Use of Satellite Radar Bistatic Measurements for Crop Monitoring: A Simulation Study on Corn Fields

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1 Reote Sens. 3, 5, ; doi:.339/rs5864 Article OPEN ACCESS Reote Sensing ISSN Use of Satellite Radar Bistatic Measureents for Crop Monitoring: A Siulation Study on Corn Fields Leila Guerriero, *, Nazzareno Pierdicca, Luca Pulvirenti and Paolo Ferrazzoli Departent of Civil Engineering and Coputer Science Engineering, Tor Vergata University of Roe, Via del Politecnico, I-33 Roe, Italy; ferrazzoli@disp.uniroa.it Departent of Inforation Engineering, Electronics and Telecounications, Sapienza University of Roe, Via Eudossiana 8, I-84 Roe, Italy; s: nazzareno.pierdicca@uniroa.it (N.P.); pulvirenti@diet.uniroa.it (L.P.) * Author to who correspondence should be addressed; guerriero@disp.uniroa.it; Tel.: ; Fa: Received: Deceber ; in revised for: 6 February 3 / Accepted: 5 February 3 / Published: February 3 Abstract: This paper presents a theoretical study of icrowave reote sensing of vegetated surfaces. The purpose of this study is to find out if satellite bistatic radar systes can provide a perforance, in ters of sensitivity to vegetation geophysical paraeters, equal to or greater than the perforance of onostatic systes. Up to now, no suitable bistatic data collected over land surfaces are available fro satellite, so that the electroagnetic odel developed at Tor Vergata University has been used to perfor siulations of the scattering coefficient of corn, over a wide range of observation angles at L- and C-band. According to the electroagnetic odel, the ost proising configuration is the one which easures the VV or HH bistatic scattering coefficient on the plane that lies at the aziuth angle orthogonal with respect to the incidence plane. At this scattering angle, the soil contribution is iniized, and the effects of vegetation growth are highlighted. Keywords: new easureent concept; bistatic radar; crop status. Introduction A bistatic radar syste is defined when antennas for reception and transission are physically separated []. In principle, the transitting and receiving antennas could be located on ground, on an aircraft or on-board a spacecraft; ied solutions are also possible, e.g., the transitter is spaceborne,

2 Reote Sens. 3, while the receiver is airborne. The syste could be either cooperating (transitter and receiver designed for the specific bistatic application) or non-cooperating (transitter designed independently of the receiver). If both receiver and transitter, or illuinator, operate in the icrowave band, the latter could be a radar, a counication or navigation satellite. For instance, non-cooperating systes can use already-eisting satellite Synthetic Aperture Radars (SARs) as transitters [,3], as well as the signal transitted by Global Positioning Syste (GPS) satellites [4,5]. Bistatic applications were investigated in the fields of target detection [6,7] and planetology [8]. As for Earth Observation, oceanographic studies eploiting the GPS signal were carried out, including altietric applications (easure of the sea level and of the associated oceanographic features) and scatteroetric applications (easure of the near surface wind field) [9,], while interferoetric applications were addressed in []. In consequence of the recent launch of the new generation of X-band radars (TerraSAR-X, COSMO-SkyMed), eperients involving X-band have been accoplished in order to evaluate the additional inforation contained in the bistatic reflectivity of targets (e.g., []). The TerraSAR-X ission has been etended into the TanDEM-X ission [3] with the purpose of generating global Digital Elevation Model fro radar interferoetry. This is the first bistatic syste in orbit, and it successfully provided bistatic iages of urban features [4]. However, its quasi-onostatic configuration does not appear suitable to observe vegetated surfaces whose directional scattering properties can be detected under large bistatic angles, as will be shown in this study. The effect of soil oisture (SM) and roughness on the aplitude of the incoherent backscattered signal was largely investigated, and the effectiveness for their retrieval by radars working in the low-frequency range of the icrowave band ( 5 GHz) was deonstrated (e.g., [5 9]). The sensitivity to vegetation paraeters of onostatic radar easureents was assessed in [,], while the possibility to etract quantitative inforation on crop height fro interferoetric coherence and phase has been eploited in [,3]. Up to now, few works are available on the use of a bistatic radar configuration for easuring land bio-geophysical paraeters, such as vegetation and soil paraeters. The first attept to retrieve soil reflectivity and dielectric constant fro Global Navigation Satellite Syste (GNSS) reflected data of the SMEX capaign was reported by [4], while in [5], the Interferoetric Pattern Technique has been applied to retrieve the wheat crop height. The feasibility of retrieving SM using bistatic radar systes was assessed in [6], where a siulation study aiing at identifying the best bistatic configurations, in ters of incidence angle, observation direction, polarization and frequency band, for soil oisture content was perfored. The technical issues related to the configurations selected in [6] have been discussed in [7]. As for vegetation, soe airborne bistatic easureent capaigns at P-band have been carried out to find bistatic configurations allowing for the iniization of double bounce scattering fro vertical trees in order to detect vehicles in forest concealent [8]. Fro a theoretical perspective, the MIMICS odel was odified to allow the siulation of bistatic scattering fro forests [9]. Like its onostatic version, Bi-MIMICS follows a first order approach, which, therefore, neglects ultiple scattering contributions that, on the other hand, can be iportant at higher frequencies. The relevant features of scattering in the specular direction fro soil covered by a vegetation canopy were theoretically analyzed in [3,3], on the basis of siulations carried out by using the fully polarietric electroagnetic odel developed at the Tor Vergata University of Roe and described in [3] (hereafter, the TOV odel). The theoretical results indicated that such a bistatic syste would

