Results
In order to see the effect of different prediction variable outputs on the temperature and wind speed error we can use Fig. 7. The colored horizontal lines in these graphs show the Error=0 line. For example the first graph in the first row shows how the temperature error changes when we predict for locations with different elevations. As can be seen in this graph with higher altitude stations our predictions have had a rather bigger minus bias whereas for some height ranges (around 350 meters) we had much lower error margins. As another example we can also notice that with higher values of Predicted Mixing Ration (PMR) the errors of both temperature and wind will be rather smaller. Higher values of PMR mean more humid prediction of the weather.
Error Analysis
The Gradient Analysis technique can help us better understand the relationships between the prediction values as the independent variables and the various error measures as the response variables. Here we use the Direct Gradient Analysis with PCA to investigate these relationships.
The first two components which explain about 45% of the whole independent variables variance are the two axes of Fig. 8 in which the blue arrows show the predicted weather variables. The red arrows are the temperature and wind speed error depicted based on their correlation with the two components. As can be seen in this figure we can generally conclude that in lower height locations we have higher (signed) values of temperature error. As could be speculated based on Fig 7. this confirms that in higher altitudes we have rather minus biases for the predicted temperature. We can detect this same relationship between the predicted temperature and the (signed) values of wind speed error. With higher values of the predicted temperature we tend to have larger minus bias for the predicted wind speed. Also with higher values of the predicted wind speed we tend to have larger minus bias in wind speed error.
In another view, we are also interested in the behavior of the model in terms of its absolute errors shown in golden arrows. Based on this analysis although we have higher signed values of temperature error in lower altitudes, the absolute value of the temperature error is smaller in these locations. This means that generally the accuracy of the model's temperature predictions is lower in higher altitude locations which also have lower value for their predicted surface pressure. In addition, based on the absolute error measure when the model predicts higher grid precipitation the forecasted value of the wind speed is more reliable.
The first two components which explain about 45% of the whole independent variables variance are the two axes of Fig. 8 in which the blue arrows show the predicted weather variables. The red arrows are the temperature and wind speed error depicted based on their correlation with the two components. As can be seen in this figure we can generally conclude that in lower height locations we have higher (signed) values of temperature error. As could be speculated based on Fig 7. this confirms that in higher altitudes we have rather minus biases for the predicted temperature. We can detect this same relationship between the predicted temperature and the (signed) values of wind speed error. With higher values of the predicted temperature we tend to have larger minus bias for the predicted wind speed. Also with higher values of the predicted wind speed we tend to have larger minus bias in wind speed error.
In another view, we are also interested in the behavior of the model in terms of its absolute errors shown in golden arrows. Based on this analysis although we have higher signed values of temperature error in lower altitudes, the absolute value of the temperature error is smaller in these locations. This means that generally the accuracy of the model's temperature predictions is lower in higher altitude locations which also have lower value for their predicted surface pressure. In addition, based on the absolute error measure when the model predicts higher grid precipitation the forecasted value of the wind speed is more reliable.
Since the second two components also explain a considerable amount of the data set's variance we also look at these components in Fig. 9. This graph also shows that with higher values of predicted wind speed we are more likely to have larger absolute errors. Also there is a relationship between the predicted wind direction and temperature absolute error. With higher values of wind direction (i.e. southerly winds) being predicted the temperature forecast is less accurate. Furthermore, these components reveal that with higher grid precipitation predicted for a location the temperature output is a bit more reliable.
