Open Access
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*Sustainability*
**2019**,
*11*(24),
6886;
https://doi.org/10.3390/su11246886

Article

Failure Analysis of the Water Supply Network in the Aspect of Climate Changes on the Example of the Central and Eastern Europe Region

Department of Water Supply and Sewerage Systems, Faculty of Civil, Environmental Engineering and Architecture, Rzeszow University of Technology, Al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland

^{*}

Author to whom correspondence should be addressed.

Received: 18 October 2019 / Accepted: 30 November 2019 / Published: 4 December 2019

## Abstract

**:**

The consequences of climate changes are felt by society every day. A sudden increase or decrease in air temperature, increasingly frequent, extreme weather phenomena can cause enormous economic damage to countries and cities. The occurrence of random weather phenomena and their negative impact on technical infrastructure nowadays are the basic problem related to ensuring the safety of the functioning of each system. Climate changes and significant air temperature amplitudes have a direct impact on the functioning of the critical infrastructure of cities, which includes collective water supply systems (CWSS). The paper presents the impact of climate change on the failure of a water supply network. Correlation between failure rate and air temperature was determined. This was used to determine the number of failures for the near 2036–2050 and distant 2086–2100 future in terms of climate change (temperature increase). The results confirm the thesis known from the literature that the failure rate decreases as the temperature increases. For forecasted periods as a result of temperature rise due to climate change, the reduction of the number of water pipe failures is expected in the range of 1.22% to 2.35% for the 2036–2050 period and from 2.96% to 8.66% for the 2086–2100 period, depending on the development of Representative CO

_{2}Concentration Scenarios (RCP). The decrease in the total number of failures will have an impact on the increase in the reliability and safety of water supply to consumers.Keywords:

climate change; failure rate; reliability; water supply system## 1. Introduction

According to data from the Millennium Ecosystem Assessment organization, climate changes will be one of the most important causes affecting biodiversity in every ecosystem by the end of this century [1]. The problem of climate change has also been recognized by the United Nations (UN) at the level of national safety due to the fact that most humanitarian aid activities have been associated with extraordinary situations as a result of climate changes. Fortunately, today’s technology and research conducted around the world allow us to get to know and understand the mechanisms that shape climate changes better than we did ten years ago. Any climate changes have serious, often tragic consequences in every part of the world, affecting almost every social group. The consequences of climate changes are felt by society every day, such as a sudden increase or decrease in air temperature, melting glaciers as well as increasingly frequent, extreme weather phenomena [2]. These effects usually cause enormous economic damage to countries and cities. They carry risks associated with the proper functioning of underground infrastructure of cities, necessary for the normal functioning of their inhabitants. The occurrence of random weather phenomena and their negative impact on technical infrastructure are nowadays the basic problem related to ensuring the safety of functioning of each system. It should be noted, however, that estimating the impact of various atmospheric factors, such as air temperature, on the proper functioning of technical systems and the impact on their failure rate, would allow decision-makers to make decisions that increase the safety of, e.g., water supply for urban and rural population [3,4,5,6,7,8,9,10,11,12,13]. Climate changes and significant air temperature amplitudes have a direct impact on the functioning of the critical infrastructure of cities, which includes collective water supply systems (CWSS). The definition of critical infrastructure (CI) has been clearly defined in the Crisis Management Act [14]. Critical infrastructure means systems and component objects important for the safety of the country and its citizens, including the continuous work of public administration, institutions and entrepreneurs [14]. According to this provision, critical infrastructure includes the following systems: energy supply systems, fuel and energy resources, communication systems, tele-information network systems, financial systems, food supply systems, water supply systems, health protection systems, transportation systems, rescue systems, systems ensuring the continuity of public administration activities, systems of production, storage and use of chemical and radioactive substances, including pipelines for dangerous substances. The main task of CWSS is to provide recipients with water of quality in accordance with applicable standards, appropriate pressure, appropriate quantity and at any time of day or night [15]. One of the key elements of CWSS is the water supply network that is part of the Water Distribution Subsystem and has a direct impact on the safety of water supply to consumers. It should be remembered that the water supply network works with variable parameters of both pressure and flow, which is associated primarily with time-varying water distribution. A significant problem occurring in many municipal water supply systems is also significant oversizing of the water supply network, which causes a decrease in water flow speed, silting up the pipelines and, as a consequence, adverse flow conditions, which may cause a deterioration of water quality in the water supply network.

