https://orcid.org/0000-0002-7379-0387
Figures
Abstract
Understanding climate and vegetation trends and variations is essential for conservation planning and ecosystem management. These elements are shaped by regional manifestations of global climate change, impacting biodiversity conservation and dynamics. In the southern hemisphere, global climate change is partially reflected through trends in the hemispheric Southern Oscillation (SOI) and regional oscillations such as the Indian Ocean Dipole Mode (IOD). These phenomena influence rainfall and temperature changes, making it crucial to understand their patterns and interdependencies. Appropriately analyzing these variables and their interrelations therefore requires a robust multivariate statistical model, a tool seldom employed to extract patterns in climate and vegetation time series. Widely used univariate statistical methods in this context fall short, as they do not account for interdependencies and covariation between multiple time series. State-space models, both univariate and multivariate, adeptly analyze structural time series by decomposing them into trends, cycles, seasonal, and irregular patterns. Bivariate and multivariate state-space models, in particular, can provide deeper insights into trends and variations by accounting for interdependencies and covariation but are rarely used. We use univariate, bivariate and multivariate state space models to uncover trends and variations in historic rainfall, temperature, and vegetation for the Greater Mara-Serengeti Ecosystem in Kenya and Tanzania and potential influences of oceanic and atmospheric oscillations. The univariate, bivariate and multivariate patterns reveal several insights. For example, rainfall is bimodal, shows significant interannual variability but stable seasonality. Wet and dry seasons display strong, compensating quasi-cyclic oscillations, leading to stable annual averages. Rainfall was above average in both seasons from 2010–2020, influenced by global warming and the IOD. The ecosystem experienced recurrent severe droughts, erratic wet conditions and a 4.8 to 5.8°C temperature rise over six decades. The insights gained have important implications for developing strategies to mitigate climate change impacts on ecosystems, biodiversity, and human welfare.
Citation: Ogutu JO, Bartzke GS, Mukhopadhyay S, Dublin HT, Senteu JS, Gikungu D, et al. (2024) Trends and cycles in rainfall, temperature, NDVI, IOD and SOI in the Mara-Serengeti: Insights for biodiversity conservation. PLOS Clim 3(10): e0000388. https://doi.org/10.1371/journal.pclm.0000388
Editor: Tao Zhang, Northeast Normal University, CHINA
Received: February 19, 2024; Accepted: August 20, 2024; Published: October 2, 2024
Copyright: © 2024 Ogutu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All the data used in this paper are included in the supplementary materials.
Funding: The Masai mara Ecological Monitoring Program was funded by the Worldwide Fund for Nature-East Africa Programme (WWF-EARPO) and Friends of Conservation (FOC). The programme also received financial, material or logistical support from WWF-Sweden, the Darwin Initiative through DICE, Cottar’s Camp, Kichwa Tembo and Ker and Downey Safaris. JOO was supported by a grant from the German Research Foundation (DFG, Grant # 257734638). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 641918. IOB was supported by the German Research Foundation (DFG) (OB 490/2–1).
Competing interests: The authors have declared that no competing interests exist.
Introduction
Global climate change and variation are now widely recognized, yet their regional manifestations and consequences for biodiversity conservation and dynamics, especially in the southern hemisphere, are less well understood [1–5]. In the Southern hemisphere and particularly in East Africa, climate change is primarily manifested through fluctuations in the hemispheric El Niño-Southern Oscillation (ENSO), the regional IOD and local rainfall and temperature variations [6–8]. It follows that understanding trends and variation in rainfall and temperature and how these are influenced by SOI and IOD is basic to understanding regional consequences of global climate change. While many studies have focused on analyzing individual climatic components using univariate statistical methods, such analyses often overlook the potential interdependencies and covariation among these components. This is evident, for instance, in the extensive univariate research conducted on trends and variation in individual climatic components in the Greater Mara-Serengeti Ecosystem (GMSE) of Kenya and Tanzania [2, 3, 9–13].
Whereas such univariate analyses can reveal useful and interesting patterns in trends and variation in climatic and vegetation components, they fail to account for the potentially complex interrelationships among climatic and vegetation components. Accounting for interrelationships and covariation between multiple climatic and vegetation components requires using bivariate or multivariate models for temporal trends and variation. As a result, joint analyses of trends and variation in climatic and vegetation components using bivariate or multivariate statistical models can reveal insights that go beyond those obtainable from univariate statistical models alone [14–16]. Bivariate and multivariate state-space models are a particularly powerful, flexible and useful class of models for joint analysis of trends and variation in multiple time series [14, 15, 17].
State-space models are especially well suited for analysing trends and variation in time series of climatic and vegetation variables [3, 18, 19] because they decompose such series into intuitively interpretable but unobservable additive components [14, 17, 20, 21]. These include trend (level and slope), cyclical, seasonal and irregular (random) components. The trend component quantifies change, the cycles characterize periodic or quasi-periodic oscillations and can be deterministic and persistent or stochastic and transient whereas the seasonal component defines intra-annual oscillations and can be stable and persistent or time-varying. Yet, despite their intuitive appeal, utility and elegant decomposition of time series of climatic or other variable types into readily understandable components, state-space models have only rarely been used to analyse trends and variation in climatic variables, including for the GMSE [3, 11, 18, 19].
Bivariate and multivariate models for trend and variation in climatic variables can potentially reveal more subtle patterns and insights than can univariate models. For example, bivariate models can better characterize bivariate cycles in weather components, such as rainfall and temperature, which can have widely different impacts on vegetation and animals than can independent cycles in both components. Moreover, univariate models are less likely to accurately characterize rainfall, temperature and vegetation cycles that are inextricably linked through physical processes that may have confounding interrelationships. For instance, rising air masses driven by heat can generate rainfall due to convection in the upper, cooler layers of the atmosphere [22]. But in regions influenced by moisture influx from water bodies such as oceans or large lakes, temperature warming can entail an increase in rainfall [23]. In contrast, if temperatures increase but moisture influx remains low, for example, under continental weather conditions, prolonged and severe droughts may result [23].
The intricate feedback mechanisms among temperature, rainfall and vegetation productivity further complicate their interrelationships, highlighting the importance of allowing for interdependence and covariation among multiple variables. For example, temperature-driven rain cloud formation enhances the albedo effect, resulting in a greater reflectance of the solar radiation back into space in the daytime [22]. Moreover, clouds absorb infrared radiation from the Earth’s Surface, resulting in higher temperatures predominantly during night time [22]. On global scales the cooling effects of clouds predominate [22]. Furthermore, the interplay among rainfall, temperature and vegetation can significantly impact plant productivity, rainfall and temperature with potential for both enhancement and reduction under varying conditions [23–26].
Seasonal cycles, driven by phenomena such as the Intertropical Convergence Zone (ITCZ), also play a crucial role in the African savannas, affecting plant and animal populations and, consequently, biodiversity dynamics and conservation. Seasonal cycles in rainfall and plant productivity are pervasive features of many biomes including African savannas. The seasonal fluctuations in the African savannas are driven by phenomena such as the movement of the ITCZ, a belt of rising and convecting air masses around the equator [27, 28]. The seasonal oscillations in solar radiation affect evaporation, convection and consequently rainfall, inducing wet and dry phases during the climatic year.
Furthermore, the GMSE is subject to both seasonal and inter-annual cycles of rainfall and temperature, which are critical in shaping the migration patterns of wildlife and the productivity of plants and animal populations. These cycles, varying in length and influenced by oceanic and atmospheric oscillations, can significantly affect the ecosystem’s dynamics. In the GMSE, rainfall during the wet season is the major driver of the phenology and synchrony of reproduction in many plant and animal species [29–31]. Seasonality and spatial gradients in rainfall in the GMSE also drive the migration of thousands of wildebeest (Connochaetes taurinus), zebra (Equus quagga), Thomson’s gazelle (Eudorca thomsoni) and eland (Tautragus oryx) that track the rainfall-mediated vegetation greening to feed, give birth and raise their young [32–35]. The wet season rainfall generates most of the annual forage production but the dry season rainfall is indispensable for the survival of plants and animals in times of resource limitations [36–38]. Failure of the dry season rainfall is thus associated with severe food scarcity and elevated herbivore mortality [18, 19, 39, 40]. Cyclic relationships have also been established between rainfall and population dynamics [41] and fecundity and fertility [31, 42] of African savanna ungulates. Oscillations in rainfall, temperature and vegetation can therefore strongly influence plant and animal population dynamics, with important implications for biodiversity dynamics and conservation in savannas and other biomes.
