Estimating Gravimetric Water Content of a Winter Wheat Field from L-Band Vegetation Optical Depth

A considerable amount of water is stored in vegetation, especially in regions with high precipitation rates. Knowledge of the vegetation water status is essential to monitor changes in ecosystem health and to assess the vegetation influence on the water budget. In this study, we develop and validate an approach to estimate the gravimetric vegetation water content (mg), defined as the amount of water [kg] per wet biomass [kg], based on the attenuation of microwave radiation through vegetation. mg is expected to be more closely related to the actual water status of a plant than the area-based vegetation water content (VWC), which expresses the amount of water [kg] per unit area [m2]. We conducted the study at the field scale over an entire growth cycle of a winter wheat field. Tower-based L-band microwave measurements together with in situ measurements of vegetation properties (i.e., vegetation height, and mg for validation) were performed. The results indicated a strong agreement between the in situ measured and retrieved mg (R2 of 0.89), with mean and standard deviation (STD) values of 0.55 and 0.26 for the in situ measured mg and 0.57 and 0.19 for the retrieved mg, respectively. Phenological changes in crop water content were captured, with the highest values of mg obtained during the growth phase of the vegetation (i.e., when the water content of the plants and the biomass were increasing) and the lowest values when the vegetation turned fully senescent (i.e., when the water content of the plant was the lowest). Comparing in situ measured mg and VWC, we found their highest agreement with an R2 of 0.95 after flowering (i.e., when the vegetation started to lose water) and their main differences with an R2 of 0.21 during the vegetative growth of the wheat vegetation (i.e., where the mg was constant and VWC increased due to structural changes in vegetation). In addition, we performed a sensitivity analysis on the vegetation volume fraction (δ), an input parameter to the proposed approach which represents the volume percentage of solid plant material in air. This δ-parameter is shown to have a distinct impact on the thermal emission at L-band, but keeping δ constant during the growth cycle of the winter wheat appeared to be valid for these mg retrievals.


Introduction
In the present context of climate change, it is of key importance to closely monitor the vegetation conditions of agricultural fields to secure yield and prevent damage from widespread flood and drought episodes. In this regard, our research aims to develop and validate at the field scale a new approach to retrieve the gravimetric vegetation water content (m g ) from the vegetation attenuation of L-band microwave radiation (τ parameter). Tower-based L-band (1.4 GHz) microwave measurements above a winter wheat field were acquired over an entire growing cycle together with in situ measurements of vegetation properties [1]. The proposed attenuation-based approach to retrieve m g is built on the τ model of Schmugge and Jackson [2] and on the Debye-Cole dual dispersion dielectric model of Ulaby and El-Rayes [3]. The motivation of our study is to get a direct estimate of the plant water status (i.e., m g ) which, unlike the area-based vegetation water content (VWC), is independent of biomass variations. The VWC can be defined as the amount of water [kg] per unit area [m 2 ] and the gravimetric vegetation water content (m g ) as the amount of water [kg] per wet biomass [kg] [4,5]. The retrieval of VWC was frequently investigated in past studies using optical sensor measurements; global estimates have been validated by using (limited) available in situ measurements (e.g., [6,7]) or by first upscaling ground observations to regional scales via air-borne observations that were later related to space-borne measurements (e.g., [8]). Additionally, several studies were performed at the field scale to retrieve VWC using L-band (e.g., [9] for alfalfa) or a combination of L-and C-band passive microwave measurements (e.g., [10] for soy bean and winter wheat). At L-band, the VWC was shown to be linearly related to the vegetation optical depth (VOD) parameter (τ) [11] using a vegetation structural parameter (i.e., the so-called b-parameter with τ = b · VWC) [11]. This b-parameter was estimated at the local scale in field studies for multiple vegetation types (e.g., [11][12][13][14]) and has been defined globally for different land cover types based on the International Geosphere-Biosphere Program (IGBP) classification system [15]. However, while the use of b for the retrieval of the VWC is a common and established method considered in ESA's Soil Moisture and Ocean Salinity (SMOS) [16] and NASA's Soil Moisture Active Passive (SMAP) [17] retrieval algorithms [12,15], it is not fully physically-based and it is generally defined using empirical methods. In addition, most VWC retrieval approaches were developed at the field scale and require in situ datasets as an input (e.g., vegetation density) [12], which are usually not available on a global scale. Finally, the limited availability of ground measurements makes the validation of globally estimated VWC products very challenging.
The gravimetric vegetation water content (m g ) is expected to be more closely related to the actual water status than VWC and, therefore, better suited for eco-hydrological studies [18]. However, studies addressing the estimation of m g based on passive microwave measurements are scarce. At the field scale, the m g was shown to be highly dependent on the absorption and the scattering of microwave emissions at L-, C-, and X-bands for leaves of a soybean canopy [13]. In addition, a strong relationship to the complex vegetation dielectric constant (ε veg ) for different plant parts (i.e., stalks and leaves of wheat and corn plants [14] or wheat heads [19]) was reported. A few studies proposed approaches for the global estimation of m g from τ estimates [5,18]. However, the retrieval of m g still needs further investigation and improvement, especially at the global scale, since in situ reference datasets for validation are also missing at this scale [18,20]. In particular, a proper characterization of the canopy volume is a pre-requisite information to estimate m g . Such information is generally unknown and often fixed as a constant or neglected in actual retrieval algorithms (e.g., the τ-ω model [21]). The vegetation volume fraction (δ) can be defined as the volume percentage of solid plant material of a canopy in air [22]. The δ-parameter has a high impact on the emission-band radiation originating from the vegetation and is therefore directly related to water absorption within the canopy [13]. Thus, an improved estimate of δ may lead to more accurate estimates of the attenuation of microwave emissions by the vegetation layer [2,13], and therefore more accurate estimates of m g . Only a few field studies have investigated δ so far. They state that δ typically ranges between 0 and 0.01 for most vegetation layers [2] and that it can in general be assumed to be smaller than 0.01, like that shown by Wigneron et al. [13] for a soybean canopy. The objectives of our study are to investigate the information on water content and above-ground biomass contained in the vegetation optical depth parameter and to develop an algorithm to extract m g from τ under controlled field experiment conditions. The decision to use L-band data was made as the L-band is a promising frequency to monitor crop vegetation, as it penetrates into the canopy (i.e., measurements of the whole above-ground plant layer are possible), is less affected by scattering within the vegetation than higher frequencies, and is located within a protected band leading to low radio frequency interference (RFI) [23]. However, the L-band is more sensitive to soil moisture than higher frequencies, especially if the vegetation density is low to moderate. C-and X-band radiometer measurements (e.g., as provided by AMSR-E and WindSat) are less sensitive to the soil moisture content and could be better suited to characterize the (upper) vegetation layer [24,25]. Nonetheless, we performed our measurements in the L-band for the reasons given above, and designed our experiment specifically to block the soil surface emission and thus avoid the soil moisture influence on the radiometer measurements. Furthermore, vegetation indices retrieved from passive L-band measurements differ from indices deducted from optical or active microwave observations. Optical sensors do not penetrate into the canopy and only sense the very top of the vegetation layer (leaf component) [4]. Active microwave sensors, in turn, are more strongly affected by scattering within the vegetation than their passive counterparts [26,27]. Passive microwave observations at L-band allow to estimate the vegetation permittivity (dielectric constant), which can be directly related to properties, like water content, density, and structure [28,29]. In this context, the vegetation water status is a key variable for global and regional climate models to improve water budget estimations [30,31].
The following research questions were investigated during our study: (a) Can we retrieve the gravimetric moisture (m g ) of vegetation using the vegetation optical depth (τ) parameter, i.e., the degree to which vegetation attenuates microwave radiation in the L-band?; (b) Is m g influenced by changes of the vegetation canopy (e.g., structure, biomass) over the growing season of a winter wheat field?; (c) Is the retrieval of m g influenced by the applied vegetation dielectric mixing model (i.e., assuming different vegetation shapes in the dielectric mixing model)?; and (d) Is the assumption of a constant δ valid for the retrieval of m g at the field scale? Section 2 presents the experimental setup and the methodology of the microwave attenuation-based approach to estimate m g . Section 3 shows the results of the retrieved m g and its correlation to in situ measured m g . Additionally, a sensitivity analysis of m g for varying δ is presented, as well as a comparison between the in situ measured m g and the in situ measured VWC values. In Section 4, we discuss the results of the m g -retrieval, our findings concerning the δ-parameter, and the potential of our attenuation-based approach to provide estimates of m g . Section 5 provides a summary and our conclusions.

