Water provision planning on the basis of human population growth forecasts: A case study of the City of uMhlathuze, KwaZulu-Natal Province, South Africa

The most critical municipal service that rural and urban communities require is a reliable and adequate supply of water (Dighade et al. 2014; Javadinejad et al. 2019). In South Africa (SA), water boards, district and local municipalities have the sole mandate, as water services authorities, to supply and distribute the minimum required amount of potable water in their areas of jurisdiction. According to the Constitution of the Republic of SA, every citizen is entitled to a certain amount of water regardless of their ability to pay for it (South African Government 1996).

SA is currently facing a serious water distribution challenge as municipalities across the country are finding it hard to meet increased demands for water, largely driven by an increase in human population growth in both rural and urban areas (Department of Water and Sanitation 2018). As a result, the average water available per day per person becomes limited because, as the human population increases, consumption patterns change, economies develop and pressures on natural water resources increase which in turn affects water distribution in rural and urban areas (Sonaje & Joshi 2015; Oki & Quiocho 2020; Loubser et al. 2021).

The human population in King Cetshwayo District Municipality (KCDM), particularly in the City of uMhlathuze, has been continuously growing ever since the first Census data collection in the year 1996, followed by Censuses collected in 2001, 2011 and the Community Survey (CS) conducted in 2016 (Statistics South Africa 2016). In just over five years between 2011 and 2016, the human population growth increased by over 22%. With the City of uMhlathuze being one of the fastest developing cities in SA and the third economic and tourism hub in the KwaZulu-Natal (KZN) province, a rapid increase in human population is probable in the coming years, largely to be influenced by its growing industrial development zone (IDZ), adjacent to the Richards Bay harbour (Aurecon South Africa 2015a, 2015b; City of uMhlathuze 2020).

The main economic sectors in the City of uMhlathuze include manufacturing (45.9%), mining and quarrying (11.6%), financial, real estate and business (10.7%), community, social and personal services (10.4%), transport and communication (9.1%), trade (6.3%), as well as agriculture, forestry, and fishing (3.2%) (KZN Provincial Government Communication 2022). Large industrial companies in the municipality include Mondi Richards Bay, South 32/BHP Billiton, Tronox, Fairbreeze mine, Foskor, Hillside and Bayside Aluminium and the Richards Bay Coal Terminal (RBCT).

Other significant industrial companies within the municipality include the Tongaat-Hulett sugar mill, uMfolozi sugar mill and Mpact (previously known as Mondi Felixton), both in Felixton. In addition to the industrial development in the City of uMhlathuze, there are large-scale agricultural activities, which consist principally of citrus and sugarcane, both irrigated, and commercial forestry or plantations owned mostly by Sappi and Mondi.

Water is observed to be available in the reservoir tanks at the City of uMhlathuze; however, it is not sufficient for the demand, as the number of people requiring water is greater than what the reservoir tanks can supply, especially in rural areas (Zulu 2017). The findings of a research conducted by Mthethwa (2018) has also indicated that the City of uMhlathuze is grappling with poor and inadequate water infrastructure. In a case where the demand for water is human population-driven, high population growth levels put pressure on the amount of water available, leading to per capita water shortages (Mohammed & Sahabo 2015; Parks et al. 2019; Mnisi 2020; Mulwa et al. 2021). Consequently, there is a great demand on water sources in the City of uMhlathuze, especially on the uMhlathuze River, due to water demands from Empangeni and Richards Bay (City of uMhlathuze 2021).

The findings of the studies conducted by Kassa (2017), Parks et al. (2019), Oki & Quiocho (2020), Faye (2021), Heidari et al. (2021) and Mulwa et al. (2021) have indicated that an increase in human population growth also puts pressure on existing water infrastructure that was built decades ago. As a result, water does not reach users due to burst pipes and leaks in the water distribution network (Gunawan et al. 2017). SA's water distribution infrastructure is estimated to be 39 years old because it was mostly built during the apartheid regime (Department of Water and Sanitation 2017; South African Institution of Civil Engineering 2017). Not only has the infrastructure aged, but there has been further deterioration as a result of poor maintenance and operation which leads to increased water demand.

It is important to note that water demand will be impossible to manage in the future unless municipalities are able to address the present water distribution challenges; including water security, water demand management, water conservation, equity, water efficiency and sustainable consumption (Department of Water and Sanitation 2018; Development Bank of Southern Africa 2022). Increased water demand leads to water shortages for a few days and the net results are often communities seeking alternatives through illegal water connections (Karuaihe et al. 2016). Consequently, illegal water connections affect the pressure or volume supply of water in pipelines, either to or from the public communal standpipe or reservoir tank (Water Integrity Network 2020).

