Hydrology and Earth System Sciences Soil Moisture Retrieval through a Merging of Multi-temporal L-band Sar Data and Hydrologic Modelling

The objective of the study is to investigate the potential of retrieving superficial soil moisture content (m v) from multi-temporal L-band synthetic aperture radar (SAR) data and hydrologic modelling. The study focuses on assessing the performances of an L-band SAR retrieval algorithm intended for agricultural areas and for watershed spatial scales (e.g. from 100 to 10 000 km 2). The algorithm transforms temporal series of L-band SAR data into soil moisture contents by using a constrained minimization technique integrating a priori information on soil parameters. The rationale of the approach consists of exploiting soil moisture predictions, obtained at coarse spatial resolution (e.g. 15– 30 km 2) by point scale hydrologic models (or by simplified estimators), as a priori information for the SAR retrieval algorithm that provides soil moisture maps at high spatial resolution (e.g. 0.01 km 2). In the present form, the retrieval algorithm applies to cereal fields and has been assessed on simulated and experimental data. The latter were acquired by the airborne E-SAR system during the AgriSAR campaign carried out over the Demmin site (Northern Germany) in 2006. Results indicate that the retrieval algorithm always improves the a priori information on soil moisture content though the improvement may be marginal when the accuracy of prior m v estimates is better than 5%.


Introduction
The monitoring of the spatial and temporal distribution of soil moisture content (m v ) 20 is of major importance for a better understanding of the water cycle on land surfaces with an impact on several applications ranging from drought and flood prediction (e.g. Hong and Kainay, 1996;Pauwels et al., 2002) to meteorology (Betts et al., 1996) and agriculture (Bastiaanssen et al., 2005). Due to the high sensitivity to soil moisture content (e.g. Du et al., 2000), microwave remote sensing holds a great deal of potential yet available, while numerous research approaches exist (for a review see Moran et al., 2004). An important part of the limitations to monitor superficial soil moisture contents by means of SAR systems, is due to the fact that the observed backscatter significantly depends not only on soil roughness, soil moisture and plant water content but also on crop structure. As a consequence, there generally exist many combinations of surface parameters mapping the same SAR observable, so the retrieved "optimal" solutione.g. most probable or minimum root mean square (rms) error -may be characterized by poor accuracy (Satalino et al., 2002). This problem can be tackled by introducing a priori information about the surface parameters and using multi-temporal SAR data (Mattia et al., 2006). 15 In this context, the objective of this paper is to assess an algorithm for the retrieval, at high spatial resolution, of superficial soil moisture content underlying agricultural crops from multi-temporal L-band SAR data and hydrologic modelling. The higher penetration of L-band SAR signal into the canopy, with respect to shorter wavelengths such as C-or X-bands, reduces the sensitivity to vegetation constituents and is expected to improve 20 the SAR capability to monitor soil moisture content. In particular, for cereal crops it is possible to disregard the interaction between L-band SAR signal and crop canopy, at least at HH polarization (Mattia et al., 2007). For this reason, the presented algorithm focuses on soil moisture retrieval of cereal fields.
The rationale of the approach consists of exploiting soil moisture predictions, ob- 25 tained at coarse spatial resolution by point scale hydrologic models (or by simplified m v estimators), as a priori information for the SAR retrieval algorithm. An important aspect for the study is also to obtain indications about the errors affecting the modelling of prior soil moisture predictions. The latter may arise from several factors including incor- Interactive Discussion extensive in situ measurements of bio-physical parameters. The principal objective of the campaign was to assess the impact of the future ESA Sentinel-1 and -2 missions for land applications and to provide a well documented database to investigate the biophysical parameter retrieval. In the following sections, a short summary of the data set is reported, more details can be found in (Hajnsek et al., 2008). 5

