Analyzing Trends in Rainfall and Their Impacts in Water Management in a Cerrado Region in Brazil

This study presents a trend analysis related to a Cerrado Region in Brazil surrounded by multiple climatic inuences and which lived a recent water crisis (2016-2018). This crisis could be associated with climatic changes or population growth. To verify the rst possibility, an analysis was performed on a series of rainfall data (21 rain gauges spread throughout the region) divided by season periods (December/January/February – DJF, March/April/May – MAM, June/July/August – JJA, September/October/November – SON, and Water Year – WY) to provide information about the presence of trends or lack thereof. Four statistics tests were used in this procedure: Cox-Stuart, Mann-Kendall, Spearman, and Wald-Wolfowitz. The overall results indicate that the percentage of gauges/periods displaying trends by the Mann-Kendall was 10.48%, Cox-Stuart 9.52%, Spearman 12.38, and Wald-Wolfowitz 8.57%. Of these gauges/periods, 70% were classied as highly skewed, 10% as moderately skewed, and 20% as symmetric. Most of the trends are concentrated in the JJA period where it registered about 22 mm of rainfall average while the annual mean total precipitation is ~1500 mm.


Introduction
It is believed that the greatest in uence on the future is related to population growth, economic expansion, and climatic change (Love 1999). In turn, climatic change is altering several environmental variables around the world which increases the importance to understand the spatial and temporal patterns of rainfall (Yavuz and Erdoğan 2012) since precipitation is the main variable linked to major climate impacts (Li et al. 2019). This way, this knowledge about a determined place is the primary condition for water resources management (Zeleňáková et al. 2017) and planning (Paquin et al. 2016).
Moreover, this identi cation seeks to minimize damage that may be caused by extreme events such as oods (Petineli and Radin 2012) or drought (WMO 1997;Mishra and Singh 2010). Changes in precipitation regimes can be caused by several factors, including deforestation, urbanization, and emission of polluting gases into the atmosphere, along with intensi cation of solar activity and other natural phenomena (Marengo 2010). Regardless of the causes of scarcity, whether by natural climatic variations or by anthropic interference, each unit of the federation (States) should monitor and verify the real situation of its water resources and their relations with border states. Continuous monitoring and consistent water management are critical for future planning (Loucks et al. 2005).
According to the "Summary for Policymakers" (2007), there is observational evidence from all continents that natural systems are being affected by regional climate changes. Related to South America, previous studies relate an increase in frequency and magnitude of extreme events (Coelho et  From 2016 to 2018, the state experienced severe drought conditions . The usable water volume in the reservoirs fell to their minimum levels and a series of procedures to control the situation were implemented such as pipe control, water rotation among neighborhoods, and emergency withdrawals from new water sources, etc. . Aside from aforementioned issues, some studies pointed out that a large part of the scarcity had occurred due to reduction of rainfall in the region (Lorz et al. 2012;Borges et al. 2016). Hence, an analysis of rainfall data is fundamental for water management related to the DF.
In environmental sciences, a time series as precipitation is assumed stationary in variance with no trend in mean (Um et al. 2018), and statistical tests can be performed to analyze this behavior (WMO 2009).
The present study analyzed 21 rain gauges, looking at rainfall trends over time using four statistical methods: the Mann-Kendall test, Cox-Stuart, Wald-Wolfowitz, and Spearman. The results obtained are expected to support public policy for water resources resulting in more effective management of land use and occupation, as well as better understanding of water availability in DF. This type of analysis is important for decision-makers because identi cation of trends and/or stationary behavior is signi cant for planning and generation of future scenarios.

Material And Methods
In the following sections, the study area, as well as the statistical measures used in the paper will be described.

Study area
The Federal District (DF) is located in the central-west region of Brazil, within the parallels 15° 30' S and 16º 03' S and has an area of 5,802 km² (Fig. 1). Contains headwaters of three important Brazilian hydrographic basins, the São Francisco River basin, the Tocantins basin, and the Paraná basin (ANA 2005) which characterizes the region as made up of rivers and basins with low amounts of water ow (the mean annual stream ows vary from 3 m³/s to 23 m³/s) . Regional climate is under the in uence of the South American monsoon system (SAMS) and presents two well-de ned seasons: a rainy and warm period from October to April, and dry and cold season from May to September (Baptista 1998

Rainfall Data
Rainfall data was retrieved from 21 rain gauges in the Federal District region (Fig. 1). Rain gauges were chosen in order to have a minimum of 30 years in time series length, from January/1971 to December/2017. However, due to missing data or deactivation of some gauges, the studied period for the analyzed sites is not coincident (see Table Table 48 in the appendix for details). The rainfall data were obtained from Companhia de Saneamento Ambiental do Distrito Federal (CAESB) and Instituto Nacional de Meteorologia (INMET) and the mean seasonal values are shown in Fig. 2 where it is shown that most of the rainfall happens in quarter DJF. Quarters SON and MAM display similar behavior as they correspond to the beginning of wet season and dry season, respectively. Quarter JJA is the driest period of the year, registering lower rainfall values.

