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Using A Priori Information to Improve Soil Moisture Retrieval From ENVISAT ASAR AP Data in Semiarid Regions Francesco Mattia, Member, IEEE, Giuseppe Satalino, Laura Dente, and Guido Pasquariello
Abstract—This paper presents a retrieval algorithm that estimates spatial and temporal distribution of volumetric soil moisture content, at an approximate depth of 5 cm, using multitemporal ENVISAT Advanced Synthetic Aperture Radar (ASAR) alternating polarization images, acquired at low incidence angles (i.e., from 15 to 31 ). The algorithm appropriately assimilates a priori information on soil moisture content and surface roughness in order to constrain the inversion of theoretical direct models, such as the integral equation method model and the geometric optics model. The a priori information on soil moisture content is obtained through simple lumped water balance models, whereas that on soil roughness is derived by means of an empirical approach. To update prior estimates of surface parameters, when no reliable a priori information is available, a technique based solely on the use of multitemporal SAR information is proposed. The developed retrieval algorithm is assessed on the Matera site (Italy) where multitemporal ground and ASAR data were simultaneously acquired in 2003. Simulated and experimental results indicate the possibility of attaining an accuracy of approximately 5% in the retrieved volumetric soil moisture content, provided that sufficiently accurate a priori information on surface parameters (i.e., within 20% of their whole variability range) is available. As an example, multitemporal soil moisture maps at watershed scale, characterized by a spatial resolution of approximately 150 m, are derived and illustrated in the paper. Index Terms—A priori information, ENVISAT, model inversion, retrieval algorithms, synthetic aperture radar (SAR), soil moisture, soil roughness, surface scattering.
I. INTRODUCTION
S
OIL moisture content is a parameter of major importance for land applications at both watershed and regional scale such as hydrology and agriculture (see [1] and [2] for a topical review). In the past, the sensitivity of radar measurements to soil moisture content (via the soil dielectric constant and the soil texture) and to soil roughness was demonstrated through experimental and theoretical studies as in the case of [3] and [4]. The inverse problem of retrieving soil moisture and roughness information from the observed radar response of the surface has also been widely investigated (see [5] for an updated review).
Manuscript received April 15, 2005; revised July 29, 2005. This work was supported in part by the European Space Agency, European Space Research and Technology Centre, under Contract 17011/03/NL/JA and in part by the Ministero delle Politiche Agricole e Forestali under Contract D.M. 209/7303/05. The authors are with the Istituto di Studi sui Sistemi Intelligenti per l’Automazione, Consiglio Nazionale delle Ricerche, I-70126 Bari, Italy (e-mail:
[email protected]). Digital Object Identifier 10.1109/TGRS.2005.863483
Relatively good results (i.e., root mean square errors on volumetric soil moisture content ranging from between 3% and 7%) were obtained, for instance in [6]–[8] by adopting either purely statistical or semiempirical relationships relating synthetic aperture radar (SAR) backscatter and observed soil moisture content. However, the above methods are specific to the site conditions where the relationship was observed and cannot be generalized to different areas. More general results could be achieved, at least in principle, by inverting theoretical direct scattering models, which should be adaptable to drastically different site conditions. Nevertheless, to date the use of SAR data to retrieve soil moisture content has been generally limited. The main reason is the intrinsic difficulty of estimating more than one unknown (i.e., soil moisture, soil roughness, soil texture, etc.) using single-parameter radar measurements as provided by the first generation of spaceborne SAR systems (i.e., ERS, JERS, RADARSAT). Typically, there exists many combinations of surface parameters mapping the same SAR observation. In this sense, the problem is “ill-posed experimentally” and the retrieved soil moisture content is characterized by poor accuracy [9]. The recent launch of the new European ENVISAT system, with the Advanced Synthetic Aperture Radar (ASAR) system onboard, which is able to provide C-band SAR data at two polarizations and at different incidence angles, has certainly improved the scenario. In particular, the higher potential of ASAR system for monitoring environmental parameters relies on its ability to revisit the same site with a relatively short repeating cycle (i.e., between three and seven days in Europe). However, the soil moisture retrieval from ASAR data still remains an ongoing problem. In this respect, a valuable method in improving the accuracy of retrieval algorithms is to constrain the set of their possible solutions by assimilating into the inversion scheme a priori information on geophysical parameters [10], [11]. This is the methodology adopted in this study in order to estimate spatial and temporal distribution of volumetric soil moisture content, at a depth of approximately 5 cm, using horizontal (HH) and vertical (VV) multitemporal C-band ASAR backscatter measurements. The a priori information assimilated in the retrieval algorithm concerns both soil moisture and soil roughness. The former was obtained through simple lumped water balance models, whereas the latter was derived by using an empirical approach. The developed retrieval algorithm finds the “best” solution for this problem by appropriately inverting theoretical direct models. In order to accept a large variability of roughness conditions
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of agricultural fields, two complementary models were used, namely the integral equation method (IEM) model, which is suitable for both smooth and medium rough surfaces, and the geometrical optics (GO) model for very rough surfaces [12]. Two main aspects characterize the present retrieval algorithm: 1) the use of a priori information both on soil moisture and soil roughness and 2) the use of multitemporal SAR information to update prior estimates of surface parameters. The first aspect renders the estimate of soil moisture maps, for dates in which reliable a priori information is available, more accurate, and robust. Conversely, the second aspect is particularly useful in deriving accurate a priori information for dates in which they are not available. In this study, bare or sparsely vegetated soil surfaces were considered, so that the effect of volume scattering can be disregarded. This requirement may not be critical for semiarid sites, where fields are not irrigated and soils are bare or sparsely vegetated for several months in a year. The developed retrieval algorithm was experimentally assessed using multitemporal ground and ASAR data acquired on the Matera site (Italy) in 2003. Soil moisture maps both at summer and winter time were derived and their information content in terms of accuracy and spatial resolution discussed. In Section II, experimental datasets are described. Then in Section III, the retrieval algorithm is illustrated and its error characterized through a simulation study. Subsequently, the methodology adopted in order to obtain and to update a priori information on soil moisture and on soil roughness parameters is detailed. In Section IV, the algorithm is applied to the Matera site and results are discussed. Finally, in the last section the work is summarized and conclusions are given. II. MATERIALS A. Ground Data
Fig. 1. (a) Matera test site in the Basilicata region (Italy). (b) Land cover map of the study area.
