The Length of the Beach Season at Lake Balaton—An Estimation Based on Operative Temperature

Abstract

The length of the beach season at Lake Balaton (Hungary, Central Europe) in the period 2002–2024 is estimated using daily data of air temperature, water temperature and wind speed. Daily thermal load is approached by calculating operative temperature using operative temperature-air temperature relationships on monthly scale. We introduced the concepts of beach day and bath day in order to estimate when the environmental conditions were suitable for lakeside activities. Data are taken from meteorological station Siófok. The main results are as follows. In the summer months, the median number of beach days and bath days is 72 and 68, respectively. The unbiased standard deviation of beach days and bath days is 4.62 and 6.4 days, respectively. As regards bath days, the best year was 2023, then the number of bath days was 105. The smallest number of bath days was 57; this occurred in the year 2010. As regards beach days, the best year was 2018 with 114 days, the worst year was 2021 with 72 days.

1. Introduction

The science of tourism climatology began in the 1970s’, and after a short period of decline, it gained popularity again in the 1990s’. Now it is a relevant multidisciplinary area, with a growing number of studies filling scientific gaps. There is also an international working group called Commission on Climate, Tourism and Recreation (CCTR), which deals with the actual issues of tourism climatology [1]. Atmosphere had a Special Issue in 2021, entitled Tourism Climatology: Past, Present, and Future, which contains seven original articles and two review reports. These works cover various relevant topics in this field, showing that this is a versatile research area, which has great importance in this decade [2].

Tourism is always influenced by the weather and general climate of the given region, and different kinds of activities (e.g., sightseeing, hiking, beach tourism) require different indices that help tourists or tourist services to plan the holiday season. According to de Freitas [3], there are three distinct aspects of climate that are relevant to tourism: thermal, physical, and esthetic aspects. The thermal component expresses the thermal comfort of tourists, and it is expressed by thermal indices that often rely on physiological research. The physical component is generally a single meteorological variable such as wind or precipitation that can disturb tourists in some physical way. The esthetic component refers to the aspect of whether tourists can enjoy the landscape and other sights, and usually relies on sunshine duration, cloudiness or fog. In this study, the first and the second components are applied.

The climate of the given site is relevant for tourists before the holiday season, they can use tourist guidebooks or the internet to collect information. During the holiday season, the actual weather of the holiday resort is more important, and tourists generally use mobile apps or read the news during their stay [4]. On the other hand, the effect of weather conditions often can be seen only after a lag of up to one year in foreign tourism [5]. Here, we concentrate on the climate of Lake Balaton during the holiday season.

Another issue is the occurrence of meteorological disasters, such as severe storms or even hurricanes. They cannot be accurately predicted before the holiday season, only a few days in advance. These disasters can cause high losses to the tourism industry and may discourage tourists from visiting the given country [6]. Fortunately, such severe weather disasters are not common in Hungary.

In Europe there have been studies, for instance, for Italy [7] using the Mediterranean Outdoor Comfort Index (MOCI) [8] and Predicted Mean Vote (PMV) [9]; for Serbia using the Tourism Climate Comfort Index (TCCI) [10]; for Spain [11] utilizing the weather types method of [12]; for Poland, Ukraine, and Serbia [13] applying the Weather Suitability Index (WSI) [14]; for Romania [15] using the enhanced version of the Tourism Climatic Index (ETCI) [16]; and for Hungary as well [17,18] using the modified Tourism Climate Index [19,20]. There has been studies focusing on beach tourism [21,22,23] examining lakeside activities.

As far as Lake Balaton–which is the largest lake of Central-Europe–is concerned, there has been various studies on it. There are special studies on tourism as well [24,25,26,27]. Németh [24] used Tourism Climatic Index (TCI) [28] to assess the suitability of environmental conditions for lakeside activities. They also applied Climate-Tourism-Information-Scheme (CTIS) [29,30], which depends on threshold values of Physiological Equivalent Temperature (PET) [31,32], and meteorological variables. Based on CTIS, from a thermal point of view, the optimal period lasts from early May until the first third of October, the best time for bathing is from the middle of July until the beginning of August.