Statistical Evaluation
Rainfall trends were analyzed for water year (WY), and by hydrological quarters (December/February, March/April/May, June/July/August, and September/Octuber/November). The latter was proposed to avoid seasonal variations (Hirsch et al. 1982;Hamed and Ramachandra Rao 1998). We used four nonparametric statistical tests to improve the analysis as suggested by Machiwal and Jha (2008): Mann-Kendall, Cox-Stuart, Wald-Wolfowitz, and Spearman. Non-parametric tests are more suitable for natural time series because assumptions required for parametric testing are not usually present in this type of data (Hirsch and Slack 1984;Hipel and McLeod 1994). Rainfall data, for example, seldom follows normal distribution (Yue et al. 2002).
The Mann-Kendall test, hereafter referenced as MK, (Gilbert 1987) is commonly used to check for trends in climatic conditions (WMO 2009). It is the most appropriate test to identify climatic change according to Goossens and Berger (1987) and is the most widely used test for trend identi cation (Yue et al. 2002). This test has been used in several studies in Brazil  , studies using MK tend to assume that sample data is independent. Although, as noted by Rao and Hamed (2019) and , the correlation can signi cantly in uence results. According to them, a positive correlation can increase the possibility of rejecting the null hypothesis, while a negative correlation acts to accept the null hypothesis. Therefore, other trend tests were also used in order to improve our analysis.

2017). As observed by
The Cox-Stuart test, hereafter referenced as CS, (Cox and Stuart 1955) is another test recommended to identify hydrologic changes (McCuen 2003) and it was used to verify if rainfall datasets present variability and a monotonic tendency (Fatichi and Caporali 2009; Jasim Hadi and Tombul 2017). In addition, as suggested by Chen and Huang (2020), CS has the advantage of being independent of the data sequence structure, however, it is considered slightly weaker than Mann-Kendall (Rutkowska 2015).
In addition, CS was also used following recommendations proposed by Chen and Huang (2020). According to them, when the null hypothesis is rejected, it is interesting to observe the number of Positive Differences compared to Negative Differences as well as the signi cant p-value (0.05 < p-value < 0.1). According to Chen and Huang (2020), this condition can be used to classify gauges as presenting a "Strong" trend while p-value < 0.05 would be considered "Extremely Strong".
The Wald-Wolfowitz test, hereafter referenced as WW, (Wald and Wolfowitz, 1940) also known as a run test, was applied to verify independence among the data series, as well as another perspective on trends in the rainfall dataset (WMO 2009; Rao and Hamed 2019). The WW test seeks to verify oscillations above and below the median, with each oscillation in a direction followed by an oscillation in a different direction counted as a run (Wald and Wolfowitz 1940). Too few runs, i.e. the constant occurrence of values over/under the median, could be identi ed as trends in the median during the period analyzed (Thom 1966). Hence, this test explains variations around the median. This test has also been commonly used to examine trends in rainfall datasets ( The Spearman's correlation, hereafter referenced as SP, (Spearman 1904) was the last test we used and is another recommended for trend analysis (WMO 2009). It is used to verify trends in rainfall datasets (Ogallo 1979;Tabari et al. 2012) and is recommended for environmental engineering applications (Hipel and McLeod 1994). All four tests have also been used to verify trends in January rainfall data in DF (Steinke et al. 2017).
For all tests, the null hypothesis represents that a trend was not identi ed. According to Goossens and Berger (1987), succession of precipitation records must be independent and probability distribution the same during the entire period for null hypothesis, identifying a stable climate. Hence, null hypothesis is accepted if the p-value is higher than α. The α value for all analyzed tests was determined to be 0.05, a common value for the signi cance test (Hipel and McLeod 1994;Conover 1999

Results And Discussion
The results of the analysis are divided into ve sections corresponding to each statistical method applied in this study along with a discussion. Table 42 lists rain gauges where trends were identi ed using MK. In quarter DJF, a single station (1547003) presented a decreasing trend. This quarter is representative for the rainfall analysis since most of the rain occurs during this time. For quarter JJA, a decreasing trend was identi ed in seven gauges.

