Christian Mätzler

Microwave emission model of layered snowpacks

Abstract A thermal microwave emission model of layered snowpacks (MEMLS) was developed for the frequency range 5–100 GHz. It is based on radiative transfer, using six-flux theory to describe multiple volume scattering and absorption, including radiation trapping due to total reflection and a combination of coherent and incoherent superpositions of reflections between layer interfaces. The scattering coefficient is determined empirically from measured snow samples, whereas the absorption coefficient, the effective permittivity, refraction, and reflection at layer interfaces are based on physical models and on measured ice dielectric properties. The number of layers is only limited by computer time and memory. A limitation of the empirical fits and thus of MEMLS is in the range of observed frequencies and correlation lengths (a measure of grain size). First model validation for dry winter snow was successful. An extension to larger grains is given in a companion article (Matzler and Wiesmann, 1999) . The objective of the present article is to describe and illustrate the model and to pave the way for further improvements. MEMLS has been coded in MATLAB. It forms part of a combined land-surface-atmosphere microwave emission model for radiometry from satellites (Pulliainen et al., 1998) .

Dielectric properties of fresh-water ice at microwave frequencies

So far, knowledge about the dielectric properties, especially the loss factor, of ice at microwave frequencies has been unsatisfactory. In this work the authors report on new measurements made over the frequency range from 2 to 100 GHz by a resonator method (2-10 GHz) and a radiometer method (10-100 GHz). Measurements were made with pure and with slightly saline (10 to 13 p.p.m.) ice. The results agree with the assumption of a single minimum of the dielectric loss at 2 to 4 GHz. For pure ice the data are a natural link between the measurements of Westphal made below 1 GHz and the far-infrared spectrum. The influence of small impurities on the dielectric loss is compared with the behaviour of sea ice, and it is found that the same linear relationship with salinity can be applied to both cases.

Microwave permittivity of dry sand

The relative dielectric constant, or relative permittivity, /spl epsiv/ of dry snow, is independent of frequency from about 1 MHz up to the microwave range of at least 10 GHz. New measurements of with improved accuracy were made with a specially designed resonator operating near 1 GHz. The coaxial sensor accurately defines the sample volume whose actual mass can be determined to give the density of the snow sample. A special electronic instrument, called a resometer, enabled accurate and rapid measurements under field conditions. Some 90 measurements of different kinds of dry snow (fresh, old, wind-pressed snow, depth hear, and refrozen crusts) were made at test sites in the Swiss and Austrian Alps. The data indicate that /spl epsiv/ is a function of snow density only, given that the standard deviation of 0.006 from the fitted curve is just due to the expected measurement errors. The interpretation of these data in terms of physical mixing theory favors the effective medium formula of Polder and van Santen (1946). The data allow to relate the average axial ratio X as a function of ice volume fraction. Both prolate and oblate spheroids can explain the data. Independent reasoning gives preference to oblate particles. In both cases, the axial ratio increases with increasing fraction up to a critical value of 0.33, followed by a decrease at still higher fractions. The destructive metamorphism of slowly compacting snow explains the increase of X, while the following decrease might be due to sintering. So far, no effect on /spl epsiv/ by a liquid-like surface layer on the ice grains at temperatures between -10/spl deg/C and 0/spl deg/C has been observed.

Passive microwave signatures of landscapes in winter

SummaryThe successful application of passive microwave sensors requires signatures for the unambiguous inversion of the remote sensing data. Due to the large number of object types and large variability of physical properties, the inversion of data from land surfaces is a delicate and often ambiguous task. The present paper is a contribution to the assessment of multi-frequency passive microwave signatures of typical objects on land in winter. We discuss the behaviour of measured emissivities at vertical and horizontal polarization over the frequency range of 5 to 100 GHz (incidence angle of 50 degrees) of water and bare soil surfaces, grass and snowcovers under various conditions. These data and their variabilities lead us toward a classificaion algorithm for some, but not all object classes. Most snowcovers can easily be discriminated from other surfaces, difficulties occur for fresh powder snow if 94 GHz data are not available. The problem of wet snow has found a solution by using a certain combination of observables.In addition to snowcover types we find large differences between frozen and unfrozen bare soil. On the other hand the different situations of grasscovers show all very similar emissivities.For the estimation of physical parameters we propose algorithms for certain object classes. The estimation of surface temperature, especially for snow-free land, seems to be feasible, also the estimation of the snow liquid water content at the surface. For estimating soil moisture lower frequencies (e.g. 1.4 GHz) should be used.For the estimation of the Water Equivalent, WE, we cannot yet find a definitive solution. Certain correlations exist for dry winter snow between WE and observables at frequencies between 10 and 35 GHz. Especially the polarization difference at 10 GHz shows a monotonous increase with increasing WE. Algorithms using higher frequencies are more sensitive to WE, however, they are subject to ambiguities.

