，，，

1.College of Civil Aviation，Nanjing University of Aeronautics and Astronautics，Nanjing 211106，P.R.China；

2.Nanjing LES Information Technology Co.，Ltd，Nanjing 210014，P.R.China

Abstract:In order to improve the accuracy and stability of terminal traffic flow prediction in convective weather，a multi-input deep learning（MICL）model is proposed.On the basis of previous studies，this paper expands the set of weather characteristics affecting the traffic flow in the terminal area，including weather forecast data and Meteorological Report of Aerodrome Conditions（METAR）data.The terminal airspace is divided into smaller areas based on function and the weather severity index（WSI）characteristics extracted from weather forecast data are established to better quantify the impact of weather.MICL model preserves the advantages of the convolution neural network（CNN）and the long short-term memory（LSTM）model，and adopts two channels to input WSI and METAR information，respectively，which can fully reflect the temporal and spatial distribution characteristics of weather in the terminal area.Multi-scene experiments are designed based on the real historical data of Guangzhou Terminal Area operating in typical convective weather.The results show that the MICL model has excellent performance in mean squared error（MSE），root MSE（RMSE），mean absolute error（MAE）and other performance indicators compared with the existing machine learning models or deep learning models，such as K-nearest neighbor（KNN），support vector regression（SVR），CNN and LST M.In the forecast period ranging from 30 min to 6 h，the MICL model has the best prediction accuracy and stability.

Key words：air traffic management；traffic flow prediction；convective weather；deep learning

0 Introduction

It is well known that convective weather is one of the main causes of flight delays.It accounts for over 50%of the factors that cause flight irregularity（delays，divert，return）in China in recent years，while up to 60%of the flight delays in the United States are caused by convective weather［1］.To improve the efficiency of airspace operations and to reduce flight delays，air traffic flow management initiatives must be made dynamically taking into account airspace condition and weather uncertainty.

Given the weather forecast data，the traffic flow management（TFM）department in collaboration with the air traffic control（ATC）center and the meteorological department，will study the weather and operational condition for the following day［2］.Several traffic management initiatives，for instance，the ground delay program（GDP）and the mile-in-trail（MIT）strategy，will be prepared after dicussions［3］.During the pre-tactical phase，i.e.，2—6 h before the flight taking off，the traffic management strategies are further revised based on the updated weather information.Most likely，this step is manually implemented according to the experience of air traffic controllers（ATCOs）.If the MIT strategy was carried out based on the overestimation of weather impact，it would not only waste airspace resources but also cause delay propagation［4］.There-fore，the translation of convective weather forecasts into air traffic flow impact is very important to air traffic flow management，which requires accurate statistics and prediction of the situation of air traffic，as well as its evolution trend.

The study of quantifying convective weather impacts to airspace capacity has been well investigated in the United States for more than a decade［5］.The convective weather information，such as the echo top and the vertically integrated liquid（VIL）level，is collected to build the weather avoidance field（WAF）and route blockage concept［6-7］.And convective weather avoidance models，such as the weather severity index（WSI）and the maximum flow and minimum cut metric，are developed to calculate capacity decreases［8-13］.However，these models are obviously restricted by the airspace geometry and cannot reflect the traffic demand.

And，various techniques have been developed and applied for the air traffic flow prediction（ATFP）task.The 4-D trajectory prediction estimates the fly over time of each waypoint and is further used to predict the air traffic flow［14-16］.Terrab et al.［17］established a stochastic dynamic model that takes into account unfavorable weather conditions to predict traffic flow.Ashley et al.［18］proposed an autoregressive and average moving model to predict traffic flow.Weinreich et al.［19］established a time series forecasting flow model based on historical data.Guo et al.［20］established a grey-Markov forecast model for air traffic flow management.However，these methods cannot capture the random and complex dynamic features of traffic situation under convective weather［21］.

With successful applications of deep learningbased model on other fields，it is also introduced to solve the existing problems of aviation research［22］.The support vector machine for regression（OLSVR）and the linear regression combined with the neural network based algorithms were proposed and improved to predict the air traffic flow［23-24］.A LSTM-XGBoost model was proposed to predict the short-term airport arrival traffic flow using the Meteorological Report of Aerodrome Conditions（METAR）as input［25］.

