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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
are found to be very sensitive to snow crystal size 
(Foster et al., 1999). 
The purpose of this paper is to present a methodology 
for deriving unbiased SWE estimates from PM 
observations. Systematic errors due to simplifying 
assumptions of the retrieval algorithm and effects of 
vegetation cover and crystal size are quantified. This 
paper presents results for the snow season 1990-91 as 
an example, using Special Sensor Microwave/Imager 
(SSM/T) data. 
2. PASSIVE MICROWAVE RADIOMETRY 
If a snowpack is not too shallow (> 5 cm or contains 
more than about 10 mm SWE), scattering of naturally 
emitted microwave radiation by snow crystals occurs 
and can be detected at frequencies greater than about 
25 GHz. Otherwise, the snow will be virtually 
transparent. By comparing brightness temperatures 
detected at an antenna at frequencies greater than 25 
GHz (typically scattering dominated) with those 
brightness temperatures detected at frequencies less 
than 25 GHz (typically emission dominated), it is 
possible to identify scattering surfaces. Generally, the 
strength of scattering signal is proportional to the 
SWE, and it is this relationship that forms the basis for 
estimating the water equivalent (or thickness) of a 
snow pack (Chang et al, 1976; Pulliainen and 
Hallikainen, 1999; Tsang et al., 2000; Kelly et al., 
2003). 
From November 1978 to the present, the SMMR 
instrument on the Nimbus-7 satellite, and the SSM/I 
on the Defense Meteorological Satellite Program 
(DMSP) series of satellites have acquired PM data that 
can be used to estimate SWE. The SMMR instrument 
failed in 1987, the year the first SSM/I sensor was 
placed in orbit. On SMMR, the channels most useful 
for snow observations are the 18 and 37 GHz 
channels. For the SSM/I, the frequencies are slightly 
different (19.35 and 37.0 GHz). The data are projected 
into % degree latitude by '^ degree longitude grid 
cells, uniformly subdividing a polar stereographic map 
according to the geographic coordinates of the center 
of the field of view of the radiometers. Overlapping 
data in cells from separate orbits are averaged to give 
a single brightness temperature, assumed to be located 
at the center of the cell (Armstrong and Brodzik, 1995, 
Chang and Rango. 2000). 
We propose a modified SWE algorithm based on the 
original algorithm by Chang at al. (1987), where 
brightness temperature differences between the 19 
GHz (or 18 GHz for SMMR) and 37 GHz channels are 
multiplied by a constant related to the average grain 
size to derive the water equivalent of the snowpack. 
The simple algorithm is 
SWE = c (T;9 - T37) [mm] (1) 
where SWE is snow water equivalent in mm, c is 4.8 
mm K', and 7j, and T;; are the horizontally polarized 
brightness temperatures at 19 GHz (or 18 GHz for 
SMMR) and 37 GHz, respectively. The performance 
of this algorithm is similar when either vertical or 
horizontal polarizations are utilized — horizontal 
polarization was used in this study (Rango at al., 
1979). If the brightness temperature from the 19 GHz 
channel is less than that from the 37 GHz channel, 
then the snow depth and SWE are zero. 
To derive snow depth, SWE is simply divided by the 
snow density. It has been determined that in general, a 
snow density value of 300 kg/m? is representative of 
mature mid winter snow packs in North America 
(Foster et al., 1996). The effect of this is to modify the 
coefficient in (1) such that c is 1.60 cm K'! (1.59 em 
K' for SMMR). 
SWE underestimation (%) 
  
+23 
| 
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rii] = 
0 10 20 30 40 50 60 70 80 90 100 
fractional forest cover (%) 
SWE underestimation (%) 
  
  
  
  
(a) 
Forest factor F 
2.5 
2 + + 
© 15 | + 
Gi. 
5% 11€ + 
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d uuo —_ d 
0 10 20 30 40 50 60 70 80 90 100 
fractional forest cover (%) 
(b) 
Figure 1. (a) Underestimation of SWE due to forest cover. 
The error bars denote uncertainty of the underestimation. (b) 
The forest factor F as a function of fractional forest cover. 
3. A NEW RETRIEVAL ALGORITHM 
There are typically two kinds of errors associated with 
a given observation, systematic error (bias) and 
random error. In this study, the emphasis is to 
evaluate the bias in the original algorithm (1) by 
comparing with a new algorithm (2). We use the term 
“bias” as if the new algorithm gives the "true" values 
of SWE.