Int J Appl Earth Obs Geoinformation

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1 Int J Appl Earth Obs Geoinformation 79 (219) Contents lists available at ScienceDirect Int J Appl Earth Obs Geoinformation journal homepage: Joint estimation of Plant Area Index (PAI) and wet biomass in wheat and soybean from C-band polarimetric SAR data T Dipankar Mandal a,, Vineet Kumar a, Heather McNairn b, Avik Bhattacharya a, Y.S. Rao a a Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay, Mumbai, India b Agriculture and Agri-Food Canada, Ottawa, Canada ARTICLE INFO Keywords: Crop Model inversion Multi-target regression Random forest SMAPVEX16-MB Water Cloud Model ABSTRACT Retrieval of the Plant Area Index (PAI) and wet biomass from polarimetric SAR (PolSAR) data is of paramount importance for in-season monitoring of crop growth. Notably, the joint estimation of biophysical parameters might be effective instead of an individual parameter due to their inherent relationships (possibly nonlinear). The semi-empirical water cloud model (WCM) can be suitably utilized to estimate biophysical parameters from PolSAR data. Nevertheless, instability problems could occur during the model inversion process using traditional inversion approaches. Iterative optimization (IO) can have difficulty in finding the global minima while look up table (LUT) searches have a lower generalization capability. These challenges reduce the transferability of IO and LUT search inversions in computational efficiency and seldom account for the inter-correlation among the parameters. Alternatively, a machine learning regression technique with a regularization routine may provide a stable and optimum solution for ill-posed problems related to the inversion of the WCM. In the present work, the crop biophysical parameters viz. PAI and wet biomass are estimated simultaneously using the multi-target Random Forest Regression (MTRFR) technique. The accuracy of the retrieval method is analyzed using the insitu measurements and quad-pol RADARSAT-2 data acquired during the SMAPVEX16 campaign over Manitoba, Canada. The inversion process is tested with different polarization combinations of SAR data for wheat and soybean. The validation used ground measured biophysical parameters for various crops, indicating promising results with a correlation coefficient (r) in the range of.6.8. In addition, the relationship between PAI and wet biomass using the multi-target and single output model is also assessed based on in-situ measurements. The results confirm that the inter-correlation between biophysical parameters is well preserved in the MTRFR based joint inversion technique for both wheat and soybean. 1. Introduction Crop biophysical parameters viz. leaf area index (LAI), biomass and height are descriptors of plant growth status and serve as key inputs to yield forecasting models (Bouman, 1992; Betbeder et al., 216). LAI is correlated directly with canopy foliage and canopy structure (Jonckheere et al., 24). The wet biomass is related to canopy water content and carbon accumulation during the crop growth stages. In the past decades, Earth observation (EO) data have been successfully utilized to estimate crop biophysical parameters. In particular, Synthetic Aperture Radar (SAR) data have drawn considerable attention for agricultural applications due to its all weather monitoring and sensitivity towards dielectric and geometric properties (Ulaby, 1975; Brakke et al., 1981; Steele-Dunne et al., 217). In order to retrieve vegetation information from SAR observations, a model is first required to simulate the backscatter intensities for a crop canopy. This model can then be inverted to estimate canopy characteristics (Prevot et al., 1993). In the literature, a semi-empirical water-cloud model (WCM), proposed by Attema and Ulaby (1978), has been widely used to retrieve vegetation parameters for various crops using SAR data (De Roo et al., 21; Graham and Harris, 23; Bériaux et al., 211; Hosseini et al., 215; Hosseini and McNairn, 217; Wiseman et al., 214). Furthermore, the assumptions in the WCM were modified in several studies, improving generalization of the model (Kweon and Oh, 215; Tao et al., 216). Paris (1986) pointed out the issues with the assumption in the transmittance component (Ulaby et al., 1984) in the WCM. The transmittance term in the WCM is expressed as the product of the water mass (kg) of single scattering elements and the canopy height. This product is the areal water content of the canopy as a whole. It is assumed that the Corresponding author. address: dipankar_mandal@iitb.ac.in (D. Mandal). Received 24 November 218; Received in revised form 12 February 219; Accepted 14 February / 219 Elsevier B.V. All rights reserved.

