidence angles was the largest possible. IEMsimulations suggest that the backscatter differences becomemore sensitive to surface roughness as the difference inincidence angle increases and are helpful for estimation ofroughness. The ASAR images acquired on July 14 and August2, 2004 corresponded to relatively wet surface conditions andwere used for soil moisture mapping.

A median filter consisting of a 9-pixel moving window wasapplied for optimal speckle reduction (Thoma et al., 2006).Despite the filtering, some extreme high and low values of radarbackscatter were detected in all output maps. Particular pixelvalues that deviated from the mean value of pixels (plus orminus) by more than three times the standard deviation wereconsidered extreme values. The prevalence of extreme valueswas not large, and they seemed to associate with the mountaintops and surrounding areas, indicating likely effects oftopography on the radar backscatter. A mode filter based on a3-pixel moving window was applied over the image to replaceextreme values with the mode of the surround values. This filterwas effective in relatively flat areas where extreme values wereless prevalent. In mountainous regions, a second pass of anothermode filter based on a 10-pixel moving window was needed.

A good image-to-image registration was essential for this studysince backscatter of corresponding pixels of two images weredifferenced in computing roughness of that pixel. Visualinspection indicated that the geocoded images that were used inthis study had good image-to-image registration; therefore, furtherimage registration was not applied. However, deviations up tothree pixels were observed in image-to-ground registration insome parts of the study area, when geocoded images werecomparedwith geo-registered aerial photographs. The accuracy ofthe computation needed for mapping surface roughness should beunaffected by this deviation, however, the deviationmay affect thevalidation process. For validation of the results, that is, comparingoutput maps values with field data, an area of 110 by 110 mcorresponding to each sample site was extracted from theroughness and soil moisture maps based on their knowncoordinates and was clipped. The averages of the values withinclipped areas were compared with the field measurements ofroughness and soil moisture. The 3-pixel deviation in registrationmay have affected the clipping part of validation process. To checkif the 3-pixel deviation in registration had an impact, the size of theclipped area was increased to 150 by 150 m and the validationprocess was repeated. The increase in window size used forclipping was likely to capture effects of 3-pixel registration error.

2.3. Ground measurements of soil moisture and roughness

The top 5-cm surface soil moisture (θS) was measured at 13sites over the two most dominant soil types of the WGEW (very

gravelly sandy loam Elgin–Stronghold complex and verygravelly sandy loam Luckyhills–McNeal complex) at the timeof Envisat overpasses on July 14 and August 2, 2004.Depending on the level of moisture, approximately 20–30measurements were made with a Theta Probe over a 110 by110 m area at each of the 13 sites. The objective of thesemeasurements was to capture the spatial variability of θS over9×9 Envisat image pixels for each training site. The time spanover which the field measurements were undertaken wasdivided equally before and after the satellite overpass. Soilmoisture data during dry season overpass of Envisat (June 9 andJune 15, 2004) was measured with a Vitel Probe installed at5 cm depth at all 13 sites for automatic and year roundmonitoring of soil moisture. For the WGEW study site, theabundance of rock fragments may have caused problems for theTheta Probe or Vitel Probe to capture the true moisture contentof the soil. The problem caused by the presence of rockfragments is the differential content of moisture in soil and inrock fragments of the targeted material. Rock fragments havelittle moisture even when the surrounding soil is saturated.Radar backscatter may be sensitive to moisture content of rock–soil composite as opposed to the moisture content of the soilonly measured by the Theta Probe signal. The pins of the ThetaProbe instruments need to penetrate into the soil in order to get amoisture reading. This requires a spot on the ground that hasnegligible amount of rock fragments. A rock fragmentcorrection was made by subtracting the rock fraction effectfrom the field measure of volumetric soil moisture in themanner described by Thoma et al. (2006). The adjustmentinvolves reducing the field measured moisture content by theaverage proportion of rock fragment in the study site, which is47%, to represent moisture content of rock–soil composite. Thiscomputation was based on the assumption that the rock containsnegligible amounts of moisture and the Theta Probe measuredmoisture constitutes the soil portion of the rock–soil composite.It was further assumed that all experiment locations have thesame rock fragment content, the magnitude of which is equal tothe watershed average. This later assumption may have someimplication to the accuracy of the result, given the unavailabilityof rock fragment data for all study locations.

