Istanbul 2004
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udy. The
percentage of forest cover in a PM pixel was
calculated from the total number of forest
classification pixels at 1 km divided by the total
number of pixels. Based on this fractional forest cover,
the systematic error in the SWE value obtained from
(1) can be estimated. À multiplicative “forest factor” F
is introduced to remove the bias due to forest cover
from (1)
SWE = F ce (T,9— T37) [mm]. (2)
We derived the values of forest factor F by assigning
underestimation errors for algorithm (1). In Figure la,
the diamonds denote the underestimation error in (1)
due to forest cover. For example, if the fractional
forest cover at a given pixel is 6596, we assume (1)
underestimates SWE by 30%. These nonlinear values
are inexact, but are our best approximations at this
time. The error bars are our estimates of uncertainty
associated with the underestimation estimate of a
particular forest cover fraction. The more mixed the
pixel, the more uncertainty there is on the forest
influence of the PM signal. In other words, untangling
the contribution of the signal due to scattering from
the underlying snow and emission from trees is harder
to assess when the mixture is more even.
Figure 1b shows the forest factor F as a function of
fractional forest cover fr in North America (maximum
of 2.0). Note that the F factor increases (nonlinearly)
with forest cover. This is to correct for more severe
underestimation of SWE due to dense forest cover.
The values for F are based on the underestimation of
SWE at different values of fr.
grain size coefficient C
= X: —— TUNDRA
£5 — Fe IL | - TAIGA
$4 EE PRAIRIE
ë em E LM ALPINE
33 | -x- MARITIME
à 2 -«— EPHEMERAL
= — OLD
: —OLD |
0 * A
OCT NOV DEC JAN FEB MAR APR MAY
Figure 3. Monthly grain size coefficient c for six Sturm
classes. The constant value 4.8 (mm/K) used in the original
algorithm is also plotted and labeled as “OLD”.
3.2 Error due to grain size variability
The secondary source of SWE error results from the
retrieval algorithm assumption that snow crystal size
and shape is spatially uniform and remains constant
throughout the snow season. This assumption is
reflected in the original SWE retrieval algorithm (1)
where c is a constant. The constant coefficient c (4.8
mm K”') is associated with an average crystal size of
0.3 mm (radius). In fact, snow crystals vary with
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
location and evolve with time. Since microwave
scattering increases as the crystals grow in size as the
snow season progresses, the algorithm (1) typically
overestimates SWE, except when the snowpack is
thin.
Sturm et al. (1995) have characterized the seasonal
snowpack into six classes (excluding continental ice
caps and ocean/water bodies), based on vegetation and
meteorological conditions: tundra, taiga, alpine,
prairie, maritime and ephemeral. In this investigation,
we use these classes to address the issue of spatial
inhomogeneity of snowpacks. In addition, we consider
the evolution of snow crystal size of these different
snow classes. As a result, the c value used in (2) now
varies with location and time.
In this study, it is assumed that crystals grow
throughout the snow season — an exception to this is
the *ephemeral" snow class. Where temperature and
vapor gradients are greater (northern interior climates
— taiga, tundra, and prairie snow classes), the rate of
growth and the associated crystal size errors are
typically larger.
Figure 2 shows the systematic errors for six different
*Sturm" snow classes due to grain size variability. For
each Sturm snow class calendar month, a percentage
error in SWE due to differences in snow crystal size
over time is prescribed. They are assigned based on
various field campaign results with snow crystal
samples collected and analyzed, as well as subjective
analysis (based on previous work and personal field
experience). Negative values denote underestimation
of SWE, while positive values denote overestimation.
The greatest systematic error occurs in the tundra
snow and the least in maritime or ephemeral snow.
The largest uncertainty in c random errors occur in the
tundra and prairie during the late winter and early
spring period, whereas the smallest uncertainty is for
the maritime and ephemeral snow classes.
Note that for November, (1) underestimates SWE for
each snow class. That is because when the snow cover
is shallow (« 5 em), as it generally is at the beginning
of the snow season, microwave radiation at all
observed frequencies passes through the snowpack
virtually unimpeded.
Figure 3 shows the different values of c for each of the
six Sturm snow classes for each month of the snow
season from October to May for North America. These
values are derived from estimates of snow crystal size-
related errors (Fig. 2). When the average crystal size is
smaller than 0.3 mm, c becomes larger than 4.8; when
the crystal size is larger, c becomes smaller.
In summary, to compute unbiased SWE value for each
pixel using (2), the forest factor F is first determined
based on the forest cover fraction of this pixel, and
then the c value is assigned based on its snow class
category and time of the year. The introduction of
