1 Introduction

Precipitation extremes have been intensifying with the warming of climate on a global scale and in most regions of the world (Sun et al. 2021). According to the Clausius–Clapeyron law, the sensitivity of precipitation to temperature increase is about 6–7% K−1 (Trenberth et al. 2003). Lenderink and van Meijgaard (2008) stated that this sensitivity may be much higher for precipitation in a subdaily scale, that is, close to 14% per degree of warming for 1 h of precipitation. Also Berg et al. (2013) found that the intensity of hourly precipitation extremes in response to higher temperature exceeded the Clausius-Clapeyron rate. In contrast, according to Ban et al. (2015) future heavy precipitation events may become more frequent and more intense, in both daily and hourly time scales, but this increase will be consistent with the Clausius-Clapeyron scaling. Myhre et al. (2019) presented an almost doubling of the total precipitation from intense events (the 95th to the 99.97th percentiles of precipitation) per degree of warming, mainly due to increases in their frequency. Short-duration rainfall is more likely to exhibit greater increases (Fowler et al. 2020).

The observed global increase in air temperature (Seneviratne et al. 2021) is clearly visible also in Poland. In the reconstructed time series of the average daily air temperature over 200 years, the temperature change surpassed 2 °C (Ustrnul et al. 2021). During the summer months, the number of hot days (with maximum temperature equal to or above 30 °C) in a large area of Poland has doubled. The length of these heatwaves has also increased significantly in the Wielkopolska region (Graczyk et al. 2019, 2022). Some high-intensity heatwaves may end in violent events, which generate heavy rainfall, especially when heatwaves are short and hot (You and Wang 2021). Studies from China presented by Chen et al. (2021) and Ning et al. (2022) also confirmed the increasing and accelerating trends in the contribution of hot weather to extreme precipitation events. As Hettiarachchi et al. (2018) showed, in a developed urban watershed future extremely intense short-duration storms will cause flooding at all locations of the studied area. Similarly, Zhou et al. (2018) projected a 52 % increase in urban flooding under a Representative Concentration Pathway (RCP) 8.5 scenario in China. Analysis of the 99th percentile of daily precipitation for Poland for the two periods of 1959–1988 and 1989–2018 of Pińskwar (2022) indicated an increase in the sensitivity of precipitation to temperature (5.26%/°C and 6.06%/°C, respectively), and therefore the potential for more extreme precipitation is growing. Increases in intense precipitation can pose a threat for both urban (Wan Mohtar et al. 2020) and rural areas (Choryński et al. 2022), but densely populated towns are especially vulnerable. The capacity of stormwater drainage systems is often insufficient to deal with rainwater flowing off impermeable surfaces after torrential rainfall. This is mostly because these systems were designed to cope with much less water and they are often poorly maintained. Therefore the concentration of infrastructure and capital (or lack thereof) in such areas increases potential losses.

In recent years, severe urban floods have occurred in Poland, not only causing material damage, as in Elbląg in 2017, where the River Kumiela flooded after daily precipitation of 81 mm (Konieczny et al. 2018), or in Poznań and Swarzędz (part of the Poznań agglomeration) in 2021, after daily precipitation of 79.4 mm and 136.9 mm, respectively, but also bringing fatalities, as during a flash flood in Gdańsk in 2001 where four people died, when the daily amount of precipitation was about 120 mm. In 2016, an event also in Gdańsk resulted in two fatalities after 160 mm of precipitation fell over 14 h (Majewski 2016; Skonieczna et al. 2021). More often after prolonged dry periods, precipitation may occur in a short time as concentrated rainfall. Such a correlation between drought and heavy precipitation was presented by Hänsel et al. (2019). In Poland, after the very pronounced spring drought of 2020, in June of that year abundant precipitation was recorded in many places in just a few days. This included daily rainfall of 152 mm observed in the Małopolska region (Jodłownik) or the aforementioned urban flood in the area of the Poznań agglomeration in June 2021 (Pińskwar et al. 2020; Skonieczna et al. 2021).

In preventing or limiting the effects of extreme meteorological phenomena, it is very important to indicate particularly vulnerable areas and the factors that have an impact on the occurrence of potential losses. Identifying the minimum rainfall thresholds to assess the risk of landslides triggering, which is crucial in warning strategies to mitigate geohydrological risk and reduce the socioeconomic damage, can serve as an example (Luino et al. 2020). Insurance data make it possible to create models supporting crisis management strategies (Cortès et al. 2018). These data are not always available and concern only losses of insured properties. In Poland, 60% of companies’ property is insured, and 60% of households are insured in case of a flood occurrence, including urban flash floods (Polish Chamber of Insurance 2019). Although detailed insurance-related information on losses due to heavy rainfall is missing, according to a report of the Polish Chamber of Insurance (2019), densely populated agglomerations in Poland (for example, Warszawa, Kraków, and Gdańsk) are the most exposed to the risk of extreme weather events. But the most socioeconomically vulnerable are the smaller urban areas, such as Włocławek, Tarnów, Inowrocław. This is due to the fact that larger towns have better living conditions and higher infrastructural potential to reduce the socioeconomic consequences of disasters. On the other hand, Voss and Wagner (2010) stated that smaller towns are in possession of different features that may be useful to deal with such threats.

