In this article, we develop a hybrid method for studying wave scatterings and propagation in a vegetation field. The coherent multiple scatterings among the plants and the gaps in the vegetation ...field are considered through a two-step hybrid method. First, the T-matrix of a single plant is calculated using the Huygens principle and the vector cylindrical wave (VCW) expansion based on the full-wave solutions from the Ansys High Frequency Structure Simulator (HFSS). Second, the multiple scatterings between different plants are considered through the Foldy-Lax (FL) multiple-scattering equations using the calculated T-matrix and the translational addition theorem. The convergence and the accuracy of the hybrid method are verified with the HFSS by comparing the solutions of scatterings from four wheat plants. The full-wave Monte Carlo simulations of a field with 169 wheat plants at the <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>-band are subsequently performed using the hybrid method. Numerical results show that the transmission in the gap region is significantly higher than that of the inner region with the difference given quantitatively. The transmissivity of microwave through the wheat field with a large vegetation water content (VWC) can be significantly underestimated by the classical radiative transfer equation (RTE) and distorted Born approximation (DBA) model.
Data from the Cyclone Global Navigation Satellite System (CYGNSS) mission augmented with a physical surface scattering model were analyzed to develop a semiempirical model, which consists of three ...main modeling components for soil moisture, vegetation, and surface roughness. CYGNSS data collected from March 2017 to March 2020 were collocated with the soil moisture data from the Soil Moisture Active Passive (SMAP) mission and climatology vegetation water content (VWC) derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) normalized difference vegetation index (NDVI) data. The matchup data were binned as a function of soil moisture, VWC, and incidence angle. The CYGNSS data were calibrated using a coherent reflection equation to obtain an effective reflectivity. The response of CYGNSS effective reflectivity to soil moisture changes is consistent with the change of the Fresnel reflectivity based on Mironov's soil dielectric constant model used by the SMAP and Soil Moisture Ocean Salinity (SMOS) missions for soil moisture retrieval. The CYGNSS effective reflectivity decreases approximately linearly (in dB) with respect to the NDVI-VWC. The estimated values of vegetation attenuation parameter (<inline-formula> <tex-math notation="LaTeX">b </tex-math></inline-formula>) agree with values published in the literature and are corroborated with the estimated values of <inline-formula> <tex-math notation="LaTeX">b </tex-math></inline-formula> using the SMAP dual-polarized channel algorithm based on land cover types. A CYGNSS surface scattering map has been derived and reveals a mixed contribution of coherent and incoherent scattering effects and the effects of topography. The semiempirical model, leveraging two of the key modeling functions used by microwave radiometry, will pave the way for a synergistic use of reflectometry and radiometry data for multiparameter retrieval and development of consistent soil moisture products.
To calculate scattering of a vegetation field consisting of a large number of plants, an improved fast version of the hybrid method (FHM) combining fast multiple scattering theory (FMST) and a ...numerical electromagnetic approach has been developed. In the HM, we use a library of T-matrices and the Foldy-Lax (FL) equation to calculate the electromagnetic field interactions outside of the cylinders enclosing the individual plants. To improve CPU time and memory requirements, the FL equation is solved by a triplet of fast Fourier transforms (FFTs) consisting of two FFTs solving 2-D FFTs of spatial distribution of plants and one 1-D FFT for solving the transformation of the order of cylindrical waves in the translation addition theorem. The triple FFTs minimize the CPU time and the memory requirement for computing translation addition matrix, which has been the bottleneck of large-scale simulations in the HM. To account for nonperiodic distribution of scatterers in a corn field, the premultiplication and the postmultiplication processes were applied to the FHM. The proposed method is validated at L-band (1.4 GHz) for 100 corn plants of height 1.25 m occupying an area of 9.54 by 9.54 <inline-formula> <tex-math notation="LaTeX">\text{m}^{2} </tex-math></inline-formula>. On a standard laptop, the CPU time is less than 6 min and the memory consumption is less than 710 Mbytes. The CPU time and the memory requirements are orders of magnitude more efficient than those required for solving the problem with a commercial software or using the previous version of the HM.
