NASA Technical Reports Server (NTRS) 20170003577: Comparison of Commonly-Used Microwave Radiative Transfer Models for Snow Remote Sensing

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by  NASA Technical Reports Server (NTRS)

1 Comparison of commonly-used microwave radiative transfer models
2 for snow remote sensing
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4 Alain Royera,b, Alexandre Roya,b, Benoit Montpetita*, Olivier Saint-Jean-Rondeaua,b, Ghislain
5 Picardc, Ludovic Bruckerd,e and Alexandre Langloisa,b
6 a Centre d’Applications et de Recherches en Télédétection (CARTEL), Université de Sherbrooke,
7 2500 boul. Université, Sherbrooke, QC, Canada, J1K 2R1.
8 b Centre d’Études Nordiques, Québec, Canada
9 c Université Grenoble Alpes - CNRS, LGGE UMR5183, 38041 Grenoble, France
10 d NASA Goddard Space Flight Center, Cryospheric Sciences Laboratory, Code 615, Greenbelt,
11 MD 20771, USA
12 e Universities Space Research Association, Goddard Earth Sciences Technology and Research,
13 Columbia, MD 21046, USA.
14 * Now at the Canadian Ice Service, Environment and Climate Change Canada, Ottawa.
15
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17 Abstract
18 This paper reviews four commonly-used microwave radiative transfer models that take different
19 electromagnetic approaches to simulate snow brightness temperature (T ): the Dense Media
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20 Radiative Transfer – Multi-Layer model (DMRT-ML), the Dense Media Radiative Transfer –
21 Quasi-Crystalline Approximation Mie scattering of Sticky spheres (DMRT-QMS), the Helsinki
22 University of Technology n-Layers model (HUT-nlayers) and the Microwave Emission Model of
23 Layered Snowpacks (MEMLS). Using the same extensively measured physical snowpack
24 properties, we compared the simulated T at 11, 19 and 37 GHz from these four models. The
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25 analysis focuses on the impact of using different types of measured snow microstructure metrics
26 in the simulations. In addition to density, snow microstructure is defined for each snow layer by
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27 grain optical diameter (Do) and stickiness for DMRT-ML and DMRT-QMS, mean grain
28 geometrical maximum extent (D ) for HUT n-layers and the exponential correlation length for
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29 MEMLS. These metrics were derived from either in-situ measurements of snow specific surface
30 area (SSA) or macrophotos of grain sizes (D ), assuming non-sticky spheres for the DMRT
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31 models. Simulated T sensitivity analysis using the same inputs shows relatively consistent T
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32 behavior as a function of Do and density variations for the vertical polarization (maximum
33 deviation of 18 K and 27 K, respectively), while some divergences appear in simulated variations
34 for the polarization ratio (PR). Comparisons with ground-based radiometric measurements show
35 that the simulations based on snow SSA measurements have to be scaled with a model-specific
36 factor of Do in order to minimize the root mean square error (RMSE) between measured and
37 simulated T . Results using in-situ grain size measurements (SSA or D , depending on the
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38 model) give a mean T RMSE (19 and 37 GHz) of the order of 16-26 K, which is similar for all
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39 models when the snow microstructure metrics are scaled. However, the MEMLS model
40 converges to better results when driven by the correlation length estimated from in-situ SSA
41 measurements rather than D measurements. On a practical level, this paper shows that the SSA
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42 parameter, a snow property that is easy to retrieve in-situ, appears to be the most relevant
43 parameter for characterizing snow microstructure, despite the need for a scaling factor.