2 LAI is proportional to areal water content. Tao et al. (216) also used a look-up table algorithm to calculate the value of vegetation water content and retrieved the LAI according to a linear relationship between vegetation water content and LAI. However, this is only approximately true when one compares the leaf area index to the leaf areal water content. In general, the stems have ample contribution to the total canopy water content for various crops (Steele-Dunne et al., 217). For corn, the contribution by the stalks is > 5% of the total biomass, while it is 35% for soybean. Hence, the total wet biomass (or fresh biomass) might be a better canopy descriptor along with the LAI. The crop parameter retrieval using the WCM involves the model calibration and inversion processes. However, the retrieval of biophysical parameters using such a model is hindered by the ill-posed nature of the problem (Bériaux et al., 215; Durbha et al., 27). In traditional inversion methods, an optimum parameter set is searched for a given particular combination of backscatter intensities, using numerical optimization techniques, e.g. the Nelder Mead and the Newton Raphson methods (Kelley, 1999). The optimization starts with an initial guess and minimizes the error through an iterative process. However, this approach is computationally intensive in the process of determining a stable solution as the search algorithm may get trapped in a local minima before attaining the global minimum. This makes the retrieval of biophysical variables challenging for large areas (Houborg et al., 27). Instead of an iterative method, the look-up table (LUT) search method for inversion of the WCM is an alternative approach (McNairn et al., 212b). The simulated radar backscatter is derived by varying crop parameters in forward modeling to generate a LUT. Next an observed backscatter intensity is compared against the LUT backscatter using a cost function. Although look-up table techniques may provide an efficient alternative, the definition of the cost function to be minimized remains contentious for an operational context (Verrelst et al., 214). In addition, LUT approaches lack good generalization capacity (Fang et al., 23) and often require a priori knowledge (Rivera et al., 213). Conversely, machine learning regression techniques with a regularization method may provide a stable and optimum solution for the ill-posed problems associated with WCM inversion (Durbha et al., 27). Regression techniques estimate a functional relationship between a set of variables (e.g. Plant Area Index (PAI) and biomass) and the corresponding target (i.e., backscatter coefficients). Typically, machine learning regression techniques can map the strong nonlinearity of the functional dependence between the biophysical parameters and the observed backscatter intensities. Moreover, these algorithms are fast to apply, once trained, and as such would be a more applicable technique for operational applications (Caicedo et al., 214). Different machine learning methods have been used for addressing regression problems, e.g., principal component regression (PCR), neural networks (NN), Gaussian process regression, kernel ridge regression, support vector regression (SVR) and random forest regression (Alpaydin, 214; Pedregosa et al., 211; Mandal et al., 218). Various linear and nonlinear regression algorithms have been assessed for biophysical parameter estimation with hyperspectral data (Caicedo et al., 214). This study reported that nonlinear regression algorithms outperformed linear techniques in terms of accuracy, bias, and robustness. Among various machine-learning algorithms, the ensemble learning technique viz. Random Forest (RF) (Breiman, 21) has attracted growing interest in classification and regression, as this algorithm can model complex interactions among input variables and is impacted less by outliers (Rodriguez-Galiano et al., 212). In addition, RF has fewer hyper-parameters compared to other algorithms (e.g. NN or SVR) as applied to biophysical parameter estimation (Wang et al., 216). A recent study by Kumar et al. (217) compared RF regression (RFR), SVR, ANN and linear regression (LR) algorithms for estimation of wheat parameters from Sentinel-1A time series data. RFR algorithm yielded a higher adjusted R 2 (.95) than SVR, ANN and LR algorithms (with R 2 of.89,.86 and.76 respectively). Also, a lower RMSE (.29 m 2 m 2 ) was reported using the RFR, in comparison to these other methods for the estimation of LAI. Standard machine learning algorithms map multiple inputs to a single output. For example, the predictors are backscatter coefficients in co (HH and VV) and cross (HV) polarizations, and the response is a single output (the LAI of crop) (Mountrakis et al., 211). When multiple outputs are desired, standard practice is to run two independent regression models: first predicting one variable, and then the next. However, this approach ignores the potential inter-correlations (potentially non-linear) among the outputs (LAI and wet biomass) (Tuia et al., 211; Xu et al., 213). As well, the retrieval is optimized for a single target rather than all targets simultaneously. Estimates of multiple biophysical descriptors are of value for yield modeling (Ghosh and Singh, 1998). Simultaneous estimation of crop biophysical parameters is important given their underlying relationships and incoherent variations (Borchani et al., 215). For example, as LAI increases often stem height increases. Yet, exceptions occur for crops like wheat where canopy at different heights can have the same LAI. As such, simultaneous retrieval of