In addition to seasonal cycles, inter-annual rainfall cycles can exert major impacts on the productivity of plant and animal populations [41, 43]. The dominant inter-annual rainfall cycle periods in East Africa typically range from 2 to 13 years but can vary markedly in space and time [3, 18, 19, 44–47]. Thus, wet and dry phases can last as long as 10 to 20 years [48]. For minimum and maximum temperatures, cycle periods can range between 2 and 30 years [49]. In the GMSE in particular, dominant rainfall cycles have time-varying periods ranging between 3 and 10 years [3, 10]. Signals have also been detected with longer but weaker cycles with periods spanning 20 to 40 years [10] and 15–25 years [29]. The cycle periods are likely related to hemispheric oceanic and atmospheric oscillations that operate on time scales of less (SOI, IOD) or more (Atlantic Multidecadal Oscillation-AMO) than a decade [50, 51]. The oscillations are largely driven by variations in sea surface temperatures in the Indian [52], Pacific [53] and Tropical Atlantic [54] Oceans.
Here, we use state-space models to characterize and understand long-term trends, cycles and seasonality in historic station rainfall, minimum and maximum temperatures, regional oceanic (IOD) and hemispheric atmospheric (SOI) oscillations and remotely sensed vegetation data, indexed by the Normalized Difference Vegetation Index (NDVI) in the Greater Mara-Serengeti Ecosystem of Kenya and Tanzania (Fig DE in S1 File). Our primary aim is to detect and quantify trends and oscillations in the weather and vegetation components in the GMSE. Moreover, we aim to explore the potential influences of oceanic (IOD) and atmospheric (SOI) oscillations, on regional rainfall and temperature trends and variation. To achieve this, we establish if the cycles are deterministic and persistent or stochastic and transient. As well, we test if rainfall seasonality is stable or changing over time. We use univariate, bivariate and multivariate state-space models to uncover individual and joint trends and variations in the climatic and vegetation components and interpret their implications for biodiversity dynamics and conservation in the GMSE and possibly elsewhere. We interpret and illustrate the consequences of climate change and variability for wildlife population dynamics and biodiversity conservation by drawing on historical records from the annual reports of Kenya’s Game Department, its successor, the Wildlife Conservation and Management Department (WCMD), and district administrations of Kenya. These records collectively date back to the 20th century.
The data
The data set includes time series of SOI (January 1913 to May 2024; S1 Data), IOD (January 1913 to January 2024; S2 Data), as well as average monthly minimum and maximum temperatures (January 1960 to May 2024; S3 and S4 Datas) and total monthly rainfall (January 1913 to May 2024; S4 and S5 Datas) recorded in Narok Town, southwestern Kenya. The average monthly minimum and maximum temperatures are daily records averaged for each month. The rainfall and temperature data were provided by the Kenya Meteorological Department (KMD). Each digital record of Narok Town’s total monthly rainfall from April 1913 to May 2024 was cross-checked against the corresponding original, handwritten monthly data cards and ledger book from the Narok Meteorological Station. This verification process detected numerous errors in the initial digital data set from the KMD, which were subsequently corrected with KMD’s assistance. Consequently, the total monthly rainfall data set for Narok Town presented here is the most accurate for the 1913 to 2024 period. However, the temperature data was only partially verified due to the unavailability of some of the original records. Station rainfall data were also available for 15 rain gauges in the Masai Mara Ecosystem for the various recording periods from January 1965 to August 2020 (S6 and S7 Datas). We also analyse total monthly rainfall series recorded at Seronera in the Serengeti National Park (January 1981 –December 2015; S8 and S9 Datas) and at Ngorongoro Conservation Area Authority Headquarters (January 1963-December 2014; S10 and S11 Datas) in northern Tanzania. We verified these digital records against original paper records where available, but most original records were unavailable for both stations.
The SOI data set was downloaded from https://psl.noaa.gov/gcos_wgsp/Timeseries/Data/nino34.long.anom.data (accessed on 14 August 2024) and the IOD data set from
https://psl.noaa.gov/gcos_wgsp/Timeseries/Data/dmiwest.had.long.data (accessed on 14 August 2024).
The SOI is a standardized index calculated from the observed sea level pressure differences between Tahiti and Darwin, Australia. It tracks large-scale fluctuations in sea surface air pressure across the western and eastern tropical Pacific, reflecting the state of the Southern Oscillation during El Niño and La Niña episodes. El Niño, the oscillation’s warm phase, is typically associated with increased rainfall, whereas La Niña, the cold phase, often correlates with droughts in East Africa ([2] https://www.climate.gov/enso). NDVI indexes plant productivity. A combination of NDVI and rainfall indexes forage availability. NDVI generally does not distinguish between woody and herbaceous green biomass, and therefore quantifies different resources on treeless plains and woodlands [34, 55, 56]. The SPOT NDVI data set covered 1998 to 2014 because the CHIRPS 2017 blended station-satellite minimum temperature data used in the multivariate model ended in December 2013 (Climate Hazards Centre (2016) CHIRPS Diagnostics—Global station density—0.25 degrees. Available from: https://data.chc.ucsb.edu/products/CHIRPS-2.0/diagnostics/global_monthly_station_density/tifs/p25/; Accessed: August 21, 2017). The multivariate model involving SPOT NDVI used the CHIRPS minimum and maximum temperature and rainfall data (predicted using spatio-temporal hierarchical Bayesain state space model [11] averaged over a 5 × 5 km grid in Narok County (S12 Data). All the data sets used in the analyses are available in S1–S12 Datas in the supplementary materials.
The models
State-space models for trends and variation in climate and vegetation
The unobserved components model (UCM) for univariate time series of climate and vegetation.
We applied the unobserved components model (UCM) to analyse trends in univariate time series of SOI and IOD from 1913 to 2024, as well as the average monthly minimum and maximum temperatures in Narok Town from 1960 to 2024. Unlike these four variables, rainfall data were previously subjected to UCM modelling for univariate time series in Bartzke et al. [3]. Therefore, we do not repeat the univariate state space analysis for rainfall but instead consider aspects of the rainfall data not covered in that paper.
The UCM is a useful method for analysing temporal variations in univariate time series, which consist of observations collected at regular time intervals. This structural time series technique decomposes the series into easily interpretable additive components, including level, slope, cyclical, seasonal and irregular components. The level and slope components together form the trend component, while the irregular component represents the model’s overall random error, typically modelled as a white-noise process or an autoregressive moving average (ARMA) process. The UCM’s versatility and power lie in its ability to accommodate multiple cyclical components, serial autocorrelation in the residuals or auto-regression terms for the dependent variable. The parameters for the components can be fixed or time-varying, allowing considerable flexibility. In addition, the model supports explanatory covariates and handles missing values embedded in the dependent variable. But, our UCM model does not permit missing values in predictor variables.
The relationship between covariates and the dependent variable can be linear and time-invariant, linear and time-varying (random regression) or nonlinear (spline regression). Using the UCM modelling approach we searched for two main types of changes, namely additive outliers (AO) and level shifts (LS). An additive outlier is an unusual value in the series, possibly due to a data recording or processing error or a temporary shock to the series generation process. By contrast, a level shift is a permanent shift, upward or downward shift, in the series’ level. We examine different aspects of the outliers and level shifts, most notably their standard errors and statistical significance at all the time points in the series, with particular emphasis on those that are statistically significant.
We consider several special cases of the UCM including the 1) Random Walk Model, 2) Local Linear Trend Model, 3) Integrated Random Walk Model, 4) Random Walk With Drift and 5) Damped Local Linear Trend Model. The Random Walk Model consists of a stochastic or time-varying level trend component. The Local Linear Trend Model consists of both a random walk level trend and a random walk slope. The Integrated Random Walk Model, a special case of the Local Linear Trend Model, sets the disturbance variance of the level component to zero. The Random Walk With Drift is similar to the Local Linear Trend Model, but with a constant slope, as the disturbance variance of the slope component is zero. Lastly, the Damped Local Linear Trend Model, akin to the Local Linear Trend Model, has a slope following a first-order autoregressive model [3, 14, 17–19, 57].