To this end, it is assumed that the demand of water in the City of uMhlathuze will continue to increase as the human population increases. Therefore, greater efforts are needed to ensure that water is adequate for every household in both rural and urban areas. For these reasons, the goal of this study is twofold: first to predict human population growth over a 50-year period and secondly, on the basis of human population growth forecasts, the number of additional reservoir tanks to be used to meet a possible increase in water demand will then be determined.

Prediction of human population growth is important to plan service delivery accordingly, that is to estimate basic human needs such as demand for food, water supply and distribution infrastructure, power supply, and transportation amongst other things (Gulseven 2016). Moreover, it plays an important role in decision making for the socio-economic and demographic development of the region.

Most research on human population prediction involves the application of traditional demographic and statistical models like the Exponential growth model, Verhulst Logistic growth model, Grey prediction model of population growth based on a logistic approach, Malthusian growth model, linear regression and non-linear regression models (e.g., Gompertz growth models), and Box-Jenkins time series models to name a few, which often need to be adjusted (Ofori et al. 2013; Kulkarni et al. 2014; Omony 2014; Wei et al. 2015; Patel & Prajapati 2016; Zabadi et al. 2017; Mondol et al. 2018; Stephano & Jung 2019; Tong et al. 2020; Wang et al. 2021).

However, this study proposes the application of machine learning-inspired automated time series models like the Auto-Regressive Integrated Moving Average (ARIMA) model, Error Trend Seasonal (ETS) model, and Box-Cox Transformations, ARMA errors, Trend and Seasonal components (BATS) model, to predict the growth in human population over a 50-year period. The proposed time series forecasting models are automated because they do not need any human judgment and therefore adjust automatically (Anvari et al. 2016; Hyndman & Athanasopoulos 2018).

The originality of this study therefore incorporates an important dimension, such as formulating our own linear programming model to determine the provision of reservoir tanks to satisfy human water demand for the next 50 years. The formulation of a new linear programming model will be useful in terms of planning for building new water infrastructure in the future, based on the prediction of human population growth and its direction of expansion so that a basic water consumption requirement of about 25 litres per person per day within a 200 metres (m) radius from the public standpipe is achieved. It is considered a minimum; therefore, it is not considered adequate for a full, healthy, and productive life (Department of Water and Sanitation 2018).

The municipality's total land area covers 795,971 km² and incorporates Richards Bay, Empangeni, eSikhaleni, Ngwelezane, eNseleni, and Vulindlela (City of uMhlathuze 2020). Climatic conditions in the municipality are characterised by a warm to hot and humid subtropical climate, with warm, moist winters (City of uMhlathuze 2020). Average daily maximum temperatures range from 29 °C in January to 23 °C in July, and extreme temperatures can reach more than 40 °C in summer. The average annual rainfall is 1228 millimetres (mm), and 80% of the rainfall occurs between spring and summer, that is from September to February (City of uMhlathuze 2021). The remaining 20% occurs between autumn and winter, that is from March to August.

Human population data (secondary) of the City of uMhlathuze for the first Census data collection in the year 1996, followed by Censuses collected in 2001, 2011 and the Community Survey (CS) conducted in 2016 was obtained from Statistics SA (StatsSA) as indicated in Table 1. The polygon features (in the form of shapefiles) used to draw the map of the City of uMhlathuze (municipal boundary, municipal wards, river lines or lakes, roads, and towns) were obtained from the Human Sciences Research Council (HSRC). Analysis of data was carried out using RStudio software package version 3.4.4 (R Core Team 2020), to interpolate data as well as to predict human population growth, while Microsoft Excel Solver was used to solve the linear programming model which was used to determine the number of additional reservoir tanks to be built in future. Finally, ArcGIS version 10.5 was used to draw the graphical location of the City of uMhlathuze.

Time series data is often recorded and analysed to predict future values, understand phenomena and to understand the behaviour of variables, among other things (Lepot et al. 2017). However, for several reasons, the data contains missing values, gaps, irregular time steps of recordings, or removed data points that often need to be filled for data analysis. Census human population data of the City of uMhlathuze contains gaps because the first Census data collection in SA was in 1996, followed by Censuses conducted in 2001, and 2011, and the CS conducted in 2016. Censuses are not annually implemented; therefore, estimates are needed for the intercensal period (Fukuda 2010).

The following automated time series forecasting models were applied in this study with the aim of predicting the human population of the City of uMhlathuze. The reason for using multiple automated time forecasting models was mainly to compare their forecast results and select the best forecasting model, and to maximise accuracy and minimise bias.