Field data collected from 13 sites spread over 150 km2 ofWGEW were summarized in Table 2. The moisture content ofthe study site was generally low, with an average of roughly0.05 during the study period. The average moisture content was0.04 m3 m−3 in July and had increased to 0.07 m3 m−3 inAugust. The variability of moisture content across space wasgreater (0.02 to 0.06 m3 m−3 in July, and 0.02 to 0.10 m3 m−3 inAugust). The soil moisture contents were the same in June 9 andJune 15 (0.03 m3 m−3).

Surface roughness for the 13 sample sites was measuredusing a pin meter of 3-m profile length in December, 2004. Thepin meter traced the surface height variation at 1-cm intervalsand the trace was documented in a photograph with a digitalcamera. Ten pin-meter measurements were made randomly overan area of 35×35 m around each sample site. The photographswere processed with a computer program to generate values ofhRMS and Lc averaged over each site (Bryant et al., 2007). An

Fig. 1. The ranges of roughness parameters, correlation length (Lc) and RMSheight (hRMS), valid for IEM (area under the curve), Mametsa et al. (2002).

Table 2Summary statistics of field measured moisture content (θS), roughness RMSheight (hRMS) and correlation length (Lc)

Field measurements, 13sites

June 9,2004

June15,2004

July 14,2004

August 2,2004

Moisture content a (θS), in m3 m−3

Mean 0.03 0.03 0.04 0.07SD 0.01 0.01 0.01 0.01

Surface roughness in cmMean hRMS 0.79SD hRMS 0.29 Conducted once in December, 2004Mean Lc 8.20SD Lc 2.47

a Correction for rock fragment applied.


exponential autocorrelation function was assumed for comput-ing Lc. This assumption was based on an experiment in whichexponential and Gaussian correlation functions were used forestimation of Lc and the exponential function worked betterwith these data. This method of measuring roughness may havesome limitations. When radar signal penetrates a few cen-timeters below ground surface it experiences multiple bounceby the subsurface rock fragments, which results in volumescattering. This is in addition to the scattering due to surfaceroughness. As a result, radar-perceived roughness is likelylarger than that of field measurements. The roughnessmeasuring field device, the pin meter, is not designed toaccount for subsurface nature of roughness. Therefore,roughness measurements by the pin meter may not be adequateto characterize surface roughness for input to IEM, especiallyfor study sites with large amounts of rock fragments.

The average hRMS across all sites was found to be 0.79 cm,with a maximum of 1.3 cm and a minimum of 0.48 cm. Theaverage field measurement for Lc was 8.2 cm, ranging from5.0 cm to 12.2 cm.

2.4. Radar model and implementation

The Integral Equation Model (IEM) is the most widely-used,physically based radar backscatter model, and is well suited for thesparsely vegetated landscapes of the study site. In general, IEMquantifies the magnitude of backscattering as a function ofmoisture content and surface roughness, which are unknown, andthe known radar configurations. Estimating surface roughnessor soil moisture by solving the IEM with two unknowns is thecore of the problems associated with the use of radar imagerycoupled with IEM-like models. The conceptual model for solvingthis problem and mapping surface roughness and soil moisturewithout the use of ancillary data is outlined in Eq. (1) thru Eq. (6).To implement this model, the specific forms of Eqs. (2), (3) and (6)need to be derived in simple form for the radar imageconfigurations used in this study. Because of the complex formof the IEM, analytically deriving these equations can be difficult.However, approximations of these equations with high level ofprecision may be possible by fitting polynomials with the IEMsimulated data. This process is independent of field data andsimply transforms IEM approximately into simple polynomialswith parameter estimates.

