Precipitation Nowcasting with Weather Radar Images and Deep Learning in S ã o Paulo, Brasil

: Precipitation nowcasting can predict and alert for any possibility of abrupt weather changes which may cause both human and material risks. Most of the conventional nowcasting methods extrapolate weather radar echoes, but precipitation nowcasting is still a challenge, mainly due to rapid changes in meteorological systems and time required for numerical simulations. Recently video prediction deep learning (VPDL) algorithms have been applied in precipitation nowcasting. In this study, we use the VPDL PredRNN ++ and sequences of radar reﬂectivity images to predict the future sequence of reﬂectivity images for up to 1-h lead time for S ã o Paulo, Brazil. We also verify the feasibility for the continuous use of the VPDL model, providing the meteorologist with trends and forecasts in precipitation edges regardless of the weather event occurring. The results obtained conﬁrm the potential of the VPDL model as an additional tool to assist nowcasting. Even though meteorological systems that trigger natural disasters vary by location, a general solution can contribute as a tool to assist decision-makers and consequently issue e ﬃ cient alerts. agreed to the


Introduction
The occurrence of severe weather events, such as storms, tornadoes, lightning, strong winds, can cause damage to human lives and social, economic and environmental assets of communities and countries [1][2][3]. According to Golnaraghi et al. [1], between 1970 and 2012, floods, mass movement, and storms accounted for 85% of disasters linked to weather, climate and water extremes, responsible for more than 1 million deaths and caused an economic loss of about USD 2 billion across the globe. Moreover, floods are expected to be more complex and affect more people with temperature rise due to climate change [4,5].
In addition to people in situations vulnerable to severe weather phenomena, floods also affect decision-makers in disaster management, energy, agriculture and aviation agencies, which are responsible for safety and administration. The possibility of obtaining accurate hazardous weather warnings at least one hour in advance could help in the planning and mobilization of the responsible agencies and may contribute to reducing losses, mitigating damage and saving lives.
Precipitation nowcasting tools have been used to forecast severe weather events. Briefly, this comprises a detailed description of the current weather to make predictions for a small range (meters to few kilometers) and for a short period of time (0 to 6 h) [6]. In general, severe storms are localized, with a small spatial area and a short duration (life cycle). One type of precipitation Tran, and Song [31], following the suggestions of Klein et al. [32] and Mathieu et al. [33], adapted the TrajGRU model using image quality assessment metrics as the loss function for the same problem of precipitation nowcasting, in order to reduce the blurry image issue.
Franch et al. [25] presented a method to improve the nowcasting skills of VPDL models, in particular for extreme rain rates, by combining orographic features with a model ensemble. They used the TrajGRU algorithm as a baseline model to build the ensembles, where the ensemble members have different rain thresholds as input. The proposed method doubled the forecasting skill of the VPDL model in extreme precipitations.
Purely VPDL models are subject to the same restriction as any model using just mathematical extrapolation of images. Both lack the physics and dynamics behind cloud formation and dissipation that would differentiate the application of video prediction for nowcasting problems from common video prediction problems, such as the movement of digits [34]. Nevertheless, we expect the VPDL to learn the effect of the topography and dynamics of the cloud life cycle from a series of reflectivity images.
In this study, we evaluate the applicability of a VPDL model as a tool to support nowcasting. We also evaluate the feasibility of the continuous use of the VPDL model, providing the meteorologist with trends and forecasts in precipitation edges regardless of the weather event occurring. We predict reflectivity images and precipitation edges from weather radar images for up to 1-h lead time using the PredRNN++ model [35] as a VPDL model and radar reflectivity at only one level of measurement (0.5 • Plan Position Indicator-PPI) as a single input. The PredRNN++ model is compared to the conventional precipitation nowcasting model, Ensemble NowCASTing (ENCAST), which is the model operationally used by the Hydraulic Technology Center Foundation (FCTH, Portuguese acronym), in three case studies. We evaluate the model's performance and propose a number of improvements. Even though meteorological systems that trigger natural disasters vary by location, a general solution can contribute as a tool to assist decision-makers and consequently issue efficient alerts. This paper is organized as follows. The next section presents the datasets used in this work and briefly discusses the models. Section 3 presents the experimental setup and evaluation measures. Section 4 presents results and discussion, and Section 5 the conclusions of the work.

