The Conditionality of Outdoor Sports Events on Weather-Induced Impacts and Possible Solution

Abstract

All over the globe, outdoor sports events are highly affected by weather conditions that frequently influence the comfort of the players and sports fans, the duration, or even the cancelation of the event. To verify the range of weather-induced impacts on selected Major League Baseball events, this interdisciplinary study investigated the causes of unexpected postponements of several Major League Baseball games in March and April 2018, according to official weather reports in the event host destinations. The impact was measured by a recurrent neural network with long short-term memory as an investigation model. Autocorrelation analysis was conducted between all input and target fields. The research focused on the explanation of the influence of weather risks on the event host destinations. Moreover, the study is based on projecting an effective instrument for managing weather risks and then evaluating the tourism services that the future climatic conditions will support. The long short-term memory analysis revealed that solar activity had the greatest influence on the temperature. On the other hand, humidity and air pressure depended very little on solar activity; this finding was confirmed by the zero values of the sensitivity. These values encourage further research on weather disturbances and their connections with outdoor sports and tourism activities.

Keywords

sports event MLB games natural hazards weather risk recurrent neural network

Introduction

The travel industry is an extremely climate-sensitive economic sector. Climate affects the appropriateness of destinations for a broad range of activities and could significantly influence the estimation of visitors’ flows and the organization of outdoor events of any kind. It should be highlighted that the nature and the force of climate fluctuation impacts differ among destinations worldwide. Nonnatural hazards (e.g., terrorism, sports fans’ fights, etc.) and natural ones (e.g., volcanos, earthquakes, and especially extreme weather conditions) have an enormous impact on international sports tourism and visitors’ decisions and behavior. Many event host destinations around the globe significantly depend on atmospheric disturbances, therefore there is necessary to evaluate the climatic appropriateness for events for use in making proper decisions by events’ organizers. Hence, contemporary and future climate fluctuations will certainly be very important for the destinations, as well as for the sportsmen and visitors themselves.

Weather and climatic conditions are an essential base for outdoor sports events, and they must be accurately assessed. An appropriate model is essential to achieve this mission. The model must consider the multidimensional character of weather and the compositive methods the atmospheric variables jointly give to the climatic research in tourism and events planning. Due to its manifold nature, there is a need to devise climate indicators that would be capable of combining and rating climate resource for any activity in the travel industry, including sports events. These factors are expected to make it easier to apprehend the integrated impacts of numerous atmospheric features (e.g., temperature, humidity, atmospheric pressure, etc.) and enable the assessment of climate conditions for the events (de Freitas et al., 2008). Moreover, extreme weather conditions are some of the climatic influences that could affect not only sports events’ duration or cancelation, visitors’ satisfaction and sportsmen’s activities but also the safety of all participants. Possible distinctions in visitors’ flows and demand forms would make an impact on destination development, revenue redistribution, local employment, and considerably affect the profitability of tourism and events businesses (Bafaluy et al., 2014; World Tourism Organization & United Nations Environment Programme, 2008). In this regard, organizers of events will need to concentrate on weather risk with the aim of minimizing associated hazards and capitalizing on new economic, social, and environmental outlooks (Michailidou et al., 2016; Parent & Smith-Swan, 2013; Weed & Bull, 2004).

The effect of weather instability is particularly relevant to outdoor events’ businesses because the natural surroundings are some of the most important factors regulating the overall quality of their services and plans (Scott et al., 2003). Regarding this fact, our objective was to explain and recommend that recurrent neural network with long short-term memory (LSTM) could be a helpful instrument for handling weather impacts in outdoor events activities. LSTM networks are capable of categorizing, processing, and creating projections based on time series data (Graves & Schmidhuber, 2005), because there can be lags of an unspecified period between critical events in a time series. This could be a very useful method for long-term sports events planning. The model allows us to memorize values for short or long time frames and does not use activation functions within its recurrent components. Although there have been several studies promoting the use of the weather risks tools (e.g., climate index) in the travel industry (Bafaluy et al., 2014; Čavlek et al., 2019; de Freitas, 2003; de Freitas et al., 2008), very little, if any, the effort has been made in researching ways to examine the practical aspects of such an idea. Thus, one of the main aims of this study is to make an attempt to contribute to the scarce literature sources and to make events’ organizers more aware of the fact that LSTM could be of great help when managing weather risks. Having in mind the effective usage in the energetics (Capizzi et al., 2011; Medsker & Jain, 2000) and agriculture (Ndikumana et al., 2018), LSTM could have a similar potential in other weather-sensitive economic activities, such as outdoor events in sports and tourism.

