The Copernicus Imaging Microwave Radiometer (CIMR) is a Copernicus Expansion Mission with an expected launch in 2028+. The satellite will carry a multi-frequency microwave radiometer operating in the L-, C-, X-, Ku-, and Ka-bands. In addition to providing L-band continuity from other missions (e.g., SMOS, SMAP), the CIMR mission brings new soil moisture remote sensing opportunities due to its multi-frequency, multi-resolution, and high temporal revisit characteristics. This study outlines a preliminary version of a soil moisture retrieval approach designed within CIMR preparatory activities. It aims to provide two soil moisture products: the first is based on the inversion of L-band brightness temperature measurements at their native resolution (<60 km). The second product is based on the inversion of enhanced resolution L-band measurements (<15 km) achieved through sharpening the L-band with higher resolution C/X-band measurements. In both cases, the soil moisture retrieval is based on the inversion of the zeroth-order tau-omega radiative transfer model. We present current efforts of algorithm development and performance evaluation based on simulated CIMR L1B data. The results presented here showcase the potential of CIMR to provide soil moisture estimates not only at hydroclimatological scales (<60 km, from L-band) but also at hydrometeorological scales (~10 to 25 km, from L-band, sharpened with C/X bands), meeting the needs of a wide range of science and applications.

Abstract In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is needed in which parts of the image space. Furthermore, it is guaranteed that after finitely many iterations, an enclosure of the nondominated set of prescribed quality is returned. We demonstrate the advantages of this approach by applying it to multiobjective energy supply network problems.

Abstract Given a Henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any Henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show that in this case, one parameter is optimal in the sense that one cannot obtain definability without parameters. To this end, we present a construction method for a t-Henselian non-Henselian ordered field elementarily equivalent to a Henselian field with a specified value group.

The NASA Soil Moisture Active Passive (SMAP) satellite mission aims to produce enhanced resolution surface soil moisture products by combining coincident but multiresolution L-band active and passive microwave measurements. Since the SMAP radar ceased operations early in the mission, Copernicus Sentinel-1 C-band radar observations are used in the combined product. The synergy is built on two basic foundations: first, active and passive signals covary in a known and systematic fashion, and second, measurements are available at multiple resolutions. In this study, we perform numerical simulations and assess global satellite observations to test the first foundation (covariation). Specific focus lies on the role of the vegetation canopy in modulating the active–passive relationship. We use a discrete radiative transfer model to simulate the slope$\beta $and coefficient of determination$R^{2}$of the relationship between active and passive signals, considering three vegetation types for which the model has been extensively assessed in previous experimental studies. We find that a linear relationship between backscatter and emissivity can be established over a range of vegetation conditions. The coupling between active and passive signals decreases with increasing vegetation water content, such that moderate or higher correlations (nonzero slopes) are retained up to 4 kg/m2(6.3 kg/m2) for L-band/L-band and 1.5 kg/m2(2 kg/m2) for the C-band/L-band configuration. We decompose the effects of different soil-vegetation scattering mechanisms, such as double-bounce, and different measurement error levels on the active–passive relationship. Comparisons with satellite data confirm that our simulations capture magnitudes and major trends found across global vegetated land masses.

