3.4.2 CTSK2b1
A. Algorithm Outline(1) Algorithm Code: CTSK2b1(2) Product Code: SNGI, SNGI_p(3) PI Name: Dr. Knut Stamnes(4) Overview of Algorithm
The algorithm presented here for the retrieval of snow grain size, using GLI channels 5(0.46 µm) and 19 (0.865 µm), is based on the principle that the reflectance of snow is known to
be dependent on snow grain size in the near infra-red (NIR) range and pollution in the visible
range. This algorithm works only under clear-sky conditions. It can be applied at high latitude(polar) as well as mid-latitude regions. In this algorithm several lookup tables have been
constructed by using atmospheric optical properties obtained from MODTRAN in conjunction
with the DISORT radiative transfer code. The bi-directional reflectance of snow is taken into
account. In the lookup tables the radiances that would be measured by the satellite instrument
are simulated as a function of snow grain size and mass fraction of soot mixed in the snow.
The rationale behind the retrieval procedure of this algorithm is that the snow properties can be
determined through a comparison of measured (by ADEOS-II/GLI) and simulated (the lookup
table) radiance. The comparison will be done for GLI channels 5 and 19 in order to retrieve themass fraction of soot and the snow grain size, respectively. The snow grain size and massfraction of soot are obtained by requiring the simulated radiances to be consistent with themeasured ones in both GLI channel 5 and channel 19. The retrieval of snow grain size issensitive to the aerosol type. The effect of aerosol has been taken into account here. The
tropospheric aerosol and Antarctic background aerosol models have been applied to the Arctic
and Antarctic regions, respectively. The standard rural, urban, and Navy maritime aerosol
models adopted from MODTRAN are employed for the mid-latitude area.
From Ver. 2 release new snow grain size retrieval algorithm at 1.64 µm is also considered
to be included in the processing of global type product. We developed an algorithm, which isusing GLI channel 28 (1.64 µm) independently to retrieve snow grain size at very top surface.
Because the satellite measured reflectance at TOA (top of atmosphere) is no longer sensitive tosnow impurity and aerosol properties at this wavelength, we can simply use the measured
reflectance to retrieve snow grain size. It should be kept in mind, however, that this retrieved
snow grain size is the grain at very top surface due to the very small penetration depth.

GLI Algorithm Description

3.4.2-1

B. Theoretical Description(1) Methodology and Logic Flow
1. Retrieval procedures
To relate the reflectance of snow to its physical properties such as grain size, the radiativetransfer model has been used to generate a lookup table. In this lookup table, simulated
radiances in GLI channels 5 and 19 have been calculated as a function of the snow grain size
between 50 and 2000 µm and the mass fraction of soot ranging from 0.02 to 2.5 ppmw (parts
per million by weight). Because the average grain size lies in the range 40-100 µm for newsnow, 100-300 µm for fine-grained older snow, and 1000-1500 µm for old snow near themelting point, this table covers the range of snow grain sizes encountered in nature.
Dependencies of the radiances on solar zenith angle (30-75°), sensor view angle (0-45°,
according to GLI view angle), and relative azimuth angle between the sun and the sensor (0180°) are also taken into account in the table. For each aerosol model, we have two look-up
tables for retrieving grain size and soot, respectively.
We use lookup tables to maintain the accuracy of the retrieval and to save computation time.
The retrieval is implemented by finding the best match between the measured satellite radiancefor the pixel being analyzed in the GLI image and an entry in the lookup table. Lookup tables
are generated by radiative transfer calculations for GLI channels 5 and 19, respectively. Figure
2.1 illustrates the reflected radiance in channels 5 and 19 as a function of the mass fraction ofsoot and snow grain size, and shows that the reflected radiance in channel 19 is generally moresensitive to snow grain size than to the amount of soot mixed in the snow. Therefore, thealgorithm for retrieving snow grain size and soot mixed in the snow consists of three steps: (i)adjust the snow grain size in channel 19 until the computed TOA radiance agrees with themeasured one; (ii) estimate the mass fraction of soot in the snow using the radiance of channel
5, after the grain size is determined from measurements 19; and (iii) compare the computed
TOA radiances with the measured ones in channels 5 and 19, and, if inconsistent, repeat steps(i) and (ii) until the computed radiances agree with the measured ones for both channels 5 and19.

