Statistics of in situ soil moisture measurements
Soil moisture, defined as the water content in the upper layer of soil, is the hydrologic variable that controls the interactions (and feedbacks) between land surface and atmospheric processes (Hossain and Anagnostou, 2005). Soil moisture is important in the distribution of precipitation between runoff and infiltration (Baghdadi et al., 2006). Soil moisture monitoring and characterization of the spatial and temporal variability of soil moisture at scales from small catchments to large river basins is important in the understanding of subsurface – land surface – atmospheric interactions as well as, drought analysis, crop yield forecasting, irrigation planning, flood protection, and forest fire prevention (Georgakakos and Baumer, 1996, Robock et al., 2003). Surface soil moisture distribution information is a critical forcing variable in many Soil Vegetation Atmosphere Transfer (SVAT) models to estimate profile soil moisture at daily time steps. Soil moisture distribution also plays a key role in the prediction of erosion and sediment loads in watershed streams and ponds. In arid and semi-arid watersheds soil moisture content has been used as a surrogate indicator of general plant health (Moran et al., 2004).
Research in the extraction of soil surface moisture information from remotely sensed imagery has been an important research topic in the last decade. Optical remote sensing data have been used successfully for mapping and monitoring relative variations in soil moisture when reflective data are combined with thermal data from the same sensors (e.g., Carlson et al., 1995, Lambin and Ehrlich, 1996, Gillies et al., 1997, Hossain and Easson, 2008& 2006). Microwave remote sensing techniques provide a direct measurement of the surface soil moisture for a range of vegetation cover conditions within reasonable error bounds (Jackson, 2002). Passive microwave remote sensing uses radiometers that detect and measure the natural thermal microwave emissions of a particular frequency, within a narrow band. This measurement provides the brightness temperature, which includes contributions from the atmosphere, reflected sky radiation, and the land surface. The Advanced Microwave Scanning Radiometer - Earth Observing System (AMSR-E) sensor on NASA's Aqua satellite and the Soil Moisture and Ocean Salinity (SMOS) mission of European Space Agency (ESA) are the two major currently operating passive microwave sensors dedicated to soil moisture mapping. Active microwave sensors produce energy and measure the amount of energy returned from the target to yield a variable called the backscattering coefficient (o or βo). The backscattering coefficient is related to the surface reflectivity, which is used to determine surface soil moisture (Ulaby et al., 1986). Radarsat 2 Synthetic Aperture Radar (SAR), ENVISAT Advance Synthetic Aperture Radar (ASAR) and Advanced Land Observing Satellite (ALOS) Phased Array Type L-band Synthetic Aperture Radar (PALSAR) are the most widely used currently operating spaceborne active microwave sensors.
This chapter provides a brief overview of active microwave soil moisture remote sensing and presents a case study of soil moisture mapping in a semi-arid environment. The overview of active microwave soil moisture remote sensing includes a discussion of the basic principles of microwave remote sensing emphasizing soil surface moisture information extraction and different methods for soil moisture estimation using SAR data with emphasis on the existing algorithms for SAR based soil moisture mapping in semi-arid environment. The case study presents research in southeastern New Mexico that explored the linear and the non-linear relationships between radar reflectivity (backscatter) and soil moisture and determined the impact of vegetation in soil moisture estimation.
1.1. Basic Principles of Synthetic Aperture Radar (SAR)
RADAR (RAdio Detection And Ranging) sensors operate in the microwave portion of the electromagnetic spectrum beyond the visible and thermal infrared regions. Imaging radars are generally considered to include wavelengths from 1 mm to 1 m. RADAR is an active sensor, transmitting a signal of electromagnetic energy, illuminating the terrain, and recording or measuring the response returned from the target or surface. Thus, the term “active microwave” is often synonymous with radar (Henderson and Lewis, 1998). As an active sensor, radars are independent of the sun and sun conditions and can operate day or night. Radar can, in effect, collect data on a 24 hour basis. Unlike optical sensors, imaging radars are not affected by cloud or haze and operate generally independent of weather conditions.
