Biomass Assessment of Agricultural Crops Using Multi-temporal Dual-Polarimetric TerraSAR-X Data

Abstract

The biomass of three agricultural crops, winter wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), and canola (Brassica napus L.), was studied using multi-temporal dual-polarimetric TerraSAR-X data. The radar backscattering coefficient sigma nought of the two polarization channels HH and VV was extracted from the satellite images. Subsequently, combinations of HH and VV polarizations were calculated (e.g. HH/VV, HH + VV, HH × VV) to establish relationships between SAR data and the fresh and dry biomass of each crop type using multiple stepwise regression. Additionally, the semi-empirical water cloud model (WCM) was used to account for the effect of crop biomass on radar backscatter data. The potential of the Random Forest (RF) machine learning approach was also explored. The split sampling approach (i.e. 70% training and 30% testing) was carried out to validate the stepwise models, WCM and RF. The multiple stepwise regression method using dual-polarimetric data was capable to retrieve the biomass of the three crops, particularly for dry biomass, with R² > 0.7, without any external input variable, such as information on the (actual) soil moisture. A comparison of the random forest technique with the WCM reveals that the RF technique remarkably outperformed the WCM in biomass estimation, especially for the fresh biomass. For example, the R² > 0.68 for the fresh biomass estimation of different crop types using RF whereas WCM show R² < 0.35 only. However, for the dry biomass, the results of both approaches resembled each other.

1. Introduction

The ability to assess and monitor biophysical parameters, such as biomass, is of vital importance for the study of different processes (e.g. crop growth monitoring, crop productivity, and the carbon cycle). Monitoring with passive optical satellite imagery faces the problems of frequent cloud cover and changing solar lightning geometry (depending on region) which limit the acquisition of high-quality remote sensing time series data and may even preclude to detect and analyse crucial growing stages of the vegetation. Thus, the use of radar sensors becomes a feasible means to continuously acquire remote sensing data irrespective of weather and illumination conditions.

The interaction of microwaves with vegetation is complicated because vegetation forms a heterogeneous volume with structural components of varying size and density (Ulaby et al. 1996). Active microwave systems, such as air- or space-borne synthetic aperture radar (SAR) systems, are capable of measuring the backscattering response from the vegetation using different polarization configurations. Active microwave sensors can usually measure backscatter as single-, dual, or quad-polarized. In case of TerraSAR-X, dual-polarized data can be acquired as co-polarized (HH and VV) and cross-polarized (HV and VH) datasets (Breit et al. 2010).

The retrieval of vegetation characteristics and parameters using microwave remote sensing is influenced by two main parameter types. First, parameters that are related to sensor specifications and configurations (i.e. frequency/wavelength, incidence angle, and polarization), and second, parameters and elements that are related to the surface and target characteristics (i.e. soil and surface roughness and moisture, topography, vegetation characteristics, and the dielectric constant) (Ahmadian et al. 2016). The radiation frequency has a direct relationship with the penetration depth into the surface and vegetation canopy. The X and C bands are the most commonly used wavelengths for the retrieval of agricultural crop-parameters, due to the sensitivity of the short wavelength to the rather short stature of the crops compared to L or P band systems. The incidence angle affects the relative contribution of each surface characteristic to the back-scattering signals. Typically surface scattering from soil or canopy components is observed at steep incidence angle (Cable et al. 2014a, b).

Previous studies have demonstrated that there is no significant relationship between biophysical crop parameters (e.g. biomass) and single co-polarized channels at X band (i.e. HH or VV) when the entire growing season of a crop is considered using multi-temporal SAR data (Sonobe et al. 2014). However, it is well documented that the backscattering coefficient changes during the different growing stages of crops (Kim et al. 2013; Cable et al. 2014a, b). Mechanisms involved when assessing agricultural crops using radar include direct backscatter from the underlying ground (e.g. the soil), direct backscatter from plant components (i.e. leaves, stems, fruit), double-bounce backscatter between the soil surface and crop canopy, and in certain cases groundv-egetation-ground and multiple scattering mechanisms (Cable et al. 2014a, b; Adams et al. 2014). For instance, when seeds are still below the surface, the main contributor to a radar signal is single-bounce backscatter due to soil moisture and surface roughness (Cable et al. 2014a, b; van Zyl 2009). As plant elements start to develop, the co-polarized backscatter intensities tend to increase. The increase in co-polarized backscatter is due to a combination of single-bounce backscatter directly from the leaves or stems and soil-vegetation double-bounce backscatter (Cable et al. 2014a, b). McNairn et al. (2002) used multiple regression and demonstrated that certain biophysical parameters, such as the leaf-area index, biomass and height, can be explained by the variance of the C-band HH backscatter.

Various semi-empirical and empirical approaches were tested for the assessment of crop biophysical parameters with SAR data. The semi-empirical water cloud model (WCM) for instance can be implemented to derive soil moisture and biophysical parameters of vegetation (e.g. biomass, leaf area index) from remotely sensed radar data (e.g. Yoshio et al. 2014; Hosseini et al. 2015; van Emmerik et al. 2015; Kumar et al. 2015; He et al. 2014). A diversity of machine learning regression methods such as artificial neural network, random forest, support vector machine and, more recently, Gaussian processes have also been used to estimate the biophysical parameters of vegetation during the last years (Camps-Valls et al. 2016; Verrelst et al. 2012, 2015). However, rigorous, crop-specific comparisons of those methods to derive crop biomass from SAR data are missing, especially in the light of the aforementioned backscatter variations during the vegetation period.

This study aims to compare the performances of different approaches using a combination of different polarization channels of TerraSAR-X [TSX, Multi Look Ground Range Detected (MGD)] data for the retrieval of crop biomass. The approaches include the semi-empirical water cloud model (WCM) and statistical approaches, namely multiple linear regression (MLR) and random forest (RF) regression. To analyse the ability of HH/VV-polarized TSX data for biomass retrieval, three crop types (i.e. barley, winter wheat, and canola) were investigated.