The study explains empirical cooperation between researchers in tourism and climatology that points to the development of an event host destinations’ projected weather conditions and the activities that can be reinforced by these weather scenarios using the results of LSTM. The teamwork will provide a toolkit that can be used for events’ organizers to improve their strategies, giving directions on how to potentially predict a similar situation in the future. Hence, in our research, we give special attention to weather elements that are characterized by short-term inconsistency (e.g., instability in snowfall on daily basis) instead of the ones with long-term differences (e.g., temperatures rise in the last decades). The weather data were collected at Coleman A. Young International Airport (previously called Detroit City Airport) in Detroit (MI, USA), according to the available sources of the National Oceanic and Atmospheric Administration (NOAA) Weather Service.

Interrelation Between Weather Conditions and Outdoor Events

Weather and climatic conditions are prevalent factors in many economic activities involving sports events and the travel industry in general. Significant organizational and financial problems arise due to sudden atmospheric disturbances that cannot always be predicted accurately. Even though the climatic types do not automatically determine tourism activities, they are usually observed as relevant factors of both financial inflows expected by travel operators and as a measure of visitors’ individual experiences (de Freitas, 2003). The international events sector now undoubtedly acknowledges that it is an activity that is highly climate-sensitive, and they have started observing it as a sustainability challenge that requires adaptation to weather conditions. Climate is an essential component in outdoor tourism activities and an important part of a destination’s resource and economic base. Any variation in climate characteristics could represent a possible risk to an event host destination’s sustainability, attractiveness, and economic feasibility (Čavlek et al., 2019). Rutty et al. (2015) highlighted that weather influences the capacity to brace for outdoor events and can have a direct impact on planning the schedule in terms of postponements or even the cancelation of events. The advancement of business strategies and technology over the past decades has made it highly feasible to manage weather risks. Using climate data systematically and holding events indoors, along with the provision of more accurate weather forecasting, have proven to be almost essential aspects of having effective events programs.

Moreover, Thornes (1977) claimed that the interface between outdoor sports events and weather conditions is more complex in the aspect that we need to consider meteorological variables that we are not able to exactly predict or strictly control. Diverse sports activities are permissive to various ranges of each of the meteorological variables, so the impact of weather on outdoor sports can be classified into the following segments: (1) specialized weather sports, (2) weather interference sports, and (3) weather advantage sports (including baseball). According to the same author’s categorization (Thornes, 1977), the dependency of outdoor/indoor sports events on weather condition can be classified into the following types: those that depend on specific weather conditions (e.g., skiing or sailing); those in which weather conditions might result in an unfair advantage (e.g., golf, athletics), and those team games, largely played on grass, in which weather interferes with the play but the division of a match into two halves compensates for any adverse effect (e.g., football, rugby, hockey, and baseball; Kay & Vamplew, 2006). The connection between destinations and climatic conditions is multifaceted, defining activities, seasonality, and locations (Leggio, 2007; Matzarakis, 2006; Tang & Jang, 2012).

In addition, Kay and Vamplew (2006) stated that the subject of weather conditions on human activity in sports events remains strangely neglected by academics, even as authors emphasized that sports organizers are commonly ignoring the importance of the weather despite high-safety risks and possible discomfort of sportsmen, visitors, and organizers. Events organizers’ economic problems can also be caused by climatic deviations or unpredicted circumstances. The rationale of most of the research on events climate seems to be the potential impact of weather information during the planning of outdoor events. Therefore, depending on how weather sensitive the outdoor sports events are, the climatic information can be of great help in their planning and scheduling in the future. It is happening that standard weather data or even secondary climatic variables cannot consistently indicate the conditions in the atmosphere. For instance, whatever the air temperature is, the thermal conditions experienced by individuals will be different, depending on the relative influence and the offsetting of other factors such as wind, humidity, solar radiation, and the level of individual activity (de Freitas et al., 2008). How important it may be, can be seen in climate and recreation research (Bauer, 1976; Reifsnyder, 1983), but so far there have been few convincing articles that focused on investigating the way tourism is sensitive to atmospheric influences (de Freitas, 2003). Few studies have described climate for visitors in simple narrative terms (Masterton & McNichol, 1981; Maunder, 1970; Smith, 1985), and only in a few cases (Bafaluy et al., 2014; Paul, 1972), have standard thermal climatic indices been included and generalized using quantitative calculations of weather variables.

Progressively, sports events are elements of wider local and national policies directed on increasing the host destination’s profile and consequently achievement cannot be evaluated simply on profit or loss (Gratton et al., 2000). As Mules and Faulkner (1996) stated, choosing the host of sports events is often justified by the host destination regarding long-term economic and social consequences that are the results of staging the event. These outcomes are mainly shown in financial terms, through the additional inflow generated in the local community as the result of the event, in terms of the profits gathered from events and the activities related to it and the subsequent reimaging of the destination that comes as a result of the success of the event (Roche, 1994). According to Kay and Vamplew (2006), dealing with overcoming this crucial issue was not only the task for sports police-makers to provide improved services for the audience but also to be more conscious of the weather impacts on financial and athletic performances.