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45 Keywords: Snow microwave-emission model; Snow microstructure; Radiative transfer model;
46 Canada; Ground-based measurements; Brightness temperature
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48
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49 1. Introduction
50 In snow remote sensing, a better parameterization of the radiative transfer models (RTM) for
51 simulating snow microwave emission improves our ability to retrieve snowpack characteristics
52 from space-borne observations. Snow microstructure metrics are the main input parameter of the
53 microwave RTM (e.g. Rutter et al., 2009) and its characterization can strongly impact the
54 retrievals from microwave emission measurements for snow monitoring (e.g. Mätzler, 1994;
55 Armstrong and Brodzik, 2002; Kelly et al., 2003; Mätzler et al., 2006; Löwe and Picard, 2015).
56 Thus, given that the available models that are well-defined in the literature and commonly used
57 for snow remote sensing are defined by different snow microstructure parameterizations, a review
58 appears essential. We consider here the following four models: the Dense Media Radiative
59 Transfer– Multi layers (DMRT-ML) model (Picard et al., 2013), the Dense Radiative Transfer
60 Model – Quasi-Crystalline Approximation (QCA) Mie scattering of Sticky spheres (DMRT-
61 QMS) model (Chang et al., 2014), the multi-layer Helsinki University of Technology model
62 (HUT-nlayers) (Lemmetyinen et al., 2010a), and the Microwave Emission Model of Layered
63 Snowpacks (MEMLS) (Proksch et al., 2016; Wiesmann and Mätzler, 1999; Mätzler and
64 Wiesmann, 1999). Several aspects of these models are based on different electromagnetic
65 theories or semi-empirical approaches (multiple scattering and absorption coefficient
66 computations, for example), and they are often driven by sets of different measured inputs for
67 snow grain metrics, such as snow specific surface area (SSA), correlation length or snow grain
68 geometrical extent obtained from visual analysis.
69 Tedesco and Kim (2006) compared earlier simplified single-layer versions of the DMRT, HUT
70 and MEMLS models based on the snow grain metric given by visual inspection (average size
71 over the snowpack depth of representative small, medium, and large grains in each layer
72 measured using a microscope). MEMLS and HUT-nlayers were compared by Lemmetyinen et al.
73 (2010b) and Pan et al. (2016). DMRT theory and IBA were also recently compared and analyzed
74 (Löwe and Picard, 2015), while Roy et al. (2013) compared DMRT-ML and HUT-nlayers.
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75 Sandells et al. (2016) compared DMRT-ML, HUT-nlayers and MEMLS models considering only
76 the optical diameter generated by snow models. But the four multi-layer models considered were
77 never compared together using coincident sets of measured snow properties. The main challenge
78 in comparing these RTM models is that the input snow microstructure parameters differ in each
79 model and are in some cases difficult or impossible to measure in the field. Three different snow
80 microstructure representations are considered in these models: optical diameter (D ) and
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81 stickiness for DMRT-ML and -QMS, correlation length (p ) for MEMLS and maximum
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82 geometrical extent (D ) for HUT-nlayers. Consequently, some hypotheses are needed for their
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83 estimation allowing coherent intercomparison of models (Löwe and Picard, 2015). For example,
84 it was previously shown that the optical diameter derived from the SSA needs to be scaled by a
85 factor in order to be in agreement with measurements when considering DMRT-ML with non-
86 sticky medium (Brucker et al. 2011; Roy et al., 2013; Montpetit et al., 2013; Picard et al. 2014;
87 Dupont et al., 2014). As the physical aspects of each model had already been extensively
88 analyzed, we put the emphasis in this paper on comparing the models with surface-based
89 measured brightness temperature (T ). The objective is to compare the simulations using the
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90 same in-situ measurements of improved snow parameterization, which had never been done.
91 This paper briefly recalls the main basic fundamentals of these four models and more specifically
92 the different grain size definitions involved (Section 2). After presenting datasets and snow
93 microstructure measurement methods (Section 3), we first compare the four models using a
94 synthetic snowpack to perform a sensitivity analysis (Section 4.1), and we then compare the
95 simulated T using sets of measured snow properties against measurements of surface-based
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96 radiometric T at 11, 19 and 37 GHz (Section 4.3).