From above discussion，we can see that existing approaches failed to consider the spatial and temporal dependencies of the traffic situation and convective weather comprehensively due to their input organization.To our limited knowledge，there is no relevant research that is proposed for the ATFP under convective weather.

This paper focuses on establishing a set of convective weather geometry features and flight statistical features，then proposes a novel deep learningbased terminal traffic flow prediction model，in which the spatial and temporal features of weather and flight are well captured by the proposed data representation.A multi-input deep learning model（MICL）is introduced to learn the complex weather impact patterns of terminal traffic system.MICL combines one-dimensional CNN（CNN-1D）and long short-term memory（LSTM），which can reduce the variance as much as possible to make the prediction more accurate.

1 Data and Features

1.1 Data preparation

1.1.1 Meteorological data

The radar basic reflectance image used in this paper is generated from the original products of 11 radar stations in Guangdong Province.The image product is drawn based on the basic reflectance of 0—70 dBZ defined by the 14-level color scale from light to dark，which more intuitively reflects the local weather information of the area.As shown in Fig.1，the original image size is 1 188 pixel×880 pixel，with the horizontal resolution of 0.01°and the update cycle is 6 min.Another source of the meteorological data is from METAR，which records the weather conditions of the airport every half an hour.

1.1.2 Flight data

The flight data are obtained from the flight data recording（FDR）which contains all the details of every flight in Guangzhou Terminal Area.The following information is used in this study.

（1）Flight ID：The flight identity in the flight management database.

（2）ICAO designator of departure and arrival airport.

（3）Terminal entry time of arrival（UTC+8）.

（4）Terminal exit time of departure（UTC+8）.

（5）Actual departure time（UTC+8）.

（6）Actual landing time（UTC+8）.

（7）Estimated departure time（UTC+8）.

（8）Estimated landing time（UTC+8）.

1.2 Feature analysis

1.2.1 Meteorological features

Although the convolution operation can extract weather features directly from the images，the number of convolution cores will increase sharply due to the huge amount of information in the original images.In order to reduce the computational complexity，we need to extract the key information in the weather pictures and convert it into quantifiable weather features.Among many indicators，WSI indicator represents the proportion of airspace affected by severe weather，which can effectively measure the impact of weather on airspace.Some research results show that when WSI exceeds 70%，it has a non-negligible impact on airspace capacity［10］.WSI is given as

whereSw xis the area covered by weather，andSrepresents the total airspace area.The value of WSI is between 0 and 1.

As severe weather covers different positions in the terminal area，such as runways，arrival routes，departure routes and handover points，it has different influences on the traffic flow［13］.Therefore，the airspace of Guangzhou terminal Area is divided into nine small airspace marked asA—H，as shown in Fig.2.HereAindicates the airspace above the runway，Bthe airspace near the runway，Cthe ATAGA/IGONO approach corridor，Dthe LMN departure corridor，Ethe IDUMA approach corridor，F(xiàn)the VIBOS departure corridor，Gthe GYA approach corridor，andHthe YIN departure corridor.Based on the direction of the traffic flow，the terminal area is further divided into the northwest arrival and departure direction，the east arrival and departure direction，and the south departure direction，marked asI，J，K.Finally，Lis used to represent the whole terminal area.The WSI features are defined as

Fig.2 General structure of the Guangzhou Terminal Area

In addition，the METAR feature is given asFMETAR={METARj|j=DIR,SPD,GUST,

wherejis the observed variable in METAR，including wind direction，wind speed，gust，wind direction change ranges，visibility，cloud，rain，thunderstorm，and cumulonimbus.

1.2.2 Flight features

Based on the actual arrival or departure time of the flight，the number of aircraft entering the terminal area within a certain time is calculated and arranged in chronological order to obtain the actualflight feature.The actual flight feature is

In addition，the flow of a day is not only affected by the weather，but also by demand at different time of the day.For example，there are fewer flights in the early morning.Adding flight plan can improve the traffic features through the number of scheduled flights，specifically，the scheduled flight feature is

Then，we have the flight features as

1.3 Data processing

The data setF t={FWSI，F(xiàn)METAR，F(xiàn)flight}used in this paper includes not only numeric data but also image data.We used flight data，quantified basic radar reflectance images and METAR，forming a mixed input forecast flow structure of multiple data information，as shown in Fig.3.