In this article, we present a multipolarimetric estimation approach for two model-based vegetation structure parameters (shape A and orientation distribution ψ of the main canopy elements). The approach is based on a reduced observation set of three incoherent (no phase information) polarimetric backscatter intensities (|SHH|2, |SHV|2, and |SVV|2) combined with a two-parameter (APand ψ) discrete scatterer model of vegetation. The objective is to understand whether this confined set of observations contains enough information to estimate the two vegetation structure parameters from the L-band radar signals. In order to disentangle soil and vegetation scattering influences on these signals and ultimately perform a vegetation only retrieval of vegetation shape A and orientation distribution ψ, we use the subpixel spatial heterogeneity expressed by the covariation of co- and cross-polarized backscatter ΓPP-PQof the neighboring cells and assume it is indicative for the amount of a vegetation-only co-to-cross-polarized backscatter ratio μPP-PQ. The ratio-based retrieval approach enables a relative (no absolute backscatter) estimation of the vegetation structure parameters which is more robust compared to retrievals with absolute terms. The application of the developed algorithm on global L-band Soil Moisture Active Passive (SMAP) radar data acquired from April to July 2015 indicates the potential and limitations of estimating these two parameters when no fully polarimetric data are available. A focus study on six different regions of interest, spanning land cover from barren land to tropical rainforest, shows a steady increase in orientation distribution toward randomly oriented volumes and a continuous decrease in shape arriving at dipoles for tropical vegetation. A comparison with independent data sets of vegetation height and above-ground biomass confirms this consistent and meaningful retrieval of APand ψ. The retrieved shapes and orientation distributions represent the main vegetation elements matching the literature results from model-based decompositions of fully polarimetric L-band data at the SMAP spatial resolution. Based on our findings, APand ψ can be directly applied for parameterizing the vegetation scattering component of model-based polarimetric decompositions. This should facilitate decomposition into ground and vegetation scattering components and improve the retrieval of soil parameters (moisture and roughness) under vegetation.

Microwave brightness temperature (Tb) and backscatter (σ0) observations from the Soil Moisture and Ocean Salinity (SMOS) mission, Soil Moisture Active Passive (SMAP) mission, Advanced Microwave Scanning Radiometer 2 (AMSR2) instrument, and Advanced Scatterometer (ASCAT) instrument provide a wealth of operationally available satellite data for soil moisture retrieval and data assimilation purposes. To assist the synergistic and efficient use of such techniques, the soil moisture information content in the respective Level-1 observations needs to be determined. Within this context, we compare L-, C-, and X-band Tb and σ0signatures of the above-named sensors to in situ SM observations in Spain, Australia, and USA. We find that L-band Tb observations from SMOS and SMAP show the best overall performance given the considered diagnostics (correlation, anomaly correlation, and sensitivity), while all sensors provide significant soil moisture information. This finding is consistent across the analyzed incidence angle range for SMOS (25°-60°). The results are discussed with respect to physical processes governing the dynamics of Tb and σ0, noting dependencies on vegetation seasonality and land surface temperature.

Active and passive low-frequency microwave measurements from a number of space- and airborne instruments are used to estimate soil moisture. Each of the sensing approaches has distinct advantages and disadvantages. There is increasing interest in combining active and passive measurements in order to realize the advantages and alleviate the disadvantages. In order to combine active and passive measurements, their covariations with respect to soil moisture need to be known. The covariation is dependent on how the active and passive microwaves interact with vegetation canopy and soil surface. In this paper, we introduce a physics-based model for the covariation of active and passive microwaves over soil surfaces with vegetation cover. The analytical form for a covariation function is derived which depends on the scattering and absorption of microwaves by soil and vegetation with different orientations, structures, and water contents. The main finding is that the covariation function β is related to the roughness and vegetation losses in the two measurements. An increase in soil roughness or in vegetation cover leads to less negative values of β, which is pronounced for dense and moist vegetation. Both the soil and vegetation components introduce a polarization dependence of β that is caused by polarization-induced differences in soil scattering and oriented plant structures. The forward modeled covariations are plotted together with statistically derived covariation estimates from two months of global active and passive L-band observations of the Soil Moisture Active Passive mission. The physically modeled and statistically derived estimates of covariation are comparable in magnitude and scale.

In this study, the τ-ω model framework is used to derive extinction coefficient and canopy penetration depths from multi-frequency SMAP and AMSR2 retrievals of vegetation optical depth together with ICESat LiDAR vegetation heights. The vegetation extinction coefficient serves as an indicator of how strong absorption and scattering processes within the canopy attenuate microwaves at L and C-band. Through inversion of the extinction coefficient, the penetration depth into the canopy can be obtained, which is analyzed on local (Sahel, Illinois) and continental scale (Africa, parts of North America) as well as for a one year time series (04/2015-04/2016). First analyses of the retrieved penetration depth estimates reveal strongest attenuation for densely forested areas, therefore vegetation attenuation should be accounted for when retrieving soil moisture in these areas. For the continents of North America and Africa penetration depths decrease in average with an increase in frequency from L- to C-band. Moreover penetration depth time series were found to match with expected seasonal variations (e.g. vegetation growth period & rainy season) for analyzed local regions.

