An observation system simulation experiment for the impact of landsurface heterogeneity on AMSR-E soil moisture retrieval

Using a high-resolution hydrologic model, a land surface microwave emission model (LSMEM), and an explicit simulation of the orbital and scanning characteristics for the advanced microwave sensing radiometer (AMSR-E), an observing system simulation experiment (OSSE) is carried out to assess the impact of land surface heterogeneity on large-scale retrieval and validation of soil moisture products over the U.S. Southern Great Plains using the 6.925 GHz channel on the AMSR-E sensor. Land surface heterogeneity impacts soil moisture products through the presence of nonlinearities in processes represented by the LSMEM, as well as the fundamental inconsistency in spatial scale between gridded soil moisture imagery derived from in situ point-scale sampling, numerical modeling, and microwave remote sensing sources. Results within the 575000 km² Red-Arkansas River basin show that, for surfaces with vegetation water contents below 0.75 kg/m², these two scale effects induce root mean squared errors (RMSEs) of 1.7% volumetric (0.017 cm_water³/cm_soil³ ) into daily 60 km AMSR-E soil moisture products and RMS differences of 3.0% (0.030 cm_water/3cm_soil³ ) into 60 km comparisons of AMSR-E soil moisture products and in situ field-scale measurements of soil moisture sampled on a fixed 25-km grid     

Stochastic gradient adaptation under general error criteria

Examines a family of adaptive filter algorithms of the form W_k+1=W_k+μf(d_k-W_k^t X_k)X_k in which f(·) is a memoryless odd-symmetric nonlinearity acting upon the error. Such algorithms are a generalization of the least-mean-square (LMS) adaptive filtering algorithm for even-symmetric error criteria. For this algorithm family, the authors derive general expressions for the mean and mean-square convergence of the filter coefficients For both arbitrary stochastic input data and Gaussian input data. They then provide methods for optimizing the nonlinearity to minimize the algorithm misadjustment for a given convergence rate. Using the calculus of variations, it is shown that the optimum nonlinearity to minimize misadjustment near convergence under slow adaptation conditions is independent of the statistics of the input data and can be expressed as -p'(x)/p(x), where p(x) is the probability density function of the uncorrelated plant noise. For faster adaptation under the white Gaussian input and noise assumptions, the nonlinearity is shown to be x/{1+μλx²/σ_k ²}, where λ is the input signal power and σ_k² is the conditional error power. Thus, the optimum stochastic gradient error criterion for Gaussian noise is not mean-square. It is shown that the equations governing the convergence of the nonlinear algorithm are exactly those which describe the behavior of the optimum scalar data nonlinear adaptive algorithm for white Gaussian input. Simulations verify the results for a host of noise interferences and indicate the improvement using non-mean-square error criteria     

RMS bandwidth constrained signature waveforms that maximize thetotal capacity of PAM-synchronous CDMA channels

Optimum time-limited signal sets of equal and unequal energies are obtained under root mean square (RMS) bandwidth constraints. The total capacity and the total asymptotic efficiency of the PAM synchronous Gaussian CDMA (PSG-CDMA) channel are considered as the optimality criteria. The latter measure is monotonic with the determinant of the correlation matrix, R, and the former is monotonic with det(I+σ ^-2R), where σ² represents the noise level. Average as well as maximum RMS bandwidth constraints are considered in the equal-energy case, and the energy-weighted RMS bandwidth constraint is considered for unequal energy signals. For the equal-energy problem, signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum RMS bandwidth constraints. For the total capacity measure, such simultaneously optimal signal sets are also obtained, albeit under the restriction that the number of signals n be a Hadamard matrix dimension. When the Hadamard dimension is in particular a power of two, we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded PSG-CDMA channel. Unequal energy signal sets are also found under an energy-weighted RMS bandwidth constraint for both optimality criteria     