2. Methods

2.1. Study area

The study area (Fig. 1) is located in northeast Germany and part of the Durable Environmental Multidisciplinary Monitoring Information Network [DEMMIN, (http://www.dlr.de/eoc/en/desktopdefault.aspx/tabid-5395/10255_read-40097/)]. DEMMIN is linked with the German observatory network TERENO (Zacharias et al. 2011). Various crops are planted in this area (e.g. barley, wheat, canola, rye, maize, sugar beets and potatoes). The dominant crop types are winter crops, which cover nearly 60% of the fields in DEMMIN. The soils in the area are primarily loamy sands and sandy loams alternating with pure sand patches or clayey areas (Gerighausen et al. 2007). The region’s climate is temperate and humid. The mean annual temperature in the Mecklenburg-Western Pomerania state varies from 8.2 °C to 9.0 °C, and the mean annual precipitation is around 600 l/m². Within the site, a study area was chosen for ground truth data collection. The study area included three fields, each one with winter wheat, barley and canola fields with the sizes of approximately 225 ha, 117 ha, and 25 ha, respectively.

Fig. 1.

Upper left part: Location of the study area DEMMIN (Durable Environmental Multidisciplinary Monitoring Information Network) in Germany. Central part: Study area, which included barley (A), winter wheat (B), and canola (C). The sub-figure exemplarily shows the sampling strategy

Each of these three crops has a unique morphology on reaching maturity, which theoretically results in unique scattering mechanisms (Cable et al. 2014a, b). Since barley (Hordeum vulgare) (Fig. 2a) and wheat (Triticum aestivum) (Fig. 2b) belong to the grass family, their early development stages are similar. However, once mature, their seed-bearing structures differ extremely (Cable et al. 2014a, b) (Fig. 2a, b). Canola (Fig. 2c) is a broadleaf plant that undergoes a distinctive change in canopy structure over the growing season. On emergence, the crop develops a thick rosette of leaves close to the ground before sending up a flowering stalk (Wiseman et al. 2014). Once a maximum height (~ 1.5 m) is reached, the flowers begin to fall off as the plant produces long, skinny pods filled with seeds. The increase in biomass creates a thick canopy because the pods from neighbouring plants often intertwine with one another (Cable et al. 2014a, b).

Fig. 2.

Growth stages that coincide with the closest TerraSAR-X data acquisitions in 2013: A barley: a 23 May b 19 June c 10 July d 17 July. B Winter wheat: a 23 May b 19 June c 10 July d 24 July e 07 August f 21 August. C Canola: a 07 May b 23 May c 19 June d 24 July (DOY = day of year)

2.2. In Situ Data and Laboratory Analysis

Ground truth data collection was performed over 20 weeks, from April 17 to August 28, 2013. Data were collected at weekly intervals during the growing season. The field campaign spanned nearly all of the growing stages of winter wheat, barley, and canola. During each field trip, two random centres in each field were chosen (two plots), and five sampling locations were established with five squares of 50 cm × 50 cm around each centre (Fig. 1). The distance to the centre was listed, and the GPS coordinates were recorded with a handheld Trimble GPS device so that the data could be then mapped in a geographic information system. The squares were used to collect the ground truth data. The fresh plant biomass (kg/m²) was collected (i.e. ten samples per field during each field expedition). For the sampling, the crops were cutoff as close to the ground as possible, and fresh biomass was collected and placed in plastic bags, which were sealed and taken to the laboratory. The fresh biomass was weighed and oven dried at 75 °C for a minimum of 48 h until a constant weight was reached (Fig. 3).

Fig. 3.

Mean values of fresh biomass (FB) and dry biomass (DB) of agricultural crops using ground truth data during the entire growing season, the error bars indicate the standard deviation of the samples

After cutting off the biomass, soil samples were collected for the same location using a hand sledge and 5.6-cm diameter cylinders/rings (i.e. ten samples in each crop field during each field trip) from the top 0 cm–10 cm of soil surface inside the squares.

Gravimetric (GSM) and volumetric (VSM) soil moisture was measured; all of the soil samples were weighed (wet weight) and then oven dried for 24 h at 105 °C to a constant weight. Bulk density (BD) was then calculated using the oven dry weight and inner volume of the cylinder/ring (100 cm³). Equations (1–3) present the formula used to compute the GSM and VSM. The soil moisture content was determined by averaging the wet and dry weight of the samples. Equation (1) shows the ratio between the water mass present in the soil and the dry weight of the soil sample. The BD was estimated by Eq. (2) and the soil moisture content was measured as VSM using Eq. (3). VSM is defined as the ratio between the water volume and the total volume of the soil sample, refer also Fig. 4:

$$\text{GSM}(\text{g}/\text{g})=\left({\text{W}}_1(\text{g})-{\text{W}}_2(\text{g})\right)/{\text{W}}_2(\text{g}),$$ (1)

$$\text{BD}\left(\text{g}/{\text{cm}}^3\right)={\text{W}}_2(\text{g})/\text{VS}\left({\text{cm}}^3\right),$$ (2)

$$\text{VSM}\left(\text{g}/{\text{cm}}^3\right)=\text{GSM}(\text{g}/\text{g})\times \text{BD}\left(\text{g}/{\text{cm}}^5\right),$$ (3)

where W1 is the weight of the wet soil, W2 is the weight of oven-dried soil and VS is the soil volume. Table 1 shows the summary of the in situ variables and the number of samples corresponding to the satellite over passes.

Fig. 4.

Mean values of volumetric soil moisture (VSM) of agricultural crops using ground truth data during the entire growing season. The error bars denote the standard deviation

Table 1. Number of samples for ground truth data corresponding to the satellite images collected during the entire crop-growing season.

Crop type	Ground truth data samples from field observation			Satellite dataa
	Fresh biomassb	Dry biomassc	Soil samplesd	TerraSAR-X data
Wheat	73	63	73	6
Barley	61	53	61	4
Canola	49	49	49	4

^aNumber of satellite images over different fields

^bNumber of fresh biomass samples in kg/m²

^cNumber of dry biomass samples in kg/m²

^dNumber of samples used for soil granulometric analysis

2.3. Satellite Data

The TerraSAR-X (TSX) satellite sensor was used for the acquisition of high-resolution synthetic aperture radar (SAR) images during the growing season 2013 (beginning of May to end of August). The primary information of these images and the related growing stages of each crop are summarized in Table 2. The Feekes scale was used to identify the developmental stages of the winter wheat and barley (Large 1954). The BBCH-scale was used to describe the phenological development of the canola plants (Lancashire et al. 1991).