The study area is a subcatchment of the Bradano basin and is located close to the city of Matera in the Basilicata region (Italy) [see Fig. 1(a)]. The Bradano basin has a catchment area of approximately 2200 km , while the pertinent subcatchment area in this study covers an area of approximately 110 km . The soil texture of this area is predominantly silty-clay. The topography is characterized by smooth hills and flat valleys and by elevations ranging from between 300 and 600 m. The climate is typical semiarid Mediterranean with an average yearly rainfall of approximately 570 mm and an average temperature which ranges from between 6 C (in January) and 26 C (in July). A land cover map of the study area was obtained by performing a supervised classification of three LANDSAT TM images [see Fig. 1(b)]. Five major classes have been identified: Urban, Cultivated soils, Rocks, Rangeland, and Wood. Cultivated soils cover the largest part of the area (approximately 77%) and the most diffuse cultivation is wheat. According to the local crop management scheduling, the fields are usually cultivated from mid November to mid June while they are bare or sparsely vegetated for the rest of the year. In this respect, the period most suitable in which to validate soil moisture retrieval algorithms at C-band covers the second part of the year (from approximately June to December).
The experimental data employed in this study were collected during a measurement campaign carried out in 2003 simultaneously with ASAR acquisitions. Five fields, with sizes ranging from 3 to 15 ha, were selected in the test area in order to gather information on both soil and vegetation parameters. With regard to the soil, water content and surface roughness measurements were carried out. Soil moisture at a depth of 0–5 cm was measured by means of Kopechy rings. According to the field extension, a number of undisturbed soil samples ranging from between 6 and 10 were collected along a predefined grid. The soil samples were weighted before and after drying in an oven at 105 C for 48 h and then gravimetric soil moisture was computed. As the volume of the rings is known, the bulk density and then the volumetric soil moisture (cubic meters per cubic meter) were obtained. The field average values, expressed in percentage , were employed in this study. The average standard deviation (std) of the volumetric soil moisture estimates, computed considering all the measurements carried out in 2003, was approximately 3%. For the dates analyzed in this study, Table I summarizes the state of the monitored fields, namely fields 1, 2, 3, 5, and 6 (field 4 was too small to be included in this analysis).
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TABLE I STATE
OF THE FIELDS MONITORED IN THE SITE DURING THE 2003 CAMPAIGN
TABLE II ASAR DATA ACQUIRED OVER THE MATERA SITE
MATERA
spacing in range and azimuth of 12.5 and an equivalent number of looks approximately equal to 2. Subsequently the images were temporally filtered [13] preserving the pixel spacing. III. METHODS A. Retrieval Algorithm
Fig. 2. Temporal behavior of volumetric soil moisture content measured over Field 1 (stars) and Field 2 (triangles). Precipitation events are also reported.
As an example, the soil moisture temporal behavior measured during the whole 2003 at Field 1 and Field 2 is shown in Fig. 2, where the precipitation events are also reported. As can be seen, volumetric soil moisture content may range from 30%–35% during winter time to 5%–10% during summer. The relative difference of soil moisture content between the two fields is due to different soil drainage conditions as well as a differing topographic position. The drier field is located on a fairly smooth hill slope while the wetter one is on a flat area at the lowest level of the subcatchment area. The different soil moisture content of the two fields is appreciable during winter and early spring but it becomes negligible in summer and autumn. B. SAR Data The ENVISAT ASAR dataset employed in this study consists of nine alternating polarization single-look (APS) images (see Table II). The images were acquired at HH and VV polarization and at different swaths (i.e., I1, I2, and I3), which correspond to an incidence angle at central swath ranging from 15 to 31 . The main motivations to use IS1/IS2/IS3 swaths for soil moisture retrieval are as follows: 1) low incidence angles maximize the soil contribution with respect to the contribution of vegetation; 2) asymptotic surface scattering models, which are inverted in this paper in order to estimate soil moisture content, at low incidence angles, are affected by significantly smaller ). errors than at high incidence angles (i.e., The 18 ASAR images were calibrated, coregistered, and geocoded. The obtained products were characterized by a pixel
In the following, the physical assumptions underlying this study are reported. A Bayesian argument is used to illustrate the theoretical basis of the adopted soil moisture estimator. Subsequently, its retrieval error is characterized through a simulation study. Preliminary it is worth summarizing our notation. Let us presume the following. — Measurement of the SAR system at each -pixel is a vector
, where the two elements
and are estimates of the backscattering coefficient at VV and HH polarization, respectively. — Geophysical parameters which characterize the soil surface are the complex soil dielectric constant, , the profile height std, , and the correlation length, , associated to the soil surface autocorrelation function (ACF). The ACF is assumed exponential when IEM surface scattering model is used. Whereas it is Gaussian when the GO model is employed (in this case, the roughness parameter, which characterizes the very rough surfaces, is the surface root instead of and mean square (rms) slope independently). The two shapes of the ACF are adopted because smooth and medium rough soils are usually characterized by single-scale exponential ACF. Unlike, very rough soils are often better described by Gaussian ACF (see [6] and [14]). This is true when roughness profiles of only a few meters in length are analyzed. Conversely, roughness statistics of longer profiles usually present multiscale characteristics, which require specific theoretical modeling [15]. However, the use of single- or multiscale roughness description is not very critical for inversion studies as shown, for instance, in [9]. For this reason, the simplest approach has been selected in this study. For the great majority of agricultural soils, the imaginary part , is always much smaller of the soil dielectric constant, . In order to reduce the number of indethan the real part pendent soil parameters, we have approximated the imaginary . part of the soil dielectric constant as
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For each date and each -pixel, the geophysical parameters are represented by a vector random process with three elements
In particular, the soil dielectric constant depends on the soil moisture content and on the soil texture composition. To relate to the volumetric soil moisture the soil dielectric constant of a soil layer, approximately 5 cm thick, the emcontent pirical expression derived by Hallikainen et al. [16] has been employed. This expression models the soil dielectric constant , which can be analytically as a second-order polynomial in inverted. In order to obtain estimates of soil moisture content, the algorithm firstly estimates the real part of soil dielectric constant, then uses the inverted empirical expression of Hallikainen to derive the soil moisture content. To simplify, it will be ascorresponds to estimating sumed that estimating
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TABLE III VARIABILITY RANGES OF IEM AND GO SURFACE INPUT PARAMETERS
likelihood estimator for our estimation problem, is derived succinctly. It may be worth mentioning that in literature there is not a consensus on the statistics of soil parameters such as soil dielectric constant, soil moisture, and soil roughness etc. As a consequence, with regard to these parameters we have adopted a Gaussian pdf that turns out to be the easiest choice from a mathematical point of view. Let us presume the following. 1) Geophysical parameters, which characterize the surface state at -pixel position, are represented by the vector and that a first guess value of this vector is given by , i.e., (2)