Estimating parameters for global climate models via combined active and passive microwave remote sensing data has been a subject of intensive research in recent years. A variety of retrieval algorithms has been proposed for the estimation of soil moisture, vegetation optical depth and other parameters. A novel attenuation-based retrieval approach is proposed here to globally estimate the gravimetric moisture of vegetation (mg) and retrieve information about the amount of water [kg] per amount of wet vegetation [kg]. The parameter mgis particularly interesting for agro-ecosystems, to assess the status of growing vegetation. The key feature of the proposed approach is that it relies on multi-sensor data from three sensor types (microwave radar, microwave radiometer, and lidar) to solve the physics equations and obtain mg-estimates. The comparability of these estimates to literature values as well as to results of a globally applied, retrieval approach of Grant [4], reveal the potential of the developed method.

Combined active-passive remote sensing has the potential for capturing the relative advantage of each sensing approach in geophysical retrievals. One cornerstone of combined active-passive microwave sensing is the modeling of the covariation of active and passive signals, which arise from equivalent sensitivities of both sensor types to changes in geophysical properties. In this research contribution, we propose a physics-based active-passive combination of active and passive microwave observations based on Kirchhoff's law of energy conservation. This allows establishing a physics-based forward model as well as a fully data-driven, single-pass retrieval methodology for active-passive microwave covariation. The forward model and the retrieval approach are adaptable to different sensor characteristics (incidence angle, frequency & polarization). The theoretical (forward model) as well as applied (retrieval method) physics-based covariation framework is tested with SMAP (LL) and SMAP/Sentinel-1 (LC) data to reveal potentials and constraints for active-passive microwave sensing. As a result of the conducted study, a linear functional relationship between active and passive microwave observations (e.g. assumed for the SMAP mission) is confirmed, if higher-order scattering can be omitted.

Low-frequency microwave brightness temperature and backscatter observations are sensitive to surface soil moisture, a key variable for applications like numerical weather prediction, drought monitoring and climate modeling. With ESA's Soil Moisture and Ocean Salinity (SMOS) mission and NASA's Soil Moisture Active Passive (SMAP) mission, two L-band radiometers dedicated to soil moisture monitoring are currently in orbit. In addition, operational soil moisture products exist based on EUMETSAT MetOp C-band advanced scatterometer (ASCAT) and JAXA GCOM-W multifrequency radiometer (AMSR2) data. This study aims to assess the information content of Level-l data from active and passive microwave sensors for soil moisture estimation. Specific focus lies on the comparison between frequencies (L-band, C-band, X-band) and sensor types (active and passive) as well as the added value of multi-angular brightness temperature observations (e.g. from SMOS) with respect to fixed incidence angle observations. The study will provide insights into the suitability of different sensor types for soil moisture estimation irrespective of the individual Level-2 retrieval algorithm specifics. The results shall assist the definition of new observation concepts and the identification of synergies between planned or existing satellite missions.

NASA's Soil Moisture Active-Passive (SMAP) mission aims at disaggregating L-band radiometer (36 km) with L-band radar (1-3 km) observations to obtain an intermediate resolution soil moisture product (1-9 km). Since SMAP's radar stopped operations in July 2015, a substitution with ESA's Sentinel 1 C-band radar is underway. For this purpose, the relationship of L-band radiometer and C-band radar observations needs to be determined, especially considering the frequency dependent influence of vegetation. This study investigates vegetation effects on covariations of backscatter and emissivity, considering the SMAP-Sentinel 1 (C/L-band) and original SMAP (L/L-band) frequency configurations. Covariations are expressed as the linear regression slope β between backscatter and emissivity signatures, which is simulated for corn and coniferous forest stands. Backscatter and emissivity signatures are obtained from Tor Vergata model simulations, whereas random signal disturbances are accounted for by an errors-in-variables model. As a general trend, we find that β tends to zero for increasing VWC, which is mostly explained by a decrease of radar sensitivity to soil moisture. For forest, which shows overall high VWC values (~5-15 kg/m2), we thus find low magnitudes of β in all cases. For corn (~0-7 kg/m2), we find considerable non-zero magnitudes of β for both frequency configurations, whereas the L/L-band case retains high magnitudes of β longer with respect to C/L-band.

