Potential of ASAR/ENVISAT for the characterization of soil surface parameters over bare agricultural fields

The objective of this investigation is to analyze the sensitivity of ASAR (Advanced Synthetic Aperture Radar) data to soil surface parameters (surface roughness and soil moisture) over bare fields, at various polarizations (HH, HV, and VV) and incidence angles (20°-43°). The relationships between backscattering coefficients and soil parameters were examined by means of 16 ASAR images and several field campaigns. We have found that HH and HV polarizations are more sensitive than VV polarization to surface roughness. The results also show that the radar signal is more sensitive to surface roughness at high incidence angle (43°). However, the dynamics of the radar signal as a function of soil roughness are weak for root mean square (rms) surface heights between 0.5 cm and 3.56 cm (only 3 dB for HH polarization and 43° incidence angle). The estimation of soil moisture is optimal at low and medium incidence angles (20°-37°). The backscattering coefficient is more sensitive to volumetric soil moisture in HH polarization than in HV polarization. In fact, the results show that the depolarization ratio σ_HH⁰/σ_HV⁰ is weakly dependent on the roughness condition, whatever the radar incidence. On the other hand, we observe a linear relationship between the ratio σ_HH⁰/σ_HV⁰ and the soil moisture. The backscattering coefficient ratio between a low and a high incidence angle decreases with the rms surface height, and minimizes the effect of the soil moisture.     

Analysis of TerraSAR-X data and their sensitivity to soil surface parameters over bare agricultural fields

The sensitivity of TerraSAR-X radar signals to surface soil parameters has been examined over agricultural fields, using HH polarization and various incidence angles (26°, 28°, 50°, 52°). The results show that the radar signal is slightly more sensitive to surface roughness at high incidence (50°–52°) than at low incidence (26°–28°). The difference observed in the X-band, between radar signals reflected by the roughest and smoothest areas, reaches a maximum of the order of 5.5 dB at 50°–52°, and 4 dB at 26°–28°. This sensitivity increases in the L-band with PALSAR/ALOS data, for which the dynamics of the return radar signal as a function of soil roughness reach 8 dB at HH38°. In the C-band, ASAR/ENVISAT data (HH and VV polarizations at an incidence angle of 23°) are characterised by a difference of about 4 dB between the signals backscattered by smooth and rough areas.Our results also show that the sensitivity of TerraSAR-X signal to surface roughness decreases in very wet and frozen soil conditions. Moreover, the difference in backscattered signal between smooth and rough fields is greater at high incidence angles. The low-to-high incidence signal ratio (Δσ° = σ_26°–28°/σ_50°–52°) decreases with surface roughness, and has a dynamic range, as a function of surface roughness, smaller than that of the backscattering coefficients at low and high incidences alone. Under very wet soil conditions (for soil moistures between 32% and 41%), the radar signal decreases by about 4 dB. This decrease appears to be independent of incidence angle, and the ratio Δσ° is found to be independent of soil moisture.     

Development of polarization ratio model for sea surface wind field retrieval from TerraSAR-X HH polarization data

In this article, the polarization ratio (PR) of TerraSAR-X (TS-X) vertical–vertical (VV) and horizontal–horizontal (HH) polarization data acquired over the ocean is investigated. Similar to the PR of C-band synthetic aperture radar (SAR), the PR of X-band SAR data also shows significant dependence on incidence angle. The normalized radar cross-section (NRCS) in VV polarization data is generally larger than that in HH polarization for incidence angles above 23°. Based on the analysis, two PR models proposed for C-band SAR were retuned using TS-X dual-polarization data. A new PR model, called X-PR hereafter, is proposed as well to convert the NRCS of TS-X in HH polarization to that in VV polarization. By using the developed geophysical model functions of XMOD1 and XMOD2 and the tuned PR models, the sea surface field is retrieved from the TS-X data in HH polarization. The comparisons with in situ buoy measurements show that the combination of XMOD2 and X-PR models yields a good retrieval with a root mean square error (RMSE) of 2.03 m s^–1 and scatter index (SI) of 22.4%. A further comparison with a high-resolution analysis wind model in the North Sea is also presented, which shows better agreement with RMSE of 1.76 m s^–1 and SI of 20.3%. We also find that the difference between the fitting of the X-PR model and the PR derived from TS-X dual-polarization data is close to a constant. By adding the constant to the X-PR model, the accuracy of HH polarization sea surface wind speed is further improved with the bias reduced by 0.3 m s^–1. A case acquired at the offshore wind farm in the East China Sea further demonstrates that the improvement tends to be more effective for incidence angles above 40°.     