Fig.3 Framework of the deep learning model

For the image data part，since convective weather is generally the product of convective cumulonimbus clouds，it evolves with time.If there is data missing，we can fill in the convective weather picture from the previous time.Next，due to the wide area convered by the original weather picture，to accurately obtain the weather information of the terminal area，it is necessary to perform regional positioning processing and divide the terminal area according to the division rules described in the above meteorological features.Calculation is then made based on the WSI value of processed picture，which converts weather pictures into quantifiable weather metrics for follow-up research.For the numeric data part，the WSI value is originally in the range of 0—1，but features in METAR and the estimated or actual flow values are not，so they need to be normalized.Features mentioned above，including weather and flow，are normalized by

wherex'is the normalized result of datax，max(x)the maximum value of the sample data，and min(x)the minimum value of the sample data.

There are 24 features in total.This paper takes the hourly flow as the object for prediction，but the update cycle of the basic reflectivity map of the weather radar is 6 min and the update cycle of the airport METAR information is half an hour.Therefore，it is necessary to average the 10 weather snapshots and the two METAR messages within 1 h.In addition，in order to increase the sample size and continuity of the data set，the sliding time window method is used for sampling，such as 12：00—13：00，12：06—13：06，12：12—13：12...According to the above sampling principles，the final data set includes 6 880 training data generated by sliding 6 880 h in 30 d and 1 120 test data generated by sliding 1 120 h in 5 d.

2 Methodology

In this section，a deep learning（DL）model combining CNN-1D and LSTM is proposed to predict departure and arrival flow in the terminal area under convective weather.

2.1 Convolutional neur al networ k

A CNN framework generally includes a convolutional layer，a pooling layer，and a fully connected layer［22］.The purpose of convolution is to apply the convolution kernel to all points of a certain tensor and generate a filtered tensor by sliding the convolution kernel on the input tensor，that is，convolution aims to capture the spacial features［26］，as shown in Fig.4.

Fig.4 Core process of convolutional layer processing

2.2 LSTM network

The essence of LSTM is a recurrent neural network（RNN），which predicts the outcome of future events based on the features of events in the past period through a key parameter，i.e.forecast period.As Fig.5 shown，LSTM is characterized by the addition of valve nodes in each layer，including the forget gate，the input gate，and the output gate［27］.

Fig.5 Structure of a basic LSTM cell

The forget gate means that some unimportant information is forgotten in the output resultht-1at the previous moment to obtainCt-1，which is

The input gate is based on the last time andCt'obtained by the current input valuex t，so as to update the memory stateCt，which are

The output gate determines the outputht，which is

wherew f，w i，w oare the weight matrices that control the behavior of these gates，andb f，b i，b oare the bias matrices.

2.3 Multi-input deep learning model

CNN-1D has advantages in extracting internal spatial features.LSTM can play a very good role in dealing with data with sequence attributes.However，using CNN or LSTM methods alone cannot predict the traffic flow in convective weather conditions well.Therefore，we propose a mixed DL model with multiple input data sources，integrating the advantages of these two methods.The model can accurately use the weather and flow characteristics to predict traffic flow that there will be a certain period time in the future when convective weather occurs.

The first part of the model is a CNN-1D network designed to process quantitative weather data from weather images.WSI features are input through dense layer.The convolution kernel is used to extract the weather features that affect the traffic in the terminal area.The size of the convolution kernel is 1×3，and the number is 32.After being activated by the activation function Relu，the information is passed to the maxpooling layer with the windows of 2 for dimensionality reduction.The processes of convolution，activation and pooling are repeated twice to be able to extract features in depth.To prevent convolution from overfitting，we use a dropout layer with a size of 0.2 and then use a fully connected layer to connect the feature information.Finally，the dense layer outputs the feature results of the part.

The second part is LSTM，which is used to predict traffic flow of the terminal area within a period time in the form of time series.This part inputsMETAR features，actual flow data and scheduled flow data through dense layer.Then the two-layer LSTM with an output dimension of 50 is used to learn to mine the hidden information.The activation function is the same as that in the CNN part.Finally，the result is output by the Dense layer.

The two parts are connected with a simple perceptron combination，which consists of an input dense layer and an output dense layer.The Adam is selected as optimizer and the activation function is Relu.However，to ensure that the two outputs can be connected，the final output dimensions of the two parts need to remain the same.