Among the above-mentioned studies on Lake Balaton and on other beach sites, there are no studies considering the suitability of water temperature, and neither of them examines thermal load via operative temperature. As regards thermal load, they tend to apply complicated thermal indices requiring much data, instead of using simpler but more relevant variables. As far as water temperature is concerned, in our opinion, the lack of this variable as an index of beach comfort makes it hard to assess the possibilities of swimming. That is, previous studies cannot properly assess whether the environmental conditions are suitable for bathing by neglecting the consideration of the thermal conditions of the given lake or sea. To our knowledge, there has been no studies on Lake Balaton examining bath days on longer scale based on such simple but compact indices. The aim of this study is to fill this scientific gap by introducing a novel method to examine the thermal conditions of the largest lake of Central Europe in an effort to help tourists and tourist services to plan the holiday season.

The subject of this study is to analyze the suitability of the holiday season (from April to October) for lakeside activities like sunbathing and bathing by Lake Balaton between the 2002 and 2024 time period via operative temperature [33], water temperature and wind speed. The study is arranged as follows. The region and the datasets used for the study are described in Section 2, details of the methodology are provided in Section 3, while results are presented in Section 4. Section 5 and Section 6 are devoted to discussion and conclusion, respectively.

2. Data and Region

2.1. Region

Lake Balaton is the largest lake of Central Europe. It is a shallow lake (average depth is 3–3.5 m), so it warms and cools down rapidly. Its length is 77 km, its average width is 7.7 km, its water surface is 600 km². The climate of Hungary according to Köppen [34] is Cfb (warm temperate, no seasonality in the annual course of precipitation, warm summer), so we define criteria of beach day and bath day and provide results for this kind of climate. According to Feddema [35], the climate around Siófok is moderately cool and dry with a seasonality close to extreme in temperature [36].

Siófok lies on the southern shore of Lake Balaton, its geographical coordinates are 46.9108°N and 18.0408°E, it is 107.2 m above sea level. It belongs to Somogy county. Figure 1 shows Hungary with Lake Balaton and the city of Siófok besides it.

2.2. Data

Data needed for this study are daily 2 m air temperature, water temperature, and 10 m wind speed. These have been downloaded from the website of HungaroMet (https://odp.met.hu/ (accessed on 12 October 2024)). In Siófok there is a Storm Warning Observatory (46°54′ N, 18°02′ E, 108 m asl), which is ideal for tourism climatology since it is located right at the lakeside. Water temperature is measured 50 m far from the shore, in 3 m deep water, in 1 m depth.

Besides these data, climate charts available at the website of HungaroMet were also used for verification (www.met.hu/eghajlat/magyarorszag_eghajlata (accessed on 20 March 2025)).

The study period is the holiday season (from 1 April to 31 October) of the 2002–2024 time period, as most tourists come here in these months and the national meteorological service HungaroMet has storm warning service in this part of the year. Each holiday season consists of 214 days.

3. Methods

3.1. Criteria of Beach Day and Bath Day

The criteria for beach day and bath day can be summarized by indicator type functions (Equations (1)–(4)).

$$f(T_o,T_w,f_s)=\left\{\begin{array}{c}1 if T_o>25°C,T_w>20°C,f_s<5{ms}^{-1} \\ 0 else \end{array}\right.,$$

(1)

$$g(T_o,f_s)=\left\{\begin{array}{c}1 if T_o>25°C,f_s<5{ms}^{-1} \\ 0 else \end{array}\right.,$$

(2)

The number of bath days (BD):

$$BD={\sum }_{i=1}^{214}f(T_{oi}, T_{wi}, f_{si}),$$

(3)

The number of beach days (BD₂):

$${BD}_2={\sum }_{i=1}^{214}g(T_{oi}, f_{si}),$$

(4)

Based on the thermal sensation categories of [37], people start feeling warm when operative temperature (T_o) is above 25 °C, so this is chosen as a lower limit of optimal temperature. The heat sensation categories in [37] based on threshold values of T_o refer to average (mesomorphic) body shape [38], which is the most adequate for such studies [39].