A general unobserved components Model (UCM) can be expressed as
(1)
where
rt = rainfall (SOI, IOD, minimum or maximum temperature) at time t (with a maximum value T)
μt = level or time trend component
φt = cyclical component
δt = seasonal component
∂t = autoregressive component
βj = regression coefficients
xjt = regression covariates
, i.e., a Gaussian white noise process.
We selected the best-supported model from the preceding five basic UCM models (1 to 5), considering the level and slope (both modelling time trends), cycles, seasonality, auto-regression, white noise and possibly auto-correlated residuals. The UCM assumes normal distributions for both the univariate dependent series and all the disturbance variances. The UCM model fitting is accomplished using the Diffuse Kalman Filtering and Smoothing algorithm, with parameters estimated using maximum likelihood [58]. We fitted the univariate UCM models to the SOI, IOD and average monthly minimum and maximum temperature series for Narok Town using the SAS UCM procedure [17].
Multivariate (General) state space models for trend and variation in climatic or other variables.
The UCM is a special case of the general state space model which can be formulated in the general form as follows [17].
(2)
Rt is a pt ⋅ q response vector r = (r1, r2, r3, …, rq)
The states αt and the observation disturbances εt are random sequences
- ηt ∼ N(0, Qt) is the state disturbance and is independent of
- δ ∼ N(0, κΣ), κ ⟶ ∞
We use the general state space model to simultaneously analyse trends, cyclical and seasonal variation in multivariate time series of two or more of the climatic and vegetation variables. A detailed exposition of the general state space model is beyond the scope of this paper, so we will focus on its key features relevant to our bivariate and multivariate time series analyses. The general state space model offers the following features that generalize the capabilities of the univariate UCM model. (1) Multivariate trends, possibly correlated, among the individual series, including multivariate random walk and multivariate local linear trend. (2) Multivariate cycle, possibly correlated, among the individual series. (3) Multivariate season, possibly correlated, among the individual series. (4) Multivariate white noise, possibly correlated, among the individual series, including (multivariate) vector autoregressive moving average (VARMA) models. (5) Can handle either univariate, bivariate or multivariate data collected at irregular (longitudinal data) or regular (time series data) intervals. (6) Supports univariate continuous time cycle for univariate regularly and irregularly spaced data. (7) Can accommodate complex nonlinear relationships between the dependent and the explanatory series. (8) Can identify outliers and level shifts and provide the corresponding standard errors and statistical significance at each time point.
We consider only bivariate or multivariate versions of the basic models, including the Random Walk Model, Local Linear Trend Model, Integrated Random Walk Model, Random Walk Model with fixed slope and Damped Local Linear Trend Model, to select the best supported candidate model.
The general state space model assumes the multivariate dependent series follow a multivariate normal distribution. The general state space model is fitted using the Diffuse Kalman Filtering and Smoothing algorithm [58] and maximum likelihood is used to estimate the model parameters. We fitted the multivariate state space models in the SAS SSM procedure [17], and all SAS program codes used to fit both the UCM and SSM models are included in the Supplementary materials to this paper.
We performed the following analyses. (1) Univariate unobserved components model analysis or structural time series analysis of the (i) SOI, (ii) IOD, (iii) average monthly minimum and (iv) average monthly maximum temperatures recorded at the Narok Meteorological Station in Narok Town located in Narok County in Southwestern Kenya. This extends our previous work, which only covered rainfall time series analysis [3]. (2) Bivariate state space model analyses of trends and cycles in the wet and dry season rainfall components in Narok Town and in the Masai Mara Ecosystem in Kenya, Ngorongoro Crater and Seronera in Serengeti National Park in Tanzania. (3) Bivariate state space analyses of trends, cycles and seasonality in Narok Town’s average monthly minimum and maximum temperatures. (4) Trivariate state space models of trends, cycles and seasonality in Narok Town’s average monthly minimum and maximum temperatures and total monthly rainfall. (5) Trivariate state space model analyses of trends, cycles and seasonality in SOI, IOD and total monthly rainfall for Narok Town, Masai Mara Ecosystem, Ngorongoro Crater and Seronera. (6) Pentavariate state space model analyses of trends, cycles and seasonality in average monthly minimum and maximum temperatures and total monthly rainfall in Narok Town, SOI and IOD. (7) Tetravariate state space model analysis for trends, cycles and seasonality in monthly averages of SPOT NDVI, average monthly minimum and maximum temperatures and total monthly rainfall. The SAS program codes used to prepare all the data, fit all the models and produce all the graphs are provided in S1 and S2 Texts.
Results
Univariate trends and variation in station rainfall and temperature in Masai Mara Ecosystem and Narok Town of Kenya
Temporal trend and variation in monthly, seasonal and annual rainfall in Masai Mara and Narok Town.
Rainfall in the Mara and Narok regions exhibits a distinct bimodal pattern, characterized by significant temporal and interannual variations. Rainfall in the Mara is distinctly bimodal, with a minor peak in December during the short rains (November-December) and a major peak in April during the long rains (January-June). During the dry season (July-October), the average total monthly rainfall of 57.1 ± 35.2 mm (range: 52.4 to 61.7 mm) is significantly lower than that during the wet season months (November-June) of 106.1 ± 62.4 mm (range: 99.8 to 111.0 mm, Fig 1A). Despite striking temporal variation, rainfall seasonality remains remarkably stable (Fig 1A). Both the seasonal and annual rainfall components demonstrate strong, sustained quasi-cyclic oscillations, with the wet and dry season components often compensating each other to maintain a rather stable annual average rainfall of about 1000 mm (Fig 1C–1F). However, from 2010 to 2020, an unusual in-phase alignment of the wet and dry season components led to wetter conditions more favourable for agriculture and livestock ranching (Fig 1E), reflecting an extended and intensified phase of the 6-10-year local rainfall cycle, amplified by the IOD and global warming (Fig 1H). The high dry season rainfall during 2003–2020 mirrors patterns last seen in the mid-1970s, while the high wet season rainfall is unprecedented in the last half-century and is therefore rare and transient. Notably, the wet season rainfall trended upwards between 2003 and 2020 (Fig 1C).
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.
Despite increased rainfall during 2010–2020, droughts remain frequent and intense in the Mara (Fig 1G). The droughts are associated with strong interannual variations in the annual and seasonal rainfall components. During 1965–2020, the total annual rainfall averaged 1062.4 ± 193.4 mm (range: 653.4 to 1506 mm). The wet season rainfall averaged 845.6 ± 196.7 mm (range: 500.7 to 1243.5 mm), whereas the dry season rainfall averaged 228.1± 79.0 mm (range: 100.0 to 465.8 mm) (Fig 1C–1F). The annual and seasonal rainfall components exhibited quasi-periodic cycles of about 3 years for the annual, wet and dry season components (Fig 1I). Based on the annual rainfall, extreme droughts occurred in 1982, 1984, 1993, 1999 and 2006 and severe droughts in 1967, 1969, 1972, 1973, 1976, 1985–1986 and 1997. In contrast, very wet to extremely wet years were 1974, 1998, 2001, 2007, 2012, 2016 and 2018 (Fig 1G).
Likewise, rainfall in Narok is distinctly bimodal, with a minor peak in December during the short rains (November-December) and a major peak in April, during the long rains (January-May). The total monthly rainfall during 1913–2024 averaged 62.3 ± 64.8 mm (range: 0–419.6 mm) (Fig 2A). Decadal averages of the total monthly rainfall reveal a striking stability in rainfall seasonality over the last century (Fig 2B). The monthly, wet (November-May) and dry (June-October) season rainfall components all showed marked interannual variations. The wet season component averaged 626.2 ±234.6 mm (range: 256.9 to 1396.8 mm), the dry season total averaged 121.2 ±58.0 mm (range: 30.2–333.6 mm). The average total annual rainfall was 740.2 ± 238.7 mmm (range: 341.5 to 1602.3 mm) (Fig 2C–2F and 2H).
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.
