Geoscience Reference
In-Depth Information
temperature simulations as in Sect.
5.2
were used, based on the CLPX snowpits as these
represent realistic snow profiles.
Simulated DT
B
;
V
was compared on a pit-by-pit basis, where the simulation for the
Chang algorithm and the 1- to 5-layer realisations of HUT were compared to the N-layer
output. Figure
7
demonstrates the comparison for the Chang algorithm and the 1- and
5-layer HUT output.
For these snow properties, the Chang estimate shows a low bias in simulated DT
B
across
much of the range, but a very large positive bias at high values of SWE. This is due to the
CLPX snow properties differing from those assumed by Chang for the low values of SWE
and by saturation of the signal at higher SWE values.
For the HUT simulations, bias is much smaller and scatter is reduced relative to the Chang
estimate. This scatter is an estimate of the uncertainty introduced by simplifying the model to
fewer layers. At the lowest brightness temperature differences, the scatter is zero as the minimum
layer depth criterion ensures that for pits of depth\12 cm, the 1-layer and N-layer realisations are
identical. The scatter is less prominent for IOP3 than for IOP4, possibly due to IOP4 featuring a
larger number of thicker snowpacks with potentially more complex stratigraphy.
In an assimilation system, the snow model may output a single profile for each grid
point, equivalent to a single point on the graphs in Fig.
7
, and the deviation about the 1:1
line indicates that use of a simplified profile will lead to different simulated DT
B
;
V
values
relative to the best simulation provided by the N-layer realisation.
To quantify this deviation, the residuals from the 1:1 fit were considered, i.e. the values
ilayers
DT
B
;
V
Nlayers
DT
B
;
i
DT
B
;
N
¼
DT
B
;
V
ð
16
Þ
where DT
b
;
i
is the brightness temperature difference simulated with i layers, i is an integer
from one to five, and DT
B
;
V
;
Nlayers
is the brightness temperature difference when a maxi-
mum of N-layers are included in the model profile. As throughout, DT
B
;
V
represents the
brightness temperature difference described in Eq. (
1
).
The bias and standard deviation varies with snow thickness and, as such, the residual in
Eq. (
16
) was returned as a function of layer thickness in the 1- to 5-layer models and the
results are shown in Fig.
8
, where only snow pits of depths up to 100 cm are considered.
Beyond this value, signal saturation would reduce the weighting applied to the microwave
observational increment in an assimilation scheme, justifying the neglect of thicker pits.
It is apparent that, as layer thickness is increased, the average deviation from the N-layer
simulation (which contains layers of 10 cm thickness) increases, and there is also an
increase in bias, most likely due to layer boundary effects.
As the Globsnow approach is allowed to freely scale grain size at the snow depth
observation locations, it is plausible that it accounts for this bias by artificially increasing
the grain size depending on snow thickness. Changing the effective grain size is already
known to account for variation in vegetation outside the model assumptions.
This would have a secondary level effect on the Globsnow assimilation scheme, by
changing the variance of estimated grain size r
d
0
;
t
in Eq. (
11
) if the ensemble of stations used
for the averaging have different snow depths (and therefore different grain size biases).
The main concern for the assimilation scheme, however, is the random variance that is
introduced, as this means that the simulated DT
B
;
V
;
mod
in the assimilation cost minimisation
function (Eq. (
10
)) should have additional variance associated with the neglect of snow
stratigraphy. This variance is not accounted for in Eq. (
11
), which defines the weight given
to the observational increment based on the estimated variance. Instead, it is calculated