Effects of corn on C- and L-band radar backscatter: A correction method for soil moisture retrieval

This paper discusses the effects of vegetation on C- (4.75 GHz) and L- (1.6 GHz) band backscattering (σ^o) measured throughout a growth cycle at incidence angles of 15, 35 and 55°. The utilized σ^o data set was collected by a truck mounted scatterometer over a corn field and is supported by a comprehensive set of ground measurements, including soil moisture and vegetation biomass. Comparison of σ^o measurement against simulations by the Integral Equation Method (IEM) surface scattering model (Fung et al., 1992) shows that the σ^o measurements are dominated either by an attenuated soil return or by scattering from vegetation depending on the antenna configuration and growth stage. Further, the measured σ^o is found to be sensitive to soil moisture even at peak biomass and large incidence angles, which is attributed to scattering along the soil-vegetation pathway.For the simulation of C-band σ^o and the retrieval of soil moisture two methods have been applied, which are the semi-empirical water cloud model (Attema & Ulaby, 1978) and a novel method. This alternative method uses the empirical relationships between the vegetation water content (W) and the ratio of the bare soil and the measured σ^o to correct for vegetation. It is found that this alternative method is superior in reproducing the measured σ^o as well as retrieving soil moisture. The highest retrieval accuracies are obtained at a 35° incidence angle leading to RMSD's of 0.044 and 0.037 m³ m^− 3 for the HH and VV-polarization, respectively. In addition, the sensitivity of these soil moisture retrievals to W and surface roughness parameter uncertainties is investigated.     

Soil moisture estimation in a semiarid rangeland using ERS-2 and TM imagery

Soil moisture is important information in semiarid rangelands where vegetation growth is heavily dependent on the water availability. Although many studies have been conducted to estimate moisture in bare soil fields with Synthetic Aperture Radar (SAR) imagery, little success has been achieved in vegetated areas. The purpose of this study is to extract soil moisture in sparsely to moderately vegetated rangeland surfaces with ERS-2/TM synergy. We developed an approach to first reduce the surface roughness effect by using the temporal differential backscatter coefficient (Δσ_wet-dry⁰). Then an optical/microwave synergistic model was built to simulate the relationship among soil moisture, Normalized Difference Vegetation Index (NDVI) and Δσ_wet-dry⁰. With NDVI calculated from TM imagery in wet seasons and Δσ_wet-dry⁰ from ERS-2 imagery in wet and dry seasons, we derived the soil moisture maps over desert grass and shrub areas in wet seasons. The results showed that in the semiarid rangeland, radar backscatter was positively correlated to NDVI when soil was dry (m_v<10%), and negatively correlated to NDVI when soil moisture was higher (m_v>10%). The approach developed in this study is valid for sparse to moderate vegetated areas. When the vegetation density is higher (NDVI>0.45), the SAR backscatter is mainly from vegetation layer and therefore the soil moisture estimation is not possible in this study.     