With multiple runs of IEM, two data sets of σ0 weresimulated for the radar configurations similar to the June 9 andJune 15 Envisat ASAR images (Table 1), and for validcombinations of Lc and hRMS (Fig. 1). The moisture contentθS was kept fixed at 0.03 m3 m−3 to simulate a dry conditionsimilar to the June 9 and June 15 images. The only difference inconfiguration between these two images, and therefore the twodata sets, is the incidence angle (25° and 41°, respectively). Thetwo data sets of backscatter were subtracted from one another(Δσ0) and the z-index was computed from correspondingvalues of Lc and hRMS. Backscatter difference was regressedwith the z-index to get a best fit function to relate the twoparameters, the general form of which is specified in Eq. (2). Inorder to get the specific form of Eq. (3), simulated backscatterassociated with the June 15 image configuration was regressedwith roughness parameters to fit a polynomial function ofrequired order. The resulting equation, therefore, became anapproximation of IEM under low moisture conditions, which issimilar to the dry season. This procedure for determining thespecific form of Eq. (3) was described in great detail by Rahmanet al. (2007).

Two more data sets of IEM simulated backscatter werecreated for radar configurations similar to wet season imagesacquired on July 14 and August 2, 2004 (Table 1) and for validcombinations of Lc and hRMS (Fig. 1) and θS (0.03 to 0.40 m3

m−3). For each data set the moisture content (θS) was regressedwith simulated backscatter, Lc and hRMS to fit a polynomial.These fitted polynomials represent the inverted IEM, which isspecified in general terms in Eq. (6) for conditions on July 14and August 2, 2004.

3. Results and discussion

The objectives of the study were to produce surface soilmoisture and roughness maps using radar remote sensing dataand to compare the map values with the ground measurements.The derivations of the specifics of the conceptual model toachieve the objectives are presented and their application forproducing desired outputs are demonstrated. The strength andweaknesses of the whole approach are discussed.

Fig. 2. Relation between roughness z-index (hRMS2.5 /Lc) and radar backscatter

difference (Δσ0) between two images of same target under unchanged groundconditions with different incidence angle (41° and 25°) as specified in Eq. (7).


3.1. Mapping roughness

Surface roughness is often expressed by its statisticalcharacteristic parameters, such as hRMS, Lc and the shape ofthe autocorrelation function. In this study, mapping of surfaceroughness refers to mapping of hRMS and Lc, while an a-prioriassumption was made on the shape of the autocorrelationfunction. Mapping of hRMS and Lc was achieved by explicitlysolving the specific form of Eqs. (2) and (3) as indicated inEq. (4) and described below.

The specific form of Eq. (2) was derived by the use of asimulated data set, the description of which is given before inthe Radar Model and Implementation subsection. The data setincluded IEM-simulated backscatter difference (Δσ0) betweentwo incidence angles (25° and 41°), and the surface roughnessand moisture information for which the data set was simulated.The incidence angles selected for simulation match the radar

Fig. 3. IEM embedded relationship among roughness RMS height (hRMS), correlationm−3. The graphs are plots of Eq. (10) that approximates IEM with negligible moist

images acquired for roughness mapping (Table 1). Using thatdata set, a function was fitted through z-index and Δσ0 toget a specific form of Eq. (2). It was found that the definitionsof z-index as well as the specific functional form used by Zribiand Dechambre (2002) needed a slight change to better fit theradar configurations used in this study. With the newly definedz-index, which is hRMS

2.5 /Lc, the specific form of Eq. (2) became

h2:5RMS=Lc ¼ ð0:618þ 0:09Dr0Þ=ð1� 0:138Dr0Þ; ð9Þwith R2 =0.998 and RMSE=0.02 (Fig. 2). Note that this is notan empirical model derived from field data, but rather, anapproximation of IEM using simple functions based on IEMsimulated data.

Plugging the backscatter difference (Δσ0) between consecu-tive pixels of two images acquired over the study site with dif-ferent incidence angles (25° and 41°) into the above equation, amap of z-index was produced. These images were acquired in thesummer time under dry surface conditions over a short temporalinterval (June 9 and June 15), thereby satisfying the invariant soilmoisture, roughness and vegetation conditions on which Eq. (9) isbased.

