A basic study on a new satellite algorithm for snow
* H. Tsutsui 1, T.Koike1, T.Graf1, K.Tamagawa1, H.Fujii1( 1:Department of Civil Engineering, The University of Tokyo )* The University of Tokyo, 7-3-1,Bunkyo-ku, Tokyo, 113-8656, Japane-mail: tsutsui@hydra.t.u-tokyo.ac.jp
Abstract
This study developed a satellite algorithm for snow depth and snow grain size based on the microwave radiativetransfer theory used the dense Media model and the 4-stream fast model and validated by using the in-situ snow
depth data at the 75 ground-based stations in the northern hemisphere and the Advanced Microwave ScanningRadiometer for the Earth Observation System (AMSR-E) on Aqua launched by NASA in 2002. The results ofvalidation were shown good correspondence of observation value and estimation value.
Keyword: snow, radiative transfer theory, remote sensing, microwave

1. Introduction
The climate conditions that exist in the various regionsof the earth are formed by the water cycle on the scale ofthe earth on the land, atmosphere and ocean.
The water cycle between the land and the atmospherecauses climate variations on the scale of the earth as aresult of significant hydrological variations over both thelong term and short term over the land. Moreover, overland, the various land surface conditions are formed byvegetation and snow. Hence, it is difficult to grasp thehydrological variations of land in a quantitative way.
Particularly, the snow has the peculiarity as follows.
- Snow has high reflectance (albedo).
- Soil moisture increase by the melted snow watersuppresses the rise of heat in the soil surface at springand summer.
Accordingly, snow is greatly affecting the water cycle on
the scale of the earth. Hence, it is a monumental challengethat grasps the snow quantity in a quantitative way.
In order to quantify snow conditions in some way, theobservation way that the observation instruments arrange
uniformly over the snow area of earth is idealized way.
However, this is unrealistic from the point of view of theobservation scale.
As alternate solution against such observation way, theapplication of satellite remote sensing for snow
observations was inspired by the significant growth in theuse of the microwave observation technique using various
number of vibration and observation frequencies. In
addition, the development of an all-weather snow observa tion method that utilizes a microwave radiation instrument
continues to attract attention.
This study devises a satellite algorithm that
automatically estimates the snow grain size and snow
depth based on microwave radiative transfer basis
theory. Finally, we evaluate the validity of the algorithm
by comparison between the estimated snow depth andthe observed snow depth.

2. Previous microwave radiative transfer modeland Satellite algorithm
In the past, many satellite algorithms based on micro wave radiative transfer theory have been developed for

calculating snow depth.
In this section, explains about microwave radiativetransfer model (Koike & Suhama(1993)) and satellite
algorithm (Koike et al (1999)) became the prototype of a
new algorithm at this study.

2.1. Microwave radiative transfer model for snow
by Koike & Suhama(1993)
Koike & Suhama(1993) applied the England radiativetransfer model(1975) to snow. And they proposed theMicrowave radiative transfer model from snow layers asshown in Fig.1.
In addition, The England radiative transfer model (1975)
is a model based on the theory that the radiation from ascattering medium consists of two components; direct
radiation and diffuse radiation. And this scattering medium
is a medium of homogeneous thickness of average
including spherical scatterers of average number on ahalf-infinite medium. In this algorithm, the scattering
medium is assumed to be snow layers which consisted ofuniformly spherical ice particles.
Direct radiance
Solar radiation
Atmosphere
Attenuation
by reflectionAttenuation
by transmission

Attenuation
by snow

Snow
Emission of snow

Attenuation
by transmission

Soil

Emission of soil

Direct radiance
Diffuse radianceAtmosphere

Snow

Scattering ice particle
Soil

Diffuse radiance

Fig.1: The microwave radiative transfer model for snow
by Koike & Suhama (1993)

3. Introduction of a new microwave radiativetransfer model

Koike et al (1999) assumed the snow grain size and thesnow density in this England radiative transfer model. And
they developed satellite algorithm as follows.
- By the snow depth and the snow temperature changes,calculates the brightness temperature for twofrequencies (19GHz&37GHz) from snow layer.
- Based on the result of this calculation, a transform
table is made for transforming the brightness
temperature of two frequencies into snow depth andsnow temperature.
- By using a transform table, calculates the snow depth
and snow temperature from the brightness temperaturecorresponding to the two frequencies.
As just described, the satellite algorithm of Koike etal (1999) calculated snow depth and snow temperatureusing a difference of 19GHz brightness temperature and37GHz.