Dataset
This study uses a dual-polarization S-band (SPOL) Doppler weather radar from the Department of Water and Electric Energy, DAEE (Portuguese acronym), manufacture Selex ES GmbH, installed at Ponta Nova [36], State of São Paulo, Brazil, at latitude 23 • 36 S, longitude 45 • 58 20" W ( Figure 1a). The radar is operated by the Hydraulic Technology Center Foundation, FCTH (Portuguese acronym) and it is configured to cover a distance of 240 km with 250 m gate resolution (gate or bins are discrete illuminated volume that are sampled by pulsed weather radars). It makes measurements at eight elevation angles and completes a volume scan every 5 min. As a note, one sweep represents a Plan Position Indicator (PPI). At each sweep the radar beam rises in the atmosphere as it moves away from the radar due to Earth curvature and variation of the refractive index in the atmosphere, for example, the beam at an elevation angle of 0.5 • rises to approximately 1 km about 100 km far from the radar [37].
In this study, we have used a total of 254,270 PPIs of the radar reflectivity factor. These radar measurements represent sweeps at 0.5 o of elevation restricted to 100 km of range (Figure 1b) for the period of March 2015 to December 2019 with a time interval of 5 min. Each PPI has been quality controlled to avoid ground clutter and anomalous propagations by means of the coincident polarimetric measurements of this radar [38]. Based on these data, the following pre-processing steps were performed:

1.
Transformation from polar to Cartesian coordinates: with the objective of obtaining images on a regular grid, with a horizontal grid resolution of 4 km per pixel (the matrix had 40 × 40 pixels). Thus, each new image represents a matrix of Cartesian coordinates with 4 × 4 km 2 resolution;

2.
Defining the boundaries: To utilize a regular square grid and eliminate the area without data as measured by radar, the images were cut into a square inscribed in a circle of 100 km ( Figure 1); 3.
Normalization of the reflectivity values: Reflectivity values range typically from 0 to 60 dBZ.
To obtain values of reflectivity in the interval (0,1), the data were divided by 60. Pre-processed dataset used in this study is available at https://doi.org/10.7910/DVN/ZADDNQ.

ENCAST
Ensemble NowCASTing (ENCAST) [16] is the nowcasting algorithm available at SELEX weather radar and it is used operationally by SPOL-FCTH radar. The model identifies, tracks, and extrapolates rain cells by using the differences between pairs of consecutive derived images from the weather radar. The tracking algorithm is based on the cross-correlation procedure that derives one movement vector for each area of precipitation analyzed and performs cross-correlation over this area. Moreover, ENCAST converts pseudo radar reflectivity factor CAPPIs (Constant Altitude PPI, a horizontal cross-section of PPIs obtained from radar scans at different elevation angles) to the rainfall rate by using a fixed Z-R relation Z = 300R 1.4 and uses it to represent the closest surface rainfall as the image input. It uses a rain threshold in cell identification. Based on the cell's position in the present and previous scans a forecast is computed for a user-defined time interval.
For this study, FCTH provided the ENCAST outputs with 500-m × 500-m resolution. For each output, ENCAST forecast 7 time steps, ranging from 0 to 60 min lead time. Later, the rain fields were downscaled to a pixel of 4 km × 4 km.

PredRNN++
PredRNN++ is the model proposed by Wang et al. (2018) [35,39] as an improvement of PredRNN [28]. To increase the temporal and spatial long-term memory, the model utilizes two structures: "causal LSTM", to capture complex dependencies and variations, and "gradient highway unit" (GHU), to keep the gradients during training. The Causal LSTM adopts a cascaded mechanism [40,41], where spatial memory is a function of temporal memory. Inspired by LSTM [42,43], GHU facilitates the training of deep neural networks. It uses adaptive units to regulate information flow inside the model, preventing the gradient backpropagated from quickly vanishing [35,43]. Figure 2 illustrates the PredRNN++ information flow. Where t denotes time step, k denotes kth hidden layer in the stacked model, M k t is the spatial memory, C k t is the temporal memory, H k t is the final output (determined by the dual memory states) and Z t is the hidden state, provided by "gradient highway unit" (GHU). Source: adapted from Wang et al. [35].
The PredRNN++ model predicts 10 future frames (target) given 10 previous inputs, so each register is a sequence of 20 images. The input was organized in such a way that, between one record and the next, there is one time-step forward in the dataset.
The model architecture and the hyperparameters established by the authors were maintained [35,39]: 4 layers of causal LSTM with 128, 64, 64, 64 units in each layer, respectively, one gradient highway layer with 128 units, convolution filter of size 5. The loss function was used with ADAM optimization algorithm with a starting learning rate of 10 −3 , and a batch size of 8 records, also organized in sequence.
To train and test the PredRNN++ model, we considered the entire dataset, which means that we did not separate the days with and without reflectivity. Further, we considered all the reflectivity range, from 0 to 60 dBZ, but we scaled the data into the (0,1) interval. The period of data used for training includes the complete years of 2016, 2017 and 2019; the data from March 2015 to December 2015 were used as validation sets; the data from the complete year of 2018 were used as a blind test set. The time step used between images was 15 min instead of 5 min so that the training set comprises around 51,800 images, the validation set 15,800 images, and the test set 19,900 images.
The VPDL model was run on the Santos Dumont supercomputer, installed in the National Laboratory for Scientific Computing, LNCC (Portuguese acronym). The hardware used was two NVIDIA Tesla V100-16 GB with NVLink and 384 Gb of RAM.
The model was trained for 20 epochs and validated every 1 epoch (51,800 iterations). Each output comprises 10 time steps, ranging from 15 min to 150 min lead time. It should be mentioned that the training of the model is time-consuming (about 12 h/epoch) and requires computational resources to speed up the training (such as GPU) in addition to RAM and storage capacity. However, once the model is trained, the execution of the test set is fast (about 3 s/iteration).