Derivation of Eq. (3) was achieved by the use of the IEM-simulated data set for dry surface condition and a singleincidence angle (41°). The dry surface condition was simulatedby the use of low and invariant value of moisture level(θS=0.03 m3 m−3). The data set was described in the RadarModel and Implementation subsection. Following Rahman et al.(2007), a polynomial of required degree was fitted with the datato get the specific form of Eq. (3) as

r0dry ¼ �27:94þ 32:58hRMS � 1:40Lc � 18:78h2RMS

þ 0:05L2c þ 0:86hRMSLc þ 2:65h3RMS

þ 0:12h2RMSLc � :04hRMSL2c ; ð10Þ

where R2 =0.987 and RMSE=0.65 (Fig. 3). Again, this is anapproximation of IEM with a simple function. Multiple

length (Lc) and Radar backscatter (σ0) for a fixed moisture content, θS=0.03 m

3

ure condition. The numbers inside the graphs are σ0 in dB unit.

Fig. 4. Roughness map (hRMS in cm) derived from radar images by the use of IEM, as formulated in Eq. (4). The solid line represents the boundary of USDA ARSWalnut Gulch Experimental Watershed.


solutions for hRMS and Lc exist for a particular value ofbackscatter, which is an inherent character of IEM. Theestimated equation reflects this character. The first solution isalways accepted following Baghdadi et al. (2004).

The Lc as a function of hRMS and z-index from Eq. (9) wassubstituted in Eq. (10) to obtain

r0dry ¼ �27:94þ 32:58hRMS � 18:78h2RMS þ 2:65h3RMS

þ 1z� index

�1:40⁎h2:5RMS þ 0:86⁎h3:5RMS þ 0:12⁎h4:5RMS

� �

þ 1z� index

� �2

0:05⁎h5RMS � :04⁎h6RMS

� �:

ð11ÞThis equation was solved numerically to obtain hRMS as a

function σdry0 and z-index (and z-index, in turn, as a function of

Δσ0). The resulting hRMS was then substituted back in Eq. (9)to solve for Lc. Thus, the solution of hRMS and Lc as a functionof σdry

0 and Δσ0 indicated in Eq. (4) was achieved. Using ArcInfo programming facilities, the solution process was conductedon a per-pixel basis, where the radar image acquired on June 15,2004 was used for extracting σdry

0 and the z-index map producedin an earlier stage was used for extracting the value of z-index ofthe corresponding pixel. The resulting value of hRMS wasassigned to the corresponding pixel of a new map referred to as

Fig. 5. Roughness map (Lc in cm) derived from radar images by the use of IEM, as forGulch Experimental Watershed.

hRMS map (Fig. 4). The map of Lc was obtained by the simpleArc Info grid operation as Lc=hRMS

2.5 / z-index (Fig. 5). In Figs. 4and 5, blue colors represent high roughness, which seem to beassociated with the mountainous areas, for both hRMS and Lc.The river stream beds and adjacent areas, and mountain valleyareas look smoother with low roughness values represented bythe red color. In this application, Eq. (10) was derived for a fixedincidence angle, close to angles of the experimental fields. Errormight increase with distance from these fields and with changesin local incidence angle caused by rough terrain.

3.2. Mapping soil moisture

The general framework for estimating soil moisture throughparameterizing IEM with the image-derived roughness maps wasprovided in Eq. (6). In order for the framework to be operational,the approximate specific form of Eq. (6) needed to be determined.IEM simulated data were used again for this purpose. This timethe radar configurations were chosen to simulate July 14 andAugust 2, 2004 images for valid combinations of hRMS, Lc andθS. Using the data set in a regression analysis, Eq. (12) and Eq.(13) were derived as approximations of Eq. (6) for July 14 andAugust 2, 2004 respectively. These are fourth order polynomialequations, for which multiple solutions are theoretically possible.However, within the domain of our parameter values unique

mulated in Eq. (4). The solid line represents; the boundary of USDAARSWalnut

Fig. 7. Comparison of roughness (hRMS), where field measurements from 13experimental sites were plotted in the x-axis and image-derived roughnessestimates extracted from same sites were plotted in the y-axis.