There are few studies taking into account the impact of temperature on the failure of the water supply network, therefore continuous monitoring taking into account the impact of atmospheric factors on the failure rate of the water supply network is necessary [4,16,17,18,19,20,21,22,23]. As available literature on the subject shows, the factors affecting the damage of the water supply network are the material of the pipes, the age of the network, the function of the pipes, water pressure in the network and the quality of repair works. As a result of research [18,24,25] it was also found that the type of ground and its instability have an impact on the condition of the water supply network and the frequency of failures. Research carried out in this area confirm the impact of seasons, air and ground temperature on the failure rate of water pipes [26,27,28,29]. In the era of climate changes and thus changes in hydrogeological conditions, the foundation of the water supply network can also have a significant impact on changes in the value of failure rate. This impact should be recognized in order to verify the technical conditions for the design and operation of the water supply network. The analysis of the impact of air temperature on the depth of ground freezing and thus on the damage of water pipes can be used in the development of more durable installation materials, resistant to significant temperature changes in both air and ground. The aim of the work was to examine the impact of climate change on the number of failures in water supply networks in the Central and Eastern Europe region with a moderate warm climate in the perspective of 2036–2050 and 2086–2100. The paper also presents the impact of selected parameters characterizing the water supply network, i.e., the material and diameter of the pipe, on the number of failures and its variability during the year in the form of the average monthly number of failures. The paper proves the thesis about a correlation between the air temperature and failure of water pipes. The results presented in the paper can be used in the process of law amending related to the designing and construction of water supply networks, especially in terms of determining the new foundation depth of water supply pipes depending on the zones of the ground frost heave.

## 2. Materials and Methods

This research was carried out for cities located in Central and Eastern Europe. The climate of the research area is determined, according to the Köppen–Geiger climate classification [30], in general as a type of continental climate with warm summers and as its subtype Dfb—humid continental climate with mild summers and rainfall throughout the year [30]. For this climate subtype, the average temperature of the coldest month is equal to or below −3 °C, while the average temperature of the warmest month is above 10 °C, but does not exceed 22 °C. The rainfall is distributed evenly throughout the year. Progressive climate changes increasing deviations from the identified climate subtype have been observed in recent years. There are more and more severe floods and troublesome periods of drought due to disturbances in temperature distribution or rainfall throughout the year. The occurrence of intensified weather phenomena is observed: During winter—strong frosts—and during summer periods of prolonged heat waves and violent storms [31].

The water supply network is made of water pipes and is a basic element of CWSS. The main task of the water supply network is to supply the consumers with water of the right quality and quantity, under the required pressure, at any time. Failures of the water pipes have a direct impact on the loss of safety and reliability of CWSS operation [7]. The first stage of the analysis was the preparation of historical data regarding the water supply network failures. The failure logs from two cities located in south-eastern Poland—City A (2004–2018) and City B (2006–2015)—were analysed, where 4529 water supply network failures were reported. Simultaneously, daily air temperature was assigned to the dates of failure, based on measurement data from the databases of the National Institute of Meteorology and Water Management. The frequency of failures at a given temperature in the range <t
where:

_{i};t_{i+1}) and the frequency of days with a given temperature in the range <t_{i};t_{i+1}) were determined. Then, the values of the failure rate depending on the temperature were calculated according to Equation (1) [32]:
λ

_{Ti}= n_{Ti}/d_{Ti}, number of failures/day at T_{i}temperature,- Ti—this index refers to the temperature range <t
_{i};t_{i+1}, and its value is the average temperature for a given range, - λ
_{Ti}—the failure rate at a given air temperature T_{i}, - n
_{Ti}—number of failures occurring at daily air temperature T_{i}, and - d
_{Ti}—number of days with daily air temperature T_{i}.

The next step was to examine the existence of a correlation between the failure rate and the daily air temperature T
where:

_{i}. It was observed that for extreme temperatures there are large fluctuations in the failure rate values, which significantly distorts the correlation result. This is due to the fact that there were few cases of days with such temperatures. The lack of a sufficient number of measurements negatively affected the correlation result. Therefore, the minimum required number of measurements—d_{min}, which should be taken into account during calculations—was determined. For this purpose, the average number of days and standard deviation of the number of days per unit temperature, were determined. Their difference (according to Dependence 2) is the minimum number of measurements (days) required to include the measurement in the correlation calculations. This problem is also taken into account, among others, in Reference [32].
d

_{min}= d_{av}− d_{σ}, days,- d
_{av}—the average number of days per unit temperature (169), and - d
_{σ}—the standard deviation of the number of days per unit temperature (146).

The determined minimum required number of measurements is d
where:

_{min}= 23. Temperatures that during the analysed period were recorded for less than 23 days were omitted in the calculations. For the remaining measurements, a graph of the relationship between the failure rate and the daily air temperature Ti was created. Using Excel software, the correlation coefficient R, the determination coefficient R^{2}and the linear regression equation, using the least squares method, were determined. For the obtained results, a test for the significance of the correlation coefficient, in accordance with the method presented in [32], was carried out. The result of this test will confirm the existence of a negative correlation between the failure rate and daily air temperature and will determine the confidence level for the linear regression model. The search for a negative correlation between these variables will confirm the thesis that as the temperature increases, the failure rate and the number of failures decrease. This test uses the t-Student statistics [33]. After making the null and alternative hypothesis, the test parameter t should be determined, according to Equation (3) [34]:
t = r∙√(n − 2)/√(1 − r

^{2}),- r—the linear correlation coefficient, and
- n—sample size.