Traditionally (before 1978) radar imaging was conducted using Real Aperture Radar (RAR) systems. RAR transmits a narrow angle beam of pulse radio wave in the range direction at right angles to the flight direction (called the azimuth direction) and receives the backscatter from the targets, which is transformed into a radar image from the received signal. Aperture is the opening used to collect the reflected energy used to form an image. In the case of radar imaging the aperture is the antenna and for RAR systems, only the amplitude of each echo return is measured and processed. The spatial resolution of a RAR system is mainly determined by the size of the antenna. For any given wavelength, the larger the antenna the better the spatial resolution. It is difficult to attach large antenna to aircraft or spaceborne sensor systems. For example a 1 km diameter antenna is needed in order to obtain 25 m resolution with L band (λ=25 cm) at a distance of 100 km from a target.
In order to overcome this limitation, radar systems with a synthetic aperture have been developed, which simulate an artificial (or virtual) antenna. Synthetic Aperture Radar (SAR) takes advantage of the Doppler history of the radar echoes generated by the forward motion of the spacecraft to synthesize a large antenna, enabling high azimuthal resolution in the resulting image using a physically small antenna and longer radar wavelength.
Active Microwave Region in EMS
The microwave portion of the Electromagnetic Spectrum (EMS) is large, relative to the visible, and there are several wavelength ranges or bands used in radar imaging. Imaging radar systems operate at specific wavelengths or frequencies in the EMS. The active microwave regions include X, C, L and K band, which refers to specific segments of the microwave portion of the EMS. For example, an X band system would be radar that operates at a single wavelength within this band (e.g., 3.2 cm) (Henderson and Lewis, 1998). Most of the spaceborne radar systems operate in C (5.7 cm) and L (24 cm) bands.
Radar Imaging Geometry
Interpretation of SAR imagery for information extraction requires an understanding of radar imaging geometry, the nature of interaction between radar energy and surface features, and the parameters used to characterize the performance of different SAR systems. Figure 1 is a schematic diagram that illustrates the geometry of radar imaging and related radar terminology. In radar imaging systems, the platform (a) travels forward in the flight direction (b) with the nadir point (c) directly beneath the platform. The microwave beam (k) is transmitted obliquely at right angles to the direction of flight, illuminating a swath (usually the width of the imaging area) (f), which is offset from nadir. Range (e) refers to the across-track dimension perpendicular to the flight direction (b), while azimuth (d) refers to the along-track dimension parallel to the flight direction (b). Near range (h) is the portion of the imaging swath closest to the nadir track and far range (g) is the portion of the imaging swath farthest from the nadir track. Depression angle (α) is the angle between the horizontal and a radar ray path. Slant range distance (i) is the radial line of sight distance between the radar and each target on the surface. Ground range distance is the true horizontal distance along the ground corresponding to each point measured in slant range. Incidence angle (θ) is the angle between the radar beam and the perpendicular to the ground surface. Look angle (β) is the angle at which the radar looks at the surface, or the angle between vertical and the ray path.
In active microwave system, the energy received by a radar derives from one or more individual reflections. In a typical scene, there are many scatterers contributing to the energy received from a given region, and the locations of the individual scatterers are random (not necessarily maintaining any pattern). Usually the net signal for the scene is described by using an average over the region, leading to a distributed or diffuse scatterer model (Raney, 1998). In active systems, the brightness or darkness of the image is dependent on the amount of the transmitted energy that is returned back to the radar from targets on the surface as a measure of reflectivity (backscatter). Bright areas are produced by strong radar responses and darker areas are from weaker radar responses. Sigma-naught (o) is commonly used to describe the average reflectivity or scattering co-efficient of a radar scene. Beta-naught (βo) interprets the brightness estimates of mean reflectivity. Beta-naught (βo) separates the radiometric response and reflectivity dependent on the terrain properties, such as local slope. According to Glen and Carr (2004):
Where, DN = Digital number, A 3 = fixed offset from the radiometric data record, A 2 = look-up table (LUT) value, and l = local incidence angle.
Beta-naught (βo) is suggested as standard terminology for the output product of most imaging radars (Raney, 1998).
Response to radar energy (for a given wavelength and polarization) by the target is primarily dependent on three factors: surface roughness, local incident angle and the dielectric constant of the target materials (Raney, 1998). Surface Roughness is measured as the average height variation in the surface cover (measured in cm). Rayleigh (1945) proposed that the criterion for roughness depended on three parameters; incident angle, wavelength and surface irregularities. A surface is considered smooth if the height variations are smaller than the radar wavelength. Specular reflection is caused by a smooth surface where the incident energy is reflected and not backscattered. This results in smooth surfaces appearing as darker toned areas on an image. Diffuse reflection is caused by a rough surface, which scatters the energy equally in all directions. A significant portion of the energy will be backscattered to the radar, such that a rough surface will appear lighter in tone on an image.