L-Band microwave radiometry over land mainly focuses on observations of horizontally (H) and vertically (V) polarized brightness temperatures. However, it has been demonstrated that measurements of the full Stokes vector [1] are sensitive to additional environmental properties, e.g. azimuthal plant row orientation. Furthermore, model simulations show that also a smooth surface with a periodic permittivity pattern can cause azimuthal dependencies of the Stokes parameters. The objective of this paper is to present fully polarimetric Lband measurement results from observations of a striped wood and styrodur target, when rotated 360° in small steps. Measurement results of a striped soil and open water target are also reported. Finally, measurements are compared to model simulations, with very good agreement within the validity range of the model (stripe thickness <; λ/2).

In this study the framework of the τ - ω model is used to derive vegetation loss coefficients and canopy penetration depths from SMAP multi-temporal retrievals of vegetation optical depth, single scattering albedo and ICESat lidar vegetation heights. The vegetation loss coefficients serve as a global indicator of how strong absorption and scattering processes attenuate L-band microwave radiation. By inverting the vegetation loss coefficients, penetration depths into the canopy can be obtained, which are displayed for the global forest reservoirs. A simple penetration index is formed combining vegetation heights and penetration depth estimates. The distribution and level of this index reveal that for densely forested areas in the tropics the soil signal is attenuated considerably, and this attenuation must be carefully accounted for in soil moisture retrieval algorithms.

Vegetation optical depth and scattering albedo are crucial parameters within the widely used τ-ω model for passive microwave remote sensing of vegetation and soil. A multi-sensor data integration approach using ICESat lidar vegetation heights and SMAP radar as well as radiometer data enables a direct retrieval of the two parameters on a physics-derived basis. The crucial step within the retrieval methodology is the calculus of the vegetation scattering coefficient KS, where one exact and three approximated solutions are provided. It is shown that, when using the assumption of a randomly oriented volume, the backscatter measurements of the radar provide a sufficient first order estimate and subsequently lead to effective estimates of vegetation optical depth and scattering albedo acquired with the novel multi-sensor approach.

After failure of the SMAP L-band radar, its substitution by the Sentinel-1A/B C-band instruments for combined active-passive retrieval of soil moisture demands an algorithm update for this dual-frequency (L/C) case. In order to account for the different frequencies and acquisition geometries of the two sensor types, the microwave covariation, being the fundamental building block of the moisture retrieval algorithm, is modeled using a fully physics-based approach. Moreover, a data-driven, single-pass retrieval methodology for dual-frequency microwave covariation is proposed and tested on SMAP and Sentinel-1 data. The retrieval is also physics-based, incidence angle independent and therefore globally applicable without any empirical or statistical calibration.

The NASA Soil Moisture Active Passive (SMAP) mission aims to disaggregate L-band microwave brightness temperatures (~40 km2) with finer resolution radar backscatter (1-3 km2) to obtain an intermediate resolution soil moisture product. The disaggregation is based on a linear functional relationship between backscatter and emissivity microwave observations that is captured by a covariation parameter β. Since SMAP's L-Band radar has stopped operations in July 2015, the substitution of Sentinel 1's C-Band radar for an operational soil moisture product is in preparation. However, while multiple studies have provided understanding of active-passive covariation for the L/L-Band case, little is known about the C/L-Band case. We utilize the Tor Vergata discrete backscatter and emission model to simulate growing wheat and corn stands and calculate the covariation parameter β for the L/L-Band and C/L-Band case. The study aims to provide insights into the strength, temporal dynamics and underlying scattering mechanisms of active-passive covariation for different vegetation types and frequency combinations. Our results indicate that for the C/L-Band case, vegetation cover limitations are generally more severe, and different β-dynamics and underlying scattering mechanisms are observed with respect to the L/L-Band case.