Sports organizations do not need to face weather risks unaided. In this respect, the forecasting has a task to alert them of the need to take preemptive policy. Price (2008) underlined the fact that the weather risks and losses are rising dramatically and consequently increase the significance of monitoring extreme weather events on tourism tendencies. While better observing the weather hazards will not significantly impair the number or organizational difficulties of these events, early warnings can substantially reduce the overall damage or even prevent the loss of lives.

The Importance of Weather on Sports Events: A Study of Postponed MLB Games in Detroit, 2018

Major League Baseball (MLB) is a professional baseball organization and one of the oldest professional sports leagues in North America. Today, MLB is composed of 30 teams, 29 from the United States and one from Canada, that play 162 games in one season. Five teams in each league move ahead to a four-round postseason tournament that finishes with the World Series. There are 15 teams each in the National League and the American League (Barrow, 2018). Baseball broadcasts are aired on numerous media throughout the United States, Canada, and the rest of the world. MLB has the greatest season attendance of any sports league worldwide involving more than 67 million visitors in 2018 (ESPN News, 2018).

The unexpectedly cold weather conditions in March and April 2018 in the Midwest of North America forced several MLB postponements. As much of the United States and Canada dealt with extreme, unpredictable cold weather in early spring, MLB games kept getting postponed, forcing some teams to miss three days straight of baseball due to unplayable situations (Sports Illustrated, 2018). The same source reported that according to the Associated Press, the total for the 2018 season matched 2007 for the most weather-related postponements through April since MLB started keeping records in 1986. To illustrate the serious situation as a result of the weather postponements, Forbes’ (2018) report highlighted that there were 21 weather-related postponements through the observed period resulting in paid attendance down for over 316,000 U.S. dollars during the same time when 11 of the 30 clubs in the league were seeing attendance up over the previous season. According to the report of Sports Illustrated (2018), the list of postponements of MLB games in Detroit due to inclement weather conditions in March and April 2018, included:

March 29: Pirates at Tigers;

March 31: Pirates at Tigers;

April 4: Royals at Tigers;

April 14: Yankees at Tigers;

April 15: Yankees at Tigers; and

April 15: Yankees at Tigers.

The cause of the mentioned postponements will be examined in this study by using results of LSTM. The goal is to provide readers with the findings on how it is possible to deal with similar issues in the future.

Materials and Methods

Research Procedure

This research involved interdisciplinary teamwork from several scientific organizations: experts in the tourism and event industry from Serbia and Russia and specialists in climatology, mathematical geography, and astrophysics from Serbia, China, and Ukraine. In order to develop a forecast of weather conditions that could give more precise announcements important for outdoor events, the basic aim of the study was to elaborate a new method based on the modeling of high-energy solar flows. The research null hypothesis (H1₀) is formed according to the assumption that atmospheric disturbances (in this case, above the Midwest of the United States) could precede the sudden inflow of sunburns. This would be accepted or rejected in accordance with the values of the Autocorrelation analysis (Serial correlation) outcomes. According to the available data, the mission was to explore whether there is a mathematical relationship between the parameters of the solar wind and the measured data for temperature, air pressure, and humidity in Detroit. The Autocorrelation analysis, as a mathematical tool, was conducted in order to present the connection between the observations as a function of the time lag between them. This analysis aims to find repeating patterns, such as the existence of a periodic signal obscured by some obstacle or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. The method provides a unified approach to assessment that is well-defined in the case of the normal distribution and many other problems.

Data for Analysis

The list of input parameters included 5-minute averaged real-time integral flux of high-energy solar protons, 5-minute averaged real-time differential electron and proton flux, 1-minute averaged real-time bulk parameters of the solar wind plasma (NOAA, 2018a), and 10.7 cm radio flux. Five-minute averaged real-time integral flux of high-energy solar protons included >10 MeV and >30 MeV (NOAA, 2018b; units: proton flux p/cs2-sec-ster). A 5-minute averaged real-time differential electron and proton flux included

differential flux electron 38-53;

differential flux electron 175-315;

differential flux protons keV 47-68;differential flux protons keV 115-195;

differential flux protons keV 310-580;

differential flux protons keV 1060-1900 (NOAA, 2018b; units: differential flux particles/cm2-s-ster-MeV).

One-minute averaged real-time bulk parameters of the solar wind plasma included: proton density (particles/cc), bulk speed (km/s), and ion temperature. Daily data on 10.7 cm radio flux (sfu) were downloaded from the database on the daily flux values for the year 2018 (Natural Resources Canada, 2018). The list of output parameters included weather data for Coleman A. Young International Airport in Detroit: air temperature (degrees Celsius) and humidity (%). Air pressure (hPa) was obtained from the database of TuTiempo (2018)—Climate Data.

