Refractive Mixing Dielectric Model Research Articles

A dielectric model of thawed and frozen Arctic organic soils at 435 MHz

ABSTRACT A refractive-mixing dielectric model for frozen and thawed organic-rich soils at a frequency of 435 MHz was developed in this letter. The model was developed based on the dielectric measurements of five soil samples in which organic matter content was variated from 35% to 80% (by weight). Dielectric measurements were conducted in the range of volumetric soil moisture from ~2% to 60%, and the range of temperature from −30°C to 25°C. Coefficient of determination (R2) and root mean square error (RMSE) between predicted by the model and measured values for real () and imaginary () part of complex relative permittivity are = 0.989 (=0.602) and = 0.906 (=0.404), respectively. The developed dielectric model can be used for creating remote sensing algorithms (soil moisture retrieval in the root zone, active layer thickness and ice content measuring in permafrost area, etc.) in P-band.

A dielectric model for frozen mineral soils at a frequency of 435 MHz

ABSTRACT A single frequency refractive mixing dielectric model at 435 MHz for frozen mineral soils is proposed. The model was created based on the laboratory dielectric measurements of three soil samples in the ranges of soil moisture from 0.01cm3 cm−3 to 0.42cm3 cm−3, temperature from– 30°C to– 1°C, clay content (by weight) from 9.1% to 41.3%. Coefficient of determination R 2 and root mean square error (RMSE) predicted by the model and measured values for real () and imaginary () part of the complex relative permittivity (CRP) are = 0.988 (= 0.323) and = 0.987 (= 0.100). Compared to well-known spectroscopic models, this model is simpler in practical engineering use. The input parameters of the model are the volumetric soil moisture, temperature and the content of the clay fraction. The output parameters are the real and imaginary parts of the CRP. The created model may be used to develop new remote sensing retrieval algorithms of temperature, the content of unfrozen water and ice in the root zone of frozen soils for northern regions.

Retrieving soil moisture profiles based on multifrequency polarimetric radar backscattering observations. Theoretical case study

ABSTRACT In this theoretical work, a dual-frequency polarimetric method is proposed for measuring moisture profiles in the topsoil up to 0.30 m thick. A case of measuring soil moisture profiles, which monotonically changes with depth, during 37 days after irrigation is considered. Original values of backscattering coefficients are calculated by the Oh model and by the small perturbation method at frequencies of 5.4 GHz and 435 MHz, respectively. In these calculations, we used measured moisture profiles and spectroscopic refractive mixing dielectric model of non-saline mineral soil with a clay fraction of 9.1%. Soil moisture profiles are retrieved by solving the inverse problem, the cost function of which is constructed based on the co- and cross-polarized ratios, calculated at two frequencies for the measured and modelled soil moisture profiles. An exponential function is used as a modelled soil moisture profile. It is shown that the standard deviation between the retrieved and measured soil moisture values in the surface layer 0.30 m thick appears to be ≤0.02 m3 m−3 (theoretical limit), and the determination coefficient is 0.881. The study shows a promising path towards developing multi-frequency radar systems for remote sensing of soil moisture profiles using satellites-based and unmanned aerial vehicles air-based platforms.

Experimental Investigation of Ground Radiation on Dielectric and Brightness Temperature of Soil Moisture and Soil Salinity.

Soil moisture and salinity are crucial parameters of the Earth’s ecosystem; how to understand the radiation properties of them is of great significance for remote sensing monitoring. In this study, the application of mixed soil dielectric models (Dobson and generalized refractive mixing dielectric model (GRMDM)) and saline soil dielectric models (Dobson-S, HQR (Qingrong Hu), and WYR (Yueru Wu)) were analyzed to select the optimal models to simulate brightness temperature based on observational data. The brightness temperature of the soil moisture and multilevel salinity was simulated by using the Q-H (parameter of polarization mixing and parameter of characterizing height) model and Holmes parameterization scheme of soil effective temperature. The results show that both the Dobson model and the GRMDM model can well reproduce the real part and imaginary part of the dielectric constant of non-saline soil, and the GRMDM model was better. With the increase of the frequency, the simulation error of the dielectric constant of the saline soil by using the Dobson-S model, HQR model, and WYR model also increased, and the simulation result of the WYR model was better in the L band. The simulated result of the brightness temperature of soil moisture between the observation value and simulation value presented a high correlation both in the horizontal polarization and vertical polarization, with R greater than 0.967 and 0.948, and the root mean square error smaller than 3.998 K and 2.766 K, respectively. Meanwhile, the correlation coefficients of the brightness temperature of the saline soil in the horizontal polarization and vertical polarization were 0.935 and 0.971, and the root mean square errors were 5.808 K and 4.65 K, respectively. The brightness temperature decreased as the soil salinity increased, and the higher the salinity content was, the quicker the brightness temperature decreased. We expect that the experimental results can be used as a reference for algorithm developers to further enhance the accuracy of soil moisture and soil salinity retrievals.