Experimental Setup
To evaluate the performance of the PredRNN++ model, we calculate standard categorical statistics, enumerated below, for the test set (the year of 2018), between the results of the VPDL model and the observed reflectivity images and between the results of the ENCAST precipitation nowcasting model and the observed reflectivity images.
Different precipitation nowcasting systems cannot be compared if they are designed for different purposes [10]. However, ENCAST works with both convective and stratiform precipitation [16] and PredRNN++ is also expected to work with both types of precipitation.
It is worth mentioning that although the radar reflectivity images have been quality controlled, we observed random noise that could be attributed to anomalous propagation, especially over the metropolitan area of São Paulo, which changes the refractivity index. As an approximation, based on the Z-R relation Z = 300R 1.4 , to avoid such spurious contamination, we considered that pixels above the threshold of 20 dBZ represent rainy pixels in the radar images, which is equivalent to approximately 0.5 mm/h. This threshold will also be compared with the ENCAST precipitation forecast.
As ENCAST predicts precipitation rate and PredRNN++ predicts radar reflectivity, we used binary metrics to evaluate the results of the VPDL model against the ENCAST results. We converted the values of the pixels into a 0/1 (e.g., no/yes) matrix using a dBZ threshold (defined below) for the observed and predicted fields of the VPDL model, and a mm/h threshold for the ENCAST forecast, where values lower than or equal these thresholds were converted to 0, and values greater than the thresholds were set to 1. As shown in the results section, some analyses of the reflectivity dataset and preliminary analysis of the results of the VPDL model reinforced the choice to evaluate the results in binary form.
We calculated the verification statistics up to 1-h lead time, using pairs of forecast and observation for second subsets and three rain cases (listed below). Pixel by pixel, the forecast hits and misses for each case or subset were accumulated in confusion matrix (Table 1), and then we calculate the statistics. The subsets are the complete test set (the year of 2018), named "All", and the summer season set, from January to March of 2018), called "Summer". The dates of the three rain cases are: 31 July 2018, 05 December 2018 and 22 December 2018.
The following are the forecast and observation pairs of the thresholds used to evaluate the model's performance: • 1 dBZ for reflectivity predicted and observed; • 10 dBZ for reflectivity predicted and 20 dBZ for reflectivity observed (the choice of the predicted threshold is explained in the results section). These values are compared with the ENCAST forecast; • 1 mm/h for precipitation predicted from ENCAST, and 20 dBZ for reflectivity observed.
In the analyses of the results, we refer to pixels with and without reflectivity as wet and dry pixels, respectively. In Table 1, a positive event corresponds to a wet pixel (reflectivity greater than the threshold) and a negative event corresponds to a dry pixel (reflectivity lower than or equal to the threshold). where: TP: corresponds to the number of observed positive events (yes) that were correctly predicted; FP: corresponds to the number of observed negative events (no) that were predicted incorrectly; FN: corresponds to the number of observed positive events that were not predicted; TN: corresponds to the number of observed negative events that were correctly predicted as negative.
Based on the confusion matrix, six standard categorical statistics were calculated: 1.
The Probability Of Detection (POD) or Recall: the fraction of observed positive events that were correctly predicted. The range of possible values is 0 to 1, where the best possible POD is 1 and the worst is 0. 2.
The False Alarm Rate (FAR): the fraction of predicted positive events that did not occur. The range of possible values is 0 to 1, where the best possible FAR is 0 and the worst is 1. 3.
The Probability Of False Detection (POFD) or the probability of false alarm: the fraction of observed negative events that were incorrectly predicted as positive. The range of possible values is 0 to 1, where the best possible POFD is 0 and the worst is 1.
4. The Bias score: the ratio between the number of predicted positive events and the number of observed positive events. This indicates how many times the number of predicted positive events exceeds the number of observed positive events [44]. BIAS = 1 indicates unbiased forecast, BIAS > 1 overforecast and BIAS < 1 underforecast.