In situ data
The Demmin site is an agricultural area characterized by an average annual rainfall of approximately 489 mm and an average temperature ranging between 18 • in July and 1 • in January. The study area, extending over approximately 25 km 2 nearby the Goermin village (53.98 • N, 13.25 • E), is cultivated mainly with winter wheat, winter barley, maize, 10 winter rape and sugar beet. From 19 April through 26 July, in situ measurements of volumetric soil moisture content and fresh biomass were collected, roughly every week, over two winter wheat fields (namely field 230 and 250) and two winter barely fields (namely field 440 and 450), all of which larger than 5 ha. Figure 1 shows a land use map of the study area on which the location of the investigated fields is also identified. 15 In total 44 observations (4 fields×11 dates) have been considered in the analysis. In addition, on field 250 there was a ground station with Time Domain Reflectometry (TDR) probes continuously measuring soil moisture content at five different depths, a Bowen Ratio Energy Balance (BREB) station and a Large Aperture Scintillometer (LAS) (a detailed description of these stations is given in . Figure 2 shows 20 the temporal behavior of in situ soil moisture measurements for the above-mentioned four cereal fields and also the continuous TDR observations at 0-9 cm. It is worth emphasizing that the study area is characterized by an almost flat topography (

SAR data
A time series of 11 geocoded and coregistered L-band SAR images acquired, from April to July 2006, by the airborne E-SAR system along the West-East track have been used in the analysis. Data were acquired at incidence angles ranging between 25 • and 55 • and processed by DLR (Hajnsek et al., 2008). 5 In order to better understand the extent to which it is possible to disregard the interaction between L-band SAR signal and wheat canopy, an assessment of the sensitivity of L-band backscatter to surface parameters is carried out, in the next subsection.

Sensitivity study
Figures 3 and 4 show the sensitivity of L-band backscatter to soil moisture content 10 and fresh biomass, respectively. The data refer to the entire experimental campaign and were acquired over field 230. The sensitivity to m v is better at HH than at VV polarization and better for fairly dry than wet soils. In average, there is an increment of approximately 2 dB at HH polarization per 5 vol. % increments in soil moisture content. However, there is also an important scatter of HH and VV backscatter, which is proba-15 bly partly due to calibration errors (error bars equal to ±1 dB) and partly to changes in vegetation and in soil conditions. For instance, the crop canopy clearly attenuates the VV backscatter as can be inferred by the fact that, in Fig. 3, the VV backscattering coefficients are lower than the HH ones (for bare fields the opposite is true). Conversely, Fig. 4 shows that at H polarization there is a negligible interaction with the crop canopy 20 as almost no correlation is found between the HH backscattering and the fresh biomass sampled on fields 230. While Fig. 3 shows that the backscatter increases in average by approximately 7 dB when the soil moisture increases from 5 to 35%, a strong increase in the biomass leads to an almost zero increase in the backscatter (the contribution from the ground corresponds to the lowest biomass value in Fig. 4). In other words, 25 the wheat canopy has only a very minor impact on the HH backscatter value. This conclusion is supported by previous modelling studies (e.g. Toure ' et al., 1994), which Introduction

Conclusions
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Interactive Discussion have pointed out that the soil contribution is dominant in the HH backscatter of winter wheat, at least at low-medium incidence angles (e.g. 20 • -40 • ). As a consequence, the HH backscatter of cereal fields is expected to be well predicted simply by a surface scattering model, such as the Integral Equation Model (IEM) (Fung and Chen, 1992), particularly at low-medium incidence angles. IEM is an asymptotic surface scattering 5 model developed to bridge the gap between Small Perturbation Method (SPM) model and the Kirchhoff approximation (KA) (Ulaby et al., 1982), thus covering a wide range of roughness conditions particularly at L-band. From an electromagnetic point of view, the IEM essentially is a second iteration of the iterative Kirchhoff approximation (Liszka and McCoy, 1982). One drawback of this approach is that the conditions for the con-10 vergence of the iterative series are not known a priori. It is worth noting that the IEM model was built to predict both single and multiple scattering contributions to surface scattering. It was expected to predict well both co and cross polarized components over a quite wide range of roughness parameters. However, some of the assumptions made in the IEM development have been subsequently recognized as simplistic by the 15 same original authors (for a critical review of the IEM see Alvarez-Perez, 2001). An improved version of IEM was released in Hsieh et al. (1997), a further version was published in Chen et al. (2000). The expressions of cross-polarised scattering coefficient have been continuously amended until recently (Chen et al., 2003). However, the expressions of co-polarized backscattering coefficient (i.e. single scattering contribu-20 tion) have not changed with respect to the original IEM. It is for this reason that in this paper the expressions of the original IEM model are used.