3 Reote Sens. 3, aintain an appreciable sensitivity to the plant water content of crops and forest bioass over a considerably wider range than in the onostatic operation ode [3,3], because of the attenuation due to vegetation of the coherent specular reflection fro the soil. Etending the well-established TOV odel to bistatic configurations different fro the specular one, this paper investigates the bistatic radar potential in view of vegetation paraeter estiation. The bistatic scattering siulations, provided herewith, focus on the identification of the configuration, which provides the ost accurate crop height retrieval; in particular, corn plants are considered for this purpose. The sensitivity yielded by the selected bistatic configurations is copared with that of standard onostatic radar. Moreover, the potential of cobining both easureents, considering that backscatter is epected to be easured by conventional SAR issions (ultistatic case) is assessed. We have used the Craér Rao Lower Bound to quantify and copare the retrieval perforances of the different configurations. In Section, a suary of the electroagnetic odel used to perfor the bistatic siulations will be given, together with a description of the paraeters used for the sensitivity analysis of the bistatic configurations carried out in the following Section 3. The directional properties of vegetation are deeply investigated and, in particular, it will be shown that co-polar bistatic easureents, acquired on a plane orthogonal with respect to the incidence one, show an interesting sensitivity to bioass. Finally, a bistatic configuration will be selected on the basis of the sensitivity analysis, and its perforance will be copared against the one of a onostatic syste.. The Methodology and the Selected Electroagnetic Model Bistatic configurations are defined in ters of frequency, polarization and transitter-target-receiver relative geoetry. This geoetry is shown in Figure, in which the plane of incidence is assued as a reference coordinate plane and the configuration is identified through the incidence angle (θ i, red in Figure ) with respect to the vertical, the zenith (θ s ) and aziuth (φ s ) scattering angles (green in Figure ). The easureent perfored by a bistatic radar consists in the bistatic scattering coefficient, i.e., the bistatic radar cross section per unit area: ( f, p, q,,,, pq i s s n 4P s ) ( f, p, q, i, s, s, n) A P ( q, ) i i () where P s is the scattered power per unit solid angle, P i is the power density ipinging on the surface target and A is the considered area. It is function of syste paraeters (i.e., frequency, f, incident and observed polarizations, q and p), of the easureent geoetry (θ i, θ s, φ s ) and of the target paraeters ( n ), such as vegetation height, soil oisture and roughness. q and p ay be Horizontal or Vertical polarization. In order to identify the set of bistatic syste paraeters (especially geoetric paraeters, but also polarization and frequency), which optiize the sensitivity to the crop height, the adopted ethodology is based on a set of siulations of σ carried out by running the TOV odel in correspondence of a range of syste and target paraeters. For the purpose of identifying the best configurations in ters of polarizations, incidence and scattering angles, the retrieval accuracy is quantified by using the Craér Rao Lower Bound (CRLB), already used in [6], which is based on the Bayesian theory of paraeter estiation. Note that, even though forecasting the retrieval accuracy

4 Reote Sens. 3, using siulations is a tricky proble, in this work, we are only interested on a relative coparison between the estiated retrieval perforances in order to identify the optial bistatic configurations. Although we cannot predict the actual accuracy without eperiental data, this relative coparison is suitable for our purposes. Figure. Geoetric eleents that identify the transitter-target-receiver (T-TG-R) bistatic configuration. The selected electroagnetic odel is described in the net section, with additional details reported in the Appendi. Then, soe results of the siulations perfored by running the odel are presented. The TOV odel is fully polarietric, since it can siulate the backscattering coefficient corresponding to any polarization of the incident and scattered power. However, in this work, siulations related to linear polarization only are discussed. This section ends by describing the paraeters chosen to identify the best configurations for crop status onitoring... The Selected Electroagnetic Model The TOV odel, which has been selected to predict the bistatic scattering coefficient of crops, is based on the radiative transfer theory. It adopts a discrete approach [3] in which vegetation eleents are described as discrete dielectric scatterers and suitable electroagnetic theories [33] are used to copute their absorption and scattering cross sections; in their turn, the latter are calculated using suitable perittivity odels [34]. The soil is described as a hoogeneous half-space with rough interface, producing surface scattering, which ay be subdivided into two coponents: a coherent and an incoherent one. The coherent coponent is coputed following the theory developed in [35], which takes the sphericity of the wavefront into account. The derived coherent scattering coefficient of the soil depends not only on the surface paraeters, but also on the receiving and transitting antenna paraeters. In this study, the beawidth of the receiving and transitting antennas has been supposed to be equal to 3. Furtherore, in order to account for coherent phenoena outside the plane of incidence, the forulation in [35] has been etended to any directions. The incoherent bistatic scattering coefficient of soil is coputed through the Integral Equation Model (IEM) [36]. Although several advances have been achieved in representing the statistics and the