The seasonal rainfall components showed quasi-cyclic oscillations, with approximate cycle periods of 5.2 (and 2.5) years for the wet season and annual rainfall and 2.2 (and 4.2) years for the dry season. The wet season rainfall increased from 1914 to 1974 and then declined. Overall, the wet and dry season rainfall totals were below average for extended periods but above average at other times during 1913–2024 (Fig 2C–2F and 2I). Classification of the 112 years into dry and wet years using quantiles of the frequency distribution of the annual and seasonal rainfall totals identified many extreme (1918, 1924, 1933, 1934, 1938, 1943, 1949, 1953, 1976, 1984 and 2000) and severe (1915, 1928, 1929, 1941, 1944, 1946, 1948, 1961, 1965, 1986, 1991, 1992, 1999, 2005, 2009, 2017 and 2019) drought years, a few very wet (1917, 1942, 1957, 1963, 1978 and 2003) and extremely wet (1930, 1962, 1964, 1998, 2020 and 2024 (wet season only)) years (Fig 2G). This demonstrates droughts are recurrent and often severe to extreme in Narok. The bimodal rainfall patterns in the Mara and Narok regions are thus marked by significant temporal and interannual variations. Despite the recent increase in rainfall, both regions remain highly susceptible to extreme droughts, reflecting the complex interplay of local and global climatic factors. Understanding these patterns is crucial for effective agricultural, livestock and ecosystem management in the face of climate change and variability.
Temporal trend and variation in station temperature in Narok Town, Kenya.
Monthly minimum temperature in Narok Town increased significantly from 1960 to 2024, reflecting broader climate trends with notable fluctuations and an overall rise of 5.3°C.
Monthly temperatures in Narok Town have exhibited significant changes, particularly the minimum component, which has risen markedly from 7.9°C (95% CL: 7.2 to 8.6°C) in May 1960 to 13.2°C (CL: 12.0 to 14.4°C) in May 2024. The increase from 7.7°C in January 1960 to 9.4°C in May 1968 was followed by a decrease to a low of 4.0°C in June 1973, after which temperatures increased steadily, reaching 14.4°C in May 2024. This represents a substantial rise of 5.3°C over the six decades (Fig 3A).
The red solid curve is the penalized cubic basis spline smoothed temperature trend whereas the golden band is the approximate 95% pointwise confidence band.
Concurrently, monthly maximum temperature has also varied widely, rising above the average of 24.8°C during periods when minimum temperature was at its lowest. The average monthly maximum temperature increased by 1.4°C from 25.1°C (95% CL: 23.1 to 27.5°C) in May 1960 to 26.5°C (24.2 to 29.0°C) in May 2024 (Fig 3A).
Throughout the seasons, the monthly minimum temperature averaged across all months has risen consistently. In the wet season, it increased from 8.8°C (8.1 to 9.5°C) in 1960 to 12.5°C (12.0 to 13.1°C) in 2024, while in the dry season, it rose from 7.8°C (7.8 to 8.5°C) in 1960 to 11.5°C (10.9 to 12.0°C) in 2024. Similarly, the monthly maximum temperature has increased persistently, rising in the wet season from 25.0°C (24.2 to 25.7°C) in 1960 to 26.2°C (25.6 to 26.8°C) in 2024 and in the dry season from 23.0°C (22.3 to 23.8°C) in 1960 to 24.1°C (24.2 to 24.8°C) in 2023 (Fig 3). These findings highlight the significant warming trend in Narok Town, with rising minimum temperatures indicating potential impacts on local climate, agriculture and ecosystems. The persistent increase in both minimum and maximum temperatures underscores the broader implications of climate change in the region.
Univariate unobserved components model analysis of the SOI series
All the results related to the state-space model that are not included in the main results section are reported in S1 File that contains all supplementary figures (Figs A–CT in S1 File) and supplementary tables (Tables A–U in S1 File).
The UCM analysis of the SOI series spanning January 1913 to May 2024 reveals significant stochastic oscillations and cycles, despite an overall constant trend. The analysis of the SOI series, comprising 1337 months of data, without missing values, spanning January 1913-May 2024, averaged -0.04839 ± 0.7716 (1 SD, range: -2.18 to 2.57). The best UCM model for the trend in the SOI series incorporates a constant and insignificant level, two cyclic and irregular components, achieving an adjusted r2 = 0.86503 (Table A in S1 File). Residual statistics and loess smoothed residuals for the UCM model fit to the SOI time series (Figs A and B in S1 File) affirm a satisfactory model fit. Table 1 presents the estimated model parameters, their standard errors and t-tests, showing that the disturbance variance of the level component is not significant but that the error variances for the irregular and both cycle components are, revealing that the latter three components are stochastic. The reported t-values are approximations, dependent on the model’s validity and the series length and should be cautiously interpreted, due to potentially misleading probabilities, especially for parameters near the boundary of the parameter space [14, 57]. This is because the distributional properties of the maximum likelihood estimate of the general UCMs are yet to be fully studied. For certain parameters, such as the cycle period, the t-values in the UCM parameter estimates are uninformative because it is never necessary to compare the estimated parameter with zero. In such cases, both the t values and their probability values should be simply disregarded.
The estimated cycle periods are 1.6 years (18.7 months) for Cycle 1 and 4.0 years (48.2 months) for cycle 2. Towards the estimation span’s end, chi-square tests with approximate p-values indicate the insignificance of the irregular, level and the first cycle component but the significance of the second cycle component (Table 2).
These are tests of the significance of each component at the end of the estimation span.
The SOI series showed a flat and statistically insignificant level trend (Fig 4A), stochastic and transient oscillations with a 1.6-year cycle period (Fig 4B) and a deterministic and persistent 4-year cycle (Fig 4C). Both cycles exhibit quasi-periodic behaviours with time-varying amplitudes and phases. The smoothed level trend component superimposed on the observed SOI series (Fig 4D) corroborates the flat and statistically insignificant, level trend in SOI during 1913–2024.
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.
Univariate unobserved components model analysis of the Indian Ocean Dipole Mode Index IOD
The UCM analysis of the IOD from January 1913 to January 2024 reveals significant and deterministic trends in level and slope components alongside a notable stochastic cycle, indicating a persistent curvilinear increase over the study period (Table 3). Likewise to the SOI, we analysed the 1333 records of the IOD, covering January 1913 to January 2024, all without missing values. The IOD values averaged -0.41954 ± 0.41075(1SD, range: -1.383 to 1.149). The UCM model fit to the IOD time series had an adjusted r2 = 0.85843 (Table B in S1 File). Residual diagnostics plots (Fig C in S1 File) and loess smoothed residuals (Fig D in S1 File) confirmed a good model fit. Parameter estimates for the UCM components comprising level, slope, cycle and autoregressive irregular components (Table C in S1 File) along with their t-tests, revealed significant disturbance variances for the cyclical component and autoregressive irregular components, indicating a stochastic cycle. But the error variances of the level and slope components were insignificant (Table C in S1 File), suggesting they are deterministic.
Towards the end of the estimation period, the level, slope and both cyclical components became significant, highlighting that the level and slope are both deterministic and significant (Table 4). This signifies that the time trend in the IOD, characterized by the level and slope components, exhibits significant and deterministic variation over time trend coupled with significant, deterministic and persistent cycles (Table 4).
The smoothed level component illustrates a significant and persistent curvilinear increase in the IOD from 1913 to 2024 (Fig 5A). Similarly, the smoothed slope component suggests an initial decrease in the IOD from 1913 to around 1950, followed by an increase from 1950 to 2024, punctuated by a deceleration and levelling off of the rate of increase between 1990 and 2010 (Fig 5B).
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.
The two smoothed cyclical components reveal deterministic and persistent cycles with periods of 4.1 and 5.4 years, time-varying amplitudes and phases (Fig 5C and 5D).
The smoothed level trend component superimposed on the IOD series further confirms the curvilinear rise in the IOD values between April 1913 and January 2024 (Fig 5E). Overall, the UCM analysis highlights significant and deterministic long-term trends in the IOD, coupled with two notable persistent cycles, providing critical insights into the temporal dynamics of the IOD over the course of the 112 years.