The retrieval algorithm
The proposed algorithm transforms a temporal series of L-band SAR data, acquired at HH polarization and low-medium incidence angles (approximatively 20 • -40 • ) over 25 cereal fields, into soil moisture values. According to the above-reported sensitivity analysis, at L-band and HH polarization, there is a reduced sensitivity of backscatter to the fresh biomass of cereal fields. On the contrary, the most important contribution to 3485 Introduction

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Printer-friendly Version Interactive Discussion HH backscatter comes from the soil and its moisture variations. As a consequence, the adopted approach disregards the presence of vegetation and inverts the IEM surface scattering model by using a constrained optimization technique, which integrates a priori information on soil parameters (such as vertical surface roughness and soil moisture content) to obtain robust and accurate estimates of soil moisture content (Mattia et al., 5 2006). More precisely, the technique minimizes the following cost function: where N is the number of σ 0 observations, F (·) is the IEM model (depending on the SAR incidence angle and wavelength, i.e. θ and λ, and on the M surface parameters p m ),p m are the a priori estimates of surface parameters, ∆ s (σ 0 ) includes the backscat-10 ter calibration, statistical and model errors and ∆ i (p) is the error affecting the prior estimates of surface parameters. The latter basically consist of the surface height standard deviation (s), the surface autocorrelation function, assumed exponential, the surface correlation length (l ) and the soil relative dielectric constant ( r ). In particular, the soil dielectric constant depends on the soil moisture content and on the soil texture 15 composition. To relate the soil dielectric constant to the volumetric soil moisture content, the empirical expression derived by Hallikainen et al. (1985) has been employed. This expression models the soil dielectric constant as a second order polynomial in m v , which can be analytically inverted. In order to obtain estimates of soil moisture content, the algorithm firstly estimates the soil dielectric constant, and then uses the 20 inverted empirical expression of Hallikainen to derive the soil moisture content. To simplify, it will be assumed that M=3 and (p m=1,M )= (s, l , m v  Interactive Discussion the number of surface parameters to be estimated is N+2 (N soil moisture values and 2 surface roughness parameters, namely s and the correlation length l ). For N equals to 1 there is the worst ratio (i.e. 1/3) between independent measurements and parameters to be estimated (highly inaccurate retrieval). Whereas for N large the ratio tends to 1 (highly accurate retrieval). In order to minimize (Eq. 1) an iterative efficient ap-5 proach based on the Generalized Reduced Gradient Method (Lasdon et al., 1978) was employed.