In this context, the objective is to find the best estimate of ) soil moisture and soil roughness spatial distribution (i.e., given HH and VV SAR observations (i.e., ) and prior estimates of soil parameters (i.e., ). The latter are needed because SAR observations are affected by errors and are not sufficient in retrieving the correct soil geophysical parameters. In addition, SAR data are not linearly related to geophysical parameters. A , which may also be direct forward theoretical model, i.e., affected by model errors, provides a nonlinear relationship between predicted SAR backscatter and geophysical parameters, . Under these circumstances, the “best” , i.e., for an observed and is subject which inverts to prior estimate of geophysical parameters (both of them are affected by errors), is sought. Using the Bayes’s theorem, conditioned by the the probability density function (pdf) of is observed
is a zero-mean Gaussian uncorrelated error. where subject to a prior estimate is Then the pdf of (3) where
is the diagonal covariance matrix (4)
and the index indicates the transpose operator. 2) There exists a direct forward mathematical model relating the geophysical parameters to the expected surface backscattering. If the model is exact then (otherwise their difference can be modeled by an ). Additionally, SAR observations proerror term vide estimates of the expected backscattering vectors . These estimates are affected by measurement and statistical (i.e., speckle) errors . As a result we have
(1) where
is the pdf of
, given the knowledge of its
is the pdf of , knowing prior estimate , and that the geophysical parameters are . To obtain the “best” es, either the mean or the mode of , timate of which are, respectively, the minimum variance and the maximum-likelihood estimates of , can be used. It is worth mentioning that if the pdf in (1) are Gaussian, the minimum variance and the maximum-likelihood estimators coincide. B. Derivation of Variational Equation In this subsection, the stochastic framework of the problem and explicit definitions of pdf appearing in (1) are introduced. Thus, the variational equation, which provides the maximum-
(5) Under the assumption that both and are zero-mean required Gaussian uncorrelated vectors, the pdf given a in (1), i.e., the probability of measuring a certain geophysical parameter , is given by
(6) where
is the diagonal covariance matrix (7)
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TABLE IV INITIAL RMS ERRORS OF EACH PARAMETER OF THE IEM AND GO MODELS, COMPUTED ON THE DATASET LABELED GUESS MEAN. THE RMS VALUE OF THE m PARAMETER IS OBTAINED BY " USING THE EMPIRICAL RELATIONSHIP OF HALLIKAINEN [16]
Substituting (6) and (3) into (1), the Bayesian likelihood function is obtained as
(8) Since maximizing (8) is equivalent to minimizing , the Bayesian maximum-likelihood for a generic observed and subject to estimator of prior estimate is obtained by minimizing the following functional:
(9) In this study, represents either the IEM or the GO model, both of which predict nonlinear relationships between soil roughness parameters and the backscattering coefficient. As a consequence, an analytical solution that minimizes does not exist. Thus, an iterative approach must be sought in order to minimize the functional in (9). An efficient and is reasonable accurate algorithm employed to minimize the generalized reduced gradient method [17]. When no prior information on the geophysical parameters is available, the pdf in (1) may be modeled as a constant term, which can be dropped (i.e., it is incorporated into in (9) the normalization constant). Then the functional reduces to its first term only, which represents the traditional minimization of the mean square errors between measured and values, i.e., predicted
(10) C. Retrieval Error Characterization Given a SAR observation of the soil surface and a guess value for each surface parameter, it is expected that the above-described minimization algorithm, after some iterations, can fit the SAR measurement and return a set of estimated parameters closer to the true ones. It follows that the error, in terms of discrepancy between estimated and expected parameters, reduces from an initial value (computed on the guesses) to a final value (computed on the output parameter returned by the algorithm). Then the gain that qualifies the retrieval algorithm is the difference between the initial and final error on a given parameter (e.g., soil moisture content).
In this subsection, a simulation study on the impact of measurement, model and a priori information errors on the accuracy of volumetric soil moisture content retrieved using C-band SAR data is carried out. The attention has been focused on two ENVISAT ASAR configurations in which both VV and HH polarizations are acquired either at 23 or at 45 incidence angle. For the sake of comparison, some plots include the European Remote Sensing (ERS) SAR configuration (i.e., VV at 23 incidence angle) and a virtual configuration corresponding to HH and VV polarizations acquired contemporary at 23 and 45 incidence angles. SAR measurements were simulated by the IEM and GO models. Since, GO predictions at HH and VV polarizations are equal, VV polarization only is considered. The selected model input parameters describe a wide range of roughness and moisture conditions, i.e., from smooth to very rough surfaces and from extremely dry to wet soils. In Table III, the variability range of surface parameters are summarized. Under the assumption of a soil texture having clay, sand and silt in equal percentage, the adopted interval approximately corresponds to a volumetric soil moisture content ranging between 3% and 38%. To quantitatively study how measurement, model and a priori information errors propagate on the retrieved parameter accuracy, noisy data of different quality have been simulated. , and For the sake of simplicity, measurement errors, i.e., model errors, i.e., , have been represented as a unique total error, i.e., in (5). Then, the noisy measurements have been obtained by adding to the backscattering values predicted by IEM and GO, a zero-mean Gaussian random noise with increasing standard deviation (std), denoted as , which ranges between 0.5 and 2.0 dB. Four datasets of a priori information characterized by increasing quality have been simulated. The first dataset, labeled as guess mean, endeavors to model the case of absence of any a priori information (i.e., guesses of lowest quality). For each in (2) (i.e., a given surface parameter), the corelement of (i.e., the adopted guess) is equal to responding element of the mean value of its variability range (see Table III). The initial error associated to this dataset has been estimated by computing the rms error between the guess value and the values of corresponding true parameter, as uniformly sampled over their variability range. The initial errors associated to the guess mean dataset are reported in Table IV. The other three datasets of a priori information, referred to as pb30, pb20, and pb10, are characterized by increasing quality in all the surface parameters but in the correlation length. This is because, it seems unrealistic to provide valuable a priori information on correlation length (this issue will be further addressed in Section III-D2). For this reason, the guess value for the correlation length parameter is assumed constant and equal to the
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TABLE V STANDARD DEVIATION ~ USED TO SIMULATE THE GUESS FOR EACH VALUE PARAMETER OF THE IEM AND GO MODELS. THE OF THE m PARAMETER IS ESTIMATED BY " USING THE EMPIRICAL RELATIONSHIP OF HALLIKAINEN [16]
Fig. 4. Inversion of simulated data with a priori information. RMS error of volumetric soil moisture content versus increasing quality levels of a priori information datasets for four different standard deviation of the noise ~ " and for the HH and VV 23 SAR data configuration.