Passive microwave remote sensing at L-band (1.4 GHz) provides an unprecedented opportunity to estimate global surface soil moisture (SM) and vegetation water content (via the vegetation optical ...depth, VOD), which are essential to monitor the Earth water and carbon cycles. Currently, only two space-borne L-band radiometer missions are operating: the Soil Moisture and Ocean Salinity (SMOS) and the Soil Moisture Active Passive (SMAP) missions in orbit since 2009 and 2015, respectively. This study presents a new mono-angle retrieval algorithm (called SMAP-INRAE-BORDEAUX, hereafter SMAP-IB) of SM and L-band VOD (L-VOD) from the dual-channel SMAP radiometric observations. The retrievals are based on the L-MEB (L-band Microwave Emission of the Biosphere) model which is the forward model of SMOS-IC and of the official SMOS retrieval algorithms. The SMAP-IB product aims at providing good performances for both SM and L-VOD while remaining independent of auxiliary data: neither modelled SM data nor optical vegetation indices are used as input in the algorithm. Inter-comparison with other SM and L-VOD products (i.e., MT-DCA, SMOS-IC, and the new versions of DCA and SCA-V extracted from SMAP passive Level 3 product) suggested that SMAP-IB performed well for both SM and L-VOD. In particular, SMAP-IB SM retrievals presented the higher scores (R = 0.74) in capturing the temporal trends of in-situ observations from ISMN (International Soil Moisture Network) during April 2015–March 2019, followed by MT-DCA (R = 0.71). While the lowest ubRMSD value was obtained by the new version of SMAP DCA (0.056 m3/m3), SMAP-IB SM retrievals presented best scores for R, ubRMSD (~ 0.058 m3/m3) and bias (0.002 m3/m3) when considering only products independent of optical vegetation indices (e.g., NDVI). L-VOD retrievals from SMAP-IB, MT-DCA, and SMOS-IC were well correlated (spatially) with aboveground biomass and tree height, with spatial R values of ~0.88 and ~ 0.90, respectively. All three L-VOD products exhibited a smooth non-linear density distribution with biomass and a good linear relationship with tree height, especially at high biomass levels, while the L-VOD datasets incorporating optical information in the algorithms (i.e., SCA-V and DCA) showed obvious saturation effects. It is expected that this new algorithm can facilitate the fusion of both SM and L-VOD retrievals from SMOS and SMAP to obtain long-term and continuous L-band earth observation products.
•A new algorithm (SMAP-IB) is proposed for the retrieval of SM and L-VOD from SMAP.•Performances of SMAP-IB SM and L-VOD are inter-compared with four other products.•SMAP-IB SM showed best scores for correlation and similar to SCA-V for ubRMSD.•SMAP-IB L-VOD showed high scores according to all used criteria.
This paper describes an algorithm to simultaneously retrieve ocean surface salinity and wind from combined passive/active L-band microwave observations of sea surfaces. The algorithm takes advantage ...of the differing response of brightness temperatures and radar backscatter to salinity, wind speed, and direction. The algorithm minimizes the least square error (LSE) measure, signifying the difference between measurements and model functions of brightness temperatures and radar backscatter. Three LSE measures with different measurement combinations are tested. One of the LSE measures uses passive microwave data only with retrieval errors reaching 2 psu for salinity and 2 m/s for wind speed. The second LSE measure uses both passive and active microwave data for vertical and horizontal polarizations. The addition of active microwave data significantly improves the retrieval accuracy by about a factor of five. To mitigate the impact of Faraday rotation on satellite observations, we propose the third LSE measure using measurement combinations invariant under the Faraday rotation. For Aquarius, the expected root-mean-square SSS error will be less than 0.2 psu for low winds and increases to 0.3 psu at 25-m/s wind speed for warm waters, and the accuracy of retrieved wind speed will be high (about 1-2 m/s or lower). Our results suggest that combining passive and active microwave observations will allow retrieval of sea surface salinity along with the wind speed and direction. In particular, the LSE measure invariant under the Faraday rotation will be directly applicable to spaceborne missions, such as the NASA Aquarius and Soil Moisture Active Passive missions.
Surface roughness and foam are two main components of ocean surface microwave thermal emission. Surface roughness provides scattering element and modifies local incidence angle. Air in foam alters ...the dielectric property of the surface layer. Bubbles in foam also alter the curvature of foam-water interface and modify emission and scattering properties of the water surface itself. Whitecap coverage <inline-formula> <tex-math notation="LaTeX">W_{\mathrm {c}} </tex-math></inline-formula> is the most accessible oceanographic information to represent surface foam. For emission analysis, it is necessary to establish a function relating to <inline-formula> <tex-math notation="LaTeX">W_{\mathrm {c}} </tex-math></inline-formula> and the effective air fraction <inline-formula> <tex-math notation="LaTeX">F_{\mathrm {a}} </tex-math></inline-formula> interacting with electromagnetic (EM) waves. An empirical relation is established through analyzing several microwave radiometer data sets in high winds covering a wide range of frequency, incidence angle, and vertical and horizontal polarizations. A physical interpretation of the proposed <inline-formula> <tex-math notation="LaTeX">F_{\mathrm {a}} </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">W_{\mathrm {c}} </tex-math></inline-formula>) relationship is discussed. The relationship is used to quantify several important characteristics of surface foam relevant to microwave emission, including effective air fraction and skin depth as functions of wind speed, microwave frequency, and incidence angle.
This paper presents analysis of P-band radio signal propagation through forest based on 3D Numerical Method of Maxwell's equations (NMM3D). The simulation domain of the forested region covers an area ...of 35.8 by 35.8 m 2 that includes 112-121 coniferous trees with a height in the range of 8 to 16 meters. The modelled trees have primary and secondary branches to account for their impact on scattering and attenuation at P-band. The Fast hybrid method (FHM) has been successfully developed to complete the NMM3D full wave simulations of trees with efficient use of CPU time and memory. The accuracy of the proposed FHM model is validated by comparing scattered fields to that of FEKO for the case with 9 trees. To account for the seasonal variation of water content in trees and hence dielectric constant, the wave scattering model is applied to a range of dielectric constants. Analysis of the P-band signal propagation is performed by computing the average loss and correlation of the transmission fields. The results show that the transmissivities are about 0.9 for winter conditions (low dielectric constant) and about 0.7 for summer conditions (high dielectric constant). Simulations with randomly positioned trees (off the periodic grid) demonstrate that the transmissivity shows a maximum variation of 4.3% relative to the non-randomly positioned trees. The correlation analysis of P-band radio signals with two different dielectric constants indicates a high correlation amplitude above 0.89 and a phase change of less than 6 degrees. A sensitivity analysis is carried out for a range of tree heights and trunk radii.
