The bulk of research in the last quadrennium centered on integrating radar data with data from other remote sensors, such as satellites, radiosondes, and ground stations, into predictive models of rainfall. The framework for integration has been mathematical models describing the physics of the convective precipitation process.
The potential utility of radar reflectivity as an additional
input to a physically based spatially lumped rainfall model was
explored by Georgakakos and Krajewski [1991]. Their model was
intended for making predictions of mean areal rainfall over river
basins of the order of 100--1000 km
, with the lead time of
one hour. The question was by how much can the forecast
uncertainty be reduced as a result of augmenting the model input
with radar data. A comparison of forecast error variances
obtained with and without radar data indicated that a reduction
of 5--15% in variance could be attained.
Seo and Smith [1992] formulated a two-component model for
prediction of convective rainfall under the radar umbrella.
Their principal assumption is that the vertically integrated
liquid water, as a function of time and space, is equal to the
sum of a time-varying mean and a residual that varies in time and
space. A physically based model predicts the mean using radar
data, surface measurements of temperature, dew point temperature
and pressure, and radiosonde profiles of environmental
temperature and water vapor density. A statistical
autoregressive model predicts the residual. Validation was
limited to seven historical storms that also provided data for
parameter estimation. Rainfall fields estimated from radar
reflectivities were assumed to be the ground truth. Predictions
were made every 10--12 minutes, for one hour ahead and an area of
80,000 km
. Based on the mean square error criterion, the
model forecasts outperformed, though not substantially, the
advection forecasts (obtained via a translation of the current
rainfall field, estimated from radar data at the forecast time,
by the mean velocity vector one hour into the future).
Another predictive model was developed by French and
Krajewski [1994]. The model rests on the conservation of mass
and momentum laws in which states and boundary conditions are
parameterized directly in terms of radar reflectivity (a
predictor of liquid water content), satellite infrared brightness
(a predictor of cloud top temperature), and surface air
temperature, dew point temperature and pressure. For
applications, state dynamics are linearized and states are
updated based on sensor measurements via a Kalman filter. In a
verification study, reported by French et al. [1994] and using
historical data from three storms, predictions of the rainfall
rate were computed every 10--15 minutes for the lead time of one
hour and an area of 170,000 km
. According to the mean
error, mean square error, and the correlation between forecasted
and measured (via the same radar) rainfall rates, the model
forecasts outperformed the persistence forecasts (obtained under
the assumption that the currently observed rainfall will continue
for one hour) and performed somewhat better than the advection
forecasts.