A dielectric model of thawed and frozen Arctic soils considering frequency, temperature, texture and dry density

ABSTRACTA dielectric model was developed for thawed and frozen mineral soils, based on the refractive mixing dielectric formula and the dielectric measurement data for three soils collected in the Arctic tundra of the Yamal Peninsula. The refractive mixing dielectric model was used in conjunction with the Debye multi relaxation equations as a theoretical model to fit the measured complex relative permittivity spectra as a function of soil moisture and temperature. As a result, the dielectric spectroscopic parameters for the various components of water in the soil, such as the low- and high-frequency limits of the complex relative permittivity, the times of the corresponding relaxations, and the specific conductivity, were simultaneously determined for soils with different clay contents for all measured temperatures. As the theoretical temperature dependences of these parameters, the Clausius–Mossotti, Eyring, and linear equations for the conductivity were used. By using approximations of the measured data with these formulas, the parameters of the temperature-dependent model were derived, such as the coefficient of volume expansion, energy and entropy of activation, and coefficient of thermal conductivity. A set of the parameters discussed above in conjunction with the refractive mixing formula is a temperature- and mineralogically dependent multi-relaxation spectroscopic dielectric model, which enables estimation of the permittivity of moist soils as a function of dry soil density, moisture, frequency, temperature, and texture. The statistical error of the proposed dielectric model was estimated in terms of the normalized root-mean-square error (nRMSE), which was equal to 5% and 25% for the dielectric constant and dielectric loss factor, respectively.

Comparison of different soil dielectric models for microwave soil moisture retrievals

ABSTRACTSoil dielectric model is an essential part of the microwave soil moisture retrieval process. This study compared the performance of four widely used dielectric models, the Wang-Schmugge model (WS), Dobson model, generalized refractive mixing dielectric model (GRMDM), and multi-relaxation generalized refractive mixing dielectric model (MRGRMDM), and investigated the effects of the uncertainties of each model on soil moisture retrievals. Furthermore, the simulated soil dielectric constants were evaluated by measured dielectric data at the P/L/C/X bands. The results showed that the uncertainties induced in soil moisture retrievals by an alternative dielectric model exceeded 0.09 m3 m−3 in the worst case. The Dobson model is sensitive to the sand content. WS, GRMDM, and MRGRMDM model are sensitive to the clay content. The measured dielectric data further verified that the applicability of each dielectric model depends on the soil texture type and soil moisture condition. Compared with Dobson model, WS showed better performance at dry soil. GRMDM and MRGRMDM provided better results under lower clay content soil. Especially, MRGRMDM has better simulation accuracy than GRMDM in the low-frequency range (< 1 GHz).

Temperature- and texture-dependent dielectric model for frozen and thawed mineral soils at a frequency of 1.4 GHz

A single-frequency dielectric model at 1.4GHz for frozen mineral soils was developed, with the temperature and gravimetric clay content varying from −1 to −30°C and from 9.1 to 41.3%, respectively. The model is based on the refractive mixing dielectric model and the dielectric data measured for the three typical soils collected in the Yamal tundra. The refractive mixing dielectric model was applied to fit the measured dielectric data as a function of soil moisture at a number of fixed temperatures. As a result, the parameters of the developed model were derived as a function of temperature and texture. This set of parameters consists of the maximum gravimetric fraction of unfrozen bound water and the values of the complex refractive indexes relating to soil solids, unfrozen bound water, and moistened ice. The developed model for frozen mineral soils in conjunction with the previously developed by us dielectric model for thawed mineral soils is considered as an integral dielectric model which is applicable for permittivity calculations of soil in both thawed and frozen states.The developed integral dielectric model for frozen and thawed mineral soils was validated using the dielectric data for five measured soils, and the statistical errors were estimated in terms of the root mean square error and the determination coefficient. In addition, the only known in the literature dielectric model for frozen soils suggested by Zhang was validated based on dielectric data for soils measured in this research. The comparative analysis proved substantially better accuracy of predictions in the case of the developed model as compared to those related to the Zhang model.