Finally，as shown in Fig.6，MICL model with 1-hour forecast period is formed.The left side of each box represents the layer of the model，and the right side is the three-dimensional tensor of the input and output of the layer.The first dimension“None”refers to the size of the batch sample，where None indicates that samples can be of any size，the second dimension is the time steps of the model，and the third dimension is the features of the sample.

Fig.6 Structure and parameters of MICL model with 1-hour forecast period

2.4 Model performance evaluation

To evaluate the performance of the traffic prediction model，we select the following three commonly-used regression evaluation metrics：Mean squared error（MSE），root mean squared error（RMSE），and mean absolute error（MAE），whichare calculated as

whereNTis the total number of samples in the test dataset，y ithe true value of the test samplei，fthe mapping learned from the training data，andx ithe input feature vector of the test samplei.

3 Case Study in Guangzhou Terminal Airspace

3.1 Feature correlation analysis

To validate whether the model can accurately estimate the traffic flow and to gain a better understanding of the dataset，the correlation analysis of the features and the target flow is carried out.The first correlation analysis is shown in Fig.7，in which the color indicates the correlation of any two features.The number in the box is the correlation coefficient.Color represents the coefficients as well.It can be seen that the most relevant to the actual flow is the flight plan flow，and the remaining meteorological features account for 10%.If two airspace zones or routes are close in space，two metrics are highly correlated，such asAandBfor runway zones，and then a strong correlation will occur.This is to be expected because the weather is mainly systemic and usually wide in scope to affect many airspace units simultaneously.The reason why there is high correlation among RA，TS and TCUCBis that the occurrence of convective weather is often accompanied by thunderstorms and cumulonimbus clouds.The SPD and CLOUD in the METAR have nothing to do with Actflow.Therefore，these two features are removed and not used as input features.

Fig.7 Correlation coefficient heat map of features

3.2 Model accuracy

To evaluate the performance of our model，we compare our MICL model with three deep learning models including CNN-1D，LSTM and MICL model without WSI features，and two machine learning models includingK-nearest neighbors（KNN）and support vector regression（SVR）.Various forecast periods were tested，including 6 min，30 min，1 h，2 h，and 6 h.The evaluation results are presented in Table 1.Note that the target values are standardized，thus，the predictions are not integers to be inconsistent with the actual operation.Therefore，we have to convert the predicted results into integer to evaluate performance.

Table 1 Performance evaluation results of various models

Compared with machine learning models（KNN and SVR），deep learning models are far superior when we focus on regression evaluation metrics.Especially with the increase of the forecast period，the difference between the metrics of the two types of methods also gradually increases，which also verifies the superiority of the neural network in time series forecasting.

The values of MICL in MSE，RMSE and MAE are smaller than that of CNN-1D or LSTM in all forecast periods，which indicates that MICL model has the advantages of CNN model to capture spatial features and LSTM model to capture temporal features.We also conduct experiments using the MICL model without the WSI features，the prediction results are worse than results of CNN-1D，LSTM and MICL model with WSI features.That means WSI features improve the model performance obviously.

When the forecast period is 6 min，the LSTMXGBoost model has the best prediction performance，and the MICL model is the second.But when the forecast period gets longer，the prediction performance of LSTM-XGBoost is getting worse and worse.This indicates that although LSTM-XGBoost has superiority in the prediction of airport arrival flow［25］，it is relatively insensitive to the spatial domain meteorological features used in this paper，and its predictive performance is correspondingly reduced.On the contrary，the performance of the MICL model is better in all forecast periods.When the forecast period is 1 h，the MICL model gets the lowest MSE（6.49），RMSE（2.55）and MAE（1.97）of all.CNN-1D and LSTM also get their own minimum performance indicator values，but higher than those of MICL.While MICL model without WSI and LSTM-XGBoost model get their minimum performance indicator value when the forecast period is 6 min.

In order to further test the performance of the above algorithms，we select three typical weather impact scenarios，each with a duration of 1 h and covering different locations in the terminal area，as shown in Fig.8.KNN and SVR algorithms are not used in the following experiments because of their poor prediction performance.