There are a number of methods used to analyze flooding. Among them are approaches with hydrodynamic models (Guerreiro et al. 2017; Lu et al. 2022), hydrological modeling (Van der Knijff et al. 2008; Rojas et. al. 2012; Hirabayashi et. al. 2013), integrated hydrological-hydrodynamic modeling (Graham and Butts 2005; Wang et al. 2019), as well as methods based on neural network and deep learning models (Löwe et al. 2021; Zanetti et al. 2022). Another approach is exploratory data analysis (Gaitan et al. 2016), especially common on data provided by emergency services. In Poland, immediate consequences of extreme rainfall are handled by rescue services, especially firefighters. Formalized emergency services, that is, fire brigades, play a crucial role during the flood response process, participate in joint command-control systems, and are central to rescue and relief efforts (Anderson 2016; Coles et al. 2017; Kox et al. 2018). Information from the fire services may help in improving the overall warning system (Einfalt et al. 2016), spatial analyses of urban floods (Walczykiewicz and Skonieczna 2020), or investigation of the causes of urban floods (Veldhuis et al. 2011). Pardowitz and Göber (2017) documented that the correspondence of severe thunderstorm events (based on radar reflectivity) and places where operations of the fire brigades take place is quite good. Also Pardowitz (2018) demonstrated the usefulness of data such as topographic features, land use based on satellite images, urban infrastructure, and occurrence of local fire brigade operations in estimating local vulnerability to severe weather. The number of State Fire Service (SFS) unit interventions related to rainfall was also analyzed for the agglomeration of Kraków (Piotrowicz et al. 2020). In that area, for days with rainfall exceeding or equal to 20 mm, in 28% of the cases no intervention was recorded, but for 18% of the cases there was a large number of interventions (from 21 to 349). Therefore, in this research we also focused on data on State Fire Service unit interventions resulting from torrential rain or storms.

In Poland, the issuance of warnings against potentially dangerous rainfall results from a regulation that sets announcement thresholds for heavy rainfall of at least 30 mm for up to 12 h or 40 mm for up to 24 h (Journal of Laws 2019). Flash floods occur mostly on a local scale; therefore local authorities are the bodies that deal with the threat. In accordance with the Act on Crisis Management (Journal of Laws 2007), crisis management and coordination are in the hands of the head of authorities at a particular level of the country’s administration (municipal, district (in Polish: powiat), regional). However, in the case of operational issues, firefighting units are an important part of the crisis management system in Poland. The reaction to extreme events is mostly an activity undertaken by the rescue services, where State Fire Service units play a key role (Choryński et al. 2022). There are 76 SFS units in the Wielkopolska region that are specialized in different types of risk and rescue operations.

Flood risk is affected by both climatic and anthropogenic factors. In explaining urban flood risks, additional factors are involved, such as natural as opposed to the built environment, and the social characteristics of both urban and rural environments (Gaitan et al. 2016). Our study analyzed the number of interventions by State Fire Service units in the Wielkopolska region triggered by extreme precipitation. It focused on the estimation of predictors that describe local and regional vulnerability and exposure. Potential factors, beside hazard that is expressed by the number of days with extreme precipitation, include topographic features, land use information based on high-resolution data from the Database of General Geographic Objects (BDOO) with housing density, population density, distance from the homebase of a SFS unit, and mean terrain slope. We used a statistical model to determine the areas that are most vulnerable to extreme precipitation in the Wielkopolska region in the context of a warming climate. The analyzed area is very diverse in terms of population density and land use, but quite similar in other dimensions to lowland areas in Europe for the comparative analysis of the effects of global warming and the intensity of precipitation. Therefore the results of our research might be valuable to other researchers (and vice versa) despite having taken place at different scales of analysis or undertaken in other countries.

2 Materials and Methods

This section summarizes the data and methods used for the work presented in this article. First the Wielkopolska region is characterized, then data about interventions of the State Fire Service units and precipitation are discussed, and information about the statistical model used in research is presented.