Corner reflection occurs when the target object reflects most of the energy directly back to the antenna resulting in a very bright appearance to the object. This occurs where there are buildings, metallic structures (urban environments) and cliff faces, folded rock (natural environments).
Image geometry and radiometry are influenced by the angle of the incident illumination with respect to the local slope of the scene towards the radar. The image brightness per pixel is sensitive to the local incident angle, however, variations in the aspect angle due to the component of slope in the azimuth direction has negligible impact on image brightness (Guindon, 1990). Maxwell’s formulation considered the propagation of electromagnetic waves through media characterized by certain physical constants, one of which is the dielectric constant. The dielectric constant (or the complex permittivity) is the principal description of the medium’s response to the presence of an electrical field (Raney, 1998). The dielectric constant is measured as the ratio of the permittivity of a substance to the permittivity of free space. The material’s dielectric constant depends weakly on frequency, but its loss tangent depends strongly on frequency (Raney, 1998).
Along with wavelength (or frequency), polarization and resolution are the two most important system parameters that are used to interpret the performance of an imaging radar system. Polarization of the radar signal is the orientation of the electromagnetic field and is a significant factor by which the radar signal interacts with objects on the ground, reflecting back the resulting energy. Most radar imaging sensors are designed to transmit microwave radiation either horizontally polarized (H) or vertically polarized (V), and receive either the horizontally or vertically polarized backscattered energy. Polarizing radar has four possible combinations of both transmit and receive polarizations: HH - for horizontal transmit and horizontal receive, VV - for vertical transmit and vertical receive, HV - for horizontal transmit and vertical receive, (cross-polarized), VH - for vertical transmit and horizontal receive (cross-polarized). The spatial resolution of a radar system is the ability to distinguish between different objects, and it is dependent on the properties of the microwave radiation and geometric effects. There are two types of spatial or ground resolution: range resolution (across-track resolution) and azimuth resolution (along-track resolution). Range resolution requires that the objects be separated by more than half the pulse length. Azimuth resolution is dependent on the angular width of the radiated microwave beam and the slant range distance. The azimuth resolution becomes more coarse with increasing distance from the sensor. More detail discussion on the imaging radar’s system parameters can be found in Henderson and Lewis (1998). Table 1. shows the system parameters of commonly used radar imaging systems.
1.2. Estimation of Soil Moisture Using SAR
Measuring and mapping soil moisture has been investigated using scatterometers, satellites, space shuttles, and airborne synthetic aperture radars (SAR) for many years. SAR data are well suited for estimating soil moisture due to the relationship of the dielectric constant and soil moisture. According to Ulaby et al. (1987), for a given soil condition (roughness or texture) radar backscatter is linearly dependent on volumetric moisture (m v ) in the upper 2 to 5 cm of soil with a correlation R2 ~ 0.8 to 0.9.
In bare soil conditions, radar scattering is determined by surface roughness (geometry of the air soil boundary) and the microwave dielectric properties of the soil medium. The geometric factors affect the shape of the scattering pattern for an incident wave while the dielectric properties control the magnitude of reflection, absorption and transmission (Dobson and Ulaby, 1998). The average dielectric properties of the soil medium are dependent on the engineering properties of the soil including moisture content, density, texture, mineralogy and fluid chemistry. The dielectric constant of a material consists of two parts: real (Є’) and imaginary (Є”). In case of a perfectly dry soil, the relative dielectric constant is independent of soil type (Dobson et al., 1985). Dielectric constant in liquid water shows strong dependence on the microwave frequency and weak sensitivity to physical temperature. When compared to dry soil the real part of the relative dielectric constant is 30 times greater and the imaginary part is about two orders of magnitude larger (Dobson and Ulaby, 1998). Due to the relationship between the dielectric constant in liquid water and microwave frequency the addition of water in liquid form to soil changes the dielectric constant of the mixture markedly.