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98 2. Models and their respective snow microstructure metric
99 A synthesis matrix of the four models considered in this study is presented in Table 1. These
100 models are all publicly available (thus specific details of their implementations can be known)
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101 and are extensively described in the references given in Table 1. Readers are invited to consult
102 these references for detailed descriptions of the models, which are based on conceptually
103 different approaches for computing snow electromagnetic properties and radiation transfer in the
104 multi-layers of the snowpack. In this paper, all the simulations were performed using the
105 recommended configuration for DMRT-ML and -QMS, the Improved Born Approximation
106 (IBA) (option 12) for MEMLS and the original version of the extinction coefficient in HUT (see
107 Table 1).
108 One of the main difficulties in snow radiative transfer is the parameterization of snow
109 microstructure consisting of a high density of scatterers per unit of volume. DMRT-ML and –
110 QMS consider the snow as a collection of sticky spherical ice particles defined by their radius
111 and stickiness (Tsang and Kong, 2001; Tsang et al., 2007), while MEMLS parameterizes snow
112 microstructural properties by a second order statistical function, the two-point correlation
113 function, giving the mutual relationships between two scatterers within a given volume, such as
114 the autocorrelation function (the exponential correlation length p is generally used, see Section
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115 2.2 below). HUT is based on empirical scattering and extinction coefficients fitted with the
116 observed maximum dimension of snow grains (D ), or more recently an effective grain size
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117 radius (Kontu and Pulliainen, 2010). When using in-situ ground-based measurements of snow
118 microstructure parameterization, practical comparison of these models requires hypotheses to
119 retrieve and link the different metrics. The metrics used in this study are briefly defined below.
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121 Table 1 Comparison between basics of DMRT-ML/-QMS, MEMLS and HUT-nlayers models.
122 See the Table at the end of the paper.
123 2.1 DMRT snow microstructure metric
124 DMRT-ML considers snow grains as spherical particles of ice defined by their radius. Their
125 position (clustering) is controlled by stickiness. For snow having a wide range of grain shape, the
126 radius of equivalent spheres can be objectively defined by their optical radius (Ro), which can
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127 always be derived from the SSA via the optical equivalent radius. The snow SSA is the surface of
128 the air/snow interface (S) per unit of mass: M=ρ •Volume: SSA=S/M = S/(ρ •Volume) in m2
snow ice
129 kg-1, where ρ is the ice density (917 kg m-3). SSA measurements are described in Section 3. For
ice
130 spheres or snow assimilated as sphere equivalent (see the review paper by Domine et al., 2008),
131 the optical radius (Ro) is expressed as (Ro in mm, ρ in kg m-3 and SSA in m2 kg-1):
ice
132 Ro = 3.103/(ρ •SSA) (1).
ice
133 Since any measurements can be used to estimate stickiness, Brucker et al. (2011), Roy et al.
134 (2013), Dupont et al. (2014) and Picard et al. (2014), considering a non-sticky medium, have
135 shown that Ro should be multiplied by the scaling factor φ when Ro is derived from SSA
DMRT
136 measurements (R'o in mm):
137 R'o = φ Ro = 3.103 φ /(ρ •SSA) (2).
DMRT DMRT ice
138 This scaling factor is discussed in Section 4.2. Roy et al. (2013) also showed that the following
139 relationship (inspired by Kontu and Pulliainen, 2010) can be used for an effective optical radius
140 of snow grains derived from SSA measurements:
141 R''o [mm] = 1.1 [1 – exp(-24.6.103/(ρ •SSA)] (3).
ice
142 The stickiness parameter (τ), used by DMRT theory (Tsang and Kong, 2001), is inversely
143 proportional to the contact adhesion between spheres. It can be linked to the cohesion or to a
144 degree of connectivity between grains. Thus, for non-sticky spheres: τ = ∞; for snow with
145 clusters (aggregates) or grains with high strength of adhesion, τ decreases (for example τ = 1 to
146 0.2 or less). DMRT-ML uses the “short range” approximation (Tsang and Kong, 2001) which
147 implies that grains and aggregates should remain small compared to the wavelength. Roy et al.,
148 (2013) hypothesized that the needed scaling factor (φ ) is related to the assumption of non-
DMRT
149 sticky spheres (τ = ∞) and to the assumption of monodisperse grain size distribution. This scaling
150 factor is therefore a surrogate of the stickiness parameter which cannot practically be measured in
151 the field (see Löwe and Picard, 2015).