Only few studies have analyzed which the comfort water temperature for tourists is. Established on the work of [40], water temperature (T_w) is acceptable above 21 °C. Considering that water is warmer near the shore where it is shallower than farther where the measurment takes place, 20 °C is chosen as measured minimum comfort temperature. The round value of 20 °C has also some psychological meaning and tourists start bathing and in the news can be read when Lake Balaton reaches this critical temperature in late spring. Established on observations, wind speed (f_s) becomes uncomfortable when daily average wind speed reaches 5 ms⁻¹, since this involves high wind gust speed during the day which may disturb tourists. The relative occurence of such average wind speed is 5% in Hungary [41]. A certain day is considered a beach day if it is suitable for lakeside activities such as sunbathing, that is, when operative temperature and wind speed meet the criteria. A day is referred to as a bath day if it is suitable for bathing, that is, when water temperature is acceptable as well.

Table 1. The summary of the definition of beach day and bath day.

Name	Criteria	Activity
Beach day	To > 25 °C, fs < 5 ms−1	sunbathing
Bath day	To > 25 °C, fs < 5 ms−1, Tw > 20 °C	swimming and sunbathing

summarizes the definitions.

3.2. Definition of Operative Temperature

Thermal comfort of tourists is expressed via operative temperature (T_o) [33]. T_o depends upon air temperature (T_a), isothermal net radiation (R_ni) (Wm⁻²), and the combined resistance for heat exchanges (r_aHr), and can be calculated by the following formula [33]:

$$T_o=T_a+{\displaystyle \frac{R_{ni}}{\rho ·c_p}}·r_{aHr},$$

(5)

ρ is density of air (1.2 kgm⁻³) and c_p is the specific heat of air at constant pressure (1005 Jkg⁻¹°C⁻¹).

R_ni can be given by the formula below:

$$R_{ni}=R_s·\left(1-{\alpha }_{sk}\right)+R_a-{\epsilon }_{sk}·\sigma T_a^4,$$

(6)

where R_s is incoming solar radiation (Wm⁻²), α_sk is the albedo of skin (0.26 in this scheme), R_a is atmospheric downward longwave radiation (Wm⁻²), ε_sk is the emissivity of skin (1 in this scheme), σ is the Stefan Boltzmann constant (5.67 × 10⁻⁸ Wm⁻²K⁻⁴).

Based on the work of [33], and [42], r_aHr can be estimated with the following formula:

$${\displaystyle \frac{1}{r_{aHr}}}={\displaystyle \frac{1}{r_{aH}}}+{\displaystyle \frac{1}{r_r}}={\displaystyle \frac{1}{7.4·41}}\sqrt{{\displaystyle \frac{u_{1.5}}{D}}}+{\displaystyle \frac{4{\epsilon }_{sk}\sigma T_a^3}{\rho c_p}}$$

(7)

where r_aH and r_r are the resistances for thermal convective and radiative heat exchanges (sm⁻¹), respectively; u_1.5 is the wind speed (ms⁻¹) at 1.5 m (chest height), D is the diameter of the human body at the chest (0.33 m in this study).

In this article, T_o is calculated by the simpler formulae of Ács et al. [43] for each day of the given month.

$${T_o}^{April}=1.06{T_a}^{April}+4.30,$$

(8)

$${T_o}^{May}=1.11{T_a}^{May}+5.79,$$

(9)

$${T_o}^{June}=1.15{T_a}^{June}+6.03,$$

(10)

$${T_o}^{July}=1.18{T_a}^{July}+5.09,$$

(11)

$${T_o}^{August}=1.17{T_a}^{August}+3.86,$$

(12)

$${T_o}^{September}=1.13{T_a}^{September}+1.82,$$

(13)

$${T_o}^{October}=1.06{T_a}^{October}+0.25$$

(14)

where T_a is daily air temperature and T_o is daily operative temperature. That is, daily air temperature is used to calculate daily operative temperature, but there are different regression equations for each month. The coefficients change with climate; they are smaller in cold and greater in hot climates. The presented ones are for the climate of the Hungarian lowland.

3.3. Other Methods Used in This Study

The significance of the Pearson correlation coefficients was decided by random sampling following the work of Pitman [44]. Random results are created 100,000 times, and values are resampled with the permutation testing method in order to keep the original distribution of the results. Calculation and visualization was carried out using the R (version 4.2.3.) [45] and the Python (version 3.10.5.) [46] programming languages.