Kernel estimation of the instantaneous frequency

Considers kernel estimators of the instantaneous frequency of a slowly evolving sinusoid in white noise. The expected estimation error consists of two terms. The systematic bias error grows as the kernel halfwidth increases while the random error decreases. For a nonmodulated signal g(t), the kernel halfwidth that minimizes the expected error is proportional to h~[(σ²)/(N|∂_t² g|2)]^1/5 where σ² is the noise variance and N is the number of measurements per unit time. The author shows that estimating the instantaneous frequency corresponds to estimating the first derivative of a modulated signal, A(t)exp(iφ(t)). For instantaneous frequency estimation, the halfwidth which minimizes the expected error is larger: h_1,3~[(σ²)/(A²N|∂_t ³(e^iφ¯(t/))|sup 2/)]¹/$ u7. Since the optimal halfwidths depend on derivatives of the unknown function, the authors initially estimate these derivatives prior to estimating the actual signal     

An empirical model and an inversion technique for radar scatteringfrom bare soil surfaces

Polarimetric radar measurements were conducted for bare soil surfaces under a variety of roughness and moisture conditions at L -, C-, and X-band frequencies at incidence angles ranging from 10° to 70°. Using a laser profiler and dielectric probes, a complete and accurate set of ground truth data was collected for each surface condition, from which accurate measurements were made of the rms height, correlation length, and dielectric constant. Based on knowledge of the scattering behavior in limiting cases and the experimental observations, an empirical model was developed for σ°_hh, σ°_vv, and σ° _hv in terms of ks (where k=2π/λ is the wave number and s is the rms height) and the relative dielectric constant of the soil surface. The model, which was found to yield very good agreement with the backscattering measurements of the present study as well as with measurements reported in other investigations, was used to develop an inversion technique for predicting the rms height of the surface and its moisture content from multipolarized radar observations     

A method to dramatically improve subcarrier tracking

A method is presented for achieving a considerable improvement in phase tracking of square-wave subcarriers or other square waves. The amplitude of the phase quadrature reference signal is set to zero, except near the zero crossings of the input signal. Without changing the loop bandwidth, the variance of the phase error can be reduced by approximately Wσ₀² where σ ₀² is the phase error variance without windowing and W is the fraction of cycle in which the reference signal has a nonzero value. Simulation results confirm the results of the analysis and establish minimum W versus SNR (signal-to-noise ratio). Typically, the window can be made so narrow as to achieve a phase error variance of 1.5 σ₀⁴     

Inferring Vegetation Water Content From C- and L-Band SAR Images

This paper addresses the capability of synthetic aperture radar and optical images in combination with theoretical models to detect the vegetation water content (VWC) at field level. In this paper, a retrieval algorithm for the estimation of VWC from AirSAR acquired on vegetated fields during the SMEX'02 experiment is addressed. The aforementioned campaign has been chosen because, along with sensor observations, extensive ground truth measurements were acquired. The retrieval procedure, which is based on a Bayesian approach, has been initially developed for soil moisture extraction. It consists of two modules: one is pertinent to bare soils and the other one has been modified for vegetated fields. The last one uses the synergy with optical images to correct for the contribution of VWC. The VWC, a variable in the inversion procedure, as well as soil moisture can be estimated. The results indicate a good correlation with both ground measurements and VWC calculated from Landsat images through the use of normalized difference water index (NDWI). Furthermore, in the inversion procedure, the introduction of the dependence on roughness improves the estimates. This indicates that, even for dense vegetation, the contribution from bare soil greatly influences the radar signal. Three main levels of VWC are discriminated in the inversion procedure: values below 1 kg/m², values between 1 and 3 kg/m², and values greater than 3 kg/m².     

95-GHz scattering by terrain at near-grazing incidence

This study, consisting of three complimentary topics, examines the millimeter-wave backscattering behavior of terrain at incidence angles extending between 70 and 90°, corresponding to grazing angles of 20° to 0°. The first topic addresses the character of the statistical variability of the radar backscattering cross section per unit area σ_A. Based on an evaluation of an extensive data set acquired at 95 GHz, it was determined that the Rayleigh fading model (which predicts that σ_A is exponentially distributed) provides an excellent fit to the measured data for various types of terrain covers, including bare surfaces, grasses, trees, dry snow, and wet snow. The second topic relates to the angular variability and dynamic range of the backscattering coefficient σ⁰, particularly near grazing incidence. We provide a summary of data reported to date for each of several types of terrain covers. The last topic focuses on bare surfaces. A semi-empirical model for σ⁰ is presented for vertical (VV), horizontal (HH), and cross (HV) polarizations. The model parameters include the incidence angle &thetas;, the surface relative dielectric constant ϵ, and the surface roughness ks, where k=2π/λ and s is the surface root mean square (RMS) height     