Table 2. Overview on TerraSAR-X Stripmap (SM) acquisitions in ascending (A) and descending (D), and, the growing stage of Canola, Wheat and Barley.

Date	Day of year	Crop field (s)	Growing stage	Mode	Product	Pass	Incidence angle (°)	Polarization
20130504	124	Canola	Inflorescence emergence (55)	SM	MGD	D	~ 27	HH and VV
20130519	139	Wheat	Stem elongation (8)	SM	MGD	A	~ 31	HH and VV
	139	Barley	Stem elongation (10)
	139	Canola	40% of flowers on main raceme open (64)
20130621	172	Wheat	Beginning of flowering (10.5.1)	SM	MGD	A	~ 31	HH and VV
	172	Barley	Flowering (10.5.3)
	172	Canola	Ripening (80)
20130709	190	Wheat	Flowering over at base of ear (10.5.3)	SM	MGD	D	~ 27	HH and VV
	190	Barley	Milky ripe (11.1)
20130713	194	Barley	Kernel hard (11.3)	SM	MGD	A	~ 31	HH and VV
20130724	205	Wheat	Milky ripe (11.1)	SM	MGD	D	~ 27	HH and VV
	205	Canola	Plant dead and dry (97)
20130804	216	Wheat	Mealy ripe, contents of kernel soft but dry (11.2)	SM	MGD	A	~ 31	HH and VV
20130822	216	Wheat	Ripe for cutting, straw dead (11.4)	SM	MGD	D	~ 27	HH and VV

All images were MGD products that were operated in Stripmap mode with dual-co-polarized channels HH and VV. The MGD is a detected multi-look product with reduced speckle and approximately square resolution cells. The image coordinates are oriented along the flight (azimuth) and the ground range directions. The pixel spacing is equidistant in azimuth and in the ground range. A simple polynomial slant to ground projection is performed in range using a WGS84 ellipsoid and an average, constant terrain height parameter (Roth et al. 2005). The spatial resolution of all images is approximately 6 × 6 m².

Initially, all the images were georeferenced using digital elevation model of the Shuttle Radar Topography Mission (SRTM) with a spacing of 1-arc-second. Since all the image data were delivered already multilooked, a time series of images was constructed and co-registered to perform De Grandi multi-temporal filtering (De Grandi et al. 1997).

All images were geocoded and radiometrically calibrated to retrieve the sigma nought (σ°) using SARScape 5.1 from ENVI 5.1 (Harris Geospatial). Expressed in decibels (dB), the σ° is the conventional measure of the radar backscattering coefficient. This parameter is defined as a normalized dimensionless number that compares the strength of the signal observed to the “expected signal” from an area of 1² m (Raney 1998). To account for the fact that the data were acquired in two different incidence angles (i.e. 27° and 31°) the widely used square cosine correction were implemented in the dataset (Ulaby et al. 1982). The model is based on Lambert’s law for optics and considers two assumptions. First, the amount of power that is radiated back to the sensor follows a cosine law. Second, the radiation variability as a function of the observed area is cosine dependent (Topouzelis et al. 2016; Mladenova et al. 2013).

The measured radar backscatter, ${\sigma }_{\theta i}^0$, is related to the cosine square of the incidence angle and can be expressed as:

$${\sigma }_{\theta i}^{\circ }={\sigma }_0^{\circ }{\text{cos}}^n\left({\theta }_i\right),$$ (4)

where n = 2 and ${\sigma }_0^{\circ }$ is the backscatter independent from the incidence angle. After calculating ${\sigma }_{\theta i}^0$, at an incidence angle θ_i, the radar backscattering can be normalized to approximate the image backscattering at any specific reference angle $\left({\sigma }_{\text{ref}}^{\circ }\right)$ using the following equation:

$${\sigma }_{\text{ref}}^{\circ }=\frac{{\sigma }_{e\text{i}}^{°}{\text{cos}}^n\left({\theta }_{\text{ref}}\right)}{{\text{cos}}^n\left({\theta }_i\right)},$$ (5)

where θ_Ref stands for reference angle. For this study, 31° was selected because of two reasons: first, half of the TSX images is acquired in 31° incidence angle, second, the shallower incidence angle is more appropriate for vegetation studies compared to a steeper one (i.e. 27°).

2.4. Analysis

2.4.1. Water Cloud Model

The water cloud model (WCM) developed by Attema and Ulaby (1978) was used to assess the relationships between the polarization channels (i.e. HH and VV) and the FB and DB of each crop. In this model, the total backscatter σ⁰ is expressed as the incoherent sum of backscatter from the vegetation $\left({\sigma }_{\text{veg}}^0\right)$ and the underlying surface $\left({\sigma }_{\text{soil}}^0\right)$, which is attenuated by the vegetation layer through the two-way attenuation factor τ² according to Eqs. 6–8.

$${\sigma }^0={\sigma }_{\text{veg}}^0+{\tau }^2{\sigma }_{\text{soil}}^0,$$ (6)

$${\sigma }_{\text{veg}}^0=A{V}_1\text{cos}\theta \left(1-\exp \left(-\frac{2B{V}_2}{\text{cos}\theta }\right)\right),$$ (7)

$${\tau }^2=\exp \left(-\frac{2B{V}_2}{\text{cos}\theta }\right).$$ (8)

In these equations, A and B are the parameters of the model that depend on vegetation type and the incident angle θ (Jackson and Schmugge 1991). V1 and V2 are descriptors of the canopy, and the backscatter (σ⁰) is expressed in power units.

The backscatter from the soil surface ${\sigma }_{\text{soil}}^0$ can be expressed through solving Eq. 9.

$${\sigma }_{soil}^0=C+D{M}_v,$$ (9)

where parameters C and D are dependent on soil moisture, and M_v is the VSM.

