# A comparison of a second-order snow model with field observations

TL;DR: A microwave scattering model based on second-order solution of radiative transfer equation has been developed for dry snow and it could be seen that particle shape had a significant effect on the cross-polarization signals.

Abstract: A microwave scattering model based on second-order solution of radiative transfer equation has been developed for dry snow. Advanced integral equation model (AIEM) and a semiempirical model were included in the model to account for ground contribution. Also, ellipsoid grain shape was adopted to describe ice particle. This model was compared with the groundbased scatterometer data (frequencies are 1.25GHz and 15.5 GHz) from NASA Cold-land Processes Field Experiment (CLPX). Inputs to the model were from Local-Scale Observation Site (LSOS) snow pit measurements, except that particle size and shape were computed as free parameters. The comparison shows that the model agrees well with the field data. Also from the comparison, it could be seen that particle shape had a significant effect on the cross-polarization signals. Keywordssnow; second-order model; CLPX

## Summary (1 min read)

### INTRODUCTION

- Active microwave remote sensing can provide useful information on snow parameters, such as snow cover extent and snow water equivalent (SWE) or the product of snow density and depth, for hydrological, climatological, and meteorological applications.
- In order to understand dry snow scattering behavior, theoretical models, many of which are based on radiative transfer theory, have been developed.
- Another factor affecting theoretical simulation results is the description of particle shape.
- Ice particle is generally modeled as spherical particles.
- A second-order model, with ellipsoid scatterer considered, is described and compared with measured data.

### II. MODEL DESCRIPTION

- The proposed scattering model for dry snow was based on second-order solution of radiative transfer equation.
- To calculate scattering effects from surface, surface scattering model AIEM is applied.
- AIEM kept the absolute phase term in Greens function, meaning better accuracy than the old IEM. at the Local Scale Observation Site (LSOS) test site.
- Snow input parameters were from snow pits measurements, which were taken at the same time as the ground-based scatterometer measurements, at LSOS except that particle size and shape were computed as free parameters.

### IV. SIMULATION RESULTS AND DISCUSSION

- As stated above, comparison with the measurement at Lband is used to find proper ground parameters.
- Particle size and shape were best-fit parameters in this case.
- It can be seen from Fig. 1 that simulation agrees well with the measured data at L-band with the selected ground parameters.
- In order to illustrate the effects of particle shape on snow backscattering, simulation was made by considering a slightly larger but more sphere-like snow particle as Fig. 3 shows.

### V. CONCLUSION

- A second-order model for snow was described and comparisons were made between the model and measured data from CLPX.
- Model inputs were represented by the average values of measured snow parameters, with the exception of the particle radius and shape, which were regarded as effective values to the model.
- The model shows good agreement with the measured data.
- Also from the comparison, it can be seen that particle shape has a significant effect on snow backscattering signals, especially for the cross-polarization.

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##### Citations

40 citations

### Additional excerpts

...The low-order snow scattering models have been implemented according to the iterative solutions of radiative transfer equation (Shi & Dozier, 2000; Du et al., 2005)....

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...Du et al. / Remote Sensing of Environment 114 (2010) 1089–1098...

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29 citations

### Cites background from "A comparison of a second-order snow..."

...…how to link snowpack observations of microstructure to the microstructure parameter required in electromagnetic models (e.g Kendra et al., 1998; Du et al., 2005; Tedesco et al., 2006; Liang et al., 2008; The Cryosphere, 11, 229–246, 2017 www.the-cryosphere.net/11/229/2017/ Durand et al., 2008;…...

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27 citations

### Cites background from "A comparison of a second-order snow..."

...Using field snow and underlying-ground property measurements, Du [4] showed good agreement between this model and microwave backscattering measurements at both X-band and Ku-band....

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...The ratio κa(X)/κa(Ku), however, depends mainly on snow temperature since the effect of ice fraction can be canceled out as shown in [4]....

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3 citations

### Cites methods from "A comparison of a second-order snow..."

...Dry snow has negligible effects on L-band radar backscattering, so L-band measurements were used to retrieve ground parameters [8]....

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3 citations

### Cites background from "A comparison of a second-order snow..."

...Surface roughness for top surface was estimated based on the paper in [13] between range 0....

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...Research works [12, 13] show that the shape of scatterers could have significant contribution on total backscattering coefficient....

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...54 mm which was estimated based on the paper in [13]....

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##### References

1,380 citations

### "A comparison of a second-order snow..." refers methods in this paper

...Volume term T could be derived from two iterative processes when solving the radiative transfer equation [3], [4]....

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...It is noted that Rayleigh Approximation was applied to ellipsoid particles when calculating the phase matrix of snow [4]....

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1,302 citations

### "A comparison of a second-order snow..." refers methods in this paper

...AIEM kept the absolute phase term in Greens function, meaning better accuracy than the old IEM....

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...According to AIEM, the bistatic scattering coefficient can be expressed as the sum of Kirchhoff term, complementary term and cross term, as (4) shows....

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...2649 }),;','( )',';,( 1)exp( 12 2 2 ir irR d φµφµ φµφπµ κ κ −−⋅ + − + P S where S is the phase matrix of surface calculated by AIEM, T is the transmitivity matrix, R is the reflectivity matrix, P is the phase matrix of snow, the subscripts 0,1,2 in S ,T and R denote air, snow and ground medium respectively, d is the depth of snow layer and )'/1/1(1 µµκκ += ie , )'/1/1(2 µµκκ −= ie ....

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...To calculate scattering effects from surface, surface scattering model AIEM is applied....

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...Bistatic scattering coefficient 0σ calculated by AIEM could be linked with surface phase matrix as (5) shows....

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1,139 citations

498 citations

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