Water poverty assessment based on the random forest algorithm: application to Gansu, Northwest China

Water poverty can be defined as a situation in which a country or a region cannot provide sustainable, clean, and affordable water continuously for all people (Feitelson & Chenoweth, 2002). Water poverty is highly relevant to the United Nations 2030 Agenda for Sustainable Development, which sets clean water and sanitation as a sustainable development goal (Cetrulo et al., 2020; Koirala et al., 2020; Ladi et al., 2021; Liu & Liu, 2021). Therefore, alleviating water poverty is a key objective of the water and development policy (Hope, 2015).

The water poverty index (WPI) has been widely adopted as a tool to indicate the extent to which societies are impacted by water poverty. The WPI is a multi-disciplinary index that considers physical and socioeconomical factors associated with water accessibility and affordability, thereby inviting policymakers to monitor the availability of water resources and track the socioeconomical factors that shape water accessibility and affordability (Sullivan, 2002; Ladi et al., 2021). The influence of the WPI is palpable in the water poverty literature, with numerous studies applying this tool to examine the water poverty situation at the national (Jemmali, 2017; Pan et al., 2017; Goel et al., 2020; Ladi et al., 2021; Prince et al., 2021), regional (Huang et al., 2017; Thakur et al., 2017; Wurtz et al., 2019; Koirala et al., 2020), and local scales (Azqueta & Montoya, 2017; Kallio et al., 2018).

Whereas the WPI has become one of the most widely adopted assessment tools in the field of water poverty, new methods, models, and technologies are constantly being proposed to improve the WPI. One particularly promising approach is the use of machine learning techniques to aid in the classification of the water poverty levels. The evaluation of the WPI involves complex subsystems with the characteristics of multiple indicators, high dimensionality, and nonlinearity, and is therefore suitable for evaluation with the help of machine learning. Furthremore, machine learning can avoid the subjectivity of determining index weights that results from the rule-based method with human experts – the original WPI weighting system proposed by Sullivan (2002) is often criticized for its arbitrariness (Baquero et al., 2017). However, commonly used machine learning methods, such as back propagation (BP) neural networks and support vector machines (SVM), rely heavily on the distribution of training samples and may have problems such as insufficient robustness and over-fitting that, to a certain extent, affect the practicability and accuracy of the model (Jing et al., 2012; Wang, et al., 2016).

To address these problems, we developed a WPI evaluation method based on the random forest algorithm. Random forest is a non-parametric, supervised learning algorithm based on multiple decision tree classifiers (Breiman, 2001) and has been adopted by researchers to solve classification problems in diverse fields, including water resource management (Naghibi et al., 2017; Naghibi et al., 2019; Shirzad & Safari, 2019; Pahlavan-Rad et al., 2020). A random forest can be understood as a special bagging algorithm and involves the following steps (Ibrahim & Khatib, 2017). First, a bootstrapped dataset is generated from randomly sampling the original data with replacement (i.e., same sample can be selected more than once). Second, a decision tree is created by using the bootstrapped dataset, but only uses a random subset of features. Third, multiple decision trees are created by repeating the first two steps. Fourth, the classification results of each decision tree are integrated, and the most popular category is regarded as the final result. The introduction of randomness prevents the models from overfitting (Pal, 2005). Studies applying the random forest algorithm demonstrate that the method has strong advantages compared to other machine learning classification methods, including a good anti-noise ability, low error risk, and better performance in terms of accuracy and operating efficiency, particularly when there is a large dataset with many input variables (Gao et al., 2009; Cui & Bo, 2014; Lai et al., 2015).

We conducted a case study in Gansu, China, to demonstrate the proposed method. As a water-scarce country, water poverty is a serious issue in China (Pan et al., 2017; Liu et al., 2018). In particular, Northwest China is one of the most arid areas in East Asia and experiences severe water shortages and economic poverty (Lo et al., 2016; Rogers et al., 2020; Gao et al., 2021). With a population of 26 million, Gansu is the second most populous province in Northwest China. Hence, understanding the situation of water poverty in Gansu provides guidance to alleviate water poverty in China's arid and semi-arid areas.

