278
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
methods for spatial precipitation estimation using rain gauge observations. When
combining NEXRAD and rain gauge observations data to estimate spatial precipitation, the NEXRAD estimates are often taken as an auxiliary variable or external
drift. The simple BA method, which aims at calibrating the NEXRAD estimated
mean to match the rain gauge observed mean precipitation, has been widely used
to calibrate NEXRAD data for distributed hydrologic modeling (e.g., Steiner et al.
1999; Zhang et al. 2004). Relatively complex geostatistical procedures are promising
methods for combining rain gauge observations with NEXRAD data for better spatial precipitation estimation (Seo 1998; Seo and Breidenbach 2002; Seo et al. 1990;
Haberlandt 2007; Li et al. 2008; Zhang and Srinivasan 2010). Based on the above
research, several multivariate methods (BA, SKlm, RK, and KED) are included in
NEXRAD-VC. The following sections describe a few key methods.
12.3.2.1 Bias Adjustment
Operational radar precipitation estimates rarely match amounts recorded by rain
gauges; therefore, the radar precipitation estimates are adjusted using the information provided by rain gauges (Steiner et al. 1999). A simple BA method is to remove
the average difference between the radar estimates at the rain gauge locations and
the corresponding gauge precipitation amounts:
R adj = B ⋅ R ori
(12.2)
B
Z
N
R
N
i
i
N
i
i
N
=
=
=
∑
∑
( )
( )
x
x
1
1
,
(12.3)
where R adj is the bias-adjusted NEXRAD, R ori is the original NEXRAD, B is the BA
factor, and Z(x i ) and R(x i ) are the rain gauge–observed and NEXRAD-estimated
precipitation at a location x i . Steiner et al. (1999) applied this BA method in Goodwin
Creek, a small research watershed in northern Mississippi, and achieved radar precipitation estimates with root mean square errors of approximately 10% for stormbased total precipitation accumulations of 30 mm or more.
12.3.2.2 Ordinary Kriging
Kriging is a group of advanced geostatistical techniques that provide the best linear
unbiased estimate. The aim of these spatial prediction techniques is to estimate the
value of a random variable (precipitation amount), Z, at one or more unsampled
points from a set of sample data (Z(x 1 ), Z(x 2 ),…,Z(x n )) at points (x 1 , x 2 ,…,x n ) within
a spatial domain. In kriging methods, the random variable Z is decomposed into
a trend (m) and a residual (ε), where Z(x) = m(x) + ε(x). The kriging estimator is
given by a linear combination of the surrounding observations (Goovaerts 1997).
The weights of the points that surround the predicted points are calculated based
on the spatial dependence (i.e., semivariogram or covariance) of the random field.
Previous studies (e.g., Goovaerts 2000; Hengl et al. 2004; Haberlandt 2007; Li et al.
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
methods for spatial precipitation estimation using rain gauge observations. When
combining NEXRAD and rain gauge observations data to estimate spatial precipitation, the NEXRAD estimates are often taken as an auxiliary variable or external
drift. The simple BA method, which aims at calibrating the NEXRAD estimated
mean to match the rain gauge observed mean precipitation, has been widely used
to calibrate NEXRAD data for distributed hydrologic modeling (e.g., Steiner et al.
1999; Zhang et al. 2004). Relatively complex geostatistical procedures are promising
methods for combining rain gauge observations with NEXRAD data for better spatial precipitation estimation (Seo 1998; Seo and Breidenbach 2002; Seo et al. 1990;
Haberlandt 2007; Li et al. 2008; Zhang and Srinivasan 2010). Based on the above
research, several multivariate methods (BA, SKlm, RK, and KED) are included in
NEXRAD-VC. The following sections describe a few key methods.
12.3.2.1 Bias Adjustment
Operational radar precipitation estimates rarely match amounts recorded by rain
gauges; therefore, the radar precipitation estimates are adjusted using the information provided by rain gauges (Steiner et al. 1999). A simple BA method is to remove
the average difference between the radar estimates at the rain gauge locations and
the corresponding gauge precipitation amounts:
R adj = B ⋅ R ori
(12.2)
B
Z
N
R
N
i
i
N
i
i
N
=
=
=
∑
∑
( )
( )
x
x
1
1
,
(12.3)
where R adj is the bias-adjusted NEXRAD, R ori is the original NEXRAD, B is the BA
factor, and Z(x i ) and R(x i ) are the rain gauge–observed and NEXRAD-estimated
precipitation at a location x i . Steiner et al. (1999) applied this BA method in Goodwin
Creek, a small research watershed in northern Mississippi, and achieved radar precipitation estimates with root mean square errors of approximately 10% for stormbased total precipitation accumulations of 30 mm or more.
12.3.2.2 Ordinary Kriging
Kriging is a group of advanced geostatistical techniques that provide the best linear
unbiased estimate. The aim of these spatial prediction techniques is to estimate the
value of a random variable (precipitation amount), Z, at one or more unsampled
points from a set of sample data (Z(x 1 ), Z(x 2 ),…,Z(x n )) at points (x 1 , x 2 ,…,x n ) within
a spatial domain. In kriging methods, the random variable Z is decomposed into
a trend (m) and a residual (ε), where Z(x) = m(x) + ε(x). The kriging estimator is
given by a linear combination of the surrounding observations (Goovaerts 1997).
The weights of the points that surround the predicted points are calculated based
on the spatial dependence (i.e., semivariogram or covariance) of the random field.
Previous studies (e.g., Goovaerts 2000; Hengl et al. 2004; Haberlandt 2007; Li et al.