2.1 Wielkopolska Region

In this study our focus is on the province of Wielkopolska, located in the mid-western area of Poland. The area is mostly lowland, much of which lies below 150 m above sea level (a.s.l.), except for a part in the south that rises up to 275 m a.s.l. (Fig. 1a). Wielkopolska is a part of the Central European Lowland, where most of the inhabitants live in larger cities; Poznań is Wielkopolska’s capital and its biggest urban area. The province covers 29,827 km2, which is 9.5% of the whole country of Poland. The region is inhabited by 3.491 million people, and the average population density is 117 people per km2, with the population density of built-up and urbanized areas of 2022 inhabitants per km2 (Statistics Poland 2020). With 226 municipalities, including 19 urban, 94 urban-rural, and 113 rural, the urbanization rate is about 53.73% and is below the Polish average, while urban areas represent 5.4% of the area of Wielkopolska. Agricultural land use covers most of the region (65.2%). Forests occupy a further 27.7% of the area (Fig. 1b).

Fig. 1
figure 1

The Wielkopolska region of Poland: a Digital elevation model (DEM) with the largest city of Poznań and four smaller cities; b Land cover based on Corine Land Cover CLC 2018 (https://clc.gios.gov.pl/index.php/clc-2018/o-projekcie)

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2.2 Interventions of the State Fire Service (SFS) Units

An important element of the study is information on firefighters’ interventions. This research is based on data obtained from the regional headquarters of the SFS in Poznań on interventions undertaken by 44 SFS units in the region of Wielkopolska. The data cover 12 years (2010–2021) and consist of 23 thousand records of interventions resulting from heavy rainfall. This intervention database includes information on the date of an intervention, the address as well as geographical coordinates, the name of the SFS unit, and the reason for intervention (mostly water pumping and infrastructure protection). These data were reviewed carefully in order to eliminate inadequate records. This relates mostly to mistakenly recorded entries not linked to extreme rainfall or without proper geographical coordinates or an address, which makes it impossible to indicate the precise location of the event.

In Poland, extreme precipitation events mainly occur during the warm part of the year, so the database was narrowed and analyses were conducted for the period from April to September. Every intervention was linked to the nearest precipitation station (data of 102 gauge stations were obtained from the Institute of Meteorology and Water Management (IMGW-PIB). A maximum radius of 20 km from a precipitation station to incident site was considered a representative distance, in which reduced the database to 17,793 interventions. In the case of extreme events, sometimes interventions were also undertaken on the following days. Figure 2 presents local headquarters of the State Fire Service in the Wielkopolska region and precipitation stations used in this study.

Fig. 2
figure 2

Wielkopolska Province, Poland: a Municipalities (communities) where units of State Fire Service (SFS) are located; b Precipitation stations

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2.3 Precipitation Data

In this study, observed daily precipitation datasets (subdaily resolution data were unavailable) from gauge stations provided by the Institute of Meteorology and Water Management (IMGW-PIB) in the Wielkopolska region were used. These records covered the three time intervals: 1961−2021, 1981−2021, and 2010−2021 (Fig. 2b). Data from 2010 to 2021 were linked to the interventions. A distance of up to 20 km was considered valid for representing precipitation at the intervention sites (in nearly 70% of cases the distance was within 10 km), and therefore among the 102 stations only data from 90 stations were used in the analyses.

All available precipitation data (also outside the research area, see Fig. 2b) were used for the best possible spatial coverage of the total number of days with extreme precipitation (20–50 mm) during 2010−2021. Data for 1961–2021 and 1981–2021 were used to identify changes in extreme precipitation. Analyses of change detection were conducted for 61 stations for the shorter period, 1981–2021, and for 41 stations with the longest dataset, 1961–2021 (Fig. 2b). Characteristics of extreme precipitation in the warm part of the year (April–September), such as the number and the average number of days with precipitation above different thresholds (20, 30, 40, and 50 mm), were examined.

The Mann-Kendall test was used to detect precipitation change. Although extreme events are rare and statistical methods may not detect the change, as stated by Frei and Schär (2001), it does not necessarily imply the absence of a trend. Their study also demonstrated the difficulty of determining trends of very rare events, and recommended a careful interpretation of statistically insignificant trend results. We used boxes and mean values to compare the periods 1961–2010 and 2010–2021, and 1981–2010 and 2010–2021.

2.4 Statistical Model

Following Pardowitz (2018), we set up a multiple linear regression model to analyze the predictability of the spatial distribution of long-term interventions based on potential impacting factors. Data were assigned to the administrative units (municipalities). The risks associated with climate and weather can be understood as an interaction of hazard, exposure, and vulnerability, which form a “risk triangle” (Crichton 1999). Risk in the model presented in this study (interventions km2) is a function of:

  • hazard expressed as the number of days with extreme precipitation (20, 30, 40, and 50 mm);

  • vulnerability factors such as population density per km2;

  • exposure including mean distance from SFS (calculated for municipalities based on distance from SFS to intervention), mean terrain slope, and land use factors based on information from BDOO, including proportion of dense, compact, and loose building cover, proportion of water bodies, forest and green areas, agricultural areas, and infrastructure areas (street, railroad tracks, airports).