Fig. 6. Soil moisture map (in m3 m−3) for July 14, 2004 derived from radar images by the use of IEM, as formulated in Eq. (6). The solid line represents the boundary ofUSDA ARSWalnut Gulch Experimental Watershed. A similar soil moisture map was produced for August 2, 2004, but the maps were nearly identical in color and thesecond map was not included here.


solutions for soil moisture were achieved. As with Eqs. (9) and(10), Eqs. (12) and (13) were not derived from field data, but froman approximation of the inverted IEM.

lnðhSÞ ¼ :353þ 1:384 lnð�r0Þ � :913flnð�r0Þg2�1:735lnðLcÞ þ :947flnðLcÞg2 þ :013flnðLcÞg3 � :017flnðLcÞg4�1:791lnðhRMSÞ þ 5:475flnðhRMSÞg2 þ :743flnðhRMSÞg3þ:087flnðhRMSÞg4 � 1:95lnðhRMSÞlnðLcÞ�1:0flnðhRMSÞg2lnðLcÞ � :187flnðhRMSÞg3lnðLcÞþ:006flnðLcÞg2lnðhRMSÞ þ :048flnðLcÞg3lnðhRMSÞþ:055flnðLcÞg2flnðhRMSÞg2 þ 1:291lnð�r0ÞlnðhRMSÞþ:1lnð�r0ÞlnðLcÞ � :112lnð�r0ÞflnðLcÞg2�:79 lnð�r0ÞflnðhRMSÞg2

ð12Þwhere R2=0.996 and RMSE=0.04.

lnðhSÞ ¼ �:064þ 1:765lnð�r0Þ � :986flnð�r0Þg2�1:83lnðLcÞ þ :866flnðLcÞg2 þ :028flnðLcÞg3 � :019flnðLcÞg4�:515lnðhRMSÞ þ 5:366flnðhRMSÞg2 þ :885flnðhRMSÞg3þ:112flnðhRMSÞg4 � 2:089lnðhRMSÞlnðLcÞ�1:071flnðhRMSÞg2lnðLcÞ � :197flnðhRMSÞg3lnðLcÞþ:017flnðLcÞg2lnðhRMSÞ þ :048flnðLcÞg3lnðhRMSÞþ:053flnðLcÞg2flnðhRMSÞg2 þ 1:003lnð�r0ÞlnðhRMSÞþ:07lnð�r0ÞlnðLcÞ � :084lnð�r0ÞflnðLcÞg2�:688lnð�r0ÞflnðhRMSÞg2

ð13Þwhere R2=0.996 and RMSE=0.04.

The inversion of IEM derived in Eqs. (12) and (13) wasimplemented in the Arc Info grid environment to produce soilmoisture (θS) maps, where image-derived roughness maps(hRMS and Lc) and radar images (σ0) under wet condition wereused as inputs. Thus, soil moisture maps were produced for theimages acquired on July 14 and August 2, 2004 (Fig. 6). InFig. 6, the dominant red colors in the map represent low level ofmoisture across almost the entire watershed, except river streamsandmountain valley areas, where the color is bluish representingrelatively higher level of moisture. However, this map maycontain some error caused by varying incidence angles inlocations far from the experimental fields and in rough terrain.

3.3. Field validation of surface roughness and soil moisture maps

Field measurements of soil moisture were made over the 110by 110 m area of each of the 13 sample sites, whereasmeasurements of roughness are made over a 35 by 35 m area.The 110 by 110 m areas corresponding to each sample site wereidentified on the soil moisture maps based on their knowncoordinates for clipping. The same operation was conducted onthe surface roughness map, but the clipped areas were 35 by35 m. The average of the map values within clipped areas wascompared with the field measured values of roughness (Figs. 7and 8) and soil moisture (Fig. 9).

It was found that the field-data-derived surface roughnessparameters were generally low both for hRMS and Lc comparedto the same derived from radar images (Table 3). The image-derived hRMS and Lc averaged over all experiment locationswere 2.19 cm and 13.3 cm as opposed to 0.79 cm and 8.2 cmrespectively for field measurements. This may be a confirmation

Fig. 8. Comparison of roughness (Lc), where field measurements from 13experimental sites were plotted in the x-axis and image-derived roughnessestimates extracted from same sites were plotted in the y-axis.

