g

a P

ara

18

Abstract

1. Introduction

potential of microwave data as a crop classier has beendocumented by researchers (Bush and Ulaby, 1978; Briscoand Protz, 1980; Shanmugan et al., 1983). Due to penetra-

tion ability of microwaves, the backscattered energy con-

cation has relatively often been studied (Hoogeboom,1983; Stiles et al., 1993; Frison and Mougin, 1996; Wagneret al., 1999; Frate et al., 2003), but the estimation of cropparameters has been less addressed (Bouman, 1991).Bouman (1991) has investigated that the microwave signalat high frequency (i.e. 10 GHz) is primarily sensitive to dry

* Tel.: +91 9415780999.E-mail address: rprasad1@redimail.com

Available online at www.sciencedirect.com

Advances in Space Research 43Comprehensive, reliable and timely information on agri-cultural resource is necessary for day-by-day increasingpopulation on the worldwide. Nowadays remote sensingtechnology is considered as a powerful tool for the estima-tion of natural resource evaluation and management.There is an interest in using microwave remote sensing datafor a variety of agronomic applications due to all weatherimaging capabilities of microwave sensors and synergismwith optical data (Jongschaap and Schouten, 2005). The

tains information regarding both crop canopy and theunderlying soil. For bare soil, the primary target character-istics governing the microwave reectivity are soil moisturecontent and surface roughness (Ulaby et al., 1978). Thecharacteristics of the soil (bulk density, texture, etc.) inu-ence its moisture holding capacity which inuences theradar backscattering coecient.

In agriculture, the estimation of crop variables can beused for crop type identication and growth monitoring.In the radar domain of remote sensing, crop type identi-Modeling in agriculture has been widely used to retrieve and monitor various soil and crop growth variables. Remote sensing, espe-cially radar sensors can be useful for temporal and spatial monitoring of the soil and plant variables. Therefore, in this paper eld mea-surements of crop ladynger were carried out to examine the dependency of radar backscatter on cropsoil variables and to develop amethod for monitoring and retrieving crop variables for ladynger. A crop-bed was prepared to observe scatterometer response in theangular range of incidence angle 2070 at 9.89 GHz in the X-band for VV- and HH-polarization. At the same time, soil moisture, plantheight, leaf area index and aboveground biomass were measured at various growth stages of crop ladynger. The angular variation ofscattering coecient decreases with the age of crop ladynger shows the dominance of crop eect on soil moisture eect at the older age.Thus, angular trends are more at as the plant grows since the eects of soil is masked by developing vegetation. Scattering coecientincreases with the increase of leaf area index for both polarizations (i.e. VV- and HH-). It was found that leaf area index and above-ground biomass of crop ladynger are highly correlated with microwave frequency more than with plant height and soil moisture. Leafarea index and biomass of ladynger crop were retrieved by polarization based model and non-linear least square optimization model.These two models gave very good results for the retrieval of leaf area index and aboveground biomass. 2009 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Remote sensing; Scattering coecient; Soil moisture; Leaf area index; Aboveground biomassRetrieval of crop variables withremote sensin

Rajendr

Department of Applied Physics, Institute of Technology, Ban

Received 2 June 2008; received in revised form0273-1177/$36.00 2009 COSPAR. Published by Elsevier Ltd. All rights resedoi:10.1016/j.asr.2008.12.017eld-based X-band microwaveof ladynger

rasad *

s Hindu University, Varanasi, 221 005 Uttar Pradesh, India

December 2008; accepted 19 December 2008

www.elsevier.com/locate/asr

(2009) 13561363rved.

The major problem is to solve the multiple scatteringequations.