5 Reote Sens. 3, electroagnetic properties of soil surfaces, soil backscattering coefficient easured at HV polarization is generally underestiated by surface odels, IEM included. On the other hand, eperiental data point out that the backscattering coefficients at HV and VV polarizations are highly correlated. For this reason, we have linked the odeled σ HV of bare soil to the odeled σ VV of bare soil itself. This correction basically consists in ultiplying the σ VV IEM output by the average ratio between HV and VV backscattering easureents over bare soil available through the ERA-ORA library ( The result is ultiplied by the canopy transission atrices at horizontal and vertical polarizations []. This sei-epirical correction has been applied to backscattering only, due to the lack of eperiental bistatic data, which would be required to calculate the correction factor at every direction. In order to cobine vegetation and soil contributions, the TOV odel adopts the Matri Doubling algorith [3] that accounts for the ultiple scattering effects that take place between vegetation eleents and the terrain. The ain steps of the etension of the TOV odel to the bistatic case are reported in the Appendi. As for the coherent coponent, attenuation by the vegetation layer has been superiposed to the soil contribution entioned previously. We recall here that odel siulations showed a good fitting with polarietric backscattering signatures easured over sunflower fields at L-band and two angles [3], bearing an error of about.5 db at all polarizations over developed crops. The sae odel was able to eplain the polarietric features observed over several kinds of agricultural and forest areas at P-, L- and C-band [37]. Recently, the odel siulated the backscattering signatures of wheat and corn at C-band [,33], and in these cases, the accuracy was also good (less than.5 db) for developed crops. The validation of the bistatic odel for vegetation cannot be perfored, because of the lack of suitable eperiental data. Nevertheless, the ability of the odel to predict the surface reflectivity, that is, the integral of the bistatic scattering coefficient over all the scattering directions, can be assessed. In fact, one inus the reflectivity provides the surface eissivity, which has been easured and copared with vegetation conditions in any eperients. Validations of the surface eissivity coputed by the odel have been carried out in [38,39], with a resulting accuracy equal to. at the L-band and to.4 at the C-band... The Corn Crop Scenario The reliability and accuracy of a theoretical odel depends on its capacity to reproduce real easureents and, as just entioned, the Tor Vergata odel has been tested and validated against data collected under different conditions. Furtherore, a reliable odel can also be used to predict easureents in order to evaluate the potential of a novel syste. The odel ust then ensure the correct electroagnetic representation of the processes under study, but also a correct representation of the environental scenario to be observed. To this end, the TOV odel is ade up of an electroagnetic odule and of a growth odule. Indeed, the TOV odel takes plant height as an input paraeter, and it includes equations that, for a given height, calculate all other vegetation paraeters, which are used to odel corn bistatic scattering, i.e., leaf area inde, leaf diensions and oisture content, twigs diensions, density and oisture content, ste diensions, density and oisture content. As a consequence, all these paraeters vary siultaneously in a realistic way, since the regression equations ipleented within

6 Reote Sens. 3, the TOV odel have been established on the basis of ground truth easureents perfored in the course of past various reote sensing capaigns. Most of the were derived by ground easureents collected during eperiental capaigns carried out in the Central Plain site in Switzerland and can be found in table forat in [33]. Therefore, the results presented in this study consist of theoretical siulations of bistatic easureents over a realistic corn crop scenario. The sensitivity study carried out here is focused on the capability to retrieve plant height, fro which it is possible to get inforation about the vegetation bioass. Height is related to plant water content in a way that depends on geographical characteristics and on working procedures of the agricultural site. As an eaple, in Figure, the easured plant height and water content of two corn sites, in Switzerland and Belgiu [33], are shown together with regression lines. The reference corn crop scenario of this paper is the Central Plain one, and the plant heights considered for the sensitivity study are 5 and c. This eans that the other plant paraeters, such as Leaf Area Inde, diensions, oisture content, etc., vary in such a way to give a Plant Water Content equal to about.5 and kg/, respectively. In order to take into account different plant developents with respect to that of the Central Plain (like in the Belgian site reported in Figure ), the plant coverage fraction has been introduced as an additional input paraeter, besides plant height. In particular, a plant cover fraction increasing with plant height faster than at the Central Plain has been also considered in soe of the eaples presented in the following sections. This situation can correspond to ore intensive agricultural practices. Figure. Plant Water Content vs. Plant Height easured on two agricultural sites. Diaonds: Central Plain (CH) and Loay (B). Regression lines are also reported..3. Siulations Results The bistatic TOV odel has been run in order to siulate the bistatic scattering of corn fields, and the results are outputted as a atri whose rows represent the scattering aziuth angles and whose coluns represent the scattering look angles. In order to represent the bi-diensional scattering properties of this vegetation ediu, a color ap has been used, as that reported in Figure 3, where colors represent the bistatic scattering coefficient values, with shades towards the red representing

7 Reote Sens. 3, 5 87 highest scattering and shades toward the blue the lowest scattering. In these aps, the horizontal ais represents the scattering look angle θ s in the range [5, 55 ]; the vertical ais represents the aziuth scattering angle φ s in the range [, 8 ]. Due to the aziuthal syetry of the vegetated ediu, syetric bistatic scattering coefficient values are epected for 8 φ s 36. In the color ap representation, the backscattering coefficient can be found on the upper side of the aps (φ s = 8 ; θ s = θ i ), whereas the specular direction lies on the botto (φ s = ; θ s = θ i ). Figure 3. Bistatic scattering coefficient σ (db) of corn plants with 5 c and 5 c height (left and right colun, respectively), at L-band, θ i =, soil roughness σ z =.5 c (height standard deviation), SM = %. Fro top to botto: VV, HV, HH polarizations.