Input and Output Parameters

The main task was to calculate and investigate the functional dependence of the influence of solar activity on climatic parameters of air: temperature (T), humidity (H), and atmospheric pressure (P) and its influence on observed sports events. Real-time integral flux of high-energy solar protons (>10 and >30 MeV), differential electron (38-53, 175-315 keV), and proton flux (47-68, 115-195, 310-580, 795-1193, & 1060-1900 keV), real-time bulk parameters of the solar wind plasma (proton density, bulk speed, and ion temperature), and 10.7 cm radio flux were selected as input factors. This task can be solved by data mining methodology—the search for complex functional parameters, taking into account the time delay. Therefore, the calculations algorithm are presented in Figure 1.

Figure 1

The Model of Algorithm of Calculations

Preliminary Analysis of Input and Target Data

The study was conducted in the early spring of 2018: from March 22 to April 6. The feature of the target data is that they were received directly from the sensors; therefore, the time difference between the two subsequent measurements could vary significantly. The input data were downloaded from the internet and represented average values at certain time ranges, except for 10.7 cm radio flux that was measured at 17, 20, and 23 hours daily. This means a different scale of data ranges and the availability of the missing data at times when averaging was performed in the absence of sensor data. It should be noted that the time of input data measurement was fixed at the universal time for Greenwich. The target data were measured at Coleman A. Young International Airport in Detroit, which differs by −5 hours from the universal time. The information about time ranges is given in Table 1. Conveniently, the data received from one resource are grouped into the corresponding frames.

Table 1

Information About Input and Target Parameters

Frame No.	Factors (Units)	Measurement Time Range
Input data
1	Field 1: >10, Field2: >30 (MeV)	5 minutes
2	Field 1: 38−53, Field 2: 175−315, Field 3: 47−68, Field 4: 115−195, Field 5: 310−580, Field 6: 795−1193, Field 7: 1060−1900 (keV)	5 minutes
3	Field 1: Proton density (p/cc), Field 2: Bulk speed (km/s), Field 3: Ion temperature (K)	1 minute
4	Field 1: 10.7 cm radio flux	3 per day
Target data
5	Field 1: T (°C), Field 2: H (%), Field 3: P (hPa)	2 seconds—2 hours (1-hour average)

As seen in Table 1, the sampling rate of the target data varies over a wide range of values from 2 seconds to 2 hours. The sampling rates of the input parameters of the frames 2, 3, and 4 are 5 minutes and 1 minute, respectively. The time series of the input and target parameters are shown in Supplemental Figures S1 to S6 (available online).

In addition, Supplemental Figures S1 to S4 indicate the time series with a lot of missing data. Abnormal fluctuations in the direction of small and large values are observed as well. The sampling rate of 10.7 cm radio flux is generally very small and needs to be increased substantially.

Results and Discussion

Data Transformation

Import and Consolidation of Data

For further analysis, presented in this segment of the article, all input and target data fields were imported from various sources into the matrix structures of the DataFrame, the index fields of which are the date and time of the received data:

D F_{f} = (K e y = D a t e & T i m e : D a t a = 〈 F i e l d_{f 1}, \dots, F i l e d_{f n} 〉)

(1)

where f is the frame number from Table 1 and $F i e l d_{f i}$ is the іth field of frame f. The next step is to concatenate all DF_f accordingly to the index fields into one DataFrame:

D F = D F_{1} \cdot D F_{2} \cdot D F_{3} \cdot D F_{4} \cdot D F_{5}

(2)

The resulting DataFrame contains all possible values of the index field from all $D F_{f}$ . All the input and target fields are included in this DataFrame. The data field values for which the data from the sensor (source) are missing at some point in time are filled with NaN (Not a Number) values.

Aggregating Data to Equal Sampling Rates

The result is a sparse matrix containing the $D a t e & T i m e$ index field with uneven sampling rates. For further analysis, it is necessary to unify the sampling step. As seen in Table 1, the maximum of the target fields sampling steps equals 2 hours, and the average is about 1 hour. It means that resampling target data to greater than 2 hours will not contain missing data but will lead to a sharp decrease in the size of the DataFrame for analysis (96 rows). Reducing the sampling rate will increase the number of rows that contain NaN data. As our test calculations show, the optimal sampling time was 30 minutes, which corresponds to 384 rows in the DataFrame and consists of less than 5% NaN data in the target fields. When changing the sampling rate, the average or max method was used if several values of the data fields belonged to a resampled time interval. The max method showed better results in subsequent calculations. This is explained by the fact that, on one hand, it was possible to remove abnormal negative oscillation, and on the other hand, to take into account the flashes of the parameters of solar activity, because they led to the fluctuations in temperature, humidity, and pressure.