MK results
However, this result does not affect water management since this period is classi ed as a dry season, and average value for this quarter is signi cantly lower than the other periods as observed in Table 41. Analyzing MK results related to the WY, 3 gauges registered trends. Gauge 1547020 presented an increasing trend and the other 2 gauges (1547021 − 1547003) exhibited decreasing trends. These last two also presented decreasing trends in quarters DJF (1547003) and JJA (1547021). Both gauges are not used for water supply and are located in urban or semi-urban areas. The overall results indicate that the percentage of gauges/periods displaying trends by the MK was 10.48%.

CS results
The results based on CS are summarized in Table 43. For quarter DJF, it is possible to see that, as in the MK test, a single gauge (1547020), had a decreasing trend. For quarter MAM, gauge 1547013 presented a decreasing trend, different from the MK results, where a trend was not identi ed in this period for any gauge. Quarter JJA also presented multiples gauges, 1547014, 1547019, 1547020, 1547021, 1548008, and 1548010, describing decreasing trends. The last four replicated behavior described in MK. Stations 1547021 and 1548006 were identi ed as having trends for the Water Year, and the rst also repeated the classi cation obtained by the MK. Table 43 brings together the number of positive and negative differences, making it possible to see the magnitude of the trends. Chen and Huang (2020) presented an analysis based on these values, and the pvalue to identify the degree of a trend. In this way, using the de nition proposed by Chen and Huang (2020), some gauges that presented trends for MK could also be identi ed presenting some level of a trend for CS. Despite the null hypothesis being rejected, these gauges showed a high number of Positive Differences compared to Negative Differences in the CS as well as signi cant p-value (0.05 < p-value < 0.1). Following the classi cation proposed by Chen and Huang (2020), Table 44 depicts the gauges classi ed as "Strong", where most could be classi ed as trending by MK. Gauge 1548005 was an exception, and did not present a tendency for MK, displaying signi cant contrast between positive and negative differences.  Following the classi cation proposed by Chen and Huang (2020), a "Weak" trend can be identi ed if 0.1 < p-value < 0.25. Six gauges presented a "Weak" trend for quarter DJF, three for quarter MAM, four for JJA, three in SON, and three for the WY. Gauge 158007 showed a weak trend for quarters DJF and JJA, and for the WY. This gauge is located in the watershed used for water supply. The overall results indicate that the percentage of gauges/periods displaying a trend by CS was 9.52%.

WW results
The results from the WW test executed for the rainfall data which were considered as having trends are described in Table 45. Three gauges presented trends in quarter DJF, one in MAM, two in quarter JJA, and three in the SON quarter. From the nine rainfall gures presented in Table 45, only two were classi ed as having trends for the CS: 1547020 for quarter DJF and 1547014 for JJA. The trending gauges by the run test were not classi ed as trending by MK and vice-versa. Additionally, as WW can be used to test the independence of a dataset (Rao and Hamed 2019), the results presented here reject the hypothesis of independent concern the gauges show in Table 45. The overall results indicate that the percentage of gauges/periods displaying a trend by the WW was 8.57%.