A semi-empirical backscattering model at L-band and C-band for asoybean canopy with soil moisture inversion

Radar backscatter measurements of a pair of adjacent soybean fields at L-band and C-band are reported. These measurements, which are fully polarimetric, took place over the entire growing season of 1996. To reduce the data acquisition burden, these measurements were restricted to 45° in elevation and to 45° in azimuth with respect to the row direction. Using the first order radiative transfer solution as a form for the model of the data, four parameters were extracted from the data for each frequency/polarization channel to provide a least squares fit to the model. For inversion, particular channel combinations were regressed against the soil moisture and area density of vegetation water mass. Using L-band cross-polarization and VV-polarization, the vegetation water mass can be regressed with an R ²=0.867 and a root mean square error (RMSE) of 0.0678 kg/m ². Similarly, while a number of channels, or combinations of channels, can be used to invert for soil moisture, the best combination observed, namely, L-band VV-polarization, C-band HV- and VV-polarizations, can achieve a regression coefficient of R²=0.898 and volumetric soil moisture RMSE of 1.75%     

QuikSCAT geophysical model function for tropical cyclones andapplication to Hurricane Floyd

The QuikSCAT radar measurements of several tropical cyclones in 1999 have been studied to develop the geophysical model function (GMF) of Ku-band radar σ₀ values (normalized radar cross section) for extreme high wind conditions. To account for the effects of precipitation, the authors analyze the co-located rain rates from the Special Sensor Microwave/Imager (SSM/I) and propose the rain rate as a parameter of the GMF. The analysis indicates the deficiency of the NSCAT2 GMF developed for the NASA scatterometer, which overestimates the ocean σ₀ for tropical cyclones and ignores the influence of rain. It is suggested that the QuikSCAT σ₀ is sensitive to the wind speed of up to about 40-50 m s^-1. The authors introduce modifications to the NSCAT2 GMF and apply the modified GMF to the QuikSCAT observations of Hurricane Floyd. The QuikSCAT wind estimates for Hurricane Floyd in 1999 was improved with the maximum wind speed reaching above 60 m s^-1. The authors perform an error analysis by comparing the QuikSCAT winds with the analyses fields from the National Oceanic and Atmospheric Administration (NOAA) Hurricane Research Division (HRD). The reasonable agreement between the improved QuikSCAT winds and the HRD analyses supports the applications of scatterometer wind retrievals for hurricanes     

Seasat over-land scatterometer data. I. Global overview of theKu-band backscatterer coefficients

Statistics on the backscatter coefficient σ⁰ from the Ku-band Seasat-A Satellite Scatterometer (SASS) collected over the world's land surfaces are presented. This spaceborne scatterometer provided data on σ⁰ between latitude 80° S and 80° N at incidence angles up to 70°. The global statistics of vertical (V) and horizontal (H) polarization backscatter coefficients for 10° bands in latitude are presented for incidence angles between 20° and 70° and compared with the Skylab and ground spectrometer results. Global images of the time-averaged V polarization σ⁰ at a 45° incidence angle and its dependence on the incidence angle are presented and compared to a generalized map of the terrain type. Global images of the differences between the V an H polarization backscatter coefficients are presented and discussed. The most inhomogeneous region, which contains the deserts of North Africa and the Arabian Peninsula, is studied in greater detail and compared with the terrain type     

Using ENVISAT ASAR Global Mode Data for Surface Soil Moisture Retrieval Over Oklahoma, USA