Experiment Description, Vegetation Conditions, and Datasets
Tower-based passive microwave measurements over a winter wheat (Triticum aestivum L.) field were carried out using the ELBARA-II radiometer during summer 2017 [1]. The measurements were performed at the Selhausen remote sensing field laboratory (Germany) [21]. The ELBARA II device operates in the L-band with a center frequency of 1.4 GHz. The measurements were performed at horizontal (p = H) and vertical (p = V) polarization (p) using a 3 s integration time to provide an accuracy of about 1 K and the −3 dB full beam width was 23 • in the far field. The radiometer was mounted on an aluminum bridge at about 4 m height.
The experiment was conducted during a period of about four months from tillering of the winter wheat on April 10th (DOY 100) to the late senescence stage on August 14th (DOY 226). The microwave measurements were performed twice a week over a gridded plot (i.e., soil covered by a perfect reflector (metal grid) to block the soil surface emission, but allowing vegetation to grow through the mesh grid) for different incidence angles (i.e., 40-60 • in increments of 5 • ) during the morning (i.e., from 8 to Remote Sens. 2019, 11, 2353 4 of 18 12 a.m.). The collected brightness temperature (T B ) data showed that the T BV measurements had a higher temporal variability with generally higher values over the entire growing period, and also a larger increase and dynamic range during crop development, compared to T BH (e.g., a STD of 18.4 K for T BH and 53 K for T BV using a 40 • incidence angle). This can be explained by the stronger vertical orientation of the wheat canopy leading to a higher emission contribution in the V polarization [1]. In addition, weekly in situ measurements of vegetation properties were performed for: leaf area index (LAI), total above ground biomass (TOB), vegetation water content (VWC), growing stages (BBCH), and vegetation height (d). The field experimental setup and the changes in the vegetation layer during the growing season are depicted in Figure 1 for selected phenological stages. The vegetation layer changed significantly during the phenological cycle of the winter wheat plants with a leaf-dominated vegetation structure between DOY 100 and 120, followed by a period of stalk-dominated vegetation structure (DOY 120-180) where the highest VWC was reached during flowering, and a period where the vegetation turned into senescence (DOY ≥ 200) and the heads as well as the stems of the wheat began to bend towards the soil surface. For a more detailed description of the field setup and the collected measurement datasets (i.e., in situ and radiometer) see Meyer et al. [1]. period, and also a larger increase and dynamic range during crop development, compared to TBH (e.g., a STD of 18.4 K for TBH and 53 K for TBV using a 40° incidence angle). This can be explained by the stronger vertical orientation of the wheat canopy leading to a higher emission contribution in the V polarization [1]. In addition, weekly in situ measurements of vegetation properties were performed for: leaf area index (LAI), total above ground biomass (TOB), vegetation water content (VWC), growing stages (BBCH), and vegetation height (d). The field experimental setup and the changes in the vegetation layer during the growing season are depicted in Figure 1 for selected phenological stages. The vegetation layer changed significantly during the phenological cycle of the winter wheat plants with a leaf-dominated vegetation structure between DOY 100 and 120, followed by a period of stalk-dominated vegetation structure (DOY 120-180) where the highest VWC was reached during flowering, and a period where the vegetation turned into senescence (DOY ≥ 200) and the heads as well as the stems of the wheat began to bend towards the soil surface. For a more detailed description of the field setup and the collected measurement datasets (i.e., in situ and radiometer) see Meyer et al. [1]. In the current study, we used the polarization (p) dependent vegetation optical depth (τ) parameter, which was retrieved from the 40 • incidence angle brightness temperature measurements using the τ-ω model [32]. Optimal values for τ (H and V polarizations) were simultaneously estimated for one measurement angle using T B data at both polarizations. Additionally, information on canopy temperature (measured at 15 cm above ground) was used. The T B data consisted of mean values of the five measurements performed per day (n = 33 days, from which only 20 measurement days correspond to the in situ measured vegetation properties) at the 40 • incidence angle and for each polarization. The estimated τ V as well as in situ measurements of vegetation height (d) were used as an input in our m g retrieval approach. Finally, to be able to compare our retrievals of m g with a reference dataset, the in situ VWC was converted to m g by calculating first the dry matter fraction (m d ) as defined by Mätzler [33] (i.e., m d = dry mass f resh mass ) and subtracting it afterwards from 1 (i.e., m g = 1 − m d ). This calculated m g will be called in situ measured m g in our study. Figure 2 shows, conceptually, the retrieval scheme of m g . For the estimation of m g , the in situ measured vegetation height (d), a constant value of the vegetation volume fraction (δ), and the canopy dielectric constant (ε can ) (i.e., which was derived from the modelled complex vegetation dielectric constant (ε veg )) were used as input for the τ model. The output modelled τ values were then compared to the radiometer-derived τ values (i.e., which were estimated from L-band brightness T B measurements using the τ-ω model (see Section 2.1) by minimizing the objective function (ϕ), which is defined as the cumulative squared error between the modelled and measured τ. Finally, the optimal (opt) ε veg is obtained from the best fit between τ-model and the radiometer-derived τ, and is converted to m g using the model of Ulaby and El-Rayes [3]. The different vegetation dielectric mixing models used to estimate ε can will be explained in Section 2.2.2. In addition, further explanations regarding the conversion of the ε veg to the corresponding m g and vice versa will follow in Section 2.2.3.