The automated ARIMA model uses an automatic forecasting model known as the ‘auto.arima function’, which is provided through the forecast package in RStudio (Hyndman et al. 2008). By using the ‘auto.arima function’, the model overcomes a limitation of selecting the appropriate parameters and being considered subjective by automatically selecting the best number of time lags of the autoregressive model, the degree of differencing needed to reach stationarity as well as the order of the moving average model (Hyndman & Athanasopoulos 2018).

The Error Trend Seasonality (ETS) model uses an automatic forecasting model known as the ‘ets function’ which is provided through the forecast package in R programming code (Hyndman et al. 2008). By using the ‘ets function’, the model overcomes a limitation of failing to provide a method for easy calculation of prediction intervals (Hyndman & Athanasopoulos 2018).

From the forecast package, the model considers the error, trend, and seasonal components in choosing the best exponential smoothing model from over 30 possible options by optimising initial values and parameters using the Maximum Likelihood Estimation (MLE), and selecting the best model based on the Akaike Information Criterion (AIC) (Hassani et al. 2017).

The BATS model uses an automatic forecasting model known as the ‘BATS function’ which is provided through the forecast package in R programming code (Hyndman et al. 2008). By using the ‘BATS function’, the model overcomes the limitation of being slow to estimate, especially with long time series (Hyndman & Athanasopoulos 2018). However, on the positive side, the model has the option of implementing a multi-seasonality analysis without too many parameters, it can work under non-integer seasonality, and it can work under high frequency data (Hassani et al. 2018). Furthermore, the model allows for any autocorrelation in the residuals to be considered; and lastly, it involves a much simpler, yet more efficient estimation procedure.

One of the goals of this study is to predict the human population growth of the City of uMhlathuze for the next 50 years (from 2017 until the year 2067), therefore water provision for future human population must be made. As such, a linear programming model from Equations (18)–(20) was formulated with the aim of determining the number of additional reservoir tanks to be built in the future, based on the prediction of human population growth. The model considered the following input notations:

• = the unit cost of building a reservoir tank

• = reservoir tank type to be built in future

• = capacity of reservoir tanks to be built in future

• m = the total number of additional reservoir tank type to be built in future,

• = human population growth (demand) in the next 50 years,

• k = minimum amount of potable water available per person per day,

• = capacity of current reservoir tanks,

• i = the index of potential facility sites.

Decision variable

• where

The objective function in Equation (18) seeks to minimize the total unit cost of building an additional reservoir tank in the future while satisfying all the supply and demand restrictions. The constraint in Equation (19) requires that demand from human population (demand) should be less or equal to water supplied per person per day. Lastly, the constraint in Equation (20) is an integer decision variable.

The factors that could have influenced this annual slow growth rate include the cholera outbreak as well as the human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) cumulative deaths experienced by the KZN province and its municipalities between 2000 and 2001 (Department of Health KwaZulu Natal: Epidemiology Unit 2001; Dorrington et al. 2002), according to information presented in Tables 2 and 3 respectively. The HIV, AIDS and cholera outbreak resulted in many premature deaths which affected the human population in rural and urban areas of the KZN province and the City of uMhlathuze at large (Eshowe, Nkandla, uMfolozi, and Ngwelezane).

From 2011 the human population growth increased at a pace of 4.181% per year on average until it reached another peak in 2016. This indicates that quite a large number of people migrated (in-migration) to the KZN province as well as the City of uMhlathuze between the years 2011 and 2016 (Statistics South Africa 2016), according to the in-migration statistics presented in Table 4.

The human population growth of the City of uMhlathuze was then predicted from 2017 until 2067 as illustrated in Figure 2(b)–2(d). The human growth curves for ETS(A,Ad,N) model, ARIMA(1,1,0) with drift model and BATS(1, {0,0}, 1, -) model have shown an upward trend from the year 2017 until 2067. Based on the performance results of these automated time series forecasting models, the human population growth is expected to triple by 2067, at a higher pace than at any period since 1996 according to the ARIMA(1,1,0) with drift model. The findings are in agreement with those obtained by Aurecon South Africa (2015a, 2015b) and the City of uMhlathuze (2019, 2020, 2021), that with the City of uMhlathuze being the fastest developing municipality in SA, an increase in human population is probable in the coming years; largely to be influenced by an enlarged municipal area following the inclusion of three wards from the former Ntambanana, post the 2016 local government elections.

Economic opportunities from the growing industrial centre as well as agricultural activities might be factors that contribute to a continuously growing human population in the City of uMhlathuze in the near future, as more people will be coming (in migration) from neighbouring rural and urban communities seeking employment (City of uMhlathuze 2021). Increased demand for water may also emanate from water users located outside the municipality's catchment but supplied from it; and this may lead to the number of people requiring water being more than what the reservoir tank can handle (Aurecon South Africa 2015a).