5.
The Critical Success Index (CSI), also known as the Threat Score: the ratio of correctly predicted observed positive events by the total number of positive events, predicted or needed. The CSI is an alternative to the POD when the positive event occurs substantially less than the negative event [44]. The CSI depends on the number of TNs compared to the total number of cases [45]. The range of possible values is 0 to 1, where the best possible CSI is 1 and the worst is 0. where: 6. The Equitable Threat Score (ETS) or the Gilbert Threat Score: this is a skill score based on the CSI [44,45]. The ETS quantifies the improvement of the forecast compared to a random forecast. The range of possible values is −1/3 to 1, where the best possible ETS is 1 and 0 indicates no skill.
Different from the CSI, the ETS depends directly on the TN due to the R. The frequency of observed positive events ((TP + FN)/Total) determines how close the ETS and CSI are; so, as the positive event becomes rarer, the ETS gets closer to the CSI [45].
The CSI and ETS are generally used in the assessment of quantitative precipitation forecasting [46][47][48]. A subjective analysis of the images must be made in order to visually certify the quality of the results.

Results and Discussion
The training and test sets of PredRNN++ include both dry (without rain) and wet days (with rain). When considering wet days, all types of weather events (e.g., rain, hail) are included in the dataset and can occur anywhere in the image. We did not discriminate isolated storms from storms caused by frontal systems, for example. However, it is evident that all storms do not behave in the same way [16], and the formation of storms can be associated with diverse characteristics, such as development speed, variable intensity, atmospheric and terrain forcing (e.g., surface and ocean), and association with other weather systems.  Figures 3 and 4, we observed that in general the PredRNN++ model smoothed the predicted reflectivity values; this was another reason why we chose to evaluate the results in binary form, by analyzing the occurrence and non-occurrence of reflectivity above the defined thresholds. We associate the model smoothing to a forecast error, instead of systematic bias, as shown in the scatter plot in Figure 5.

Evaluation of the Models
First, the performance of the PredRNN++ model was evaluated against the reflectivity image (ground truth) by calculating the following verification statistics: False Alarm Rate (FAR), Probability Of Detection (POD), Probability Of False Detection (POFD), BIAS, Critical Success Index (CSI), Equitable Threat Score (ETS). From Figure 6, we can quickly visualize the expected degradation of the forecast with increasing prediction period up to 150 min lead time. Table 2 shows these statistical values for the subsets "All" and "Summer" for 15, 30, 45 and 60-min lead times. Table 2 considers the 1 dBZ threshold for both observed and predicted reflectivity.    The 15-min lead time, the first output, has the best statistics. In general (in the "All" subset) the model overforecasts by 1.6 times the number of predicted positive events (BIAS); 90% of the observed positive events were correctly predicted (POD); 45% of the predicted positive events did not occur (FAR); and 10% of the observed negative events were predicted as positive (POFD). The frequency of observed positive events was 12% of the total, and the CSI and ETS were 0.52 and 0.46, respectively. As observed in Figure 6, as time increases, the forecast skills decrease. The statistics for 60-min lead time are: BIAS of 2.09, POD of 79%, FAR of 62%, POFD of 17%, CSI of 0.35, and ETS of 0.27.
"All" considered all dry and wet weather events in a whole year. By including dry days in statistical computations, the number of TNs increased, and the number of TPs decreased. The presence of other echoes (ground clutter for example) throughout the dataset also had an influence as this can increase the number of FPs. As a note, the return from particulates in the atmosphere is usually very similar to the return from raindrops or cloud particles; the concentration and size of these particles can be enough to give a radar detectable echo [44]. In the summer, the percentage of wet days is expected to be greater than when considering an entire year. This difference can be seen in Table 2 when comparing "All" and "Summer". The frequency of observed positive events increased to 15% of the total.
"Summer" compared with "All" has a lower FAR (43% for 15-min, and 59% for 60-min lead time); and the number of correctly predicted positive events (POD) was also higher (91% for 15-min, and 81% for 60-min prediction). However, the number of events incorrectly predicted as positive increased to 12% for 15-min, and 21% for 60-min prediction. The BIAS, CSI and ETS showed similar values.