Filling Missing Data

Spline cubic interpolation was used for each field to eliminate the missing data in the resulting matrix (Hang et al., 2017). This made it possible to interpolate the missing data in the middle, beginning, and end of all the time series from DataFrame. The rolling window analysis based on 4 points was used to reduce white noise (Hyndman, 2011). The interpolation results are shown in the Figure 1 and Supplemental Figures S1 to S5. As can be seen from Figure 1 and Supplemental Figure S1 to S3, max-cubic-spline interpolation allowed for the elimination of the minimum abnormal values of the time series and for the emphasis of the greatest flashes of solar activity parameters. It allowed for determining the intermediate values of 10.7 cm Radio Flux factor for a 30-minute period, taking into account that it had the biggest sampling rate. This transformation practically did not change the target fields (see Supplemental Figure S5), which is important for further analysis. As a result, the even sampling rates DataFrame— $D F$ without NaN values are obtained on this step.

Reducing of Task Dimension

An autocorrelation analysis was performed over all the fields of the resulting matrix to reduce the number of the input parameters. As a result, a matrix of all possible pairwise coefficients of correlation between all the input and target fields was obtained (see Table 2).

Table 2

Results of Autocorrelation Analysis

	>10 MeV	>30 MeV	Proton Density	Bulk Speed	Ion Temperature	10.7 cm Radio Flux	38−53	175−315	47−68	115−195	310−580	795−1193	1060−1900	Temperature (in degrees celsius)	Humidity	Air Pressure
>10 MeV	1.00	0.96	0.42	−0.48	−0.38	−0.16	0.09	0.48	−0.07	−0.14	−0.17	−0.10	−0.14	−0.20	0.05	−0.26
>30 MeV	0.96	1.00	0.39	−0.43	−0.36	−0.15	0.16	0.44	−0.03	−0.07	−0.13	−0.09	−0.13	−0.22	−0.04	−0.19
Proton density	0.42	0.39	1.00	−0.43	−0.21	−0.14	0.07	0.25	−0.05	−0.14	−0.14	−0.11	−0.08	−0.39	0.02	−0.27
Bulk speed	−0.48	−0.43	−0.43	1.00	0.80	0.19	−0.08	−0.18	0.11	0.05	0.15	0.28	0.16	0.22	−0.21	0.66
Ion temperature	−0.38	−0.36	−0.21	0.80	1.00	0.12	−0.09	−0.09	0.07	0.12	0.32	0.39	0.27	0.10	−0.27	0.64
10.7 cm Radio flux	−0.16	−0.15	−0.14	0.19	0.12	1.00	−0.49	−0.15	0.17	0.13	0.15	0.13	0.07	0.15	0.01	0.24
38−53	0.09	0.16	0.07	−0.08	−0.09	−0.49	1.00	0.28	−0.09	0.18	0.00	−0.13	−0.11	−0.33	−0.20	−0.05
175−315	0.48	0.44	0.25	−0.18	−0.09	−0.15	0.28	1.00	−0.02	−0.16	−0.24	−0.12	−0.21	−0.36	−0.08	0.00
47−68	−0.07	−0.03	−0.05	0.11	0.07	0.17	−0.09	−0.02	1.00	0.43	0.10	0.07	0.06	0.01	−0.23	0.12
115−195	−0.14	−0.07	−0.14	0.05	0.12	0.13	0.18	−0.16	0.43	1.00	0.74	0.33	0.19	−0.02	−0.23	0.07
310−580	−0.17	−0.13	−0.14	0.15	0.32	0.15	0.00	−0.24	0.10	0.74	1.00	0.81	0.67	0.04	−0.03	0.14
795−1193	−0.10	−0.09	−0.11	0.28	0.39	0.13	−0.13	−0.12	0.07	0.33	0.81	1.00	0.78	0.15	0.13	0.26
1060−1900	−0.14	−0.13	−0.08	0.16	0.27	0.07	−0.11	−0.21	0.06	0.19	0.67	0.78	1.00	0.17	0.29	0.03
Temperature (in degrees celsius)	−0.20	−0.22	−0.39	0.22	0.10	0.15	−0.33	−0.36	0.01	−0.02	0.04	0.15	0.17	1.00	0.15	−0.08
Humidity	0.05	−0.04	0.02	−0.21	−0.27	0.01	−0.20	−0.08	−0.23	−0.23	−0.03	0.13	0.29	0.15	1.00	−0.55
Air pressure	−0.26	−0.19	−0.27	0.66	0.64	0.24	−0.05	0.00	0.12	0.07	0.14	0.26	0.03	−0.08	−0.55	1.00

As can be seen from Table 2, all correlation coefficients are essentially small except >10 MeV and >30 MeV, which is equal to 0.96. So, this means that one of them can be neglected. For calculations, the >30 MeV was selected because it considered precisely the high-energy protons. The result was a DataFrame containing 12 input fields and 3 outputs.