Thus, these models are either very complex to solve orrequire a large number of input data to retrieve the cropvariables and to understand the individual response of cropvariables on microwave scattering/absorption. The quanti-tative understanding of the contribution by each crop vari-ables to scattering, attenuation and the relative magnitude

2. Materials and methods

Research 43 (2009) 13561363 1357canopy biomass, amount of crop water, soil cover and cropheight. In microwave remote sensing, the eect of canopyleaf shape is not very important factor in the low-frequencyregion (Karam and Fung, 1983). However, in the frequencyregion where the leaf dimensions are of the order of inci-dent wavelength, the leaf shape signicantly aects thebackscattering coecient (Karam et al., 1988). In orderto analyze radar data and to generate valuable informa-tion, it is necessary to understand the interaction of micro-wave radiation with soil and vegetation. Microwavescattering depends upon various factors like surface rough-ness, target geometry, its dielectric properties and the inci-dent wave properties. The dielectric properties of soilconsiderably depend upon water content in the soil, whichis related to the water retentivity properties of the soil. Theconductivity and dielectric constant as well as growth stageof crop dominantly aect the scattering and emission ofmicrowave. Generally, a decrease in the soil moistureresults in a decrease in the backscatter coecient. Experi-mental researches have shown that the microwave back-scattering is sensitive to water in the crop and is aectedby the shape and dimension of plant parts (i.e. leafs andstems). For example, the L-band (25 cm) seems the mostconvenient frequency band for studying the contributionfrom crop with relatively large leaves, while the use of ahigher frequency (C-band) is suitable for investigatingsmall leaf crops. The electromagnetic response in theextended frequency range, look angle variation and polar-ization eects are being exploited by the researches toobtain the information of materials forming earth crustand vegetation. This information is then utilized for theinterpretation of the microwave scatterometer and radiateddata obtained through remote sensing satellite.

Various modeling approach have been developed andanalyzed by researchers (Cookmartin et al., 2000; Brownet al., 2003; Picard et al., 2003; Maity et al., 2004). Thesemodels can be very useful to retrieve the crop growth vari-ables and enhancing the understanding of scattering/absorption mechanism of microwave with cropsoil vari-ables. However, an accurate retrieval of the crop variablesrequires numerous biophysical and soil parameters. Thereare some practical limitations of the requirement of a largenumber of input observations which cannot be fullled eas-ily over a large number of scattered elds. Further, thesemodels and approaches have to be tested for more generalapplications (Singh, 2006). Cookmartin et al. (2000) devel-oped a multilayer second-order radiative transfer model.The limitation of Cookmartin et al. (2000) model is thatit needs the attenuation parameters of various layers andinversion of this formulation is quite complex to retrievethe crop variables. Picard et al. (2003) have developed mul-tiple scattering coherent models for understanding C-bandradar backscatter from wheat canopy. In Picard et al.(2003) model, it is dicult to calculate multiple scatteringinteractions which increase the complexity of electromag-

R. Prasad / Advances in Spacenetic problem. Multiple scattering equations were appliedto the case of vertical cylinders over an innite surface.The specication of scatterometer system used in ourinvestigation is shown in Table 1. Ground based scatterom-eter measurements were performed to study the reectivity/scattering coecient of an outdoor crop-bed of crop lady-nger at its various growth stages. For this study, the crop-bed having an area 4 4 m2 of ladynger was preparedespecially for the microwave scattering/reection measure-ment. Ladynger is taken as a broad leafs crop andattained the maximum average height of 71.5 5 cm dur-ing observation. The leaf of crop ladynger was broad inshape and almost camouaging the background surfaceon which it was grown. Therefore, the response of micro-wave reection/scattering observed from ladynger cropgave interesting results. The fruit lling stage of this cropcomes around 45 5 days from the date after sowing.The matured stage of this crop comes around 65 5 days.The age of the crop was counted from the date after sow-

Table 1Scatterometer specications.

Central frequency 9.89 GHzAntenna type Dual polarized pyramidal hornAntenna gain 20 dBPlatform height 3 mCross polarization isolation 40 dBCalibration accuracy 1 dBof the scattering from the soil and the vegetation is still amatter of debate for most crops. Therefore, the retrievalof crop variables is dicult and thus, it is necessary tostudy the crop/vegetation characteristics based on groundtruth observation.

The objective of this paper is to examine the dependenceof scattering coecient on various plant variables, i.e.plant height (PH), leaf area index (LAI), aboveground bio-mass (Bm) and soil moisture (Sm) and to develop a methodto monitor and retrieve the crop variables at 9.89 GHz inthe X-band. The polarimetric properties of crop ladynger(Abelmoschus esculentus) have been used to retrieve thecrop variables.

