Using Ranked Probability Skill Score (RPSS)
as Nonlocal Root-Mean-Square Errors (RMSEs)
for Mitigating Wet Bias of Soil Moisture Ocean
Salinity (SMOS) Soil Moisture
Ju Hyoung Lee
Abstract
To mitigate instantaneously evolving biases in satellite retriev-
als, a stochastic approach is applied over West Africa. This
stochastic approach independently self-corrects Soil Mois-
ture Ocean Salinity (
SMOS
) wet biases, unlike the cumulative
density function (
CDF
) matching that rescales satellite retriev-
als with respect to several years of reference data. Ranked
probability skill score (
RPSS
) is used as nonlocal root-mean-
square errors (
RMSEs
) to assess stochastic retrievals. Stochastic
method successfully decreases
RMSEs
from 0.146 m
3
/m
3
to
0.056 m
3
/m
3
in the Republic of Benin and from 0.080 m
3
/m
3
to
0.038 m
3
/m
3
in Niger, while the
CDF
matching method exacer-
bates the original
SMOS
biases up to 0.141 m
3
/m
3
in Niger, and
0.120 m
3
/m
3
in Benin. Unlike the
CDF
matching or European
Centre for Medium-Range Weather Forecasts (
ECMWF
) Re-
Analysis (
ERA
)–interim soil moisture, only a stochastic retriev-
al responds to Tropical Rainfall Measuring Mission rainfall.
Based on the effects of bias correction, RPSS is suggested as
a nonlocal verification without needing local measurements.
Introduction
The quality of satellite-based soil moisture is important,
particularly if used as an initialization for numerical weather
prediction (
NWP
) or land surface models (Massey
et al.
2016).
However, satellite microwave sensors often produce large re-
trieval errors for various reasons (Gruhier
et al.
2008; Zhu
et al.
2019). In extremely dry soils, de Jeu
et al.
(2008) explain that
the linear relationship between soil moisture and soil dielectric
constant becomes invalidated, resulting in retrieval errors (Lou-
vet
et al.
2015). The linear relationship between microwave
emission and soil moisture is also invalid in the event of rain
(Dogusgen and Hornbuckle 2015). The presence of vegetation
also contributes to retrieval errors, because vegetation attenu-
ation underestimates brightness temperature, and it overesti-
mates soil moisture as a consequence (Al-Yaari
et al.
2014).
Although data assimilation is often used for error correc-
tion, it only reduces random errors. Thus, the cumulative
density function (
CDF
) matching technique is widely used for
reducing systematic errors in satellite retrievals. This ap-
proach rescales the
CDF
of satellite-derived soil moisture data
with that of a long period of reference data. However, there
are several limitations in that approach (Dee and Uppala
2009; Lee and Im 2015). First,
CDF
matching only considers
stationary errors from 1–10 years of climatology, meaning
that it does not mitigate retrieval errors that nonlinearly or
abruptly evolve in every moment of satellite measurements
(Reichle
et al.
2007). However, the root-mean-square error
(
RMSE
) used for establishing the Soil Moisture Ocean Salinity
(
SMOS
) and the Soil Moisture Active Passive retrieval goals
indicates such instantaneous field of view (the angle over
which a measurement is being made by an instrument in a
single moment) satellite errors (Crow
et al.
2012).
CDF
match-
ing does not consider such retrieval errors made in an instant.
However, instantaneous soil moisture data estimated in a
specific time step is used for model initialization rather than
time-averaged estimation. Secondly,
CDF
matching results may
change, depending on the selection of reference data. When
the satellite observations are rescaled to imperfect reference
data, the original satellite observations can be exacerbated by
its own biases of reference data (Muñoz-Sabater 2015). Con-
sidering that no perfect data exist, this aspect suggests that
CDF
matching inherently transfer biases.
For an alternative method, a Monte Carlo method is sug-
gested in this study. Unlike deterministic retrievals of a single
estimation, it uses a probability distribution function (
PDF
)
for multiple retrievals. The statistical likelihood of optimal
soil moisture values is determined from the mean value of the
PDF
(Kornelsen and Coulibaly 2013). A stochastic approach
has been widely used for improving satellite-retrieved soil
moisture (Lee and Im 2015; Lu and Gong 2012; Notarnicola,
Angiulli, and Posa 2006; Pierdicca, Pulvirenti, and Big-
nami 2010; Verhoest
et al.
2007). That is because it resolves
ill-posed retrieval problems with several unknown inputs,
and enhances structural stability (Barabási and Albert 1999;
Dhanya and Nagesh Kumar 2010; Lee and Ahn 2019).
However, none of those stochastic approaches introduced
above has suggested a method to optimize
PDFs
(i.e., a re-
duction of
RMSE
in retrievals). In addition to computational
costs (Parinussa
et al.
2011), optimization is required for the
purpose of bias correction. Not every
PDF
exhibits the correct
estimation when taking an average. For example, if a spread
of the
PDF
is not enough, the mean value of the
PDF
is biased.
If the distribution is too wide, the mean of the
PDF
loses
information of soil moisture dynamics. Although the field
measurements-based
RMSEs
or biases are a local standard of
verification, they do not cover the entire global domain that
satellites operate. Thus, a nonlocal optimization of stochastic
system is needed. Several studies in weather or climate mod-
els suggest an ensemble optimization via a ranked probability
score (
RPS
) in that the ensemble method approximates the
PDF
by a finite set of multiple realizations (Dhanya and Nagesh
Research Institute for Mega Construction, 145 Anam-ro,
Seongbuk-gu, Korea University, Seoul, Republic of Korea
(
).
Photogrammetric Engineering & Remote Sensing
Vol. 86, No. 2, February 2020, pp. 91–97.
0099-1112/20/91–97
© 2020 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.86.2.91
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
February 2020
91