Fig. 3. Inversion of simulated data without a priori information. RMS error of volumetric soil moisture content versus standard deviation of the noise ~ " for different SAR configurations.
mean of its variability range (as in the case of the guess mean dataset). Unlike, the guess values for the other surface parameters, namely the surface height std and the volumetric soil moisture content (or the corresponding dielectric constant ), were obtained by adding to the and true input parameters a zero-mean Gaussian uncorrelated noise (i.e., ), with std . For datasets pb30, pb20, and pb10 the values on and are equal to 30%, 20%, and 10% of the whole variability range of each parameter, respectively (see Table V). It is worth mentioning that for the error on the correlation length parameter the same value displayed in Table IV was employed. Soil Moisture Retrieval Accuracy: In order to better understand the need for introducing a priori information into soil moisture retrieval algorithms, we firstly present in Fig. 3 the behavior of soil moisture estimates obtained by minimizing the cost function (10). This basically corresponds to the retrieval of soil moisture and soil roughness from backscattering values without any a priori information. Fig. 3 shows the rms error of the retrieved volumetric soil as a function of the std of the noise moisture content for different SAR data configurations (VV 23 , HH and VV 23 , HH and VV 23 and 45 ). As can be seen, the rms increases as a function of and decreases going error of from the single-parameter configuration (i.e., ERS, VV and 23 ) to the multiparameter configuration (i.e., HH and VV, 23 and 45 ). When is equal to zero, there is considerable difference between rms errors of the different SAR configurations. However, as soon as increases, the performances of the three configurations tend to get closer and closer. In particular, starting dB the ERS and the ENVISAT configurations are from
characterized by almost the same performances in terms of rms (i.e., ). Since it is unrealistic to have total error on error budget significantly smaller than 1.0 dB, a priori information needs to be assimilated into the retrieval algorithm to improve the accuracy of retrieved soil moisture. The attention is now focused on the performances of the retrieval algorithm using a priori information obtained by minimizing the function in (9). The diagonal terms of the covariance and have been set equal to the variance of matrixes and of the noise , respectively. For the SAR the noise configuration at HH and VV polarization and at 23 incidence angle, Fig. 4 shows the rms error of the retrieved volumetric soil as a function of the guess quality level (remoisture content of the noise . On lated to the std ) for different std the figure, the initial guess rms errors are also shown. When the dataset of a priori information pb30 is used, the plots show that reduces from approximately 9.6% to the initial rms error of dB). This rms error can the final rms error of 5.9% (at be further reduced by using backscattering with a lower noise dB) or by using a priori informalevel (for example tion with a higher quality level (for example pb10). In the first rms error reduces by up to 4.4%. In the second case, the case, it decreases to 2.8%. This means that the quality level of the a priori information is the main factor that can significantly . A direct comparison reduce the rms error of the retrieved of Figs. 3 and 4 is also useful. For instance, Fig. 4 shows that by using a medium quality dataset of a priori information (i.e., is less than 4.5% (at dB). pb20), the rms error of Whereas, Fig. 3 shows that using no a priori information the cor. Additionally, if the measureresponding rms error is ment/model error in Fig. 4 doubles from 1 to 2 dB, the rms error increases by up to 5.1%. Unlike, under the same circumon stances, in Fig. 3 the rms error on goes up from 6.7% up to 8.4%. In other words, the use of a priori information makes the soil moisture retrieval algorithm both more accurate and more robust with respect to measurement/model errors. Fig. 5 shows the same plot as Fig. 4, but at a 45 incidence angle. Results shown in Figs. 4 and 5 are in substantial agreement though slightly higher errors are found at 45 than at the 23 incidence.
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Fig. 5. Inversion of simulated data with a priori information. RMS error of volumetric soil moisture content versus increasing quality levels of a priori information datasets for four different standard deviation of the noise ~ " and for the HH and VV 45 SAR data configuration.
Fig. 7. Volumetric soil moisture content values predicted by the Thornthwaite-type water-balance model over a four-year period and over 2003 only, compared with averaged experimental values measured in different ground campaigns over the Matera site.
D. How to Derive A Priori Information
Fig. 6. Scatter plot of retrieved versus expected volumetric soil moisture content m . Simulated data at HH and VV polarization, 23 incidence angle, noise = 1 dB, and a priori information dataset equal to pb20.
Fig. 6 shows the scatter plot of values for the configuration HH and VV at 23 incidence angle, a noise of 1.0 dB and initial guess values correspondent to a priori information described by the dataset pb20 are employed. The results of a linear fit between expected and retrieved soil moisture values are reported. is less In summary, provided that the total error budget than 1.5 dB, and that the a priori information for soil moisture is correct within 20% of their whole variability range, the can be estimated with a volumetric soil moisture content rms error of approximately 5% by using HH and VV C-band SAR data either at 23 or at 45 incidence angle. However, it is worth underlining that currently available surface scattering models are prone to larger errors at high than at low incidence angles. Additionally, at low incidence angles (i.e., at 23 incidence) we have gathered much more knowledge on the relationship between surface backscattering and soil parameters than at high incidence angles. This is due to the numerous ground campaigns carried out during ERS-1/2 missions (this aspect is particularly important in obtaining a priori information on surface roughness as will be illustrated in Section III-D2). In Section III-D, the issue of how to derive such a priori information on soil moisture and soil roughness will be addressed.