Fig.8 Convective weather scenarios at the beginning of each period(the avoided area marked in red)

Scenario 1 started from 21：12 on June 1，2019.Convective weather covered most of GYA arrival and a small part of YIN departure and ATAGA/IGONO arrival airspace.GYA is the arrival fix with the largest arrival flow，followed by ATAGA and IGONO.YIN is also the most important departure point.Therefore，this weather condition greatly increased the difficulty of dispatching arrival and departure flights，and the airport traffic volume was significantly reduced.

Scenario 2 started from 9：00 on June 3，2019.The convective weather mainly covered the arrival airspace of ATAGA/IGONO.However，because the weather distribution was relatively scattered，there were more airspace for aircraft to avoid bad weather，so the airspace flow in this scenario did not decrease much.

Scenario 3 started from 14：24 on June 4，2019.The weather coverage extends from near the runway to the south arrival and departure direction，including GYA，VIBOS and IDUMA.This situation not only affects the traffic flow of the terminal area but also affects the take-off and landing of the airport runway.Aircraft can only hold in the air-space or return，resulting in a sharp drop in traffic flow.

By comparing the predicted flow curve with the actual flow curve，it can be found that the MICL model without WSI features model has the largest prediction deviation in all scenarios，which indicates that the WSI features play a key role in improving the prediction accuracy.The prediction accuracy of LSTM-XGBoost model in Scenario 2 is higher than that of the other two scenarios，because the convective weather in Scenario 2 has little impact on flow，indicating that the model is not suitable for the airspace environment with high uncertainty.The prediction results of CNN model and LSTM model are consistent with the actual flow trend，but the prediction accuracy is lower than MICL model.

According to the different weather coverage in scenarios 1—3 and the comparison between the predicted flow and the actual flow in Fig.9，we can find that if the airspace near the runway is covered by the weather，the flight will be unable to take off and land on the runway，which will have the greatest impact on the airport flow.If the severe weather covers the main arrival and departure routes，the greater the coverage，the more obvious the flow reduction.At the same time，the distribution of weather also affects the airspace flow.If the weather cells are loosely distributed，there is still a certain space for flight regulation and allocation，and the impact on the flow will be reduced.

Fig.9 Actual and predicted flow value compared in three scenarios

Based on the above analysis，the MICL model has good prediction accuracy and stability under dif-ferent weather scenarios.

4 Conclusions

For the research of terminal traffic flow prediction under convective weather，we apply a deep learning model called MICL in this paper.The proposed model is a deep neural network model，combined with CNN-1D and LSTM，which were proved to be effective for modeling spatial and temporal dependencies of air traffic.The MICL module not only preserves the advantages of the LSTM block on sequence modeling but is also very suitable for processing spatiotemporal data due to its inherent convolutional structure.By analyzing spatial characteristics of convective weather in terminal area，we establish a set of meteorological features such as WSIs，which represent the severe weather coverage ratio of runway adjacent airspace，arrival and departure routes，etc.By removing these meteorological features from MICL model，we have shown that these features are very effective in improving model performance because they contain rich information about meteorological location and intensity.Our experiments show that deep learning models are generally superior to machine learning models in terminal traffic flow prediction，and MICL model is proved to have the best accuracy and robustness by our designed experiments on real weather forecast data and flight data.

This paper provides an effective method for traffic controllers to predict the future traffic situation in convective weather.However，due to the uncertainty of the weather，all weather scenarios could not be enumerated.Therefore，how to cluster convective weather，extract important features，and provide auxiliary decision support for traffic management department under severe weather is one of the future research directions.

AcknowledgementThis work was supported by the Civil Aviation Safety Capacity Building Project.

AuthorDr.PENG Ying received the B.S.degree in air traffic management and dispatch from Nanjing University of Aeronautics and Astronautics（NUAA）in 2003 and the Ph.D.degree in air traffic management and dispatch from NUAA in 2014.She joined the College of Civil Aviation，NUAA in 2003.She is currently the director of the Airspace and Flow Collaborative Research Office of the National Air Traffic Control Flight Flow Management Technology Key Laboratory.Her research is focused on airspace capacity assessment and relevant fields.

Author contr ibutionsDr.PENG Ying designed the study，complied the models，conducted the analysis，interpreted the results and wrote the manuscript.Miss WANG Hong contributed to data processing and feature extraction of the model.Mr.MAO Limin concluded the research background.Miss WANG Peng contributed to figures and tables.All authors commented on the manuscript draft and approved the submission.

Competing interestsThe authors declare no competing interests.