LAI and biomass would consider not only the underlying relationship between the inputs (i.e. backscatter intensities from HH, VV, HV) and the corresponding outputs (LAI, biomass, crop height) but also the relationship amongst the outputs. Simultaneous estimation of crop biophysical parameters (e.g. LAI, fcover, and chlorophyll concentration) using a multi-output SVR was successfully illustrated by Tuia et al. (211) for hyperspectral images from CHRIS/PROBA. However, SVMs are memory intensive and the hyper-parameters are hard to tune. Moreover, the selection of an appropriate kernel is tedious, and the learning machine does not scale well to larger datasets. This problem can be overcome with Random Forest regression. The RF algorithm presents several advantages over kernel methods. It performs efficiently on large datasets while being insensitive to noise and over-fitting. It has fewer hyper-parameter settings compared to other machine-learning algorithms (e.g. ANN or SVR) (Jin et al., 213; Pedregosa et al., 211). Stojanova et al. (21) reported that a multi-target ensemble method performed better than single model algorithms for forest tree height and canopy cover estimation from LiDAR and Landsat7 ETM+ data. In this present work, the multi-target random forest regression (MTRFR) is utilized for simultaneous estimation of two biophysical parameters (viz. PAI and wet biomass) by inverting the calibrated WCM. The branching structure of the RF allows regression trees to learn the non-linear relationships among the parameters naturally. The MTRFR is used to estimate PAI and wet biomass from full-polarimetric (PolSAR) RADARSAT-2 data acquired over Manitoba, Canada. The retrieval accuracy is also tested for different polarization combinations (e.g. HH+VV, HH+HV, VV+HV, HH+VV+HV). Subsequently, the relationship between PAI and wet biomass is also assessed using multitarget and single output models based on the in-situ measurements. The rest of the manuscript is organized in the following order. Section 2 briefly describes the study area and the datasets. Section 3 discusses in detail the methodology used in this study. Section 4 presents and discusses the results. Finally, the work is summarized in Section Study area and dataset The site and in-situ measurements used in this study are part of the Soil Moisture Active Passive Validation Experiment 216-Manitoba (SMAPVEX16-MB). The campaign was conducted for post-launch validation activities in support of SMAP satellite data products. The SMAPVEX16-MB campaign site is located in the Red River watershed of southern Manitoba, Canada. The test site is shifted east and south of the SMAPVEX-12 field campaign (McNairn et al., 215). The study area is shown in Fig. 1. The test site covers an area of km 2 and is 25

3 Fig. 1. PauliRGB image of RADARSAT-2 acquired on 17 July 216 during the SMAPVEX16-MB campaign in Manitoba (Canada) along with the sampling field location for wheat and soybean crop. Sampling locations within a field is presented in the yellow box. characterized by a range of crop and soil conditions. The area is dominated by an annual crop mix of soybean, wheat, canola, corn, winter wheat, oats, and beans. Clay and fine loam soils account for 76% of this study domain, while coarse loam and sand soils account for 14%. Field data were collected during two Intensive Observation Periods (IOPs). The first IOP was conducted from June 8 2 during the period of early vegetative growth. The second IOP (July 1 22) was held during the period leading up to maximum biomass accumulation (McNairn et al., 216). In this study, the analysis is performed for soybean and wheat crops as they account for almost 55% of cropland in the test site Sampling strategy During the campaign, 5 fields of various crops were selected for sampling. Of these 5 fields, soybean was cultivated in 14 and wheat in 13 fields. The nominal size of each field was approximately 8 m 8 m. In each field, soil moisture was measured at 16 sampling points which were arranged in two parallel transects, each containing 8 points (shown in the yellow box in Fig. 1). Sampling points were separated by approximately 75 m and each transect was separated by 2 m. Soil moisture measurements at each point were taken using hydra-probes with calibration supported by one soil core collected during each field visit. Vegetation sampling was performed at 3 locations (i.e. point 2, 11, 14 in the first week and 3, 1, 13 in the second week of each IOPs) out of 16 sampling points. Plant area index (PAI), biomass and plant height was measured at these three sampling points. Biomass was collected by destructive sampling whereas PAI and height were measured by non-destructive means. PAI was collected using hemispherical photography. Here it is important to note that PAI is expressed as a square meter of plant area per square meter ground. The interception of the electromagnetic wave is due to the interaction by all the vegetative parts of a crop canopy. However, LAI is defined as the one-sided leaf area per unit ground surface area (LAI = leaf area/ ground area, m 2 /m 2 ), thus the LAI does not compensate for the other canopy elements e.g. stems, shoots, and flower. Moreover, the indirect measurement of LAI using the digital hemispherical photography (used during SMAPVEX16-MB Campaign) does not distinguish between leaves and other plant elements. The detailed description of soil and vegetation sampling can be reviewed in McNairn et al. (216, 215), Bhuiyan et al. (218) Satellite Data and PolSAR image processing In this study, eight RADARSAT-2 fine quad-pol wide (FQW) swath images in single