Statistical modeling of annual highest monthly rainfall in Zimbabwe

The first statistical analysis of maximum rainfall in Zimbabwe is provided. The data are from 103 stations spread across the different climatic regions of Zimbabwe. More than 90% of the stations had at least 50 years of data. The generalized extreme value distribution was fitted to maximum rainfall by the method of maximum likelihood. Probability plots, quantile plots and Kolmogorov–Smirnov tests showed that the generalized extreme value distribution provided an adequate fit for all stations. The vast majority of stations do not exhibit significant trends in rainfall. Twelve of the stations exhibit negative trends and three of the stations exhibit positive trends in rainfall. Estimates of return levels are given for 2, 5, 10, 20, 50 and 100 years.

Zimbabwe is one of the poorest countries in the world. A global business magazine has ranked Zimbabwe as the second poorest country in the world, see https:// bulaw ayo24. com/ index-id-news-sc-natio nal-byo-70943. html Its economy in recent years has been battered by lack of rainfall, drought, sanctions, AIDS pandemic, mass unemployment and hyper inflation. One of the major factors has been the lack of rainfall. Zimbabwe has experienced many periods of droughts. The most recent drought has been in December 2019, which ignited the worst hunger crisis the country has faced in nearly a decade. In November 2019, farmers received only 55% of normal rainfall. Livestock losses reached 2.2 million people in urban areas and 5.5 million in rural ones.
The aim of this paper is to provide the first statistical analysis of annual highest monthly rainfall in Zimbabwe. The following questions and more can then be answered: What are the wettest areas with respect to annual highest monthly rainfall? What are the driest areas with respect to annual highest monthly rainfall? Which areas are most variable with respect to annual highest monthly rainfall? Which areas are least variable with respect to annual highest monthly rainfall? The answers to these questions and more could lead to actions (for example, increased agricultural production in wet areas and planting of crops withstanding droughts in dry areas) which may be of help to improve the economy of Zimbabwe.
To the best knowledge of the authors, there have been no papers on maximum rainfall in Zimbabwe. A related paper on minimum rainfall is due to Chikobvu and Chifurira 1 . Focus on maximum rainfall than minimum rainfall is more meaningful. Minimum rainfall will be mostly zero for a country like Zimbabwe.
However, there have been several papers focusing on rainfall (not maximum rainfall) in specific regions of Zimbabwe. For example, Mooring et al. 2 examined the effect of rainfall on tick challenge at Kyle-Recreational-Park, Zimbabwe; Gargett et al. 3 examined the influence of rainfall on Black Eagle breeding in the Matobo Hills, Zimbabwe; Bourgarel et al. 4 studied the effects of annual rainfall and habitat types on the body mass of impala in the Zambezi Valley; Muchuru et al. 5 assessed variability of rainfall over the Lake Kariba catchment area in the Zambezi river basin; Sibanda et al. 6 studied long-term rainfall characteristics in the Mzingwane catchment of south-western Zimbabwe; and so on.
Many papers have been published on extreme rainfall from several other African countries. These papers have been written mostly by scientists from the West, with no collaboration with scientists based in Africa; see, for example, Williams et al. [7][8][9] , Williams and Kniveton 10 , Pohl et al. 11 , De Paola et al. 12 , Woodhams et al. 13 and Finney et al. 14 . This adds to the sickening attitude that the West has looked to Africa only for exploitation; not stopping with slave trade, not stopping with colonization, not stopping with stealing of minerals to make among others computers, the West continues scientific exploitation of Africa at an alarming level, see Wiegand et al. 15 . This paper is part of a crusade initiated by the second author to empower Africans to conduct their own research, see http:// educa teafr ica. org/.

Method
Let X denote a random variable representing the annual highest monthly rainfall. According to extreme value theory (see Leadbetter et al. 24 , Resnick 25 and Embrechts et al. 26 ), the cumulative distribution function of X can be approximated by denotes a location parameter, σ > 0 denotes a scale parameter and −∞ < ξ < ∞ denotes a shape parameter. Note that if ξ > 0 then X has a heavy tail bounded below by µ − σ/ξ . If ξ < 0 then X has a short tail bounded above by µ − σ/ξ.
The distribution in (1) is known as the generalized extreme value (GEV) distribution. The GEV distribution was fitted to the data in "Data" by the method of maximum likelihood, see Coles 27 for details. The command fgev in the R package evd 20,28 was used to compute the maximum likelihood estimates. Other distributions (for example, the normal distribution) may provide better fits to the annual highest monthly rainfall. But the GEV distribution is theoretically justified.
Let µ , σ and ξ denote the maximum likelihood estimates of µ , σ and ξ , respectively. A quantity of interest based on (1) is the T-year return level loosely interpreted as the annual highest monthly rainfall expected on average once in every T years. Let x T denote the T-year return level corresponding to (1). It must satisfy Consent to participate. All authors gave explicit consent to participate in this study.
(3)  www.nature.com/scientificreports/ Consent to publish. All authors gave explicit consent to publish this manuscript.