Extension of the Microwave Emission Model of Layered Snowpacks to Coarse-Grained Snow

The microwave emission model of layered snowpacks (MEMLS) is a multilayer and multiple-scattering radiative transfer model developed for dry winter snow using an empirical parametrization of the scattering coefficient (se the copanion article). A limitation is in the applicable range of frequencies and correlation lengths. In order to extend the model, a physical determination of the volume-scattering coefficients, describing the coupling between the six fluxes, is developed here, based on the improved Born approximation. An exponential spatial autocorrelation function was selected. With this addition, MEMLS obtains a complete physical basis. The extended model is void of free parameters. The validation was done with two types of experiments made at the alpine test site, Weissfluhjoch: 1) radiometry at 11 GHz, 21 GHz, 35 GHz, 48 GHz, and 94 GHz of winter snow samples on a blackbody and on a metal plate, respectively, and 2) radiometric monitoring at 4.9 GHz, 10.4 GHz, 21 GHz, 35 GHz, and 94 GHz of coarse-grained crusts growing and decaying during melt-and-refreeze cycles. Digitized snow sections were used to measure snow structure in both experiments. The coarsest grains were found in the refrozen crusts with a correlation length up to 0.71 mm; the winter snow samples had smaller values, from 0.035 mm for new snow to about 0.33 mm for depth hoar. Good results have been obtained in all cases studied so far.

Rough bare soil reflectivity model

A semiempirical model for the reflectivity of rough bare soil is presented. One of the main objectives of this new model development was to derive a simple model with few model parameters and a wide applicability. A large number of ground-based measurements in the 1-100-GHz range at H and V-polarization and incidence angles between 20/spl deg/ and 70/spl deg/ were used for the model development.

Thermal microwave radiation : applications for remote sensing

* Chapter 1: Radiative transfer and microwave radiometry * Chapter 2: Emission and spectroscopy of the clear atmosphere * Chapter 3: Emission and scattering by clouds and precipitation * Chapter 4: Surface emission * Chapter 5: Dielectric properties of natural media * Appendices

Relation Between Grain Size and Correlation Length of Snow

In the past it has often been difficult to compare results of different types of snow-structural information. Grain-size and correlation length are such parameters of granular media, and there exist different definitions and different measurement methods for both of them. The relation between these parameters is analyzed from theoretical and from experimental points of view, considering optical and microwave properties. For spherical ice grains the connecting formulas are simple, but for other shapes the two parameters are not directly related. Care must be taken in the measurement procedure. Especially if grain-size is regarded as the maximum extent of connected ice particles, the results are likely to lead to extreme overestimates. Therefore it is concluded that grain-size should be complemented by an additional size parameter, namely, the surface-to-volume ratio of equivalent spheres, i.e. a measure of the correlation length. Methods to determine this quantity in the laboratory have been known for a long time. Methods to obtain such measurements in the field are described here.

Technical note: Relief effects for passive microwave remote sensing

The signal of a microwave radiometer observing a land surface from space is composed of surface and atmospheric contributions, both of which depend on the relief. For proper interpretation of the data these effects should be quantified and, if necessary, taken into account. Relief effects are twofold. First, the path through the atmosphere between the surface and the sensor depends on the altitude of the emitting surface, thus leading to a height-dependent atmospheric influence. The effect can be taken into account by standard atmospheric radiative transfer models if the elevation of the surface and the atmospheric state are known. Second, more relevant for the present discussion is the variable topography of land surfaces, consisting of slopes, ridges and valleys, sometimes with characteristic alignments, and surfaces surrounded by elevated terrain. These surfaces interact radiatively, not only with the atmosphere, but also with each other, leading to the tendency to enhance the effective emission. Under such circumstances, deviations occur from the standard hemispheric emission of a horizontal surface. The interactions do not only depend on topography and emissivity, but also on the bistatic scattering behaviour. Special attention will be paid to the radiation enhancement in a landscape of Lambertian surfaces with elevated horizons. As an example, simulated data for southern Norway are shown.

A comparative study of instruments for measuring the liquid water content of snow

Different dielectric sensors for measuring the liquid water content of snow are compared and described in detail. The instruments make use of the significant difference in the dielectric properties of ice and liquid water at radio frequencies; they are operated with frequencies ranging from 1 MHz up to 1.3 GHz. Plate condensers in connection with ac bridges are used as sensors in the frequency range up to 100 MHz whereas open resonators are used in the GHz regime. Test measurements with the different sensors on homogeneous samples like dry sand and mixed and prepared snow showed the same results for the dielectric constant: the discrepancies are less than 1%. In the natural, inhomogeneous snow cover, the special properties of the different sensors appear. Snow wetness is calculated from the measured dielectric constant and the snow density using the model of Polder and van Santen. The comparative field measurements were made with Alpine snow in the Stubai Alps in Austria.