Application of the model used in this research creates the potential for the identification of risk and improved crisis and emergency management.

$${\text{Risk}}\,({\text{interventions}}\,{\text{per}}\,{\text{km}}^{2} ) = b_{0} + b_{1} \times x_{1} + b_{2} \times x_{2} + \ldots + b_{14} \times x_{14}$$
(1)

where b0, b1, b2...b14 are the coefficients that can be interpreted as the average effect on risk of a one unit increase in predictor, holding all other predictors fixed; x1, x2, x3…x14 are predictors:

$$\begin{gathered} {\text{Vulnerability}}\quad\quad x_{{1}} {\text{ - Population density per km}}^{{2}} \hfill \\ {\text{Predictors related to exposure}}\left\{ \begin{gathered} \begin{array}{*{20}c} {x_{{2}} {\text{ - Proportion of dense building cover}}} \\ {x_{{3}} {\text{ - Proportion of compact building cover}}} \\ {x_{{4}} {\text{ - Proportion of loose building cover}}} \\ {x_{{5}} {\text{ - Proportion of water bodies}}} \\ {x_{{6}} {\text{ - Proportion of forest and green areas}}} \\ {x_{{7}} {\text{ - Proportion of agricultural areas}}} \\ {x_{{8}} {\text{ - Proportion of infrastructure areas }}\left( {{\text{streets}},{\text{ railroad tracks}},{\text{ airports}}} \right)} \\ {x_{{9}} {\text{ - Mean slope }}\left( \% \right)} \\ {x_{{{10}}} {\text{ - Mean distance from SFS }}\left( {{\text{km}}} \right)} \\ \end{array} \hfill \\ \hfill \\ \end{gathered} \right. \hfill \\ {\text{Predictors related to hazard}}\left\{ {\begin{array}{*{20}c} {x_{{11}} {\text{ - Number of days with precipitation }} \ge { 2}0{\text{ mm}}} \\ {x_{{{12}}} {\text{ - Number of days with precipitation }} \ge { 3}0{\text{ mm}}} \\ {x_{{{13}}} {\text{ - Number of days with precipitation }} \ge { 4}0{\text{ mm}}} \\ {x_{{{14}}} {\text{ - Number of days with precipitation }} \ge { 5}0{\text{ mm}}} \\ \end{array} } \right. \hfill \\ \end{gathered}$$

Based on the lowest values of Akaike and Bayesian Information Criterion (AIC, BIC) and the highest value of the multiple coefficient of determination R2, the set of predictors were established.

The model was applied to sub-datasets for rural municipalities, urban municipalities, and for the area of Poznań district. The R package relaimpoFootnote 1 was used to calculate measures of relative importance for each of the predictors in the model (Groemping 2006). Metrics were not normalized. Global validation of linear model assumptions from the R package gvlmaFootnote 2 (Peña and Slate 2006) was used to indicate whether the model assumptions are acceptable—whether the relationship between the dependent and independent variables is roughly linear; skewness and kurtosis assumptions show that the distribution of the residuals are normal; link function checks to see if the dependent variable is continuous and the heteroskedasticity assumption means the error variance is equally random. The procedure from the test can also be used to detect unusual observations.

3 Results

In this section interventions of State Fire Service units during extreme precipitation events are presented, followed by changes in extreme precipitation for the Wielkopolska region.

3.1 Interventions of State Fire Service (SFS) Units during Extreme Events in 2010–2021

Figure 3 shows population density and spatial location of interventions in towns and municipalities in the Wielkopolska region for the period April–September 2010–2021. As expected, high numbers of interventions mostly coincide with densely populated areas. The most vulnerable area is the region’s largest city, Poznań (1139 interventions).

Fig. 3
figure 3

Wielkopolska Province, Poland: a Populations at the end of 2020 in municipalities in Wielkopolska Province according to Statistics Poland (2020); b Number of interventions within a distance below 20 km to the nearest precipitation station for Wielkopolska during April−September 2010−2021

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Among the 17,793 interventions of SFS units in the Wielkopolska region for the analyzed period, over a quarter of them took place during a very wet year with significant flooding in Poland, 2010 (4664), and among them 54% in May (2508). The 2010 flood was a very destructive event, followed by a wet spring with highly saturated soil. Precipitation in May was long-lasting and high in volume for several days. Moreover, extreme precipitation this year also occurred in June, July, and August (Kundzewicz et al. 2012). The lowest number of interventions (516) was recorded in the very dry year of 2015.