4. Results

First the relationship between operative temperature and water temperature is analyzed. Then, the number of bath days and beach days is presented for each year. At last the monthly number of beach days is assessed for each year.

4.1. Relationship Between Operative Temperature and Water Temperature

The relationship between operative temperature and water temperature is presented in Figure 2 for the days when wind speed is suitable for lakeside activities. This means 3868 days out of the total 4922 days. It can be seen that when operative temperature is over 25 °C, water temperature is between 12 °C and 30 °C. The right side of the figure–where T_o is over 25 °C but T_w can be too cold (under 20 °C)—represents beach days. The upper right corner of the figure–where both T_o and T_w meet the criteria—represents bath days. The Pearson correlation between the two variables is high (0.89) and significant at the level of 0.01. The relationship between them can be characterized by a linear function, the form of which in the case of Siófok is T_w = 0.5974T_o + 4.2394. The correlation is also examined in each month separately, this is presented in

Table 2. The Pearson correlation coefficient between operative temperature and water temperature on days when wind speed is less than 5 ms⁻¹, for the time period of 2002–2024 for each month separately.

Month	April	May	June	July	August	September	October
Correlation	0.58	0.39	0.39	0.22	0.47	0.84	0.81

. The relationship between the two variables is the strongest in the autumn (around 0.8) and the lowest in the middle of summer (around 0.2). The correlation is always positive, so rising operative temperature means rising water temperature. Note that only days when wind speed is acceptable are considered.

This means that there is a strong linear relationship between T_o and T_w. T_w is also proportional to T_a, R_n and with the state when the wind speed is low (weak wind). T_o is an integral indicator for the whole near surface atmosphere. This regression equation may be used in later studies when using hourly data and some water temperature measurements are missing.

The correlation between wind speed and operative temperature is low and negative (−0.12). The reason for this is that higher wind speed contributes to higher convective and evaporative exchange between the human body and the environment, so T_o will not be so high as when the wind is lower.

4.2. Annual Number of Bath Days and Beach Days

The count of days that fit the criteria of T_o, T_w and f_s is presented in Figure 3a,b. The evolution of the number of bath days is without clear tendency, the best year for bathing was 2023 with 105 bath days, which is more than three months; the worst year was 2010 with 57 bath days, which is less than two months. As the curves show, in 2023, both operative temperature and water temperature were quite favorable for bathing, as opposed to 2010, when on very few days were both operative temperature and water temperature suitable. As no clear tendency is shown by the curves, this may not be attributed to climate change. In 2010 probably the huge amount of precipitation caused the unfavorably cold environmental conditions. Since 1901, the most precipitation occurred in this particular year [41]. As far as the year with the most bath days is concerned, it was 2023 and not 2024, although the temperature was higher in 2024 than in 2023, but the water temperature was lower. This may be attributed to the more precipitation in the holiday season this year, which caused Lake Balaton to not be as warm. In general, there are more days when T_o meets the criterium than days when T_w meets the criterium, but this is not always true (see years 2008 and 2009). As regards beach days, the best year was 2018 with 114 days, the worst year was 2021 with 72 days.

4.3. Monthly Number of Bath Days

Figure 4 presents the number of bath days for each month separately. Again, neither of the months show a clear tendency in these decades. It can be seen that in April and in October there were no bath days, the weather was only suitable for other lakeside activities, that is, there were only beach days. This means that operative temperature was suitable (over 25 °C), but water temperature was not acceptable for bathing (under 20 °C). This shows that in April Lake Balaton warms slowly, probably due to the usual late spring precipitation peak, and in October it becomes cold easily as it is shallower after the drier summer period. It also occurred in a few years that in May or in September there were no bath days, for example, in 2010 (note that this was the year with the most precipitation since 1901). The differences between August and September are large, although these are nearby months; the greatest difference is 28 days, which occurred in 2013. (In 2013, August was warmer and drier, and September was colder and wetter than the climatological average.) This difference is generally true for May and June as well. In May the air and water temperature may be lower than in June, due to the usual late spring precipitation peak in Hungary. The most bath days occurred in the summer months as expected. In summer the weather is generally very warm and often dry as well in Hungary, so Lake Balaton can warm easily. However, in 2018 there were more bath days in May than in June (22 vs. 20 days). Both months were very hot in this year, but May was much drier (by 85%) and June was much wetter (by 35%) than the climatological average. In the summer months, the median number of beach days is 68, the unbiased standard deviation of it is 6.4 days. Although July is considered to be the warmest summer month, the number of bath days is not always the greatest in the middle of summer, see, for example, 2003. In 2003, much more precipitation occurred in July (more than 80 mm) than in June or August (less than 30 mm).