As has been previously described, the conventionalradiative transfer model such as England radiative transfer
model has many issues.
Accordingly, this study introduced a new microwave
radiative transfer model. That is Dense Media radiativetransfer model(Tsang(1992)) and 4-Stream Fast radiativetransfer model(Liu(1998)).
In the conventional radiative transfer model, conceives
snow particles (scatterers) are independent. Hence, theextinction coefficient becomes linear dependent on thenumber of particles (the fractional volume).
On the contrary, Dense Media radiative transfer model
conceives correlation of each scatterers. Hence, theextinction coefficient calculated by Dense media radiativetransfer model becomes lower than conventional model.
And the behavior of extinction coefficient becomes such as
the diagram below indicates.

2.3.2. Restriction on Frequency
High frequency plays an important role in detection of
the volume scattering influence with increase snow grain
size.
However, England radiative transfer model can not use
except frequencies of 19GHz and 37GHz. This condition ismajor fault in this model.

2.3.3. Overestimation of the attenuation effects
inside snowEngland radiative transfer model overestimates theattenuation effects inside snow. And the calculated
brightness temperature severely decreases with increase ofsnow thickness and frequency. Moreover, the difference of
19GHz brightness temperature and 37GHz brightness
temperature increases in size. As the result of thischaracteristic, this model and algorithm calculates shallow
snow depth against deep snow depth.

0.010
0.005

0.5

0.4

0.3

0.000
0.2

England radiative transfer model has restriction on snow
grain size and snow density.
Snow grain size can not use except 0.6mm or thereabout.
And Snow density can not use except 0.3 g/cm3.
When snow depth is calculated using the difference ofbrightness temperature by a microwave radiative transfer
theory, deep snow depth is calculated by small snow grain
size and low snow density and shallow snow depth iscalculated by big snow grain size and high snow density.
Hence, England radiative transfer model having a
restriction on snow grain size and snow density can notcalculate snow quantity matching actual snow.

Dense Media ModelConventional Model

0.015

0.1

2.3.1. Restriction on Snow grain size and Snowdensity

0.020

0.0

England radiative transfer model for snow (Koike &Suhama(1993)) has issues as follows.

Freactional volume(-)

Fig.2: The difference of the extinction coefficient by
conventional model and the extinction coefficient byDense media model.
As has been previously described, Dense Media
radiative transfer model calculates optimum extinction
coefficient. Then, this model calculates optimum
atenuation effects inside snow. And the difference of19GHz brightness temperature and 37GHz brightness
temperature decreases in size. Hence, this radiative transfer
model can calculate deep snow when snow depth iscalculated using the difference of brightness temperature.
This model characteristic is important advantage.
Brightness temperature (K)2.3. Point at issue

Extinction coefficient (Ke)2.2. Satellite algorithm by Koike et al (1999)

250

250

19GHｚ

19GHｚ
20020037GHｚ

150150

37GHｚ
100

100
0100200
Snow depth (cm)Dense Media Model

0100
200
Snow depth (cm)Conventional Model

Fig.3: The difference of the brightness temperature by
conventional model and the brightness temperature byDense media model.

In this satellite algorithm, the extinction coefficient andalbedo calculated by the Dense Media radiative transfer
model introduced to 4-Stream Fast radiative transfer modeland calculated the brightness temperature.

37GHz Brightness Temperature(K)

4. The structure of a new satellite algorithm
In this new satellite algorithm, inputted snow depth(1-200cm) and snow temperature (223-273K) into theradiative transfer model and calculated the brightness
temperature of 19GHz&37GHz and made a snow
depth transformation table such as the diagram below
indicates. 300

3) Calculates the modulus of difference of the calculated
89GHz brightness temperature and the 89GHz satellite
brightness temperature(⊿TB89).
4) Compares ⊿ TB89(89GHz brightness temperaturedifference) corresponding to each grain size, andselects the 89GHz minimum brightness temperature
difference(⊿TB89min).
5) Decides on the optimum snow grain size corresp onding to the selected ⊿TB89min.
6) Decides on the optimum snow depth and the optimum
snow temperature by using optimum snow grain size.
Snow grain size (mm)：2500.30.4