GLI Algorithm Description

3.4.2-2



Figure 2.1
The reflected radiances of channels 5 and 19 as a function of the mass fraction of soot andsnow grain size.
Figure 2.2 is a flow chart of the retrieval algorithm for snow grain size. The retrieval
procedure of the algorithm can be summarized as follows:
1. Input the initial values of the snow grain size into lookup table 19, to provide a firstestimate of the radiance in GLI channel 19.
2. Determine the snow grain size by adjusting it until the computed radiance from the lookup
table agrees with the measured one in channel 19.
3. After the grain size is determined, the initial mass fraction of soot and the retrieved grain
size are used as input to lookup table 5. Then the mass fraction of soot in the snow isdetermined by adjusting it until the computed radiance from the lookup table agrees withthe measured one in GLI channel 5.
4. Use current grain size and soot as input to lookup table 19 and lookup table 5 to get theestimated radiances, and compare to the measured values at both channel 5 and channel 19.
If inconsistent, go back to steps (1) and (2), and adjust grain size or soot until the estimatedradiances agree with the measured results for both channel 5 and channel 19.

GLI Algorithm Description

3.4.2-3

Thus, the final retrieval results will be obtained when the estimated radiances in both GLI
channel 5 and 19 are consistent with the measured radiances. This retrieval procedure will be
implemented for all snow-covered pixels under clear-sky conditions. A color picture with the
distribution of snow grain size and soot will be generated by running the algorithm code toprovide a visual display of the retrieval results.


Figure 2.2
Flow chart of the retrieval algorithm for snow grain size and the mass fraction of soot. Rs is
snow grain size, mF is mass fraction of soot mixed in the snow, Rmod and Rsat are the radiances
calculated from the model and measured by the GLI sensor, respectively.
Regarding the new algorithm which uses the GLI channel 28 (1.64 µm) for grain size
retrieval, one corresponding lookup table "snow28.table" has been generated by using
DISORT radiative transfer model pertinent of the coupled atmosphere-surface system.
In this lookup table, simulated reflectances in GLI channel 28 have been calculated as afunction of the snow grain size between 50 and 2000 µm. There are 6 candidate snow grain
sizes (50, 100, 200, 500, 1000, and 2000 µm). Dependencies of the radiances on solar zenith

GLI Algorithm Description

3.4.2-4

angle (20-80 degree), sensor viewing angle (0-56 degree, for the GLI sensor), and relative
azimuth angle between the sun and the sensor (0-180 degrees) are also taken into account in
the table.

(2) Physical and Mathematical Aspects of the Algorithm
1. Background for snow grain size retrieval
It is well recognized that snow cover has a strong impact on the surface energy balance inany part of the world. Satellite remote sensing provides a very useful tool for estimating spatial
and temporal changes in snow cover, and for retrieving snow optical characteristics. So far,Landsat TM (Thematic Mapper) data (Fily et al., 1997; Bourdelles and Fily, 1993) and
AVIRIS (the Airborne Visible/Infrared Imaging Spectrometer) data (Nolin and Dozier, 1993;
Painter et al., 1998) have been used for this purpose. Such retrieval is possible because snow
reflectance depends primarily on the concentration of pollution (soot-contamination) in thevisible range, but on snow grain size (Warren, 1982) in the near-infrared, as shown in Figure
2.3 (after Wiscombe and Warren, 1980).
Figure 2.3 Spectra albedo of snow as a function of wavelength for grain size 50-1000 µm(after Warren and Wiscombe, 1980).

Nolin and Dozier (1993) estimated snow grain size using reflectance at 1.04 µm. However
Bourdelles and Fily (1993) found that the grain size retrieved from Thematic Mapper band 4(TM4) at 0.84 µm lies in the 420–430 µm range, which is much larger than the 145–165 µm
grain size obtained from TM5 (1.65 µm) and TM7 (2.22 µm). They noted that retrieved size