The penetration depth into a soil by microwave is proportional to radar wavelength (Dobson and Ulaby, 1998). Significant penetration can occur in low loss materials, such as arid soils. Maximum penetration can occur in dry soil condition, whereas, the least penetration will occur in wet soils.
Studies, particularly in the past decade, have resulted in many methods, algorithms, and models relating satellite-based imagery from radar backscatter to surface soil moisture, however, no operational algorithm exists using radar data acquired by existing spaceborne sensors (Borgeaud and Saich, 1999). According to Moran et al. (2004) the promising approaches using SAR sensors for soil moisture estimation include: semi-empirical approaches, change detection, data fusion, and SAR with microwave scattering models.
Semi-empirical algorithms generally use SAR imagery of single wavelength, incident angle and polarization. Multiple passes and/or ancillary information are required for better accuracy. This approach is often scene or site dependent (Moran et al., 2000; Quesney et al., 2000). The change detection algorithms require multiple passes of SAR data and this approach has potential as an operational application (Engman, 1994). The reason for the operational suitability of this approach is that the algorithm is based on the assumption that the temporal variability of surface roughness and vegetation is at longer time scale than that of soil moisture content, and therefore, the change in radar backscatters between repeat passes results from the change in soil moisture. (Lu and Meyer, 2002). Research has been conducted into data fusion using passive and active microwave data, and microwave and optical data. Passive-active microwave data fusion algorithms use active backscattering coefficient to determine fine resolution vegetation biomass and surface roughness, and passive brightness temperature to estimate soil moisture content (Bindlish and Barros, 2002). The microwave-optical data fusion algorithms simplify the inverse problem for soil moisture content estimation on the basis of complementarily or interchangeability of optical and SAR data (Changey et al., 1995). Empirical, semi-empirical and theoretical microwave scattering models are available for use with the SAR data for soil moisture estimation. The Water Cloud Model (WCM) (Attema and Ulaby, 1978) and the Integral Equation Model (IEM) (Fung et al., 1992; Colpitts, 1998) are common examples of this kind of models. The models are inverted to estimate soil moisture content from radar backscattering coefficient. Soil moisture estimation accuracy is higher by this approach, however, model parameterization is complex. These SAR based soil moisture estimation algorithms are described and explained in detail in Henderson and Lewis (1998) and in Moran et al. (2004).
1.3. Microwave Remote Sensing of Soil Moisture in Semi-arid Environment
The presence of vegetative cover introduces complexity into soil moisture mapping due to the interaction of the microwave energy with the vegetation and soil. Depending on the amount of vegetation present, its dielectric properties, height and geometry (size, shape and orientation of its component parts), the sensitivity of microwave backscatter to volumetric soil moisture may be significantly reduced. Previous studies indicate that in a semi-arid environment the influence of sparse vegetation on the linear relationship between radar backscatter and soil moisture is negligible or can be ignored (Thomas et al., 2004, Lin and Wood, 1993, and Dubois et al., 1995).
The research results presented in this chapter attempted to verify this concept in the semi-arid environment of southeastern New Mexico. This research also explores the non-linear relationship between soil moisture and radar backscatter, and investigates the impact of vegetation in soil moisture estimation using microwave imagery in this area.
2. Study Site
Nash Draw, located in part of the northeastern Chihuahua desert in southeastern New Mexico (Figure 2), is a karst valley that developed in response to subsurface dissolution of evaporites and subsidence of the overlying strata (Holt et al., 2005). It is a complex example of the localized effects of evaporite karst on surface topography, near-surface geology, and hydrology (Powers et al., 2006). Although this area is in a semi-arid environment, the vegetation pattern is not uniform. Nash Draw covers an area of 400 sq. km and a subset area of 225 sq. km was selected as the study site.
3. Data Used
Rainfall in Nash Draw is unreliable and erratic. Hydrologic data shows that August is commonly the wettest part of the season and October marks the end of the rainy season. It was assumed that imagery acquired during the months of August through November would record the maximum variation of soil moisture in the study site.