For the purposes of the test, the critical area depending on the adopted hypotheses for a given level of significance and n−2 degrees of freedom, should be determined [33]. If the test parameter t belongs to the area, then the null hypothesis should be rejected in favour of the alternative hypothesis, whereas if the test parameter does not belong to the critical area, we do not reject the null hypothesis. After determining the truth of the hypothesis, one should determine the confidence level for the regression model by reducing the level of significance α and then determine a new critical area and check whether the test statistics belong to it. The whole procedure should be repeated until it is impossible to reject the null hypothesis.

Maintaining the thesis that as the temperature increases the failure rate decreases [35], it was assumed that for the highest temperature covered by the analysis, i.e., <25;26) °C, the air temperature does not affect the size of the failure rate. This assumption was also presented in [32,36]. The failure rate obtained for this temperature range (according to the linear regression model) is the “absolute” failure rate of the pipes, independent of the temperature change.

In the next stage, the percentage share of failure rate dependent on the temperature change in the total failure rate for temperatures in the tested range, on the basis of the obtained linear regression model, according to the Equation (4) [32], was determined:
where:

λ

_{%}= (ax + b − λ_{b})/(ax + b), number of failures/day at T_{i}temperature,- λ
_{%}—the percentage share of the failure rate dependent on the temperature change in the total failure rate, - ax + b—the linear regression equation, and
- λ
_{b}—the absolute failure rate.

The failure rate dependent on the temperature change for individual temperature ranges from −11 °C to 25 °C, using the regression model and historical data, according to the Equation (5) [32], was calculated:
where:

λ

_{TiH}= λ_{%}∙λ_{Ti}, number of failures/day at T_{i}temperature,- λ
_{TiH}—the failure rate at a given air temperature T_{i}, associated with the temperature changes, - λ
_{%}—the percentage share of the failure rate related to the temperature changes, and - λ
_{Ti}—the failure rate at a given air temperature T_{i}.

Representative CO

_{2}Concentration Scenarios (RCPs) were used to determine the temperature values over the forecasted periods (2036–2050 and 2086–2100). RCP scenarios refer to the level of greenhouse gas emission in 2100 compared to 1750 (pre-industrial times). There are four RCP scenarios [37]:- RCP 2.6—inhibiting greenhouse gas emission to the level of 2.6 W/m
^{2}, - RCP 4.5 and RCP 6.0—stabilization of greenhouse gas emission at 4.5 W/m
^{2}or 6.0 W/m^{2}, and - RCP 8.5—high increase in greenhouse gas emission to 8.5 W/m
^{2}.

In this work, the RCP 4.5 and RCP 8.5 scenarios were used. The RCP 4.5 scenario corresponds to the level of emission declared in the national declarations submitted to the Paris Agreement, which aimed to reduce the EU greenhouse gas emission by at least 40%, while the RCP 8.5 scenario was chosen as the most extreme [37].

Projections of the temperature changes were determined as part of the CHASE-PL project using the empirical and statistical downscaling method with a 90% confidence level for mean values [37]. The determined predicted temperature increase for the forecasted periods and RCP 4.5 and RCP 8.5 scenarios are summarized in Table 1.

Temperatures during the forecasted periods were calculated as the sum of historical temperature from the reference period 1986 to 2000 and temperature increase, according to the Equation (6):
where:

t

_{p}= t_{h}+ Δt_{s}, °C,- t
_{p}—predicted temperature, - t
_{h}—historical temperature, and - Δt
_{s}—predicted temperature increase.

Based on the predicted temperature values, the frequency of their occurrence in the periods 2036–2050 and 2086–2100 was calculated. Knowing the number of days with the temperature in the tested range, it was possible to determine the number of failures caused by the temperature changes during the forecasted periods, according to the Equation (7):
where:

n

_{fTi}= d_{fTi}∙λ_{TiH}, number of failures,- nfTi—number of failures in the forecasted period f (2036–2050 or 2086–2100) for a given air temperature T
_{i}, - d
_{fTi}—number of days in the forecasted period f (2036–2050 or 2086–2100) with daily air temperature T_{i}, and - λ
_{TiH}—the failure rate at a given air temperature T_{i}, associated with the temperature changes.