8 Reote Sens. 3, 5 87 In Figure 3, the L-band is considered, and a soil characterized by SM = % and by a standard deviation of surface height (σ z, representing roughness) of.5 c has been assued. Two values of corn height have been considered, i.e., 5 c (low/oderate stage of growth) and 5 c (well-developed plant). Looking at Figure 3, it can be noted that, in the co-polarized cases, the highest scattering is encountered toward the specular direction (φ s = ; θ s = θ i = ). In this direction, coherent scattering fro the soil is very strong, and it is only partially attenuated by the above lying vegetation. The lowest co-polar scattering is et at horizontal polarization on the plane orthogonal to the incidence one (φ s = 9 ), while on this sae plane, the highest cross-polarized scattering occurs. This behavior is due to a reversal of the polarization vectors on the orthogonal plane, with respect to the polarization vectors defined in the plane of incidence. Indeed, the horizontal polarization vector defined in the plane of incidence, is seen as a vertical polarization vector on the plane with φ s = 9. Conversely, the vertical polarization vector defined in the plane of incidence is partially seen as a horizontal polarization vector on the plane with φ s = 9. The increase of plant height (copare right and left colun of Figure 3) deterines an increase of vegetation volue scattering and an attenuation of soil scattering. The agnitude of these two contributions depends on the field plant cover fraction, but the bistatic scattering directional pattern does not. The results presented in Figure 3 refer to cover fractions of % at 5 c height and 6% at h = 5 c, which were recorded in the field easureents perfored in the Central Plain site []. It has been found that an increase of plant coverage eans a higher attenuation of the coherent contribution, besides a volue scattering contribution ore significant with respect to soil contribution (especially for the highest plant). Consequently, the bistatic scattering coefficients are larger, ecept around the specular direction, where a decrease is observed. The effects of increasing soil roughness or oisture content are to increase bistatic scattering in ost of the scattering directions, due to a higher soil contribution, which is visible due the incoplete coverage of crop (6%) and to higher interactions between soil and vegetation. However, it has been found (not shown in this paper) that, around the specular direction, an increase of roughness causes a decrease of coherent scattering, while an increase of oisture content causes an increase in all directions. Changing incidence angle does not change the considerations previously drawn for θ i =, bearing in ind that the high incidence angles give rise to a lower scattering, for any soil roughness and oisture content. At C-band, where volue scattering is ore significant and gives rise to a general increase of bistatic σ values (ecept, of course, for the specular direction, where an increase of attenuation produces a decrease of scattering), the angular trends are in general analogous to those at L-band (as it can be deduced by coparing Figure 4 and Figure 3). Fro Figure 4, it can be appreciated as at C-band the contrast between specular direction and the other directions is reduced (the color scale used in all these σ aps is unique, so their color can be directly copared).

9 Reote Sens. 3, 5 87 Figure 4. Bistatic scattering coefficient σ (db) of corn plants with 5 c and 5 c height (left and right colun, respectively), at C-band, θ i =, soil roughness σ z =.5 c (height standard deviation), SM = %. Fro top to botto: VV, HV, HH polarizations..4. Paraeters for the Evaluations of the Bistatic Configurations The retrieval accuracy of a given relevant target paraeter (here, the crop height) obviously depends on the sensitivity of the easureent (the bistatic scattering coefficient, in this case) to the paraeter itself. In order to evaluate the sensitivity to plant height, the soil paraeters have been kept constant, and the following increental ratio has been calculated fro the odel output:

10 Reote Sens. 3, z SM h c h c h z SM h s s pq s s pq s s pq, ) 5,, ( ) 5,, (, ), ( () where h = c. The soil paraeters can assue the values SM = % or 5% and σ z =.5 or.5 c. The increental ratio can then be seen as the difference between the right and left colun of the figures in the previous section, noralized to the height difference. Besides the sensitivity, the Craér Rao Lower Bound (CRLB) inde has been used to better evaluate the potentiality of bistatic easureents and ultistatic ones (that foresee the eploitation of the onostatic data, too, see Section 3) for retrieving the height of a corn plant. It is derived fro the Bayes theory of paraeter estiation and already used in [6]. Let us assue that we perfor several easureents, σ,σ,,σ n (different polarizations and/or observation directions and/or frequencies), i.e., that we easure a n-coponent vector σ to estiate a given target paraeter i. The easureents do not depend only on i, but also on other paraeters, j, that act as nuisance paraeters. CRLB gives the best achievable accuracy of any unbiased estiator. By assuing a Gaussian easureent error with zero ean and a coon variance, σ n, the iniu variance of the estiate, i ˆ, is defined by the following inequality [6]: σ J J J T T ii T n CRLB ) ( ) ( ) ( ) ( ) var( ˆ i (3) where J is the Jacobian atri of the forward odel, whose eleents are the sensitivities of the easureents to the paraeters. Superscripts T and indicate atri transposition and inversion, respectively, and subscript ii denotes the eleents of the principal diagonal of the atri. For instance, in the case of two easureents, σ and σ, and two paraeters, (the target paraeter) and (the nuisance paraeter), the CRLB is:,,, J J J J J J J CRLB n i i i i i i n (4) where the eleent J ij of the Jacobian atri is the sensitivity of easureent σ i to paraeter j. When three easureents and two paraeters are available, the following forula applies: CRLB n (5) CRLB is a positive quantity; the nuerator contains the sensitivity to the nuisance paraeter,, so that the greater the nuerator, the larger the variance of the estiator. As for the denoinator, it is equal to the deterinant of [J()] T [J()]. Although it could be epected an increase of the denoinator (i.e., an iproveent of the retrieval perforance) if the sensitivity to the target paraeter rises, this condition is not sufficient to achieve a reliable estiation of the paraeter. In fact, if the ter