Grouping these terms (Eqs. 6–9) results in following equation:

$$\begin{array}{c}{\sigma }^0=A{V}_1\text{cos}\theta \left(1-\exp \left(-\frac{2B{V}_2}{\text{cos}\theta }\right)\right)\\ +\left(C+D{M}_v\right)\times \exp \left(-\frac{2B{V}_2}{\text{cos}\theta }\right).\end{array}$$ (10)

For estimating the biomass using WCM, two scenarios were considered. In the first scenario, it is assumed that V1 = V2 = Biomass (FB or DB). Therefore, Eq. (11) can be written as follows:

$$\begin{array}{c}{\sigma }^0=A*\text{Biomass}*\text{cos}\theta \left(1-\exp \left(-\frac{2B*\text{Biomass}}{\text{cos}\theta }\right)\right)\\ +\left(C+D{M}_v\right)\times \exp \left(-\frac{2B*\text{Biomass}}{\text{cos}\theta }\right).\end{array}$$ (11)

The second scenario considers that V1 = 1 and V2 = biomass (Eq. 12):

$$\text{Biomass}=-\frac{\text{cos}\theta }{2B}Ln\frac{{\sigma }^0-A\text{cos}\theta }{C+D\left(M_v\right)-A\text{cos}\theta }.$$ (12)

All parameters of the model (i.e. A, B, C, D) are first calculated using the non-linear least-squares method. The estimated backscattering coefficients were then calculated using the known model parameters. Afterwards, the biomass (FB and DB) was estimated using the parameters in two different polarization channels (i.e. HH and VV), and at the end, the estimated biomass values which were closest to the actual ground truth data were chosen using a minimum function. The “Levenberg–Marquardt” algorithm was chosen to evaluate the residual sum of squares (RSS) for the parameter values. The WCM was calibrated for each crop type and polarization, and as such, different parameters were obtained for each crop polarization.

2.5. Regression Analysis

The polarization variables were retrieved from the satellite data based on a pixel-to-pixel calculation. The mathematical combinations (i.e. HH, VV, HH + VV, HH – VV, HH/VV, VV/HH) were used to produce a higher variety of image variables in the regression modelling. Such manipulation was for example done by Omar et al. (2017) or Ahmadian et al. (2016) in the context of linear regression modelling for the retrieval of aboveground biomass and LAI. The ratios (HH/VV; VV/HH) and difference (HH–VV) can be related to differences in polarization that are caused by the different physical stature of the crops and by different growing stages of the crops, respectively. Co-polarization ratio is frequently used in land cover characterization and classification, e.g. for wetlands (Heine et al. 2016), but also in terms of biomass (Sonobe et al. 2014). The sum HH + VV is the total received energy (span). The multiplicative form HH × VV has no physical meaning to our knowledge but was added as a straightforward addition.

Index and regression models are based on preconceived mathematical expressions, and the model parameters are found by regressions. Regressions based on microwave channels rely on the sensitivity of certain microwave channels to surface properties (Saleh et al. 2006). The disadvantages of these models are the dependence of model parameters and the little information provided on the physics of the involved scattering events (Richards 1990). Beside the above-stated polarization channels and their mathematical combinations, the polarization discrimination ratio (PDR) was also used as an independent variable to investigate its relationship with the biophysical parameters of the crops (i.e. FB, DB). PDR is defined according to Singh (2006, Eq. 13):

$$\text{PDR}=\frac{\left({\sigma }^{\circ }\text{VV}-{\sigma }^{\circ }\text{HH}\right)}{\left({\sigma }^{\circ }\text{VV}+{\sigma }^{\circ }\text{HH}\right)}.$$ (13)

These variables were applied to construct the multiple stepwise linear regression models. Stepwise approach was used to identify the optimal set of polarization channels and variables for providing estimates of FB and DB. For the stepwise method, in addition to R² and RMSE and MSE values were calculated to assess the goodness of fit.

Forward stepwise regression was used to construct the models. In this technique, the model starts with no terms and then it adds the most statistically significant term (i.e. polarization channels or variables). This significant term is the one with the highest F statistic or lowest p value at each step until no terms remain (Statistics Toolbox User’s Guide). Additionally, to determine how well the stepwise models are constructed, a split sampling approach based on 70% training and 30% validation procedure was performed. RMSE, the correlation between the observed and predicted responses and the mean absolute error (MAE) were calculated to evaluate the ability of each model to predict the crop biomass.

2.5.1. Machine Learning

To compare the pursued approach (WCM) against another purely data-driven approach, the analysis was evaluated with random forests (RF) regression algorithm. RF builds an ensemble of individual decision trees working with different subsets of features (bands) and eventually different training data points both selected randomly, from which a final prediction is made using particular combination schemes. RF can handle a large number of training samples, does not suffer from overfitting and is robust to outliers and noise (Belgiu and Drăguţ 2016), which makes it an attractive method for dealing with multiple radar channels. The validation of RF approaches was performed by the split-sample technique for a comparison with WCM based on 70% training and 30% testing.

3. Results

3.1. Temporal Backscatter Behaviour of Agricultural Crops

The differences between the mean VV and HH backscattering coefficient (σ⁰) were generally small for the different crops (0 dB–2 dB) during the different stages of crop development (Fig. 5). For winter wheat, X-band HH is slightly higher than the VV polarization. The σ⁰ extracted for VV polarization display a dynamics of approximately 7 dB from stem elongation to harvest. The σ⁰ for both polarizations, HH and VV, at an incidence angle of 31° initially increased between stem elongation (DoY 139) and the start of flowering (DoY 172), as well as, during the beginning and end of flowering stages (DoY 172–DoY 190) by ~ 1 dB. Noticeably, this increase exceeded that of VV polarization. In addition, between the end of flowering (DoY 190) and the milky ripe stage (DoY 205), σ° decreased (~ 1.5 dB), whereas between milky ripe (DoY 205) and mealy ripe (DoY 216) σ⁰ again increased. A reason for that might be that when the content of the kernel was dry, and the dry soil conditions beneath the canopy were more visible to the sensor. Until the end of the growing stage (DoY 234), σ⁰ decreased by 3 dB. For wheat, the average VV backscattering at this incidence angle resembled that of HH and was lower (1 dB – 2 dB) from stem elongation (DoY 139) to harvest (DoY 234).

Fig. 5.

