Deriving a more complex, theoretically-based relationship using those practical observables would be too difficult. A neural network (NN) approach, however, provides a means to produce an empirical relationship that can take into account the available inputs and produce a more accurate rainfall rate estimate. Furthermore, a NN can be trained for a particular radar, producing an Artificial Intelligence (AI) that is tuned to the region's climate. It is the purpose of this project to show that even the use of indirect measures of the quantities that are directly related to rainfall rate can provide added value to a rainfall rate estimation model. This is the key difference from similar attempts to improve rainfall rate using NN, which only used radar data. It should be noted that the inability to directly measure DSD is largely limited to single-polarization radars and not dual-polarization radars, however both types of radars are incapable of directly measuring the relative fallspeed of the precipitation. Therefore, both kinds of radars can potentially benefit from this project's approach.
For this project, the NN is a multi-layered perceptron (MLP) implemented using WEKA (Waikato Environment for Knowledge Analysis) – a useful 'workbench' for developing machine learning techniques. The training data are comprised of surface observations from the Oklahoma Mesonet and reflectivities from the KTLX radar for many precipitation events for over ten years. Then, a trial-and-error process for determining a good design of the NN structure ensued. After a satisfactory design is found, the AI model is then compared to the Z-R model used by the National Weather Service (NWS). To ensure that the trained model is not over-fitting the training data, the comparison is done using the results from the untrained records by running the training 3 times, withholding 33% of the training data each time.
The NN model had improved rainfall rate estimation by approximately 10 mm/hr over the NWS's Z-R model. Its root mean squared error was almost 25 mm/hr better than the NWS's Z-R model. Because a significant amount of the NWS's Z-R model errors come from gross overestimation in high-reflectivity situations (because it is an exponential relationship), it is found that much of the improvements come from the NN's ability to better handle these high-reflectivity inputs. Not being constrained to a strict exponential relationship, the NN is able to 'spread out' its rainfall rate estimates for a given input reflectivity. There is still an existing problem of the NN slightly overestimating the rainfall rate in low reflectivity situations, and slightly underestimating the rainfall rate in high reflectivity events, however, this problem is expected to be eliminated with additional research.