Fig 1.
A) The distribution of the total monthly rainfall (mean ± 1SD = 89.5 ± 59.4 mm) across months in the Masai Mara Ecosystem of Kenya averaged over 1965–2020. B) The decadal averages of the total monthly rainfall. The interannual variations in standardized deviates of the C) wet season rainfall (845.6 ± 196.5 mm), D) dry season rainfall (228.1 ± 79.0 mm), E) wet and dry season rainfall and F) annual rainfall (1062.4 ± 193.4 mm). The vertical needles are the standardized deviates, the solid curves are the 3-year moving averages and the dashed horizontal lines are percentiles of the frequency distributions of the rainfall deviates. G) Percentiles of the total annual, dry and wet season rainfall components used to classify years or seasons as extreme (≤ 10%), severe (10–25%) or moderate (25–40%) drought years (seasons), normal (40–75%), wet (75–90%), very wet (90–95%) or extremely wet (95–100%) years (seasons). H) Temporal variation in the original (blue vertical needles) and smoothed (red solid curve, smoothing done using generalized semiparametric linear mixed model) total monthly rainfall in Masai Mara from 1965 to 2020. I) Spectral density versus period of cycles (in years) for the annual, wet and dry season rainfall components. A large value of spectral density means strong evidence for the corresponding cycle period.
Fig 2.
A) The distribution of the total monthly rainfall (mean ± 1SD = 62.3 ± 64.8 mm) across months in the Narok Town of Kenya averaged over 1913–2024. B) The decadal averages of the total monthly rainfall. The interannual variations in standardized deviates of the C) wet season rainfall (626.2 ± 234.6 mm), D) dry season rainfall (121.2 ± 58.3 mm), E) wet and dry season rainfall and F) annual rainfall (740.2 ± 238.7 mm). The vertical needles are the standardized deviates, the solid curves are the 5-year moving averages for the annual and wet season rainfall and 2-years for the dry season and the dashed horizontal lines are percentiles of the frequency distributions of the rainfall deviates. G) Percentiles of the total annual, dry and wet season rainfall components used to classify years or seasons as extreme (≤ 10%), severe (10–25%) or moderate (25–40%) drought years (seasons), normal (40–75%), wet (75–90%), very wet (90–95%) or extremely (95–100%) wet years (seasons). H) Temporal variation in the original (blue vertical needles) and smoothed (red solid curve, smoothing done using generalized semiparametric mixed model) total monthly rainfall in Narok Town. I) Spectral density versus period of cycles (in years) for the annual, wet and dry season rainfall components. A large value of spectral density indicates strong evidence for the corresponding cycle period.
Fig 3.
Trend in average monthly maximum temperatures (cadet blue points) during the dry (left panel) and wet (right panel) seasons in Narok Town, Kenya, from 1960 to 2024.
The red solid curve is the penalized cubic basis spline smoothed temperature trend whereas the golden band is the approximate 95% pointwise confidence band.
Table 1.
The Southern Oscillation Index (SOI) parameter estimates from the univariate UCM.
Table 2.
Southern Oscillation Index (SOI) components significance tests.
These are tests of the significance of each component at the end of the estimation span.
Fig 4.
A. Smoothed level trend component for the Southern Oscillation Index (SOI) series. B. Smoothed cycle 1 component (high frequency cycle) for the Southern Oscillation Index (SOI) series with a cycle period of 1.6 years (18.7 months). C. Smoothed cycle 2 component (low frequency cycle) for the Southern Oscillation Index (SOI) series with a cycle period of 4.0 years (48.2 months). D. Smoothed level trend superimposed on the Southern Oscillation Index (SOI) series.
Table 3.
The Dipole Model Index (IOD) parameter estimates.
Table 4.
The Dipole Mode Index (IOD) components significance tests.
Fig 5.
A. Smoothed level trend component for the Indian Ocean Dipole Mode Index (IOD) series. B. Smoothed slope component for the Indian Ocean Dipole Mode Index (IOD) series. C. Smoothed cycle 1 component for the Indian Ocean Dipole Mode Index (IOD) with a cycle period of 4.1 years (49.58 months). D. Smoothed cycle 2 component for the Indian Ocean Dipole Mode Index (IOD) with a cycle period of 5.4 years (65.2 months). E. Smoothed increasing curvilinear trend superimposed on to the Indian Ocean Dipole Mode Index (IOD) series.