Univariate unobserved components model analysis of the average monthly minimum and maximum temperatures for Narok Town, Kenya
The univariate unobserved components model (UCM) reveals significant long-term trends, seasonal and cyclical variations in the minimum and maximum temperatures of Narok Town, Kenya, from January 1960 to May 2024. The analysis of 773 records of average monthly minimum temperature for Narok Town from January 1960 to May 2024 shows an average of 9.6°C ± 2.41°C (±1 SD, range: 0.2 to 17.4°C). The UCM model demonstrated a good fit with an adjusted r2 = 0.75275, (Table C in S1 File), supported by residual diagnostics and loess smoothed prediction error plots (F and G in S1 File). The model components include a stochastic level, a deterministic slope, two stochastic cycles, a deterministic 12-month seasonal component and autoregressive errors. T-tests confirmed the significance of all the parameters except for the slope and the seasonal components (Table D in S1 File), while chi-squared tests indicated that the level, slope and seasonal components are significant but deterministic towards the end of the estimation span (Table E in S1 File). The estimated cycle periods were 2.2 years for the subsidiary cycle (cycle1) and 13.9 years for the primary cycle (cycle2).
The smoothed level component revealed a striking linear increase in the average monthly minimum temperature by about 5.3°C, from 7.9°C in January 1960 to 13.2°C in May 2024, equating to an average increase of 0.83°C per decade (Fig 6A). The slope component remained constant throughout the period (Fig 6B).
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.
The subsidiary cycle (cycle1) exhibited high irregularity (Fig 6C), while the primary cycle (cycle 2) showed a notable drop in the minimum temperature by over 4°C around the mid-1970s (Fig 6D). The smoothed trend further reinforced the strong linear increase in the minimum temperature (Fig 6E).
For the maximum temperature series which averaged 24.8°C ± 2.03°C (±1SD, range: 19.8–29.9°C), the UCM model also showed a good fit with an adjusted r2 = 0.74943 (Table F in S1 File). Residual diagnostics and loess smoothed residuals supported the model’s adequacy (Figs H and I in S1 File). The model included seven components: level, slope, two cycles, seasonal, autoregressive and irregular components. T-tests indicated the significance of the autoregressive component and the secondary cycle (cycle 1) (Table G in S1 File), while chi-square tests showed that the level and seasonal components were deterministic and significant towards the end of the period (Table H in S1 File).
The smoothed level trend showed a marginal increase of 1.0°C, from 24.5°C in January 1960 to 25.0°C in May 2024 (Fig 7A). The slope component was constant and insignificant (Fig 7B). The cycle periods were approximately 1.4 years and 9.9 years (Fig 7C and 7D). The primary cycle exhibited a pronounced spike in the mid-1970s, coinciding with the lowest minimum temperatures, while the amplitude of oscillations dampened from 1990 to 2024 (Fig 7D). The maximum temperature rose by 1°C from 1960 to 2024 (Fig 7E).
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.
The univariate UCM analysis highlights significant warming trends and cyclical variations in both the minimum and maximum temperatures in Narok Town, emphasizing the crucial importance of continuous monitoring and adaptive strategies to mitigate the impacts of climate change and variability on local environments, biodiversity and human communities.
Bivariate and multivariate state space models with trend, cycle and seasonal components
The comprehensive analysis of bivariate and multivariate state space models with trend, cycle, and seasonal components requires a thorough examination of model diagnostics and parameter estimates to ensure optimal model fit and performance because the t-test for parameter significance is still under development. For each bivariate or multivariate model, we performed extensive model diagnostics to assess model fit. Key diagnostics include one-step-ahead residual analysis, which is illustrated through various graphs comprising residual normality plots, histograms, Q-Q plots and time series plots of standardized residuals. Additionally, we use graphs for outlier detection and structural break analysis, including prediction error normality plots, histograms, Q-Q plots and time series plots of standardized additive-outlier statistics and maximal state shock chi-square statistics.
We also present a summary table of the parameter estimates of the unknown elements in the model system matrices. Although several other tabular results used to asses model performance are omitted for brevity, these include convergence status, likelihood-based fit-statistics, information criteria, disturbance covariance estimates, elementwise and overall state (e.g., level, trend, cycle, error) break summaries, and (7) summaries of maximal state (e.g., level, trend, cycle, error) shocks.
This approach to model diagnostics and parameter estimation helps enhance the robustness and reliability of the bivariate and multivariate state space models analyzed, ensuring their applicability and effectiveness in capturing the underlying trends, cycles, and seasonal components of the time series.
Bivariate state space model for wet and dry season rainfall for Narok Town, Masai Mara, Seronera and Ngorongoro
A bivariate state space model with trend, seasonal and cycle components effectively captures the dynamics of wet and dry season rainfall across Narok Town, Masai Mara, Seronera, and Ngorongoro in East Africa, revealing significant trends, oscillations, structural breaks, and correlations between seasonal rainfall patterns. The bivariate state space model used to analyze rainfall patterns in Narok Town, Masai Mara, Seronera, and Ngorongoro, focused on wet and dry seasons. The identified patterns underscore the variability and extremity of weather patterns in specific regions, highlighting the importance of localized climate studies for understanding and addressing local environmental challenges in African savannas.
The residual and prediction error diagnostic plots indicate approximate normality of one-step-ahead residuals, validating the model’s accuracy for Narok Town (Figs I–L in S1 File), Masai Mara (Figs Q–T in S1 File), Seronera (plots not shown) and Ngorongoro (Figs U–X in S1 File). Notably, the standardized prediction error and residual plots identified outliers in specific years, with extreme rainfall events disrupting normal patterns. In particular, outliers in seasonal rainfall were detected for Narok Town, Seronera, and Ngorongoro, revealing significant variations during specific years, but no such anomalies were found for the Masai Mara in either season. Narok Town experienced exceptionally high rainfall in the wet seasons of 1962 and 2020 (Figs M and O in S1 File), and the dry seasons of 1917 and 2011 (Figs N and P in S1 File). The maximal shock statistics plot (with reference line at the 80th percentile) identified structural breaks in Narok Town’s rainfall series in 2020, further highlighting the variability. Narok Town’s rainfall data revealed significant deviations from the historical average, with the wet season in 1962 receiving 1396.8 mm of rainfall, 2.2 times the average from 1914 to 2024. Similarly, the dry seasons of 1917, 1996, and 2011 received rainfall amounts of 312.7 mm, 272.9 mm, and 333.6 mm, respectively, which were 2.6, 2.3, and 2.8 times higher than the average from 1913 to 2024. Seronera received unusually high rainfall in the wet season during the El Niño floods of 1998 (χ2 = 8.11, P = 0.0044), but no outlier was detected for the dry season. In Ngorongoro, an outlier, corresponding to exceptionally high rainfall, was identified for the dry season in 1967, with no anomalies in the wet season (Figs Y–AB in S1 File). These anomalies highlight the region’s vulnerability to extreme weather events, emphasizing the need for comprehensive climate monitoring and adaptive strategies to mitigate the impacts of such variability.
The rainfall trends for Narok Town, Masai Mara, Seronera, and Ngorongoro exhibit distinct patterns influenced by both seasonal variations and historical oscillations, reflecting the complex interplay of climatic factors in these regions. In Narok Town, the smoothed bivariate random walk trends for both wet and dry season rainfall, positively correlated, revealed an initial decline in rainfall from 1913 to a low between 1930 and 1940. This was followed by an increase peaking between 1969 and 1976, a subsequent decline until the mid-1980s, and then a relatively stable average level before another increase from 2000 to 2024 (Fig 8A).
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.
In Masai Mara, after accounting for oscillations in rainfall in the bivariate model, no distinct directional trend was evident in either the wet or dry season rainfall components between 1965 and 1995. But both seasonal components evidently increased between 1995 and 2020, with the wet season component increasing more steeply than the dry season component (Fig 9A).
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.
In Seronera, there was no evidence of a level shift in the rainfall series during 1981–2015. Trends in the wet and dry season rainfall components were negatively correlated (Table K in S1 File). While the wet season rainfall component showed no evident trend during this period, the dry season rainfall component increased progressively from 1981, surpassing the 1981–2015 average in 2010 (Fig 10A). In Ngorongoro, the trends in the wet and dry season rainfall components were negatively correlated (Table L in S1 File, Fig 11A). Specifically, the wet season rainfall increased, surpassing the 1963–2014 average in 1985, while the dry season rainfall exhibited a decreasing trend (Fig 11A). Hence, the rainfall patterns across these regions highlight significant temporal variations influenced by both wet and dry season components. Understanding these trends is crucial for developing adaptive strategies to mitigate the impacts of climate variability on local ecosystems and communities.