Multi-temporal backscatter (σ°) variation acquired at HH and VV polarizations (mean values) using TerraSAR-X images for winter wheat, barley, and canola. The error bars show the standard deviation of σ°

The trend for barley resembles that for winter wheat with the following exceptions: First, the backscattering increased between stem elongation (DoY 139) and flowering (DoY 172). Second, σ⁰ increased again from the flowering (DoY 172) to the milky ripe stage (DoY 190) and between the milky ripe (DoY 190) through the end of the growing stage (DoY 194). The minimum level of σ⁰ of barley was some-what less than 1 dB higher than that of wheat. Another interesting phenomenon occurred during the flowering stage, when the mean sigma nought of the pixels in VV polarization was higher than that of HH polarization. VV polarization was somewhat higher (~ 0.5 dB) than HH during this stage and lower (1–2 dB) before and after this special stage.

The trend of the mean values of backscattering variation for the canola differs from that of the cereal crops. Between inflorescence emergence (DoY 124) and the flowering stage (DoY 139), σ⁰ decreased (~ 1.5 dB). Interestingly, between flowering (DoY 139) and the ripening period (DoY 172), σ⁰ of HH polarization remained relatively constant, which indicates a type of saturation. At the end of the canola growing stages between DoY 172 and DoY 205, the backscatter coefficient decreased by 2 dB and 3 dB for the HH and VV, respectively.

3.2. Semi-empirical WCM

Often, the purpose of biophysical modelling using the water cloud model is to convert in situ measurements into values that can be directly related to SAR backscatter. Most of the previous studies that have used the WCM for backscatter modelling of agricultural crops assumed that the vegetation canopy is a unified layer (Svoray and Shoshany 2002). To test its validity, this assumption is also applied in the current study. Following the derivation of the model coefficients A, B, C, and D, it was possible to derive predicted backscattering of HH and VV channel (i.e. using the ground truth biomass), as well as, the FB and DB from the σ° using Eqs. (11–13). Estimating DB from the backscatter using the WCM was proved to be successful, whereas FB was estimated with reduced accuracy only. It is also worth mentioning that considering V1 = 1 and V2 = biomass, the retrieved results show significantly lower correlation compared to the first scenario (i.e. V1 = V2 = biomass).

Figure 6 shows the measured versus estimated backscattering for wheat and canola as an example. Split-sample validation based on 70% training and 30% testing data was used to validate the results for the WCM. Errors of estimation were represented by RMSE and mean absolute error (MAE); as noted by Chai and Draxler (2014) and Hosseini et al. (2015) both measures are required to assess model performance. The R² represented the strength of the relationship between measured and estimated biomass. Differences between the predicted and measured back scattering values (Table 3), were found to be considerably lower (i.e. higher correlation) than that of FB. A strong relationship (i.e. R² ~ 0.7 except for the DB of canola in the second scenario) between the estimated and derived back scattering coefficient was observed applying the ground truth dry biomass. An example of the results of the inversion is provided in Fig. 6.

Fig. 6.

Relationship between measured and predicted backscattering coefficient (power unit) of: a winter wheat and b canola using the WCM. HH polarization was estimated using the dry biomass values of ground truth data

Table 3.

Calibration parameters and statistics retrieved using the water cloud model for the estimation of backscattering for: a V1 = V2 = biomass (fresh and dry), b V1 = 1 and V2 = biomass (fresh and dry)

	Coefficients					Estimated back scattering
	a	b	c	d		R 2	RSME	MAE
(a) V1 = V2 = biomass (fresh and dry)
HH-DB-wheat	0.003	−0.542	0.007	0.023		0.951	0.016	0.011
VV-DB-wheat	0.002	− 0.653	0.004	0.009		0.932	0.010	0.009
HH-DB-barley	0.005	− 0.436	0.016	0.027		0.677	0.013	0.011
VV-DB-barley	0.003	− 0.874	0.006	0.010		0.636	0.011	0.01
HH-DB-canola	0.099	2.236	− 88.078	548.529		0.807	0.028	0.027
VV-DB-canola	0.090	1.818	− 34.898	218.628		0.679	0.030	0.029
HH-FB-wheat	0.003	0.091	0.008	1.099		0.510	0.028	0.027
VV-FB-wheat	0.002	0.086	0.005	0.763		0.476	0.021	0.02
HH-FB-barley	0.008	0.697	− 7.870	295.845		0.433	0.014	0.014
VV-FB-barley	0.007	0.091	0.115	− 0.408		0.181	0.006	0.005
HH-FB-canola	0.005	− 0.066	0.088	− 0.033		0.206	0.027	0.021
VV-FB-canola	0.000	− 0.047	0.107	− 0.158		0.339	0.029	0.024
(b) V1 = 1 and V2 = biomass (fresh and dry)
HH-DB-wheat	0.033	− 0.589	0.029	0.012		0.974	0.008	0.007
VV-DB-wheat	0.023	− 0.631	0.020	0.006		0.972	0.007	0.005
HH-DB-barley	0.029	− 0.902	0.024	0.017		0.895	0.008	0.006
VV-DB-barley	0.025	− 0.887	0.021	0.013		0.683	0.009	0.008
HH-DB-canola	0.164	2.286	− 79.082	482.282		0.591	0.038	0.03
VV-DB-canola	0.130	1.173	− 8.497	53.015		0.518	0.034	0.025
HH-FB-wheat	0.042	0.112	− 0.046	1.372		0.513	0.028	0.018
VV-FB-wheat	0.029	0.108	− 0.033	0.971		0.479	0.021	0.012
HH-FB-barley	0.058	0.973	− 76.577	1989.686		0.415	0.014	0.009
VV-FB-barley	0.019	0.013	0.061	− 0.075		0.138	0.006	0.003
HH-FB-canola	− 34.243	0.000	0.056	0.267		0.164	0.030	0.01
VV-FB-canola	− 40.213	0.000	0.077	0.141		0.246	0.022	0.013

FB and DB estimates from the WCM for the X band are compared with the FB and DB measured in the field. For the first scenario, the estimated DB using VV channel shows higher correlation with the in situ data than that of HH channel for barley and canola (R²=0.87, R²=0.96, respectively), whereas HH polarization was more successful to estimate the DB of winter wheat (Table 4). For the estimation of FB, the VV channel could predict the ground truth sampled FB of Barley and canola more accurately (Table 4). The accuracy in estimating the FB and DB of crops is relatively the same for HH and VV, but generally better in VV polarization. This occurs because the radar backscattering trends are relatively similar in VV and HH polarization.

Table 4. Statistical information retrieved using the WCM for the validation of biomass: (a) V1 = V2 = biomass (fresh and dry), (b) V1 = 1 and V2 = biomass (fresh and dry).