The forecasted change in the number of failures was determined as a percentage in relation to the number of failures resulting directly from the temperature change and the total number of failures, according to the Dependencies (8) and (9):
where:

$${\%}_{\mathrm{T}\mathrm{i}}=1-\frac{{\displaystyle \sum _{\mathrm{i}=-10,5}^{\mathrm{n}=25,5}({\mathsf{\lambda}}_{\mathrm{T}\mathrm{i}\mathrm{H}}\cdot {\mathrm{n}}_{\mathrm{f}\mathrm{T}\mathrm{i}})}}{{\displaystyle \sum _{\mathrm{i}=-10,5}^{\mathrm{n}=25,5}({\mathsf{\lambda}}_{\mathrm{T}\mathrm{i}\mathrm{H}}\cdot {\mathrm{n}}_{\mathrm{T}\mathrm{i}})}}$$

$${\%}_{\mathrm{C}}=1-\frac{{\displaystyle \sum _{\mathrm{i}=-10,5}^{\mathrm{n}=25,5}({\mathsf{\lambda}}_{\mathrm{T}\mathrm{i}\mathrm{H}}\cdot {\mathrm{n}}_{\mathrm{T}\mathrm{i}})-{\displaystyle \sum _{\mathrm{i}=-10,5}^{\mathrm{n}=25,5}({\mathsf{\lambda}}_{\mathrm{T}\mathrm{i}\mathrm{H}}\cdot {\mathrm{n}}_{\mathrm{f}\mathrm{T}\mathrm{i}})}}}{4432}$$

- $\sum _{\mathrm{i}=-10,5}^{\mathrm{n}=25,5}({\mathsf{\lambda}}_{\mathrm{T}\mathrm{i}\mathrm{H}}\cdot {\mathrm{n}}_{\mathrm{T}\mathrm{i}})$—e total number of failures resulting from the temperature changes in the period 2004–2018,
- $\sum _{\mathrm{i}=-10,5}^{\mathrm{n}=25,5}({\mathsf{\lambda}}_{\mathrm{T}\mathrm{i}\mathrm{H}}\cdot {\mathrm{n}}_{\mathrm{f}\mathrm{T}\mathrm{i}})$—e total number of failures resulting from the temperature changes over the forecasted period 2036–2050 or 2086–2100,
- 4432—the total number of failures in the period 2004–2018, for the temperature range covered by the analysis <−11, 26) °C.

## 3. Results

The first stage of research was to analyse the impact of the selected parameters characterizing the water supply network on the number of failures. Figure 1; Figure 2 present the impact of pipe material and diameter on the number of water supply network failures and its variability during the year, in real operating conditions in 2008–2018.

Figure 3 presents the frequency of days with daily air temperature T

_{i}(representing a given temperature range <t_{i};t_{i+1}) and the frequency of failures for a given temperature T_{i}. The presented temperature range from −11 to 26 °C was determined on the basis of the minimum number of required measurements (Equation (2)), which was 23 recorded measurements. If for a given temperature the number of measurements was smaller, these data were not taken for further analysis.Air temperature is one of many factors affecting failure occurrence of water supply network [35]. It directly affects the ground temperature, on which the depth of freezing depends and the changes in tension in the ground that then occur, which may lead to pipe damage [18]. The occurrence of water supply network failure is also influenced by a number of other factors, e.g., hydraulic conditions of network operation (working pressure), technical condition of pipes (the material and age of pipes), hydrogeological conditions (ground corrosion), etc.

The highest values of the failure rate were recorded for temperatures below 0 °C. In Figure 3 we can observe that the number of failures for negative temperatures is high in relation to the number of recorded measurements (days). It confirms the statement that during negative temperatures the failure rate will be higher than for other temperatures. Table 2 presents the calculations of the failure rate for the tested temperature range from −11 to 26 °C.

Figure 4 presents a graph of the dependence of the failure rate on the daily temperature. The graph also shows the linear regression model with the equation and the value of the determination coefficient R

^{2}. The linear regression model calculated using Excel is described by the equation
y = −0.0105∙x + 0.6182.

The negative directional coefficient (a = −0.0105) indicates a negative correlation between the studied variables. It means that as the temperature increases, the failure rate decreases. The correlation coefficient of R = −0.782 and the determination coefficient of R

^{2}= 0.6116 were obtained. The value of R^{2}means that 61.16% of the changes in the value of variable y can be explained by the change in the value of x, while the remaining 38.84% of the changes depends on other factors.To determine the degree of linear regression uncertainty and confirm the existence of a statistical relationship in the form of a negative linear correlation, a correlation coefficient significance test was performed. The test specifies the null hypothesis H

_{0}and the alternative hypothesis H_{1}:**Hypothesis**

**1.**

ρ = 0—no correlation between the examined variables;

**Hypothesis**

**2.**

p < 0—there is a negative correlation between the examined variables.

The critical area for n − 2 degrees of freedom and significance level α = 0.05 was determined as a set (−∞; t

_{crit}= −1.68957>. For the tested correlation coefficient r = −0.782 and sample size n = 37 the value of the test statistics was obtained (Equation (3)) as t = −7.42264. It is within the critical area; therefore, the null hypothesis should be rejected in favour of the alternative hypothesis. The existence of a negative correlation between the examined variables was proved. By reducing the level of significance α, the null hypothesis should be rejected in favour of the alternative, to get a 1-α confidence level of 99.999995%. If the level of significance is further reduced, the alternative hypothesis cannot be accepted by rejecting the null hypothesis. It can therefore be concluded that the obtained linear regression model describes the studied variables very well.The obtained equation describes the changes in the failure rate depending on the daily temperature, taking into account all the factors that affect the failure. In order to isolate the values of the failure rate which will only be affected by temperature changes, Equations (4) and (5) were used. It was assumed that for the highest analysed unit temperature range <25;26) °C, the influence of temperature on the occurrence of failure was negligible. The value of the failure rate for this temperature is according to damage the regression model λ

_{25,5}= λ_{b}= 0,35 failure/day at T_{i}temperature. This is the value of the absolute failure rate, which is constant for each of the analysed temperature T_{i}and includes the occurrence of failure due to all other factors except air temperature.Table 3 presents the calculations of the isolated failure rate directly related to changes in daily air temperature.