On average, within the analyzed period, the highest number of interventions (5864) occurred during July. Especially wet was July 2011 (1201), when the highest daily precipitation took place (20 July 2011 at 160.7 mm), recorded at two stations (12 km away from each other). But this extreme rainfall triggered only 29 interventions in five municipalities, where the total percentage of forest and agricultural land cover for four of them is over 95%, and for their towns is 70%. In April 2020 there was no intervention, when the weather was very dry (Pińskwar et al. 2020). The highest number of interventions during one day (530) occurred on 24 July 2010. This one day accounted for nearly 3% of all 2010−2021 interventions. On that day the highest Pdaily (59.5 mm) was recorded (also 59 mm and 58 mm); jointly 14 interventions for these 3 stations. A number of the interventions resulted from heavy rainfall that occurred also the day before, because the highest P2day reached up to 122 mm (and above 100 mm occurred at another 4 stations), resulting in 31 interventions taking place in the area from 3 to 12 km around these 5 gauge stations. Altogether 60 stations are linked to the interventions, median for recorded precipitation at these stations for Pdaily was 27 mm and 61 mm for P2day. For the whole month of July there were 703 interventions.

The three highest daily numbers of interventions in relation to one station (that is, in a maximum radius of 20 km from a precipitation station to incident) occurred in 2021: (1) The highest number of interventions took place on 9 July when the area around station Sobótka experienced 99 interventions. These actions represented responses to a Pdaily of 18.8 mm, which together with the precipitation of the previous day amounted to a P2day of 69.5 mm, and resulted in close to a third of the 326 interventions for the whole Wielkopolska region. (2) The second occurred on 22 June when 85 interventions were generated by a Pdaily of 136.9 mm at Gruszczyn, near Poznań. (3) The third most active intervention scene, also on 22 June, responding to a Pdaily downpour of 79.4 mm, took place in Poznań itself. The common denominator of all of these record-setting events was a densely populated and urbanized landscape with a large percentage of impermeable surface areas. The distance between the stations of Poznań and Gruszczyn is only 16 km. At the Poznań station 1-hourly total precipitation was 75.2 mm, and the 30-minute total reached 59.4 mm. But there also were areas elsewhere in Poznań where during 10 mins periods almost 25 mm of rain fell (Skonieczna et al. 2021). On that day in the Wielkopolska region there were 277 interventions, in Poznań 108, in Swarzędz, home to station Gruszczyn, 38.

3.2 State Fire Service (SFS) Units’ Interventions in Towns, Standardized to 10 Thousand Inhabitants, and in Rural Areas

Calculation of the number of interventions per 10,000 inhabitants (Fig. 4a) reveals a different picture to Fig. 3b: the highest proportional volumes of interventions also occurred in smaller towns. The number of interventions increases from about 65 (the mean value) per 10,000 inhabitants in the smallest towns (below 10,000 inhabitants) to over 80 interventions in towns of size 15,000 to 25,000 people, where the risk of flooding appears to be the highest (Fig. 4b). Along with the increase in the number of inhabitants, the number of interventions decreased and was 21 in Poznań—the largest city in the region with more than 500,000 inhabitants.

Fig. 4
figure 4

Wielkopolska Province, Poland: a Number of interventions per 10,000 inhabitants; b Number of interventions per 10,000 inhabitants in towns of various population sizes

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Rural areas, although to a lesser extent than towns, are also at risk of potential losses associated with heavy rainfall. The number of interventions by SFS units increases with the population density, although the relationship is not simple and a relatively large number of interventions also took place in municipalities with a low population density (Fig. 5a). In municipalities located in the immediate vicinity of a large town (dots with a black line in Fig. 5a), the population density is much higher than in municipalities with a predominance of agricultural land use. There are also more densely developed areas and multidwelling houses. This results in a clearly higher—even several times—number of interventions per km2 than in less populated areas (Fig. 5b).

Fig. 5
figure 5

Wielkopolska Province, Poland: Correlation between the number of interventions per km2 and the population density per km2 in rural municipalities: a all cases; b for municipalities that belong to Poznań agglomeration

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3.3 Extreme Rainfall Hazard—Spatial Distribution of the Number of Days with Extreme Precipitation in 2010–2021

The main factor of flash flood risk is the hazard, that is, extreme rainfall. Differences in extreme rainfall hazard between municipalities in the analyzed region of Wielkopolska are quite large (Fig. 6). The least threatened area in terms of hazard for all analyzed cases is located in the northeastern part of the region. Conversely, for all cases the most at risk area is situated in the northwestern part. For the number of days with 20, 30, and 40 mm of rainfall, the highest values are observed in the central and southwestern part of the province. In the case of days with precipitation exceeding 50 mm, the western part of the region is the most exposed area, while in some areas in the eastern part such extreme precipitation was not recorded during 2010 to 2021.

