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Proceedings ArticleDOI

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

25 Jul 2005-Vol. 4, pp 2649-2651

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.

AbstractA 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

Topics: Snow (64%)

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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A Comparison of A Second-order Snow Model With
Field Observations
Jinyang Du
1
, Jiancheng Shi
1,2
, Shengli Wu
1
1.The Institute of Remote Sensing Applications, Chinese Academy of Sciences
P.O.Box9718,Beijing 100101,China
sunnydjy@hotmail.com
2. Institute for Computational Earth System Science, University of California, Santa Barbara, U.S.A
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 semi-
empirical 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 ground-
based 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.
Keywords- snow; second-order model; CLPX
I. 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. For
an optically thin layer of snow, single scattering model, which
is based on first-order solution of radiative transfer equation,
is applicable. However, as the optical depth of snow layer
increases, multiple scattering models should be considered.
Another factor affecting theoretical simulation results is the
description of particle shape. Ice particle is generally modeled
as spherical particles. However, the actual shape of ice particle
is generally non-spherical and non-spherical particles can lead
to strong depolarization return. In this paper, a second-order
model, with ellipsoid scatterer considered, is described and
compared with measured data.
II. M
ODEL DESCRIPTION
The proposed scattering model for dry snow was based on
second-order solution of radiative transfer equation. And
ellipsoid scatterer, which has the same volume as the sphere
defined by input radius, was assumed when calculating phase
matrix of snow. The advanced Integral Equation Model
(AIEM) [1] is used in the calculation of the backscattering of
subsurface and air-snow interface as well as the interactions
between ground and snow. It is noted that the surface
backscattering signals for cross-polarization were estimated by
an empirical model [2]. The received signal calculated by the
model contains the following scattering mechanisms: (a) direct
backscattering from air-snow interface, (b) direct
backscattering from ground, (c) second-order volume
scattering, (d) downward scattering by the particles followed
by the coherent scattering by the ground, (e) coherent
scattering by the ground followed by the scattering of the
particles, (f) coherent scattering by the ground, followed by
the scattering of the particles and another coherent scattering
of the ground, (g)scattering from the particles followed by
non-coherent scattering by the ground, (h) non-coherent
scattering by the ground followed by scattering from the
particles. The last five mechanisms could be regarded as
interaction term T
gv
and the first three mechanisms belong to
two surface terms T
a
, T
g
and one volume term T
v
respectively.
The mathematically expressions of T
a
, T
g
and T
gv
could be
expressed as the following equations.
),;,(
000001 iiiiR
a
ST
φµφπµ
+=
(1)
[]
rei
irirRr
g
dT
STT
µκµ
φµφπµµ
/2exp)(
),;,()(
001
1210
+=
(2)
[
+
=
),;,(
2
exp
)()(
1
0110
irir
r
e
ir
i
gv
d
T
φµφπµ
µ
κ
µµ
µ
P
TT
(3)
),;,()[(
)(
2
)/2exp(1
12
2
12
irirr
r
e
re
d
φµφπµµ
µ
κ
µκ
+
+
PR
R
]
)],;,()1)(exp(
22 irir
d
φµφπµκκ
++ P
+
π
φµ
µ
κ
2
0
1
0
1
'
)exp(
dd
d
2
2
)exp(1
κ
κ
d
),;','()',';,(
12 irRii
φµφµφµφπµ
SP +
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}
),;','(
)',';,(
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
.
Volume term T
v
could be derived from two iterative processes
when solving the radiative transfer equation [3], [4]. It is noted