A temperature-dependent multi-relaxation spectroscopic dielectric model for thawed and frozen organic soil at 0.05–15 GHz

A dielectric model for thawed and frozen Arctic organic-rich soil (50% organic matter) has been developed. The model is based on soil dielectric measurements that were collected over ranges of gravimetric moisture from 0.03 to 0.55g/g, dry soil density from 0.72 to 0.87g/cm3, and temperature from 25 to −30°C (cooling run) in the frequency range of 0.05–15GHz. The refractive mixing dielectric model was applied with the Debye multi-relaxation equations to fit the measurements of the soil’s complex dielectric constant as a function of soil moisture and wave frequency. The spectroscopic parameters of the dielectric relaxations for the bound, transient bound, and unbound soil water components were derived and were complimented by the thermodynamic parameters to obtain a complete set of parameters for the proposed temperature-dependent multi-relaxation spectroscopic dielectric model for moist soils. To calculate the complex dielectric constant of the soil, the following input variables must be assigned: (1) density of dry soil, (2) gravimetric moisture, (3) wave frequency, and (4) temperature. The error of the dielectric model was evaluated and yielded RMSEε′ values of 0.348 and 0.188 for the soil dielectric constant and the loss factor, respectively. These values are on the order of the dielectric measurement error itself. The proposed dielectric model can be applied in active and passive microwave remote sensing techniques to develop algorithms for retrieving the soil moisture and the freeze/thaw state of organic-rich topsoil in the Arctic regions.

Generalized refractive mixing dielectric model of moist soils considering ionic relaxation of soil water

A generalized multi-relaxation refractive mixing dielectric model of moist soils is suggested for frequencies in the range from 0.2 to 14.8 GHz. The model is based on dielectric measurements in this frequency range at a temperature of 20°С for relative moisture content (by weight) changing from 2 to 43%. The model expands the range of applicability of the single-relaxation model suggested previously to the megahertz frequency range with allowance for the Maxwell–Wagner ionic relaxation which is clearly manifested in this frequency range for bound soil water. It is demonstrated that the error in calculating the complex dielectric permittivity spectra of the moist soil has the same order of magnitude as the error of experimental data used for model construction.

Retrieving Temperature Gradient in Frozen Active Layer of Arctic Tundra Soils From Radiothermal Observations in $L$-Band—Theoretical Modeling

Possibility of remote sensing of both the surface temperature and the temperature gradient in the permafrost active layer from L-band brightness temperature observations is theoretically investigated at a SMOS frequency of 1.4 GHz. Bare soil emission is simulated based on the semi-empirical L-MEB model. The brightness temperature is simulated using the soil density, surface roughness, temperature, and moisture profiles measured in situ at the Biosphere Station Franklin Bluffs, Alaska, USA (69°39'N, 148°43'W) from September 2, 1999, to August 23, 2001. The soil permittivity is calculated using the temperature-dependent generalized refractive mixing dielectric model for the organic rich soil sample collected in North Slope, Alaska (68°38'N, 149°35'W). This model predicts the complex dielectric constant of moist soil both thawed and frozen at temperatures from -30°C to +25°C and moistures from 0 to 0.94 g/g. The brightness temperatures simulated for field-of-view angles from 0 to 60° are inverted into the temperature profiles, and their deviations from the temperature profiles measured in situ are estimated. The error in reconstructing temperature profiles is found to be no greater than 1.8°C to depths of 0.15 m.

Multirelaxation Generalized Refractive Mixing Dielectric Model of Moist Soils

In this letter, a multirelaxation generalized refractive mixing dielectric model (GRMDM) for moist soil is proposed and substantiated in the frequency range from 0.04 to 26.5 GHz. This model is based on the methodology of a single-relaxation GRMDM which accounts only for the dipole relaxation of water molecules in the gigahertz frequency range. The proposed multirelaxation GRMDM takes into account both the dipole (Debye) and ionic (Maxwell-Wagner) relaxations of soil water molecules. For this purpose, it uses a two-frequency Debye relaxation equation for the dielectric spectra of bound water. The spectroscopic parameters of the multirelaxation GRMDM were derived by fitting the spectra calculated by this model to the respective measured ones. The main advantage of this model is that it predicts the complex dielectric constant of moist soils throughout the megahertz and gigahertz frequency ranges with the same error as the single-relaxation GRMDM does only in the gigahertz range.