Normalizing Train and Test Data Sets

The feature of this task is that the target factors depend on the behavior of the input factors over the previous period of time tL (Lag). Besides, the target factors are a complex system that depend on other factors that are not taken into account in this task. To consider their influence, it is necessary to add themselves for the previous time like additional input factors. As previous calculations show (Vyklyuk et al., 2018), this time can be up to 4 days. That is, taking into account the sampling step of 30 minutes (twice per hour), this will result in an increase in input factors from 12 + 3 = 15 to N = 15× 4× 24× 2 = 2880. This actually makes it impossible to solve this task by classical neural networks. There are some ways to overcome this problem: We can use either a complete overview of all the possible models to identify the most important lags for factors (Radovanović et al., 2018; Srećković et al., 2017), or use recurrent neural networks (RNNs) that have been developed specifically for this class of tasks (Miljanovic, 2012; Radovanović, 2018).

In the case of this study, it is necessary to submit a two-dimensional array to the input in order to use the trained RNN. The first dimension of the array is the time lag index, and the second—the index of the input field. The input fields are all the input and target factors for the previous period of time (see Figure 2).

Figure 2

Structure of Recurrent Neural Network Input–Output

Three target fields in real time are used for output RNN. Thus, the neural network will have 15 inputs; each of them is historical data for the previous time t = [t-1, t-t_L]. The data set must have a three-dimensional structure in the case of fitting (learning). A row index (measurement from the sensor) is added to the learning sample as the first dimension: [samples, time lag, features]. The received DF needs to be transformed into the following shape:

D F_{R N N} = (K e y = t : D a t a = 〈 \begin{array}{l} I n_{1} (t - 1), \dots, I n_{12} (t - 1), T_{1} (t - 1), .., \\ T_{3} (t - 1), \dots, I n_{1} (t - t_{L}), \dots, \\ I n_{12} (t - t_{L}), T_{1} (t - t_{L}), .., \\ T_{3} (t - t_{L}), T_{1} (t), .., T_{3} (t) \end{array} 〉)

(3)

where t is the date and time of the row, T the input and target fields, respectively, and L = $4 \cdot 24 \cdot 2 = 192$ is the maximum value of time lag. The $D F_{R N N}$ was divided into two sets to form input and target DataFrames: input ( $D F_{i n} = D F_{R N N} [: - 3]$ ) and target ( $D F_{t a r} = D F_{R N N} [- 3 :]$ ). Where “−3” means the third with the end of the column, and “:”—“all” records. In turn, $D S_{i n}$ was transformed into 3D shape:

D F_{i n 3 D} = {d_{t, l, f}}_{t = \bar{1, 384}, l = \bar{1, 192}, f = \bar{1, 15}}

(4)

where index t is the time (rows), l is the lag, and f indicates the input fields. $D F_{i n 3 D}$ and $D F_{t a r}$ were divided into training and test DataFrames in a ratio of 70/30 and normalized for further training and testing of the neural networks. All further analysis was conducted with normalized data. When outputting the final results on figures and tables, inverse normalization was carried out.

Creation and Training of a Neural Network Ensemble

The LSTM was selected as an investigation model because it allows simulation of the behavior of a system that depends on time delay. This is realized by reverse transmission of the neural network output signal at the time t − 1 back to the input of one of the network layers. This complex input is used to calculate the output for time t. The overall structure of such a network in the case of this article is presented in Supplemental Figure S7.

The LSTM is a type of the recurrent neural network that allows memorizing values for long or short periods of time. This network does not use activation functions within its recurrent components. Thus, the stored value does not disappear iteratively over time. The LSTM blocks contain three or four “valves” that they use to control the information flow to or from their memory. These valves are used as logistics functions to calculate values between zero and one (0 and 1). This value multiplies to allow or deny a partial flow of information to or from that memory (Greff et al., 2017). As the test calculations have shown, the best results were obtained for the LSTM of the following configuration: the number of inputs—15, the outputs—3, the number of neurons—50, the batch size 10% (size of the training block set where LSTM fitting without changing weights), the learning period 5,000, the accuracy criterion—mean square error, learning method—Adam (Kingma & Ba, 2015). The implementation of this neural network was carried out by using the programming language Python and libraries: TensorFlow—software library for machine learning and visualization of the neural network (TensorFlow Software Library, 2018), Pandas—for working with files and DataFrames (Pandas Library, 2018), and SciKit-Learn—for the normalization of DataFrames (Scikit-learn Software Machine Learning Library, 2018). The structure of the neural network obtained by using TensorBoard of TensorFlow library is presented in Supplemental Figure S8.

The dynamics of the mean square error during the training period was investigated to determine the required number of epochs and the number of neurons (see Supplemental Figure S9). The training stopped when the mean square error of the test set error began to grow steadily over 100 periods of training. As it can be seen from Supplemental Figure S9, the neural network adapted rather quickly to the training set and for a long time to the test set. That indicates we need to use deep learning for good fitting of this LSTM. There are several peaks of error increasing on the plot, which is explained by the transition to the next block of training (batch block). As can be seen from the same figure, the errors of the test and training sets vary significantly from one another. This indicates the existence of internal complex functional dependence in this system.