GLI Algorithm Description

3.4.2-5

depends on the radiation-penetration depth, which is wavelength-dependent. Fily et al. (1997)
compared the in situ and Landsat TM-retrieved snow grain sizes and found that the in situ
optical grain size is very different from the measured one at channels TM5 and TM7, but isclose to the measured one at channel TM4. A linear relation between the measured grain sizeand optical size that depends on the wavelength has been used in their snow reflectance model.
While these previous studies have clearly shown that remote sensing holds promise formapping snow grain size, they have also pointed to the need for appropriate instrumentationand development of inversion approaches to obtain quantitative snow grain size estimates.
Pure ice is highly transparent in visible region, so that an increase in snow grain size has little
effect on reflectance. However, because ice is moderately absorptive in the near-infrared,reflectance is sensitive to grain size, especially in the wavelength region 0.8-1.3 µm (Warren
and Wiscombe, 1980) (Figure 2.3). For satellite measurements, the spectral channel should belocated in a wavelength region where the effect of atmospheric scattering and absorption is
negligible, so that when the radiance values are atmospherically corrected to yield surface
reflectance, errors in the characterization of the atmosphere, particularly atmospheric water
vapor, are minimized. For these reasons, GLI channels 19 (0.86 µm), 24 (1.05 µm), and 26(1.24 µm) would be good choices for grain-size studies, because the grain-size effect is large
when the effects of the atmosphere and snow impurities are small. The questions then arise:
What is the difference among the retrieved grain sizes from different channels? How can we
explain differences among the retrieved grain sizes? Which channel is the best choice for grain
size retrieval? In an attempt to answer these questions, we have used AVIRIS data to study inmore detail the physical meaning of the grain sizes retrieved from different channels. An
important effect of the effective penetration depth of radiation has been revealed here (seesection 3).
2. Snow reflectance model
As described above, snow reflectance is high in the visible part of spectrum and almost
independent of grain size. In the NIR spectral region between 0.8 and 1.3 µm, snow has
moderate reflectance that is very sensitive to the snow grain size (see Figure 2.3). This is why
we expect GLI channels at wavelengths 0.86, 1.05, 1.24 µm to be useful for estimating thesnow grain size. At wavelengths less than 0.8 µm, snow reflectance is affected by the presenceof absorptive impurities as well as by grain size (Warren and Wiscombe, 1980). Therefore,
visible radiation can be used to retrieve the snow impurities, while snow grain size can be
determined using a channel in the range 0.8-2.5 µm. Figure 2.4 illustrates the reflectances at
GLI channels 5 (0.46 µm) and 26 (1.24 µm) as a function of grain size and the soot mixed in
the snow, respectively. Carbon soot contaminated snow was considered here.

GLI Algorithm Description

3.4.2-6

Field measurements and model simulations indicate that snow exhibits significant bidirectional reflectance properties, which are more pronounced at large viewing angles. To
relate the reflectance of snow to physical properties such as grain size, a comprehensive
radiative transfer model based on the DISORT multiple scattering algorithm (Stamnes et al.,1988) has been applied to compute the bi-directional reflectance of the snow surface instead ofassuming a Lambertian reflector. We employ the optical properties of pure snow obtained by
Wiscombe and Warren (1980). Mie theory is used to get the extinction coefficient and thephase function, which means the snow grains are assumed to be spherical. The snow cover isconsidered as a homogeneous layer with a single grain size when we carry out the radiativetransfer calculations. Of course, the real snow particles are not spherical. Thus, the particle


Figure 2.4
The reflectances of GLI channels 5 (0.46 µm) and 26 (1.24 µm) as a function of the massfraction of soot and snow grain size.
radius used here is called the effective grain-size. It will generally be different from themeasured grain size. Also these effective grain sizes represent depth-weighted-averaged values.
The observing depth is dependent on the radiation penetration, which varies with wavelength.
In order to simulate atmospheric effect on the measured reflectance, the standard sub-arctic
winter/summer and mid-latitude winter atmospheric profiles have been employed for polar andmid-latitude regions, respectively. For gases and aerosol, we adopt absorption and scattering
properties for the GLI channels from MODTRAN. The tropospheric aerosol model and Aoki's

GLI Algorithm Description

3.4.2-7

Antarctic background aerosol model (Aoki et al., 1999) have been used for Arctic andAntarctic regions, respectively. For the mid-latitude area, there are five different aerosol
models employed: (i) rural aerosol model with 23 km visibility, (ii) rural aerosol model with 5
km visibility, (iii) navy maritime aerosol model with 10 (m/s) wind speed, (iv) urban aerosol
model with 23 km visibility, and (v) urban aerosol model with 5 km visibility. The aerosol
type for a given image will be automatically determined based on the measured reflectancedifference between GLI channels 1 (0.38 µm) and 5 (0.46 µm). (See section 4).