Ladynger commonly known as okra (A. esculentus) is aowering plant used for its edible green fruits. Ladynger iswidely used as a vegetable. It contains adequate amounts ofvitamin A (600 IU) and nutritional value per 100 g for Band C are 87.8 lg and 21 mg, respectively.Polarization modes VV and HHIncidence angle 2070

ing. Gravimetric soil moisture was determined by takingsoil sample from the depth of 5 cm in a weighing tube. Soilsample was dried in an oven at 100 C for 48 h. Soil mois-ture was determined by using the following formula:

w2 w3=w3 w1 unit : g=g 1where w1 is the weight of empty tube; w2, weight of weigh-ing tube with soil sample and w3 is the weight of dry soilalong with weighing tube.

good results for the retrieval of crop variables.

1358 R. Prasad / Advances in Space Re2.1. Water cloud model for computing calculated scattering

coecient

For the retrieval of leaf area index and abovegroundbiomass of crop ladynger by scatterometer measurement,a theoretically calculated scattering coecient value isrequired. Thus, we briey present the parametric watercloud model to compute the calculated values of scatteringcoecient. The general water cloud model (Attema andUlaby, 1978) represents the power scattered from thecropsoil complex as the sum of the contribution of thevegetation and that of the underlying soil. The soil contri-bution is attenuated by the vegetation layer. Thus, for agiven incidence angle (h) and polarization (p), the total con-tribution can be written as (Moran et al., 1998):

r0h; p r0vh; p s2rsh; p units : m2m2 2

Table 2Variation of soil moisture and crop growth variables of ladynger withage.

Age (days) Plant height (cm) LAI Biomass (kg/m2) Sm (%)

30 21.2 0.89 0.69 27.840 35.8 1.54 0.83 26.450 51.5 2.68 1.33 25.560 60.4 4.91 1.69 21.770 65.6 5.76 1.78 22.9LAI is dened as the ratio of total upper leaf surface of acrop divided by the surface area of the land on which thecrop grows. LAI is dimensionless although it is some timespresented in units of m2 m2.

The biomass of the plant is the total dry matter accumu-lation in the aboveground biomass over a period of time.The aboveground biomass was computed from samplestalks and leaves, which were dried in oven at 90 C for24 h. These samples were weight before and after dryingand weight per square meter has been computed. Theground truth data are listed in Table 2. In the currentpaper, we have retrieved crop ladynger variables withscatterometer data using polarimetric based approachand non-linear least square optimization method. The cropvariables retrieved by proposed polarization based model iscompared with another model based on non-linear leastsquare optimization method. These two models gave very80 68.7 6.27 1.83 23.690 71.5 6.65 1.84 21.5where

r0vh; p AV B1 cosh1 s2units : m2m2 3r0s h; p C Dmg units : dB 4where mg is the gravimetric soil moisture content. Thisparameterization considers the eect of soil moisture(dielectric properties) and the eect of roughness (geometryof the surface) as independent, as done by Bertuzzi et al.(1992). The sensitivity of the signal to soil moisture D isconsidered as constant. The dependence on the radar con-guration and the soil roughness is included in the param-eter C (Taconet et al., 1994). V1 is a descriptor of thecanopy. s2 is the two way attenuation through the canopy,expressed as

s2 exp2bV 2= cos h unitless 5where V2 is a second canopy descriptor and b representsthe vegetation attenuation. The canopy descriptor (V1and V2) in Eqs. (3) and (5) have been associated withLAI and aboveground bio-mass respectively of crop lady-nger. So, Eq. (2) can be written as

r0h; p AV B1 cos h1 exp2bV 2= cos h exp2bV 2= cos hr0s h; punits : m2 m2

6The value of model parameters A, B, C and b can be deter-mined by xing D and minimizing the sum of the square ofthe dierence between modeled and measured r0(h,p)based on Eq. (6), where r0s h; p is evaluated by Eq. (4)and converted from units of dB to m2 m2.