Retrieval Algorithm
Concerning the radiometer-derived τ parameter, τ p at vertical (p = V) polarization was used for the m g retrieval as τ at horizontal polarization (p = H) did not lead to a proper estimation of m g (i.e., a significantly deviating temporal evolution and underestimation of m g in comparison to the in situ measured m g (results not shown)). The fact that τ V performed better for the m g retrieval can be explained by the strong vertical structure of the wheat canopy which is better sensed with V-than with H-polarization. Therefore, all results presented in this work are only based on one polarization (i.e., V-polarization) and one incidence angle (i.e., 40 • ). Using τ at nadir (τ NAD ) (i.e., corrected for anisotropy) retrieved from multiple incidence angles was not an option, as the resulting estimated m g showed a similar behavior as the m g for the τ H -case in comparison to the in situ measured m g . To minimize ϕ during the m g -retrieval, the multi-level coordinate search (MCS) algorithm [34] was used. Additionally, we used the Local-Nelder-Mead simplex algorithm [35] to further improve the optimization.
Concerning δ, it is not directly measurable with the radiometer and was not measured in the field. It could be estimated from radar measurements using the Radar Vegetation Index (RVI) (e.g., as proposed in [18]) but, unfortunately, radar measurements were not performed during this experiment. Hence, we performed a sensitivity analysis to assess whether it was reasonable to set δ to a constant value along the entire growing period. Note a daily retrieval of δ was not possible (i.e., a global minimum could not be found and several δ-values led to the smallest ϕ (local minima)). A range of literature values for constant δ (between 0 and 0.01 [18,20]) were tested in the m g retrieval approach and the δ which led to the smallest ϕ was chosen based on a model selection. The search step for finding the optimum δ for the entire growing period was set to 10 −6 , to ensure that the global minimum could be found. Finally, a sensitivity analysis was performed where the influence of the constant δ-parameter assumption on the estimated m g using the attenuation-based approach was investigated (as presented in Section 3.2).
The proposed attenuation-based m g -retrieval concept was first applied in a previous study to global SMAP radiometer data for τ estimation and radar for δ estimation [5]. It has been adapted here for application at the field scale. Note that it was not possible to retrieve both parameters simultaneously, since V-polarization data at one incidence angle (i.e., 40 • ) does not contain enough information to retrieve two variables simultaneously (i.e., m g and δ) (see Section 4).
Remote Sens. 2019, 11, x FOR PEER REVIEW 6 of 18 approach and the δ which led to the smallest φ was chosen based on a model selection. The search step for finding the optimum δ for the entire growing period was set to 10 -6 , to ensure that the global minimum could be found. Finally, a sensitivity analysis was performed where the influence of the constant δ-parameter assumption on the estimated mg using the attenuation-based approach was investigated (as presented in Section 3.2). The proposed attenuation-based mg-retrieval concept was first applied in a previous study to global SMAP radiometer data for τ estimation and radar for δ estimation [5]. It has been adapted here for application at the field scale. Note that it was not possible to retrieve both parameters simultaneously, since V-polarization data at one incidence angle (i.e., 40°) does not contain enough information to retrieve two variables simultaneously (i.e., mg and δ) (see Section 4).

Figure 2.
Conceptual scheme of the attenuation-based retrieval approach of the gravimetric vegetation water content (mg) based on radiometer-derived vegetation optical depth (τ) estimates (i.e., estimated from the brightness temperature (TB) measurements over a gridded plot using vertical polarization (p = V) [K], in situ measured vegetation height (d) [m], and a constant value for the vegetation volume fraction (δ) [-]. Different vegetation dielectric mixing models were used to derive the dielectric constant of the canopy (εcan), which was also used as an input for the τ model. Finally, mg was retrieved using the optimal (opt) vegetation dielectric constant (εveg) and based on the Ulaby and El-Rayes [3] model.