The advanced synthetic aperture radar (ASAR) onboard of the satellite ENVISAT can be operated in global monitoring (GM) mode. ASAR GM mode has delivered the first global multiyear C-band backscatter data set in HH polarization at a spatial resolution of 1 km. This paper investigates if ASAR GM can be used for retrieving soil moisture using a change detection approach over large regions. A method previously developed for the European Remote Sensing (ERS) scatterometer is adapted for use with ASAR GM and tested over Oklahoma, USA. The ASAR-GM-derived relative soil moisture index is compared to 50-km ERS soil moisture data and pointlike in situ measurements from the Oklahoma MESONET. Even though the scale gap from ASAR GM to the in situ measurements is less pronounced than in the case of the ERS scatterometer, the correlation for ASAR against the in situ measurements is, in general, somewhat weaker than for the ERS scatterometer. The analysis suggests that this is mainly due to the much higher noise level of ASAR GM compared to the ERS scatterometer. Therefore, some spatial averaging to 3–10 km is recommended to reduce the noise of the ASAR GM soil moisture images. Nevertheless, the study demonstrates that ASAR GM allows resolving spatial details in the soil moisture patterns not observable in the ERS scatterometer measurements while still retaining the basic capability of the ERS scatterometer to capture temporal trends over large areas.      

Convergence models for Rosenblatt's perceptron learning algorithm

Presents a stochastic analysis of the steady-state and transient convergence properties of a single-layer perceptron for fast learning (large step-size, input-power product). The training data are modeled using a system identification formulation with zero-mean Gaussian inputs. The perceptron weights are adjusted by a learning algorithm equivalent to Rosenblatt's perceptron convergence procedure. It is shown that the convergence points of the algorithm depend on the step size μ and the input signal power (variance) σ_x² , and that the algorithm is stable essentially for μ>0. Two coupled nonlinear recursions are derived that accurately model the transient behavior of the algorithm. The authors also examine how these convergence results are affected by noisy perceptron input vectors. Computer simulations are presented to verify the analytical models     

Measurement and modeling of the millimeter-wave backscatterresponse of soil surfaces

The millimeter-wave (MMW) backscatter response of bare-soil was examined by conducting experimental measurements at 35 and 94 GHz using a truck-mounted polarimetric scatterometer and by developing appropriate models to relate the backscattering coefficient to the soil's surface and volume properties. The experimental measurements were conducted for three soil surfaces with different roughnesses under both dry and wet conditions. The experimental measurements indicate that in general the backscattering coefficient is comprised of a surface scattering component σ^s and a volume scattering component σ ^v. For wet soil conditions, the backscatter is dominated by surface scattering, while for dry conditions both surface and volume scattering are significant, particularly at 94 GHz. Because theoretical surface scattering models were found incapable of predicting the measured backscatter, a semiempirical surface scattering model was developed that relates the surface scattering component of the total backscatter to the roughness parameter ks, where k=2π/λ and s is the rms height, and the dielectric constant of the soil surface. Volume scattering was modeled using radiative transfer theory with the packed soil particles acting as the host material and the air voids as the scattering particles. The combined contribution of surface and volume scattering was found to provide good agreement between the model calculations and the experimental observations     

Estimation of snow water equivalence using SIR-C/X-SAR. I. Inferring snow density and subsurface properties

Algorithms for estimating dry snow density and the dielectric constant and roughness of the underlying soil or rock use backscattering measurements with VV and HH polarization at L-band frequency (1.25 GHz). Comparison with field measurements of snow density during the first SIR-C/X-SAR overpass shows absolute accuracy of 42 kg m/sup -3/ (13% relative error). For the underlying soil, comparisons with the ground scatterometer measurements showed errors of 4% by volume for soil moisture estimation and 4 mm for the surface root mean square (RMS) height. Values of snow density and the properties of the underlying soil are necessary for the estimation of snow water equivalence.     