2.2. Empirical approach

The water cloud model as described in Eq. (6) showsthat scattering coecient depends on both soil properties(i.e. dielectric, roughness) and crop variables (i.e. PH,LAI, Bm). To analyze the dependence of r0 on the soilmoisture and on the crop variables, we express r0 as aproduct of two independent functions (Ulaby et al., 1982)

r0h; p F sSm;hF cPH;LAI;Bm;h 7where Fc(PH, LAI, Bm, h) is a function corresponding tocrop variables (i.e. PH, LAI, Bm) of crop ladynger andFs is a function of soil moisture (Sm). The functions Fc(PH,LAI, Bm, h) can be written as

F cPH;LAI;Bm;h F 1PHF 2LAIF 3Bm 8Now Eq. (7) can be written as

r0h; p F sSmF 1PHF 2LAIF 3Bm 9We can write Eq. (9) in dB form as

r0h; p K1Sm K2PH K3LAI K4Bm c 10where K1, K2, K3 and K4 are the sensitivity factors of

search 43 (2009) 13561363r0(h,p) on Sm, PH, LAI, Bm, respectively, and c representsnoise which depends upon the system parameters and crop

geometry (Singh, 2006). The roughness of crop covered soilis considered as a constant during the entire observation.Therefore, we are considering rst order radiative transfermodel where the roughness of crop covered soil is consid-ered as a constant as shown in Eqs. (4)(6). Multiple andpartial regression analysis of Eq. (10) has been done to ana-lyze the individual eect of crop variables and Sm on scat-tering coecient at X-band.

3. Result and discussion

Figs. 1 and 2 depict the angular variation of scatteringcoecient for crop ladynger at dierent stages of growthfor VV- and HH-polarizations, respectively. For bothpolarizations, the scattering coecient decreases with theincrease of incidence angle at each stage of crop ladynger.However, the magnitude of decrease in r0 is small in latter

respectively. The value of coecient of determination(R2Sm) shows the degree of dependence of r

0 on Sm. The val-ues of R2Sm were found to be higher in lower range of theincidence angles and decreases with the increase of inci-

-4ien

-10

-8

-6

-4

-2

0

Scat

terin

g co

effic

ient

(dB)

30 days 50 days 70 days 80 days 90 days

15 20 25 30 35 40 45 50 55 60 65 70

Incidence Angle (degrees)

Table 3Variation of coecient of determination (R2) with incidence angle for soilmoisture (Sm), plant height (PH), leaf area index (LAI) and biomass (Bm)for VV-polarization.

Angle () R2

Sm PH LAI Bm Polarization

20 0.83 0.73 0.85 0.75 VV25 0.80 0.74 0.91 0.78 VV30 0.81 0.80 0.94 0.83 VV35 0.76 0.73 0.94 0.79 VV40 0.76 0.77 0.97 0.84 VV45 0.77 0.84 0.99 0.91 VV50 0.75 0.79 0.94 0.82 VV55 0.75 0.78 0.91 0.80 VV60 0.57 0.62 0.80 0.65 VV

R. Prasad / Advances in Space Research 43 (2009) 13561363 1359-14

-12

-10

-8

-6

Scat

terin

g co

effic

30 days 50 days 70 days 80 days 90 daysage of the crop. The dynamic range is the angular variationof scattering coecient between the incidence angles 2070. The dynamic range of r0 at dierent growth stage isquite dierent enough to discriminate the soil moistureand ladynger eect. At early stage of crop when crop vari-ables are small, it is found that dynamic range of r0 isgreater than in the older age of crop i.e. after 30 daysof sowing when PH = 21.2 cm, LAI = 0.89 andBm = 0.69 kg/m2, the dynamic range of r0 is 11.94 dB forVV-polarization and 10.27 dB for HH pol., whereas, after90 days of sowing when PH = 71.5 cm, LAI = 6.65, andBm = 1.84 kg/m2, the dynamic range is 3.23 dB for VV-and 3.58 dB for HH-polarization. Soil moisture eect wasobserved to be dominant at early growth stage, when themagnitudes of the crop variables (Table 2) were less.