The temperature increase for the forecasted periods 2036–2050 and 2086–2100 was based on two representative CO

_{2}concentration scenarios RCP 4.5 and RCP 8.5, according to Table 1. Temperature increase values according to RCP scenarios refer to temperature values from the reference period 1986–2000. Figure 5 presents the frequency of days with daily temperature T_{i}(in the range <t_{i};t_{i+1}) from −11 °C to 26 °C for the reference period 1981–2000, the analysed period 2004–2018 and for the forecasted periods 2036–2050 and 2086–2100, depending on the RCP scenario.Depending on the development of the RCP scenario, the temperature increase will fluctuate between +1.5–+2.1 °C for the period 2036–2050 and +2.4–+5.3 °C for the period 2086–2100. Therefore, the incidence of days for individual temperature ranges will change. The number of days with freezing temperatures will decrease, while more days with higher temperatures will be observed. Therefore, the failure rates and the number of failures associated with the occurrence of negative temperatures will be reduced. Comparing historical data for the reference period 1986–2000 and the examined data from the period 2004–2018, we can already observe a decrease in the number of days with temperatures below 0 °C, and an increase in the number of days with temperatures above 20 °C. The forecasted scenarios further emphasize these changes, shifting the shape of the frequency curve towards higher temperatures. Based on the frequency of days with a given T

_{i}temperature and knowledge of the relationship between the failure rate resulting from direct temperature change and the daily air temperature T_{i}, the predicted number of failures was determined depending on the RCP scenario and the forecasted period. The results are presented in Table 4.Figure 6 presents the forecasted number of failures directly related to the daily air temperature for the periods 2036–2050 and 2086–2100, depending on the temperature increase, according to RCP 4.5 and RCP 8.5 scenarios. A significant decrease in the number of failures with future temperature increase was observed, as shown in Table 5.

For the forecasted period 2036–2050, the reduction in the number of failures related to the daily air temperature may range from 3.74% to 7.20%, while for the forecasted period 2086–2100 the reduction in the number of failures may be from 9.07% to 26.57%, depending on the development of the RCP scenario. For the total number of failures for the period 2036–2050, the reduction may range from 1.22% to 2.35%, while for the period 2086–2100, from 2.96% to 8.66%.

## 4. Discussion

From the data available in the literature it can be concluded that the phenomenon of water supply network failure is influenced by many factors. The first group are factors of internal origin that are associated with the processes of design, construction and operation of the network, i.e., the used material, the diameter of the pipe, the age of the pipe, the function of the pipe, water pressure in the network, flow rate and quality of performed repair work. The second group are external factors, which include environmental impact, e.g., ground instability, ground and groundwater corrosivity, climate impact, season, the air temperature, the ground temperature, the ground freezing depth and water temperature in the water supply system. The paper presents the impact of daily temperature on the failure of the water supply network. The research was based on actual data on water supply network failures in the Central and Eastern Europe region with a moderate warm climate. It has been shown that in winter months the most often failed pipes made of cast iron and in summer months pipes made of steel. The average number of failures of pipes made of plastic (PE and PVC) are on an equal level throughout all months of the year. It can be seen from the performed analysis that 80, 100 and 150 mm diameter pipes failed in winter, while 32, 40, 50 and 80 mm diameter pipes in summer months. It has also been shown that there is a correlation between the daily air temperature and the failure rate. It is observed that for days with low negative temperatures higher failure rates are obtained than for days with higher positive temperatures, hence the occurrence of failures on days with low negative temperatures is more likely. Based on the determined linear regression equation, it can be stated that for each temperature drop by 1 °C, the failure rate increases by 0.0105.

The obtained correlation at a later stage allowed forecasting the number of failures and its changes for the near future 2036–2050 and the far future 2086–2100 due to the increase in daily temperatures resulting from climate change. The RCP climate models for the Polish region, developed in the CHASE-PL climate research program, were used to determine the frequency pattern for temperatures during the forecasted periods [37]. The analysis showed that a reduction in the total number of water supply network failures between 1.22% and 2.35% should be expected for the near future, while for the distant future, 2086–2100, between 2.96% and 8.66%, depending on the development of the RCP scenario. Considering the case of failures resulting directly from daily temperature changes, the obtained reductions in their number for the period 2036–2050 are 3.74%–7.20%, and for the period 2086–2100, 9.07%–26.57%, depending on the RCP scenario. These results can be used when carrying out renovation work and making repair plans for networks with planned long service life (from 50 to 100 years). Forecasting for such a long period is always burdened with a certain degree of uncertainty. The obtained results represent two extreme cases of RCP scenario development; therefore, for further research it is recommended to adopt the average size reduction of the number of failures, i.e., for the period 2036–2050, 1.79%, and for the period 2086–2100, 5.81%. Taking climate change into account when planning investments related to the repair of water supply networks can primarily bring financial benefits (savings), social benefits (fewer repairs burdensome for consumers) and environmental benefits (less waste).