Potential of SAR sensors TerraSAR-X, ASAR/ENVISAT and PALSAR/ALOS for monitoring sugarcane crops on Reunion Island

Multi-temporal TerraSAR-X, ASAR/ENVISAT and PALSAR SAR data acquired at various incidence angles and polarizations were analyzed to study the potential of these new spaceborne SAR systems for monitoring sugarcane crops. The sensitivity of different radar parameters (wavelength, incidence angles, and polarization) to sugarcane growth stages was analyzed to determine the most suitable radar configuration for better characterisation of sugarcane fields and in particular the monitoring of sugarcane harvest.Correlation between backscattered signals and crop height was also carried out. Radar signal increased quickly with sugarcane height until a threshold height, which depended on radar wavelength and incidence angle. Beyond this threshold, the signal increased only slightly, remained constant, or even decreased. The threshold height is higher with longer wavelengths (L-band in comparison with C- and X-bands) and higher incidence angles (~ 40° in comparison with ~ 20°).The radar backscattering coefficients (σ°) were also compared to the Normalized Difference Vegetation Index (NDVI) calculated from SPOT-4/5 images. Results showed a high correlation between the behaviors of σ° and NDVI as a function of sugarcane crop parameters. A decrease in NDVI for fully mature sugarcane fields due to drying of the sugarcane (water stress) was also observed in the radar signal. This decrease in radar signal was of the same order as the decrease in radar signal after the sugarcane harvest. In general, it is more suitable to monitor the sugarcane harvest using high incidence angles regardless of the radar wavelength. SAR data in L- and C-bands showed an ambiguity between the signals of ploughed fields and those of fields in vegetation because of the high sensitivity of the radar signal at these wavelengths to surface roughness of bare soils. Indeed, sometimes the radar signal of ploughed fields was of the same order as that of harvested or mature sugarcane fields. Results showed better discrimination between ploughed fields and sugarcane fields in vegetation (sugarcane canopy) when using TerraSAR-X data (X-band).Concerning the influence of radar polarization, results showed that the co-polarizations channels (HH and VV) were well correlated, but had slightly less potential than cross-polarization channels (HV and VH) for the detection of the sugarcane harvest. Finally, SAR data at high spatial resolution were shown to be useful and necessary for better analysis of SAR images when the fields were of small size.     

The use of a microwave backscatter model for retrieving soil moisture over bare soil

Abstract

Most attempts at predicting soil moisture from C-band microwave backscattering coefficients for bare soil are made by fitting experimental calibration relations obtained for limited ranges of incidence angle and soil surface roughness. In this paper, a more general approach is discussed using an inversion procedure to extend the use of a single experimental calibration relation to a wider range of incidence angle and surface roughness. A correcting function is proposed to normalize the backscattering coefficients to the conditions (incidence angle and surface roughness) of the calibration relation. This correcting function was derived from simulated data using the physical optics or KirchhofTs scatter model using the scalar approximation. Before discussing the inversion procedure, the backscattering coefficients calculated by the model have been compared with experimental data measured in the C-band, HH polarization and three incidence angles (Θ= 15°, 23°, 50°) under a wide range of surface soil moisture conditions (0.02H_v  0.35cm³ cm^-3) and for a single quite smooth soil surface roughness (0–011 _s  OOI4/n)m. The model was found to be experimentally validated from 15° to 23° of incidence and for surface soil moistures higher than 0-I0cm³cm^-3. For the inversion procedure, it is assumed to have a wider range of validity (15°  Θ 35° ) for ihc incidence angle. A sensitivity analysis of the model to errors on roughness parameter and incidence angle was performed in order to assess the feasability and suitability of the described inversion procedure.     