11 Reote Sens. 3, (J J + J J ) copensates for the ter, CRLB tends to rise. Such copensation occurs if the different easureents have siilar sensitivity to the bio-geophysical paraeter to be estiated (the crop height in this case), so that the deterinant of [J()] T [J()] becoes close to zero. In other words, to ensure a reliable estiation of, the sensitivity to ust be high, and the various easureents ust provide non-redundant inforation. The CRLB diverges to infinity when only one easureent is available or the Jacobian atri is singular, since in both cases it is not possible to solve for the two unknowns and. Note that introducing in Equation (4) a constant average value of the sensitivity, as it will be done in the sequel, corresponds to assuing that the forward proble is linear. If we copute the sensitivity around different values of the paraeter (for instance coputing sensitivity to plant height for sall, ediu and tall plants), we could obtain slightly different results. However, here, we are interested to find the bistatic configuration, which provides on average the best retrieval perforance, so that the consideration of an average sensitivity within a large range of the target paraeters is justified. 3. Analysis of the Bistatic Configurations for Crop Height Monitoring 3.. Analysis of the Sensitivity of Single Polarization Data As previously stated, the sensitivity analysis for the vegetated target has been carried out by considering corn, which is one of the world ost coon agricultural crops. In order to eplore a wide range of bistatic configurations (polarizations and geoetry) with a reasonable nuber of odel runs, the syste paraeters reported in Table have been chosen. Polarization Table. Syste paraeters considered for the sensitivity analysis. Incidence Angle (θ i ) [deg] Aziuth Scattering Angle (φ s ) [deg] Zenith Scattering Angle (θ s ) [deg] HH, VV, HV, 35, 5 to 8, step to 6 step Furtherore, two frequencies, i.e.,. GHz (L-band) and 5.3 GHz (C-band), have been considered. As discussed in Section, scattering fro vegetated areas is also influenced by soil roughness and oisture. In order to siulate the variability of soil conditions, the paraeters reported in Table have been chosen as representative of sooth and rough soils and dry and oist soil beneath vegetation. The above roughness paraeters eet the IEM applicability criteria (which can be found in graphical for in [4]) at the frequencies of interest. Table. Paraeters of underneath soil considered for the sensitivity analysis. Soil Roughness (c) Soil Correlation Length (c) Soil Moisture Content (%).5,.5 5 (eponential autocorrelation function), 5 The following sensitivity analysis will be perfored on single configuration data, that is, assuing that the easureent is acquired along a single observation direction. The sensitivity to plant height is defined by Equation (). Fro the sensitivity point of view, a negative and a positive value of the increental ratio, defined by Equation (), are equivalent. For this

12 Reote Sens. 3, reason, the absolute value will be considered hereafter. However, it ust be underlined that, around the specular direction (where the coherent soil coponent is generally predoinant), a negative σ / h is obtained, differently fro all other directions. The sensitivity aps are given in units of db/( c); blue represents a low sensitivity, while red corresponds to a high sensitivity. The above plots (Figure 5) refer to siulations carried out at L-band for two corn plant heights (h = 5 and 5 c), as representative of young and well-developed corn plants, and the soil paraeters are SM = 5% and σ z =.5 c. Figure 5 shows that the aiu sensitivities of bistatic σ are shown at different directions, depending on the polarization: at horizontal polarization, it occurs on the scattering plane orthogonal to the incidence one, that is, for directions with φ s = 9 ; at vertical polarization for soe directions with φ s ~ 8 ; at cross-polarization, on directions contained in the plane of incidence, both in the backward (φ s = 8 ) and forward (φ s = ) sei-planes. All this happens because, on these planes, the soil contribution is very low and the vegetation growth gives rise to increasing volue scattering (at HH or HV polarizations) or interaction with soil (at vertical polarization). Aong the three polarizations, the vertical one shows the aiu sensitivity that, depending on soil conditions and observation angle, can reach ore than.9 db/( c), which is considerably higher than that ehibited for the onostatic case. The latter, corresponding to θ s = θ i = and φ s = 8, ehibits a sensitivity not larger than.3 db/ c. At other polarizations, the aiu obtained value is.5. In the case study of Figure 5, the specular configuration does not provide good sensitivities, because of the low cover fraction characterizing the corn field: indeed, in the specular direction the coherent soil contribution is the doinant one, but attenuation introduced by the crop is not enough to produce a significant change of σ in the specular direction. Figure 5. Sensitivity to corn plant height [db/( c)] at L-band, θ i =, soil roughness σ z =.5 c, SM = 5%. On top: VV (left), HV (right); botto: HH.