Fig. 6
figure 6

Spatial distribution of the total number of days with extreme precipitation during 2010−2021 in Wielkopolska Province, Poland: a 20 mm; b 30 mm; c 40 mm; d 50 mm

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3.4 Multiple Linear Regression Model Results

The model includes a set of 14 predictor variables (Table 1), explaining from 55% of the variance in the spatial pattern of interventions for towns, through 72% for villages, to 99% for Poznań and adjacent municipalities forming the district of Poznań.

Table 1 Results from multiple linear regression models
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Correlation analysis of each of the predictors shows that population density per km2 plays the most important role in explained variation for all three models. The second most important is the proportion of dense building. For interventions in rural municipalities and in Poznań district the presence of infrastructure areas such as streets, railroad tracks, and airports is also significant. Distance from a SFS unit plays a role as well for interventions in urban municipalities. Extreme precipitation seems to have an impact in relation to dense buildings: in rural areas, where there is less dense cover, high precipitation plays a role (number of days with P ≥ 50 mm), because only heavy rainfall is responsible for the emergence of intervention. Along with an increasing proportion of dense cover, lower precipitation is responsible for triggering intervention, for example, 40 mm in towns or 30 mm in Poznań district.

Figure 7 presents the result of estimated interventions from the model and recorded observations shown as mean interventions of SFS per year (from April to September) for the period 2010–2021. Differences between modeled data and observations revealed that there was 51% match within the range of −1 to 1 day difference. There were more underestimated data (reddish color) than overestimated (bluish color): 18% and 15% for 1 to 3 days and 10% and 6% for above 3 days, respectively.

Fig. 7
figure 7

Observed yearly mean interventions and model estimates and differences between model results and observations in Wielkopolska Province, Poland: a–c for rural municipalities; d–f for urban municipalities; g–i for the district of Poznań

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3.5 Trend Detection in Extreme Precipitation

The total number of extreme precipitation days calculated for all stations shows an increasing trend, although statistically insignificant trends are noted for the thresholds of 20, 30, 40, and 50 mm for the period 1981–2021 at 61 stations. For a longer period, 1961–2021 and for 41 stations, the trend is slightly increasing or without changes. Figures 8 and 9 present boxes with the total number of days with extreme precipitation for different time periods. Natural variability was high, but the last years were characterized by more days with extreme precipitation. The yearly mean value of extreme precipitation days for the period 2010–2021 was much higher than for the periods 1961–2010 and 1981–2010. Table 2 presents these findings. The mean number of days with precipitation equal to or above 50 mm doubled between 1981−2010 and 2010−2021 (from 0.12 to 0.24 day/year) and nearly doubled between 1961−2010 and 2010−2021 (from 0.14 to 0.23 day/year). All minimum (except for days with P ≥ 50 mm for the period 1961−2021) and half maximum values for the 2010−2021 period are much higher than for the previous 50 and 30 years.

Fig. 8
figure 8

Number of days for the Wielkopolska region with extreme precipitation for a longer period (1961−2021) and smaller number of stations (41): a with P ≥ 20 mm; b with P ≥ 30 mm; c with P ≥ 40 mm; d with P ≥ 50 mm

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Fig. 9
figure 9

Number of days for the Wielkopolska region with extreme precipitation for a shorter period (1981−2021) and greater number of stations (61): a with P ≥ 20 mm; b with P ≥ 30 mm; c with P ≥ 40 mm; d with P ≥ 50 mm

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Table 2 Mean, maximum, and minimum (total from all stations) numbers of days exceeding a threshold for analyzed stations for the periods 1961−2021 (41 stations) and 1981−2021 (61 stations) located in the Wielkopolska region
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4 Discussion

Exceptionally extreme precipitation of nearly 100 mm, especially those events that lasted for a short time, triggered up to 100 interventions during the day of occurrence in a large town, such as Poznań, and up to 40 interventions in smaller towns, such as Swarzędz. On the other hand, very extreme precipitation taking place outside urbanized areas triggered in most cases only a few interventions.

An interesting finding is that in small and medium-sized towns the risk of losses related to heavy rainfall is higher than in the largest towns of the region (per 10,000 inhabitants). This is probably because they have the same features that increase this risk, such as dense development and large areas of impermeable surfaces, while, at the same time, they have less ability to reduce the risk, such as extensive rainwater drainage systems and multidwelling housing, as well as fewer material resources. Yet smaller towns possess different resources, mainly social capital and governance structure, that make them able to deal with extreme weather events by setting up a specific type of effective community resilience through good crisis communication as well as previous experiences in dealing with extreme meteorological events (Choryński et al. 2022).