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152
153 2.2 MEMLS snow microstructure metric
154 MEMLS uses the correlation length (p ) for describing snow microstructure, which is the slope of
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155 the spatial autocorrelation function at the origin (i.e. the derivative of this function). This
156 parameter might be derived from micro-computed tomography measurements (micro-CT) (Löwe
157 et al., 2013) or by high-quality stereological method (see Riche et al., 2012), but its rapid
158 derivation from field measurements is still difficult. Recently, Proksch et al. (2015) proposed a
159 relationship between Snow-Micropen measurements and correlation length that has not yet been
160 validated for microwave emission applications.
161 Here, we first estimate the correlation length from the equivalent sphere grain radius (Ro) as
162 proposed by Mätzler (2002), following the Debye relationship:
163 p =4/3 Ro (1 – ν) (4),
c
164 where ν is the ice volume fraction: ν = ρ /ρ .
snow ice
165 While there is no experimental relationship between simultaneous measurements of p (from
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166 micro-CT measurements) and SSA measurements, Montpetit et al. (2013) showed that the
167 following relationship gives optimized simulated T using MEMLS driven with SSA
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168 measurements (p' in mm and SSA in m2 kg-1):
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169 p' [mm] =4.103 φ (1 – ν)/(ρ •SSA) (5),
c MEMLS ice
170 where φ is a scaling factor and SSA is measured in-situ.
MEMLS
171 If the autocorrelation function is approximated (fitted) by an exponential function of the form:
172 exp(-x/p ), one can derive the exponential correlation length p . According to the type of snow,
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173 p is different from p (Krol and Löwe, 2016; Matzler, 2002). For microwave measurements, p
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174 is generally preferred to p , and Mätzler (2002) found in general that p ≈ 0.75p , giving from (1)
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175 and (4):
176 p [mm] ≈ Ro (1 – ν) = 3.103 (1 – ν)/(ρ •SSA) (6).
ex ice
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177 On the other hand, previous studies from Mätzler (1997) have shown that p is closer to the
c
178 minimum characteristic extent of the grain than related to the maximum geometrical particle
179 extent. Mätzler (2002) gives a series of measurements of p , p and visually estimated grain size
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180 D (defined below) for 20 samples of different snow types showing the correspondence
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181 between these parameters. Using these data, p (or p ) can be expressed as a logarithmic function
ex c
182 of D :
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183 p = a + b ln(D ) for ν> ν and D > D in mm
ex max th max max,th
184 p = Cst otherwise (7),
ex
185 where ν and D are thresholds delimitating the range of validity of the proposed model, and
th max,th
186 Cst is a constant for values below these thresholds.
187 Using the Mätzler (2002) data, Durand et al. (2008) found that a = 0.18 and b = 0.09 for ν > 0.2
188 and D > 0.125 mm , and that p = 0.05 ± 0.017 otherwise.
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189
190 2.3 HUT snow microstructure metric
191 HUT input is based on individual grain size. There are many ways to describe the geometrical
192 grain size of snow (Colbeck et al., 1990; Lesaffre et al., 1998; Fierz et al., 2009). Among them,
193 one can cite the circle (or ellipsoid) that better encompasses the snow grain; the equivalent radius
194 given by the ratio between projected grain area and its perimeter; the mean convex radius of
195 curvature; or the greatest extent of the prevailing or characteristic grains: Dmax. The latter
196 corresponds to the maximum dimension of the "intermediate grain size" and has long been a
197 classical parameter routinely used to visually characterize snow structure in the field (see
198 Colbeck et al., 1990; Fierz et al., 2009). The HUT model can be driven either directly by D , or
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199 by an effective grain diameter (D ) derived from Dmax following the relationship that
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200 minimized the differences between measured and simulated T , as proposed by Kontu and
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201 Pulliainen (2010) (see also Lemmetyinen et al., 2010a and 2015; Pan et al., 2016):
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202 D = 1.5 (1 – exp(-1.5 D )) (8),
max,eff max
203 where D , and D are in mm.