The dynamic range of r0 decreases with the age of cropshows the dominance of crop eect on soil moisture eectat 9.89 GHz. Thus, angular trends are more at as theplant grows since the eects of soil is masked by developingvegetation. The dynamic range of r0 at dierent growth

-2

0

2

t (dB

)

15 20 25 30 35 40 45 50 55 60 65 70 Incidence Angle (degrees)Fig. 1. Angular variation of scattering coecient for crop ladynger atdierent stages of growth for VV-polarization.stage is quite dierent enough to discriminate the soil mois-ture and crop lady nger eect. The dierence in crop cov-ered soil moisture eect and crop eect at early and latterstage of crop is useful to analyze the data acquired bythe space borne sensors. A comparison of angular variationof scattering coecient was done with other research(Ulaby et al., 1982, 1988; Karam et al., 1988; Singhet al., 1996) and it was found that the nature of variationis similar but not the same. No claim in comparing themagnitude with other reported results was done due to dif-ference in sensitivity of our system and the dierence in cli-matic and environment condition.

The regression analysis based on Eq. (10) has been doneto analyze the microwave response of crop variables andsoil moisture eect. The result of regression analysis isshown in Tables 3 and 4 for VV- and HH-polarization,

-12

Fig. 2. Angular variation of scattering coecient for crop ladynger atdierent stages of growth for HH-polarization.65 0.49 0.53 0.72 0.56 VV70 0.57 0.54 0.71 0.56 VV

3.1. Discussion on model parameters retrieval

The parameters C and D of Eq. (4) were determined bythe linear regression of r0s h; p with gravimetric soil mois-ture (Sm) measured for a bare soil eld over a drying per-iod (Moran et al., 1998) while assuming that moisture and

Table 4Variation of coecient of determination (R2) with incidence angle for soilmoisture (Sm), plant height (PH), leaf area index (LAI) and biomass (Bm)for HH-polarization.

Angle () R2

Sm PH LAI Bm Polarization

1360 R. Prasad / Advances in Space Research 43 (2009) 13561363dence angle. Therefore, soil moisture eect decreases withthe increase of incidence angles. However, the values ofR2LAI and R

2Bm were found to be greater than R

2Sm at higher

incidence angles in both i.e. VV- and HH-polarizations.Thus, the crop variables eect is more prominent than soilmoisture at higher incidence angle. Therefore, the eect ofcrop covered soil moisture can be neglected for the retrievalof crop variables at higher angle i.e. 45. Researchers inves-tigating the eects of system parameters and target proper-ties on the radar scattering coecient of crop concludedthat to eectively monitor the crop corn with radar, inci-dence angle of 40 or larger are imperative in order toinsure a large ratio of canopy scatterer (Ulaby and Bush,1976). The analysis of radar backscattering indicates thatthe backscattering coecient of the canopy is dominatedby the leaf contribution for crops like corn and sorghumat angle of incidence 50 (Ulaby et al., 1984). While com-paring the values of R2 with each other, it is observed thatthe values of R2 for LAI and Bm of crop ladynger were

20 0.90 0.67 0.78 0.67 HH25 0.85 0.75 0.92 0.77 HH30 0.83 0.79 0.94 0.82 HH35 0.79 0.74 0.95 0.78 HH40 0.78 0.78 0.97 0.82 HH45 0.75 0.88 0.99 0.93 HH50 0.76 0.79 0.95 0.82 HH55 0.77 0.79 0.92 0.81 HH60 0.63 0.63 0.81 0.65 HH65 0.56 0.53 0.73 0.55 HH70 0.67 0.54 0.72 0.56 HHhigher than for PH. This shows that LAI and Bm of cropladynger interact more with r0 in comparison to PH.Therefore, LAI and Bm of crop ladynger are consideredas plant variables in water cloud model Eq. (6). The bestsuitable angle of incidence for observing the LAI and Bmof ladynger is 45 for both polarizations. Some research-ers (Cookmartin et al., 2000; Brown et al., 2003; Picardet al., 2003) also found (for crops wheat, sunower, alfa-alfa, etc.) that measurements at 45 incidence angle, micro-wave interacts strongly with the vertical stem, LAI and Bm.The higher incidence angle should provide better sensitivityto the wave attenuation than at lower incidence angle.