that Rayleigh Approximation was applied to ellipsoid particles
when calculating the phase matrix of snow [4].
To calculate scattering effects from surface, surface
scattering model AIEM is applied. AIEM is the a recent
development of Integral Equation Method (IEM) [5], which
was verified by laboratory measurements of bistatic scattering
from surfaces with small, intermediate and large scale
roughness. AIEM kept the absolute phase term in Greens
function, meaning better accuracy than the old IEM. According
to AIEM, the bistatic scattering coefficient can be expressed as
the sum of Kirchhoff term, complementary term and cross term,
as (4) shows.
!
),(
)](exp[
2
)(
2
1
2
222
2
n
kkkkW
Is
kks
k
ysyxsx
n
n
pq
n
n
szz
c
qp
kc
qp
k
qp
s
qp
+=++=
=
σσσσ
(4)
where
k
qp
σ
denotes Kirchhoff term,
c
qp
σ
for complementary
tem,
kc
qp
σ
for cross term, pq denotes polarization state, s is the
standard deviation of the surface height, k is wave number,
φθ
cossinkk
x
= ,
φθ
sinsinkk
y
= ,
sssx
kk
φθ
cossin= ,
sssy
kk
φθ
sinsin= ,
θ
coskk
z
= ,
ssz
kk
θ
cos= ,
ϕ
θ
,
are for
incident direction
ss
φθ
, are for the scattered direction,
n
W
is the Fourier transform of the nth power of a known surface
correlation function. And detailed expression of
n
pq
I could be
referred to [1]. Bistatic scattering coefficient
0
σ
calculated
by AIEM could be linked with surface phase matrix as (5)
shows.
=
dII
i
s
ss
ss
s
),(]
cos
);,(
[
4
1
),(
0
φθ
θ
φφθθσ
π
φθ
(5)
where
I
s
and I
i
are scattering and incident intensity respectively.
III.
FIELD MEASUREMENTS
In order to verify the proposed model, data from NASA
Cold-land Processes Field Experiment (CLPX) were used for
comparison. The data were measured by University of
Michigan truck-mounted L band (1.25 GHz) and Ku band
(15.5 GHz) scatterometers during the third Intensive
Observation Period (IOP3, dry snow), February 19 -25, 2003
at the Local Scale Observation Site (LSOS) test site. The test
site consisted of a small (0.8-ha) clearing surrounded by trees
and located within the CLPX Fraser Intensive Study Area
(ISA), near the Fraser Experimental Forest Headquarters
Facility, Colorado. The incidence angles are 20, 35 and 50
degrees. 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.
Actually, measurements on particle size along the snow-pack
vertical profile were available, but the proposed one-layer
model needs an effective radius, which should be the radius
having particle size distribution and near-field effects
considered. Similarly, the shape used in simulation could be
regarded as an effective shape. The contribution from the air-
snow surface is assumed to be negligible since the
discontinuity between air and dry snow is normally small.
Also, since there is a lack of ground information and snow
contribution is quite small at L-Band in this case, comparisons
between simulated data with variant ground situations and
measured data were made in order to estimate ground
parameters. The ground and snow inputs could thus be
concluded as the following:
Ground rms-height 0.5 cm
Ground surface correlation length 10cm
Soil moisture 25%
Snow depth 0.99 meter
Snow volume fraction 22.4%.
IV.
SIMULATION RESULTS AND DISCUSSION
As stated above, comparison with the measurement at L-
band is used to find proper ground parameters. Fig. 1 shows the
result of comparison between the model and the measurement
on the morning of Feb 23, 2003 at L-Band. Grain radius is
0.46mm and a prolate ellipsoid with 0.7 as the ratio of short
axis to long axis is considered. Fig. 2 shows the comparison
result at Ku band. Particle size and shape were best-fit
parameters in this case. A 0.42 mm radius and 0.1 short axis to
long axis ratio were selected in the simulation.
Figure 1. Comparison between proposed model and measured data at L-
Band (scatter points are for measured data)
2650
0-7803-9050-4/05/$20.00 ©2005 IEEE. 2650