0.5

0.60.7

Snow depth transformation table

200150Calculates Snow depth & Snow Tem perature
100100150200250300
19GHz Brightness Temperature (K)Fig.4: The snow depth transformation table

Brightness Temperature transformation table

And inputted snow depth (1-200cm) and snow
temperature (223-273K) into the radiative transfer modeland calculated the brightness temperature of 89GHz andmade a brightness temperature transformation table such as
the diagram below indicates.

Calculates 89GHz Brightness Temperature(TB89cal)

300

89GHz Brightness Temperature(K)0.2

Satellite BrightnessTemperature(19GHz・37GHz)

Satellite Brightness
Temperature(89GHz)250
Snow Temperature(K)
223K

200

⊿TB89 = ¦ TB89− TB89cal｜

233K
243K
253K
263K

¾ Compares ⊿TB89 corresponding to each grain size,

273K

150
050

100

150

Calculates the modulus of difference of calculated
89GHz brightness temperature and 89GHz satellite
brightness temperature(⊿TB89)

200

and selects the 89GHz minimum brightness
temperature difference(⊿TB89min).

Snow depth (cm)Fig.5: The 89GHz brightness temperature transformation table
Moreover, considered the structure of a satellite
algorithm as follows.
1) The first, input satellite brightness temperatures(19GHz&37GHz) to the snow depth transformationtable of the six kinds of snow grain sizes. Andcalculates snow depth and snow temperature of eachsnow grain size.
2) The second, input 89GHz satellite brightness
temperature
tothebrightness
temperaturetransformation table of the six kinds of snow grainsizes. And calculates 89GHz brightness temperature ofeach snow grain size.

¾Decides on the optimum snow grain size

corresponding to the selected ⊿TB89min.

¾Decides on the optimum snow depth andthe optimum snow temperature by using
optimum snow grain size.

Fig.6: The snow quantity calculation satellite algorithm
in this study
The above process is a new snow quantity calculation
satellite algorithm in this study.

Moreover, world distribution map shown conditions ofcompatibility is shown in Fig.10.
As shown in Fig.10, the compatibility of a Russia federal
northern part (region of heavy snows) was improved.

5. The estimation of a new snow quantity
calculation satellite algorithm
In this study, we estimated the validity of a new satellite
algorithm by comparing the calculated values of thisalgorithm and the GTS snow depth data.
The findings below were made using the average of themodulus of the difference in the observed snow depth andthe calculated snow depth as the estimation index.
1) When this value is 20cm or less, the compatibility isgood.
2) When this value exceeds 20cm, the compatibility ispoor.
In this result, the good compatibility was 65 sites among
75 sites.
The snow depth correlation chart of observed snow
depth and estimated snow depth is shown in Fig7, 8.
Fig.7 is result of estimation by conventional algorithm.
And Fig.8 is result of estimation by algorithm of this study.
And an example among 75 sites of time-series estimationsnow depth is shown in Fig.9.
As shown in Fig.7 & 8 & 9, accuracy of estimation wasenhanced at deep snow by using a new algorithm.
Estimation snow depth (cm)100

Estimation snow depth (cm)

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Conventional algorithm
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Acknowledgements
050

100

100

This study was funded by the Japan Science and Technology
Corporation, Core Research for Evolution Science andTechnology (Development of Modeling and Satellite Remote
Sensing of Atmosphere-land Interaction) and Special
Coordination Funds for Promoting Science and Technology(Promotion of leading researches) as part of the CoordinatedEnhanced Observing Period (CEOP) and AMSR/AMSR-E
verification experiment of the Japan Aerospace Exploration
Agency (JAXA).

References
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Observation snow depth(cm)Fig.8: The snow depth correlation chart by the newalgorithm
Snow Depth (cm)▲50

Fig.7: The snow depth correlation chart by the conven tional algorithm

Observation snow depth
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Conventional algorithm

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0Fig.10: The world distribution map about compatibility▲:Good compatibility ●:Poor compatibility

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Fig.9: An example of time-series estimation of snow
depth

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