In this study, 11 municipalities in Gansu were selected as basic evaluation units, including Lanzhou, Baiyin, Jiuquan, Jiayuguan, Jinchang, Wuwei, Pingliang, Qingyang, Tianshui, Dingxi, and Zhangye (Figure 1). These 11 municipalities form the Gansu Section of the Silk Road Economic Belt (hereafter, Gansu Section), which is long and narrow from the east to the west, with a length of approximately 1,555 km, accounting for 39% of the total length of the Silk Road in China. There are four types of geomorphic areas: the Longzhong region of the Loess Plateau, the Hexi Corridor, the Qilian Mountains, and the north of the Hexi Corridor. It has a significant continental temperate monsoon climate, with hydrothermal conditions decreasing from southeast to northwest. The Gansu Section covers three basins: the inland river basin, the Yellow River basin, and the Yangtze River in the Hexi Corridor. Most of these areas are arid. In 2018, the total amount of water resources in the Gansu Section was 13.03 billion m³, accounting for 36.7% of the province's total water resources; of which surface water resources were 12.12 billion m³, accounting for 92.26% of the total water resources (Gansu Provincial Department of Water Resources, 2019).

The remainder of this paper proceeds as follows. First, we examine the steps involved in adopting the random forest algorithm to classify the levels of water poverty. Next, we analyze the results, both spatially and temporally. Finally, we offer certain concluding thoughts regarding the key lessons of this study.

The WPI typically includes five main components: resources, access, capacity, use, and environment (Ladi et al., 2021). ‘Resources’ measure the availability of ground and surface water. ‘Access’ indicates the public availability of water resources. ‘Capacity’ measures a set of socioeconomical and institutional factors that influence water accessibility and affordability. ‘Use’ evaluates the amount of water use and water consumption efficiency in different sectors (for example, domestic, agricultural, industrial). Finally, ‘environment’ measures the environmental indicators related to water supply and management. Each of the five components of the WPI contains a set of criteria that can be used to calculate the composite index. Following this five-component approach, we developed a set of indicators suitable for China's local context. The evaluation index system comprised 17 positive and 8 negative indicators – a positive indicator implies that the larger the original data value, the better is the water poverty condition, whereas a negative indicator implies that the larger the original data value, the worse is the water poverty condition. The 25 indicators are shown in Table 1.

In Equations (2) and (3), represents the value of the j-th evaluation index of the i-th municipality, min represents the minimum value of the j-th evaluation index in all years, and max represents the maximum value. Then, we used Natural Breaks to divide the processed values into five levels, with a total of 25 × 5 label information. Table 2 presents the resulting classification criteria for water poverty. The range of the different levels of the indices may be discontinuous because we used the distribution of the original data to determine the range of the different levels. Considering R5 as an example, the original data are typically concentrated below 98, with a few outliers greater than 128, and there are no values between 98 and 128. Therefore, there is a gap between levels 1 and 2.

We randomly selected 100 sets of samples from each classification level (that is, the total number of samples was 500). We randomly extracted 70% of the sample and designated them as the training set, which was used to train the classification tree and generate a label classifier. We used the remaining 30% of the samples as the test set. We imported training and test samples into the R software.

After importing the training and testing sets, we loaded the random forest package in R and set the ntree and mtry values to run the algorithm. We tested the ntree values of 100, 300, 500, 800, and 1,000. Figure 3 shows the trend of the out-of-bag (OOB) error of the random forest classification model for water poverty in Gansu with different ntree values. The error rate value in the range of 0–400 was relatively large, with significant fluctuations. When the ntree value was 800, the error converged. Therefore, we set the ntree value to 800. Subsequently, with a fixed ntree value of 800, the k-fold cross-validation method was used to traverse the mtry parameters to determine the best mtry value. K-fold cross-validation can ensure that when the total number of data samples is small, each sub-sample participates in training and testing, effectively reducing the generalization error of the model. When mtry is 8, the minimum error value reaches the inflection point; therefore, we set the mtry parameter value to 8.

Using the optimized parameters, a random forest model was trained using the samples. As shown in Table 3, the trained random forest model was the most accurate for classifying ‘very severe’ water poverty level, and the classification error was 0%. The accuracy was also high for ‘mild’ water poverty level, with a classification error of 11.11%. The classification error for the ‘severe’ type was 33.33%, and 1/6-th of the samples were misjudged as ‘moderate’ and ‘very severe’. The classification error for the ‘moderate’ water poverty level was the highest (38.46%), with nearly 30% of the samples misclassified as ‘severe,’ and one sample misjudged as ‘very severe’ and one sample as ‘mild’. The OOB error in the confusion matrix was calculated to be 15.2%.