In this research, population density per km2 and proportion of dense building stock have played a major role in determining highly vulnerable areas. Paliaga et al. (2019) pointed out that reducing risk is essential at those areas with high inhabitant density, strong anthropogenic modifications, and high hazard. In research conducted for Berlin, where population density was not a predictor, the degree of urbanization (both expressed by the areal coverage of housing and indicated by continuous urban fabric areas) was a key predictor (Pardowitz 2018). For urban municipalities also distance from SFS units matters.

Increase in vulnerability to extreme rainfall, which triggers firefighters’ interventions, is related to urban sprawl together with a decrease of permeable surfaces due to development of built-up areas. The Wielkopolska region is also subject to development processes of ever larger suburban areas. The issue of urban sprawl is very clear when looking at Poznań and the surrounding 25 municipalities, which form the Poznań Metropolitan Area. This agglomeration covers 10% of the area of the region, but is inhabited by about 1/3 of the population of the province. According to Budner (2018), between 2007 and 2016 the number of people who inhabited central Poznań decreased by almost 25 thousand (ca. 4% of the population), whereas population of the municipalities of the Poznań Metropolitan Area increased by more than 59 thousand. This illustrates that apart from high migration inflow, urban sprawl is an issue here. About 80% of the migration from Poznań is in the direction of the suburbs in the city’s immediate vicinity. Within the decade analyzed by Budner, the housing area increased by 147.4% in the closest municipalities; for comparison, in Poznań the built-up area increased by 112.1% (Budner 2018). This intensification process has consequences in the form of local flooding for such communities and contributes to the extension of the so-called “urban” flooding to suburban areas (Mrozik 2022). Nevertheless, the capital of the region is not the only city that is subject to the problem of urban sprawl. In Wielkopolska there are four major cities that form districts (the second level of local administration) by themselves. These are Poznań, Leszno, Konin, and Kalisz. In all of them the migration balance between 2015 and 2020 was negative (Statistical Office in Poznań 2021). On the other hand, three districts surrounding these towns have a positive migration balance, apart from the vicinity of Kalisz, where it is approximately neutral.

As far as the problem of urban sprawl is considered by the Polish administration, that is, the Ministry of Infrastructure and Construction and the Institute of Urban Development in Kraków (2016), the issue of a reduction in permeable surfaces seems to be unnoticed, which is opposite to the already long-lasting trends in Western Europe. Both problems are interlinked (Sung et al. 2013). Mencwel (2020) gave a number of examples of how the revitalization processes in Poland are concentrated around replacing more or less natural green areas in towns with concrete surfaces. This problem concerns not only large towns (Jaszczak et al. 2022). Apart from high investment and maintenance costs (municipalities of all sizes have to take into account rainwater and sewage system maintenance and improvement) development also brings the risk of urban floods (Sohn et al. 2020), because increasingly the stormwater is not able to infiltrate into the soil.

Detection of changes in extreme events is difficult due to strong natural variability and the occurrence of rare events (Frei and Schär 2001). Furthermore, local conditions influence the results and do not give a consistent picture of changes (Seneviratne et al. 2021). Pińskwar (2022) found that for Poland there is an increasing trend in dew point series and the correlations between simple daily intensity index and the annual number of days in which daily precipitation and annual mean dew point temperature have been positive in most cases.

In our work, only the period from April to September was considered. In the future, more extreme events might be expected also in the cooler half of the year. Nowadays in Poland yearly maximum precipitation mostly occurs during the summer, but the contribution of precipitation in other seasons to the yearly maximum is increasing, especially from the autumn (25%) and the spring (6%). A slight participation of winter maxima, although small, has nearly doubled in comparison to the two periods of 1959–1988 and 1989–2018 (Pińskwar 2022). According to projections for the future, under both RCP scenarios (RCP2.6 and RCP8.5), the majority of Europe except the southern part will experience large increases of extreme precipitation. Additionally, short-duration extreme precipitation may prevail more than long-duration extremes and the magnitude of most extreme events (100- and 200-year) may increase more than the precipitation generated by storms with 5- and 10-year return periods (Huo et al. 2021). Tabari et al. (2020) in their study for Europe, based on the CMIP6 multimodel ensemble median during 1995–2014, stated that warming has an impact on larger increases in very extreme precipitation anomalies (99.5% percentile), in all seasons.