look complex (SLC) format are utilized. All these images were acquired during the intensive observation periods of the field campaign. The beam mode for these acquisitions varies from FQ7W to FQ2W. The detailed specification of the acquired RADAR- SAT-2 images is given in Table I. The single-look complex (SLC) RADARSAT-2 data were multilooked to form the 3 3 covariance matrix [C]. Subsequently, all the images (Table 1 ) were speckle filtered using a 5 5 boxcar filter (Lee et al., 1994) and co-registered using ground control points. Finally, the backscattering intensities σ and local incidence angle for each site is calculated as the average of a 3 3 window centered on each site, from the elements of the covariance matrix [C] (McNairn et al., 212a; Hosseini et al., 215). Table 1 Specification of RADARSAT-2 data used for this study. Acquisition date Beam mode Incidence angle range (deg.) Orbit 12/6/216 FQ2W Descending 15/6/216 FQ7W Descending 22/6/216 FQ11W Descending 29/6/216 FQ16W Descending 3/7/216 FQ15W Ascending 1/7/216 FQ11W Ascending 17/7/216 FQ7W Ascending 2/7/216 FQ2W Ascending 26

4 3. Methodology 3.1. Vegetation modeling In this study, a semi-empirical modeling approach (Graham and Harris, 23) is considered for radar backscatter simulation from the crop canopy. The Water Cloud Model (WCM) is used to simulate the radar backscatter in different polarizations upon its calibration with insitu measurements Water Cloud Model (WCM) The Water Cloud Model (WCM) was originally developed by Attema and Ulaby (1978). In this model, the total backscatter σ is expressed as the incoherent sum of backscatter from vegetation σ veg and the underlying soil surface σ soil Eqs. (1) (3). The soil component is attenuated by the vegetation layer through the two way attenuation factor τ 2. σ = σveg + τ2 σ soil (1) 2BV σveg = AV cos θ( 1 exp( )) 2 1 cos θ (2) τ2 = exp( 2BV 2 /cos θ) (3) where V 1 and V 2 are bulk vegetation parameters that accounts for the direct canopy backscatter and attenuation, respectively. The θ parameter indicates the radar incidence angle. Due to the complexity of vegetation structure and the relative simplicity of the WCM model, various canopy descriptors have been used in literature (Ulaby et al., 1984; Prevot et al., 1993; Lievens and Verhoest, 211; Hosseini et al., 215; Mandal et al., 218). In this present study, V 1 = PAI E and V 2 = W F are considered. A and E are fitting parameters, respectively describing the vegetation scattering and associated with Plant Area Index (PAI). The attenuation is described with wet biomass (W) with fitting parameters B and F, respectively. The backscatter intensity of the soil component σ soil is expressed as proposed in (Ulaby et al., 1978): soil σ = CM v + D where M v is volumetric soil moisture. The model parameter C can be considered as the sensitivity of SAR to soil moisture and D indicates the backscatter due to surface roughness. Finally, Eq. (5) is obtained by substituting Eqs. (2) (4) into Eq. (1). σ F ( ( )) cos θ 2BWF ( ) = ALE cos θ 1 exp 2BW + (CM + D) exp v cos θ Calibration of the WCM In the model calibration step, the parameters (A, B, C, D, E, and F) of Eq. (5) are estimated. The most commonly used method for parameter estimation is the non-linear least square optimization with Levenberg- Marquardt (LM) algorithm (Moré, 1978). It is a standard technique for solving nonlinear least square problems which arise in the context of fitting a parameterized function to a set of observed data points by minimizing the sum of the squares of the errors between the observed data points and the function output. The LM algorithm is an iterative process which combines the Gauss- Newton method and the gradient descent method. It starts with an initial guess of the model parameters and iteratively approaches toward a minimum. However, if the initial guess is not correctly selected, it may fall into local minimums. In such a case, the direction of the search may be altered, and the finding of the optimal results may be hampered. Therefore, a different approach is adopted in the present study to overcome the problem associated with the initial guess in the LM algorithm. This local minimum problem can be alleviated with (4) (5) differential evolution (Pedregosa et al., 211) which is an efficient heuristic global optimization technique. This approach finds the global minimum of a multivariate function in a stochastic way and can search large candidate spaces. As described in Section 2, the in-situ vegetation measurements were collected in each field at sites 2, 11 and 14 (or 3, 1 and 13). These measurements were divided into two parts for model calibration and validation following the standard method used in the SMAPVEX-12 campaign (Hosseini et al., 215). Site 2 (or site 3) is used to calibrate the model, whereas measurements at sites 11 and 14 (or 1 and 13) are used for validation. Subsequently, the model is calibrated separately for wheat and soybean for HH, HV and VV polarizations. The model performance is measured in terms of the correlation coefficient (r) and normalized RMS error (nrmse) (Shcherbakov et al., 213) between observed and estimated backscatter intensities as (6): nrmse = i n = 1( σ Observed σ Predicted ) 2 n i n = 1 σ Observed n (6) To test the significance of the model parameters, an F-test (Blackwell, 28) is performed for each polarization and crop type. The F-test is a joint significance test of model parameters with a zero model (i.e. all model parameters are considered as zero in a null hypothesis) while calculating the significance level (p-value). If the p-value for the F-test is less than