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.
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.
The bivariate models for wet and dry season rainfall in Narok Town, Masai Mara, Seronera, and Ngorongoro reveal significant and persistent oscillations, characterized by both negative and positive correlations between the two seasonal components across different regions. In Narok Town, the bivariate model indicates a negative correlation between wet and dry season rainfall cycles, with a cycle period of 9.3 years and a damping factor of 1.0, signifying persistence over time (Table I in S1 File). This negative correlation suggests that increases in wet season rainfall typically correspond to decreases in dry season rainfall, and vice versa, with stable amplitude from 1913 to 2024 (Fig 8B). Similarly, in the Masai Mara, a negative correlation between the cycles of wet and dry season rainfall is evident, with a bivariate cycle period of approximately 20.4 years. Here, the oscillation amplitude is significantly greater in the dry season than in the wet season (Fig 9B), and the damping parameter of 1.0 indicates persistent oscillations over time (Table J in S1 File). In Seronera, a 10.4-year cycle period is identified, with negatively correlated oscillations between wet and dry season rainfall (Fig 10B). The amplitude of dry season oscillations surpasses that of the wet season from 1980 to 2015 (Fig 10B).
Contrastingly, Ngorongoro exhibits positively correlated bivariate oscillations between wet and dry season rainfall, with a cycle period of 21.4 years. The amplitude of oscillation is greater in the dry season, and it remained stable between 1963 and 2014 (Table L in S1 File, Fig 11B).
Overall, the bivariate models highlight the intricate dynamics of rainfall patterns across different regions, emphasizing the importance of understanding these patterns for better resource management and planning in the face of climate change and variability. The persistent oscillations and their varying correlations further underscore the need for localized strategies to mitigate the impacts of fluctuating rainfall on ecosystems and human activities. The bivariate state space model therefore provides a robust framework for understanding the complex rainfall dynamics in these regions, highlighting significant oscillations and correlations that can inform future climate resilience strategies.
Bivariate state space model with trend, cycle and seasonal components for the average minimum and maximum temperatures for Narok Town, Kenya
The bivariate model of monthly minimum and maximum temperatures reveals significant trends and outliers, highlighting key changes in temperature patterns over time. The residual (Figs AC and AD in S1 File) and prediction error (Figs AE snd AF in S1 File) normality diagnostics for average monthly minimum and maximum temperature were as expected, with a few notable exceptions. Three significant outliers were detected in the minimum temperature data by standardized prediction error plot (Fig AG in S1 File). These outliers correspond to significant temperature drop in September 1974 and rises in October 1982 and March 2015 (Table M in S1 File). Conversely, the maximum temperature data revealed five extreme observations (Fig AH in S1 File), two of which represented statistically significant temperature drop in September 1974 and December 2020.
Both temperature series show similar upward trends, evidenced by their positive correlation (Table N in S1 File, Fig 12). The minimum temperature, which reached a record low in September 1974, has shown a persistent increase since 1985, surpassing the 1960–2024 average in November 1993 (Fig 12). The maximum temperature follows a comparable, though less marked, upward trajectory, exceeding the 1960–2024 average in December 1991 (Fig 12). Overall, these findings highlight the significant warming trends in both minimum and maximum temperatures, with specific anomalies marking pivotal moments in the data series. The identification of outliers and the persistent upward trends provide critical insights into the changing climate patterns, requiring continuing monitoring and mitigation efforts.
Trivariate state space model with trend, cycle and seasonal components for total monthly rainfall, average monthly minimum and maximum temperatures in Narok Town, Kenya
The climatic patterns in Narok Town, Kenya, derived from the trivariate model, exhibit a complex interplay between temperature and rainfall, revealing significant trends and correlations over the decades. In Narok Town, the minimum and maximum temperature series are positively correlated with each other but negatively correlated with rainfall (Table O in S1 File, Fig 13). Notably, 1972 recorded the lowest rainfall, which coincided with the highest maximum temperature. During 1972–1974, the highest rainfall periods corresponded with the lowest and below-average minimum temperatures. Conversely, during 1974–1985, rainfall remained below average while minimum temperature was above average (Fig 13). From 1985, a progressive rise in minimum temperatures was accompanied by a declining trend in rainfall up to 1990 followed by an increase thereafter (Fig 13). These findings highlight how the trivariate model can reveal the intricate relationship between temperature and rainfall, important for understanding climatic trends as a basis for sound ecosystem management and biodiversity conservation.
Trivariate state space model with trend, cycle and seasonal components for total monthly rainfall for Narok Town, Masai Mara, Seronera and Ngorongoro, Southern Oscillation Index (SOI) and Dipole Mode Index IOD
The state space model demonstrates robust accuracy in capturing trivariate patterns of rainfall, SOI and IOD across different regions, although some anomalies exist in the predictions for specific large rainfall values. The diagnostic plots for Narok Town reveal a generally good model fit for total monthly rainfall, SOI and IOD (Figs AI–AN in S1 File). However, there is a tendency to underestimate some large rainfall values. In contrast, the diagnostic plots for the Masai Mara (Figs AR–AW in S1 File) indicate that the state space model effectively captures the trivariate patterns in rainfall, SOI and IOD. Similarly, for Seronera, the residual and prediction error normality diagnostic plots (Figs AX–BC in S1 File) confirm that the model accurately represents these patterns. In Ngorongoro, the model also shows effective performance, as evidenced by the diagnostic plots (Figs BG–BL in S1 File). The residual diagnostics show that the state space model is a valuable tool in accurately modelling the complex interactions between rainfall, SOI and IOD across multiple regions, despite some minor underestimations in specific cases. This reliability across different geographical areas underscores its utility in climate pattern analysis and forecasting.
Outlier diagnostics for Narok Town, Masai Mara, Seronera, and Ngorongoro regions reveal significant anomalies in rainfall and SOI, underscoring the variability and extremity of climatic events in these areas. Outlier diagnostics identified five unusually high rainfall observations for Narok Town (Jan 1925, April 1951, Dec 1961, Jan 1970 and Mar 1978), no significant anomalies for SOI and IOD, highlighting the region’s climatic volatility (Figs AO–AQ in S1 File). For Masai Mara, January 2002 (, P = 0.0002) experienced notably high rainfall whereas Jan 1967 and Jan 2001 had exceptionally low IOD values, marking these months as outliers. Seronera’s data revealed exceptional rainfall in April 1988, December 1997, January 1998, Dec 2011 and April 2015 (Figs BD–BF in S1 File). Similarly, Ngorongoro received unusually high rainfall in November 1963, March 1974, April and December 1997, and January 2001, and no significantly outlying SOI or IOD values (Figs BM–BO in S1 File). These findings highlight the critical need for adaptive strategies in these regions to manage and mitigate the impacts of extreme climatic events effectively.