3.1. Synthetic Aperture Radar (SAR) Imagery
Due to its high spatial resolution, Radarsat 1 SAR Fine imagery was considered to be the best imagery for estimating soil moisture in the study site. The Alaska Satellite Facility (ASF) in Fairbanks, Alaska served as the Radarsat 1 data node for the United States. The ASF acquired 5 scenes of Radarsat 1 SAR Fine imagery covering the Nash Draw area for this research. The imagery was acquired at 10 m spatial resolution with 50 X 50 km swath coverage. The scenes were acquired in descending mode at 37 º incidence angle. The image acquisition dates include August 02 and 26, September 19, October 13 and November 06 of 2006. Figure 3 shows the acquired SAR imagery.
Initially all acquired SAR imagery were received as Level 0 products and then converted to level 1 products. These Level 1 SAR data have undergone several pre-processing phases including terrain correction, calibration and filtering to be ready for soil moisture estimation.
An initial experiment was conducted using one radar scene to determine the suitability of o or βo for soil moisture estimation in our study site. It was found that backscatter values as βo had a better correlation with field measured soil moisture than backscatter values as o in our study site (Hossain and Easson, 2007). We believe that due to the low topographic relief in the study site variations in radar backscatter expressed as βo produced better results. Based on these observations we decided to calibrate all the radar scenes as βo for this project.
Coherent imaging systems produce images with a granular appearance, with a multitude of bright and dark spots caused by random constructive and destructive interference of the wavelets returning from the various scatterers within the resolution cell of the system (Goodman, 1975). From the mathematical point of view, the effect of this interference process can be regarded as a multiplicative noise, called speckle. In Synthetic Aperture Radar (SAR) imagery, the presence of speckle affects the procedures for texture class discrimination. Speckle noise needs to be reduced to preserve edges and image texture (D’Elia et al., 2004). The most well known model used as the basis for the development of many of the existing speckle filters is the multiplicative model with an exponential probability density function (Touzi, 2002). To remove the speckles in the radar scenes we applied different types of filtering techniques with different window sizes. We found 5x5 Lee filtering provided better results and this method was used to de-speckle the acquired radar scenes.
The processed (calibrated and filtered) SAR data and the GIS coverage of the sample locations were georectified to the same projection system. All imagery and GIS data were georectified using recent aerial photograph and Universal Transverse Mercator (UTM) projection system.
3.2. Elevation Data
The knowledge of the local incident angle is essential for the quantitative estimation of soil moisture and roughness from SAR data. In the absence of topographic relief, the local incident angle equals the radar look angle. This is not true for terrain with larger topographic variations where the local incident angle becomes a function of the radar look angle and the local terrain slope. This makes the straightforward surface parameter estimation difficult (Hajnsek and Pottier, 2000). It is necessary to terrain correct the SAR data to allow geometric overlays of remotely sensed data from different sensors and/or geometries. The average elevation of the study site varies from 900 m to 1100 m, which is considered low relief for processing SAR imagery. However, despite the minimal topographic influence, a terrain correction was performed using USGS 30 m digital elevation model (DEM) to achieve greater geometric accuracy of the data.
3.3. Insitu Soil Moisture Data
Near-real time soil moisture data is needed to quantitatively map soil moisture with reasonable accuracy from SAR data. Soil samples were collected in selected parts of Nash Draw and analyzed to calculate volumetric soil moisture for calibration of the SAR imagery acquired on August 02, 2006 and November 06, 2006. Eighty soil samples were collected within a site covering 225 sq. km in Nash Draw.
A stratified soil sampling technique (Dane and Topp, 2002) was used in the acquisition of the soil samples. Using this method, the study site was divided into several grids and a simple random sampling technique was used in each grid with prior definition of sample size. The study site was divided into 4 equal parts and random sample points were selected in each part using a 500 m grid spacing, with 20 samples collected in each quadrant. Accessibility and variation in soil types was given preference for selecting sampling sites. Samples were collected for measuring volumetric soil moisture. Figure 4 shows the distribution of the collected soil sample locations in the study site.
RADARSAT 1 acquires imagery in HH polarization and in C band with 5.7 cm wavelength and 5.3 GHz frequency (RADARSAT International, 1995). The RADARSAT 1 beam should be able to penetrate the ground at least up to 3 cm in dry conditions. Therefore, sample collection was limited to within 3 cm below the land surface. A cylinder with 3 cm length and 5.7 cm diameter was used to collect soil cores. Figure 4 shows the procedure of soil sample collection.
