In another data analysis example, scientists often need to map data onto a physical coordinate system. Meteorologists, for example, collect data on weather conditions across a region and generate color contour maps of properties such as temperature,  pressure or precipitation. The scattered data must be converted into maps that will convey entire trends. Neural networks can be extremely effective at processing this data into uniform contour data for mapping. A neural network’s ability to develop a complex, nonlinear, discontinuous data fits from non-uniform, scattered sources make Qnet the perfect tool for this type analysis. In fact, with automation, the complete process of generating maps can be reduced to a matter of minutes. Furthermore, once automated, entire motion pictures of weather histories and forecasts can be simulated with minimal effort. Beyond this practical data analysis, meteorological researchers are exploring the use of neural networks in advanced weather forecasting models.

Our neural network example will be a simple temperature data fitting model. Temperature data will be modeled from various locations across the United States. Our input nodes will contain the latitude and longitude of the cities reporting the temperature. The single output target will be the temperature. Once trained, the neural network will take an input latitude, longitude pair and produce a temperature. The model will then be used to generate high fidelity temperature information from uniform latitude, longitude pairs (done with Qnet's Color Contour option).

Figure - US temperature Color Map from Qnet Model

The example neural network is contained in "Temps.net" (the untrained network) and "TempsTrained.net" (the trained network).   The input layer has 2 nodes. The first for latitude and the second for longitude. The output layer has 1 node that represents the target temperature. A five layer design offers both a sophisticated data fitting model and a short training time. The training data contains 233 temperature reporting cities from across the country. No test set is used since the resulting fit can be visually checked with the final map (note: data fitting rarely requires the use of test sets).

The results are very good considering the simplicity of our model. We did find that a response problem exists in high mountain areas. A better model for temperature mapping would be to include a third input node for altitude. With temperature being a strong function of altitude, the addition of this input would improve the ability of the model to generate accurate temperatures. Otherwise temperature trends were accurately captured in our model. The temperature map above was generated with Qnet's Color Contour option and then superimposed over a map of the US.