Abstract
Whitecaps manifest surface wave breaking that impacts many ocean processes, of which surface wind stress is the driving force. For close to a half century of quantitative whitecap reporting, ...only a small number of observations are obtained under conditions with wind speed exceeding 25 m s
−1
. Whitecap contribution is a critical component of ocean surface microwave thermal emission. In the forward solution of microwave thermal emission, the input forcing parameter is wind speed, which is used to generate the modeled surface wind stress, surface wave spectrum, and whitecap coverage necessary for the subsequent electromagnetic (EM) computation. In this respect, microwave radiometer data can be used to evaluate various formulations of the drag coefficient, whitecap coverage, and surface wave spectrum. In reverse, whitecap coverage and surface wind stress can be retrieved from microwave radiometer data by employing precalculated solutions of an analytical microwave thermal emission model that yields good agreement with field measurements. There are many published microwave radiometer datasets covering a wide range of frequency, incidence angle, and both vertical and horizontal polarizations, with maximum wind speed exceeding 90 m s
−1
. These datasets provide information of whitecap coverage and surface wind stress from global oceans and in extreme wind conditions. Breaking wave energy dissipation rate per unit surface area can be estimated also by making use of its linear relationship with whitecap coverage derived from earlier studies.
The spaceborne aperture radar (SAR) technique based on a combination of P-band signals of opportunity (SoOp) reflectometry with a sparse array of receivers at low earth orbits (LEOs) and transmit ...signals from the United States Navy's Mobile User Objective System operating on a geosynchronous altitude has been analyzed. The design focuses on the forward-looking geometry near the specular direction, which allows a high surface reflectivity, in order to obtain adequate signal-to-noise ratio (SNR) with a moderate receiving antenna gain. The sparse array is utilized to sharpen the across-track resolution and reduce the iso-range ambiguity. The formulation for match filtering and illustrations of point target response are presented. This work shows that an array of five to seven receivers is able to achieve an across-track resolution of about 200 m in the outer portion of swath and about 1 km in the center part of swath. The along-track resolution can reach 10 m or better due to the feasibility of a long dwell time for Doppler filtering. We find that the sparse array allows the reduction of the iso-range ambiguity to a level of lower than 5% for a major portion of swath, ~70% or greater depending on the number of receivers and spacing. We have completed an SNR formulation, which can consistently account for both coherent and incoherent scattering regardless the spatial resolution. An analysis of SNR based on the Kirchhoff approximation for rough surface scattering has been performed. We find that it is possible to obtain a swath width of 100 km with an SNR of 5 dB or better for a constellation of seven satellites with a receiving antenna directivity of 15 dBi at a LEO altitude of 675 km for a wide range of surface roughness. Our study suggests the promise of the SoOpSAR concept for high-resolution remote sensing of land surfaces.
Microwave vegetation optical depth (VOD) and soil moisture (SM) can be simultaneously retrieved based on L-band radiometry with polarization information. VOD is indicative of the vegetation water ...content (VWC) because it captures the extinction of land surface emission. If the connectivity of VOD to VWC is robust, the pair of VWC-SM observations can be viable bases for understanding soil-plant-atmosphere water relations, providing new perspectives on ecosystem science. Simultaneous SM-VOD retrievals are feasible by inverting the <inline-formula> <tex-math notation="LaTeX">\tau -\omega </tex-math></inline-formula> model with two independent datasets in dual-channel algorithms. However, given correlated satellite vertical and horizontal brightness temperatures (TBs; TB v and <inline-formula> <tex-math notation="LaTeX">{{\mathrm {TB}}}_{h} </tex-math></inline-formula>), an ill-posed inverse problem arises where TB errors result in high uncertainties of retrievals. In this study, we apply the degrees-of-information (DoI) metric and propose a signal-to-noise ratio (SNR) metric to assess the "retrievability" of VOD given the Soil Moisture Active Passive (SMAP) TB v -TB h linear dependence. The application of these metrics allows determining where the VOD retrievals are robust and reliable. This is a necessary step in supporting the applications of VOD in ecology and hydrology. Results show that regions with mainly nonwoody vegetation have the best potential for VOD retrievals, though regularization is necessary. We then assess VOD time variations from two regularization products that reduce the impact of underdetermined inversions: the L3 dual-channel algorithm (L3-DCA) and the multitemporal dual-channel algorithm (MTDCA), which constrain VOD time dynamics with and without using a priori VOD climatology, respectively. Though they both reduce noise, especially in the VOD retrievals, they result in differences in VOD seasonal amplitude and coupling to SM at high frequencies as we outline here.
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