Volumetric Soil Moisture Measurement
Gravimetric soil moisture was measured and values were converted to volumetric soil moisture using sample volume. The ASTM D 2216-98 standard procedure (with modification) was used to calculate the gravimetric soil moisture and Equations (3) and (4) were used to calculate the volumetric moisture content.
Where, w v = volumetric soil moisture (%), V w = volume of moisture content (cc), V = volume of sample = 76.55 (cc), W ms = weight of moist soil (gm), W ds = weight of dry soil (gm), V w = W ms – W ds (volume of 1 gm water = 1 cc).
Soil moisture measurements for sample # 15 and sample # 115 were excluded from all analysis due to the proximity of these samples to a lake in the study area (Figure 5). Samples # 15 and # 115 had soil moisture measurements of 24.6% and 22.48%, respectively. Soil moisture measurements for samples # 31 and # 32 (from August data set) and for samples # 131 and # 132 (from November data set) were also excluded from the analysis due the distortion of SAR backscatter at these sample locations. These samples are located in dune sand and the backscatter values in the SAR imagery for that area are distorted apparently due to total reflection of the radar signal (Figure 6). Table 2. shows the statistics of the in situ soil moisture measurements.
Enrollment in local colleges, 2005
|Statistics||Mea surement Dates|
|August 01-03, 2006||November,04- 06,2006|
3.4. Vegetation Maps
Vegetative cover can strongly influence soil moisture mapping with SAR imagery due to the interaction of the microwaves with the vegetation and soil. The amount of vegetation, its dielectric properties and distribution pattern can significantly impact the sensitivity of microwave backscatter to volumetric soil moisture. A vegetation distribution map is needed for mapping soil moisture using SAR with reasonable accuracy.
A vegetation map for the study site was not available at the same resolution as the SAR imagery. The acquired SAR imagery was used to produce a time series of vegetation maps for the study site.
General Vegetation Distribution Pattern Map
We combined the acquired five radar scenes to produce a temporal data set [Figure 7(a)]. The temporal data set was then used to perform multi-temporal analysis to create a vegetation map of the study site. Vegetation signatures were obtained from the multi-temporal data for areas with little or no vegetation, sparse vegetation and dense vegetation. The obtained signatures were applied to the radar imagery to produce the vegetation map [Figure 7(b) and 7(c)]. Finally we simplified the vegetation map by dividing the study site into two zones: Zone 1 represents the area characterized by sparse, thin or no vegetation and Zone 2 represents areas characterized by comparatively denser vegetation [Figure 7(d)].
The algorithms developed by a semi-empirical approach are the most common and widely used (Moran et al., 2000). In this study simple linear regression was performed between soil moisture obtained from the field data and radar backscatter to study the linear relationship between radar reflectivity and soil moisture. An Artificial neural network (ANN) was used to study the non-linear relationship between radar backscatter (reflectivity) and soil moisture. Correlation coefficient (R2) values were used to evaluate the suitability of the numerical models to map soil moisture in southeastern New Mexico
4.1. Simple Linear Regression
According to Ulaby et al. (1996), the radar backscatter from a surface with vegetation consists of three components: (1) product of the backscatter contribution of bare soil surface ( ) and the two way attenuation of the vegetated layer (τ2), (2) the direct backscatter contribution of the vegetation layer ( dv), and (3) multiple scattering involving the vegetation elements and the ground surface ( int.).
In case of densely vegetated surface, τ2~0 and is determined largely by volumetric scattering from the vegetation canopy (Moran et al., 2004). For sparsely vegetated surfaces, τ2~1 and the second and third terms in the Equation (5) are negligible, and in this situation is determined by the soil roughness and moisture content (Moran et al., 2004). Therefore, for bare soil, s has a functional relation with soil moisture, m s and surface roughness, R (Engman and Chauhan, 1995), and it can be expressed as follows:
This indicates that for a target with uniform R, m s can be estimated using the following expression:
Where a and b are regression coefficients, which are usually determined from field experiments encompassing the target-invariant R and the scene-invariants SAR wavelength (λ), incidence angle (θi), polarization, and calibration. However, Equation (7) is only valid for a given sensor, land use, and soil type, and for targets when τ2, dv and int are known or negligible (Moran et al., 2004).