The findings also confirm a theory developed by Malthus (1798), that the human population will grow exponentially (for instance, doubling or tripling with each cycle) while basic means of subsistence like food, water supply and distribution, and electricity amongst other things, will grow at an arithmetic rate (for instance, by the repeated addition of a uniform increment in each uniform interval of time). Growth in human population does not only indicate the changes in human population size, but also indicates the changes in the distribution of basic services such as water (Kılıç 2020). It also means mounting demand and competition for water for domestic, industrial, agricultural, and municipal uses. As a result, the challenges to meet user demands for basic services may also increase.

An implication of these findings is the possibility that, should anticipated human population growth materialise, the current reservoir tanks are likely to come under stress due to increased water demand (Mulwa et al. 2021). This is supported by a recent finding from studies conducted by Parks et al. (2019), Heidari et al. (2021), Mulwa et al. (2021), that a continuous increase in urbanisation and human population growth affects water infrastructure resources, and this may in turn cause water shortages in rural and urban communities.

Table 5 presents the forecast performance of ARIMA(1,1,0) with drift model, ETS(A,Ad,N) model, and BATS(1, {0,0}, 1, -) model by means of the RMSE, MAE, MAPE, and MASE. For each of these measures, a smaller value indicates higher prediction accuracy of the model (Karabiber & Xydis 2019). As shown in Table 5, ARIMA(1,1,0) with drift model outperformed the ETS(A,Ad,N) model, and BATS(1, {0, 0}, 1, -) model, because it has the smallest errors across four forecast evaluation measures. This indicates that the ARIMA(1,1,0) with drift model is the best model to forecast human population growth of the City of uMhlathuze.

A linear programming model was formulated with the goal of determining the provision of reservoir tanks in the City of uMhlathuze to satisfy the possible human water demand for the next 50 years. The analysis takes into consideration the estimated unit cost of building a reservoir tank, human population growth forecasts (demand) in the next 50 years, existing reservoir tank capacity as well as the minimum amount of potable water (25 litres) available per person per day, amongst other things.

The results of a linear programming model presented in Table 6 have indicated that a total number of 687 additional water reservoir tanks with a capacity of 47,500 kilolitres should be built annually in the City of uMhlathuze within the period of 50 years in order to supplement the anticipated increase in demand for water as a result of a rapid increase in human population growth and urbanization. Below is the description of the notations used in Table 6:

• RN* - Reservoir number,

• EBC* - Estimated building costs in SA Rands (R),

• RCK* - Reservoir capacity in kilolitres,

• DV* - Decision variables,

• TC* - Total costs (x),

• TCK* - Total capacity in kilolitres

This study has succeeded in applying machine learning-inspired automated time series models such as ARIMA(1,1,0) with drift, ETS(A,Ad,N), and BATS(1, {0, 0}, 1, -) model to predict the growth in human population of the City of uMhlathuze over a 50-year period. Significant increases in human population raises many concerns since human population growth, without corresponding expansion of the reservoir tanks, might cause a shortfall in terms of water provision and distribution in future, unless a feasible plan based on the prediction of human population growth forecasts is developed (Mohammed & Sahabo 2015; Parks et al. 2019; Mulwa et al. 2021).

This is the first study of its kind to demonstrate a linear programming model to be used for water provision planning for half a century in advance. The findings of this study could be useful as knowledge of how human population will grow in future and how many additional reservoir tanks will be needed to satisfy the human water demand is extremely important in terms of guiding the City of uMhlathuze towards policy formulation, development, implementation as well as facilitating planning with the aim of accommodating a continuously growing population and the competing demands from human settlements. The study also highlighted the importance of managing the increased demand for water in order to avoid water shortages in rural and urban communities.

Future work to be derived from this study may include formulating the facility location problem to determine the optimal locations where additional reservoir tanks can be built, based on how settlements are growing and their spatial direction of expansion; also, where demand is likely to be located in future, so that water can be distributed to all applicable rural or urban communities. Moreover, hybrid forecasting models can also be developed and applied for predicting the human population growth of the City of uMhlathuze and therefore the forecast accuracy can be compared in terms of their reliability and robustness. Some of the suggested hybrid combinations include:

• Hybrid neural network auto-regression (NNAR) + ARIMA model,

• Hybrid ARIMA + ETS model,

• Hybrid ETS + NNAR model, and

• Hybrid ARIMA + ETS + NNAR model.

The combination of different time series forecast methods should allow researchers to maximise the chance of capturing both the linear (if any) and nonlinear patterns and may achieve better performance and forecast accuracy (Panigrahi & Behera 2017).

This work is based on research supported wholly by the National Research Foundation of South Africa (Grant Number; 110415).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.