## 5. Conclusions

A review of the literature indicates several factors affecting the failure of the water supply network. The main ones are the material and diameter of the pipes, the network age, the function of the pipe, water pressure in the network, quality of repairs carried out, ground instability and its type, impact of seasons, the air temperature, the ground temperature and associated with them the ground freezing depth. The main purpose of the work was to present the impact of air temperature, as one of the factors shaping climate change, on the change in the number of water supply network failures in the region of Central and Eastern Europe with moderate warm climate, in the near (2036–2050) and distant (2086–2100) future. In both cases, an increase in air temperature associated with progressive global warming will be observed. The frequency of failure will change depending on the air temperature. The reduction in the number of failures will range from 1.22% to 2.35% for the period 2036–2050 and from 2.96% to 8.66% for the period 2086–2100. The decrease in the total number of failures will have an impact on the increase in the reliability and safety of water supply to consumers. The work complements the current state of knowledge in the field of water supply network failure. The correlation model between failure rate and daily temperature was determined on the basis of real data. It can be used to determine the failure frequency of networks in connection with weather forecasts or future climate changes for water supply networks located in the region of Central and Eastern Europe with a warm moderate climate. Certain failure reduction values for periods of near and distant future can be used by the water-work companies operating in similar climatic conditions.

## Author Contributions

Conceptualization, B.T.-C., I.P. and J.Ż.; methodology, J.Ż.; validation, B.T.-C., I.P. and J.Ż; formal analysis, I.P., J.Ż.; resources, I.P., J.Ż.; data curation, I.P., J.Ż.; writing—original draft preparation, I.P., J.Ż.; writing—review and editing, B.T.-C., I.P. and J.Ż.; visualization I.P., J.Ż.; supervision, B.T.-C.; project administration, B.T.-C.; funding acquisition, B.T.-C.

## Funding

This research was funded by subsidies for statutory activity (number: DS.BR.19.001).

## Conflicts of Interest

The authors declare no conflict of interest.

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**Figure 1.**The average number of failures related to water supply network material and months (years 2008–2018).

**Figure 5.**Frequencies of days with temperatures in the range <t

_{i};t

_{i+1}for the analysed periods.

**Figure 6.**Forecasted number of failures related directly to the daily air temperature during the forecasted periods 2036–2050 and 2086–2100 for RCP 4.5 and RCP 8.5 scenarios.

**Table 1.**Temperature increase in the periods 2036–2050 and 2086–2100 according to RCP 4.5 and RCP 8.5 scenarios [37].

Period: | 2036–2050 | 2086–2100 | ||
---|---|---|---|---|

Representative CO_{2} Concentration Scenarios: | RCP 4.5 | RCP 8.5 | RCP 4.5 | RCP 8.5 |