Quesney et al. (2000) resolved Equations (5)-(7) to derive soil moisture information from ERS SAR measurements over an agricultural watershed in France on the basis of a priori vegetation classification of the site and in situ soil moisture measurements. This study separated the areas with low vegetation biomass for soil moisture estimation.
Similarly, for a semiarid watershed in Arizona, Moran et al. (2000) utilized the difference between dry- and wet-season SAR (Δ ) to normalize the effects of surface roughness and topography on ERS SAR measurements. Thoma et al. (2004) improved on this approach to minimize empiricism and used a quantitative form of Δ to map soil moisture for an entire watershed with RADARSAT for three dates in 2003. In these studies, the effects of sparse vegetation were found to be negligible and could be ignored. These observations were also supported with similar findings by Lin and Wood (1993), Chanzy et al. (1997), Demircan et al. (1993), Dobson et al. (1992), and Dubois et al. (1995).
Our study site, Nash Draw is characterized by a semi-arid environment and generally sparse vegetation cover. According to the previous researchers, the effects of sparse vegetation in the radar backscattering should be insignificant and can be ignored for soil moisture estimation in this type of study site. It is important to note for our study site we modified the Equation (7) by using βo instead of o as the input of SAR reflectivity values.
Radar βº backscatter values were extracted for the soil sample locations where in situ soil moisture measurements were made and compared with volumetric soil moisture values for the sample locations. As discussed above, we used simple linear regression for the comparison and to calculate the coefficients a and b in the numerical model. We developed the model for the entire study site and also for different zones in the study site, based on vegetation density, to determine how well the model works for different land cover types, including vegetated areas and bare lands.
4.2. Non-Linear Regressions
Many SAR-based soil moisture estimation models assume that soil moisture distribution is linearly related to the radar reflectivity of the soil surface (e.g., Ulaby et al., 1996, Moran et al., 2000; Dobson et al.,1992, Dubois et al., 1995). Limited studies were conducted in the past to explore the non-linear relationship between soil moisture and radar backscatter (reflectivity). In this study we developed neural networks based numerical models to estimate soil moisture using SAR data in Nash Draw and to explore the non-linear relationship between soil moisture and SAR backscatter.
Artificial Neural Networks
Artificial neural networks, are a branch of artificial intelligence (Gardner and Dorling, 1998) in which the solution to a problem is learned from a set of examples (Bishop, 1994). A neural network can be regarded as a nonlinear mathematical function, which transforms a set of input variables into a set of output variables. The use of neural networks has been shown to be effective alternatives to more traditional statistical techniques (Schalkoff, 1992). Neural networks can be trained to approximate any smooth, measurable function (Hornik, et al., 1989), can model highly non-linear functions and can be trained to be accurately generalized when presented with unseen data (Gardner and Dorling, 1998). In a typical neural network model, a single neuron forms a weighted sum of the inputs x 1 ,...,x d given by a = S i w i x i , and then transforms this sum using a non-linear activation function g( ) to give a final output z=g(a) (Figure 8).
A feed forward neural network can be regarded as a nonlinear mathematical function, which transforms a set of input variables into a set of output variables. The multilayer perceptron is the most widely used feed forward neural networks. Figure 8 shows a single processing unit of neural networks. If we consider a set of m such units, all with common inputs, then we arrive at a neural network having a single layer of adaptive parameters (weights). The output variables are denoted by z j and are given by Equation (9).
Where w ji is the weight for input i to j, and g( ) is an activation function as discussed previously.
The neural network model developed to estimate soil moisture in Nash Draw includes only one input, the radar backscatter values. This model demonstrates the nature of non-linear relationship between radar backscatter and soil moisture.
5.1. Simple Linear regressions
The simple linear regression models for the entire study site are shown in Figure 9. Figure 10 shows the regression models for different vegetation zones for August, 2006 data set, and Figure 11 shows the regression models for different vegetation zones for November, 2006 data set. Equation (10) and Equation (11) represent the numerical models for the entire study site for August, 2006 data set and November 2006 data set respectively. Equation (12) and Equation (13) represent the numerical models for thinly vegetated areas (Zone 1) for August, 2006 data set and November 2006 data set respectively. Equation (14) and Equation (15) represent the numerical models for densely vegetated areas (Zone 2) for August, 2006 data set and November 2006 data set respectively. Table 3 shows the results of the regression models for August, 2006 and November, 2006 respectively.