13 Reote Sens. 3, As entioned in Section, a plant cover fraction of approiately 6% has been assued for the tallest plant, whereas for h = 5 c, the % of coverage has been assued. We have also increased these fractions (to % and 4%, respectively), obtaining higher volue scattering and attenuation. The latter produces an increase of sensitivity in the specular direction, while volue scattering produces a general increase of sensitivity that, as it can be observed in Figure 6, is ore or less rearkable, depending on the bistatic scattering angles. The general angular trend keeps, however, the sae behavior. Even with this kind of phenology, the best sensitivities are presented by vertical polarization at φ s ~8 and θ s ~, besides the specular direction. Figure 6. Sensitivity to corn plant height [db/( c)]. Sae paraeters as in Figure 5, but for a denser vegetation cover. On top: VV (left), HV (right); botto: HH. Indeed, the sensitivity in the specular configuration is connected to the attenuation by the plant canopy, which akes it very suitable to vegetation bioass onitoring. The scattering phenoena, which take place in this direction, were theoretically analyzed in [3,3], so that considerations on this specific configuration are ecluded fro the present study. In order to understand this behavior, we singled out the contributions originating fro the various scattering sources along the directions, which presented the aiu variability of sensitivity, i.e., along the so-called forward scattering cone. In the following figures (Figure 7, corresponding to input paraeters, as in Figure 6), scattering contribution fro the vegetation volue, interactions between vegetation and soil including double bounce and the soil contribution are shown as a function of the aziuth scattering angle φ s, once the incidence and scattering look angles have been fied equal to. A corn canopy in the early developent (i.e., with h = 5 c and 4% vegetation cover) and a fully developed one (h = 5 c, cover of %) are considered on the left and right

14 Reote Sens. 3, coluns, respectively. In backscattering (φ s = 8 ), soil contribution is doinant at L-band for short plants, as epected. For fully developed plants, volue scattering and interaction effects are iportant. In the specular direction, soil coherent scattering gives rise to a high co-polar bistatic scattering coefficient. However, it can be observed fro the plots that the relative weights of the various contributions are aziuth-dependent. Volue scattering and, ainly, the soil contribution show the iniu value of bistatic σ HH on the direction at aziuth scattering angle φ s = 9, that is, orthogonal with respect to the plane of incidence, and at the sae scattering angle, they are aiu at cross-polarization. At vertical polarization, the iniu is slightly shifted toward φ s ~ 8. Figure 7. The scattering coponents along the scattering cone with s = i =. L-band, σ z =.5 c, g = 5%. Corn height = 5 c, vegetation cover = 4% (left colun) and 5 c, vegetation cover = % (right colun). VV polarization (top row), HV polarization (iddle row) and HH polarization (botto row).

15 Reote Sens. 3, We can conclude that the aiu sensitivity to plant height is displayed when the soil contribution is very low and the plant growth can appear with the aiu contrast. The effects of changing incidence direction (i.e., θ i = 35 and 5 ) have been studied, and it has been observed that the considerations drawn previously still apply. In particular, the highest sensitivities at horizontal polarization appear on the orthogonal plane (φ s = 9 ) and on the backward plane (φ s ~8 ) at cross-polarization. As far as the vertical polarization is concerned, a shift of the bistatic direction showing the best sensitivity is observed. In particular, for θ i = 35, the best sensitivity is shown at θ s = 35, φ s = 7. This effect is due to the fact that the direction at which the soil contribution shows its iniu is dependent on the incidence direction, according to the IEM siulations of soil bistatic scattering [36] (p. 66) We also note that the sensitivity decreases with increasing incidence angle. The best sensitivity to corn plant height is therefore shown at vertical polarization in the bistatic configuration with θ i = and φ s = 8, θ s =. The sensitivity to plant height has been evaluated at C-band too. Although it is reduced with respect to L-band, it is still significant at vertical polarization at the sae angles of the lower frequency. At C-band, the two co-polar linear polarizations show siilar values (around.5 db/( c)), with horizontal polarization showing the best sensitivity on the orthogonal scattering plane. 3.. CRLB for Multipolarization Data In this section, it will be assued that easureents at two polarizations, with the sae bistatic observation direction, are available. It is understood that this analysis includes the special case of the observation of backscattered waves. Three different possible cobinations of polarization are considered: bistatic easureents at VV and VH polarizations, bistatic easureents at HH and HV polarizations and bistatic easureents at VV and HH polarizations. To evaluate the perforance of these ultipolarized bistatic systes, the CRLB defined in Section was coputed. As previously discussed, this paraeter is ore powerful than just looking at the sensitivity, if one wants to analyze a ultidiensional data set. The paraeter to be onitored ( ) is the corn plant height, h, the nuisance paraeter ( ) has been supposed to be the soil oisture content, while the soil roughness has been assued to be constant (i.e., σ z =.5 c). The standard deviation error of the easureents σ n has been supposed to be db. In the aps presented in Figure 8, the square root of the CRLB paraeter is reported. In order to have the sae scale on all the following aps, the square root of CRLB has been noralized to c, so that the standard deviation is epressed in tens of c. Furtherore, for the sake of figure clarity, the values of the square root of CRLB have been saturated to c in the following color aps, in order to ephasize directions where the estiated retrieval error is lower than this value. We reind that CRLB is inversely proportional to the sensitivity to plant height and that it gets to the aiu values (lower retrieval quality) when the two easureents are in soe way correlated, while it is at iniu (higher retrieval quality) when the two available easureents are uncorrelated or they have opposite sensitivities. As a consequence of the sei-epirical correction applied on the backscattered σ HV, the following CRLB aps show a high value in the backward direction (i.e., low retrieval quality), due to the high correlation eisting between HV and VV easureents in this