Numerical assessment of the algorithm performances
To characterize the performances of the developed retrieval algorithm a simulation study was carried out. A synthetic data set of ground data was built simulating three 10 different acquisition dates (i.e. N=3), Table 1 reports the average values of the considered surface parameters. Then, the IEM model was employed to obtain the backscatter values at L-band, HH polarization and 23 • incidence, associated to the surface parameters of Table 1. In order to simulate the presence of measurement errors (including radiometric, statistical and model errors) a zero-mean Gaussian noise with increas- 15 ing standard deviation (std, ranging from 0.5 to 1.5 dB) has been superposed to the IEM predictions. A priori information for the retrieval algorithm have been obtained by perturbing the surface parameters reported in Table 1 with a zero mean Gaussian noise with increasing std (ranging from 10 to 30% of the total variability range of surface parameters). It should be emphasized that the simulated a priori information still 20 represents an ideal unbiased case (the error was at zero mean). Finally, the retrieval algorithm has been applied to the synthetic data set and the results have been analyzed. A necessary condition that should be always fulfilled by the algorithm is that the final error, computed as the rms error between retrieved and observed soil moisture values, i.e. ∆ f (m v ), is smaller than the initial error, computed as the rms error between 25 prior and observed soil moisture values, i.e. ∆ i (m v ). Of course, the higher the ratio reason, the G parameter has been adopted to synthetically represent the algorithm performances in the numerical study. Figure 5 shows the gain parameter (G), obtained by applying the retrieval algorithm over the synthetic data set, versus the initial rms error ∆ i (m v ) for increasing values of measurement errors, i.e. ∆ s (σ 0 ). Figure 5 shows that the algorithm gain increases with the initial error ∆ i (m v ) and that lower measure-5 ment errors ∆ s (σ 0 ) coincide with increasing values of G. In other words, if the prior information on soil moisture content is already quite good (e.g. better than 5%), the algorithm gain is expected to be marginal (i.e. G≈1) unless the measurement error is very small (e.g. less or equal to 0.50 dB). On the other hand, for ∆ i (m v ) approximately equal to 7% and ∆ s (σ 0 ) equal to 0.75 dB, the expected gain is approximately 1.3, corre-10 sponding to a final rms error ∆ f (m v ) approximately equal to 5%. The above-illustrated characteristics of the algorithm together with the fact that its output provides soil moisture maps at high resolution (e.g. 0.001 km 2 ), prompts the following didactic example on the potential of the method. Let us consider a study area of 25 km 2 consisting of three homogeneous sub-areas (of the same size): one fairly wet (e.g. 24%±2%), one 15 medium wet (e.g. 17%±2%) and the third one fairly dry (e.g. 10%±2%). Over this area, the SAR retrieval algorithm is applied using as a priori information an average value of 17% (in this case the rms error between the constant guess and the true soil moisture values of the fairly wet, medium wet and dry areas is approximately 7%, 2% and 7%, respectively). Under these circumstances, the algorithm is expected to retrieve ap-20 proximately the following mean and rms error values for the three classes: 24%±5%, 17%±2% and 10%±5%. Hence, the three sub-areas with different soil moisture content can be identified and separated (within 1-std). In other words, despite the gain of the retrieval algorithm may often be relatively small (mainly due to the high measurement error budget), still the asset of providing soil moisture maps at high resolution can 25 be regarded as a valuable feature. In the following an experimental assessment of the algorithm performances will be carried out. 5,2008 Soil moisture retrieval

Modelling of prior soil moisture values
In order to obtain a priori information on soil moisture content, at coarse scale, the TOPLATS and PROMET hydrologic models and the API index have been exploited.
In the next subsections the three approaches are briefly described, Sect. 4.4 then illustrates a comparison between modelled and observed soil moisture values.

TOPLATS
The TOPMODEL-based land atmosphere transfer scheme (TOPLATS) model has its foundation in the concept that shallow groundwater gradients set up spatial patterns of soil moisture that influence infiltration and runoff during storm events, and evaporation and drainage between these events. The assumption is made that these gradients 10 can be estimated from local topography (through a soil-topographic index Sivapalan et al., 1987). From this foundation, the model was expanded to include infiltration and resistance-based evaporation processes, a surface vegetation layer, and a surface energy balance equation with an improved ground heat flux parameterization, and the effect of atmospheric stability on heat fluxes (Famiglietti and Wood, 1994;Peters-Lidard 15 et al., 1997). The model was originally developed to simulate the surface water and energy balance for warm seasons Famiglietti and Wood, 1994;Peters-Lidard et al., 1997. Afterwards, winter processes (frozen ground and a snow pack), an improved water and energy balance scheme for open water bodies, and a two-layer vegetation parameterization were added (Pauwels and Wood, 1999). For a detailed model description, 20 we refer to Famiglietti and Wood (1994), Peters-Lidard et al. (1997), and Pauwels and Wood (1999). Loaiza Usuga and  list an overview of the field experiments and test sites for which the model has been applied, based on which it can be concluded that the model can adequately simulate the partitioning of the energy and mass balances into their different terms.