An algorithm for the retrieval of sea surface wind fields using X-band TerraSAR-X data

TerraSAR-X (TS-X) is a new, fully polarized X-band synthetic aperture radar (SAR) satellite, which is a successor of the Spaceborne Imaging Radar X-band Synthetic Aperture Radar (SIR-X-SAR) and the SRTM. TS-X has provided high-quality image products over land and oceans for scientific and commercial users since its launch in June 2007. In this article, a new geophysical model function (GMF) is presented to retrieve sea surface wind speeds at a height of 10 m (U ₁₀) based on TS-X data obtained with VV polarization in the ScanSAR, StripMap and Spotlight modes. The X-band GMF was validated by comparing the retrieved wind speeds from the TS-X data with in situ observations, the high-resolution limited area model (HIRLAM) and QuikSCAT scatterometer measurements. The bias and root mean square (RMS) values were 0.03 and 2.33 m s^?1, respectively, when compared with the co-located wind measurements derived from QuikSCAT. To apply the newly developed GMF to the TS-X data obtained in HH polarization, we analysed the C-band SAR polarization models and extended them to the X-band SAR data. The sea surface wind speeds were retrieved using the X-band GMF from pairs of TS-X images obtained in dual-polarization mode (i.e. VV and HH). The retrieved results were also validated by comparing with QuikSCAT measurements and the results of the German Weather Service (DWD) atmospheric model. The obtained RMS was 2.50 m s^?1 when compared with the co-located wind measurements derived from the QuikSCAT, and the absolute error was 2.24 m s^?1 when compared with DWD results.     

Spectral unmixing model to assess land cover fractions in Mongolian steppe regions

The land cover fractions (LCFs) and spectral reflectance of photosynthetic vegetation (PV), nonphotosynthetic vegetation (NPV), and bare soil were measured at 58 sites in semi-arid and arid regions of Mongolia in the summers of 2005 and 2006. These data sets allowed a detailed assessment of the impact of measurement geometry as represented by the solar zenith angle θ_s, sensor view zenith angle θ_v and azimuth view angle ? in the estimation of LCF values by means of the spectral unmixing model (SUM). The bidirectional distribution function (BRDF) was fitted to the reflectance data and then used to produce reflectance at various measurement geometries. LCFs from these reflectance data for a given combination of θ_s, θ_v, and ? were compared with visually determined LCFs. It was found that θ_s in the range of 30-45° produced a better agreement of LCFs. For θ_v, the agreement is not very sensitive to the choice of angle for the range 30-70°, although θ_v = 50° showed a slightly better performance. The azimuth view angle does not have strong influences to the LCF estimation, except for the case of ? = 180° (view toward the sun), which does not allow precise fitting of BRDF function over a tall vegetation site. Overall, this study verified the results of earlier studies obtained mostly for the American continents that SUM is capable of producing LCF estimates accurately and also found that its accuracy was, in general, much better than that by the more traditional approach of the supervised classification method (SCM) applied to images of a digital camera.     

Optimal evaluation of generalized Euler angles with applications to control

Given two linearly independent matrices in so(3), Z₁ and Z₂, every rotation matrix, X_f∈SO(3), can be written as the product of alternate elements from the one-dimensional subgroups corresponding to Z₁ and Z₂, namely X_f=e^Z₁t₁e^Z₂t₂e^Z₁t₃?e^Z₁t_s. The parameters t_i, i=1,…,s are called Generalized Euler Angles. In this paper, the minimum number of factors required for the factorization of X_f∈SO(3), as a function of X_f, is evaluated. An algorithm is given to determine the generalized Euler angles, in the optimal factorization. The results can be applied to the bang-bang control, with minimum number of switches, of some classical and quantum systems.     