Modelling the Vegetation Optical Depth Including a Two-phase Dielectric Mixing Model
Our approach is based on the attenuation model proposed by Schmugge and Jackson [2]. They found that for a wavelength (λ) [m] at frequencies between 0.2 and 20 GHz the nadir vegetation optical depth VOD (τ) can be related to the imaginary part of the complex dielectric constant of the canopy (εcan) by: where the square root of εcan is applied, since it is directly related to the refractive index of the canopy, and the imaginary part (Im) (also called loss factor) refers to the loss of the electromagnetic energy when the waves propagate through a vegetation layer with thickness d [m]. Thus, τ describes the . Different vegetation dielectric mixing models were used to derive the dielectric constant of the canopy (ε can ), which was also used as an input for the τ model. Finally, m g was retrieved using the optimal (opt) vegetation dielectric constant (ε veg ) and based on the Ulaby and El-Rayes [3] model.

Modelling the Vegetation Optical Depth Including a Two-Phase Dielectric Mixing Model
Our approach is based on the attenuation model proposed by Schmugge and Jackson [2]. They found that for a wavelength (λ) [m] at frequencies between 0.2 and 20 GHz the nadir vegetation optical depth VOD (τ) can be related to the imaginary part of the complex dielectric constant of the canopy (ε can ) by: where the square root of ε can is applied, since it is directly related to the refractive index of the canopy, and the imaginary part (Im) (also called loss factor) refers to the loss of the electromagnetic energy when the waves propagate through a vegetation layer with thickness d [m]. Thus, τ describes the attenuation of the surface emission when it passes through the vegetation canopy. For the description of ε can , different two-phase dielectric mixing models can be used, as proposed by de Loor [36] who extended the work of Polder and van Santen [22] on the dielectrics of mixtures of solids. Thus, the vegetation layer can be described as a two-phase mixture with air as the host material with a dielectric constant (ε air ) equal to one and the vegetation as inclusions with a specific shape (i.e., spheres (s), needles (n), discs (di)), orientation (i.e., random (r) or vertical (v)), complex vegetation dielectric constant (ε veg ), and volume fraction (δ). For the winter wheat field, the vertical needles (vn) dielectric mixing model is expected to perform best to retrieve m g , as the winter wheat canopy is mainly vertically oriented (distinct stalk component) and therefore anisotropic attenuation effects should be significant. The randomly-oriented discs (rdi) dielectric mixing model will also be tested as the leaves have a disc like shape without a dominant orientation (i.e., random). The equations used to calculate ε can for vegetation inclusions with vertical needles (vn) and randomly-oriented discs (rdi) can be found in [19]. For the vertically oriented needles (vn) inclusions: where ε host is the dielectric constant of the host material (which is equal to ε air in the case of a canopy layer in nature) and the so-called shape factor (A u ) (also called depolarization factor) which describes the influence of the inclusion shape on the dielectric constant along its semi-axis (u = a, b, or c). The semi-axes a and b are symmetric in the vn mixing model (i.e., a = b) and c >> a. The A parameter is than A a = A b = 0.5 and A c was set equal to zero in our case because we did not perform measurements of the stalk diameter to calculate the ellipsoid eccentricity. The sum of the three shape factors is always equal to 1 [19]. When assuming that the vegetation inclusions have the shape of randomly oriented discs (rdi) the semi-axes are a = b and c << a and the following equation should be used: The A-parameter can be assumed to be equal to A a = A b = 0 and A c = 1, in this case. In general, it has to be stated that for vegetation layers with an anisotropic structure, vegetation dielectric mixing models which account for the orientation (i.e., random or vertical) and the shape of the inclusions (i.e., needles or discs) seem to perform better at the field scale (e.g., [13]) than mixing models which do not account for the orientation and shape of the vegetation inclusions (i.e., assuming the shape of spheres) [5]. Hence, the choice of the dielectric mixing model should be adapted to the actual phenological stage and the vegetation species. In addition, it is also important to mention that on large scales (kilometer resolution of radiometers) the vertical and horizontal structure in natural vegetation are usually mixed and do not appear monotonically oriented over large areas. In these cases, dielectric mixing models which describe the vegetation as isotropic structures would describe the vegetation layer in a more appropriate way (i.e., the spheres (s) or random needles (rn) mixing models [19]), as was shown by Fink et al.
[5] using SMAP data. However, for our field scale study on a single winter wheat field, s and rn dielectric mixing models did not succeed in representing the anisotropic structure of the wheat stalks and will, therefore, not be considered here.

Conversion of Vegetation Dielectric Constant into Gravimetric Vegetation Water Content
Ulaby and El-Rayes [3] developed the semi-physical Debye-Cole dual-dispersion dielectric mixing model. It is a low-parameterized and well-established model to convert the gravimetric vegetation water content (m g ) [kg kg −1 ] into the corresponding complex vegetation dielectric constant (ε veg ) and vice versa (e.g., applied by [13,37]). It assumes that ε veg is a mixture of three components . These three components in turn depend on m g . Therefore, ε veg can be defined as [3]: where ε r is the nondispersive residual component of the complex dielectric constant, with the following equation: ε r = 1.7 − 0.74 m g + 6.16 m g 2 .
The ε f w and ε b of Equation (4) are the free-water and the bulk vegetation bound water components of the complex dielectric constant, respectively. They are defined as follows: ε b = 2.9 + 55.0 where f is the measurement frequency [GHz] and σ is the ionic conductivity of the aqueous solution [S m −1 ] (σ is assumed to be equal to 1.27 as in Ulaby and El-Rayes [3]). j denotes the imaginary number. v f w and v b of Equation (4) are the associated volume fractions of the free-water and bound vegetation bound-water mixture, respectively. They are described as: Furthermore, parameters in Equation (4) depend on frequency, temperature, and salinity. As suggested in [3], plant temperature and salinity are fixed to 22 • C and 10% , respectively. This allows keeping the conversion static and avoids the need of accounting for any additional bias in the subsequent analysis. By using Equatoin (4) any value of m g (between 0 and 1) can be associated to a certain value of ε veg and vice versa.