PROMET
The physically based land surface model PROMET (Process Oriented Multiscale Evap-oTranspiration model) is used in the present study to simulate the surface energy budget and exchange of water and matter within the soil-plant-atmosphere continuum. The model describes the actual evapotranspiration and water balance at different scales, 5 ranging from point scale, to microscale and mesoscale (Mauser and Schädlich, 1998;Mauser and Bach, 2008). The model consists of a kernel which is based on five submodules (radiation balance, soil model, vegetation model, aerodynamic model, snow model) to simulate the actual water and energy fluxes and a spatial data modeler, which provides and organizes the spatial input data on the field-, micro and macroscale. The 10 simulations are made on hourly basis. PROMET solves the surface energy balance in an iterative way. The ground heat flux is estimated using a soil temperature model (Muerth, 2008). Actual evapotranspiration is simulated within PROMET using the Penman-Monteith equation (Monteith, 1965). Canopy surface resistance is simulated as a function of vegetation type using a 15 resistance network approach (Baldocchi et al., 1987), while the soil resistance is estimated based on the approach of Eagleson (1978). A four layer soil model (0-5, 5-20, 20-65, 65-200 cm) is used to calculate soil water fluxes and soil temperature profiles. The change of volumetric soil moisture content, percolation, exfiltration, capillary rise and surface runoff are explicitly considered. The infiltration into the soil layer is de-20 scribed using the model of Philip (1957). The soil water retention model of Brooks and Corey (1964) is used to relate soil moisture content to soil suction head. A detailed description of the model is given by Mauser and Schädlich (1998) and Mauser and Bach (2008). A physical snow model extends PROMET to allow for simulations in cold climates (Strasser and Mauser, 2001). 25 PROMET simulations are based on GIS information as e.g. soil maps and land use information. Meteorological forcing data might be either provided from station networks as well as from gridded forcing fields. PROMET has been extensively validated HESSD 5,2008 Soil moisture retrieval Bavarian Alpine Foreland -200×100 km 2 , Upper Danube catchment -76 000 km 2 , Weser catchment -35 000 km 2 ) using evapotranspiration measurements of micrometeorological stations at the local scale and by comparison to thermal remote sensing informations at the regional scale (Mauser and Schädlich, 1998;Ludwig and Mauser, 5 2000). It provides interfaces to integrate remote sensing derived information into the model. It has been used together with optical and microwave remote sensing data to improve land surface simulations. Bach and Mauser (2003) used the model to improve crop yield prediction and surface runoff prediction by combining PROMET results with 10 optical (Landsat-TM) and microwave (ERS) remote sensing data. Schneider (2003) used LANDSAT-TM data to determine vegetation model parameters and improve plant growth simulations. Loew et al. (2007) compared PROMET simulations at different spatial scales with soil moisture information derived from active microwave data (Loew et al., 2006), and found a good agreement between the spatial patterns of observed 15 and simulated soil moisture at multiple scales.