	Estimated biomass HH				Estimated biomass VV				Estimated closest biomass
	R 2	RSME	MAE		R2	RSME	MAE		R2	RSME	MAE
(a) V1 = V2 = biomass (fresh and dry)
Biomass–dry–wheat	0.686	0.396	0.342		0.615	0.507	0.436		0.794	0.292	0.265
Biomass–dry–barley	0.836	0.383	0.291		0.879	0.243	0.204		0.938	0.204	0.175
Biomass–dry–canola	0.961	0.076	0.069		0.966	0.089	0.078		0.967	0.088	0.074
Biomass–fresh–wheat	0.202	3.516	2.618		0.167	3.972	3.024		0.199	3.510	2.601
Biomass–fresh–barley	0.086	0.963	0.8		0.321	1.835	1.085		0.311	0.627	0.516
Biomass–fresh–canola	0.033	3.444	3.033		0.239	2.446	1.912		0.252	2.500	1.888
(b) V1 = 1 and V2 = biomass (fresh and dry)
Biomass–dry–wheat	0.844	0.273	0.208		0.851	0.263	0.193		0.873	0.239	0.172
Biomass–dry–barley	0.832	0.507	0.318		0.838	0.585	0.442		0.876	0.442	0.290
Biomass–dry–canola	0.308	1.052	0.695		0.443	0.995	0.434		0.609	0.557	0.285
Biomass–fresh–wheat	0.021	5.970	4.963		0.029	5.512	4.885		0.029	5.384	4.52
Biomass–fresh–barley	0.002	12.810	6.535		0.051	32.210	29.562		0.002	12.140	6.335
Biomass–fresh–canola	0.001	9.460	7.039		0.028	8.112	5.903		0.009	7.754	5.36

3.3. Stepwise Regression Models

As shown in Table 5, stepwise regression successfully predicted the quantities of fresh and dry biomass of the different agricultural crops, and the corresponding R² values are high except for the fresh biomass of canola. Additionally, the stepwise technique could predict the dry biomass of the studied crops better than the fresh biomass. However, the performance polarization variables employed to select the coefficients for use in the predictive models varied between vegetation types (Table 5a).

Table 5.

Stepwise regression models with biomass of crops: (a) transfer functions and statistical information on the calibration of the fresh (FB) and dry biomass (DB) of winter wheat, barley, and canola. HHdVV, HHmVV, HHpVV, VVdHH, and VVmulHH correspond to σ0HH–σ0VV, σ0HH + σ0VV, σ0VV/σ0HH, and σ0HH×σ0VV, respectively; (b) Statistical information on the validation of the fresh and dry biomass models for winter wheat, barley, and canola using the split sampling approach (all the equation in table below are in p value < 0.05 range)

Models	Transfer function	R2	RMSE	MAE
(a) Transfer functions
FB-winter wheat	= (−0.077 × HHpVV) + (0.007 × VVmulHH) + 2.55	0.743	0.574	0.41
DB-winter wheat	= (−0.209 × HHmVV) + (0.043 × HHpVV) + (0.185 × VV) + 5.572	0.854	0.791	0.418
FB-barley	= (−0.832 × HHpVV) + (0.894946 × VVmHH) – 14.056	0.863	0.591	0.475
DB-barley	= (0.0989 × HHpVV) + (−0.006 × VVmulHH) + 4.958	0.901	0.188	0.151
FB-canola	= (−0.409 × HHmVV) + (0.556 × VV) + 10.577	0.667	0.705	0.676
DB-canola	= (−0.756 × HH) + (0.31 × HHpVV) + (3.819 × PDR) + 0.247	0.72	0.284	0.234

Models	R2	RMSE	MAE
(b) Validation using split sampling approach
FB-winter wheat	0.754	0.565	0.32
DB-winter wheat	0.8	0.735	0.54
FB-barley	0.874	0.614	0.377
DB-barley	0.929	0.197	0.165
FB-canola	0.656	0.743	0.626
DB-canola	0.743	0.237	0.184

As mentioned before split, sampling approach based on 70% training/calibration and 30% testing/validation was also implemented on the stepwise regression models.

To study the multi-collinearity between the predictors (i.e. polarization variables), multi-collinearity analysis was performed, and the polarization variables (i.e. predictors) that had high correlation with the most significant term of stepwise regression were omitted from the analysis. The collinearity between the predictors is less than 0.3 (R² < 0.3) in all equations of Table 5. This analysis should be performed when the independent variables are not independent from each other (Ahmadian et al. 2016). However, due to the length of the paper, the results of this step have not been shown. Spatial maps on biomass were generated using the transfer functions listed in Table 5. Figure 7 exemplarily shows the predicted DB for canola, wheat and barley in May, June and July.

Fig. 7. The variations of dry biomass within the fields retrieved from the equations of stepwise regression models for May, June and July 2013.

3.4. Machine Learning—Random Forest

The evaluation of RF remarkably demonstrated superiority compared to WCM specially for retrieving the FB of the three crop types. As it can be observed from Table 6, validation of results using RF approach shows highly significant correlation with FB and DB of different crops (i.e. > 0.7) except for the fresh biomass of canola (i.e. < 0.7). The highest correlation was achieved for retrieving the biomass of barley (both FB and DB) with more than 0.95. Based on Table 6, RMSE of the models are less than 0.4 kg for different crop types except for fresh biomass of canola. It should be noted that the results of Table 7 is based on 30% validating data as we did for WCM.

Table 6. Statistical information retrieved using the RF for the validation of biomass.

Machine learning model: random forest (fit ensemble)
Crop type	R 2	RMSE	MAE
Biomass-dry-wheat	0.800	0.346	0.205
Biomass–dry–barley	0.959	0.173	0.114
Biomass-dry-canola	0.736	0.324	0.255
Biomass–fresh–wheat	0.920	0.367	0.261
Biomass–fresh–barley	0.955	0.366	0.313
Biomass–fresh–canola	0.683	1.380	1.184

Table 7. Significance T test between the best models.