a predefined significance level (95%), the null hypothesis can be rejected. Subsequently, it can be concluded that the proposed model provides a better fit than the zero-model Model inversion Estimation of crop biophysical parameters from the WCM with the observed backscatter responses can be cast as a model inversion problem (Bériaux et al., 211). Several combinations of crop biophysical parameters have a mutually compensating effect on canopy backscatter which might lead to very similar solutions. Moreover, backscatter response from vegetation involves intricately coupled physical processes (i.e., canopy characteristics, soil background effects, radar geometry), making it difficult to determine the influence of a single biophysical parameter from experimental data (Verrelst et al., 21). In this study, a hybrid approach is proposed in which the LUT is generated to feed the RF to tackle the ill-posed inversion problem. The model inversion strategy includes three major steps: (a) LUT generation; (b) MTRF regression model development by utilizing the LUT generated by forward modeling; and (c) joint estimation of the crop biophysical parameters LUT generation with forward WCM The calibration dataset (in-situ measurements) of crop parameters and incidence angle are used to generate the corresponding backscatter intensities using the calibrated WCM and forward modeling. The estimated model parameters (A, B, C, D, E and F) derived during the model calibration step (Table 2 ) are used for forward modeling. At each calibration site (site 2 or 3) the backscatter intensities (HH, VV, and HV) were simulated from the calibrated WCM for each crop type and subsequently the look-up table is generated. Furthermore, these LUTs are then used to feed the RF Multi-target Random Forest Regression (MTRFR) Random Forest (RF) being an ensemble learning technique (Breiman, 21) combines a large set of independently generated decision trees. The independence between the trees is achieved by randomly selecting one-third of the predictors at each node for node splitting and by using a random bootstrap sample comprising 67% of the training samples to build each tree of the RF. The remaining 33%, which are called the out-of-bag (OOB) samples, are then used to obtain 27

5 Fig. 2. Comparison of measured and estimated σ from the parameterized Water Cloud Model for HH, VV and HV polarization for wheat and soybean using calibration data. an error estimate based on the bootstrap subset. At each node, the best split is chosen to form the child nodes. The value of each child node is the average of the sample values in that node (Liaw et al., 22). Multi-target regression trees deal with the simultaneous prediction of multiple continuous targets. Moreover, Struyf and Džeroski (25) demonstrated that this method has advantages over building a separate regression tree for each target. A single multi-target regression tree is usually much smaller than the total size of the individual single-target trees for all variables. Also, a multi-target RF regression tree better identifies the dependencies between different target variables (De Ath, 22). Segal (1992) proposed a novel design for multivariate regression trees which are based on the least squares split function proposed in the CART framework (Breiman et al., 1984). For a univariate response regression tree, the least square function aims to minimize the sum of squared errors amongst the child nodes. It aims to partition t into two child nodes, a left node t L, and a right node t R. Thus, the task is to minimize the split function as, ϕ( s, t) = SSE( t) SSE( tl) SSE( tr ) (7) where SSE(t) is the sum of squared error in node t, defined as: SSE() t = ( y y ()) t i t i 2 where yt ( ) is the mean of y i in node t. Segal (1992) added a covariance weighting term to the squared error which drives the tree induction algorithm into forming child nodes. SSE() t = ( y yt ()) V 1(, t η)( y yt ()) i t i i where η represents parameters which characterize the covariance (8) (9) structure. Using Eq. (8), a multi-response split function is created. The prediction for each leaf of a multi-response regression tree is the mean of the vector response for each attribute reaching that leaf. Segal and Xiao (211) proposed a multivariate RF ensemble using the covariance weighted multivariate regression trees proposed by Segal (1992). Predictive performance improved compared to other methods for multivariate as well as univariate predictions (Borchani et al., 215). In this present research, the LUT elements were used to build the RF regression model. The MTRF regression model is developed with the simulated backscatter intensities and incidence angle as predictors and the crop parameters as the response. Subsequently, an experimental setup is designed where the MTRFR models were built with different predictor combinations. Moreover, the combination of polarization channels is found to be a better estimation of crop parameters when compared to a single channel (Hosseini et al., 215; Bériaux et al., 215). Hence, the experiment is designed with combinations of co-pol and cross-pol backscatter intensities as predictors. The combinations were kept as HH+VV, HH+HV, VV+HV, and HH+VV+HV. However, the model responses (crop biophysical parameters PAI and wet biomass) are kept the same for each experiment for an individual crop. 5 trees were used for the RF regression. The node impurity is measured with the Mean Square Error (MSE) Joint estimation of crop biophysical parameters The MTRF regression model is developed with the simulated backscatter intensities (in the LUT) and incidence angle as predictors and the crop parameters (in the LUT) as the response. Subsequently, an experimental setup is designed where the MTRFR models were built with different predictor combinations. The experiment is designed with combinations of co-pol and cross-pol backscatter intensities as 28