Antecedent soil moisture simulation
Precipitation information is available on a regular basis from a large number of stations. Simple concepts to derive information on actual soil moisture status, based exclusively on precipitation data, have therefore been developed. One simple approach is based 20 on the concept of the so called Antecedent Precipitation Index (API). As the API is exclusively based on precipitation data as model input, it has been widely used in rainfall-runoff applications to parameterize the soil moisture conditions in hydrological catchments (e.g. Sittner et al., 1969;Rose, 1998;Descroix et al., 2002;Vries and Hromadka, 1993). The API i for day i is defined as HESSD 5,2008 Soil moisture retrieval where P i is the observed precipitation [mm] on day i and γ i is the corresponding API recession coefficient at that day which is used to parameterize the loss of water in the soil column due to evapotranspiration, groundwater recharge and lateral soil water fluxes. Given some information on the antecedent precipitation, one might use the API as a 5 prior proxy for soil moisture conditions on an operational basis as precipitation information is (at least) available in terms of short term forecasts on the global scale. However, large uncertainties in API result from uncertainties in the available precipitation information as well as in the parameterization of the corresponding recession coefficient γ. Different approaches to parameterize γ i have been proposed. Its value might vary 10 in between 0.7 for dry conditions and 1.0 for wet soil conditions (Crow, 2007). An exponential decay of the form γ=e −δ has been proposed, whereas the factor δ is the inverse of the characteristic time of soil moisture depletion. Its value might be empirically calibrated or it might be parameterized using additional information like e.g. the ratio of potential evapotranspiration to maximum available soil moisture (Chodhury et 15 al., 1993;Descroix et al., 2002). In the present study we follow the parameterization proposed by Crow (2007) whereas the variation of γ i is defined as with the parameters A=0.85 and B=0.1 and JD the julian day, which is a very simple approach to roughly estimate the seasonal effects of evapotranspiration loss. The 20 model parameters could be calibrated using available in situ soil moisture data. In order to keep the model as general as possible, no calibration of the model is done for the test site in the present study. The API modelling approach is used in the present study to provide a further prior guess on soil moisture for the SAR based soil moisture retrieval algorithm. Two sets of precipitation data (P ), acquired by two weather stations 25 located approximately 10 km apart, were used to estimate two API series. The first weather station (referred to as Goermin station) was located on the study area (nearby the Goermin village), whereas the second one (referred to as Greisfwald station) was located in the town of Greisfwald. surface soil moisture a linear regression between the TDR measurements, collected at 5 cm depth on field 250, and API was calculated. In a previous study,  have thoroughly investigated the water and energy balance for a winter wheat of the Demmin site (i.e. field 250). In particular, a remarkable agreement between the time series of TDR measurements reported in Fig. 1 and TOPLATS and PROMET predictions, i.e. an rms error better than 4%, was found. However, the objective of this section is to assess the extent to which point scale 10 hydrologic model predictions can represent not only the temporal but also the spatial variability of soil moisture content over the Goermin study area. For this reason, the TOPLATS, PROMET and API predictions have been compared to in situ measurements of volumetric soil moisture content (sampled at a soil depth of between 5 and 10 cm) collected over four different cereal fields during the entire AgriSAR 2006 cam-15 paign (see Fig. 1). In the analysis two sets of meteorological forcing data, acquired by the weather stations located at the Goermin village and at the town of Greisfwald, were employed. For each of the aforementioned simulated data sets, Table 3 reports a comparison with the time series of m v measured in situ. The rms error (∆ i (m v )), the correlation (R) and the parameters of a linear fit between observed (i.e. X ) and 20 modelled (i.e. Y ) soil moisture values are shown. In all but one case, i.e. TOPLATS (Greisfwald), the mean soil moisture values predicted by the models underestimate the observed ones (the bias ranges between 1 and 4%). The effect is more pronounced for simulations based on Goermin than Greisfwald weather data (though, in general, the impact of using meteorological data collected by a station located 10 km a part from 25 the study area seems to be quite limited). The rms error of PROMET and TOPLATS predictions (∆ i (m v )) is always better than 5%, the R-values are higher than 0.8 and the Interactive Discussion slope parameters range between 0.47 and 1.05. API predictions are affected by rms errors larger than 6.0%, while the slope and correlation parameters are lower than 0.3 and 0.55, respectively. Under these circumstances, it is confirmed that API should be regarded as a weak prior proxy for surface soil moisture conditions. Nevertheless, it is worth emphasizing that the API asset is its simplicity and the fact that it requires as 5 input solely precipitation information. On the contrary, SVAT models, such as PROMET and TOPLATS, hold a strong potential to provide quite accurate (i.e. better than 5%) prior estimates of m v , at least at coarse resolution. However, they require significant more information on a specific site as model input (e.g. meteorological data, soil and land cover maps, etc.). A drawback of these findings is that, according to the numerical 10 analysis of Sect. 3.1, the m v prior predictions of PROMET and TOPLATS are too accurate to represent a stringent test-bed for the SAR-retrieval algorithm. For this reason, two further data sets, referred to as perturbed PROMET and perturbed TOPLATS, characterized by a bias and an rms error of approximately 7% and 8%, respectively, have been included in the analysis. These two perturbed data sets have been obtained by 15 subtracting from the m v predictions of the PROMET and TOPLATS models a constant value of approximately 5% (more precisely 4.98%). This choice was aimed at obtaining two data sets affected by biases and rms errors higher than those obtained by means of API but still characterized by high correlations with the m v in situ measurements. Table 4 reports information similar to Table 3 but it refers to the data sets obtained by 20 perturbed PROMET and perturbed TOPLATS (based on meteorological data acquired at the Goermin weather station). Furthermore, Fig. 7 shows the scatterplot between the soil moisture values simulated by all the illustrated modelling approaches, namely the PROMET and TOPLATS (based on meteorological data acquired at the Goermin and Greisfwakd weather stations), the API (based on meteorological data acquired 25 at the Goermin and Greisfwald weather stations) and the perturbed PROMET and TOPLATS (based on meteorological data acquired at the Goermin weather station), and those measured in situ. Figure 7 shows that in general model predictions tend to cluster around a few discrete values whereas the in situ measurements are evenly distributed. In addition, it is observed that the model underestimation is more important for medium-high than for low m v values (similar results were found in .