Gravimetric Vegetation Water Content Retrieval
The complex dielectric constant of vegetation (ε veg ) will be analyzed (before conversion to m g , see Figure 2) to illustrate the dielectric variation with changing vegetation water content. Figure 3 depicts the estimated ε veg values for the vertical needles (vn) (open and filled black squares) and random discs (rdi) (open and filled cyan diamonds) dielectric mixing model (retrieved from V polarization data only) and the ε veg values derived from in situ measurements as a reference (open and filled magenta triangles). The real and imaginary parts of the ε veg (i.e., ε veg and ε veg , respectively) show for both mixing models an increase of the ε veg between DOY 100 and 140 reaching a peak value around DOY 140 of about 35 (ε veg ) and 10 (ε veg ), respectively, and a decrease of ε veg afterwards to minimum values around 6 (ε veg ) and 4 (ε veg ), respectively, at the end of the experiment (senescence phase). In comparison to the in situ measured ε veg (which were converted from the in situ measured m g using the Ulaby and El-Rayes model [3]) the modeled ε veg seems to be underestimated during the beginning of the experiment (i.e., between DOY 100 and 120) and overestimated during the senescence phase (i.e., after DOY 180). The mean and STD values of the modelled and measured ε veg can be found in Table 1.
The obtained ε veg values are comparable to vegetation dielectric constant values found for crops in literature. Ulaby and Jedlicka [14] performed measurements of the dielectric properties of wheat and corn leaves and stalks at a frequency of 1.5 GHz and found values between 2.5 and about 35 for ε veg and values between 0 and about 10 for ε veg .  [14] performed measurements of the dielectric properties of wheat and corn leaves and stalks at a frequency of 1.5 GHz and found values between 2.5 and about 35 for and values between 0 and about 10 for . The complex (i.e., real ( ) and imaginary part ( ) of the) vegetation dielectric constant was considered in the dielectric mixing model to calculate εcan, which was used as an input in Equation (1) (i.e., the τ-model). After minimization, Figure 4a depicts the estimated mg using different vegetation dielectric mixing models (i.e., vn and rdi) as well as the in situ measured mg (ref) as a reference. In addition, linear regressions between the in situ measured and retrieved mg using the vn and the rdi dielectric mixing model are shown in Figures 4b and 4c, respectively. Table 2 contains the corresponding slope, intercept, and squared Pearson correlation coefficient (R 2 ) values of the linear regression analysis. As can be seen for both the vn and the rdi dielectric mixing models, there is good agreement between measured and modelled mg, with an R 2 of 0.89 and root mean square error (RMSE) values of 0.10 and 0.11, respectively, showing a mean and STD of 0.57 and 0.19 (vn) and 0.55 and 0.18 (rdi). The mean and STD of the in situ measured mg are 0.55 and 0.26, respectively. The smallest bias can be found for the rdi mixing model with a value of 0.009. However, the vn and rdi models still underestimate the in situ mg between DOY 100 and 120 and overestimate mg after DOY 180. This is probably due to the fact that we had to assume a constant value of δ over the whole growing period due to an insufficient number of measurements, i.e., too low degree of information, to determine δ, whilst knowing that, in reality, the volume/structure of the vegetation is actually changing along with the phenological development. The complex (i.e., real (ε veg ) and imaginary part (ε veg ) of the) vegetation dielectric constant was considered in the dielectric mixing model to calculate ε can , which was used as an input in Equation (1) (i.e., the τ-model). After minimization, Figure 4a depicts the estimated m g using different vegetation dielectric mixing models (i.e., vn and rdi) as well as the in situ measured m g (ref ) as a reference. In addition, linear regressions between the in situ measured and retrieved m g using the vn and the rdi dielectric mixing model are shown in Figure 4b,c, respectively. Table 2 contains the corresponding slope, intercept, and squared Pearson correlation coefficient (R 2 ) values of the linear regression analysis. As can be seen for both the vn and the rdi dielectric mixing models, there is good agreement between measured and modelled m g , with an R 2 of 0.89 and root mean square error (RMSE) values of 0.10 and 0.11, respectively, showing a mean and STD of 0.57 and 0.19 (vn) and 0.55 and 0.18 (rdi). The mean and STD of the in situ measured m g are 0.55 and 0.26, respectively. The smallest bias can be found for the rdi mixing model with a value of 0.009. However, the vn and rdi models still underestimate the in situ m g between DOY 100 and 120 and overestimate m g after DOY 180. This is probably due to the fact that we had to assume a constant value of δ over the whole growing period due to an insufficient number of measurements, i.e., too low degree of information, to determine δ, whilst knowing that, in reality, the volume/structure of the vegetation is actually changing along with the phenological development.
This can be also seen in the linear regression plots (Figure 4b,c), where the retrieved m g during the vegetative growth stages (i.e., open black circles) are located below (underestimation) and the retrieved m g during the senescence stages (i.e., filled black circles) are located above (overestimation) the ideal correlation  This can be also seen in the linear regression plots (Figure 4b,c), where the retrieved mg during the vegetative growth stages (i.e., open black circles) are located below (underestimation) and the retrieved mg during the senescence stages (i.e., filled black circles) are located above (overestimation) the ideal correlation (1:1) line. Concerning the slopes and intercepts of the regression lines, the vn dielectric mixing model shows a slightly closer fit to the 1:1 line. Table 2. Slope, intercept, and squared Pearson correlation coefficient (R 2 ) values of the linear regression between measured and modelled mg using the vn and rdi dielectric mixing models. Furthermore, the bias and RMSE between the measured and retrieved mg are shown.