Fig 6.
A. Smoothed level trend component for the average monthly minimum temperature for Narok Town, Kenya. B. Smoothed slope component for the average monthly minimum temperature for Narok Town, Kenya. C. Smoothed secondary cycle (cycle1) component with a period of 2.2 years (26.4 months) for the average monthly minimum temperature for Narok Town, Kenya. D. Smoothed primary cycle (cycle 2) component with a period of 13.9 years (166.8 months) for the average monthly minimum temperature for Narok Town, Kenya. E. Smoothed trend superimposed over the observed average monthly minimum temperature series for Narok Town, Kenya.
Fig 7.
A. Smoothed level trend component for the average monthly maximum temperature for Narok Town, Kenya. B. Smoothed slope component for the average monthly maximum temperature for Narok Town, Kenya. C. Smoothed secondary cycle component (cycle1) for the average monthly maximum temperature for Narok Town, Kenya. Approximate cycle period is 1.4 years (16.5 months). D. Smoothed primary cycle component (cycle2) for the average monthly maximum temperature for Narok Town, Kenya. Approximate cycle period is 9.9 years (118.9 months). E. Smoothed trend superimposed on to the observed series for the average monthly maximum temperature for Narok Town, Kenya.
Fig 8.
A. Smoothed bivariate random walk trends for the wet and dry season rainfall components (each divided by its mean) during 1913–2024 in Narok Town, Kenya. B. Smoothed cycles for the bivariate random walk model for wet and dry season rainfall (each divided by its mean) in Narok Town, Kenya. The bivariate cycle has a cycle period of 9.3 years.
Fig 9.
A. Smoothed bivariate random walk trends for wet and dry season rainfall components (divided by their respective means) in Masai Mara, Kenya, during 1965–2020. B. Smoothed cycles for bivariate random walk model for wet and dry season rainfall (each divided by its mean) in Masai Mara, Kenya, during 1965–2020. The bivariate cycle has a period of 20.0 years.
Fig 10.
A. Smoothed bivariate random walk trends for wet and dry season rainfall in Seronera, Serengeti National Park, Tanzania. B. Smoothed cycles for bivariate random walk model for wet and dry season rainfall in Seronera, Serengeti National Park, Tanzania. The bivariate cycle has a period of 10.4 years.
Fig 11.
A. Smoothed bivariate random walk trends for wet and dry season rainfall in Ngorongoro Crater, Tanzania. B. Smoothed cycles for bivariate random walk model for wet and dry season rainfall in Ngorongoro Crater, Tanzania. The bivariate cycle has a period of 21.4 years.
Fig 12.
Smoothed bivariate random walk trends for average monthly minimum and maximum temperature for Narok Town, Kenya.
Fig 13.
Smoothed trivariate random walk trends for average monthly minimum and maximum temperature and total monthly rainfall for Narok Town, Kenya.
Fig 14.
Smoothed trivariate random walk trends for total monthly rainfall for Narok Town, Kenya, Southern Oscillation Index (SOI) and Indian Ocean Dipole Model Index (IOD).
Fig 15.
Smoothed trivariate random walk trends for total monthly rainfall for Masai Mara, Kenya, Southern Oscillation Index (SOI) and Indian Ocean Dipole Model Index (IOD).
Fig 16.
Smoothed trivariate cycles for total monthly rainfall for Masai Mara, Kenya, Southern Oscillation Index (SOI) and Indian Ocean Dipole Mode Index (IOD).
Fig 17.
Smoothed trivariate random walk trends for total monthly rainfall for Seronera, Serengeti, Tanzania, Southern Oscillation Index (SOI) and Indian Ocean Dipole Mode Index (IOD).
Fig 18.
Smoothed multivariate integrated random walk trends for total monthly rainfall, average monthly minimum and maximum temperatures for Narok Town, Kenya, Southern Oscillation Index (SOI) and Indian Ocean Dipole Model Index (IOD).
Fig 19.
Smoothed quadrivariate random walk trends for monthly average rainfall, total monthly rainfall, average monthly minimum and maximum temperatures for Narok Town, Kenya.