Figure 2. Comparison between proposed model and measured data at Ku-
Band (scatter points are for measured data. short axis to long axis ratio is 0.1)
Figure 3. Comparison between proposed model and measured data at Ku-
Band (scatter points are for measured data. short axis to long axis ratio is 0.7)
Figure 4. Backscattering coefficients trend as particle shape changes (x-axis
is the short axis to long axis ratio of ellipsoid)
It can be seen from Fig.1 that simulation agrees well with
the measured data at L-band with the selected ground
parameters. The selected ground parameters were then used in
Ku-band simulations. Fig.2 shows that by selecting proper
particle size and shape, which were the best-fit parameters to
minimize the Mean Square Error (MSE) between simulated
and measured backscattering coefficients, the simulation
agrees quite well with measured data in terms of magnitudes
for co-polarizations and cross-polarizations as well as the
difference between VV and HH polarizations.
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.
Fig.3 only differs from Fig. 2 in that a 0.7 short axis to long
axis ratio and 0.46 mm radius were adopted. By comparing the
two figures, it can be seen that particle shape have a
significant effect on snow backscattering, especially for cross-
polarization. The needle-like particles can produce much more
cross-polarization return than sphere-like particles and this is
more evident as Fig. 4 shows, which shows how
backscattering coefficients change with ellipsoid shape.
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.
R
EFERENCES
[1] K. S. Chen, T. D. Wu, et al., “Emission of rough surfaces calculated by
the Integral Equation Method with comparion to three-dimensional
moment method simulations”, IEEE trans. Geosci. Remote Sens., vol.
41, no. 3, pp. 90-101, 2003.
[2] Y. Oh, K. Sarabandi, and F.T. Ulaby, “An empirical model
and an inversion technique for radar scattering from bare soil
surfaces,” IEEE Trans. Geosci. Remote Sensing, vol. 30, pp. 370-
381, March 1992.
[3] J. Shi and J. Dozier, “Estimation of Snow Water Equivalence
Using SIR-C/X-SAR, Part II: Inferring snow depth and particle
size”, IEEE Transactions on Geoscience and Remote Sensing, Vol.
38, No. 6, pp. 2475-2488, Nov. 2000.
[4] L. Tsang, J.A. Kong and R.T. Shin, Theory of Microwave Remote
Sensing. New York: Wiley-Interscience, 1985.
[5] A. K. Fung, Microwave Scattering and Emission Models and Their
Applications. Norwood, MA: Artech House, 1994.
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Citations
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Journal ArticleDOI
Abstract: Snow Water Equivalent (SWE) is a crucial parameter in the study of climatology and hydrology. Active microwave remote sensing is one of the most promising techniques for estimating the distribution of SWE at high spatial resolutions in large areas. Development of reliable and accurate inversion techniques to recover SWE is one of the most important tasks in current microwave researches. However, a number of snow pack properties, including snow density, particle size, crystal shape, stratification, ground surface roughness and soil moisture, affect the microwave scattering signals and need to be properly modeled and exploited. In this paper, we developed a multi-layer, multi-scattering model for dry snow based on recent theoretical advances in snow and surface modeling. In the proposed multi-layer model, Matrix Doubling method is used to account for scattering from each snow layer; and Advanced Integral Equation Model (AIEM) is incorporated into the model to describe surface scattering. Comparisons were made between the model predictions and field observations from NASA Cold Land Processes Field Experiment (CLPX) during Third Intensive Observation Period (IOP3) and SARALPS-2007 field experiment supported by ESA. The results indicated that model predictions were in good agreement with field observations. With the confirmed confidence, the analyses on multiple scattering, scatterer shape, and snow stratification effects were further made based on the model simulations. Furthermore, a parameterized snow backscattering model with a simple form and high computational efficiency was developed using a database generated by the multiple-scattering model. For a wide range of snow and soil properties, this parameterized model agrees well with the multiple-scattering model, with the root mean square error 0.20 dB, 0.24 dB and 0.43 dB for VV, HH and VH polarizations, respectively. This simplified model can be useful for the development of SWE retrieval algorithm and for fast simulations of radar signals over snow cover in land data assimilation systems.