The trivariate model reveals significant correlations between rainfall patterns and climatic oscillations in Narok Town, Masai Mara, and Seronera, highlighting the complex interplay between the SOI and IOD over multiple decades. In Narok Town, the variability in the SOI series exhibited quasi-periodic oscillations with the variability widening after around 1970. Rainfall and IOD both increased progressively from 1913 to 2024, but with evident oscillations and the increase in rainfall closely mirrored that in IOD and became steeper from 1990 to 2024 (Fig 14). Rainfall trend and oscillation were positively correlated with the trends and oscillations in both the SOI and IOD. Furthermore, the SOI and IOD trends were positively correlated but their oscillations were negatively correlated (Table P in S1 File, Fig 14), indicating that the increasing rainfall trend coincides with the strengthening of the El Niño oscillations and intensifying IOD episodes. In Masai Mara, the trivariate cycles, with a period of 9.74 years and a damping factor of 0.989, suggest a consistent increase in rainfall and IOD from 1965 to 1990, a levelling off of both rainfall and IOD during 1990 to 2000 and a further increase in both series thereafter. In contrast, the SOI series showed no apparent trend (Table Q in S1 File, Fig 15). The rainfall, SOI and IOD trends are positively correlated. Moreover, the rainfall cycle is positively correlated with the IOD cycle but negatively correlated with the SOI cycle (Fig 16). Also, the amplitude of the rainfall and IOD oscillations dampened over time especially between 1995 and 2020 (Fig 16). In contrast, Seronera showed distinct SOI and IOD oscillations but with the timing of peaks and troughs in the IOD series lagging behind those of the SOI series (Fig CI in S1 File) and the patterns differing from the rainfall and IOD series for Narok Town, which showed evidently increasing trends (Fig 14). A quasi-periodic oscillation in SOI was evident in Ngorongoro Crater, with evident positive peaks and troughs during 1963 to 2014 (Fig CJ in S1 File). Overall, the temporal variation pattern indicates that rainfall is strongly associated with SOI and IOD variations (Tables P–S in S1 File, Figs 14–17, Fig CJ in S1 File). The trivariate model thus highlights the crucial influence of climatic oscillations on rainfall patterns in different regions, with significant implications for understanding and predicting weather-related phenomena in these areas.
The trivariate model for rainfall trends in Narok Town, Masai Mara, Seronera, and Ngorongoro reveals significant correlations with the SOI and the IOD, highlighting distinct regional patterns and temporal variations. For Narok Town, the rainfall trends were positively correlated with both the SOI and IOD series, although the SOI and IOD trends themselves were negatively correlated (Table P in S1 File, Fig 14). This indicates that the rainfall patterns mirrored those of the SOI and IOD, with the rainfall and IOD series generally increasing from 1913 to 2024, while the variation in the SOI series widened over the same period. In Masai Mara, parameter estimates (Table Q in S1 File) demonstrated positive associations between the level trend components and the cyclical components of rainfall but a negative association between the cyclical components of rainfall and SOI (Fig 16). From 1965 to 2020, all three variables increased, but the increase in SOI was negligible (Fig 15). For Seronera in Serengeti, Tanzania, from 1981 to 2015, the total monthly rainfall, SOI and IOD showed pronounced and sustained quasi-cyclic oscillations (Table SR in S1 File, Fig 17). Similarly, in Ngorongoro, the trends in rainfall, SOI, and IOD were all positively correlated, with notable and persistent quasi-periodic oscillations in rainfall, SOI and IOD during 1963–2014 Table S in S1 File, Fig CJ in S1 File). These findings underscore the complex interactions between climatic indices and regional rainfall patterns, emphasizing the importance of considering multiple factors when analyzing climatic trends and their potential impacts on ecosystems.
Multivariate state space model with trend, cycle and seasonal components for total monthly rainfall, average monthly minimum and maximum temperatures for Narok Town, Kenya, Southern Oscillation Index (SOI) and Dipole Mode Index (IOD)
The pentavariate model robustly captures the intricate dynamics of total monthly rainfall, average monthly minimum and maximum temperatures, the SOI and the IOD for Narok Town, Kenya. The pentavariate state space model, encompassing trend, cycle and seasonal components, effectively modelled the joint variation in the total monthly rainfall, average monthly minimum and maximum temperatures, the SOI and the IOD for Narok Town, Kenya. The residual (Figs BP–BT in S1 File) and prediction error (Figs BU—BY in S1 File) normality diagnostic plots confirm the model’s proficiency in capturing the joint variation in these five climatic variables. Fig 18 illustrates the simultaneous variations in these five series at Narok Town, with detailed parameter estimates provided in Table T in S1 File. The salient characteristics of these trends broadly mirror those already described, and thus are not reiterated here. A noteworthy new feature is the striking similarity between the modelled trends for the SOI and minimum temperature series. The multivariate modelling approach thus enhances our understanding of the climatic interplay in Narok County and offers valuable insights for climate prediction and ecosystem management.
Multivariate state space model with trend, cycle and seasonal components for monthly average NDVI, total monthly rainfall, average monthly minimum and maximum temperatures for Narok Town, Kenya
The multivariate state space model with trend, cycle, and seasonal components effectively captures the dynamics of monthly average NDVI, total monthly rainfall, and average monthly minimum and maximum temperatures for Narok Town, Kenya. The residual (Figs BZ–CC in S1 File) and prediction error (Figs CD–CG in S1 File) normality diagnostic plots demonstrate the quadrivariate model’s accuracy in capturing patterns of total monthly rainfall, average monthly minimum and maximum temperatures and monthly average of SPOT NDVI for Narok County. The trend component indicates an overall increase in all four variables from 1998 to around 2003, stability from 2004 to about 2009, and another increase until 2014 (Fig 19). Parameter estimates for the quadrivariate model (Table U in S1 File) reveal positive correlations among the level trends of all variables, except for an inverse relationship between SPOT NDVI and minimum temperature, suggesting that higher minimum temperatures are linked to vegetation browning. The model’s cycle component has an estimated period of 12.7 years (Table U in S1 File), with cycles generally positively correlated, though rainfall and maximum temperature, and SPOT NDVI and minimum temperature cycles are negatively correlated (Table U in S1 File, Fig CH in S1 File). The quadrivariate model therefore provides a robust framework for understanding the complex covariation between climatic variables and vegetation dynamics in Narok Town, Kenya, and highlights critical correlations and trends that can inform environmental management and policy decisions.
Discussion
We detected strongly deterministic and persistent bivariate cycles in both wet and dry season rainfall components across the GMSE, encompassing the Masai Mara Ecosystem and Narok Town in Kenya and the Serengeti (Seronera) and Ngorongoro in Tanzania. While the bivariate models for all four regions demonstrate persistent rainfall oscillations over time, the patterns of variability and cycle periods differ significantly. Narok Town shows more pronounced historical fluctuations and identifiable outliers, Masai Mara has longer and stable cycles, Seronera exhibits periodic fluctuations with significant dry season impacts, and Ngorongoro Crater presents a unique pattern of positively correlated oscillations. These bivariate cycles showed a consistent compensatory pattern: low wet season rainfall was typically offset by higher dry season rainfall and vice versa, with dominant cycle periods of about 20 years. In Ngorongoro, despite a positive correlation between the wet and dry season rainfall cycles, a negative correlation between their levels led to a similar compensatory pattern as for the other regions. Notably, only in Seronera, Serengeti, did the bivariate rainfall components display a shorter cycle period of about 10.4 years. The 34-year time series from Seronera may not have been long enough to detect the longer-term oscillations observed in the other GMSE rainfall data. This pattern of compensatory bivariate oscillations in the wet and dry season rainfall components is likely crucial for the ecosystem’s stability.
The bivariate cycle periods, ranging between about 10 and 20 years, are considerably longer than the dominant cycle periods of 2.3 and 10.1 years identified in univariate analyses of wet and dry season rainfall components [59]. These bivariate cycle periods also exceed those of the IOD (4.1 to 5.6 years) and the SOI (1.6 to 4.0 years), both of which are well known to significantly influence East African rainfall, especially during the wet season [50, 60–66]. Despite the variable amplitudes and phases of the SOI and the IOD oscillations, the consistent, deterministic and persistent pattern of bivariate rainfall oscillations suggests that factors other than these known climate phenomena may be driving the observed long-term bivariate oscillations.
The long cycle periods of the bivariate rainfall cycle may reflect the influence of the Atlantic Multidecadal Oscillation (AMO). Oscillations in Atlantic ocean temperatures can significantly influence East African rainfall [60, 63, 67, 68] through their teleconnections with the West African monsoon and the El Niño Southern Oscillation (ENSO) [69–72]. Additionally, the location and intensity of the Mascarene High [73], low-level jet streams, pressure cells over the Sahara and Saudi Arabia, and local topography, also contribute to rainfall variation in East Africa [60, 74] and hence to the rainfall oscillations in the GMSE.
The amplitudes of the rainfall oscillations in Narok was rather stable despite rising temperatures. This is inconsistent with global observations of more extreme weather events, such as droughts and floods, associated with rising temperatures [22]. Furthermore, in the Serengeti and Narok regions, the amplitude of the dry season rainfall oscillations exceeded that of the wet season. This heightened variability in the dry season rainfall, crucial for the survival of plants and animals during resource-scarce periods [36, 39, 75], may have significant implications for biodiversity and animal population dynamics.