Case Studies
In this subsection, the results of the PredRNN++ model were compared with the precipitation nowcasting model ENCAST for three rain cases. As stated earlier, these cases were collected within the test set (the year of 2018). The cases were selected from the significant cases of the monthly bulletin published by the Center for Weather Forecasting and Climate Studies, part of the National Institute for Space Research (CPTEC/INPE, Portuguese acronym) [49]. The first case occurred on 31 July 2018, when a frontal system passed over São Paulo. The second case occurred on 5 December 2018, where the displacement of a frontal system by the ocean, associated with convection in the interior of the continent formed a moisture channel that extended over the state of São Paulo, among other regions, causing deep convection. The third case occurred on 22 December 2018, in which the passage of a frontal system, associated with high-level circulation, caused deep convection over São Paulo, among other regions. In the latter case, in addition to hail, a record number of trees were reported to have been blown down.
As stated earlier, the ENCAST model predicts precipitation and the output of the PredRNN++ model is reflectivity. To calculate the verification statistics, the outputs of the two models were compared to the observed reflectivity fields at the threshold of 20 dBZ. Additionally, from an analysis presented earlier, the PredRNN++ model smoothed the predicted reflectivity values. By evaluating the number of pixels per reflectivity range (as shown in Figure 7), we noted that the number of pixels above 10 dBZ in the predicted images is comparable to the number of pixels above 20 dBZ in the observed images. Thus, we established the threshold of 10 dBZ for predicted values and compared them to the observed values above 20 dBZ, in order to evaluate precipitation edges. Figures 3 and 4 illustrate examples of the cases of 31 July 2018 and 22 December 2018, respectively. We can observe the thresholds in the color bar. The arrows mark the delays between the observed (red) and predicted (blue) number of pixel peaks. The vertical red dashed lines mark the observed and predicted "rain start".
The statistics of the cases are presented in Table 3 and are organized into three blocks according to the reflectivity thresholds used in the observed (obs) and predicted (pre) data for 15, 30, 45 and 60-min lead times: Block 1 does not alter the thresholds used as input and output of the DL model, as presented in Table 2 (pre > 1 dBZ and obs > 1 dBZ); Block 2 is used to assess whether the model can generate precipitation pixels (pre > 10 dBZ and obs > 20 dBZ); Block 3 represents the statistics for comparison with Block 2, calculated on the ENCAST model (ENCAST > 1 mm/h and obs > 20 dBZ). The verification metrics are the same as shown in Table 2. Table 3. Binary statistics of PredRNN++ model (for 15, 30, 45 and 60-min prediction times) and ENCAST nowcasting model (for 10, 20, 30, 40, 50, 60-min prediction times) applied to selected cases: 31 July 2018, 05 December 2018 and 22 December 2018. The graphics and metrics are similar to those presented in Figure 5 and We highlight that two different variables, reflectivity and rain, were compared in Block 3. So, as shown before, we evaluated image patterns instead of numerical values. In these analyses, it is necessary to remember that not all echoes above 20 dBZ observed on the radar are equivalent to rain as predicted by ENCAST. The ENCAST model takes different radar fields when calculating precipitation.
In all cases, we can note the degradation of the forecast with an increasing prediction period, but in Block 3 this degradation is very subtle. Between Blocks 1 and 2, the degradation of certain statistics is noted, which can be explained by the decrease in the number of positive events predicted and observed (TP, FP and FN) and, consequently, the increase in TN due to the thresholds used in Block 2.
The observed variation between the cases in each Block is explained by the nature of the rainfall, which is different in each case. Figure 7a,c,e shows the time series of the number of pixels per image for 30-min lead time. We can observe the variations in the number of peaks and the number of pixels for each case, in the y-axis scale. In quantitative terms, ENCAST has fewer wet pixels compared with the other fields presented; this also has a negative effect on the calculation of verification statistics, as will be discussed below. Figure 7a,c,e also shows different delays between the time of occurrence and the forecast of the number of pixel peaks forecasted (shown by arrows); lags between the increase in the number of observed wet pixels, which can be seen as the start of the rain, and the increase in predicted wet pixels (vertical red dashed lines). Figure 7b,d,f specifically shows the time lag of TP events up to 60 min forecast for each case study. We can note that for the 30-min prediction, the lag is around 15 min, and for the 1-h prediction, between 15 and 30 min. We can also note the degradation of the results with an increasing prediction period.
Comparing the statistics obtained in Blocks 2 and 3 in Table 3, we note that within each Block the difference between cases is presented differently by the two models. Despite the thresholds used in Block 2, which reduced the observed and predicted positive areas, Block 2 performed better than ENCAST (Block 3). The fact that the verification statistics were calculated on small positive areas penalized the evaluation of the models. Although the pattern is similar between the images, if the centers are displaced and do not overlap, the forecast is given as wrong in the pixel by pixel confusion matrix [50]. Therefore, even though the number of hits (TP) was small in both models, TP of the PredRNN++ model was slightly higher than ENCAST, which improved its statistics when compared with ENCAST. The examples presented in the Figures 3 and 4 show the aspect of the lack of overlap in the positive areas predicted and observed, and also that the PredRNN++ model predicts a larger positive area compared with ENCAST. This can masquerade pixel by pixel statistics.