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)....

    [...]

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

    [...]


Journal ArticleDOI
Abstract: . This is the first study to encompass a wide range of coupled snow evolution and microwave emission models in a common modelling framework in order to generalise the link between snowpack microstructure predicted by the snow evolution models and microstructure required to reproduce observations of brightness temperature as simulated by snow emission models. Brightness temperatures at 18.7 and 36.5 GHz were simulated by 1323 ensemble members, formed from 63 Jules Investigation Model snowpack simulations, three microstructure evolution functions, and seven microwave emission model configurations. Two years of meteorological data from the Sodankyla Arctic Research Centre, Finland, were used to drive the model over the 2011–2012 and 2012–2013 winter periods. Comparisons between simulated snow grain diameters and field measurements with an IceCube instrument showed that the evolution functions from SNTHERM simulated snow grain diameters that were too large (mean error 0.12 to 0.16 mm), whereas MOSES and SNICAR microstructure evolution functions simulated grain diameters that were too small (mean error −0.16 to −0.24 mm for MOSES and −0.14 to −0.18 mm for SNICAR). No model (HUT, MEMLS, or DMRT-ML) provided a consistently good fit across all frequencies and polarisations. The smallest absolute values of mean bias in brightness temperature over a season for a particular frequency and polarisation ranged from 0.7 to 6.9 K. Optimal scaling factors for the snow microstructure were presented to compare compatibility between snowpack model microstructure and emission model microstructure. Scale factors ranged between 0.3 for the SNTHERM–empirical MEMLS model combination (2011–2012) and 3.3 for DMRT-ML in conjunction with MOSES microstructure (2012–2013). Differences in scale factors between microstructure models were generally greater than the differences between microwave emission models, suggesting that more accurate simulations in coupled snowpack–microwave model systems will be achieved primarily through improvements in the snowpack microstructure representation, followed by improvements in the emission models. Other snowpack parameterisations in the snowpack model, mainly densification, led to a mean brightness temperature difference of 11 K at 36.5 GHz H-pol and 18 K at V-pol when the Jules Investigation Model ensemble was applied to the MOSES microstructure and empirical MEMLS emission model for the 2011–2012 season. The impact of snowpack parameterisation increases as the microwave scattering increases. Consistency between snowpack microstructure and microwave emission models, and the choice of snowpack densification algorithms should be considered in the design of snow mass retrieval systems and microwave data assimilation systems.

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;…...

    [...]


Proceedings ArticleDOI
01 Jul 2006
TL;DR: The feasibility of using the dual frequency (X-band 9.6 GHz and Ku-band 17 GHz) and dual polarization radar to estimate snow water equivalence through numerical simulations is evaluated.
Abstract: In this study, we evaluated the feasibility of using the dual frequency (X-band 9.6 GHz and Ku-band 17 GHz) and dual polarization (W and VH) radar to estimate snow water equivalence through numerical simulations.

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....

    [...]

  • ...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]....

    [...]


Proceedings ArticleDOI
23 Jul 2007
TL;DR: A multi-layer, multi-scattering model based on recent theoretical advances in snow and surface modeling is developed and it was found that model predictions were in good agreement with field observations with proper particle size selected.
Abstract: Microwave scattering from snow is difficult to model due to the complexity and heterogeneity of natural snow. In this paper, we developed a multi-layer, multi-scattering model based on recent theoretical advances in snow and surface modeling. In the proposed multi-layer model, Matrix Doubling method is used to account for scattering from each snow layer; and Advanced Integral Equation Model (AIEM) is incorporated into the model to describe surface scattering. Comparisons were made between the model predictions and field observations from truck-mounted L- and Ku-band scatterometers (frequencies are 1.25 GHz and 15.5 GHz) at Local-Scale Observation Site (LSOS) of NASA Cold- land Processes Field Experiment (CLPX) during Third Intensive Observation Period (IOP3). It was found that model predictions were in good agreement with field observations with proper particle size selected. Analysis on scatterer shape, multiple scattering and snow stratification effects were also made based on model simulations.