6 predictors. The four combinations were selected as HH+VV, HH+HV, VV+HV, and HH+VV+HV. However, the model responses (crop biophysical parameters PAI and wet biomass) are kept the same for each experiment for each individual crop during the MTRFR training phase. During the inversion process, the trained MTRFR models were used to predict the biophysical parameters for the validation data. The backscatter intensities (HH, VV, HV) and the incidence angle of the validation sites were fed as input to the trained MTRFR models for each test case separately, for simultaneous estimation of the PAI and wet biomass. The accuracy in prediction is assessed using error estimates (correlation coefficient, RMSE, and MAE) for each experimental setup and for each individual crop, using the in-situ measurements. The inversion results were also compared with conventional techniques such as LUT search and single output RFR (Section 4.3). Furthermore, the relationship between estimated PAI and wet biomass were examined from MTRFR and RFR cases, as is explained in Section Results and discussions The proposed MTRFR technique for joint estimation of the biophysical parameter is performed using the steps described in Section and Section 3.2. Subsequently, the WCM model calibration and inversion accuracy are analyzed in Section 4.1 and Section Model calibration The parameterization of WCM is performed with a hybrid approach of differential evolution and the LM technique using the calibration data as discussed in Section The polarization state of the SAR signal affects the response from targets. Hence, WCM is parameterized individually in HH, HV and VV polarizations for wheat and soybean crops resulting in six different model equations. The model parameters for each combination (crop and polarizations) along with the F-statistics and the p-values are given in Table 2. The level of significance for all the models is found to be <.5, indicating a good fit for the data. The F-statistics for different models (HH, VV, and HV) for wheat were higher than that of soybean, whereas the trend is opposite with the level of significance. The lower value of p in wheat is characteristically the result of a larger calibration dataset as compared to soybean. For wheat, a higher value of the F-statistics is observed in VV polarization compared to HH and HV polarization, indicating a better fit of the model to data. On the contrary, the cross-pol (HV) channel shows the highest value of the F-statistics for soybean. The accuracy of the calibrated models is assessed between the observed and estimated backscatter values over training samples using 1:1 plots as shown in Fig. 2. For wheat, the correlation coefficient (r) between the observed and the estimated backscatter coefficients were.43 (HH),.74 (VV) and.53 (HV). In addition, the nrmse is lowest (.182) for the VV polarization as compared to HH and HV channels (.216 and.225, respectively). The σ HV is known to be sensitive to vegetation growth due to the effect of volume scattering within the plant canopy. However, in wheat, σ VV demonstrated higher sensitivity than σ HV. This is evident in the dynamic range of σ VV and σ HV as illustrated in the 1:1-plot. The nrmse for VV channel is 24% less than the HV channel, with VV producing the highest correlation coefficient (r =.74). The performance of VV may be due to the canopy structure of wheat where stems are vertical and leaf distribution is erectophile. Similar results are reported in a study conducted by the University of Sheffield ground-based synthetic aperture radar (GB-SAR) over wheat canopies (Brown et al., 23). The radar cross section (RCS) of wheat canopies reveal that the σ HV return is not dominated by the volume scattering of the canopy, but is strongly affected by the underlying soil in terms of multiple stem soil interaction. Moran et al. (212) reported a similar sensitivity of σ HV and σ VV for barley (with a similar crop structure) for RADARSAT-2 C-band acquisitions during the AgriSAR29 campaign in Barrax, Spain. The sensitivity is affected by the unique vertical structural characteristics associated with the plant growth. During the stem elongation stage, the vertically polarized backscatter intensity decreased more than the horizontal. This is likely due to the predominant vertical structure of the wheat canopy. In fact, a significant difference between σ HH and σ VV of 2.8 db for wheat is reported in Balenzano et al. (211) when heading started and the biomass attained 4.5 kg m 2. In addition, during the heading to the ripening stage, the VV backscatter intensity is more sensitive than the HH to changes in biomass. The HH backscatter shows almost no sensitivity to changes in the stem biomass (Mattia et al., 23). Thus, the VV polarization is found to be a better fit with the calibration dataset, given that these data were measured throughout all growing stages (leaf development to fruit development stages). Compared to wheat, the results are different for the lower biomass soybean canopy. The correlation coefficients (r) for soybean were reported as.58 (HH),.57 (VV) and.8 (HV). As compared to wheat, the nrmse is lower for the cross-pol channel (.352) for soybean. These results indicate that the WCM is better calibrated for the cross-pol than the co-pol channels. The HV backscatter intensity is