16 Reote Sens. 3, configuration (see Section.); at scattering directions with θ s θ i on the plane of incidence, CRLB presents a significant discontinuity, physically not realistic, with respect to the onostatic configuration, due to the fact that the epirical correction has been applied in the backscattering direction only. Figure 8. Square root of Craér Rao Lower Bound (CRLB) [ c] for a corn field. L-band, θ i =, σ z =.5 c. Available easureents are: bistatic σ VV and bistatic σ HV (upper left), bistatic σ HH and bistatic σ VH (upper right) and bistatic σ HH and bistatic σ VV (botto). In general, horizontal and vertical polarizations are highly correlated on a wide range of bistatic angles, which results in high values of CRLB, as shown in the botto ap of Figure 8. Conversely, the lowest values of CRLB are shown when one of the two easureents is carried out at cross polarization. The best perforances are presented in the polarization configurations σ VV and σ HV or σ HH and σ VH, at aziuthal angles close to φ s = 9. In this condition, the CRLB indicates that the estiation error standard deviation can reach a lower bound of about c. The couple of σ VV and σ HV easureents aintains this optial condition for a larger range of scattering angles and, therefore, sees to be the best configuration. Note that along this direction the cross-polarized bistatic σ HV presents its aiu, while the two co-polarized bistatic scattering coefficients reach the lowest values, so that the two easureents are uncorrelated, as discussed before The error on corn height retrieval reains above c in the onostatic case, while it ay decrease to about 3 c at the identified optial bistatic configuration (reinding that the square root of CRLB has been noralized

17 Reote Sens. 3, 5 88 to c and saturated to c in the color ap). The aps obtained for corn observation at C-band show analogous trend than at that L-band CRLB for Multistatic Configurations A bistatic syste requires the ipleentation of a suitable receiver, but the onostatic data are epected to be available through the active SAR issions, which provide the signal. Then, we can assue that the onostatic easureent (θ s = θ i and φ s = 8 ) ay copleent the bistatic ones, thus setting up the so-called ultistatic case. Like in the previous section, the CRLB paraeter was estiated, and the aps of the square root of CRLB are here reported, with the sae noralization applied in the previous plots. In each figure, two coluns are displayed. The left one reports the co-polarized CRLB s, i.e., the CRLB s calculated assuing that the bistatic and the onostatic easureents have the sae polarization (bistatic σ VV and onostatic σ VV; bistatic σ HV and onostatic σ HV; bistatic σ HH and onostatic σ HH). The right colun reports the cross-polarized CRLB s, i.e., those calculated for the following couples of easureents: bistaticσ VV and onostaticσ HV; bistatic σ HV and onostatic σ VV; bistaticσ HH and onostatic σ HV. We have verified that the CRLB aps concerning bistatic σ HV and onostatic σ VV differ fro those concerning bistatic σ HV and onostatic σ HH only for their values, but not for what concerns the dependence on the bistatic geoetry. For this reason, only one ap is reported. Note that when onostatic σ HV is available, also a co-polarized easureent is usually carried out, so that two onostatic easureents can be epected to be available fro a dual polarization SAR siultaneously with the bistatic one. We have then estiated the CRLB paraeter with three easureents too: again, is the corn plant height, h, while the nuisance paraeter,, has been supposed to be the soil oisture content and the soil roughness has been fied toσ z =.5 c. σ is the bistatic easureent, while σ and σ 3 are the two available easureents in the backscattering direction (e.g., σ HV and σ VV or σ HV and σ HH). However, it has been found that the addition of another onostatic easureent at L-band (see Equation (5)) does not change the CRLB aps, so that those obtained for the cross-polarized CRLBs (shown below) apply for the three easureents case as well. As for the C-band, the addition of the third easureent iproves significantly the perforance of the retrieval only where the variance is large with two easureents. Nevertheless, the optial bistatic configurations are obtained at the sae aziuth and zenith angles indicated in the case of two easureents. For these reasons, the aps for the three easureents case are not reported. The aps in Figure 9 indicate that co-polarized and cross-polarized ultistatic configurations (left and right colun, respectively) behave in the sae way. This is partially due to the fact that onostatic σ HV has been linked to onostatic σ VV, which, in its turn, is correlated to onostatic σ HH. Therefore, considering a cross-polarized or a co-polarized backscattering easureent does not change the CRLB aps very uch.

18 Reote Sens. 3, 5 88 Figure 9. Square root of CRLB [ c] for a corn field. L-band, θ i =, σ z =.5 c. Available easureents, first row: bistatic σ VV and onostatic σ VV on the left, bistatic σ VV and onostatic σ HV on the right; second row: bistatic σ HV and onostatic σ HV on the left, bistatic σ HV and onostatic σ VV (or σ HH) on the right; third row: bistatic σ HH and onostatic σ HH on the left and bistatic σ HH and onostatic σ VH on the right. At HH and VV polarizations (top and botto plots), bistatic scattering behaves siilarly to backscattering, as long as the aziuth scattering angle φ s is far fro 9, and this correlation akes the values of CRLB fairly high on a large range of scattering angles. The aps suggest that the scattering plane orthogonal with respect to the plane of incidence shows the best perforance at

19 Reote Sens. 3, 5 88 horizontal polarization, while at vertical polarization, the direction underlined also in the previous sensitivity analysis (see Section 3.) shows up, that is, φ s = 8, θ s = for an incidence direction with θ i =. The best achievable value of the variance of the corn height estiate is less than c, coparable with the one obtained for a purely bistatic configuration and two polarizations. Therefore, the choice between a dual polarized receiver and a receiver at single polarization copleented by a onostatic easureent should be only based on econoic considerations (we note that, as for the previous eaple of Figure 8, the variance of the corn height estiate is larger than c in the onostatic dual ode). The aps concerning HV polarization (on the nd row) always display large values of CRLB, since the sensitivity of bistatic σ HV to plant height is rather low outside the plane of incidence (see Figure 5). We reind that the HV backscattering coefficient has been epirically corrected, thus yielding a large CRLB value in the backward direction (i.e., the onostatic configuration), uch different fro adjacent bistatic configurations in the iddle plots of Figures 9 and. Figure. Square root of CRLB [ c] for a corn field. C-band, θ i =, σ z =.5 c. Available easureents, first row: bistatic σ VV and onostatic σ VV on the left, bistatic σ VV and onostatic σ HV on the right; second row: bistatic σ HV and onostatic σ HV on the left, bistatic σ HV and onostatic σ VV (or σ HH) on the right; third row: bistatic σ HH and onostatic σ HH on the left and bistatic σ HH and onostatic σ VH on the right.