Experimental assessment of the algorithm performances
The performances of the retrieval algorithm described in Sect. 3 have been assessed 5 on the AgriSAR 2006 data set. Figure 6 shows a flow chart of the implemented algorithm. Ancillary information concerning land cover and soil texture maps as well as the initial guess values for vertical surface roughness (s) and soil moisture content (m v ) are required. Conversely, no a priori information on the correlation length l was used. This is because: 1) it is extremely difficult to provide reliable values of l unless accurate 10 in situ measurements had been carried out; 2) in the inversion procedure, the use of l as a free parameter may allow to better match the observed SAR data with the IEM model. For each run, 3 L-band, HH polarized, E-SAR images, acquired at subsequent dates within a time-span (T ) of 21 days, were employed. As initial guess values for the s parameter a constant value of 1.0 cm was adopted, since all the cereal fields were al- 15 ready sown in April thus showing a fairly smooth surface roughness. Whereas, the data sets listed in Tables 3 and 4 were employed as prior estimates of m v . For each one of the simulated data set, Table 5  2.2%, significantly smaller than the bias reported in Table 3. Whereas, in the HESSD Introduction

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Printer-friendly Version Interactive Discussion case of perturbed PROMET and TOPLATS predictions, the bias reduces from approximately 7% to 1.6% and 4%, respectively; the rms error reported in Table 5, i.e. ∆ f (m v ), is always smaller than the correspondent rms error reported in Tables 3 and 4, i.e. ∆ i (m v ). The best performances, in terms of algorithm gain, are observed when the perturbed PROMET 5 and TOPLATS estimates are used as guess values, in these cases the retrieval algorithm achieves a G parameter of approximately 1.4; the R coefficient is lower (or equal) than the correspondent values shown in Ta non-optimal behaviour of the algorithm is observed in the two cases of API Goermin and API Greisfwald, where the prior estimates were not only biased but also poorly correlated (i.e. R<0.55) with the in situ measurements.
In summary, the experimental analysis substantially confirms the characteristics of 15 the retrieval algorithm as illustrated in Sect. 3.1. Besides, it is worth mentioning that the algorithm showed a strong robustness versus the presence of biases in the prior estimates of m v . Whereas, its performances were significantly lowered when the prior estimates of m v were poorly correlated to the in situ measurements.

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The investigated retrieval algorithm uses prior information on soil moisture content at coarse spatial scale (e.g. 25 km 2 ) in order to transform a temporal series of 3 SAR images, acquired at L-band and HH polarization, into multi-temporal soil moisture maps at high spatial resolution (e.g. 0.01 km 2 ). In the present form, the retrieval algorithm applies to bare and cereal fields only and it has been tested for time series of SAR images 25

HESSD Introduction
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Interactive Discussion acquired over a time-span of three weeks. The results of the experimental analysis, conducted over the data set acquired during the AgriSAR 2006 campaign and based on prior estimates of soil moisture content obtained by means of TOPLATS and PROMET hydrologic models and by means of the API estimator, showed that the algorithm has always a gain (G) greater than 1 thus implying that it always improves the prior infor-5 mation. The best performances, in terms of the G parameter, were observed in the case of perturbed PROMET and TOPLATS predictions, for which the prior information was considerably biased but highly correlated (R≥0.8) with the in situ measurements. In these cases, the algorithm was able to reduce the bias of PROMET and TOPLATS predictions from approximately 7% to less than 2% and 4%, respectively. In addition, 10 the rms error was reduced from approximately 8.2% to 5.6% and from 8.8% to 6.4%.
Conversely, when the prior information was not only biased but also poorly correlated with the in situ measurements (as it is the case of prior information provided by the API estimator) the algorithm marginally improved the initial error. In the intermediate cases, when the prior information was highly correlated with in situ measurements and 15 showed a relatively small bias, the algorithm reduced the bias (e.g. from approximately 4% to 2%) and marginally the rms error (e.g. from approximately 5% to 4%). Nevertheless, also in these cases it was argued that the algorithm can be quite useful in identifying areas characterized by significantly different soil moisture content within the swath area (e.g. 25 km 2 ).

