Geoscience Reference
In-Depth Information
Fig. 8 Magnitude of
precipitation gradients R Þ
45
=0.9085
slope ~ 0.70
ρ
j
j ¼
r x R
40
q
2
Þ 2 þr y R
versus
precipitation intensity for the
nonzero pixels of the Claudette
storm at resolution of 1 9 1km
showing that high precipitation
gradients are mostly collocated
with high precipitation
intensities. Only pixels for which
the gradient was at least 20 % of
the local precipitation intensity
were considered
ð
35
30
25
20
15
10
Data
Fitted
5
0
0
10
20
30
40
50
60
R [mm/hr]
Table 1 Error statistics obtained by comparing the HR precipitation reflectivity image of Hurricane
Claudette (true) with the LR one, the downscaled fields via Bicubic interpolation, the VarD, and the SPaD
methodologies (see text for definition of these metrics)
Quality metrics
MSE y
MAE
PSNR
KLD
Low. res.
0.305
0.260
17.834
0.089
Bicubic
0.275
0.246
18.742
0.113
VarD
0.194
0.172
22.539
0.065
SPaD
0.209
0.177
22.015
0.044
y MSE mean squared error, MAE mean absolute error, PSNR peak signal-to-noise ratio, KLD Kullback-
Leibler divergence
5 Concluding Remarks
The problem of downscaling climate variables remains of interest as more spaceborne
observations become available and as the need to translate low-resolution (LR) climate
predictions to regional and local scales becomes essential for long-term planning purposes.
Of special interest are downscaling schemes that can accurately reproduce not only overall
statistical properties of rainfall but also specific features of interest, such as extreme
rainfall intensities and abrupt gradients. In this paper, such a precipitation downscaling
scheme was introduced using a formalism of inverse estimation and solving the (ill-posed)
inverse problem by imposing certain constraints that guarantee stability and uniqueness of
the solution while also enforcing a certain type of smoothness that allows for some abrupt
gradients. Mathematically, this inverse problem is solved via what is called an ' 1 -norm or
total variation regularization. We showed the equivalence of the proposed total variation
regularized solution to a statistical maximum a posteriori (MAP) Bayesian solution, which
has
a
Laplace
prior
distribution
in
the
derivative
domain.
We
demonstrated
the
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