Geoscience Reference
In-Depth Information
1) The forecast snow depth map is generated by ordinary kriging between in situ snow
depth observations provided by the ECMWF and SCCONE (Snow Cover Changes Over
Northern Eurasia, Kitaev et al.
2002
), and the in situ measurements are given an assumed
variance of 150 mm
2
based on the comparison with coincident snow surveys. This forecast
map at time t contains the a priori snow depth D
ref
;
t
and its variance r
D
;
ref
;
t
.
2) At each grid point where a snow depth observation exists, the Helsinki University of
Technology radiative transfer model is used to simulate the brightness temperature dif-
ference DT
B
= T19V-T37V. The effect of vegetation is included in the radiative transfer,
dependent on forest cover fraction in Eurasia, or at 80 kg m
-3
ha
-1
stem volume in North
America. A single snow layer of 0.24 g cm
-3
density is assumed, and snow depth is taken
from the in situ observation. Grain size is varied at each location i with the result obtained
according to the cost function:
n
o
T37V
mod
d
0
;
i
;
D
ref
;
i
T19V
obs
T37V
obs
2
min
d
0
;
i
T19V
mod
d
0
;
i
;
D
ref
;
i
ð
Þ
ð
9
Þ
where d
0
;
i
is the grain size at the i
th
location, which is allowed to vary and D
ref,i
is the
locally measured snow depth. The final grain size (d
0
) and its error variance (r
d0
;
t
) at each
measurement location come from the ensemble of the nearest stations (N = 6).
3) A full grain size map with variances is generated by kriging between the point grain
size estimates from step 2).
4) At each grid cell, the grain size value and an assumed constant density of
0.24 g cm
-3
is used as input to the HUT radiative transfer model by varying the snow
depth D
t
to obtain:
(
)
2
2
þ
D
t
D
ref
;
t
r
D
;
ref
;
t
ð
T19V
mod
D
ðÞ
T37V
mod
D
ð Þ
T19V
obs
T37V
obs
ð
Þ
min
D
t
r
t
ð
10
Þ
where the variance at time t, r
t
is obtained from a Taylor expansion of T
B
ð
D
t
;
d
0
;
t
Þ
with
respect to grain size, which leads to
2
oT
B
D
t
;
d
0
;
t
r
t
¼
r
d
0
;
t
ð
11
Þ
od
0
This variance provides the weighting of the microwave contribution, allowing a large cor-
rection to the forecast when the SWE sensitivity is high but introducing a large cost to microwave-
based adjustments when the signal is saturated with respect to SWE but oT
B
=
od
0
grows. This
effect is seen in Fig.
2
as the increasing spread in simulated DT
B
for different grain sizes.
3.2.2 Limitations of Globsnow
Globsnow was validated with independent in situ snow depth measurements from cam-
paigns in the Former Soviet Union, Finland and Canada. RMSE values of \40 mm were
found where SWE was below 150 mm, although errors increase for thicker snow.
Assimilating the passive microwave data was found to improve on the forecast, thus
demonstrating the utility of microwave retrievals.
Hancock et al. (
2013
) considered Globsnow and the Chang-based AMSR-E and SSM/I-
only SWE products for the purpose of assessing LSMs. The Chang-based products were
found to spike towards the end of the season, which was attributed to melt-refreeze cycles