Finally, we applied the random forest model to classify the water poverty levels. We input the actual data of each indicator in each municipality in the study area from 2000 to 2017 as new data into the software. The level corresponding to the highest probability in the result was assigned to the actual yearly water poverty level of the random forest. Because the random forest algorithm is a classification tool, the classification results are integers. Table 4 presents the results of the classification.

The classification results indicated that in the Gansu Section the problem of water poverty was serious, but it gradually improved. In 2000, 9 of the 11 municipalities suffered from extremely severe or severe water poverty; in 2017, there was no more extremely severe water poverty, and only three municipalities suffered from severe water poverty. More specifically, we can distinguish between the three stages from 2000 to 2017. In the first stage (2000–2005), water poverty in the Gansu Section was serious, with level 2 being the most frequent, followed by levels 1, 3, 4, and 5. In the second stage (2006–2011), the situation of water poverty improved, with levels 3 and 2 being the highest frequency of water poverty levels, and the number of municipalities in level 2 significantly decreased. In the third stage (2012–2017), the situation of water poverty continued to improve. Significantly, there were no municipalities in level 1 in this stage.

Spatially, different municipalities in the Gansu Section exhibit different patterns of water poverty. Water poverty in Jiayuguan is relatively insignificant and has remained at level 5 for several years, and Lanzhou is another mild water poverty area with an index of level 4 for several years. As for the moderate water poverty areas, Jinchang, Jiuquan, and Zhangye have held the level of water poverty mainly at level 3 for several years. Other municipalities, including Baiyin, Tianshui, Qingyang, Dingxi, and Pingliang, are severely water poverty areas. They have experienced water poverty at level 2 or level 1 for several years.

Figure 4 presents the spatial distribution of the water poverty levels in the research area. In 2000, while most municipalities had severe water poverty issues, western and middle Gansu were better than eastern Gansu. From 2000 to 2017, the water poverty level of most cities steadily improved, particularly for municipalities in eastern and central Gansu. In 2017, western Gansu (Jiuquan) was a medium-value area, most of the municipalities in central Gansu (Jiayuguan, Zhangye, Jinchang, and Lanzhou) had good results in terms of water poverty levels, and the low-value areas were mainly distributed in the eastern section (Pingliang, Dingxi), where water poverty remains serious.

What could the municipalities with serious water poverty problems learn from the better-performing municipalities? To accurately answer this question, it is necessary to determine the constraints of water poverty in each municipality and quantify the degree of its impact. The municipalities with serious water poverty issues typically have a poor water resource availability and low water resource utilization efficiency. The municipalities with mild water poverty levels benefited from sustained and comprehensive water management measures, as evidenced by their high water resource utilization efficiency. This is a successful experience that other municipalities should learn from.

Considering Pingliang, a municipality suffering from serious water poverty, as an example, two indicators, the percentage of water supply from other sources (R1) and percentage of the drought-affected area (E1), significantly impact the classification of water poverty. First, other water sources mainly refer to unconventional water sources such as sewage treated water, which reduce the dependency on surface and underground runoff. Pingliang should take management and technological measures to expand unconventional water sources as an important supplement to conventional water sources. Second, the drought area refers to the sown area in which the actual harvest of crops is reduced by more than 30% compared to the normal annual output in the drought-stricken area. Measures such as improving the monitoring of soil moisture and crop growth and enhancing irrigation infrastructure can reduce the impact of drought.

Over the past two decades, support for addressing water poverty has been increasing worldwide. Quantitative, index-based analyses such as the WPI play an important role in monitoring and understanding water poverty problems. The random forest algorithm offers several advantages for classifying the level of water poverty. The random forest method can process high-dimensional data with less human intervention and faster training. The dimensionless processing of the original data is not required. Only a preliminary training of the model is required to run the evaluation results. The random forest algorithm is suitable for processing datasets with a large number of unknown features, without feature selection. The application to Gansu shows that the random forest method can obtain a comprehensive and highly reliable spatiotemporal evaluation of water poverty.

Not applicable.

The authors declare no conflict of interest.

This research was funded by the National Key Research and Development Program of China (Grant No.2019YFC0507402).

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