Temperature- and Texture-Dependent Dielectric Model for Moist Soils at 1.4 GHz

In this letter, a monofrequent dielectric model for moist soils taking into account dependences on the temperature and texture is proposed, in the case of an electromagnetic frequency equal to 1.4 GHz. The proposed model is deduced from a more general model proposed by Mironov and Fomin (2009) that provides estimations of the complex relative permittivity (CRP) of moist soils as a function of frequency, temperature, moisture, and texture of soils. The latter employs the physical laws of Debye and Clausius-Mossotti and the law of ion conductance to calculate the CRP of water solutions in the soil. The parameters of the respective physical laws were determined by using the CRPs of moist soils measured by Curtis (1995) for a wide ensemble of soil textures (clay content from 0% to 76%), moistures (from drying at 105 °C to nearly saturation), temperatures (10 °C -40 °C), and frequencies (0.3-26.5 GHz). This model has standard deviations of calculated CRPs from the measured values equal to 1.9 and 1.3 for the real and imaginary parts of CRP, respectively. In the model proposed in this letter, the respective standard deviations were decreased to the values of 0.87 and 0.26. In addition, the equations to calculate the complex dielectric permittivity as a function of moisture, temperature, and texture were represented in a simple form of the refractive mixing dielectric model, which is commonly used in the algorithms of radiometric and radar remote sensing to retrieve moisture in the soil.

Spaceborne radar monitoring of soil freezing/thawing processes in the Arctic tundra

In this article, the possibility of measuring the average temperature in the active topsoil of the Arctic tundra from the temperature dependence of the radar backscattering coefficient is theoretically studied. The radar backscattering coefficient is simulated by the small perturbation method at a frequency of 1.26 GHz of radars placed onboard ALOS-2 and SMAP satellites. In simulation, the soil density, surface roughness, and temperature and moisture profiles measured in situ at the biosphere station Franklin Bluffs, Alaska (69°39′ N, 148°43′ W), from August 1, 2000 to July 1, 2001 were used. The soil permittivity was calculated for the generalized temperature-dependent refractive mixing dielectric model for organic rich soil whose sample was taken on the Alaska North Slope (68°38′N, 149°35′W). This model allows the complex dielectric constant of moist thawed and frozen soil to be calculated at temperatures in the range from –30°С to +25°С. It is demonstrated that the radar backscattering coefficient is correlated with the topsoil temperature with the error less than 5.7°С during the entire period of freezing and thawing.

Temperature-Dependable Microwave Dielectric Model for an Arctic Soil

Dielectric measurements of an organic-rich permafrost soil over the range from 1.0 to 16 GHz and from -30°C to +25°C are presented. The measured shrub soil contains up to 90% organic matter and is the first soil of this composition for which the soil dielectric has been characterized. The measurements were fitted to the generalized refractive mixing dielectric model (GRMDM) recently proposed by Mironov et al., which combines the complex refractive indexes for the major components of the soil. These components were found to be the solid content, bound water, transient bound water, liquid capillary water, and moistened ice water. The dielectric properties of the frequency-dispersive components are each described by their own Debye relaxation spectrum. The GRMDM has been modified to incorporate the temperature dependence of the Debye parameters. The phase transformation of the soil water components at the freezing temperature is taken into account. As a result, a temperature-dependable GRMDM (TD GRMDM) has been developed, including model parameters which have a physical interpretation. This TD GRMDM predicts the dielectric for this soil in the whole range of moistures, frequencies, and temperatures measured. The model prediction errors are on the same order as that of dielectric measurements. The model proposed is the first of its kind to provide a physical basis for radar and radiothermal remote sensing algorithms that retrieve the freeze/thaw state and the volumetric moisture in the upper layer of an Arctic soil.

Physically and Mineralogically Based Spectroscopic Dielectric Model for Moist Soils

In this paper, the error of dielectric predictions for moist soils was estimated, regarding the semiempirical mixing dielectric model (SMDM) developed by Dobson , which is a universally recognized one, and the generalized refractive mixing dielectric model (GRMDM) recently elaborated by Mironov The analysis is based on the measured dielectric data presented in by Curtis and the papers of Dobson These data cover a broad variety of grain-size distributions observed in 15 soils and the frequency range from 45 MHz to 26.5 GHz, with the temperature being from 20 degC to 22 degC. The SMDM was found to deliver predictions with substantially larger error for the soils, whose dielectric data were not used for its development, while the GRMDM ensured dielectric predictions for all the soils analyzed with as small error as the SMDM did in the case of the soils that it was based on. To secure the same convenience in application of the GRMDM, which the SMDM possesses, the spectroscopic parameters of that model were correlated with the clay percentages of the respective soils. As a result, a new mineralogy-based dielectric model was developed. For the moist soils other than those whose dielectric data were used for its development, this model was shown to demonstrate noticeably smaller error of dielectric predictions, with clay percentage being the only input parameter, as compared with the error observed in the case of the SMDM.