About 100 different neural networks were tested and trained to test the stability of the fitting. Supplemental Figure S10 shows the forecasting results of the training and test data of the 11 best neural networks. As can be seen from the figure, all neural networks are ideally fitted to training sets but vary widely in forecasting for the test set. It is difficult to understand from the plots which network is best because each of them best describes different target data. One predicts temperature better, but the other predicts humidity, etc. In this research, we used the ensemble of LSTM models to solve the problem of forecasting stability where the generally accepted path is to determine the weighting factors of each of the 11 neural models and, by using a linear convolution, to calculate the final result of the forecasting (see Supplemental Figure S11). To do this, an ensemble of LSTM models was constructed, and its hidden layer was fitted by using multiple regression analysis:

R e s = \sum_{i = 1}^{11} A_{i} \cdot D F_{o u t}^{i}

(5)

where $D F_{o u t}^{i}$ is the vector of output values і-th LSTM RNN and $A_{i}$ is the weight component. The following results were obtained from the training presented in Supplemental Figure S12.

As can be seen from Supplemental Figures S10 to S12, the results of models forecasting are much better, and they repeat the basic features of real data. The obtained correlation coefficients were: $R (T) = 0.83$ , $R (H) = 0.74$ , $R (P) = 0.86$ . So, the best correlation coefficients were for the forecasting of pressure and temperature. The high correlation coefficient indicates the accuracy of the obtained models, and the behavior the forecast plot in comparison to real test data—on the adequacy. The lowest correlation coefficient for humidity indicates nonlinear effects, which means that solar activity indirectly influences this factor through the impact of other factors.

The obtained ensemble of LSTM models allows for the calculation of the sensitivity of the output fields to the influence of the inputs. To do this, the value of the ensemble of models $R e s_{t}$ is calculated for each row t in $D F_{i n 3 D}$ , as well as the vector of values $R e s_{t}^{f}$ for which the f-th input factor is increased by 10% throughout the lag L. Then the vector of relative changes for each record is calculated:

S_{t} = {s_{t}^{f}}_{f = \bar{1, 15}} = {\frac{R e s_{t}^{f} - R e s_{j}}{R e s_{t}}}_{f = \bar{1, 15}},

(6)

where t is the row index in $D F_{i n 3 D}$ and f is the input field index. After that, the sensitivity was calculated as the average of relative changes for all fields in $D F_{i n 3 D}$ :

S = \frac{\sum_{t = 1}^{N} S_{t}}{N}

(7)

where N is the number of rows in $D F_{i n 3 D}$ (384 in the case of this research). The results of this analysis are presented in Table 3.

Table 3

Analysis of Sensitivity of Temperature in Degrees Celsius (T), Humidity (H), and Atmospheric Pressure (P) From Factors of Solar Activity (%)

	>30 MeV	Proton Density	Bulk Speed	Ion Temperature	10.7 cm Radio Flux	38−53	175−315	47−68	115−195	310−580	795−1193	1060−1900	T	H	P
T	20.0	2.6	−10.3	−7.1	−4.8	11.7	25.6	−2.9	10.8	15.0	35.9	2.5	30.1	0.7	6.5
H	−3.0	1.0	1.8	−6.0	−3.1	−1.7	−1.8	−0.6	0.2	1.7	2.5	2.4	−1.3	1.8	5.6
P	−0.2	0.0	0.1	0.0	0.1	0.0	−0.1	0.0	0.0	0.0	0.0	0.0	0.0	0.1	0.0

The results presented in Table 3 show that solar activity has the greatest influence on the temperature. Thus, an increase of factors 795-1193 (keV) and temperature degrees (celsius) to 10% over a period of 4 days leads to a rise in temperature by 36% and 30%, respectively. This means that the temperature most significantly depends on the differential flux of protons with the above-mentioned values of energy and significantly depends on its previous value for 4 days. The next are the factors 175-315 (keV) and >30 MeV. The sensitivity on their changes is 26% and 20%, respectively. Humidity depends very little on solar activity and decreases by 6% with increasing ion temperature to 10% for 4 days. It also depends on the previous values of pressure. So, the increase in atmospheric pressure to 10% within 4 days will lead to an increase in humidity by 5%. In contrast to the other two target factors, the pressure is practically independent of solar activity, and the zero values of the sensitivity obtained to confirm this finding.

Conclusion

Climate is a significant part of the events destinations, but its role in the establishment of the appropriateness of an area for the events and travel industry is frequently supposed to be obvious and, hence, to request no elaboration. Studies on the interrelation between tourism and climate have been reviewed in this text with the aim to identify and propose a useful model that may bring climatology and tourism together in future research. This research represents an attempt to develop an interconnected set of methods and to propose a model that could create a link between cognitive and theoretical levels that may be of great help in forming an understanding base for similar research. In addition, this article has demonstrated the benefits of teamwork between specialists in travel and event industries, on one hand, and in climatology and astrophysics, on the other, in creating a methodological tool to support and understand events climate adaptation plans. Not only does this method provide a significant weather information basis for projecting future adaptation but it also offers a starting point for the creation of an adaptation toolkit that could be relevant to any event host destination. Since this approach to examining weather is based on existing research procedures, it can be regarded as a valuable improvement in the scientific area of planning for climate fluctuations adaptation that can be applicable for the whole tourism-event sector. In this regard, the policy makers and stakeholders in sports tourism should be aware of the present and expected evolution of climate circumstances all over the globe, including the observed area of North America.