Table 5Model parameter estimations for Eq. (6) based on the results for crop ladyn

Radar conguration at 9.89 GHz in X-band Model parameters

Crop dependent

A

VV-polarization, 45 0.681HH-polarization, 45 0.343eld conditions were approximately same as the cropcovered soil moisture for the crop ladynger. r0s h; p wasevaluated by Eq. (4) and converted from units of dB tom2 m2. The remaining parameters A, B, and b were deter-mined by minimizing the sum of the square of the dier-ence between the modeled and measured r0(h,p) usingGaussNewton non-linear least square optimization rou-tine (Prevot et al., 1993; Graham and Harris, 2002; Singh,2006) for VV- and HH- polarizations. Table 5 shows thevalues of the model parameters after tting on the dataset. The value of the attenuation parameter b of vegetationis dierent as obtained by Prevot et al. (1993) and Taconetet al. (1994). The attenuation parameter b depends on typeof crop and its morphology. In the present investigation,ladynger was broad leaf crop, whereas in the case of Pre-vot et al. (1993), it was narrow leaf wheat crop.

3.2. Retrieval of LAI and Bm

3.2.1. By non-linear least square optimization method

Optimization is the act of obtaining the best result undergiven circumstances. The non-linear least square optimiza-tion method (Singh, 2006) can be used to retrieve crop vari-ables, which are highly correlated with the scatteringcoecient. To retrieve LAI and Bm of crop ladynger,maximum likelihood inverse solver by non-linear leastsquare tting method (Hallikainen et al., 1985; Pulliainenet al., 1993; Roo et al., 2001) is used. The minimizationproblem is

Minimize X 1

l21

r0obs r0cal 2

1l22

LAIobs LAIret2

1l23

Bmobs Bmret2

11

where l1 is the standard deviation of measured scatteringcoecient at 45 incidence angle, l2, the standard deviationof measured LAI; l3, the standard deviation of measuredBm; r0obs r0, observed during experiment at 45 incidenceangle r0cal r0, calculated by Eq. (6); LAIobs = LAI ob-served during experiment, LAIret the LAI to be retrieved,

ger.

Soil dependent

b B C D0.028 0.972 12.7 25.980.09 0.902 11.04 23.25

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

Ret

rieve

d LA

I

Observed LAI

LAI retrieval by optimization model for VV-pol LAI retrieval by optimization model for HH-pol LAI retrieval by PDR model

Fig. 4. Observed verses retrieved LAI by non-linear least square optimi-zation model and PDR (polarimetric discrimination ratio) model.

0 1 2 3 4 5 6 7

0.02

0.04

0.06

0.08

0.10

0.12

PDR

LAI

Fig. 3. Variation of PDR (polarimetric discrimination ratio) with LAI at45 incidence angle.

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.02

0.04

0.06

0.08

0.10

0.12

PDR

Biomass (kg m-2)

Research 43 (2009) 13561363 1361Bmobs the Bm observed during experiment, and Bmret is theBm to be retrieved.

The known values of parameter l21 (l1 = 1.5171 for VV-pol, l1 = 1.5318 for HH-pol), r0obs, r

0cal, LAIobs, Bmobs,

l2 = 2.4508 and l3 = 0.4855 were substituted in Eq. (11)and ran the non-linear least square optimization routine(iterative minimization algorithms GaussNewton). Agood agreement between measured and retrieval values ofLAI and Bm were obtained. The results are shown in Figs.4 and 6.

3.2.2. By polarimetric approachThe backscatter associated with vegetation is complex as

it is inuenced by the geometry and orientation of leaves,stalks and stems. Some researchers have pointed out thatthe normalized dierence between vertical and horizontalpolarization components (polarization index) of X-band(10 GHz) emission can be correlated to leaf area index(Paloscia and Pampaloni, 1988, 1992). The advantage ofthis analytical technique is that it only depends on the ver-tically and horizontally polarized observations therebyeliminating the need of other parameters to estimate theLAI and Bm. The leaf area index (LAI) is a very goodparameter that characterizes plant growth conditions bet-ter than plant water content (Q). On the other hand, Qand LAI are correlated to each other and the relationbetween these two variables depends on crop type and onthe distribution of water storage among plant constituentsduring the life cycle of vegetation (Paloscia and Pampaloni,1988).

