Methodological problems associated with forecasting flash
floods caused by convective storms over semiarid basins have been
studied by Michaud and Sorooshian [1994a]. Using data from 24
storms which occurred over a 150 km
basin instrumented with
8 rain gauges and 10 stream gauges, they compared the performance
of three rainfall-runoff models: (1) a simple lumped model, (2)
a simple distributed model (both using unit hydrographs), and
(3) a complex distributed model (using kinematic equations).
Based on mean square error of simulated peak flow, time to peak,
and runoff volume, the lumped model was outperformed by both
distributed models, which performed about equally well. These
results corroborate the known precepts (1) that the spatial
distribution of rainfall is an important predictor of flash
floods, and (2) that the law of diminishing gains does apply to
complexity of hydrologic models.
The complex distributed model was used next in a simulation
exercise, wherein the runoff hydrograph was computed based solely
on rainfall observed up to the forecast time, and a flood warning
was declared whenever the computed flood crest exceeded a
threshold. Computations were repeated at 15-minute intervals.
After 24 flood events, the estimates of the diagnosticity of
warnings (probability of flood, given warning) and the
reliability of warnings (probability of warning, given flood)
were found equal to 0.71, and the average lead times of warnings
were on the order of 30--75 minutes. This and a follow-up study
[ Michaud and Sorooshian, 1994b] confirm the obstacles in flash
flood forecasting: (1) even a relatively dense rain gauge
network (one gauge per 20 km
) may be insufficient to detect
convective rainfall and estimate its spatial coverage and depth,
and (2) without rainfall predictions, the reliability and lead
time of warnings are severely constrained.
The effect of the rain gauge density and rainfall sampling
frequency on the accuracy of the computed hydrograph dimensions
(crest height, time to crest, and total runoff volume) has been
investigated by Krajewski et al. [1991] via a Monte Carlo
simulation. A stochastic model of convective storms generated
rain, while a distributed rainfall-runoff model with high spatial
resolution (one rain gauge per homogeneous area of 0.1 km
)
and high rain sampling frequency (every 5 minutes) was assumed to
generate the true runoff hydrograph from a 7.5 km
rural
catchment. Against true hydrographs, they compared hydrographs
from four less refined models, having one gauge per 1.5 km
and 7.5 km
, and sampling rainfall once per hour. Based on
errors of the hydrograph dimensions, the authors concluded that
the model performance was sensitive more to the frequency of
rainfall sampling (5 min versus 1 hour) than to the density of rain
gauges (one per 0.1 km
versus one per 7.5 km
). It is a
pity that only four cases of density-frequency parameters were
investigated, precluding the generality of the conclusion. But
if, indeed, this is a general law, then it holds a message for
forecasters: concentrate the limited resources not on
forecasting point precipitation, but on forecasting spatial
averages and timing of the precipitation.