As Seneviratne et al. (2021) stated, increases in heavy precipitation over cities may be linked to urbanization. Urban development intensifies extreme precipitation, especially in the afternoon and early evening. Among possible mechanisms that contribute to this increase are (1) increases in atmospheric moisture due to horizontal convergence of air associated with the urban heat island effect; (2) increases in condensation due to urban aerosol emissions, which provide nucleuses of condensation; and (3) urban structures that impede atmospheric motion. As shown in the research on the Netherlands, this may impact the occurrence frequency of maximum precipitation at urban meteorological stations compared to the nearby rural stations, and 7% more precipitation may occur in cities than in rural areas (Golroudbary et al. 2018). Lu et al. (2019) studied the impact of the effect of urban expansion on an increase of extreme precipitation intensity and its recurrence levels under different return periods. They found that the recurrence levels of R×1day and R×5day increased more for highly urbanized stations than for slightly urbanized or rural stations. Li et al. (2021) found that the effect of urbanization on extreme precipitation is significant only for convectional extreme precipitation, while for frontal or typhoon extreme rainfall the impact is low. The urbanization effects on extreme precipitation also depend on regional location: a larger impact is observed for inland sites than for coastal areas (Lin et al. 2020). Considering the frequency and intensity of extreme urban precipitation, Marelle et al. (2020) found that frequency increases far more than intensity (by +16%) for yearly maximum daily precipitation and by +26% for hourly extremes. Intensities of the yearly and hourly maximum events increase much less. Also important is how rare the event is: for the rarest intensity the frequency of extremes is increasing more, and this is more visible for hourly than for daily extremes.

Projections of changes in extreme precipitation for Polish conditions (Pińskwar and Choryński 2021) show that in the near future (2021−2050) for the two scenarios RCP4.5 and RCP8.5, one can expect that maximum daily precipitation will be higher by 20−40 mm for the Wielkopolska region. Similarly, maximum 3-day precipitation totals may increase by 25−50 mm for both RCPs. Also, in the near future during the whole 30 years, there will be 25 additional 3-day periods with precipitation totals greater than 50 mm. This means that such periods will be nearly 1 more in every year than nowadays in the area of this research for both RCPs.

5 Limitations of the Study

The present study is limited by several factors. The most prevailing are those connected to data availability and their proper quality. The results are dependent on predictors, which can be more or less adequate. Moreover, one may find more predictors that can have an influence on the number of interventions. In the study of Kaźmierczak and Cavan (2011), a set of 26 indicators known to influence the vulnerability of people to flooding was used, which showed that the most diverse and poorest communities are the most exposed to flooding. In our study only one predictor linked with vulnerability (population density per km2) has been used, together with 13 exposure and hazard predictors. But information about rainwater and sewage system operation was not included. The study of Mobini et al. (2022) indicated that the main drivers of flood damages were rainfall amount and failure of mechanisms, like clogging by tree roots, leaves, waste, and sediment in the drainage system. Sewage system type is also important: flood damage originating from a combined surface runoff water and sewage system connection were greater than from systems that separated the surface stormwater from the sewage system (44 and 17%, respectively). Moreover, based on the available data, this study used meteorological station precipitation data to generate spatial information about the average number of days with intense precipitation in the study area, and this can provide some over- or underestimation.

This study was based on data from the State Fire Service, but in smaller localities often the emergency management system is based on Voluntary Fire Brigades (VFB) for which data on interventions are lacking. Therefore for these places the number of interventions may be underestimated. Additionally, when a property is at risk, people can react on their own initiative and may not call the formal, established emergency services. Kaźmierczak and Cavan (2011) stated that greater knowledge about vulnerability, hazard, and exposure may help to address the risks.

6 Conclusion

The analysis in this study demonstrated that the most populated and urbanized towns in the Wielkopolska region are at the highest risk in the event of an extreme precipitation occurrence. These places have the highest number of interventions in total. Moreover, interventions in towns, per 10 thousand inhabitants, indicate a greater risk of flash floods also in smaller towns. Towns of between 15 and 25 thousand inhabitants experienced the highest proportional volumes of interventions. The main factor influencing the number of interventions in such towns is their population density per km2, which is similar to these in larger towns. Factors such as population density per km2, proportion of dense building cover, infrastructure areas, and number of days with extreme precipitation affect the number of interventions needed to cope with flooding and its impacts.

It must be stressed that databases of emergency services similar to those used in this study, which contain detailed information on interventions, can be a valuable resource on the spatial distribution of the risk posed by extreme weather events and their consequences, including flash floods. The model used in this research could potentially be used to identify the areas at risk where no data on interventions are available and might be helpful in risk management.

The period 2010–2021 was characterized by a higher number of days with heavy precipitation in comparison to the previous periods 1961–2010 and 1981–2010. Increasing suburbanization, a rising proportion of impermeable surfaces, and the impact of climate change are of considerable importance in urban flooding. It is necessary to prepare towns and villages to develop the potential for a higher amount of rainwater absorption. One can mention here the concept of sponge cities, well recognized in the case of the Chinese metropolitan areas (Zevenbergen et al. 2018; Yin et al. 2022). Nevertheless, in the case of much smaller Polish towns, this idea is still a case of discussions on the appropriateness and adequacy of this measure.