Sensitivity Analysis on the m g Retrieval for Varying δ
Numerical experiments were conducted to analyze the impact of assuming a constant δ on m g -retrievals. Figure 5 depicts the results of the m g -retrieval along the growing season using the vertical needles (vn) (a) and random discs (rdi) (b) dielectric mixing models with the in situ measured m g -values (ref ) as a reference, for different values of δ. Results show that mean and STD values of m g steadily decrease for increasing δ (see also Table 3). When using the vn or rdi mixing model, a high δ (i.e., 0.01) leads to an underestimation of m g and if δ is low (i.e., 0.004 (vn) or 0.002 (rdi)) m g is overestimated. A δ of 0.0049 (vn) or 0.0026 (rdi) leads to the minimum in the objective function ϕ between the measured and modelled τ V (but this minimum is not unique as mentioned before in Section 2.2.1) and to the closest fit between the retrieved and in situ measured m g . However, in general, there is no large difference in the temporal behavior of the retrieved m g when using the vn and rdi dielectric mixing models while varying δ. Concerning the m g -value range, it can be seen that m g ranges between~0.2-0.45 for δ equal to 0.01 and~0.25-0.95 for δ equal to 0.004 for the vn model and almost in the same range for the rdi model with m g values between~0.15 and 0.3 for δ equal to 0.01 and~0.25 and 0.95 for δ equal to 0.002.
Interestingly, the vn model seems to be in general more sensitive to changes of δ than the rdi mixing model. This can be seen in the fact that δ for the vn model was only varied between 0.004 and 0.01 and for the rdi dielectric mixing model δ was varied between 0.002 and 0.01 showing almost the same changes in estimated m g . Yet, it is important to note that small changes of δ result in relatively large changes in retrieved m g .
Numerical experiments were conducted to analyze the impact of assuming a constant δ on mgretrievals. Figure 5 depicts the results of the mg-retrieval along the growing season using the vertical needles (vn) (a) and random discs (rdi) (b) dielectric mixing models with the in situ measured mgvalues (ref) as a reference, for different values of δ. Results show that mean and STD values of mg steadily decrease for increasing δ (see also Table 3). When using the vn or rdi mixing model, a high δ (i.e., 0.01) leads to an underestimation of mg and if δ is low (i.e., 0.004 (vn) or 0.002 (rdi)) mg is overestimated. A δ of 0.0049 (vn) or 0.0026 (rdi) leads to the minimum in the objective function φ between the measured and modelled τV (but this minimum is not unique as mentioned before in Section 2.2.1) and to the closest fit between the retrieved and in situ measured mg. However, in general, there is no large difference in the temporal behavior of the retrieved mg when using the vn and rdi dielectric mixing models while varying δ. Concerning the mg-value range, it can be seen that mg ranges between ~0.2-0.45 for δ equal to 0.01 and ~0.25-0.95 for δ equal to 0.004 for the vn model and almost in the same range for the rdi model with mg values between ~0.15 and 0.3 for δ equal to 0.01 and ~0.25 and 0.95 for δ equal to 0.002.
Interestingly, the vn model seems to be in general more sensitive to changes of δ than the rdi mixing model. This can be seen in the fact that δ for the vn model was only varied between 0.004 and 0.01 and for the rdi dielectric mixing model δ was varied between 0.002 and 0.01 showing almost the same changes in estimated mg. Yet, it is important to note that small changes of δ result in relatively large changes in retrieved mg.
(a) vertical needles (vn) (b) random discs (rdi) Figure 5. Sensitivity analysis on the mg-retrieval by varying δ using the proposed attenuation-based approach. For this, two different vegetation dielectric mixing models were used, namely, the vertical needles (vn) (a) and random discs (rdi) (b) model. These results are compared to the in situ measured mg (ref). Note that the black circles represent the δ-value, which leads to the closest fit between the retrieved and in situ measured mg.
In general, the highest sensitivity of the mg-retrieval using either the vn or rdi dielectric mixing models to changes of δ can be found between DOY 100 and 180 (i.e., when the mg-values are relatively high with values between 0.8 and 0.5) and the lowest sensitivity appears during the senescence phase (i.e., when the mg-values are very low (≤0.25)). This means that the effect of δ on the L-band microwave thermal emission is higher when also the water content of the plants is high (e.g., varying δ between 0.002 and 0.01 decreases the mean value of mg by about 0.56 for the rdi mixing model at DOY ≤ 160). For lower water contents (i.e., low mg-values at DOY > 200) the effect of δ on the thermal emission can be assumed to be rather small (e.g., varying δ between 0.002 and 0.01 decreases the mean value of mg by ~ 0.2 for the rdi model). Table 3. Mean and STD values of retrieved mg [kg kg -1 ] for selected δ-values using the vertical needles (vn) and random discs (rdi) dielectric mixing models (cf. Figure 5) and the mean and STD of the in situ measured mg as reference (ref). Figure 5. Sensitivity analysis on the m g -retrieval by varying δ using the proposed attenuation-based approach. For this, two different vegetation dielectric mixing models were used, namely, the vertical needles (vn) (a) and random discs (rdi) (b) model. These results are compared to the in situ measured m g (ref ). Note that the black circles represent the δ-value, which leads to the closest fit between the retrieved and in situ measured m g . Table 3. Mean and STD values of retrieved m g [kg kg −1 ] for selected δ-values using the vertical needles (vn) and random discs (rdi) dielectric mixing models (cf. Figure 5) and the mean and STD of the in situ measured m g as reference (ref ).

δ-Values
Mean-m g STD-m g In general, the highest sensitivity of the m g -retrieval using either the vn or rdi dielectric mixing models to changes of δ can be found between DOY 100 and 180 (i.e., when the m g -values are relatively high with values between 0.8 and 0.5) and the lowest sensitivity appears during the senescence phase (i.e., when the m g -values are very low (≤0.25)). This means that the effect of δ on the L-band microwave thermal emission is higher when also the water content of the plants is high (e.g., varying δ between 0.002 and 0.01 decreases the mean value of m g by about 0.56 for the rdi mixing model at DOY ≤ 160).
For lower water contents (i.e., low m g -values at DOY > 200) the effect of δ on the thermal emission can be assumed to be rather small (e.g., varying δ between 0.002 and 0.01 decreases the mean value of m g by~0.2 for the rdi model).