3. Wavelength dependence of retrieved snow mean grain size
In order to compare the mean retrieved snow grain sizes from different channels, an
AVIRIS image obtained at 22:45GMT on June 4, 1995 over the Arctic ocean was studied here.
Using the method described above, the snow grain sizes were retrieved, as shown in Figures
2.5 a, b, c, and d for AVIRIS channels 54 (0.86 µm), 73 (1.05 µm), 93 (1.24 µm) and 145(1.73 µm), respectively. Spatial variation of the retrieved snow grain size was independent of
the wavelengths, but the magnitudes of the grain sizes retrieved from different channels werequite different. Figure 2.6 shows the retrieved grain size distribution for the whole image ateach channel. The mean retrieved grain sizes were 1000, 550, 400, and 60 µm for channels 54,
73, 93 and 145, respectively. The longer the wavelength, the smaller the retrieved snow grain
size. The mean grain size retrieved from channel 145 (1.73 µm) was too small to be reasonable.
These differences could be due to the variable penetration depth of radiation depending on its
wavelength as well as the grain size. What are the penetration depths of these channels? How
can one explain the unreasonable grain size retrieved using channel 145? An explanation canbe found by using the following two-layer snow model.
A two-layer snow model is adopted here to explore the effect of penetration depth ofradiation on snow grain size retrieval. We assume that the thickness and snow grain size of thelower layer are 10 cm and 2000 µm, respectively. We then change the thickness and snow
grain size of the upper layer to investigate the penetration depth and its variation with grain
size at each channel. The penetration depth is defined as follows: when the upper layer
becomes thick enough that the backscattered radiation is unaffected by the lower layer snow,
and thus the snow albedo reaches a saturation value, we call this thickness the penetration
depth. This is illustrated in Figure 2.7, which includes simulations for four different grain sizes(i.e. 100, 200, 500, and 1000 µm). Table 2.1 shows the penetration depth obtained from Figure
2.7 for different grain size at AVIRIS channels 54, 73, 93 and 145, respectively. We find thatthe penetration depth increases with increasing snow grain size, and decreases with increasing
wavelength. As expected, the radiation penetrates deeper into coarse snow than into new snow.

GLI Algorithm Description

3.4.2-8

Because the metamorphism induces the growth of the snow particles, the snow grain size
generally increases with depth. Because of its greater penetration depth the measured
reflectance from channel 54 is due to radiation backscattered by larger grains deeper within thesnow than the radiation reflected at longer wavelengths. Thus, the grain size retrieved atchannel 54 will be larger than those obtained from channels 73 and 93. The signals fromchannel 145 is only sensitive to the snow in a thin layer right below the surface. The grain
shape may also have an important influence on the grain size retrieval. Aoki et al. (1998)
found that at this wavelength (1.73 µm), the fine structure of the snow has a larger impact on

Table 2.1 The penetration depth as a function of snow grain size at AVIRIS channels 54, 73,
93 and 145, respectively
Snow grain size
(µm)
100
200
500
1000

Ch. 54
3.5
5.0
6.0
6.5

Penetration depth (cm)
Ch. 73
Ch. 93
2.0
1.0
3.0
1.5
3.5
2.0
3.5
2.0

Ch. 145
0.1
0.2
0.2
0.2

snow reflectance than the crystal radius. For example, Aoki et al. found that at theirobservation site, the surface grain shape of the snow was dendrite. However, they found thatthe retrieved optical effective grain size corresponded to the branch size (25-50 µm) of thedendrite, rather than its crystal size (1000-2000 µm) . Thus, the effective grain size retrieved
from channel 145 (1.73 µm) is quite different from those retrieved from channels 54, 73, or 93.
The differences among the retrieved snow grain sizes using AVIRIS channels 54, 73, and93 are due to the different snow penetration depths at these wavelengths. The penetration depth
is a function of wavelength and snow grain size. At AVIRIS channels 54, 73, and 93, thepenetration depths are 3.5-6.5 cm, 2-3.5 cm, and 1-2 cm, respectively, depending on the snow
grain size (see Table 2.1). The signal from channel 145 (1.72 µm) comes from a thin layer justbelow the snow surface. Therefore, we can conclude that: (i) the channel at shorter wavelength
has a larger penetration depth than those at longer wavelengths; (ii) the penetration depth
increases as the snow grain size increases; (iii) for the 1.73 µm wavelength

GLI Algorithm Description

3.4.2-9

Figure 2.5 (a) & (b)Retrieved snow grain size distribution at AVIRIS channels (a) 54 and (b) 73.

GLI Algorithm Description

3.4.2-10

Figure 2.5 (c) & (d)Retrieved snow grain size distribution at AVIRIS channels (c) 93 and (d) 145.