Table 3Comparisons of roughness measurements by image data

Validation Mean SD Min Max

Lc derived from fieldmeasurements by pinmeter, cm 8.20 2.42 4.98 12.15Lc derived from image data, cm 13.25 3.60 7.61 22.43hRMS derived from field measurements by pinmeter, cm

0.79 0.28 0.48 1.30

hRMS derived from image data, cm 2.19 0.49 1.17 2.97


that the subsurface roughness caused by the rock fragmentsplays an important role. The radar signal is probably responsiveto multiple bounce by the subsurface rock fragments when itpenetrates a few centimeters below ground surface. As a result,radar-perceived roughness may be much larger than that of fieldmeasurements. The roughness-measuring field device was notdesigned to account for subsurface nature of roughness. There-fore, roughness measurements by the pin meter may not beadequate to characterize surface roughness for input to IEM,especially for study sites with large amounts of rock fragments.

Concerning soil moisture, good association between image-derived soil moisture and averaged field measured soil moisturewere found once the fieldmeasured soil moisture was adjusted forthe effects of rock fragments (Fig. 9, Table 4). The image-derivedmoisture contents averaged over all experiment locations are

Fig. 9. Validation soil moisture maps, where field measurements from 13experimental sites were plotted in the x-axis and, image-derived moistureestimates extracted from same sites were plotted in the y-axis. Cross signs arepoints associated with July 14, 2004 overpass of Envisat and the circles are withAugust 2, 2004.

0.07 m3 m−3 and 0.08 m3 m−3 for July and August as opposed to0.04 m3 m−3 and 0.07 m3 m−3 respectively for field measuredmoisture content. Thoma et al. (2006) presented similar evidencefor the same watershed following a different technique. It appearsthat radar remote sensing is successful in providing goodestimates of soil moisture at a watershed scale, although itssuccess at the field scale remains uncertain.

In this study there are a number of potential sources of errorsthat may have some association with the uncertainty in the resultat the field scale, which is evident in the scattering of points inthe Fig. 9. The adjustment of field measured soil moistureconcerning rock fragments involves reducing the field measuredmoisture content by the average proportion of rock fragment inthe study site, which is 47%, to represent moisture content ofrock–soil composite. This computation was based on the as-sumption that the rock contains negligible amounts of moistureand the Theta Probe measured moisture constitutes the soilportion of the rock–soil composite. It was further assumed thatall experiment locations had the same rock fragment content,the magnitude of which was equal to the watershed average.This later assumption may have some impact on the accuracy ofthe results, given the unavailability of rock fragment data for allstudy locations.

Another source of error in the field validation may be relatedto the method of speckle reduction. A median filter consisting ofa 9-pixel moving window was applied for speckle reduction,which may not be adequate. Theoretically, speckle is randomerror added to the pixel values of an image, which is inherent tothe radar remote sensing. The terrain of the watershed under

Table 4Watershed scale field validation of soil moisture measurements by image data

Validation Mean SD Min Max

July 14, 2004θS by field measurements, m3 m−3 0.04 0.01 0.02 0.06θS derived by image data, m3 m−3 0.07 0.02 0.03 0.11θS derived by IEM using field measuredroughness, m3 m−3

0.16 0.10 0.03 0.35

August 2, 2004θS by field measurements, m3 m−3 0.07 0.01 0.05 0.10θS derived by image data, m3 m−3 0.08 0.03 0.04 0.12θS derived by IEM using field measuredroughness, m3 m−3

0.15 0.10 0.04 0.35

Over allθS by field measurements, m3 m−3 0.05 0.02 0.02 0.10θS derived by image data, m3 m−3 0.07 0.03 0.03 0.12θS derived by IEM using field measuredroughness, m3 m−3

0.15 0.09 0.03 0.35

Fig. 10. Performance of radar backscatter model, when field measurements ofroughness are used as inputs. Cross signs are points associated with 13experimental sites on July 14, 2004 overpass and the circles are with August 2,2004. In few cases IEM predicted moisture content fall outside valid range; thesepoints are not included in the graph.


study, which is rolling mountain, may seem a source of potentialerror, since a terrain correction was not applied. However, thesites chosen for the study were flat and should not be a majorconcern. The way equations were derived to form theframework of an equation-based solution may also have someimpact on the results. A fixed incidence angle was chosen forderiving each equation. This may appear problematic since theequations were applied in pixel-by-pixel computation for theentire image for which the incidence angles varied block wise.However, since the experiment locations were closely spaced,the difference in incidence angles among locations were verysmall and the assumption of fixed incidence angle may not be abig problem after all.