Polarization of a microwave is sensitive to the shape,size and orientation of the target elements. The horizontalpolarization gives the measure of the horizontal dimensionof the scattering elements, while the vertical polarizationgives a measure of the vertical dimension. Thus, for dis-criminating the soil and crop properties of the scatteringsurface, the polarization discrimination ratio (PDR) isgiven as (Singh et al., 2003)

PDR rVV rHHrVV rHH 12

where rVV and rHH are scattering coecients for VV- andHH-polarizations respectively. Eq. (12) is used to calculatethe PDR. The regression analysis between PDR with LAIand Bm provide suciently high values of coecient ofdetermination (R2) for all incidence angles. The high valuesof R2 show the strong relationship between PDR with LAIand Bm. However, the maximum value of R2 was found at45 incidence angle. Thus, the best suitable angle of incidenceis 45 for observing the LAI and Bm using PDR approach at9.89 GHz in the X-band. The model relation between PDRand LAI can be tted with a polynomial given as

PDR 0:00196LAI2 0:0291LAI 0:0036 13The model relation between PDR and LAI tted with

R. Prasad / Advances in Spacethe above polynomial is depicted in Fig. 3 show high cor-relation between PDR and LAI. We can retrieve the values

Fig. 5. Variation of PDR (polarimetric discrimination ratio) with Bm at45 incidence angle.

Reof LAI by inverting Eq. (13). The retrieval value of LAI byPDR method is shown in Fig. 4. There is good agreementbetween observed and retrieved value of LAI.

The model relation between PDR and Bm can be ttedwith a polynomial which can be inverted to estimate theBm as

PDR 0:01286Bm2 0:04034Bm 0:01391 14The model relation between PDR and Bm tted with the

above polynomial is depicted in Fig. 5 shows high correla-tion between PDR and Bm. The retrieval value of Bm byPDR method is also shown in Fig. 6. There is a very goodagreement between observed and retrieved value of Bm.

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Ret

rieve

d Bm

(kgm

-2 )

Observed Bm (kg m-2)

Bm retrieval by optimization model for VV-pol Bm retrieval by optimization model for HH-pol Bm retrieval by PDR model

Fig. 6. Observed verses retrieved Bm by non-linear least square optimi-zation model and PDR (polarimetric discrimination ratio) model.

1362 R. Prasad / Advances in Space4. Conclusion

The dynamic range of r0 decreases with the age of cropshows the dominance of crop eect on soil moisture eectin the latter stage of the crop in the X-band. Thus, angulartrends are more at as the plant grows since the eects ofsoil is masked by developing vegetation. The dierence incrop covered soil moisture eect and crop eect at earlyand latter stage of crop is useful to analyze the dataacquired by the space borne sensors. Soil moisture eectdecreases with the increase of incidence angles. However,the values of R2LAI and R

2Bm were greater than R

2Sm at higher

incidence angles in both VV- and HH-polarizations. Thus,the crop variables eect is more prominent than crop cov-ered soil moisture at higher incidence angle. Therefore, theeect of crop covered soil moisture can be neglected forthe retrieval of crop variables at higher incident angle. Itis observed that the values of R2 for LAI and Bm of cropladynger were higher than for PH. This shows that LAIand Bm of ladynger interact more with r0 in comparisonto PH. The best suitable angle of incidence for observingthe LAI and Bm of ladynger is 45 for both polariza-

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Karam, M.A., Fung, A.K., Antar, Y.M.M. Electromagnetic wavetions. The regression analysis between PDR with LAIand Bm provides suciently high values of R2 for all inci-dence angles. The high values of R2 show the strong rela-tionship of PDR with LAI and Bm and is maximum at45 incident angle. The retrieval of LAI and Bm of cropladynger by non-linear least square optimization methodand PDR approach are in good agreement with theobserved values. However, the retrieval of Bm by PDRapproach is very much close to the observed one. Thistypes of ground based experiment for individual crop isalso important to generate data to operate and validatedierent types of models involved to solve the interactionmechanism of particular crop for remote sensing. Thus,ground based scatterometer system study is useful for bet-ter understanding of the scattering behavior of targetunder observation.

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R. Prasad / Advances in Space Research 43 (2009) 13561363 1363

Retrieval of crop variables with field-based X-band microwave remote sensing of ladyfingerIntroduction Materials and methods Water cloud model for computing calculated scattering coefficient Empirical approach

Result and discussion Discussion on model parameters retrieval Retrieval of LAI and Bm By non-linear least square optimization method By polarimetric approach

ConclusionReferences