View azimuth and zenith,and solar angle effects on wheat canopy reflectance

Since crop canopies are not lambertian reflectors, their reflectance varies with sun and view positions. It is not always possible or convenient to make reflectance measurements from the nadir position nor at the same time of day. Therefore, ways of estimating nadir reflectance from off-nadir views and for various solar zenith angles are needed. In this study, spectral measurements were made with a Mark II radiometer five times during the day on each of four dates from 15° interval zenith and 45° azimuth positions for wheat canopies during the development interval stem extension to watery ripeness of the grain. The ratio of off-nadir [R(Z_v,A_v)] to nadir [R(0)] radiance in NIR band (0.76–0.90 μm) was described by the regression equation: $\text{R(Z}{}_{\mathrm{v}}\text{,A}{}_{\mathrm{v}}\text{)}\text{R(0)}\text{= 1.0 + [β}{}_0\text{+ β}{}_1\text{sin}\text{(}\text{A}{}_{\mathrm{v}}\text{2}\text{) + β}{}_2\text{(1/}\text{cos}\text{Z}{}_{\mathrm{s}}\text{)]}\text{sin}\text{Z}{}_{\mathrm{v}}$ where A_v is view azimuth angle relative to the sum position, Z_s is solar zenith angle, and Z_v is view zenith angle. The coefficient of determination was 0.70 or higher. The equation describes the observations that 1) the ratio of off-nadir to nadir radiance increases or decreases as view zenith angle increases depending on view azimuth angle; backscattering is stronger than forwardscattering and the pattern is azimuthally symmetric about the principal plane of the sun; and 2) the rate of change in the radiance ratio increases with increasing solar zenith angle. The coefficients, β₀, β₁ and β₂, changed as the canopies grew. Although the equation needs to be more fully tested, it should help summarize and compare various angular observation data taken in crop fields.     

A pipelined computer architecture for unified elementary function evaluation

A pipelined computer architecture for rapid consecutive evaluation of several elementary functions (x/y, √x, sin x, cos, x, e^x, ln x, …) using basic CORDIC algorithms is proposed. Continued products iterations of the form (1 + σ_im 2^?k) allow linking n-identical ALU structures to permit n different function evaluations. New algorithms for sin^?1, cos^?1, cot^?1, sinh^?1, cosh^?1 and x^v are developed. Lastly, a new functional efficiency is defined for pipeline architectures which compares favorably to iterative arrays.Index terms—Digital Arithmetic, Pipeline, Unified Elementary Functions, Iterative Algorithms, CORDIC     

Comparison of ERS-2 SAR and Landsat TM imagery for monitoring agricultural crop and soil conditions

Studies over the past 25 years have shown that measurements of surface reflectance and temperature (termed optical remote sensing) are useful for monitoring crop and soil conditions. Far less attention has been given to the use of radar imagery, even though synthetic aperture radar (SAR) systems have the advantages of cloud penetration, all-weather coverage, high spatial resolution, day/night acquisitions, and signal independence of the solar illumination angle. In this study, we obtained coincident optical and SAR images of an agricultural area to investigate the use of SAR imagery for farm management. The optical and SAR data were normalized to indices ranging from 0 to 1 based on the meteorological conditions and sun/sensor geometry for each date to allow temporal analysis. Using optical images to interpret the response of SAR backscatter (σ^o) to soil and plant conditions, we found that SAR σ^o was sensitive to variations in field tillage, surface soil moisture, vegetation density, and plant litter. In an investigation of the relation between SAR σ^o and soil surface roughness, the optical data were used for two purposes: (1) to filter the SAR images to eliminate fields with substantial vegetation cover and/or high surface soil moisture conditions, and (2) to evaluate the results of the investigation. For dry, bare soil fields, there was a significant correlation (r²=.67) between normalized SAR σ^o and near-infrared (NIR) reflectance, due to the sensitivity of both measurements to surface roughness. Recognizing the limitations of optical remote sensing data due to cloud interference and atmospheric attenuation, the findings of this study encourage further studies of SAR imagery for crop and soil assessment.     

Texture classification using features derived from random field models

This paper presents a new feature extraction method for classifying a texture image into one of the l possible classes C_i, i=1,…,l. It is assumed that the given M × M image characterized by a set of intensity levels, {y(s₁,S₂), 0≤s_s,s₂≤M?1}, is a realization of an underlying random field model, known as the Simultaneous Autoregressive Model (SAR). This model is characterized by a set of parameters φ whose probability density function p_i(φ), depends on the class to which the image belongs. First it is shown that the maximum likelihood estimate (M.L.E.) $\text{φ}{}^1$, of φ is an appropriate feature vector for classification purposes. The optimum Bayes classifier which minimizes the average probability of classification error, is then designed using $\text{φ}{}^1$. Finally the efficiency of the feature vector is demonstrated through experimental results obtained with some natural texture data and a simpler quadratic mean classifier.     

