284
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
2. Estimation bias (EB), calculated as
EB = 100 × ED/z,
(12.17)
where ED is the difference between estimated and observed precipitation
(ˆ z z
− ), and z and ˆ
z are observed and estimated precipitation, respectively.
3. Estimation efficiency (EE), calculated as
EE
z z
z z
j
j
j
S
j
j
j
S
=
−
−
−
=
=
∑
∑
1 0
1
1
.
( ˆ
)
(
)
.
(12.18)
4. Coefficient of determination (R 2 ), calculated as
R
z z
z z
z z
j
average
j
average
j
S
j
aver
2
1
=
−
−
−
=
∑ ( ˆ ˆ )(
)
( ˆ ˆ a age
j
S
j
average
j
S
z z
)
(
)
.
.
=
=
∑
∑
−
1
0 5
1
0 5
2
,
(12.19)
where ˆ
z average and z average are average values of estimated and observed precipitation, respectively. According to Xie et al. (2006), only pairs of concurrent nonzero precipitation values from both rain gauges and NEXRAD
were used for comparison.
5. Ratio of variance (RVar), calculated as
RVar
Var z
Var z
=
[ ˆ]
[ ]
,
(12.20)
where Var z
[ ˆ] and Var[z] are variances of estimated and observed precipitation.
The above six coefficients are applied to evaluate the NEXRAD data using
observed rain gauge data. Coefficients D rain and D no-rain are indicators of the capability of NEXRAD to successfully identify the presence and absence of precipitation
events, respectively; higher values of D rain and D no-rain mean better performance. R 2
measures the correlation between rain gauge observations and NEXRAD estimates;
larger R 2 means stronger correlation. EE indicates how well the plot of the rain gauge
observed value versus the predicted value fits the 1:1 line and ranges from –∞ to
1 (Nash and Sutcliffe 1970); when EE values are equal to 1, the prediction is considered to be “perfect.” The smaller the EB values, the better the performance of
predicted values. Because the interpolation algorithms usually lead to a smoothing of the observations and the loss of variance, which is considered undesired for
distributed hydrologic modeling (Haberlandt 2007), RVar is a coefficient used to
evaluate whether the predicted precipitation preserves the variance. The closer RVar
approaches 1, the better the spatial precipitation preserves the observed variance.
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
2. Estimation bias (EB), calculated as
EB = 100 × ED/z,
(12.17)
where ED is the difference between estimated and observed precipitation
(ˆ z z
− ), and z and ˆ
z are observed and estimated precipitation, respectively.
3. Estimation efficiency (EE), calculated as
EE
z z
z z
j
j
j
S
j
j
j
S
=
−
−
−
=
=
∑
∑
1 0
1
1
.
( ˆ
)
(
)
.
(12.18)
4. Coefficient of determination (R 2 ), calculated as
R
z z
z z
z z
j
average
j
average
j
S
j
aver
2
1
=
−
−
−
=
∑ ( ˆ ˆ )(
)
( ˆ ˆ a age
j
S
j
average
j
S
z z
)
(
)
.
.
=
=
∑
∑
−
1
0 5
1
0 5
2
,
(12.19)
where ˆ
z average and z average are average values of estimated and observed precipitation, respectively. According to Xie et al. (2006), only pairs of concurrent nonzero precipitation values from both rain gauges and NEXRAD
were used for comparison.
5. Ratio of variance (RVar), calculated as
RVar
Var z
Var z
=
[ ˆ]
[ ]
,
(12.20)
where Var z
[ ˆ] and Var[z] are variances of estimated and observed precipitation.
The above six coefficients are applied to evaluate the NEXRAD data using
observed rain gauge data. Coefficients D rain and D no-rain are indicators of the capability of NEXRAD to successfully identify the presence and absence of precipitation
events, respectively; higher values of D rain and D no-rain mean better performance. R 2
measures the correlation between rain gauge observations and NEXRAD estimates;
larger R 2 means stronger correlation. EE indicates how well the plot of the rain gauge
observed value versus the predicted value fits the 1:1 line and ranges from –∞ to
1 (Nash and Sutcliffe 1970); when EE values are equal to 1, the prediction is considered to be “perfect.” The smaller the EB values, the better the performance of
predicted values. Because the interpolation algorithms usually lead to a smoothing of the observations and the loss of variance, which is considered undesired for
distributed hydrologic modeling (Haberlandt 2007), RVar is a coefficient used to
evaluate whether the predicted precipitation preserves the variance. The closer RVar
approaches 1, the better the spatial precipitation preserves the observed variance.