GLI Algorithm Description

3.4.2-11]Figure 2.6 Histograms of retrieved snow grain size from AVIRIS channels 54, 73, 93, and 145.
channel, the signal comes from the snow surface and is very sensitive to the surface grain
shape, making it difficult to estimate grain size at this channel, since the assumption of
spherical particle shape may become invalid and the reflected radiation is more sensitive tofine structure (branch size) than to crystal size..
4. Channel selection for retrieving snow grain size and sootBecause the radiation penetration depths depend on wavelength, the mean retrieved snow
grain sizes will depend on the channel selection. In order to retrieve consistent values of snow
grain size and soot, we should choose wavelengths or channels with similar radiation
penetration depth. For this reason, we select GLI channel 19 (0.865 µm) for snow grain size
retrieval and channel 5 (0.46 µm) for soot retrieval. As already discussed, GLI channel 19 atwavelength 0.865 µm has penetration depths between 3.5 and 6.5 cm, depending on grain size,
which is close to the penetration depth of GLI channel 5. MAS and AVIRIS data have beenused for validation tests (see C. (2)). MAS channel 7 at 0.865 µm and AVIRIS channel 54 at
0.865µm are used for snow grain size retrieval, and MAS channel 1 at 0.546 µm and AVIRISGLI Algorithm Description

3.4.2-12channel 7 at 0.441 µm are used for retrieving soot mixed in snow. The characteristics of thecorresponding channels of GLI, MAS, and AVIRIS are described in Table 2.2.
Figure 2.7 Computed snow albedo versus the depth of the upper snow layer for a two-layersnow model. The grain size and thickness of the lower layer are 2000 µm and 10 cm,
respectively. The grain sizes inside the first layer are (a) 100 µm, (b) 200 µm, (c) 500 µm, and(d) 1000 µm, respectively.

Table 2.2 Comparison of channel characteristics
SensorChannel

GLI

5
19
1
7
7
54

MAS
AVIRIS

GLI Algorithm Description

Center position
(µm)
0.46
0.865
0.546
0.865
0.44
0.865

3.4.2-13

Width (µm)
0.01
0.01
0.046
0.042
0.01
0.01

5. Selection of aerosol models
Aerosols play an important role in the snow grain size retrieval using ch.5 and ch.19 (notimportant for the grain size retrieval using ch.28). An unsuitable aerosol model adopted in thesimulations would cause an error in the retrieved snow grain size. However, it is still achallenging issue to remotely sense and retrieve aerosol optical properties over snow surfaces.
Aerosol model selection is one important part of the snow grain size retrieval algorithm
discussed in this document.
For the Arctic area, we use the tropospheric background aerosol model included in
MODTRAN in our algorithm, instead of Arctic haze, since the volume extinction coefficientof Arctic haze is similar to that of tropospheric aerosol (Blanchet and List, 1983). For the
Antarctic area, we use an Antarctic background aerosol model (Aoki et al., 1999).
For mid-latitude areas we employ five aerosol models in our snow grain size retrieval
algorithm. These aerosol models are: (i) rural aerosol model with 23 km visibility, (ii) rural
aerosol model with 5 km visibility, (iii) Navy maritime aerosol model with 10 (m/s) windspeed, (iv) urban aerosol model with 23 km visibility, and (v) urban aerosol model with 5 km
visibility. All data of these aerosol models have been provided using MODTRAN. Better
choices of aerosol models can be included in future as deemed necessary based on the resultsof calibration and validation studies. If new aerosol models are included in the code there will
be no changes in the algorithm except for some new lookup tables. To discriminate different
aerosol models using satellite data, we employ the reflectance difference between GLI
channels 1 (0.38 µm) and 5 (0.46 µm), based on the fact that the surface reflectance of snow
stays almost constant in this spectral range. A reflectance difference between GLI channel 1
and channel 5 has been defined as follows:
R1 - R5 = a + bR1
where the coefficients a and b depend on the aerosol model and geometrical data (such as solar
zenith angle, view zenith angle, and relative azimuth angle). We have generated five lookup
tables for aerosol model discrimination in mid-latitude areas. In these tables the coefficients aand b have been computed for five different aerosol models. The dependencies of the radianceson solar zenith angle, satellite viewing angle and relative azimuth angle between the sun andthe satellite are also taken into account in the tables. For each clear pixel and sun-satellite
geometry, the model reflectance difference between channel 1 and channel 5 (i.e. R1 - R5) isavailable from these lookup tables for each aerosol model (Figure 2.8). Comparing themeasured R1 - R5 with the tabulated values allows us to determine which aerosol model
provides the best match to the measurements for each pixel. Finally, one aerosol model for aparticular image is determined from the pixel-by-pixel frequency of occurrence of these fiveaerosol models within the whole image.

GLI Algorithm Description

3.4.2-14Figure 2.8
Flow chart for aerosol model determination. Here (R1 – R5)m is the measured-reflectancedifference between channel 1 and channel 5, and (R1 – R5)1 – (R1 – R5)5 are the modelreflectance differences for aerosol models 1–5, respectively.