correlated with multiple scattering from the vegetation canopy with biomass and PAI increasing as crop growth advances. In general, a soybean canopy with its branching structure creates more multiple scattering events. Similar sensitivity of the cross-polarized (HV) backscatter with changes in biomass was reported for RADARSAT-2 C-band data acquired during the SMAPVEX12 campaign (Wiseman et al., 214) PAI and wet biomass estimation In this section, the MTRFR inversion is carried out with two (HH +VV, HH+HV, and VV+HV) and three (HH+VV+HV) polarization combinations of backscatter intensities as input to the model. The retrieval accuracy of PAI and wet biomass is assessed for wheat and soybean using the validation data Wheat The retrieval accuracy of PAI and wet biomass of wheat is evaluated using the MTRFR inversion technique. The ground measured PAI varied Table 2 Model parameters and statistics for different crops and polarization. Crop Polarization Model parameters F-statistics Level of significance A B C D E F Wheat HH <.1 VV <.1 HV <.1 Soybean HH <.1 VV <.1 HV <.1 29

7 Fig. 3. Comparison of estimated and observed PAI and wet biomass of wheat at different polarization combinations. from.8 m 2 m 2 to 8.9 m 2 m 2, spanning leaf development to fruit development stages. The performance of the retrieval varies for different polarization combinations, as shown in Fig. 3. Amongst the dualpol combinations, the HH+VV and VV+HV for PAI estimation out performed the HH+HV. It is observed from Fig. 3 that the correlation coefficients are high (r =.91 and.9) for the HH+VV and VV+HV as compared to HH +HV (r =.69). RMSE and MAE values for the HH+VV (.85 m 2 m 2 and.54 m 2 m 2 ) and VV+HV models (.85 m 2 m 2 and.51 m 2 m 2 ) are also lower than the HH+HV (1.37 m 2 m 2 and 1.6 m 2 m 2 ). With HH included in the polarization combinations, errors are higher. This increase in error may be because of errors associated with the calibration phase (Section 4.1). With VV included, performance improved. As evident from Fig. 3, the margin of estimation is spread ( 2.4 m 2 m 2 ) across the 1:1 line for HH+HV, while more concentrated within the margin of 1. m 2 m 2 for both the VV+HV and HH+VV. Hence, the uncertainty in retrieval performance is high for HH+HV as compared to the VV+HV and HH+VV. A marginal improvement is achieved by combining all three polarizations (HH+VV+HV) for PAI estimation. The RMSE is.83 m 2 m 2 and MAE is.52 m 2 m 2 with a high correlation coefficient (r =.91). Notably, using the proposed MTRFR technique, different polarization combinations (VV+HV and HH+VV+HV) resulted in a robust estimation for the entire range of PAI. However, an underestimation in PAI is observed after PAI reached 7m 2 m 2, the end of heading stage. This is likely due to scattering from the wheat heads. The retrieval accuracy of wet biomass is quite promising with different polarization combinations. The ground measured wet biomass varied from.4 kg m 2 to 6 kg m 2 during the growing stages. Similar to the PAI estimation results, the correlation coefficient is low (r =.65) for HH+HV as compared to other combinations (.68,.7,.79 for HH+VV, VV+HV and HH+VV+HV, respectively). The margin of estimation is widely spread ( 2. kg m 2 ) across the 1:1 line more for high biomass (> 2.5 kg m 2 ) than low biomass. In fact, for low biomass (< 2 kg m 2 ), the estimates are concentrated 3

8 Fig. 4. Comparison of estimated and observed PAI and wet biomass of soybean with different polarization combinations. around the 1:1 line, with a very narrow margin of estimation (.15 kg m 2 ). Saturation of EM waves likely occurs for high biomass, during the end of the heading stage of wheat. As compared to the dual-polarization combinations, a marginal improvement is observed in the error estimates for wet biomass retrieval using the HH+VV+HV combination, with low RMSE (.73 kg m 2 ) and MAE (.57 kg m 2 ) Soybean The PAI inversion results for soybean with different polarization combinations are shown in Fig. 4. The ground measured PAI varied from.2 m 2 m 2 to 5.4 m 2 m 2, covering leaf development to flowering stages. As observed in Fig. 4, the correlation coefficients for all models are higher than.81. The addition of HV in the MTRFR only slightly improved the retrieval accuracy for soybean. This result is reasonable given that HV channel fit the data well during the calibration step, as compared to HH and VV. As compared to the HH+VV combination, the RMSE and MAE is reduced to.73 m 2 m 2 and.57 m 2 m 2 for the HH+HV and VV+HV. In particular, results of VV +HV and HH+VV+HV are comparable. The overestimation of PAI as observed in Fig. 4 occurs during leaf development, with the exception of HH+HV. This overestimation is likely due to the reduced contribution from the soybean when the canopy closure is very low (PAI < 1.5 m 2 m 2 ) and the exposed soil has a greater contribution (Wiseman et al., 214). Nevertheless, the estimates follow the 1:1 line for PAI > 3. m 2 m 2, as side shoot formation concludes (relatively high canopy closure). Nonetheless, the margin of estimation is spread.7 m 2 m 2 across the 1:1 line for high PAI values. The wet biomass retrieval accuracy is similar to PAI with different polarization combinations (Fig. 4). The ground measured wet biomass varied from.2 kg m 2 to 1.6 kg m 2. It is observed from Fig. 4 that the correlation coefficient is greater than.74 for different polarization combinations except for the HH+VV. 31

