lang
essful
> global
S
iantified
matic
ve
or the
al
[ay) are
| be
be used to
10w depth
ence snow
systematic
he passive
» remotely
or climate
nd flood
| unbiased
ther than
This is à
ilation of
vegetation
the main
er concern
mospheric
number of
not affect
significant
In densely
‘anada, the
rithms can
ther major
rystal size
N season
they vary
algorithms
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
|
Y
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€ +
os |
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.