Model	p value	Comments for the best model comparisons
Biomass–dry–wheat	0.814	Between ML and WCM (V1 = 1 and V2 = biomass)
Biomass–dry–barley	0.653	Between ML and WCM (V1 = V2 = biomass)
Biomass–dry–canola	0.633	Between ML and WCM (V1 = V2 = biomass)
Biomass–fresh–wheat	0.968	Between ML and WCM (V1 = V2 = biomass)
Biomass–Fresh–barley	0.281	Between ML and WCM (V1 = V2 = biomass)
Biomass–fresh–canola	0.471	Between ML and WCM (V1 = V2 = biomass)

To evaluate and compare the results of the best models retrieved from Ml and WCM, a significant two-tailed T test was calculated. We assumed the null hypothesis based on this fact that there is no significant difference between our two datasets (i.e. results of two models). If the p value is lower than 0.05, we consider it to be low and in such a case there is a low probability that your observed results are due simply to chance and a high probability that they are due to some other variable. In this case, we would reject the null hypothesis and claim that the results of the two models are significantly different. However, based on the p values in Table 7, the p values are higher than 0.05 and we can accept the null hypothesis, stated that there is no significant difference between the model results.

4. Discussion

4.1. Measured TSX Backscatter Signatures of Crops

For the winter wheat, the higher sigma nought values (σ⁰) of HH polarization compared with the VV polarization for the X-band is likely due to the vertical structure of the plant stems. Therefore, the attenuation of VV is higher than that of HH, as mentioned in previous study (Jia et al. 2013). The increase in σ⁰ for both the HH and VV channels between stem elongation and the end of flowering was probably the result of an increase in biomass (Cable et al. 2014a, b). Additionally, the relatively open structure of the canopy and the smaller dimensions of its elements for the winter wheat during stem elongation could be another reason for the small increase of σ⁰ due to high moisture content in the soil (Cable et al. 2014a, b). The increase of σ⁰ through the stages of stem elongation to end of flowering (DOY 190) by approximately 1 dB suggests a change in the dominant scattering mechanism from soil and roughness backscattering to canopy scattering, which agrees with the findings of Koppe et al. (2012). The decrease in the scattering coefficient from the mealy ripe stage (DOY 216) until the end of the growing stage may be because the variation in σ⁰ was controlled by soil backscattering at the senescence stage (August) and the contribution of soil characteristics, components and surface roughness to σ⁰ increased (Vereecken et al. 2012; Koppe et al. 2012). Finally, the difference between the maximum and minimum σ⁰ was approximately 7–8 (dB) and this result is in accordance with the findings of Jia et al. (2012).

For barley, the in situ data show that FB increased between stem elongation and flowering. Thus, σ⁰ also increased for both polarization channels. This increase of σ⁰ can again be attributed to the increase of soil moisture following a precipitation event (19.6 mm) for the barley field. The increase in σ⁰ from the June 21 acquisition (DOY 172) to the July 13 acquisition (DOY 194) may have the following reason: after a certain threshold (approximately 0.8 kg/m²) the response was primarily dictated by changes in crop phenology (and thus structure) rather than biomass accumulation (Wiseman et al. 2014; Gao et al. 2013). In addition, the increase in σ⁰ of both polarization channels during the end of the growing stages (ripening and harvest time) is possibly related to vegetation water content. In an early study, Ulaby and Bush (1976) were surprised to find that backscatter actually increased with decreasing plant water content. Also, there is a negative correlation between backscatter and plant water content (Cloutis et al. 2007). Another interesting phenomenon occurred during the flowering stage, when the scattering coefficient of VV polarization was higher than that of HH polarization. The higher backscattering of VV polarization during the flowering stage of the barley (DOY 172) was possibly due to the effect of lodging, which is the permanent displacement of plant stems from the vertical (Bouman and van Kasteren 1990). Since the barley forms spikes during the period of grain filling, the crop structure dramatically changes, and external factors, such as wind, and influences the top layer of the crop through their effect on the orientation of the canopy elements (van Kasteren 1981). Therefore, higher VV polarization compared with HH polarization during flowering was presumptively due to the flattening effect of wind on the top layer (Fig. 2). For example, during the grain-filling period, the stems of the ears were bent and the ears lay nearly horizontally in the top of the canopy (Bouman and van Kasteren 1990).

In multi-temporal SAR data, broadleaf crops are generally separable from small-structured crops (McNairn et al. 2002) because dense canopy targets, such as that of canola, display higher co-pol backscatter responses than cereal crops (Cable et al. 2014a, b). The X-band values for σ⁰ of the canola range between − 6 and − 10 dB. The maximum values were observed during the emergence stage, and the minimum values were reached between the end of flowering to harvest. These outcomes agree with the results of Fieuzal et al. (2013). The decrease in the backscattering coefficient of both polarization channels between inflorescence emergence and the flowering stage is in line with findings of Wiseman et al. (2014) for the C band. This suggests that flowering, which precedes ripening, causes a slight decrease in response for certain SAR polarization channels. The stabilized backscattering between flowering and ripening points to a saturation at X-band. This phenomenon is explained by Taconet et al. (1994), who found that at vegetation water contents larger than 3 (kg/m²), the HH polarization of the X band becomes saturated, which means that the backscattering coefficient becomes insensitive to canopy structures and functions (Blaes et al. 2006; Bouman 1991). This stabilization was explained by Baghdadi et al. (2010) in another way. They found that the increase in the volume contribution as a function of the crop growth stage, combined with a decrease in the direct soil contribution, results in a relative stabilization of the radar signal. In addition, because of the thick canopy present, little of the signal reached the soil, and the backscatter did not display the influence of increased soil moisture following a precipitation event during these periods (Cable et al. 2014a, b). The decrease in backscatter that occurred at the end of the growing stage of the canola can also be attributed to the decrease in soil moisture according to Fig. 5.

The general trend for the studied crops is that the mean value of HH response is slightly higher than the VV response (approximately 1 dB). This outcome confirms the effect of higher attenuation at the VV polarization for the crops with a more obvious vertical structure (Baghdadi et al. 2010; Le Toan et al. 1989; Mattia et al. 2003). This presumptively indicates that the VV energy penetrated between the rows and became de-polarized after scattering off the soil, canopy or both (Cable et al. 2014a, b).

Finally, it should be noted that the timing of ground-truth data collection often exhibits a time lag with respect to the overpasses. This time lag might not be a problem for quantities that differ only slightly in time, such as the biomass during a specific growing stage. However, crops may be strongly affected by external phenomena, such as wind conditions, and this may result in additional noise on measured SAR signals that cannot be related to a specific process (Vereecken et al. 2012).