Comparison between m g and VWC
Differences between gravimetric vegetation water content [kg kg −1 ] and area-based VWC [kg m −2 ] were studied using linear regressions over the whole growing season, the vegetative growth stages (DOY ≤ 160), and the senescence stages after the peak vegetation water content (i.e., after flowering of the winter wheat; DOY > 160) (Figure 6a and Table 4). In addition, the variation of the m g and VWC over time is depicted (Figure 6b). The results show that for the whole growing season and the vegetative growth stages the correlation between m g and VWC is rather low, with a R 2 of 0.26 and 0.21, respectively. This is related to the wheat growth where the VWC increases from values around 0.1 kg m −2 to values around 3.5 kg m −2 while m g stays more or less constant during the same period with values around 0.75 (see Figure 6b). After crop flowering (i.e., DOY > 160) both the VWC and m g show the same temporal behavior with decreasing values, as the vegetation starts to lose water during the senescence phase. This results in a high correlation between the m g and VWC with a R 2 of 0.95 and slope and intercept values of 0.20 and 0.11. As expected, the VWC reflects the amount of water [kg] per unit area [m 2 ], which is lowest during the beginning and the end of the growing season and highest during flowering. m g on the contrary, is more closely describing the plant available water, which is high during the vegetative growth stages of the vegetation (i.e., no drought stress conditions were present with m g ≥ 0.7) and low during senescence.

Comparison between mg and VWC
Differences between gravimetric vegetation water content [kg kg -1 ] and area-based VWC [kg m -2 ] were studied using linear regressions over the whole growing season, the vegetative growth stages (DOY ≤ 160), and the senescence stages after the peak vegetation water content (i.e., after flowering of the winter wheat; DOY > 160) (Figure 6a and Table 4). In addition, the variation of the mg and VWC over time is depicted (Figure 6b). The results show that for the whole growing season and the vegetative growth stages the correlation between mg and VWC is rather low, with a R 2 of 0.26 and 0.21, respectively. This is related to the wheat growth where the VWC increases from values around 0.1 kg m -2 to values around 3.5 kg m -2 while mg stays more or less constant during the same period with values around 0.75 (see Figure 6b). After crop flowering (i.e., DOY > 160) both the VWC and mg show the same temporal behavior with decreasing values, as the vegetation starts to lose water during the senescence phase. This results in a high correlation between the mg and VWC with a R 2 of 0.95 and slope and intercept values of 0.20 and 0.11. As expected, the VWC reflects the amount of water [kg] per unit area [m 2 ], which is lowest during the beginning and the end of the growing season and highest during flowering. mg on the contrary, is more closely describing the plant available water, which is high during the vegetative growth stages of the vegetation (i.e., no drought stress conditions were present with mg ≥ 0.7) and low during senescence.  Table 4. Slope, intercept, and squared Pearson correlation coefficient (R 2 ) of linear regression between in situ measured gravimetric vegetation water content (mg) and the vegetation water content (VWC). Regressions were performed over the whole growing season, for only the growth stages (i.e., DOY ≤ 160), and for only the senescence stages (i.e., DOY > 160).

Discussion
This study represents a direct attempt to retrieve the gravimetric vegetation water content (m g ) under controlled conditions at the field scale over an entire growing season. The retrieved m g values agree highly with the m g reported by Grant et al. [18] for crop vegetation on global scale where m g showed a mean and STD of 0.54 and 0.18, respectively. They used the effective medium approach [38,39] to estimate the m g from L-band SMOS data. This approach calculates the canopy opacity (τ) based on a canopy structure coefficient, the wet biomass per area, the vegetation density, the wave number in air, the imaginary part of the vegetation dielectric constant, and the incidence angle [18,38]. Concerning the temporal evolution of our retrieved and in situ measured m g , the study of Grant et al. [20] derived m g from SMOS L-band optical depth (τ) values for the whole of 2010 over a coniferous forest in the U.S. and showed that the m g values stay relatively constant over the year with values around 0.8. This confirms our finding that when the ratio between the water inside the plant and the wet biomass does not change (like during the vegetative growth stages), m g is more or less unaffected because it directly represents this ratio. At the local scale, Wigneron et al. [37] found that m g varied between 0.74 and 0.84 over the whole growing season (without the senescence stages) of a soy bean field. This is in good agreement to the findings of our study where m g is generally stable during the vegetative growth stages of the winter wheat. Finally, on the basis of published reports about vegetation water content for different vegetation types (i.e., prairie grass, corn, soy beans, and others), Schmugge and Jackson [2] outlined that m g varies between 0.6 and 0.8 for green vegetation, which was also the case in our study. Regarding the decrease of the retrieved and in situ measured m g after DOY 160, such a behavior of m g was also observed by Mätzler [40]. The author showed the temporal evolution of the dry matter fraction (m d ) over the whole growth cycle of an oat vegetation (with senescence stages included), which increased after the vegetation reached its highest VWC. This increase in m d was caused by a decrease in VWC, where m d reached a peak value of about 0.9 when the vegetation was fully senescent. Assuming that the m g can be calculated from m d (see Section 2.2.1), this study confirms our findings that the m g can decrease after peaking of VWC to values around 0.1.
One unexpected result during our study was that our proposed approach underestimated m g for the period between DOY 100 and 120 and overestimated m g for DOY ≥ 180 in comparison to the in situ measured m g . Indeed, when focusing on the δ parameter as the main reason for this behavior already small changes of δ result in relatively large changes in retrieved m g (especially when the vegetation available water content was high) (see Figure 2 in Section 3.2). This was also confirmed by the study of Wigneron et al. [13] who observed that the δ of soy bean leaves had a distinct impact on the thermal emission especially for lower frequencies (i.e., L-and C-band). In addition, the study of Choe and Tsang [41] showed that for a cylindrical scatterer (i.e., stalk-dominated corn) changes of δ between 0.01% and 0.1% already led to significant changes in the measured emissivity at the L-band frequency. Hence, one possible solution to avoid these effects could be to use a daily variable δ or adapting δ according to the main phenological stages in the retrieval scheme. A daily variable δ was, for example, measured and retrieved by Wigneron et al. [37] over the whole growing season of a soy bean canopy where δ varied between 0.25 × 10 −3 and 2.5 × 10 −3 . A daily variable δ could also be retrieved from the radar vegetation index, as suggested by Fink et al. [5]. Another reason for the underestimation and overestimation of m g could have also been the assumptions made in the model of Ulaby and El-Rayes [3] (i.e., to assume a constant value for the temperature, salinity, and density of dry vegetation material (p = 0.33 g cm −3 )), which were not able to describe the real conditions of the vegetation layer during the respective phenological stages. In this regard, Grant et al. [42], found a very small influence of temperature on ε veg , but further tests are needed to investigate this option further.
Finally, to assume one static dielectric mixing model over the whole growing period of the winter wheat is also a strong simplification as the vegetation structure is actually changing (i.e., from a more leaf dominated vegetation in the beginning to a stronger stem-dominated vegetation during the main growing stages and the senescence phase). However, in our study it seems appropriate to describe the vegetation by the inclusion type which represents the dominant vegetation structure (i.e., the vn dielectric mixing model for the stalk-dominated wheat vegetation) as the linear regression between the retrieved and in situ measured m g showed the closest fit to the optimum correlation line and a slightly smaller RMSE.
Future work will be directed towards further improving and validating the proposed m g -retrieval approach by enabling a daily-varying or a phenology-adapted δ-retrieval. In addition, we will also investigate the possibility to analyze the relationship between the vegetation height and the δ-parameter allometrically, in order to have a dynamic δ along the growing season. Qin et al. [43], for example, studied the reproductive allocation of wheat plants for different growing densities and analyzed the relationship between the grain mass and vegetative mass by using an allometric function. They found a high correlation (i.e., R 2 > 0.9) between these two variables.
Moreover, the use of a more sophisticated objective function (i.e., not only using the squared difference between the measured and modelled τ as a decision criterion) could potentially improve the performance of the approach and could be investigated.
In addition, different τ-models, including polarization and/or angle-dependency on τ, could be tested (e.g., [32,44,45]). The τ-model of Schmugge and Jackson [2] was originally formulated to be used only with a nadir τ-parameter. Using a polarimetric τ for different incidence angles at the same time would certainly help to increase the accuracy of m g retrievals and may also open the opportunity to use daily retrieved δ-parameters as mentioned above, since there would be more degrees of information [46,47]. At the moment we only use one polarization (i.e., V-polarization) and one incidence angle (i.e., 40 • ), which does not contain enough information to retrieve two variables simultaneously (i.e., m g and δ) (see Section 2.2.1).
Concerning the potential of using our approach for other crop types and also at larger scales, it remains a subject of further research. We established controlled field conditions to investigate the different influences on τ and to develop an algorithm to extract m g from τ. All the findings made during our study are only valid for winter wheat vegetation at a specific field and growing season.
Our recommendation for future studies would be to also use this attenuation-based approach for other crop types at the field scale and to continue the validation of the retrieved m g with in situ measured m g over longer observation periods and at different locations. Assessing the performance of our method at the regional or global scale is challenging due to limited availability of representative in situ validation data sets for m g . In the event of having global coverage of radiometer-derived τ-values (e.g., estimated from SMOS or SMAP), LIDAR-based vegetation heights, and robust estimates for δ (e.g., radar-based as proposed by Fink et al. [5]), there might be an opportunity to use the proposed approach to generate global maps of m g .