Capacity of the Gaussian arbitrarily varying channel

The Gaussian arbitrarily varying channel with input constraint Γ and state constraint Λ admits input sequences x=(x₁,---,X_n) of real numbers with Σx_i²⩽nΓ and state sequences s=(S₁,---,s_n ) of real numbers with Σs_i²⩽nΛ; the output sequence x+s+V, where V=(V₁,---,V_n) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance σ². It is proved that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals 1/2 log (1+Γ/(Λ+σ²)) if Λ<Γ and is 0 otherwise     

Reanalysis of L-band brightness predicted by the LSP/R model-forprairie grassland: incorporation of rough surface scattering

L-band brightness predicted by the land surface process/radiobrightness (LSP/R) model for prairie grassland appears to be somewhat lower than expected. A crucial reason for the underestimate of the L-band brightness is that the soil surface was treated as smooth. In this paper, surface scattering of the soil determined by the IEM model is incorporated into the LSP/R model to examine its impact on the predicted L-band brightness. Eight sets of surface parameters, two correlation lengths (L) of 3 and 6 cm×4 root mean squared (RMS) heights (σ) of 0.3, 0.6, 0.8, and 1.0 cm, are utilized to characterize the emission of the soil surface. It is found that H-polarized, L-band brightness is expectedly increased by different levels for all of the eight rough surface cases compared to the smooth surface case. The increase in the average of the H-polarized, L-band brightness is by as much as 13.2 K for the case with L=3 cm and σ=1.0 cm. In addition, L-band's sensitivity to soil moisture is found to be approximately equal with and without the scattering effects. An increase in H-polarized, L-band brightness by about 12 K at the end of a 14-day simulation by the LSP/R model is in response to a decrease in soil moisture by 7% for all of the nine cases of concern (eight rough plus one smooth soil surfaces)     

Soil Moisture Retrieval During a Corn Growth Cycle Using L-Band (1.6 GHz) Radar Observations

This paper reports on the retrieval of soil moisture from dual-polarized L-band (1.6 GHz) radar observations acquired at view angles of 15$^{circ}$, 35 $^{circ}$, and 55$^{circ}$ , which were collected during a field campaign covering a corn growth cycle in 2002. The applied soil moisture retrieval algorithm includes a surface roughness and vegetation correction and could potentially be implemented as an operational global soil moisture retrieval algorithm. The surface roughness parameterization is obtained through inversion of the Integral Equation Method (IEM) from dual-polarized (HH and VV) radar observations acquired under nearly bare soil conditions. The vegetation correction is based on the relationship found between the ratio of modeled bare soil scattering contribution and observed backscatter coefficient $(sigma^{rm soil}/sigma^{rm obs})$ and vegetation water content $(W)$. Validation of the retrieval algorithm against ground measurements shows that the top 5-cm soil moisture can be estimated with an accuracy between 0.033 and 0.064 $hbox{cm}^{3}cdothbox{cm}^{-3}$, depending on the view angle and polarization.      

An empirical model for interpreting the relationship betweenbackscattering and arid land surface roughness as seen with the SAR

The nature of the surface in a flat arid zone located in the western Sahara desert was studied and its roughness parameters defined. The main geological units were compared with backscattering data from ERS-1 images. Results showed a close correlation between the backscattering coefficient, σ₀, and the maximum height, h_max, of the rocks making up the arid landscape. The simplified relationship σ₀=4.63.1og h_max-15.29 (with h_max in cm and σ₀ in dB) was established from field measurements, giving an r² of about 88%. This empirical relationship is confirmed by another close relation between σ₀ and the statistical parameter s, the height standard deviation. The advantage of h_max is that it can be extracted for any site, whatever its roughness may be. The spatial distribution of the rock facets and the geometric characteristics of the incidence angle of the radar signal seem to explain the results     

A numerical procedure for recovering scattering coefficients frommeasurements with wide-beam antennas

A numerical procedure for estimating true scattering coefficients, σ⁰, from measurements made using wide-beam antennas is discussed. The use of wide-beam antennas results in an inaccurate estimate of σ⁰. To reduce this error, the authors propose a correction procedure that estimates the error resulting from the use of narrow-beam approximation and utilizes the error to obtain a more accurate estimate of σ⁰. An exponential model is assumed to take into account the variation of σ⁰ with incidence angles, and the model parameters are estimated from measured data. Based on the model and knowledge of the antenna pattern, the procedure calculates the error due to the narrow-beam approximation. The procedure is shown to provide a significant improvement in the estimation of σ⁰ obtained in wide-beam antennas. The proposed procedure is also shown to be insensitive to the assumed σ⁰ model