1) Soil Moisture: The Thornthwaite-type monthly water balance models [18]–[20] are useful tools, albeit extremely simple, and often employed to approximately predict soil water content at watershed or regional scale. These are lumped conceptual models, which predict seasonal steady state allocation of water among various components of the hydrologic system. Inputs to the model are monthly temperature and precipitation. Outputs include monthly potential and actual evapotranspiration, soil moisture storage and runoff. A basic version of Thornthwaite-type model, described by Dingman [21], has been here adopted. The Thornthwaite-type model was initially run over four subsequent years (from 2001 to 2004), using the corresponding temperature and precipitation data measured by a local ground station. For each month, the average and the std of predicted soil moisture values were calculated. Subsequently, temperature and precipitation data, relating exclusively to 2003, were used as model inputs. Fig. 7 compares the monthly soil moisture predictions averaged over the four-year period (the error bar represents the estimated std) to those referring only to 2003. As can be seen, the two series are in reasonable accordance in both spring and summer while in autumn and winter the accordance is poor. The variability of the predicted volumetric soil moisture values is more significant in winter, spring and autumn, than in summer. If we express the estimated seasonal variability of volumetric soil moisture as a percentage of its whole variability range (typically assumed to be from 3%–40%), then during summer the observed variability corresponds to approximately 12% of the whole range while during the rest of the year it is approximately 30%. In order to assess as to what extent the Thornthwaite-type model accurately predicts the actual soil moisture content values over the Matera site, the experimental values measured during ground campaigns held in 1998, 2001, 2003, and 2004 are also included in Fig. 7. Volumetric soil moisture values, measured
MATTIA et al.: USING A PRIORI INFORMATION TO IMPROVE SOIL MOISTURE RETRIEVAL
at field scale, were averaged to obtain approximate estimates at watershed scale. It is worth mentioning that these estimates are extrapolations, which are possibly affected by significant errors (not yet characterized). This is due to the fact that the aforementioned ground campaigns were not planned to obtain monthly estimates of soil moisture content at watershed scale but were aimed at studying the behavior of radar response as a function of surface parameters measured at field scale. Consequently, the utmost care should be taken in interpreting these experimental data. Despite the simplicity of Thornthwaite-type models, Fig. 7 shows a reasonably good level of accordance between model predictions averaged over the four-year period and experimental values from winter to summer while an underestimation is observed during autumn starting from September. Conversely, soil moisture estimates referring to 2003 only are in poor accordance with experimental data for the whole year except for the summer period. This is due to the fact that Thornthwaite-type model predictions made on the basis of one year alone are highly instable and thus, they can be considered not reliable. To summarize, previous results indicate that, over the Matera site, water-balance model predictions of soil moisture content, averaged over several years, may be considered reliable and with a reduced annual variability (i.e., approximately 10% of the whole volumetric soil moisture variability range) during summer. In winter and spring they are affected by a high annual variability, though their averages are in overall good accordance with measurements. Conversely, in autumn water-balance model climatic averages not only significantly underestimate experimental results but are also affected by a high annual variability. 2) Soil Roughness: As reported in Section III-A, the adopted soil roughness description consists of two parameters, namely the surface height std and correlation length . While some work has been done in the past to relate with land cover/use variables (see for instance [22]), there is a lack of knowledge on how to provide a priori information on . This is due to the fact that values show unpredictable behavior. They are extremely variable not only among differing fields but also within the same, visually homogeneous, field [23]. Additionally values often depend highly on the length of the profile over which are estimated. Conversely, estimates are relatively stable within an agricultural field and they are less sensitive to the profile length over which they are estimated [24]. As a result, in this approach the a priori information on is provided only. The effect of this lack of a priori information on has been taken into account in the simulation study in Section III-C where it was assumed to have almost no a priori information on the parameter. To obtain initial guess values on , a statistical relationship between backscattering coefficient at VV and 23 incidence angle and was derived. This was accomplished by employing a database of ground and ERS SAR data, acquired on Matera (I), Marestaing (F), and Middle Zeeland (NL) sites, in the framework of an ESA study-contract [25]. To further increase the record of cases, this database was widened by adding new ground and ASAR backscatter data subsequently gathered from the Matera site. The obtained results are shown in Fig. 8. Two
Fig. 8.
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versus s for ground data acquired over different European sites.
regression curves have been derived. The first one concerns wet higher than 20%) while the second and very wet soils (i.e., smaller than one concerns dry and medium-wet soils (i.e., 15%). For the first curve a reasonably low correlation coeffiwas found, in contrast, the second curve cient . demonstrated a more than satisfactory result Due to the limited number of points and to their relative scatter, the overall statistical significance of these curves (in particular, the first) is quite poor. As a consequence, their predictions are certainly affected by significant errors. However, they are used in this study as a simple way of obtaining first guess values regarding surface roughness. Whether or not the curves can provide sufficient information on the soil roughness state will be inferred a posteriori by analyzing the retrieval algorithm results. To summarize: 1) For a semiarid site, such as Matera, a priori information on volumetric soil moisture content for a given date can be derived by using monthly average predictions of a simple Thornthwaite-type water balance model. These estimates are valid at watershed scale and are reliable at least during some months of the year (i.e., summer). estimate, a guess value for 2) On the basis of this first the surface roughness (i.e., profile height std: ) can be derived at pixel scale, by using the regression functions described above. 3) The retrieval algorithm represented by (9) can then be run and the spatial distribution of soil moisture and soil roughness obtained. E. How to Update A Priori Information A major problem of the so far described algorithm is that it can function solely for very limited periods (when prior estimates are known with sufficient accuracy). The gain in volumetric soil moisture accuracy obtained by using this algorithm may be considered as being rather low. The algorithm requires initial soil moisture estimates with an accuracy of approximately 7% and eventually provides “refined” estimates with an accuracy of 5%. Even though, the algorithm provides soil moisture estimates at a much higher spatial resolution than the initial ones (this may be considered a further gain factor), the performance of such an algorithm could be not sufficient to warrant further attention.