The results presented in Fig. 9 using image-derived estimatesof roughness can be compared to the performance of IEM whenthe field measurements of roughness were used as inputs to themodel (Fig. 10 and Table 4). It was found that the image-derivedroughness perform far better in parameterizing IEM for soilmoisture retrieval. This finding may be evidence that it isprobably the input parameters that result in poor performance ofthe IEM model rather than the model itself. This may also beconsidered an indirect and aggregated precision of the image-derived roughness parameters estimated in this study.

4. Conclusions

In previous studies, radar images have been used for retrievingdistributed surface soil moisture based on field measurements ofsurface roughness data used to parameterize the IEM. Theestimation of the characteristic parameters of surface roughnessusing field data has been unreliable and the measurement ofroughness itself is cumbersome and infeasible for large scaleapplication. In this study, a method was developed to mapcharacteristic parameters of surface roughness using radar images

as a replacement for field-collected ancillary data. The method-driven estimates of soil moisture were validated against fieldmeasurements. Results indicate that there is good associationbetween image-derived soil moisture and field measured soilmoisture. Moreover, the implementation of this method is ratherstraight forward (Fig. 11). It involves approximation of IEM andsome of its derivatives with simple functions using modelsimulated data and themanipulations of these functions by the useof image data and ArcInfo programming.

It was found that the image-derived surface roughness waslarger than field measured roughness. This may confirm that thesubsurface roughness caused by the rock fragments plays animportant role. Radar signal is probably responsive to multiplebounce by the subsurface rock fragments when it penetrates fewcentimeters below ground surface, in addition to the scatteringdue to surface roughness. As a result, radar-perceived roughnessmay be much larger than that of field measurements. Theroughness measuring field device is not designed to account forsubsurface roughness. Therefore, roughness measurements bythe pin meter may not be adequate to characterize surfaceroughness for inputting in IEM, especially for study sites withlarge amounts of rock fragments.

The conditions, under which the model is developed, appliedand validated, are best suited to its application in rangelands,where the vegetation is sparse, precipitation is low and thesurface roughness does not change between dry and wetperiods. To broaden the applicability of the model toagricultural land, especially in the mature stage of crop growthwhen the vegetation becomes dense, additional validation workmust be conducted. In particular, future research mustinvestigate the application of the model under a broader rangeof vegetation and moisture conditions. If the model is notapplicable in areas of dense vegetation (agricultural land forexample), additional research should be conducted to incorpo-rate a variable reflecting vegetation cover or density into themodel. Further, the method developed in this study is appliedfor C-band radar image and its applicability for other radarfrequencies needs to be determined.

The model developed through this research required the useof dry season radar images for estimation of surface roughness.Agricultural land preparation may change surface roughnessbetween dry and wet periods. As a result surface roughnessestimated from dry images may not be applicable to a wet imagefor soil moisture estimation. Future research is therefore neededto either establish the error introduced or eliminate therequirement for a dry season images for roughness estimation.

The method developed in this study also depends on the useof radar images from two different view angles, which can beacquired from existing radar sensors given a time span of therepeat cycle of the satellite. However, the moisture or roughnessconditions may undergo change within this time-frame makingthe method developed here less applicable. The capability of aradar sensor to acquire data at multiple view angles at the sametime should be considered in the design of future radar systems.In addition, future research into the feasibility of replacing theneed for images at two-view angles with images at two differentpolarizations could be beneficial. Existing radar sensors already

Fig. 11. Schematic diagram of the steps followed for the image-based mapping of surface soil moisture and roughness. Note that if image 1 and 2 are acquired in drycondition, one of them can serve as image 3.


have the capability of simultaneously acquiring images atmultiple polarizations. This would eliminate errors introduceddue to registration inaccuracy when merging the images at two-view angles. Research in any one of these directions is highlyrecommended.

Acknowledgements

All authors appreciate the support of the US Army EngineerResearch and Development Center, Topographic EngineeringCenter. We would like to thank all the people that made our fieldwork possible at the USDA ARS Walnut Gulch ExperimentalWatershed.

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