C. Practical Considerations(1) Programming Requirements
The following table shows information about the expected software generated from thisalgorithm:
Table 3.1 Program Requirements
Program Memory
Program Size
Required Channels
Necessary/Ancillary Data
Expected Disk Volume
Special Programs or Subroutines
Look-up tables

400 KBytes
100 KBytes
1, 5, 19, 28
5 MBytes
gr_size.f, aermode.f
5 look-up tables for aerosol model selection
19 look-up tables for grain size and soot retrieval(2) Calibration and Validation
In order to test the algorithm for the retrieval of snow grain size and mass fraction of soot in
the snow, we applied it to MAS (MODIS Airborne Simulator) data and AVIRIS data. Two
MAS data scenes were selected and processed. One is a scene observed over the Arctic Ocean,

GLI Algorithm Description

3.4.2-15

the other is over Lake Erie. The AVIRIS data scene was obtained from the same NASA ER-2
flight as the MAS data over the Arctic Ocean. Although the ground resolution between
AVIRIS and MAS is different, we can still compare the retrieved grain size and soot. AVIRIS
provides us with more appropriate channels that are at the same wavelengths as the GLI
channels. As we discussed in section B. (2) 3, AVIRIS data also provides a good opportunity
to test the wavelength dependence of our snow grain size retrieval algorithm. Further, asimulated GLI image generated by the DISORT radiative transfer model has been used here toprovide a necessary test of our algorithm.
The implementation of the algorithm will follow the flow chart in Figure 2.9. First, weapply the cloudy/clear discriminator and snow/sea-ice discriminator to the MAS imagery, todistinguish cloud from snow or other types of surfaces, in each pixel. Under clear-sky
conditions, this algorithm can be used to retrieve the snow grain size for all snow-covered
pixels. For MAS data, MAS channel 1 (0.546 µm) and 7 (0.865 µm) is employed, instead of
the GLI channels 5 and 19, to retrieve the snow grain size and the amount of soot mixed in thesnow. For AVIRIS data, AVIRIS channels 7 (0.441 µm) and 54 (0.865 µm) are used for thispurpose.
The output of this algorithm to determine snow grain size and mass fraction of soot are twobinary data stored in a HDF file. If a pixel is not classified as “snow” by the cloudy/clear andsnow/sea-ice discriminators (cf. ATBD for CTSK1a and CTSK1b submitted to NASDA by
Knut Stamnes, PI of the contract G-0052 for GLI program, 1999), the number 4000 is assigned
to this pixel in the output file. We assume that the grain size of a snow pixel should normallylie between 10 and 3000 µm, with soot content between 0 and 3 ppmw. If a snow pixel has
grain size or soot outside these ranges, the number -1000 is assigned for this pixel, implyingthat the measured value for this pixel is a bad data point. A brief description of the output data
is given in Table 3.2. These output files “grain.data” and “soot.data” are used for thecomputation of surface albedo. The frequency distributions of snow grain size and soot for the
given image are also output.
Table 3.2 Description of the data values for the output
Data value
-1000
-1000
10-3000
0-3-4000

Meaning
bad data for grain size in the snow-covered pixel
bad data for soot in the snow-covered pixel
snow grain size retrieved from 865nm channelsnow grain size retrieved from 1.64µm channelmass fraction of soot in the snow-covered pixel
non-snow-covered pixel

GLI Algorithm Description

3.4.2-16

1. Application to AVIRIS data
We use data obtained during the ARMCAS (Arctic Radiation Measurements in Column
Atmosphere-Surface) field experiment on June 4, 1995 over the Arctic ocean near Prudhoe
Bay (70°31'33'', 147°08'23''). The instrument AVIRIS was flown on the NASA ER-2 flight at
an altitude of 20 km. It is an airborne imaging spectrometer with 224 contiguous spectral
channels from 0.4 µm to 2.45 µm, with a spectral response function of 10 nm. The field-ofview (FOV) is 10.5 km and the ground resolution is 20 m.
Generally, the relationship between snow reflectance at satellite level and snow grain size,
depends on both the solar and viewing geometries. AVIRIS is a nadir viewing instrument. Its
FOV is only 10.5 km. Thus, for AVIRIS data, only the solar zenith angle is required to
calculate the bi-directional reflectance. Figure 3.1 shows curves of the simulated reflectanceversus the equivalent snow grain size for AVIRIS channels 54, 73, 93 and 145, at the solar

Figure 3.1 Simulated reflectance as a function of effective snow grain size for a solar zenith
angle 49°.

