Local modeling

Statistical modeling of highest monthly rainfall in Zimbabwe

The GEV distribution was fitted to the highest annual monthly precipitation data from each of the 103 stations. Estimates (widehat{xi }) tested positive for sixteen of the 103 stations. These 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 highest monthly annual precipitation distribution for these stations is heavy-tailed, which means that the precipitation recorded at these stations can be unlimited. The distribution of monthly highest annual precipitation for the remaining eighty-seven stations is short and bounded above by (widehat{mu } – widehat{sigma } / widehat{xi }), which will be called the probable maximum of the highest monthly annual precipitation. Estimates of the probable maximum of the highest monthly annual precipitation and their standard errors are given in Table 2.

Table 2 Estimates and standard errors of the probable maximum of the highest monthly annual precipitation.

The largest of the annual highest probable monthly precipitation maximum is for Plumtree, and the second largest of the annual highest probable monthly precipitation maximum is for Mutare Fire, but both have large standard errors. The smaller of the probable maximum of the highest monthly precipitation is for Rupike. The second smallest of the highest probable monthly rainfall maximum is for Bulawayo Goetz.

Along with Table 2, the 100-year return levels of the highest monthly annual precipitation for all stations were also calculated. These estimates and their standard errors are given in Table 3. The highest level of return is for Rukomechi, and the second highest level of return is for Chisengu, but one of them has a large standard error. The smallest of the return levels is for Rupike. The second smallest of the return level is for the Tuli Police.

Table 3 Estimates and standard errors of the 100-year return level of the highest monthly precipitation.

However, many of the localities in Tables 2 and 3 have large standard errors from the estimates of the maximum/100-year probable return level. In Table 2, these are Acturus Mine, Centenary, Chimanimani DA, Chisengu, Chivhu, Eiffel Flats Blue, Forthergill, Gwanda Rail, Harare Airport, Harare Belvedere, Hwange National Park, Kwekwe, Makoholi, Mberengwa DA, Mutare Fire , Mvuma Arex, Nkayi, Odzi Police Rail, Plumtreee, Rusape, Rutenga, Selous, Tuli Police, Trelawney West Enton, Tsholotsho and Victoria Falls. In Table 3, these are Buffalo Range, Buhera, Centenary, Chimanimani DA, Chisengu, Chisumbanje, Forthergill, Glendale Rail, Gwanda Rail, Harare Belvedere, Hwange National Park, Kezi, Lupane, Makoholi, Matopos Research Station, Mberengwa DA, Middle Sabi Tanganda, Mphoengs, Mutare Fire, Mvuma Arex, Nkayi, Nyamadhlovu, Odzi Police Rail, Plumtreee, Rutenga, Tashinga, Tuli Police, Trelawney West Enton, Tsholotsho and West Nicholson. Conclusions for these locations should be treated with caution.

The fit of the GEV distribution for each station was verified by probability plots, quantile plots and the Kolmogorov-Smirnov test. The plots are shown in Figs. 4 and 5 for two of the stations. The plots were similar for the other stations. the p-the Kolmogorov-Smirnov test values ​​for the two stations were 0.081 and 0.078. the p-the values ​​for the other stations were also greater than 0.05. Therefore, the GEV distribution provides an adequate fit for all stations.

Figure 4

Probability (left) and quantile (right) plots for Bulawayo airport with simulated 95% confidence intervals (dashed lines). R software, version 4.1.2, https://www.r-project.org/ was used for plotting.

Figure 5
number 5

Probability (left) and quantile (right) plots for Harare Airport with simulated 95% confidence intervals (dashed lines). R software, version 4.1.2, https://www.r-project.org/ was used for plotting.

After checking the goodness of fit, (3) was calculated for each station and a range of values ​​from J. Plots of (x_T) for (T = 2, 5, 10, 20, 50, 100) years are shown in Figs. 6 and 7.

Figure 6
number 6

Estimates of the 2-year return level (first row, left), 2-year to 10-year return level (first row, middle), 2-year to 20-year return level (first row, right), 5-year yield (second row, left), level of 5-year yield 10 years ahead (second row, middle), level of 5-year yield 20 years ahead (second row, right), level 10-year yield level (third row, left), 10-year yield level 10 years ahead (third row, middle), and 10-year yield level 20 years ahead (third row, right). ggplot2 version 3.3.5, https://cran.r-project.org/web/packages/ggplot2/index.html was used for plotting.

Picture 7
number 7

Estimates of the 20-year return level (first row, left), 20-year return level 10 years ahead (first row, middle), 20-year return level 20 years ahead (first row , right), 50-year yield level (second row, left), 50-year yield level 10 years ahead (second row, middle), 50-year yield level 20 years ahead (second row, right), 100-year yield level (third row, left), 100-year yield level 10 years ahead (third row, middle) and 100-year yield level 20 years ahead ( third line, right). ggplot2 version 3.3.5, https://cran.r-project.org/web/packages/ggplot2/index.html was used for plotting.

According to the 2-year return level, the wettest areas are those around Shurugwi, those around Harare and the area between Masvingo and Mutare. The driest areas are those bordering Botswana and South Africa. The chart for the 5-year return level is similar, but the wettest regions are smaller than 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 again those bordering Botswana and South Africa. The chart for the 20-year return level is similar, but the wettest regions are smaller than those for the 10-year return level.

According to the 50-year return level, the wettest area is a northern area bordering Zambia. The driest areas are again those bordering Botswana and South Africa. The chart for the 100-year return level is similar, but the wettest region is smaller than that of the 50-year return level.

Finally, the significant trends in the highest monthly annual precipitation for each station are studied. The distribution (1) with the location parameter (mu = a + b times mathrm{Year}) was installed, where b is the trend parameter. The trend was judged significant or not by comparing the fit of this model with the previous fit of the GEV distribution. Models like (mu = a + b times mathrm{Year} + c times mathrm{Year}^2) and (mu = exp left( a + b times mathrm{Year} right) ) were also adjusted, but they did not provide significantly better adjustments. The methodology used to fit models like (mu = a + b times mathrm{Year}) is described in chapter 6 of Coles27.

Table 4 Stations showing significant trends in the location parameter.

Table 4 lists the names of the stations and the estimates of the parameters of a and band p-significant values ​​of the trend (since they are all less than 0.05). For stations not listed in Table 4, the p-values ​​were greater than 0.05, so trends were not significant. Only 15 of the 103 stations show significant trends. Of the 15 stations, 12 stations show negative trends. These stations are plotted in red in Figs. 6 and 7. The remaining 3 stations show positive trends. These stations are plotted in blue in Figs. 6 and 7. The return level estimates 10 years ahead and 20 years ahead data records for (T = 2, 5, 10, 20, 50, 100) years are also shown in Figs. 6 and 7. Estimating the level of return m years before the data records was calculated using

$$begin{aligned} displaystyle x_T = widehat{a} + widehat{b} left( text{ Last } text{ year } text{ of } text{ records } + m right) + frac{widehat{sigma }}{widehat{xi }} left{ left[ -log left( 1 – frac{1}{T} right) right] ^{-widehat{xi }} – 1 right} . end{aligned}$$

The general trend is for the weather to get drier over time. However, the changes are only statistically significant at the 15 stations.

Negative trends may be due to climate change or other factors. But this should be treated with caution as seven of the fifteen stations have limited data: Gwanda Rail (1909–2011), Headlands Rail (1916–2013), Hwange Rail (1909–2011), Marula West (1909–2014), Rutenga (1955–2006), Rugare Tengwe Thurlaston (1952–2002) and Tuli Police (1898–2001).