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A strong improvement would certainly consist of extending its use to longer periods and particularly to those for which a priori estimates are not reliable. In order to accomplish this, a procedure to update reliable maps of surface parameters, obtained at a given date, to a subsequent date using multitemporal VV backscatter information only, was devised. In many cases, this was possible because soil moisture and soil roughness have a different spatial-temporal behavior at watershed scale. While soil moisture content is usually characterized by smooth changes in space and abrupt changes in time, soil roughness may drastically change spatially though it is relatively constant in time [26]. This makes it possible to seek for soils preserving their roughness state, between two subsequent dates, while changing their moisture content. Under these circumstances, it is expected that there is a significant correlation between the backscatter of fields having the same roughness state in the two dates. This is indeed the property we have employed to firstly retrieve roughness information on a certain number of soils for a date with no reliable a priori information. Then it is fairly simple to update soil moisture estimates by inverting appropriate direct models. Finally, this information is used as initial guess values for the retrieval algorithm. The main steps of the implemented procedure are: 1) the series of VV backscattering values of soils characterized by similar roughness states is selected on the first image (for which reliable moisture/roughness maps are available); 2) the series of VV backscattering coefficient, corresponding to the same soil locations on the first image, is selected on the second image; 3) the correlation between the two series of backscattering values is computed. For correlation values higher than a certain threshold it is concluded that the set of soils on the first and second images have the same roughness state (though the moisture state of the second image may be different); 4) the moisture content of selected soils on the second image is estimated assuming that their roughness state is known and appropriately inverting IEM/GO model. be The processing strategy is illustrated in Fig. 9. Let the reference VV image, acquired at time and the corresponding image acquired at time . They have been firstly temporally filtered, as reported in Section II-B, then spatially filtered, using a mean filter over a 7 7 window. The spatial filter is necessary in order to reduce as much as possible, the speckle and is an estimate as acnoise so that each pixel value of curate as possible of the backscattering coefficient. The size of the applied window is limited by the typical size of agricultural fields in the area. The following are the main procedural steps: • selecting on the locations corresponding to most ; frequent couple of soil roughness values • computing, for all pixels belonging to , the correlation between and ; • if is greater than a given threshold , computing for the pixels of the mean backscattering coefficient and assume that it corresponds to a homogeneous surface ; (if is less with roughness parameters equal to than restarting the procedure with new values); , inverting • assuming known the roughness state value corIEM (or GO direct models) to retrieve the
Fig. 9. SAR updating processing procedure.
responding to . The obtained value is the updated guess soil moisture value for the image acquired on date . Normally, the threshold value is set between 0.7 and 0.75. couple that satisfies the above However, if there is no condition, the threshold is progressively lowered to a minimum value of 0.3. In particular, when different swaths are used for the first and the second image the obtained correlation values are usually lower than when the images are acquired at the same geometry. Of course, there is no guarantee that the above-described procedure (from now on referenced to as SAR updating) will converge. It may happen that correlation values are so low value predicted by that, after a certain number of loops, the the water-balance model is adopted as an initial guess value. IV. RESULTS Fig. 10 compares the temporal behavior of a priori informaas obtained by using the water balance model and the tion on
MATTIA et al.: USING A PRIORI INFORMATION TO IMPROVE SOIL MOISTURE RETRIEVAL
Fig. 10.
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Volumetric soil moisture values at watershed scale. TABLE VI CORRELATION VALUES BETWEEN SAR IMAGES OBTAINED BY RUNNING THE SAR UPDATE PROCEDURE Fig. 11. Measured versus retrieved volumetric soil moisture over the experimental fields in Matera, plotted per field.
SAR update procedure. Additionally, experimental values, referring to volumetric soil moisture measurements averaged over all the five fields monitored during the campaign, are shown. as proDuring the first three dates, a priori information on vided by the water balance model only has been used. This is because, in this period the most important part of wheat phenological cycle (i.e., heading, ripening and finally harvesting) is concentrated, so that the majority of agricultural surfaces, on the Matera site, were not sufficiently stable in time to allow for the use of the “SAR update” procedure. Conversely, from October were obtained through to December a priori information on the SAR update procedure. As can be seen in Fig. 10, the error between SAR update estimates and experimental values is always less than 7% (i.e., 20% of the whole soil moisture varibetween ability range). In Table VI, the correlation values SAR images obtained by running the SAR update procedure are reported. values are significantly higher when calculated between the same swaths than between different swaths. On the same table, the size of area A, corresponding to the image locadefined in Section III-E, is reported, for each date, both tions as a percentage of the total subbasin area and as correspondent hectares. at watershed scale have been Once the prior estimates of obtained, the initial guess estimates of roughness parameters are derived using the regression functions illustrated in Section III-D2. Subsequently, the inversion algorithm, synthesized by (9), is run. The overall measurement error at HH and VV polarizations (i.e., the terms of the covariance matrix in (7)) has been set between 0.5 and 0.75 dB depending on the direct model used. Whereas the error characterizing the a priori information on geophysical parameters (i.e., the terms of the covariance matrix in (4) are 0.45 cm for , 5.48 cm for and 3.4 on dielectric constant (this corresponds to approximately 6.8% as error
Fig. 12. Measured versus retrieved volumetric soil moisture over the experimental fields in Matera, plotted per date.
on ; see Table V). In Fig. 11, the scatter plot of measured values for each field is shown. The total versus retrieved rms error on is 4.58%. On the same figure, the linear fit between measured and retrieved values was reported. Measured volumetric soil moisture values were considered to have been affected by an average error of 3%. As a result, the linear fit and a slope of . This estimates a bias of indicates the existence of a slight bias of estimates toward lower soil moisture values. In order to better interpret the results, the same scatter plot has been displayed in Fig. 12 as a function of the acquisition date (i.e., DoY). In the first date (DoY 115) there are two points, which were considerably underestimated. They refer to fields 5 and 6 in April 2003, when they were wheat vegetated fields at the heading stage (i.e., full growth stage). For these fields the
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TABLE VII RMS ERROR OF THE VOLUMETRIC SOIL MOISTURE VALUES ESTIMATED ON THE MATERA EXPERIMENTAL FIELDS
Fig. 13.
(a). Soil moisture maps of the Matera subcatchment in July 2003. (b). Soil moisture maps of the Matera subcatchment in December 2003.
presence of vegetation has an important impact on backscattering response thus inducing a significant error on the retrieved value corresoil moisture values. The same holds for the sponding to field 2 in June (DoY 169). On this date, field 2 was a gram vegetated field at an advanced stage so that the vegetation effect could not be neglected. for each date is reported. In Table VII, the rms error on The highest error is obtained in April, when two out of five fields were vegetated, while the smallest error is found in July, when volumetric soil moisture was low over the whole site. As a final step, volumetric soil moisture maps were derived, values refrom summer to winter time, by smoothing the trieved at pixel scale. The spatial resolution estimated on the obtained maps is approximately 150 m. In Fig. 13(a) and (b), volumetric soil moisture maps, which correspond to July 4 and December 10 are shown, respectively. Classes such as urban, rocks and woods have been masked. As can be seen, in July the subcatchment study area shows low (i.e., between 5% and 10%) and quite uniform volumetric soil moisture values. Conversely, the second map shows a typical
situation of winter time, where volumetric soil moisture content has an average value of approximately 30%. In Fig. 13(b) it is evident that there are a few drier patches and that they are not randomly distributed, rather they are concentrated in same areas likely related to site topography. Future work will be dedicated to better investigating the information content of these maps and how to integrate this information into regional ecological land process models.