The study indicated evidence of nonlinear relations between the onset of the observed unexpected cold weather conditions during the early spring MLB games and solar activity. This gives the opportunity to use nonlinear methods of soft computing for finding and analyzing the functional relationship between them. The findings show a predictive model that incorporates time lags up to 5 days and finds that they are able to calculate the occurrence of similar weather situations without causing unreasonable false positive rates. The research null hypothesis (H1₀) has been confirmed that atmospheric disturbances above the Midwest of the United States could precede the sudden inflow of sunburns. The gained results for the air temperature show that the mentioned approach has the basis for further analysis of the research hypothesis.

Potential directions in researching the linkage between tourism and climate research are diversified. They rely on what is necessary according to all stakeholders: local communities, policy makers, sportsmen, and visitors. Methods used by climatologists and astrophysicists should be clearly explained and more easily expressed. Moreover, planners search for climate data that are clearly processed and quality checked. In examining the outcomes, it should be noted that climate-related models are not unmistakable. It is evident that experimental laboratory research is necessary to be directed in order to test the introduced values. In addition, it is essential to make further endeavors to enhance the mathematical and astrophysical models that would improve the apprehension of the propagation of electrons and protons toward the lower layers of the atmosphere. When the assessment of the uncertainties in the model is concerned, one of the possible ways to do it is to compare the results for the observed period with the data measured for previous periods with similar weather circumstances. Therefore, this information should be the basis for more accurate and functional prediction of the expected future climate tendencies.

Forthcoming research should necessarily increase the database, as well as the time shifting between the input and output data for 7 to 10 days. In a methodological sense, it is necessary to improve the calculation of the correlation bonds between the input parameters, which have stochastic pulsation, and the output values, which reflect changes in the parameters of the sun’s wind, but in different time bands, even on the daily and hourly levels. In order to achieve better results, that is, correlations bond, the future possibility of developing prognostic models of weather conditions, would certainly contribute to better planning and organization of any outdoor sports and tourism events. The major limitation of this article is the relatively narrow time frame (March/April 2018) and the limited spatial coverage of the examination site (Detroit). Nevertheless, the authors rely on the fact that this restriction is compensated for by the original capacity of the access to investigate the unpredictable weather circumstances for events in detail. Future studies with an extensive interdisciplinary approach from more diverse geographic and/or climatic regions remain a relevant mission to validate the usage of the LSTM model in the management of the events and tourism industry globally.

Supplemental Material

JHTR-19-02-159_supplement – Supplemental material for The Conditionality of Outdoor Sports Events on Weather-Induced Impacts and Possible Solution

Supplemental material, JHTR-19-02-159_supplement for The Conditionality of Outdoor Sports Events on Weather-Induced Impacts and Possible Solution by Marko D. Petrović, Milan M. Radovanović, Yaroslav Vyklyuk, Milan Milenković and Tatiana N. Tretiakova in Journal of Hospitality & Tourism Research

Footnotes

The research was supported by the Ministry of Education, Science and Technological Development, Republic of Serbia (Grant III 47007), and by the Act 211 Government of the Russian Federation, Contract No. 02.A03.21.0011.

ORCID iD

Marko D. Petrović

Supplemental Material

Supplemental material for this article is available online.

Marko D. Petrović, PhD (e-mail: m.petrovic@gi.sanu.ac.rs), is a research associate at the Social Geography Department of the Geographical Institute “Jovan Cvijić”, Serbian Academy of Sciences and Arts in Belgrade (Serbia). Milan M. Radovanović, PhD (e-mail: m.radovanovic@gi.sanu.ac.rs), is a principal research fellow at the Geographical Institute “Jovan Cvijić” SASA, Belgrade, Serbia and a full professor at the South Ural State University, Chelyabinsk, Russia. Yaroslav Vyklyuk, PhD (e-mail: vyklyuk@ukr.net), is a full professor at PHEI Bukovinian University, Chernivtsi, Ukraine. Milan Milenković, PhD (e-mail: m.milenkovic@gi.sanu.ac.rs), is a research associate at the Geographical Institute “Jovan Cvijić” SASA, Belgrade, Serbia. Tatiana N. Tretiakova, PhD (e-mail: ttn1@mail.ru), is a full professor at the Institute of Sports, Tourism and Service, South Ural State University in Chelyabinsk, Russia.

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