Results and discussion
The GEV distribution was fitted to the annual highest monthly rainfall data from each of the 103 stations. The estimates ξ were found to be positive for sixteen of the 103 stations. They are Beitbridge, Bikita Agric, Buffalo Range, Buhera, Chisumbanje, Glendale Rail, Kezi, Lupane, Matopos Research Station, Middle Sabi Tanganda, Mphoengs, Nyamadhlovu, Rukomechi, Sawmills, Tashinga and West Nicholson. The distribution of annual highest monthly rainfall for these stations is heavy tailed, meaning that the rainfall recorded at these stations can be unbounded. The distribution of annual highest monthly rainfall for the remaining eighty seven stations is short tailed and is bounded above by µ − σ / ξ , which will be referred to as the probable maximum of annual highest monthly rainfall. The estimates of the probable maximum of annual highest monthly rainfall and their standard errors are given in Table 2.
The largest of the probable maximum of annual highest monthly rainfall is for Plumtree, and the second largest of the probable maximum of annual highest monthly rainfall is for Mutare Fire, but both have large standard errors. The smallest of the probable maximum of annual highest monthly rainfall is for Rupike. The second smallest of the probable maximum of annual highest monthly rainfall is for Bulawayo Goetz.
In parallel to Table 2, the 100-year return levels of annual highest monthly rainfall for all of the stations were also computed. These estimates and their standard errors are given in Table 3. The largest of the return level is     www.nature.com/scientificreports/ for Rukomechi, and the second largest of the return level is for Chisengu, but one of these has a large standard error. The smallest of the return level is for Rupike. The second smallest of the return level is for Tuli Police. However, many of the locations in Tables 2 and 3 have large standard errors compared to the estimates of probable maximum/100-year return level. In Table 2 Having checked the goodness of fit, (3) was computed for every station and a range of values of T. Plots of x T for T = 2, 5, 10, 20, 50, 100 years are shown in Figs. 6 and 7.      www.nature.com/scientificreports/ According to the 2-year return level, the wettest areas are those around Shurugwi, those around Harare and that between Masvingo and Mutare. The driest areas are those bordering Botswana and South Africa. The picture for the 5-year return level is similar, but the wettest regions are smaller compared to those for the 2-year return level.
According to the 10-year return level, the wettest areas are those around Shurugwi, an area between Masvingo and Mutare and a northern area bordering Zambia. The driest areas are once again those bordering Botswana and South Africa. The picture for the 20-year return level is similar, but the wettest regions are smaller compared to those for the 10-year return level. www.nature.com/scientificreports/ www.nature.com/scientificreports/ According to the 50-year return level, the wettest area is a northern area bordering Zambia. The driest areas are once again those bordering Botswana and South Africa. The picture for the 100-year return level is similar, but the wettest region is smaller compared to that for the 50-year return level.
Finally, significant trends in the annual highest monthly rainfall for each station are investigated. The distribution (1) with the location parameter µ = a + b × Year was fitted, where b is the trend parameter. The trend was seen to be significant or not by comparing the fit of this model with the earlier fit of the GEV distribution. Models like µ = a + b × Year + c × Year 2 and µ = exp (a + b × Year) were also fitted, but they did not provide significantly better fits. The methodology used for fitting models like µ = a + b × Year is described in Chapter 6 of Coles 27 . Table 4 lists the station names and the parameter estimates of a and b, and p-values showing significance of the trend (since they are all less than 0.05). For the stations not listed in Table 4  The driest areas are those bordering Botswana and South Africa. Drought resistent crops (including sunflower, millet, sorghum, bambara nuts and groundnuts) are being grown in these and other areas. Farmers are also using water saving "drip irrigation" methods to grow crops. According to Wikipedia, drip irrigation is a "type of micro-irrigation system that has the potential to save water and nutrients by allowing water to drip slowly to the roots of plants, either from above the soil surface or buried below the surface".
The results presented in this paper can inform positive actions by the Government of Zimbabwe: for example, further vegetables and other commodities less reliable on rain can be planted on areas showing negative trends; increased agricultural and electricity production based on water can take place in the wettest areas; increased electricity production based on solar energy can take place in the driest areas; and so on. www.nature.com/scientificreports/

Data availability
The data can be obtained from the corresponding author.

Code availability
The code can be obtained by contacting the corresponding author.