Temperature increase Δt_{i} °C: | +1.5 | +2.1 | +2.4 | +5.3 |

T_{i} | Temperature Range | d_{Ti} | n_{Ti} | λ_{Ti} |
---|---|---|---|---|

°C | °C | - | - | number of failures/day at T_{i} temperature |

−10.5 | <−11;−10) | 32 | 24 | 0.75 |

−9.5 | <−10;−9) | 50 | 45 | 0.90 |

−8.5 | <−9;−8) | 49 | 36 | 0.73 |

−7.5 | <−8;−7) | 71 | 47 | 0.66 |

−6.5 | <−7;−6) | 92 | 80 | 0.87 |

−5.5 | <−6;−5) | 114 | 67 | 0.59 |

−4.5 | <−5;−4) | 135 | 93 | 0.69 |

−3.5 | <−4;−3) | 121 | 86 | 0.71 |

−2.5 | <−3;−2) | 196 | 135 | 0.69 |

−1.5 | <−2;−1) | 224 | 156 | 0.70 |

−0.5 | <−1;0) | 269 | 198 | 0.74 |

0.5 | <0;1) | 337 | 190 | 0.56 |

1.5 | <1;2) | 312 | 182 | 0.58 |

2.5 | <2;3) | 322 | 187 | 0.58 |

3.5 | <3;4) | 317 | 170 | 0.54 |

4.5 | <4;5) | 356 | 178 | 0.50 |

5.5 | <5;6) | 300 | 157 | 0.52 |

6.5 | <6;7) | 343 | 158 | 0.46 |

7.5 | <7;8) | 313 | 150 | 0.48 |

8.5 | <8;9) | 306 | 123 | 0.40 |

9.5 | <9;10) | 294 | 131 | 0.45 |

10.5 | <10;11) | 333 | 104 | 0.31 |

11.5 | <11;12) | 346 | 143 | 0.41 |

12.5 | <12;13) | 339 | 116 | 0.34 |

13.5 | <13;14) | 346 | 140 | 0.40 |

14.5 | <14;15) | 376 | 153 | 0.41 |

15.5 | <15;16) | 409 | 171 | 0.42 |

16.5 | <16;17) | 391 | 157 | 0.40 |

17.5 | <17;18) | 352 | 163 | 0.46 |

18.5 | <18;19) | 342 | 144 | 0.42 |

19.5 | <19;20) | 310 | 136 | 0.44 |

20.5 | <20;21) | 262 | 109 | 0.42 |

21.5 | <21;22) | 232 | 108 | 0.47 |

22.5 | <22;23) | 155 | 63 | 0.41 |

23.5 | <23;24) | 120 | 65 | 0.54 |

24.5 | <24;25) | 75 | 37 | 0.49 |

25.5 | <25;26) | 60 | 30 | 0.50 |

T_{i} | Temperature Range | λ_{%} | λ_{TiH} | Number of Failures |
---|---|---|---|---|

°C | °C | - | number of failures/day at T_{i} temperature | - |

−10.5 | <−11;−10) | 0.52 | 0.39 | 9 |

−9.5 | <−10;−9) | 0.51 | 0.46 | 21 |

−8.5 | <−9;−8) | 0.51 | 0.37 | 13 |

−7.5 | <−8;−7) | 0.50 | 0.33 | 15 |

−6.5 | <−7;−6) | 0.49 | 0.43 | 34 |

−5.5 | <−6;−5) | 0.48 | 0.28 | 19 |

−4.5 | <−5;−4) | 0.47 | 0.33 | 30 |

−3.5 | <−4;−3) | 0.47 | 0.33 | 28 |

−2.5 | <−3;−2) | 0.46 | 0.31 | 42 |

−1.5 | <−2;−1) | 0.45 | 0.31 | 49 |

−0.5 | <−1;0) | 0.44 | 0.32 | 64 |

0.5 | <0;1) | 0.43 | 0.24 | 46 |

1.5 | <1;2) | 0.42 | 0.24 | 44 |

2.5 | <2;3) | 0.41 | 0.24 | 44 |

3.5 | <3;4) | 0.40 | 0.21 | 36 |

4.5 | <4;5) | 0.39 | 0.19 | 34 |

5.5 | <5;6) | 0.38 | 0.20 | 31 |

6.5 | <6;7) | 0.36 | 0.17 | 26 |

7.5 | <7;8) | 0.35 | 0.17 | 25 |

8.5 | <8;9) | 0.34 | 0.14 | 17 |

9.5 | <9;10) | 0.32 | 0.14 | 19 |

10.5 | <10;11) | 0.31 | 0.10 | 10 |

11.5 | <11;12) | 0.30 | 0.12 | 18 |

12.5 | <12;13) | 0.28 | 0.10 | 11 |

13.5 | <13;14) | 0.27 | 0.11 | 15 |

14.5 | <14;15) | 0.25 | 0.10 | 15 |

15.5 | <15;16) | 0.23 | 0.10 | 17 |

16.5 | <16;17) | 0.21 | 0.09 | 13 |

17.5 | <17;18) | 0.19 | 0.09 | 15 |

18.5 | <18;19) | 0.17 | 0.07 | 11 |

19.5 | <19;20) | 0.15 | 0.07 | 9 |

20.5 | <20;21) | 0.13 | 0.05 | 6 |

21.5 | <21;22) | 0.11 | 0.05 | 5 |

22.5 | <22;23) | 0.08 | 0.03 | 2 |

23.5 | <23;24) | 0.06 | 0.03 | 2 |

24.5 | <24;25) | 0.03 | 0.01 | 1 |

25.5 | <25;26) | 0.00 | 0.00 | 0 |

∑: | 1445 |

**Table 4.**Forecasted number of failures related to temperature changes depending on the forecasted period and RCP scenario.

T_{i} | Temp. Range | Number of Days | λ_{TiH} | Number of Failures | ||||||
---|---|---|---|---|---|---|---|---|---|---|

2036–2050 | 2086–2100 | 2036–2050 | 2086–2100 | |||||||

°C | °C | RCP 4.5 | RCP 8.5 | RCP 4.5 | RCP 8.5 | Number of Failures/ Day at T _{i} Temperature | RCP 4.5 | RCP 8.5 | RCP 4.5 | RCP 8.5 |