9 Table 3 Comparison of MTRFR, RFR and LUT based retrieval accuracy of PAI and wet biomass for the HH+VV+HV polarizations combination. Crop Biophysical parameter MTRFR RFR LUT The error estimates in wet biomass retrieval using HH+HV, VV +HV and HH+VV+HV models are also low with RMSE <.34 kg m 2 and MAE of.22 kg m 2. For HH+VV the error estimates are marginally lower than the other combinations (RMSE =.38 kg m 2 and MAE =.25 kg m 2 ). Results improve when cross-pol information is used in the inversion process Comparison of inversion methodologies r RMSE r RMSE r RMSE Wheat PAI Biomass Soybean PAI Biomass The performance of the proposed MTRFR based inversion methodology is compared with the RF-based single target regression model (RFR) and the traditional Look-up table (LUT) search approaches. A comparative analysis of retrieval accuracies for wheat and soybean is presented in Table 3 in terms of the correlation coefficient (r) and RMSE error. For the PAI of wheat, the highest accuracy (r=.91) is obtained with the MTRFR approach (RMSE of.83 m 2 m 2 ) as compared to RFR (r=.87 and RMSE =.97 m 2 m 2 ) and LUT (r =.62 and RMSE = 1.48 m 2 m 2 ). For wet biomass, all correlations are lower than reported for PAI, although a marginal improvement in both the RMSE and r is obtained for MTRFR when compared with RFR. Similar results are also obtained for soybean. The highest accuracy is obtained with the MTRFR approach for both the PAI (r =.88 and RMSE =.72 m 2 m 2 ) and wet biomass (r =.74 and RMSE =.34 m 2 m 2 ). Nonetheless, it is evident from the comparison that the proposed MTRFR based inversion technique, which incorporates the inter-correlations between the biophysical parameters, yielded acceptable inversion results Relationship between PAI and wet biomass In addition to the MTRFR based crop parameter estimation, the PAI and wet biomass were separately estimated by building two sets of the RF regression model. In one set, the backscatter intensities were used as predictors, while the PAI is used the response. Similarly, the backscatter intensities were used as predictors while the wet biomass is considered as the response. The PAI and wet biomass were estimated separately with the two RFR model using the validation dataset. Subsequently, the relationships between PAI and wet biomass were assessed with a scatter plot for RFR and MTRFR. In-situ measurements are used to assess the preservation of the correlation between the biophysical parameters during the model inversion. The relationships between PAI and wet biomass which were simultaneously estimated from the multi-target RF regression model are shown in Fig. 5. For comparison, PAI and wet biomass were estimated separately with two different single output RF regression models for each crop. Only HH+VV+HV combination is only used for this comparison. The results were compared with in-situ PAI and wet biomass measurements. For wheat, a nearly linear relationship is observed between ground measured PAI and wet biomass. A similar relationship is also observed with RFR and MTRFR. However, MTRFR is also able to capture the points (marked within the red ellipse) in Fig. 5 which is not observed in the RFR retrieved PAI and biomass scatter plot. On the contrary, a non-linear relationship (exponential pattern) is found between ground measured PAI and wet biomass for soybean. It is interesting to observe that the non-linear relationship is retained in MTRFR, while the RFR is not able to capture the inter-correlation between the PAI and wet biomass. Hence, the simultaneous biophysical parameter retrieval approach using MTRFR successfully preserved the relation between wet biomass and PAI as compared to the single-output RFR. Fig. 5. PAI and wet biomass relationship in observed measurements, RFR and MTRFR retrieval for wheat and soybean. 32

10 5. Conclusion In this study, a novel approach for simultaneous Plant Area Index (PAI) and wet biomass retrieval has been proposed by utilizing the Water Cloud Model along with the multi-target random forest regression (MTRFR). Data collected during the Soil Moisture Active Passive Validation Experiment 216, held in Manitoba (Canada), and RADAR- SAT-2 full polarimetric data, were used to calibrate and validate the proposed approach. The results of model calibration and validation suggest that high correlation and low errors of estimation are observed when all the three polarizations (HH+VV+HV) are used for the retrieval of PAI and biomass with correlation coefficients in the range of In addition to the HH+VV+HV polarization combination, the dual-pol combinations show promising retrieval accuracy, depending on the structure of crops. Notably, the performance of the VV +HV combination is particularly encouraging for the biophysical parameter estimation for wheat and soybean. These results are of interest to the agriculture community as the VV+VH mode is readily available from Sentinel-1A/B. Furthermore, the relationship between PAI and wet biomass indicates that the MTRFR successfully preserves the relationship between the crop parameters during the model inversion process. In addition, the MTRFR based inversion technique, which incorporates the intercorrelations between the biophysical parameters, yielded improved inversion results as compared to than single target Random Forest Regression (RFR) and Look-up Table (LUT) based approaches. Hence, the multi-target approach will be of particular interest for operational implementation, given that simultaneous retrieval of multiple interdependent biophysical parameters is possible. Next step might include extrapolation of the point based results to map spatio-temporal crop development in support of downstream applications like crop production risk assessment. 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