Summary and Conclusions
In this study, an approach was developed and applied to retrieve the gravimetric vegetation water content (m g ) of a winter wheat field over an entire growing season from L-band microwave radiometer observations (using V polarization data only). It is based on the inversion of a physical modeling framework describing the dependency of microwave radiation attenuation on vegetation height (d), vegetation volume fraction (δ), and m g . The approach includes the Debye-Cole dual dispersion dielectric model of Ulaby and El-Rayes [3] as well as different vegetation dielectric mixing models [19]. The δ-parameter has a distinct impact on the microwave emission originating from the vegetation in the L-band and is another key variable for absorption inside the canopy [13]. We optimized δ to a constant value for this study, and analyze the impact of this assumption. The retrieved m g agreed well with the in situ measured m g (see Section 3.1). Their temporal agreement was high with a correlation of R 2 > 0.8. As expected, the vertical needles (vn) dielectric mixing model showed the best performance for the stalk-dominated wheat vegetation, with the closest fit of the linear regression to the optimum correlation line and a slightly smaller RMSE (see Figure 4 and Table 2 in Section 3.1).
In addition, the results implied that the assumption of a constant vegetation volume fraction (δ) over the growing season leads to an underestimation of m g during the beginning of the vegetation growing phase and an overestimation of m g during the senescence stage. To better understand this, a sensitivity analysis was performed on the m g retrieval by varying the δ-input. It showed that small changes in δ already result in relatively large changes in retrieved m g , especially when the actual water content within the vegetation is high. To improve the retrieval of m g , δ could be defined on a daily basis or be adapted for dominant phenological stages (see Section 4). Additionally, no in situ measurements of δ or radar or LIDAR measurements (from which to estimate δ [5]) were available during the field experiment (see Section 2.2.1). However, results show that the assumption of a constant δ seems to be valid for the main growth stages of winter wheat (i.e., between DOY 120 and 180) (see Figure 4 in Section 3.1. and Figure 5 in Section 3.2).
Moreover, our comparison between gravimetric (m g ) and area-based (VWC) vegetation water content implied that m g reflects the plant internal water content and is more closely related to the actual amount of water per unit of fresh biomass than VWC (see Figure 6 in Section 3.3). However, this finding cannot be generalized to a larger scale, as our experiment was only conducted at the field scale for a specific crop (winter wheat) and the results are therefore only valid for the presented data set. Still, results show that plant internal water is high during the growth stages of the vegetation and low during senescence. These results highlight that m g is mainly the vegetation water content of the plants relative to their biomass amount. If both the biomass and the accompanying amount of water in the plant change (i.e., increase or decrease) at the same rate (such as, e.g., during the growing phase, for DOY 100-160), m g does not change much, whereas VWC does increase due to the overall higher amount of water as a consequence of the higher biomass per area. When the biomass still continues to increase (or stays constant) and the VWC decreases (e.g., during the senescence phase, for DOY > 160), m g begins to decrease as well.
We found that in situ measured structure parameters as vegetation height or biomass did not have a clear influence on m g (results not shown). Concerning the influence of the dielectric mixing model on the m g -retrieval, it was shown that it is appropriate to describe the vegetation over the whole growing season by the inclusion type which represents the dominant vegetation structure, i.e., vertical wheat stalks in our case. This corresponds to the vn mixing model.