Sorting streamed multisets

Sorting is a classic problem and one to which many others reduce easily. In the streaming model, however, we are allowed only one pass over the input and sublinear memory, so in general we cannot sort. In this paper we show that, to determine the sorted order of a multiset s of size n containing σ?2 distinct elements using one pass and o(nlogσ) bits of memory, it is generally necessary and sufficient that its entropy H=o(logσ). Specifically, if s={s₁,…,sn} and si₁,…,sin is the stable sort of s, then we can compute i₁,…,in in one pass using O((H+1)n) time and O(Hn) bits of memory, with a simple combination of classic techniques. On the other hand, in the worst case it takes that much memory to compute any sorted ordering of s in one pass.     

Relationship between the eccentric connectivity index and Zagreb indices

For a (molecular) graph, the first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices. If G is a connected graph with vertex set V(G), then the eccentric connectivity index of G, ξ^C(G), is defined as, ∑_vi∈V(G)d_ie_i, where d_i is the degree of a vertex v_i and e_i is its eccentricity. In this report we compare the eccentric connectivity index (ξ^C) and the Zagreb indices (M₁ and M₂) for chemical trees. Moreover, we compare the eccentric connectivity index (ξ^C) and the first Zagreb index (M₁) for molecular graphs.     

One step integration methods with maximum stability regions

One step integration methods, using K function evaluations, for the solution of a system of ordinary differential equations dv/dt=A?v are evaluated. A general expression for a class of methods is found for all positive integers K. This class of methods is proven to maximize the interval on the imaginary axis which is contained in the stability region such that the stability constraint is optimized. It is proven that every method with this optimal stability property has a polynomial M defined by y_1+,Δt=M?v_i for which M(iS_l)=exp(iS_lπ/2) where S_l=K?l.     

Mapping Between 2-D Meshes of the Same Size

1IntroductionInrece11tyears,n1a11yparallelalgoritlImshavebeendesignedtosolvedifferentproblemso1lvario1ls11etworktopologics.Bi11arytrees,meshesandhypercubesarethethreeimportal1tl1etworktop()logieswllicllhaterpcoivedintensivestlldy.WiththeadvanceofVLSI,manyllewl1etworkssuchasstargrapl1[1]havebeenorwiIlbeintroduced.Inor相似文献   

Efficient evaluation of specific queries in constraint databases

Let F₁,…,Fs∈R[X₁,…,Xn] be polynomials of degree at most d, and suppose that F₁,…,Fs are represented by a division free arithmetic circuit of non-scalar complexity size L. Let A be the arrangement of Rn defined by F₁,…,Fs.For any point x∈Rn, we consider the task of determining the signs of the values F₁(x),…,Fs(x) (sign condition query) and the task of determining the connected component of A to which x belongs (point location query). By an extremely simple reduction to the well-known case where the polynomials F₁,…,Fs are affine linear (i.e., polynomials of degree one), we show first that there exists a database of (possibly enormous) size sO(L+n) which allows the evaluation of the sign condition query using only (Ln)^O(1)log(s) arithmetic operations. The key point of this paper is the proof that this upper bound is almost optimal.By the way, we show that the point location query can be evaluated using dO(n)log(s) arithmetic operations. Based on a different argument, analogous complexity upper-bounds are exhibited with respect to the bit-model in case that F₁,…,Fs belong to Z[X₁,…,Xn] and satisfy a certain natural genericity condition. Mutatis mutandis our upper-bound results may be applied to the sparse and dense representations of F₁,…,Fs.