4.2. Modelling of Crop Biomass

In the past, many different formulations of the WCM have been proposed (Graham and Harris 2003). Since there is no general agreement regarding the precise setup of the WCM, we used the biomass values as the indicators, considering two different scenarios including V1 = V2 = biomass and V1 = 1 and V2 = biomass. In addition, there is no general theoretical background with which to predict the values of the A, B, C, and D parameters (Prévot et al. 1993). Using WCM, it was found that VV-like polarized radiation estimates the biomass of crops better than HH polarization in general (i.e. V1 = V2 = biomass). In a discussion of the WCM, one must emphasize the following points. First, according to this study, the estimation of the FB of crops is not as accurate as the estimation of DB. This outcome may be related to the fact that FB is not monotonic, and the authors believe that acquiring simultaneous ground truth data with the satellite images would increase the accuracy of the models. Second, it was found that for the estimation of crop biomass (particularly dry biomass) approximate estimates of the soil moisture content on a 4–5 day basis are sufficient to facilitate retrieval of the biomass and to obtain useful information on crop growth. This finding agrees with Wigneron et al. (1999).

The results of the stepwise regression analysis suggests that different polarization channels and polarization variables are required to better explain variations in crop variables, such as DB and FB. This is in accordance with the findings of (McNairn et al. 2002). As it can be observed, different polarization channels and variables, such as HH-VV and HH + VV, have been presented in models, as discussed above. However, the effect of the VV × HH variable has not been fully understood and requires additional investigation. It is obvious that in all cases the amount of explained variance increases as more than one polarization variable is considered. As reflected in the stepwise regressions, the DB of the crops produced the best results. For the studied crops, the described polarization variables account for more than 70% of the variation in DB. Therefore, the stepwise regression method using dual-polarimetric TerraSAR-X data was successful in deriving the DB and FB of the individual crops.

As it was observed, using this approach increases the estimation accuracy of biomass retrieval. The sensitivity of RF regression to the sampling design (number of samples) needs to be taken into account to reduce the uncertainties because though, the empirical approaches (fitting methods) yield often accurate biophysical parameters results, but they are not usually valid for application that exceed the calibration conditions. Therefore, the training sample needs to be large enough (Belgiu and Drăguţ 2016). The RF regression approach has been shown to be superior and suitable for estimation of crop biomass (Ndikumana et al. 2018; Wang et al. 2016) data especially for the fresh biomass.

Each of the approaches has advantages and disadvantages. The stepwise regression approach does not require the soil moisture as an input variable. However, this approach is only a preliminary and suggestive empirical method. Since our dataset was relatively small and restricted to a test site in northeast Germany, the generalization of the approach developed here requires additional research to assess its robustness for biophysical parameter estimation. Additionally, the stepwise regression approach cannot be used with only one polarization channel, whereas although WCM can be implemented for single polarimetric data, but it requires information on soil moisture. Finally, RF models were able to estimate the biomass accurately for FB and DB of all selected crops. However, these machine learning approaches need large data pool with relatively unbiased ground truth data for the training of data for transferring the models to similar conditions.

It is worth mentioning that we were not able to study any phase-relation between HH and VV since we were using the MGD data based on intensity only. This means that it was not possible to process the single bounce or the double bounce, or any other polarimetric feature using this format (MGD) (Ahmadian et al. 2016). The authors predict that the correlation will be even better once one can include true polarimetric indices/information (e.g. entropy/alpha decomposition features or Pauli elements); however, this would require processing the single look slant range complex (SSC) data of TSX (Ullmann et al. 2016).

5. Conclusion

As observed in this study, the complex relationships between X-band radar backscattering and crop type, crop conditions, and external factors result in large fluctuations in the back-scattering curves of HH and VV and in enormous backscatter variations. The similar structure associated with wheat and barley contributes to confusion between these crop types, whereas the polarization signature of canola clearly differs from that of the cereals.

The results revealed that the simulated data from water cloud model agree well with the measured data, particularly for dry biomass. However, the estimation accuracy was not completely satisfactory for fresh biomass (R² < 0.65), and the semi-empirical model could not exceed the quality of the selected statistical models. It was also concluded that the first scenario which consider V1 = V2 = biomass was more successful to estimate the biomass of aforementioned crops.

In the stepwise regression approach, if different polarization variables are used together to define crop biophysical parameters, more than 70% of the variance in biomass can be explained, particularly for dry biomass. However, the model parameters must be determined for each crop. This approach is evidently valuable for dry biomass assessments because of the high degree of correlation between polarization variables and dry biomass.

The results of RF showed its superiority over the other methods as it was successful to estimate both the fresh and dry biomass of different crop types with comparatively high accuracy (i.e. R² > 0.7). Despite being very flexible, the machine learning approach is, however, data-intensive and requires special attention to over-fitting.

The timing of ground-truth sampling exhibits a time lag with respect to the overpasses. This fact may introduce uncertainties in the estimation of crop-related parameters (particularly for fresh biomass). In addition, according to our results, multi-temporal data in a high frequency (i.e. the X band) are useful in determining the biomass of wheat, barley, and canola.

The presented comparison of different approaches may be valuable in guiding future research on quantifying the different responses of radar backscatter to crop variables. In future studies, the application of all three approaches may be assessed over a more fragmented landscape, and the adaptation of the presented methods to other agricultural crops is suggested to complete the picture of the usefulness of the different approaches, in particular with regard to transferability.

Acknowledgements

This study was partly funded by the Federal Ministry of Economic Affairs and Energy funded (FKZ: 50 EE 1608). We also would like to thank Deutsches Zentrum für Luft- und Raumfahrt (DLR) Neustrelitz for logistical support, as well as the German Remote Sensing Data Center (DFD, DLR) for providing the TerraSAR-X satellite images. The authors would be also indebted to the chair of Physical Geography and the lab of Department of Geology at the University of Greifswald for their contributions to this project and all the field crews and colleagues for collecting the field data and helping for boosting the content of this manuscript. J. Verrelst was supported by the European Research Council (ERC) under the ERC-2017-STG SENTIFLEX project (grant agreement 755617).