max eff max
204 However, in this study, it appears that this relationship (Eq. 8) for estimating the D does not
max,eff
205 give a good agreement, due to the lack of convergence in the optimization. This results from the
206 large digitized D measurement values obtained in this study (see Section 4.2), and Eq. 8 leads
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207 to a unique D . In the model comparison (Section 4.3), we thus consider D = 0.5 D ,
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208 derived from an optimization that reduces the difference between simulated and measured T
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209 (method of Roy et al., 2013).
210
211 When SSA is measured, Roy et al. (2013) use Equation (2), with a different scaling factor
212 (φ ) relative to the effective grain size in HUT simulations:
HUT
213 Do [mm] = 6.103 φ /(ρ •SSA) (9).
eff HUT ice
214 All the φ factors (φ , φ and φ ) are further discussed in the results section. Field
DMRT MEMLS HUT
215 measurement methods for SSA and D estimates are presented in Section 3.
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217 2.4 Scaling factors for the models driven by SSA measurements
218 The scaling factor φ depends upon the model considered and the type of snow. The change in this
219 scaling factor is linked to other microstructure parameters such as stickiness and to the fact that
220 we assume a monodisperse size distribution of snow grain (see the discussions in Brucker et al.,
221 2011; Roy et al., 2013 and Löwe and Picard, 2015). It cannot be explained by measurement
222 uncertainties (Roy et al., 2016). Löwe and Picard (2015) theoretically demonstrate the need of
223 grain size scaling between the optical diameter and the equivalent sticky hard sphere diameter.
224 For DMRT-ML with the assumption of non-sticky spheres, the φ factor obtained varies from 2.3
225 to 3.5 depending on the type of snow (Table 2). The amplitude of this factor may also partly be
226 affected by errors in snow measurements and possibly in the soil parameters. Precise explanation
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227 of these differences in the φ factor needs further study but is outside the scope of this paper. Here
228 we used φ = 3.3, 1.3 and 3.7, respectively for DMRT-ML, MEMLS and HUT-nlayers (Table 2)
229 in order to compare the known optimized models when driven by SSA measurements compared
230 to simulations driven by D measurements.
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232 Table 2. Scaling factor φ to be applied on the snow microstructure metric derived from in-situ
233 SSA measurements, as a function of the RTM considered and the type of snow. All SSA
234 measurements were derived from the DUFISSS's type approach (see Section 3.1), except *: the
235 values depend upon the method used for retrieving SSA; and **: SSA retrieved from ASSAP
236 device (see details in the given references, last column).
Radiative
Transfer Snow µstructure Metrics Sites φ References
Models
Canada:
p' =4.103 φ (1 −ν)/(ρ .SSA) Arctic, Montpetit et al.,
MEMLS c ice 1.3
Eq. 5 Subarctic, 2013
South Québec
1.89,
Dome C Brucker et al.,
2.5,
Antarctica 2011
2.85*
Dome C
2.3** Picard et al., 2014
R'o=3.103φ/(ρ .SSA) Antarctica
DMRT-ML ice
Eq. 2 Barnes Ice Cap
(no stickiness) 3.5 Dupont et al., 2014
Canada Arctic
Canada:
Arctic,
3.3 Roy et al., 2013
Subarctic,
South Québec
Canada:
Ro =3.103φ/(ρ .SSA) Arctic,
HUT-nlayers eff ice 3.7 Roy et al., 2013
Eq. 9 Subarctic,
South Québec
237
238 2.5 Radiative Transfer Model inputs
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