5. Discussion

The tourist scheme introduced here expresses the number of bath days in a year or month, which is an objective measurement for tourist services. We presented an example of Lake Balaton. In this article, operative temperature is simply calculated from air temperature, but it depends upon isothermal net radiation and wind speed as well (see Equations (5)–(7)). We did not consider precipitation in this article as we assumed that when daily precipitation was over 1 mm, either T_o or wind speed did not meet the criteria. Another issue is that a few hours of precipitation do not ruin the whole beach day or bath day and cause minimal loss to tourism. The advantage of this scheme is that it uses only a few input variables and simple methods. A disadvantage is that the effect of precipitation cannot be examined in an explicit way, it would require hourly data. Considering these reasons, the effect of precipitation is only used for verification. More precipitation means that Lake Balaton becomes deeper, so it warms more slowly.

This study focused on the most popular lakeside activities common at Lake Balaton, that is, swimming and sunbathing. This enables us to omit the esthetic component used by several tourist indices. We do not consider sightseeing in the city or hiking to enjoy the landscape, since these are fewer common activities. Another popular lakeside activity is sailing, which would need hourly data to assess the proper wind speed, which is neither too low nor too high. This is beyond the scope of this study but can be a task of future research.

As regards Lake Balaton, Németh [24] used Tourism Climatic Index (TCI) [28] and Climate-Tourism-Information-Scheme (CTIS) [29,30] in order to assess the suitability of environmental conditions for lakeside activities. TCI is based on daily values of mean and maximum air temperature, mean and minimum relative humidity, wind speed, precipitation sum and sunshine duration, from which sub-indices are created that have a certain weight in the equation of TCI. The advantage of TCI is that it is versatile and considers several aspects through various meteorological variables. This may be a disadvantage as well, since it requires many input variables. Another drawback is the lack of human variables. The output of TCI is a “comfort level for a tourism activity”. The result is a subjective category which measures the potential if tourists visit the given place to pursue a certain activity. The number of beach days in a given period of time is more exact, it is not just information for tourists, it is also meant for tourist services. CTIS depends on threshold values of Physiological Equivalent Temperature (PET) [31,32], and meteorological variables such as cloud cover, vapor pressure, relative humidity, precipitation and wind speed. This index uses less variables than TCI but considers human thermal load as well. The output of CTIS is also a subjective category, mainly meant for tourists.

To our knowledge, the only study examining beach days on longer scale was carried out by Becker in South Africa, but they applied quite a different methodology [47]. They used Predicted Mean Vote (PMV) [9] for a person lying on the beach in swimsuit in order to create Beach Comfort Index. They stated that when people feel hot, they can get comfortable by going into the water from time to time. This study has not examined water temperature whether it is comfortable for bathing. The reason for this can be that in South Africa, close to the Equator the sea is relatively warm and not too cold during the holiday season.

6. Conclusions

This article examined when the environmental conditions were suitable for bathing and other lakeside activities between 2002 and 2024 in the city of Siófok, using operative temperature, water temperature and wind speed. It has been shown that the operative temperature model can be used for practical purposes, for instance for assessing beach days. It can also be stated that the consideration of water temperature is essential to assess when the environmental conditions are suitable for bathing.

Future goals of the authors include validating the study with using higher temporal resolution data in order to examine the effect of precipitation and to consider storm warnings issued by HungaroMet as well, so as to compare it with the given wind speed limit of 5 ms⁻¹. The authors also intend to validate the study by collecting data, such as the number of visitors or overnight stays, or the income of tourist services.