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Future work will be dedicated to apply the technique to PalSAR data and to assess the use of other sources of prior soil moisture values, such as forecasts provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) or m v estimates obtained at coarse scale by spaceborne radiometers (e.g. AMSR-E, or the MIRAS system on board the satellite platform of the forthcoming Soil Moisture and Ocean 25 Salinity (SMOS) Mission). 5,2008 Soil moisture retrieval Toure', A., Thompson, K. P. B., Edwards, G., Brown, R. J., and Brisco, B. G.: Adaptation of MIMICS backscattering model to the agricultural context -wheat and canola at L and C bands, IEEE T. Geosci. Remote, 32, 47-61, 1994. 3484 Ulaby, F. T., Aslam, A., and Dobson, M. C.: Effects of vegetation cover on the radar sensitivity to soil moisture, IEEE T. Geosci. Remote, 20, 476-481, 1982. 3485 5 Vries De, J. J. and Hromadka, T. V.: Handbook of Hydrology, McGraw-Hill, 1424pp., 1993 3502 HESSD 5,2008 Soil moisture retrieval        Fig. 4. L-band, HH polarized E-SAR backscatterin sus in situ measured fresh biomass. Data were wheat field 230 during the entire growing seaso counting for the σ 0 calibration errors, i.e. ± 1 dB geometric model (i.e. y = a 0 x a 1 + a 2 ) for the line) backscatter are also shown. HESSD 5,2008 Soil moisture retrieval  Fig. 2. In situ measurements of volumetric soil moisture content (at 5-10 cm) sampled over four cereal fields (i.e. 230, 250, 440 and 450) and TDR measurements continuously collected over field 250. Fig. 3. L-band E-SAR backscattering coefficient versus in situ measured soil moisture content. Data were acquired over the wheat field 230 during the entire growing season. Error bars accounting for the σ 0 calibration errors, i.e. ± 1 dB, and a fit using a geometric model (i.e. y = a 0 x a 1 + a 2 ) for the HH (continuous line) and V V (dashed line) backscatter are also shown.  Fig. 4. L-band, HH polarized E-SAR backscatterin sus in situ measured fresh biomass. Data were wheat field 230 during the entire growing seaso counting for the σ 0 calibration errors, i.e. ± 1 dB geometric model (i.e. y = a 0 x a 1 + a 2 ) for the line) backscatter are also shown. Fig. 3. L-band E-SAR backscattering coefficient versus in situ measured soil moisture content. Data were acquired over the wheat field 230 during the entire growing season. Error bars accounting for the σ 0 calibration errors, i.e. ±1 dB, and a fit using a geometric model (i.e. y=a 0 x a 1 +a 2 ) for the HH (continuous line) and VV (dashed line) backscatter are also shown. 5,2008 Soil moisture retrieval  Fig. 4. L-band, HH polarized E-SAR backscattering coefficient versus in situ measured fresh biomass. Data were acquired over the wheat field 230 during the entire growing season. Error bars accounting for the σ 0 calibration errors, i.e. ± 1 dB, and a fit using a geometric model (i.e. y = a 0 x a 1 + a 2 ) for the HH (continuous line) backscatter are also shown. Fig. 4. L-band, HH polarized E-SAR backscattering coefficient versus in situ measured fresh biomass. Data were acquired over the wheat field 230 during the entire growing season. Error bars accounting for the σ 0 calibration errors, i.e. ±1 dB, and a fit using a geometric model (i.e. y=a 0 x a 1 +a 2 ) for the HH (continuous line) backscatter are also shown. 5,2008 Soil moisture retrieval   5. Gain of the retrieval algorithm versus initial error on soil moisture content (∆ i (m v )) for measurement errors (∆ s (σ 0 )) ranging from 0.5 to 1.5 dB.

Fig. 5.
Gain of the retrieval algorithm versus initial error on soil moisture content (∆ i (m v )) for measurement errors (∆ s (σ 0 )) ranging from 0.5 to 1.5 dB.