GLI Algorithm Description

3.4.2-17

zenith angle 49°, which is the solar zenith angle for the scene shown. We can simply use thesecurves, instead of the lookup tables, to estimate the grain size for the acquired image.
According to the method described above, the retrieved snow grain size and soot of theimage are shown in Figure 2.4 for AVIRIS channels 54, 73, 93 and 145.
2. Application to MAS data
Here are two cases for the application of algorithm to MAS data in the Arctic and midlatitude regions. First, we show one MAS observation made on June 4, 1995 (track 6) over theArctic Ocean near Prudhoe Bay, Alaska. This scene was obtained simultaneously with the
AVIRIS data shown above. So a comparison between MAS and AVIRIS retrievals is presented
here. The snow grain size for the full image is plotted in Figure 3.2 to show the spatial
distribution of the retreived grain size. Different colors are used to represent the different snow
grain sizes, as indicated in Table 3.2. Please note that the black area indicates the non-snowcovered pixels or points with bad data.
In Fig. 3.2, the red square box indicates the area that the AVIRIS data covered in Fig. 3.1.
Comparing the retrieved snow grain size from AVIRIS data in Fig. 3.1 with that from MAS
data in Fig. 3.2, the retrieved snow grain size region from MAS data is consistent with theresult from AVIRIS data. The mean retrieved grain sizes are around 1000 µm for using bothdata, although the ground resolution (50 m) and channel width (0.04 µm) of MAS are
different from that of AVIRIS (20 m for ground resolution, 0.01 µm for channel width). Thus,
the algorithm has been successfully applied to different data from different instruments withvery good agreement.
Another case is MAS observation obtained over Lake Erie on February 9, 1997 (track 3).
This is an example of applying the algorithm to mid-latitude areas. Navy maritime aerosol
model has been used here. The mean retrieved grain size and soot are about 500 µm and 1.0
ppmw, respectively, as shown in Fig. 3.3.
3 Application to a simulated GLI image
A simulated GLI image has been generated, using the DISORT radiative transfer model. In
this image, we have included snow, land, ice cloud and water cloud pixels, respectively (seeFig. 3.4). The upper part of image is under clear sky condition, and the lower part of image isunder for cloudy sky condition. We have also assumed that this image was observed insummer in the Arctic region, with a solar zenith angle of 60°. So the summer Arctic aerosol
mode is used to retrieve snow grain size and mass fraction of soot mixed in the snow.
First, the cloud/clear and snow/sea-ice discriminator is applied to this image to obtain the
result of cloud mask. The left panel of Fig. 3.5 shows the true data when we generated thesimulated GLI image (i.e. the input for forward simulation). The result of cloud mask with

GLI Algorithm Description

3.4.2-18

applying the cloud/clear and snow/sea-ice discriminator is shown in the right panel of Fig. 3.5.
The colors in Fig. 3.5 have been described in Table 3.3. From Fig. 3.5, we can find that thecloudy/clear and snow/sea-ice discriminator algorithm works well for most pixels, with the
exception of some water cloud pixels.
The second step is to retrieve the snow grain size and mass fraction of soot mixed in thesnow. Fig. 3.6 shows the true data of the grain size and soot when we generated the simulated
GLI image in the left panel and right panel, respectively (i.e. the input for forward simulation).
The results of retrieved snow grain size and mass fraction of soot mixed in the snow are
shown in the left and right panels of Fig. 3.7, respectively. Comparing Figs. 3.6 and 3.7, wehave obtained the relative retrieval error, as shown in Fig. 3.8. For snow grain size retrieval,
there are about 81% pixels with the relative retrieval error less than 10%; and about 19%
pixels with the relative retrieval error in the range 10-30%. The larger relative error has
occurred in the pixels with small grain size (50 µm) and small soot (0.02 ppmw) or large soot(2.5 ppmw). For the retrieval of mass fraction of soot mixed in the snow, there are about 83%
pixels with relative error less than 10%, and 17% pixels with the relative error in the range 1018% . The larger relative error has occurred in the pixels with larger soot (2.5 ppmw) orsmaller soot (0.02 ppmw). Generally speaking, in Arctic region the snow grain size lies inrange from 100 to 1000 µm, and soot in the range from 0.1 to 0.5 ppmw. Thus, the relative
retrieval error usually should be less than 10%.

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Figure 3.2
Retrieved snow grain size and soot distribution on June 4, 1995, over the Arctic Ocean.

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Soot
Figure 3.3
Retrieved snow grain size and soot distribution on Feb. 9, 1997, over Lake Erie.