V. CONCLUSION The developed algorithm demonstrates that by using a constrained optimization technique, which appropriately assimilates a priori information on soil parameters, it is feasible to retrieve volumetric soil moisture maps, with an rms error of approximately 5%, from HH and VV SAR backscatter, provided sufficiently accurate (i.e., within 20% of their whole variability range) a priori information on surface soil parameters is available.
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The paper shows that over a semiarid site such as Matera, it is relatively easy to obtain a priori estimates of soil moisture content during summer time. In contrast, it may be quite difficult to obtain reliable estimates of soil parameters during autumn, winter or spring. An important issue raised in this work is how to convey information on surface parameters from a certain date to a subsequent one. The solution suggested here consists of using actual multitemporal SAR observations. In this respect, a remark which stems from this study is that the main contribution of SAR data to soil moisture monitoring is probably through their multitemporal information content. In other words, if dense series of multitemporal SAR images are available (here dense refers to a site-dependent time-lag such that a consistent number of fields did not undergo roughness changes between the SAR acquisitions), then it is feasible to drastically improve soil moisture predictions with respect to a priori information. Conversely, when single or sparse SAR acquisitions are available, the accuracy of soil moisture retrieved from the SAR observations is normally expected to be slightly better than that of the required a priori information. As main limitations of this work two aspects need to be mentioned. Firstly, the use of C-band SAR data requires restricting the study to bare or sparsely vegetated soils. In some specific cases, this limitation may be relaxed introducing further information from volume scattering models, however in general it remains valid. Secondly, the use of a priori information on soil moisture content at watershed scale is well suited to semiarid sites where fields are not irrigated. However, it is not realistic when dealing with intensively cultivated sites where irrigation is a common practice. Future work will be dedicated to applying this algorithm to other sites and to longer multitemporal series of SAR data. In this respect, it will be investigated later as to what extent this approach can be also applied to temporal series of ERS SAR data. ACKNOWLEDGMENT The authors are indebted to T. Le Toan and M. Davidson for their continuous help and valuable remarks, which greatly contributed to the improvement of the paper. Additionally, the authors wish to thank U. Wegmuller for providing a temporary licence of Gamma Remote Sensing Research and Consulting AG Software package and ESA for supply of SAR data in the framework of ENVISAT AO 662. Finally, the authors wish to thank H. Rott and two anonymous reviewers for their useful comments and contribution to the amelioration of the work. REFERENCES [1] T. J. Schmugge, W. P. Kustas, J. C. Ritchie, T. J. Jackson, and A. Rango, “Remote sensing in hydrology,” Adv. Water Resour., vol. 25, no. 8–12, pp. 1367–1385, Aug.–Dec. 2002. [2] H. McNairn and B. Brisco, “The application of C-band polarimetric SAR for agriculture: A review,” Can. J. Remote Sens., vol. 30, no. 3, pp. 525–542, Jun. 2004. [3] L. Tsang, J. A. Long, and R. T. Shin, Theory of Microwave Remote Sensing. New York: Wiley, 1985.
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[4] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive. Dedham, MA: Artech House, 1986, vol. 3. [5] M. S. Moran, C. D. Peters-Lidard, J. M. Watts, and S. McElroy, “Estimating soil moisture at the watershed scale with satellite-based radar and land surface models,” Can. J. Remote Sens., vol. 30, no. 5, pp. 805–826, Oct. 2004. [6] Y. Oh, K. Sarabandi, and F. T. Ulaby, “An empirical model and an inversion technique for radar scattering from bare soil surfaces,” IEEE Trans. Geosci. Remote Sens., vol. 30, no. 2, pp. 370–382, Mar. 1992. [7] P. C. Dubois, J. J. Van Zyl, and E. T. Engman, “Measuring soil moisture with imaging radar,” IEEE Trans. Geosci. Remote Sens., vol. 33, no. 4, pp. 195–926, Jul. 1995. [8] S. Le Hegarat-Mascle, M. Zribi, F. Alem, A. Weisse, and C. C. Loumagne, “Soil moisture estimation from ERS/SAR data: Toward an operational methodology,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 12, pp. 2647–2658, Dec. 2002. [9] G. Satalino, F. Mattia, M. Davidson, T. Le Toan, G. Pasquariello, and M. Borgeaud, “On current limits and future perspectives of soil moisture retrieval from C-band SAR data,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 11, pp. 2438–2447, Nov. 2002. [10] A. Lorenc, “Analysis methods for numerical weather predictions,” Q. J. R. Meteorol. Soc., vol. 112, pp. 1177–1194, 1986. [11] A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia, PA: Soc. Indust. Appl. Math., 2005. [12] A. K. Fung, Microwave Scattering and Emission Models and Their Applications. Norwood, MA: Artech House, 1994. [13] S. Quegan, T. Le Toan, J. J. Yu, F. Ribbes, and N. Floury, “Multi-temporal ERS SAR analysis applied to forest mapping,” IEEE Trans. Geosci. Remote Sens., pt. 1, vol. 38, no. 2, pp. 741–753, Mar. 2000. [14] M. W. J. Davidson, T. Le Toan, F. Mattia, G. Satalino, T. Maninnen, and M. Borgeaud, “On the characterization of agricultural soil roughness for radar remote sensing studies,” IEEE Trans. Geosci. Remote Sens., vol. 38, no. 2, pp. 630–640, Mar. 2000. [15] F. Mattia, T. Le Toan, and M. Davidson, “An analytical, numerical and experimental study of backscattering from multiscale soil surfaces,” Radio Sci., vol. 36, no. 1, pp. 119–119, 2001. [16] M. T. Hallikainen, F. T. Ulaby, M. C. Dobson, M. A. El-Rayes, and L. K. Wu, “Microwave dielectric behavior of wet soil. Part I: Empirical models and experimental observations,” IEEE Trans. Geosci. Remote Sens., vol. GE-23, no. 1, pp. 25–34, Jan. 1985. [17] L. S. Lasdon, A. D. Waren, A. Jain, and