aggregated into a range of discrete temporal (1, 3, 6, 12, and 24 h) and spatial (0.04°,
0.12°, 0.24°, 0.48°, and 0.96°) scales. Therefore each box is divided into subgrids with
side lengths of 0.04°, 0.12°, 0.24°, 0.48°, and 0.96° latitude–longitude; each subgrid
holds rainfall intensities at time resolutions of 1, 3, 6, 12, and 24 h for this analysis.
The error analysis is conducted for each box separately.
The satellite rainfall estimates were incrementally divided into five bins according to their intensities; the reference errors are then calculated for each rain rate bin
at various spatial and temporal scales. The reference error (s E ) distribution at the
discrete temporal and spatial scales and increasing rain rates for box I in August
2003 are displayed in Figure 13.3 (left). The same reference error is shown in
Figure 13.3 (right), but as a percentage of rainfall estimates s E =
^
R(%). From Figure
13.3, the satellite rainfall estimation reference error is a function of spatial and
temporal scales where higher spatial and temporal resolution is subject to larger
reference error.
For each box shown in Figure 13.2, we divide an entire year data set at various
spatial–temporal scales and 10 bins of incremental rain intensities. By defining the
minimum satellite sampling frequency as 1 h (Dt = 1), the parameters a, b, c, and d of
Equation (13.1) were calibrated using the root mean-square error (RMSE) as the
calibration criterion. Using the calibrated optimal parameter set, Figure 13.4 plots the
reference error estimates (s E ) with respect to spatial–temporal scales and rainfall
intensities; the same reference error estimates but as a percentage of rainfall intensity
s E =
^
R are plotted in Figure 13.5. Note that in the current study we arguably assume
that the effect of sampling frequency is negligible because the PERSIANN-CCS has
relatively high sampling frequency (30 min), one of the advantages of rainfall
estimates using multiple satellites.
13.3.3 Uncertainty Propagation from Precipitation Data
to Hydrological Prediction
As the key forcing variable of hydrological processes, the precipitation is largely
responsible for the uncertainty in model outputs. Clearly, evaluation of the error
associated with precipitation products into model behavior is an indispensable
element of improving hydrological modeling and data assimilation. In the current
study, the influence of the error of input-forcing data, that is, precipitation, through a
conceptual rainfall–runoff hydrological model to output forecasting uncertainty is
evaluated by propagating the approximated PERSIANN-CCS rainfall error estimates
with a Monte Carlo simulation approach. This approach generates an ensemble of
precipitation data as forcing input to fit to the conceptual rainfall–runoff model, and
the resulting uncertainty in the forecasted stream flow is then quantified. The
applicability and usefulness of this procedure are demonstrated in the case of the
Leaf River basin, located north of Collins, Mississippi. The size of the Leaf River
basin is about 1949 km
2 . A map of the Leaf River basin is shown in Figure 13.6. We
have used a daily time step for precipitation input. This may be larger than desirable to
capture the hydrological response. See, for example, Burges (2003) for a perspective
on this issue.
PRECIPITATION UNCERTAINTY QUANTIFICATION AND ERROR PROPAGATION
257
0.12°, 0.24°, 0.48°, and 0.96°) scales. Therefore each box is divided into subgrids with
side lengths of 0.04°, 0.12°, 0.24°, 0.48°, and 0.96° latitude–longitude; each subgrid
holds rainfall intensities at time resolutions of 1, 3, 6, 12, and 24 h for this analysis.
The error analysis is conducted for each box separately.
The satellite rainfall estimates were incrementally divided into five bins according to their intensities; the reference errors are then calculated for each rain rate bin
at various spatial and temporal scales. The reference error (s E ) distribution at the
discrete temporal and spatial scales and increasing rain rates for box I in August
2003 are displayed in Figure 13.3 (left). The same reference error is shown in
Figure 13.3 (right), but as a percentage of rainfall estimates s E =
^
R(%). From Figure
13.3, the satellite rainfall estimation reference error is a function of spatial and
temporal scales where higher spatial and temporal resolution is subject to larger
reference error.
For each box shown in Figure 13.2, we divide an entire year data set at various
spatial–temporal scales and 10 bins of incremental rain intensities. By defining the
minimum satellite sampling frequency as 1 h (Dt = 1), the parameters a, b, c, and d of
Equation (13.1) were calibrated using the root mean-square error (RMSE) as the
calibration criterion. Using the calibrated optimal parameter set, Figure 13.4 plots the
reference error estimates (s E ) with respect to spatial–temporal scales and rainfall
intensities; the same reference error estimates but as a percentage of rainfall intensity
s E =
^
R are plotted in Figure 13.5. Note that in the current study we arguably assume
that the effect of sampling frequency is negligible because the PERSIANN-CCS has
relatively high sampling frequency (30 min), one of the advantages of rainfall
estimates using multiple satellites.
13.3.3 Uncertainty Propagation from Precipitation Data
to Hydrological Prediction
As the key forcing variable of hydrological processes, the precipitation is largely
responsible for the uncertainty in model outputs. Clearly, evaluation of the error
associated with precipitation products into model behavior is an indispensable
element of improving hydrological modeling and data assimilation. In the current
study, the influence of the error of input-forcing data, that is, precipitation, through a
conceptual rainfall–runoff hydrological model to output forecasting uncertainty is
evaluated by propagating the approximated PERSIANN-CCS rainfall error estimates
with a Monte Carlo simulation approach. This approach generates an ensemble of
precipitation data as forcing input to fit to the conceptual rainfall–runoff model, and
the resulting uncertainty in the forecasted stream flow is then quantified. The
applicability and usefulness of this procedure are demonstrated in the case of the
Leaf River basin, located north of Collins, Mississippi. The size of the Leaf River
basin is about 1949 km
2 . A map of the Leaf River basin is shown in Figure 13.6. We
have used a daily time step for precipitation input. This may be larger than desirable to
capture the hydrological response. See, for example, Burges (2003) for a perspective
on this issue.
PRECIPITATION UNCERTAINTY QUANTIFICATION AND ERROR PROPAGATION
257