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1. How to effectively apply dual polarization variables to improve severe convection forecasting is still a key and difficult issue in current weather forecasting. Please use the data provided in the question to establish a mathematical model that can extract microphysical feature information from dual-polarization radar data for severe convection nowcasting. The input of nowcasting is the radar observations (ZH, ZDR, KDP) of the previous hour (10 frames) , and the output is the ZH forecast of the following hour (10 frames ) .
For this problem, we can consider using deep learning models, especially time series models such as LSTM or GRU, to process radar observation data sequences. The input can be radar observations (ZH, ZDR, KDP) in the past hour, and the output is the ZH forecast in the next hour. The model can be designed as a multi-layer RNN structure, with each layer learning different levels of features and finally outputting the predicted ZH value.
2. Some current data-driven algorithms tend to generate forecasts close to the mean when making strong convection forecasts, that is, there is a "Regression to the mean" problem, so the forecasts always tend to be blurry. Based on question 1, please design a mathematical model to alleviate the blurring effect of the forecast and make the predicted radar echo details more complete and realistic.
In order to alleviate the "regression to the mean" problem, you can consider introducing some regularization techniques, such as Dropout, during model training to prevent model overfitting. In addition, uncertainty estimates of model predictions can be added, such as using Bayesian neural networks. The model not only gives a predicted value, but also gives the uncertainty of this predicted value to accurately assess the reliability of the forecast .
3. Please use the Z H , Z DR and precipitation data provided in the question to design an appropriate mathematical model and use Z H and Z DR to conduct quantitative precipitation estimation. The model inputs are Z H and Z DR and the output is precipitation. (Note: The algorithm cannot use K DP variables.)
We can use a linear regression model to estimate precipitation, where the input features are ZH and ZDR. The model can be of the form:
where R is the precipitation and a, b, c are the model parameters, learned by minimizing the difference between the predicted precipitation and the actual precipitation.
4. Please design a mathematical model to evaluate the contribution of dual-polarization radar data in nowcasting of severe convective precipitation, and optimize the data fusion strategy to better deal with sudden and local severe convective weather.
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