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Figure 3.4
The structure of the simulated GLI image.
Table 3.3 Description of colors in cloud mask image
color

meaningredsnow over ocean

blue

sea-iceyellow

land

green

high confidence cloud

sea green

middle confidence cloudcoral

low confidence cloud

magentasnow over land

cyan

water

GLI Algorithm Description

3.4.2-22Figure 3.5
The cloud mask for true data (left panel) and result data (right panel).

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3.4.2-23Figure 3.6
Snow grain size (left panel) and mass fraction soot mixed in snow (right panel) for true data.

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Figure 3.7
Retrieved snow grain size (left panel) and mass fraction of soot mixed in snow (right panel).

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Figure 3.8
The retrieval relative errors for snow grain size (left panel) and mass fraction of soot mixed insnow (right panel).

(3) Quality Control and Diagnostic Information
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3.4.2-26

(4) Exception Handling(5) Constraints, Limitations, Assumptions
At present time, this algorithm is designed for clear-sky pixels over the polar regions andmid-latitude regions (between 20° and 60° in latitude). For the Arctic and Antarctic regions,the tropospheric aerosol model and Antarctic background aerosol model (Aoki et al., 1999)
have been used, respectively. For mid-latitude regions, we adopt five aerosol models from
MODTRAN. These aerosol models are: (i) Rural aerosol model with 23 km visibility, (ii)
Rural aerosol model with 5 km visibility, (iii) Navy maritime aerosol model with 10 (m/s)
wind speed, (iv) Urban aerosol model with 23 km visibility, and (v) Urban aerosol model with
5 km visibility. These aerosol models are not enough to cover all aerosol models existing in
mid-latitude area. The accuracy of retrieved snow grain size or soot is mostly determined by
the aerosol model selection.
Because we use GLI channel 19 (0.865 µm) to retrieve snow grain size and channel 5 (0.46µm) to retrieve mass fraction of soot, the retrieved mean grain size and/or soot represent thedepth-weighted-averaged values appropriate for the radiation penetration depth of thesechannels. Model calculations indicate that the penetration depth for these two channels are 3.56.5 cm depending on the snow grain size.

(6) Publications and Papers
Li, W., X. Xiong, K. Stamnes, and B. Chen. Snow grain size determination from AVIRIS dataover Arctic ocean, Tenth conference on satellite meteorology and oceanography, California,
Jan. 9-14, 2000. (extended abstract in press).

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D. References
Aoki, Teruo, Tadao Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio, and T. Oishi,
1998: Spectral albedo observation on the snow field at Barrow, Alaska. Polar Meterorol.
Glaciol., 12, 1–9.
Aoki, Teruo, Tadao Aoki, M. Fukabori, and A. Uchiyama, 1999: Numerical simulation of theatmospheric effects on snow albedo with a multiple scattering radiative transfer model forthe atmosphere-snow system. J. of the Meteor. Soc. of Japan, 77, 595–614.
Blanchet, J. and R. List, 1983: Estimation of optical properties of arctic haze using a numericalmodel. Atmos. Ocean, 21, 444–465.
Bourdelles, B., and M. Fily, 1993: Snow grain-size determination from Landsat imagery over
Terre Adelie. Antarctica, Annals of Glaciology, 17, 86–92.
Fily, M., B. Bourdelles, J.P. Dedieu, and C. Sergent, 1997: Comparison of in situ and Landsat
Thematic Mapper derived snow grain characteristics in the Alps. Remote Sens. Environ., 59,
452–460.
Nolin, A.W. and J. Dozier, 1993: Estimating snow grain size using AVIRIS data. Remote Sens.
Environ., 44, 231–238.
Painter, T.H., D.A. Roberts, R.O. Green, and J. Dozier, 1998: The effect of grain size on
spectral mixture analysis of snow-covered area from AVIRIS data. Remote Sens. Environ.,65, 320–332.
Stamnes, K., S.-C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm
for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered
media. Appl. Opt., 27, 2502–2509.
Stamnes, K., 1998: ADEOS-II/GLI Cloudy/clear and snow/sea-ice discriminators for polar
regions, Algorithm Theoretical Basis Document (ADEOS-II/GLI), NASDA.
Warren, S.G., 1982: Optical properties of snow. Rev. Geophys. Space Phys., 20, 67–89.
Warren, S.G. and W.J. Wiscombe, 1980: A model for the spectral albedo of snow. II. Snowcontaining atmospheric aerosols. J. Atmos. Sci., 37, 2734–2745.
Wiscombe, W.J. and S.G. Warren, 1980: A model for the spectral albedo of snow. I. Puresnow. J. Atmos. Sci., 37, 2712–2733.

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