20 Reote Sens. 3, Figure. Cont. If the incidence angle is shifted to higher values, the aps show analogous correlations between easureents, but with slightly higher values of CRLB than in the case of low incidence angle discussed previously. Obviously, the iniu CRLB for the vertical polarization oves towards φ s = 7, θ s = 35, appearing at bistatic directions corresponding to the aiu sensitivity to plant height, as observed in Section 3.. Moreover, it has been found that, by increasing the cover percentage, CRLB lowers in the specular direction, where the higher coverage produces a higher attenuation and, hence, a higher sensitivity; at other bistatic angles CRLB trend is analogous to the one reported for the reference coverage. The siulations perfored at C-band (Figure ) indicate that the sensitivity to vegetation bioass in the specular configuration is quite reduced or even absent when the soil roughness is large with respect to wavelength and the percent coverage is low. At C-band, however, when φ s is close to 9, the region with low CRLB gets larger than at the lower frequency, since the vegetation contributions get stronger with respect to the soil ones and the sensitivity to plant height has a soother trend with bistatic angle. In general, however, the lowest values of CRLB at C-band are higher than the lowest values at L-band Optial Bistatic Configurations for Crop Height Monitoring The siulation results presented in the previous sections indicate that the specular configuration (especially at L-band), with a tolerance of about ±5 both in aspect and aziuth, is by far the ost sensitive to vegetation bioass. The specular configuration, however, presents soe probles in ters of achievable geoetrical resolution of a radar iaging syste, as discussed in [6]. It becoes very interesting in the case of a GNSS-R syste, as discussed, for instance, in [3,4]. Then, it is iportant to single out other interesting configurations that have eerged fro this study. If the receiver of the bistatic syste is foreseen to operate at single polarization (see Figure 5), a low incidence angle (θ i ~ ) leads to the best perforances. Furtherore, bistatic easureents present sensitivities larger than in the onostatic configuration at vertical polarization with φ s = 8, θ s ~θ i (at L-band, σ VV / h can be five-ties larger than in backscattering and, at C-band, double) and at horizontal polarization at φ s = 9 (where σ HH / h can be double that in backscattering both at L- and

21 Reote Sens. 3, C-band). VV polarization keeps the sensitivity larger in a wider range of bistatic angles with respect to other polarizations, so that, in suary, the best configuration for a receiver with single polarization is: σ VV at φ s ~8, θ s ~θ i The perforance aps developed for the bistatic ultipolarization configurations and for the ultistatic configurations have shown that several bistatic configurations can provide easureents that are epected to yield good perforances. In order to select the ost significant ones, we take as a reference the ultipolarized easureents perfored in onostatic configuration, i.e., the ones, which can be carried out by past and currently available SARs, like ALOS/PALSAR ENVISAT/ASAR, Radarsat or the forthcoing Sentinel. We copare the CRLB in this configuration with the ones found in the other scattering directions. At L-band, the onostatic couples are very uch correlated (their CRLB indicates an error standard deviation lower bound always higher than c, which basically eans the inability to easure the height of corn). When two polarizations are available through the passive coponent of the bistatic syste, the scattering angles showing a high sensitivity, entioned previously, keep their high perforances in the cobination (σ VV, σ HV) and (σ HH, σ VH), with a lower bound of the error standard deviation reduced by a factor of about five with respect to the onostatic dual-pol configuration (see Figure 8). When a bistatic easureent is accopanied by a onostatic easureent, the perfored siulations (Figure 9) give CRLBs that are uch lower than the onostatic values when θ i =, with the following ultistatic configurations: σ VV at φ s ~9, < θ s <, together with onostatic σ VV or σ HV: this configuration shows the iniu CRLB (i.e., lower bound of the error standard deviation between 5 and 5 c); σ HH at φ s ~9, < θ s <, together with onostatic σ HH or σ VH (lower bound of the error standard deviation about 5 c). At C-band, the error standard deviation is between 5 and 6 c for the three onostatic couples. Lower values are shown by: σ VV at φ s ~9, < θ s <, together with onostatic σ VV or σ HV (error standard deviation of about c); σ HH at φ s ~9, < θ s <, together with onostatic σ HH or σ VH (error standard deviation between and 3 c). To suarize, the configurations in Table 3 are recoended. Table 3. Suggested polarization cobinations for θ I = considering a single bistatic polarization, a dual-polarized bistatic and a ultistatic (active and passive systes at single polarization). The corresponding optial bistatic geoetries at L- and C-band (ecluding the specular case) are also reported. Bistatic σ VV in single configuration cobined with bistatic σ VH cobined with onostatic σ VV or σ VH Bistatic σ HH in single configuration cobined with bistatic σ HV cobined with onostatic σ HH or σ HV