Dielectric spectroscopy of oil-bearing rocks at 0.05–16 GHz

We have measured the dielectric spectra of sand and bentonite mixtures with oil and saline water (NaCl solution) in the frequency range from 50 MHz to 16 GHz at 22 °C. The measured spectra were compared with predictions in terms of the generalized refractive mixing dielectric model (GRMDM), and the respective error was estimated as a check of the model applicability to describe oil-bearing formations. The results may be useful in developing new methods of electromagnetic logging.

Temperature Dependable Microwave Dielectric Model for Frozen Soils

In this paper, the temperature dependable dielectric model for moist soils was developed on the basis of the generalized refractive mixing dielectric model (GRMDM) recently proposed by Mironov etal. to provide for substantially less error, as compared to the most popular model by Dobson etal.. This model was substantiated with the use of the dielectric data measured by Curtis etal.. For a speciflc soil type, the temperature dependable GRMDM was shown to make as accurate predictions of this value, as a function of volumetric moisture, wave frequency, and temperature, as the dielectric data measurement accuracy is. The error of dielectric predictions was tested in the range of temperatures from 10 to 40 - C, frequencies from 300MHz to 26.5GHz, and moistures varying from those of dry soil to the ones corresponding to full soil water capacity. The Silty Sand soil tested contained 14, 9, and 77% of clay, silt and sand respectively. In addition, the error of dielectric predictions with the temperature dependable GRMDM was compared with that of Dobson's model, proving a lot more accurate predictions.

Temperature and Mineralogy Dependable Model for Microwave Dielectric Spectra of Moist Soils

In this paper, a physically based dielectric model in microwave band for moist soils is developed to account for both the temperature and granulometric mineralogy of the soil. The generalized refractive mixing dielectric model (GRMDM) previously developed by V. L. Mironov etal. was used as a mean to determine the spectroscopic parameters for 5 soils which complex dielectric constant spectra were measured and presented in Technical Report EL-95-34, December 1995 by J. O. Curtis etal. The measurement results used covered the temperatures of 10, 20, 30, and 40 - C, gravimetric clay contents from 0 to 0.76g/g, and frequencies from 0.3 to 26.5GHz. Relating to each individual soil, such GRMDM spectroscopic parameters as dielectric constants in low frequency limit, relaxation times, and ohmic conductivities, pertaining to both bound and unbound soil water, were fltted as functions of temperature with the Clausiuss- Mossotii, Debye and linear equations, respectively. As a result, a set of physical parameters for a temperature dependable generalized refractive mixing dielectric model (TD GRMDM), consisting of the volumetric expansion coe-cients, activation energies, enthropies of activation and others, were obtained. Finally, the parameters of the TD GRMDM as functions of gravimetric clay content were fltted to yield the closing set of polinomial formulas, which, in conjunction with the TD GRMDM, represent a temperature and mineralogy dependable soil dielectric model (TMD SDM). Thus developed, the TMD SDM provides for predictions of the complex dielectric constant of moist soils as a function of moisture, wave frequency, temperature and gravimetric clay content. Further the TMD SDM prediction error was estimated with the use of the ndependent dielectric data.

Investigation of dielectric spectra from moist soils during freezing-thawing processes

A frequency spectrum of the complex dielectric permittivity of soils is measured in the range of frequencies from 0.5 to 15.0 GHz in the course of frost penetration and thawing. The phase transitions taking place during frost penetration and thawing are analyzed within the concept of the generalized refractive mixing dielectric model (GRMDM). Two types of water concurrently present in the soil are identified: bound and free water. Temperature dependences of the Debye model parameters for each type of water are given, and parameters of a dielectric spectroscopic model of frozen and thawed soils are found. The hysteresis phenomenon during the phase transition of the soil moisture is investigated.

Temperature dependence of dielectric properties of moist soils

Heating of soil using microwaves has several applications in geosciences, including soil remediation, neutralization of land mines, and microwave-enhanced thermography. Numerical simulation of microwave-induced soil heating processes requires knowledge of the electrical properties of the soil as a function of temperature, moisture content, and frequency of the electromagnetic wave. This paper describes a semi-empirical model for calculating the dielectric properties of moist soils at various moisture contents, temperatures, and frequencies (within the band of 1–10 GHz). The proposed model is an extension of the generalized refractive mixing dielectric model (GRMDM) for moist soils. Predictions of the proposed model were found to be in good agreement with experimental data reported in the literature. Results of a parametric study suggest that the temperature dependency of the dielectric properties of moist sand is more pronounced for higher volumetric moisture contents.