Sudden precipitations may bring troubles or even huge harm to people's daily lives. Hence a timely and accurate precipitation nowcasting is expected to be an indispensable part of our modern life. Traditionally, the rainfall intensity estimation from weather radar is based on the relationship between radar reflectivity factor (Z) and rainfall rate (R), which is typically estimated by location-dependent experiential formula and arguably uncertain. Therefore, in this paper, we propose a deep learning-based method to model the ZR relation. To evaluate, we conducted our experiment with the Shenzhen precipitation dataset. We proposed a combined method of deep learning and the ZR relationship, and compared it with a traditional ZR equation, a ZR equation with its parameters estimated by the least square method, and a pure deep learning model. The experimental results show that our combined model performs much better than the equation-based ZR formula and has the similar performance with a pure deep learning nowcasting model, both for all level precipitation and heavy ones only.

Nowcasting has always played an important role in the field of weather forecast. Whilst it also works in predicting phenomenons such as lightning [

The relationship between radar reflectivity (Z) and precipitation (R) also plays an important role in predicting precipitation in the literature. Many experiments directly used the ZR formula (Z = ^{b}) derived from the data to predict rainfall rates according to the Z values [^{1.6} where Z is in mm^{6}/m^{3} and R is in mm/h) which links radar reflectivity and precipitation rate. Although the formula was intensively used, it comes with arguably uncertainty, as the values of the parameters are usually estimated through an empirical approach, based on the comparison of radar and rain gauge. People argue that an improper selection of the parameters (for instance the conventional setting

There were quite a few efforts proposed to improve the ZR relation, for instance, [

To this end, in this paper, we propose a deep learning-based method to model the ZR relation. That is, we incorporate the estimation of the parameters of the ZR relationship into a deep learning model. By having such a model, we do not need to introduce additional features like in [

The rest of the paper is organized as follows. Section 2 introduces the dataset, followed by Section 3 that provides the example design details. In Section 4, we discuss and evaluate our model performance. Finally, Section 5 concludes the paper.

We used a dataset containing real radar images and precipitation rate at the target sites, which were collected by the Meteorological Observation Center of Shenzhen.

The characteristics of a typical sample of the dataset is as follows:

Each radar image contains a target site (located in the center of the image);

Each radar image contains the total amount of precipitation at the target site for the time interval of the next 1 to 2 h. Here we should note that it does not provide the amount of precipitation for the next hour;

In each sample, there are four groups of images, each of which contains 15 radar images of a successive time period. Each two adjacent images come with an interval of 6 min. Each group of radar images were measured at the same area but at a different height, with an interval of 1 km, ranging from a distance of 0.5 to 3.5 km;

According to the latitude and longitude of the target location, each radar image covers an area of 101 × 101 square kilometers. The area is marked as 101 × 101 grids (with the starting index as 0 for each coordinate), and the target position is in the center, that is, with a coordinate (50, 50).

Since each sample contains radar echo maps of 4 heights and covers 15 time points, it has a dimension (15, 4, 101, 101).

The following

In the dataset, there are 5000 training samples and 3000 testing samples, with around 18% heavy precipitation samples (>30 mm/h), as shown in

Size | Precipitation (mm/h) | Proportion (%) | |
---|---|---|---|

Training | 81.46 | ||

18.54 | |||

Test | 82.77 | ||

17.23 |

In our experiments, we chose the radar echo data at the fourth altitude (3.5 km) for training due to its higher prediction accuracy at this altitude. In our experiments concerning deep learning, the general idea is to use CNN to extract features from the radar images, and then use the Transformer blocks to process the features in a temporal order.

In summary, here we present four experiments to model the relation between the radar reflectivity factor (Z) and rainfall rate (R):

Case 1: We used the direct ZR formula Z = ^{b}

Case 2: We fitted the ZR relation into a deep learning model, so as to combine human knowledge and deep learning algorithms. The model hence relies on the existing mathematical equation to shape the deep learning model to reduce the potential overfitting problem.

Case 3: To compare, here we also proposed a pure deep learning model to predict the precipitation amount. We used a model that contains CNN, Transformer, and fully connected neural network blocks.

As mentioned above, we have used two parameter settings for

With the dataset setting, we then transformed the pixel values into the dbz values as follows:

The dbz values were converted into Z values by the equation:

Finally, we took the average Z-values of the central 15*15 region to be used in the ZR formula, i.e.,

With the Z values and the corresponding R values, we use the least square method to train the parameters, and get

In this model, we fit the ZR relation into a deep learning model that contains CNN, LSTM, and fully connected neural network blocks, as indicated by

Note that the equation Z = a*R^{b} can be converted into:

We replace 1/b and z/a in the above figure with b2 and a2 respectively, and we get:

With

The model structure of the CNN block used to extract feature maps is illustrated in the following two figures (

In the CNN block, six convolution layers of the same structure are used (as shown in yellow in

To compare, in this subsection, we propose a pure deep learning model to predict the precipitations. In this model, we use the transformer network to replace the working part of LSTM. The transformer block has no recursion and convolution, and its ability to process time series is entirely due to its attention mechanism. It has been shown in [

In our experiment, we made a few changes to the transformer block in [

The model structure is illustrated by the following

In this section, we evaluate the effectiveness of the ZR relation based models and the pure deep learning model on precipitation prediction. The RMSE losses of the models on test sets are presented in

Model | RMSE |
---|---|

CNN + LSTM + FC + ZR | |

CNN + Transformer + FC |

It can be found that the pure deep learning model performs the best, while the deep learning + ZR combined model gives an RMSE 18.01 which is very close to the best result (17.47), and is much better than those of the traditional ZR relationship

The same phenomena also appear in

Model | RMSE |
---|---|

42 | |

38.3 | |

CNN + Transformer + FC | |

CNN + LSTM + FC + ZR |

As an illustration, here we present how these four models behave on the samples.

From the visualized rainfall rate histogram, we can clearly see that the accuracy of the deep learning model is higher than the equation-based ZR relationships, which suggests the equation-based ZR relationship might be too simple to model real precipitation, while the deep learning model can learn more features, so the performance is better than the ZR relationship. The combination of the two also performs well and improves the accuracy over the equation-based ZR model. We should also notice that for some very concentrated heavy rainfalls, for instance the ones around the 100^{th} sample, are hardly predicted. This may imply that there should be special improvements needed for those concentrated heavy rainfalls.

Overall, our result suggests that a combination of deep learning and the traditional ZR relationship can perform similar accurate results to a pure deep learning model whilst in the meantime inherit part of the explainability of the ZR relationship, and hence could be a suitable choice for meteorologists.

In this paper, we studied how to model the ZR relationship with the help of deep learning methods. We compared a traditional ZR equation, a ZR equation with its parameters estimated by the least square model, a combined deep learning and ZR relation model, and a pure deep learning model with a meteorological dataset from Shenzhen, and found that the combined model had a similar performance to the pure deep learning model, and both models performed much better than the equation-based models. The same conclusion also holds if we focus on heavy precipitations only.

As a future work, we will try to introduce more methods to cope with the ZR relation, such as the rough set model [

We would like to thank Prof. Xi Wu and Ms. Yanfei Xiang for their great support and helpful suggestions to the paper.