Water management from the perspective of a trending scenario
The spatial distribution of all analyses can be observed in Fig. 3 and Fig. 4. The rst one shows the concentration of trend points in the JJA period, where it is possible to identify a clusterization among the trending points. Figure 4 aggregates all the trending results by season periods, where a point was classi ed as trending if it was identi ed by at least one test. JJA period is once more identi ed as a trending season for multiple points, and WY also presents three decreasing gauges.
It can be seen that for all analyses described in the previous topics, there were mixed results. In order to group the statistics obtained by MK, CS, and SP, Table 47 was built. To help with visualization, WW statistics were not included. The only gauge classi ed as having a trend was also classi ed in the same way by WW. The percentage of gauges/periods identi ed as having a trend by at least one test was approximately 10%. From the trending points, 54% presented trends with only one method, 27% with two methods, and 19% with three methods. Hipel and McLeod (1994) suggested that non-parametric tests were not developed to show the magnitude of a certain statistical characteristic, but to indicate if there is some type of behavior. That is, non-parametric tests are considered to be exploratory data analysis procedures and can be a powerful tool for environmental analysis (Goossens and Berger 1987; WMO 2009; Rao and Hamed 2019). The results here, especially those depicted in Table 47, presented just one gauge with decreasing trends during quarter DJF, the most important quarter for water management in your region of study, and it was identi ed by more than one test (MK and SP). As observed in the MK test, the site of this gauge is outside the watershed of the water supply reservoirs. Analyzing the WY, three gauges presented decreasing trends. All of them are located in urban areas that are not used for water supply. Understanding the exploratory characteristic of these tests, and their results could be a suitable condition for the study area related to the water supply. As mentioned in the introduction, a water scarcity event occurred in DF between 2016 and 2018. Lima et al. (2018) highlight the fact that during these three years, the gauge (1548007) located inside the basin most important for water supply, registered an average of 75% of the historic average. The cited gauge presented a decreasing trend behavior in JJA period for the MK, SP and the CS, the latter considering the approach proposed by Chen and Huang (2020). It presented the same behavior in DJF period for the WW. , DF presents high spatial heterogeneity for rainfall data. These variations may also be present within the series as observed in the cited triennium. Moreover, the fact that the study area is located within a monsoon region can explain these variations (Deng et al. 2018). Yue et al. (2002), analyzing the power of MK and SP, identi ed that variations within a series mask the existence of a trend. They suggest that as variations increase, the power of the test reduces. Likewise, as skewness coe cient increases, trend detection rates also increase (Yue et al. 2002). In order to corroborate this point of view, skewness veri cation was performed (D'Agostino et al. 2020). From the analyzed gauges/periods, 70% were classi ed as highly skewed, 10% as moderately skewed, and 20% as symmetric (Bulmer 1979 Rao (1998) also observe in uences related to the autocorrelation factor throughout the data series, where positive/negative autocorrelations increase/decrease rejection of the Null hypothesis.
As WW veri es variations around the median, results can indicate great disparities throughout the series which may affect trend analysis. The de nition used for a climatic trend based on Micthell (1966), and supported by Goossens and Berger (1987), points out that this type of trend is identi ed by a smooth and monotonic alteration of average value for the analyzed period. Therefore, instead of presenting a climatic trend condition, expected oscillations in the rainfall amounts can be suggested instead. As commented by WMO (2009), statistical tests serve to point to the signi cance of results but do not supply indubitable conclusions. So, it is recommended to search for other additional types of information in order to shed more light on the results. These considerations should be analyzed by decision-makers in order to effectively manage the water supply as signi cant variations in future years, especially for the trending sites, can be expected.

Conclusion
The overall results indicate that the percentage of gauges/periods displaying trends by the MK was 10.48%, CS 9.52%, SP 12.38, and WW 8.57%. Of these gauges/periods, 70% were classi ed as highly skewed, 10% as moderately skewed, and 20% as symmetric.
A decreasing trend was observed for quarter SON, but this time of year is not signi cant for the water supply. The results, especially those depicted in Table 47, showed one gauge with decreasing trend during quarter DJF, the most important for water management. The tests did not produce similar results, and results from WW suggested great variation throughout the series which can affect trend analysis. Just one rain gauge (1547003) presented a decreasing trend for quarter DJF in more than one test (SP, MK, and WW, and for CS, when using the methodology proposed by Chen and Huang, 2020). As observed in the MK topic, the site of this gauge is outside the watershed of the water supply reservoirs. Analyzing the WY, three gauges (1547003: MK and SP, 1547021: MK, CS, and SP, and 1548006: CS) presented decreasing trends and all of them are located in urban areas.
Changes in variability, length of wet and dry seasons, and shifts of the South Atlantic Convergence Zone during the last forty years reported by previous studies could be related to the trends identi ed in DF rainfall. The results obtained by this study, as opposed to presenting a climatic trend condition, suggest expected oscillations in rainfall amounts. These considerations should be analyzed by decision-makers in order to better manage the water supply as signi cant variations in future years, especially for the trending sites can be expected.

Con ict of Interest
The authors have no con icts of interest to declare.

Availability of data and material
All the data can be obtained in the water supply concessionaire website.  Spatial distribution of gauges split into Seasons (columns) and Tests (rows). There are three conditions described: No trend, Decreasing trend, and Increasing trend. * WW row received a SON map since it was not identi ed a trend in WY for this test and this test was the only which indicated trending points for SON season.