|Domain||Correlation Coefficient (R 2 )|
|August 2006||November, 2006|
|Entire study site||0 . 24||0.05|
|Thinly vegetated areas (Zone1)||0.61||0.51|
|Densely vegetated areas (Zone 2)||00.01||00.04|
The R2 values of the numerical models developed for the entire study site indicate that the linear relationship between the radar backscatter values obtained for the entire study site and soil moisture is not well defined. We observed this for both the August (R2 = 0.24) and November (R2 = 0.05) data sets. The R2 values of the numerical models developed for vegetated areas (Zone2) for both August and November data set are very low (0.01 and 0.04 respectively). We found higher R2 values for the numerical models developed for non-vegetated or sparsely vegetated areas (Zone 1) for both August and November data set (0.61 and 0.51 respectively). These findings indicate that the relationship between radar backscatter and soil moisture in densely vegetated areas is not linear.
5.2. Non-linear Regressions (Neural Networks)
We developed neural network based non-linear numerical models for soil moisture estimation for the entire study site using the August data set. We developed models using radar backscatter values as the only input to investigate the non-linear relationship between the radar backscatter (reflectivity) and soil moisture. We used JMP 6.0 statistical software to perform the neural networks based analysis. The model correlation coefficient (R2) and cross validation correlation coefficient (CV R2) were used to evaluate the model performance for soil moisture prediction. A neural network with 3 hidden nodes resulted in correlation coefficient (R2) and the cross validation correlation coefficient (CV R2) of 0.24 and 0.11 respectively. This result indicates that the non-linear relationship between radar backscatter and soil moisture is also not well defined for the entire study site.
5.3. Model Evaluation
We evaluated the correlation coefficients (R2) and cross validation correlation coefficients (CV R2) (for the neural networks based models) developed by both linear and non-linear regressions for soil moisture estimation in Nash Draw, NM and made the following observations.
Simple linear regression between radar backscatter values and in situ soil moisture measurements can be used to develop SAR based soil moisture estimation model with model R2 values of 0.51 to 0.61, but the model application should be restricted to non-vegetated to thinly vegetated areas.
Neural network based non-linear regressions using radar backscatter values and in situ soil moisture measurements can be used to develop soil moisture estimation model for the entire study site with a model R2 value of 0.24 and CV R2 of 0.11.
6. Conclusions and Discussion
Earlier researchers reported that in a semi-arid environment with sparse vegetation, there is a linear relationship between soil moisture and radar backscatter. Our research shows that in semi-arid environment the influence of vegetation can influence the accuracy of the soil moisture estimation using the linear relationship between the radar backscatter and soil moisture. This observation is supported by the lower R2 values (0.24 – August data set and 0.05 – November data set) obtained for the numerical models developed for the entire study site, the higher R2 values (0.61 – August data set and 0.51 – November data set) obtained for the numerical models developed for the parts of the study site identified as very thin or sparsely vegetated areas, and very low R2 values (0.01 – August data set and 0.04 – November data set) obtained for the numerical models developed for the parts of the study site identified as more densely vegetated areas.
The non-linear relationship between radar reflectivity and soil moisture was investigated using a numerical model developed by feed forward neural networks with radar backscatter values and near real time in situ soil moisture measurements. The model was developed for the entire study site and did not show a strong non-linear relationship between radar backscatter (reflectivity) and soil moisture. The correlation coefficient (R2) (0.24) did not improve from that obtained by simple linear regression (0.24) between radar backscatter and soil moisture.
This research indicates that in semi-arid environment vegetation coverage can significantly reduced the accuracy of soil moisture estimation and mapping using numerical models based on simple linear and non-linear relationships between radar backscatter values derived from high resolution SAR imagery and near real time in situ soil moisture measurements. This research also shows that numerical models based on only radar backscatter and near real time in situ soil moisture measurements can only be used in thinly vegetated to bare soil conditions in a semi-arid environment to estimate and map soil moisture with improved accuracy (R2 = 0.51 to 0.61).
We recommend to include soil type, soil salinity and surface elevation information (in addition to vegetation coverage and in situ soil moisture measurements) in both linear and non-linear numerical models to improve the accuracy of SAR based soil moisture estimation in semi-arid environment without separating the vegetated and non-vegetated zones.