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]....

    [...]


Journal ArticleDOI
Abstract: Remote sensing has been used widely in studying the earth terrain such as snow or sea ice due to its fast, convenient and long-term monitoring capabilities. SAR images acquired could be used to analyze the condition of snow, snow water equivalent (SWE), surface roughness and others. Theoretical models have also been developed to understand how microwave interacts with the snow medium and the scatterers embedded inside the medium. Conventionally, spherical shape of scatterers is commonly used to represent the ice particles embedded inside snow where the actual shape of scatterers can vary. This paper is to present a theoretical model based on radiative transfer formulation that utilizes computational electromagnetics in the modelling of scattering from arbitrary shape of scatterers. The paper also studies the effect of scatterer shape on scattering mechanisms and total backscattering coefficient. Numerical solution of Relaxed Hierarchical Equivalent Source Algorithm (RHESA) was integrated with existing radiative transfer theoretical model to simulate a layer of random discrete snow medium. Several shapes of scatterers were simulated, and theoretical simulation were compared with ground truth measurement data with promising results.

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....

    [...]

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

    [...]

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

    [...]


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    [...]

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"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....

    [...]

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

    [...]

  • ...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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Journal ArticleDOI
TL;DR: An inversion technique was developed for predicting the rms height of the surface and its moisture content from multipolarized radar observations, which was found to yield very good agreement with the backscattering measurements of the present study.
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Journal ArticleDOI
TL;DR: The results based on the new version (advanced IEM) indicate that significant improvements for emissivity prediction may be obtained for a wide range of roughness scales, in particular in the intermediate roughness regions.
Abstract: This paper presents a model of microwave emissions from rough surfaces. We derive a more complete expression of the single-scattering terms in the integral equation method (IEM) surface scattering model. The complementary components for the scattered fields are rederived, based on the removal of a simplifying assumption in the spectral representation of Green's function. In addition, new but compact expressions for the complementary field coefficients can be obtained after quite lengthy mathematical manipulations. Three-dimensional Monte Carlo simulations of surface emission from Gaussian rough surfaces were used to examine the validity of the model. The results based on the new version (advanced IEM) indicate that significant improvements for emissivity prediction may be obtained for a wide range of roughness scales, in particular in the intermediate roughness regions. It is also shown that the original IEM produces larger errors that lead to tens of Kelvins in brightness temperature, which are unacceptable for passive remote sensing.

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Journal ArticleDOI
TL;DR: The authors develop semi-empirical models for characterizing the snow-ground interaction terms, the relationships between the ground surface backscattering components, and the snowpack extinction properties at C-band and X-band, and with these relationships, snow depth and optical equivalent grain size can be estimated from SIR-C/X-SAR measurements.
Abstract: For pt.I see ibid., vol.38, no.6, p.2465-74 (2000). The relationship between snow water equivalence (SWE) and SAR backscattering coefficients at C- and X-band (5.5 and 9.6 GHz) can be either positive or negative. Therefore, discovery of the relationship with an empirical approach is unrealistic. Instead, the authors estimate snow depth and particle size using SIR-C/X-SAR imagery from a physically-based first order backscattering model through analyses of the importance of each scattering term and its sensitivity to snow properties. Using numerically simulated backscattering values, the authors develop semi-empirical models for characterizing the snow-ground interaction terms, the relationships between the ground surface backscattering components, and the snowpack extinction properties at C-band and X-band. With these relationships, snow depth and optical equivalent grain size can be estimated from SIR-C/X-SAR measurements. Validation using three SIR-C/X-SAR images shows that the algorithm performs usefully for incidence angles greater than 300, with root mean square errors (RMSEs) of 34 cm and 0.27 mm for estimating snow depth and ice optical equivalent particle radius, respectively.

123 citations