M. Ratner, “Design and testing of a generalized reduced gradient code for nonlinear programming,” ACM Trans. Math. Softw., vol. 4, no. 1, pp. 34–50, Mar. 1978. [18] C. W. Thornthwaite, “An approach toward a rational classification of climate,” Geograph. Rev., vol. 38, pp. 55–94, 1948. [19] W. R. Hamon, “Estimating potential evapotranspiration. Journal of the hydraulics division,” Proc. Amer. Soc. Civil Eng., vol. 87, pp. 107–120, 1961. [20] J. R. Mather, “Use of the climatic water budget to estimate streamflow,” in Use of the Climatic Water Budget in Selected Environmental Problems, J. R. Mather, Ed: Publications in Climatology, 1979, vol. 32, pp. 1–52. [21] L. Dingman, Physical Hydrology. Upper Saddle River, NJ: PrenticeHall, 2001. [22] T. J. Jackson, H. McNairn, M. A. Weltz, B. Brisco, and R. Brown, “First order surface roughness correction of active microwave observations for estimating soil moisture,” IEEE Trans. Geosci. Remote Sens., vol. 35, no. 4, pp. 1065–1069, Jul. 1997. [23] F. Mattia, T. Le Toan, J. C. Souyris, G. De Carolis, N. Floury, F. Posa, and G. Pasquariello, “The effect of surface roughness on multifrequency polarimetric SAR data,” IEEE Trans. Geosci. Remote Sens., vol. 34, no. 4, Jul. 1997. [24] F. Mattia, M. W. J. Davidson, T. Le Toan, C. M. F. D’Haese, N. E. C. Verhoest, A. M. Gatti, and M. Borgeaud, “A comparison between soil roughness statistics used in surface scattering models derived from mechanical and laser profilers,” IEEE Trans. n Geosci. Remote Sens., vol. 41, no. 7, Jul. 2003. [25] M. Davidson, T. L. Toan, T. Manninen, P. Borderies, I. Chenerie, S. Rouvier, E. Bachelier, F. Mattia, and G. Satalino, “Final report: Retrieval algorithms for active remote sensing,” ESA-ESTEC, Noordwijk, The Netherlands, Tech. Rep. 12 008/96/NL/NB, 2000. [26] A. Ceballos, K. Scipal, W. Wagner, and J. M. Fernandez, “Validation of ERS scatterometer-derived soil moisture data in the central part of the Duero Basin, Spain,” Hydrol. Process., vol. 19, pp. 1549–1566, 2005.
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Francesco Mattia (M’99) received the laurea degree (cum laude) in physics and the Master’s degree in signal processing from the University of Bari, Bari, Italy, and the Ph.D. degree from the University Paul Sabatier, Toulouse, France. From 1991 to 1992, he was a Graduated Fellow of the Italian National Research Council (CNR), Matera, Italy, working on scattering from artificial and natural targets. From 1993 to 1994, he was a Marie Curie Grantholder of the European Commission at the Institute for Remote Sensing Applications of the Joint Research Centre, Ispra, Italy, working on the analysis of polarimetric SAR data. In 1995, he joined the CNR as a Research Staff Member. From 1996 to 1999, he was a Visiting Scientist at the Centre d’Etudes Spatiales de la Biosphere (CESBIO), Toulouse, France, for two months per year. His main field of interest is the direct modeling of scattering from natural surfaces and the retrieval of surface parameters from SAR data.
Giuseppe Satalino received the laurea degree in computer science (cum laude) from the university of Bari, Bari, Italy, in 1991. In 1991, he was a “summer student” with the European Organization for Nuclear Research (CERN), Geneva, Switzerland, where he worked on applications of neural networks to high-energy physics. Since 1993, he has been with the Institute for Signal and Image Processing (IESI, and now named ISSIA), Italian National Research Council (CNR), Bari, Italy. His main research field concerns neural networks for data classification and digital image processing, and he has participated in several national and international research projects working on fields including remotely sensed data classification techniques, phase unwrapping methods, and geophysical parameter retrieval from SAR data by backscattering model inversion.
Laura Dente received the laurea degree (cum laude) in physics from the University of Bari, Bari, Italy, in 2000. She collaborated until the end of 2000 with the Remote Sensing Group, University of Bari on the analysis of acquired and simulated data of Cassini Radar. In 2001, she was a Software Engineer at Advanced Computer Systems (Italy), developing software for SAR image processing. In 2002, she was Young Graduate Trainee at ESA-ESTEC, working on soil moisture retrieval from a time series of ERS SAR images. Since 2003, she has been with the Istituto di Studi sui Sistemi Intelligenti per l’Automazione, Italian National Research Council, Bari. Her main interests are microwave scattering from vegetated and bare soils and retrieval of biogeophysical parameters from SAR images.
Guido Pasquariello received the doctor degree in physics from the University of Bari, Bari, Italy, in 1975. In 1976 he joined the Tecnopolis CSATA, Valenzano, Italy, where he worked in the field of statistical data analysis. From 1977 to 1978, he was a Scientific Fellow with the Commission of European Communities at the Central Bureau for Nuclear Measurements (CBNM), Geel, Belgium. From 1978 to 1980, he was with the National Laboratory of Frascati, Italian Institute of Nuclear Physics (INFN), Rome, Italy. Since 1980, he has worked on various problems in statistical pattern recognition. From 1980 to 1985, he was with the Tecnopolis CSATA, Bari, Italy, where he was Project Leader of projects related to the classification of satellite remote sensing images. Since 1985, he has been a Senior Scientist at the Institute for Signal and Image Processing (IESI, and now named ISSIA), Italian National Research Council (CNR), Bari, Italy. His research interests include application of artificial intelligence tools and neural networks to digital image processing in the field of image understanding, remote sensing, and medical data. He has participated in various airborne SAR experiments in Europe, such as AGRISAR 86, AGRISCAT 87, Maestro-1, AVIOSAR 580, as well as the first ERS-1 Pilot Projects and the airborne image spectrometer EISAC-JRC campaign. Dr. Pasquariello is a Member of International Users Committee of Vegetation Programme.