−10.5 | <−11;−10) | 20 | 16 | 13 | 17 | 0.39 | 8 | 6 | 5 | 7 |

−9.5 | <−10;−9) | 37 | 27 | 23 | 18 | 0.46 | 17 | 12 | 11 | 8 |

−8.5 | <−9;−8) | 35 | 37 | 37 | 17 | 0.37 | 13 | 14 | 14 | 6 |

−7.5 | <−8;−7) | 51 | 45 | 35 | 14 | 0.33 | 17 | 15 | 12 | 5 |

−6.5 | <−7;−6) | 59 | 46 | 54 | 24 | 0.43 | 25 | 20 | 23 | 10 |

−5.5 | <−6;−5) | 101 | 67 | 57 | 40 | 0.28 | 29 | 19 | 16 | 11 |

−4.5 | <−5;−4) | 106 | 112 | 108 | 38 | 0.33 | 35 | 37 | 35 | 12 |

−3.5 | <−4;−3) | 127 | 118 | 110 | 52 | 0.33 | 42 | 39 | 36 | 17 |

−2.5 | <−3;−2) | 147 | 121 | 123 | 56 | 0.31 | 46 | 38 | 39 | 18 |

−1.5 | <−2;−1) | 198 | 171 | 149 | 110 | 0.31 | 62 | 53 | 46 | 34 |

−0.5 | <−1;0) | 236 | 235 | 210 | 115 | 0.32 | 76 | 76 | 68 | 37 |

0.5 | <0;1) | 314 | 241 | 239 | 119 | 0.24 | 76 | 58 | 58 | 29 |

1.5 | <1;2) | 349 | 342 | 313 | 159 | 0.24 | 85 | 84 | 77 | 39 |

2.5 | <2;3) | 377 | 366 | 357 | 215 | 0.24 | 89 | 87 | 85 | 51 |

3.5 | <3;4) | 369 | 376 | 372 | 238 | 0.21 | 79 | 80 | 79 | 51 |

4.5 | <4;5) | 350 | 351 | 373 | 327 | 0.19 | 68 | 68 | 72 | 63 |

5.5 | <5;6) | 350 | 361 | 360 | 360 | 0.20 | 69 | 71 | 71 | 71 |

6.5 | <6;7) | 294 | 327 | 343 | 375 | 0.17 | 49 | 55 | 57 | 63 |

7.5 | <7;8) | 277 | 288 | 294 | 370 | 0.17 | 47 | 48 | 49 | 62 |

8.5 | <8;9) | 270 | 258 | 262 | 347 | 0.14 | 37 | 35 | 36 | 47 |

9.5 | <9;10) | 275 | 279 | 273 | 345 | 0.14 | 40 | 40 | 40 | 50 |

10.5 | <10;11) | 324 | 288 | 280 | 291 | 0.10 | 31 | 28 | 27 | 28 |

11.5 | <11;12) | 311 | 331 | 323 | 274 | 0.12 | 38 | 41 | 40 | 34 |

12.5 | <12;13) | 339 | 318 | 320 | 260 | 0.10 | 33 | 31 | 31 | 25 |

13.5 | <13;14) | 344 | 355 | 345 | 281 | 0.11 | 37 | 38 | 37 | 30 |

14.5 | <14;15) | 371 | 342 | 329 | 332 | 0.10 | 38 | 35 | 33 | 34 |

15.5 | <15;16) | 377 | 369 | 376 | 318 | 0.10 | 36 | 36 | 36 | 31 |

16.5 | <16;17) | 464 | 415 | 391 | 352 | 0.09 | 40 | 36 | 34 | 30 |

17.5 | <17;18) | 426 | 458 | 465 | 329 | 0.09 | 38 | 41 | 42 | 30 |

18.5 | <18;19) | 381 | 392 | 411 | 359 | 0.07 | 28 | 29 | 30 | 26 |

19.5 | <19;20) | 350 | 374 | 380 | 412 | 0.07 | 24 | 25 | 26 | 28 |

20.5 | <20;21) | 322 | 354 | 352 | 463 | 0.05 | 18 | 19 | 19 | 25 |

21.5 | <21;22) | 230 | 287 | 321 | 401 | 0.05 | 12 | 14 | 16 | 20 |

22.5 | <22;23) | 177 | 190 | 212 | 384 | 0.03 | 6 | 6 | 7 | 13 |

23.5 | <23;24) | 124 | 160 | 171 | 348 | 0.03 | 4 | 5 | 5 | 11 |

24.5 | <24;25) | 65 | 113 | 122 | 310 | 0.01 | 1 | 2 | 2 | 5 |

25.5 | <25;26) | 56 | 47 | 62 | 209 | 0.00 | 0 | 0 | 0 | 0 |

∑: | 1391 | 1341 | 1314 | 1061 |

Period | 2036–2050 | 2086–2100 | ||
---|---|---|---|---|

Representative CO_{2} concentration scenarios | RCP 4.5 | RCP 8.5 | RCP 4.5 | RCP 8.5 |

Change in the number of failures dependent from temperature change % | −3.74 | −7.20 | −9.07 | −26.57 |

Total change in the number of failures % | −1.22 | −2.35 | −2.96 | −8.66 |

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