Conclusions
In this study, we evaluate the usability of a video prediction deep learning (VPDL) model to support nowcasting. We use the PredRNN++ model as a VPDL model to predict reflectivity images and precipitation edges from weather radar images for up to 1-h lead time and compare the results with an extrapolation-based model used for precipitation nowcasting, ENCAST. We also evaluate the feasibility of a VPDL model for continuous use in nowcasting, as this gives the meteorologist an indication or a trend of the occurrence of localized precipitation regardless of the type of weather event.
We evaluate the model results against the ground truth images in two subsets and compare the VPDL model statistics with ENCAST statistics in three case studies: the entire test set ("All", the entire year of 2018), the summer season set ("Summer"), and the days 31 July 2018, 5 December 2018, and 22 December 2018, as the case studies, respectively. By using pixel by pixel confusion matrix for the architecture used in the VPDL model, we find that: the VPDL model overforecasts the prediction of wet pixels; "Summer" (more homogeneous dataset) shows a better performance than "All"; and the VPDL model outperforms the ENCAST model in the three analyzed cases. We highlight that we only had access to three cases of ENCAST and to compute the ENCAST statistics we used the binary field of precipitation as prediction and the binary field of reflectivity greater than 20 dBZ as observation.
The forecast for precipitation is an important aspect of nowcasting. However, due to model architecture, the results are smoothed, which affects the analysis of predicted reflectivity instead of the analysis of pixels with rain and no rain. As a tool to assist nowcasting, this model should be used in parallel with other data and models. In fact, the model provides trends in the localization and development of rain edges of systems that can cause damage. We recommend that caution be taken in analyzing the range of predicted values since this can lead to a tendentious prediction of a strong system.
In general, the results obtained here agree with the most recent results published on the potential of the use of a VPDL model as an additional tool to assist nowcasting. We highlight certain advantages such as rapid execution (after training), 3 s/iteration, the use of a single input with little pre-processing, but a long history for training is necessary.
From other studies, we assume that training the model with events of the same type can improve the model's performance. However, another aim of the present study is to assess the viability of a continuous execution of the VPDL model in predicting reflectivity edges regardless of the meteorological phenomena. In this respect, the model shows some lags between the "rain start" in observed images and predicted images. We assume that the addition of other variables that give an indication of the state of the atmosphere before the sudden appearance of targets in the radar image adds extra information to the model training and improves the quality of the forecast in terms of the life cycle of the weather event and even the prediction of the event.
As expected, an issue that arises in not considering physical processes is that extrapolation models are conservative: the model considers that an element will remain in the image and may only change its position (rotation and translation). Taking a cloud as an example of an image element, these models cannot predict dissipation due to rain, or the formation of a new cloud where there was nothing before. This is observed in mathematical extrapolation models as well as VPDL models. Deep learning models can fit observations very well, but only by integrating knowledge of the physical processes to train and provide constraints can the model achieve physical consistency [26].
With the addition of topography information, the model will be able to distinguish the formation of clouds by an orographic barrier, for example. It is worth mentioning that the addition of more variables to the VPDL model increases the model's complexity, storage, processing time, among other limiting factors.
The next steps in this study, which are currently being developed, also include the evaluation of possible improvements in the architecture of the VPDL model and the running of other VPDL models.
Even though meteorological systems that trigger natural disasters vary by location, a general solution can contribute as a tool to assist decision-makers and consequently issue efficient alerts.