The seasonality of minimum and maximum temperatures and rainfall in Narok was strongly persistent and deterministic. This was indicated by the extremely low stochastic disturbance variances within the seasonal components in the trivariate state space models. Additionally, there was also weak positive correlation between the seasonal cycles of temperature and rainfall. This pattern is consistent with the deterministic movements of the ITCZ. This belt of rising and convecting air masses around the equator is the major driver of seasonality in temperature and rainfall in East Africa, including in the GMSE [12, 27, 28, 76]. The movement of the ITCZ is therefore likely an extremely stable factor generating alternating wet and dry seasons each climatic year.
In contrast to the deterministic (predictable) intra-annual seasonal cycles we found highly transient (unpredictable) trivariate multiannual cycles in monthly minimum and maximum temperatures and rainfall. The multiannual cycles were highly transient, primarily due to significant variability in temperature cycles. This variability was evident from the much higher stochastic disturbance variances in the temperature cycles, compared to those in the multiannual rainfall cycle.
Interestingly, the cycles of minimum and maximum temperatures were positively correlated with each other but both were negatively correlated with the rainfall cycle. This pattern was particularly noticeable in 1972 when the rainfall was at its lowest and the maximum temperature peaked. Similarly, during 1974–1985, periods of above-average minimum temperatures coincided with below-average rainfall. For Narok Town, the persistent decline in rainfall during 1960–2024 coincided with an increase in minimum temperatures, echoing our earlier findings [59] and observations for other parts of East Africa [77–80]. These results indicate that rising temperatures generally lead to reduced, rather than increasing rainfall and enhanced evaporative cooling.
The trivariate models for Narok Town, Masai Mara, Seronera, and Ngorongoro reveal distinct, nuanced and yet interrelated patterns in rainfall, SOI, and the IOD, highlighting the complex interactions between these variables and their impacts on regional climate. While each region exhibits unique characteristics, common trends reveal that high rainfall is generally associated with strong IOD episodes and El Niño events, whereas low rainfall correlates with La Niña conditions. These insights underscore the importance of using multivariate models in understanding regional climatic interactions to better predict and manage impacts of climate change and variability.
Overall, rainfall levels during the wet and dry season across the GMSE remained relatively stable. However, some declines were apparent in the monthly, wet and dry season rainfall in Narok during 1960–2024, and in the dry season rainfall in Ngorongoro during 1963–2014. These decreases in rainfall, potentially linked to increases in temperatures, might be offset by an increasing influx of moisture from the Indian Ocean to East Africa. This moisture increase could be a result of the strengthening of the IOD [81, 82]. Similarly, the ENSO phenomenon, which is often in phase with a positive IOD [52], has historically brought rain to East Africa [53, 83]. Earlier studies suggested that this phenomenon might be intensifying with rising temperatures [84, 85]. Our results support this trend. Thus, even though the signal for the strengthening of the El Niño phenomenon still remains controversial [86, 87], our results support the notion that variability in El Niño-Southern Oscillation is widening and IOD is strengthening.
Similarly to monthly rainfall, vegetation productivity was largely invariant in terms of its cyclical, level and seasonal components. The level of NDVI increased slightly during 1999–2014 concurrent with increases in the levels of rainfall and maximum temperatures. There were also weak positive associations between the NDVI cycle and those for rainfall and maximum temperatures. This increase apparently accelerated from 2010, mirroring the effect of increasing rainfall. Apparently, the combination of high rainfall and high temperatures during daytime enhances the photosynthetic activity of plants [25]. Previously, we found that extremely high rainfall increased significantly during 1990–2000 in the Mara [59]. The 1998 flood was the worst on instrumental record for the GMSE [2, 59]. This extreme rainfall event likely facilitated the recruitment of woody plants from seedlings [88] with consequent densification of woody cover and increase in NDVI. However, confirming these findings would require a longer NDVI time series than the current 15-year dataset.
The rising temperatures contribute to increased evaporation, which might result in a net negative water balance. This is despite the possibility of more intense oceanic and hemispheric oscillations bringing more moisture to East African. Such a scenario raises concerns about the potential for increasing habitat desiccation in the GMSE. This drying could adversely affect plants and animals [2].
In conclusion, understanding regional climate and vegetation trends and variation and how these are influenced by large-scale oceanic and atmospheric oscillations is crucial for predicting future climatic behaviours, environmental planning and conservation efforts. The results highlight the complexity of the regional climatic and environmental dynamics, emphasizing the impact of hemispheric and regional climate phenomena like the IOD and SOI on local weather patterns. This impact is evident in rising temperatures and changing rainfall patterns. The findings underscore the crucial need for integrative and multivariate approaches to understand and address the challenges posed by climate change to biodiversity, ecosystems and human welfare.
Consequences of climate change and variability for wildlife and biodiversity conservation
Climate change and variability have profound and multifaceted consequences for wildlife and conservation. The frequent, protracted and intense droughts, along with infrequent but intense floods and rising temperatures, characteristic of the Mara-Serengeti, reflect broader patterns in Kenya, East Africa and the rest of Africa. Here, we discuss the consequences of droughts and floods and temperature rise for wildlife populations and biodiversity conservation drawing primarily on field observations reported in the annual reports of the Game Department (GDARs—1901–1976) and, its successor, the Wildlife Conservation and Management Department (WCMD—1977–1989), as well as administrations of the Narok and Kajiado Districts of Kenya (1914–1989) and contemporary observations.
Droughts intensify competition for scarce resources among wildlife, pastoralists, and their livestock
Droughts, caused by absolute failure or irregular spread of the rains [89], a prevalent phenomenon in East Africa, significantly increase livestock incursions into protected areas and competition for scarce resources among wildlife, pastoralists, and their livestock. During droughts, all three groups converge around the few remaining water sources and areas with better forage, such as forests, swamps, permanent streams, waterholes and along water courses [90].
This forced proximity heightens conflicts, as wildlife, driven by starvation and stress, become more aggressive and intrude into human-occupied spaces, resulting in increased human-wildlife interactions and conflicts. Consequently, the delicate balance within these ecosystems is disrupted, with severe consequences for both conservation efforts and local communities. Unsurprisingly, conservation administrations have historically discouraged livestock presence in conservation areas, owing to threats to conservation efforts [91].
The acute competition for scarce food and water resources during severe droughts leads to severe wildlife mortality from starvation, thirst and dehydration and shooting of many problem animals on control. Consequently, prolonged dry spells have devastating impacts on wildlife populations leading to significant losses [92–101]. In Kenya’s Tsavo region, for instance, a drought in 1971–72 resulted in the deaths of many rhinos and about 30,000 elephants (Loxodonta africana) due to starvation and disease, exacerbated by high population densities and mismanagement [102, 103]. Elephants also died of thirst and starvation during the severe drought in Kenya in 1933 [92–94], the exceptional drought of 1950 [104], and during the latter part of 1959 [105, 106].
Similar patterns were observed during the 1953 drought in Kenya’s Narok District, where significantly below-average rainfall led to the deaths of numerous animals [98, 99]. Furthermore, rainfall was slight and most of Kenya suffered from widespread drought in 1965. Wildlife, particularly the Kenya hartebeest (Alcelphus buselaphus keniae), suffered considerable mortality, especially among females that were either about to calve or that had recently calved [107]. Notably, guinea fowl (Numididae spp.) and francolin (Francolinus spp.) virtually disappeared from many parts of Kenya where they were once abundant because of droughts and locust infestations during 1939–1945 [108–111]. From October 2020 to February 2023, East Africa experienced the worst drought in 40 years (since the 1980s), with five consecutive failed rainy seasons primarily due to La Niña. The most affected ecosystems in Kenya during October–December 2021 and March–May 2022, were Amboseli, Laikipia-Samburu and Tsavo. In this period, the drought significantly impacted wildlife, resulting in estimated minimum mortalities of 512 wildebeest, 318 common zebra, 205 elephant, 49 Grevy’s zebra and 51 buffalo besides other species [112]. Many juveniles also died of malnutrition because their mothers could not produce enough milk, or were killed by predators, as their mothers were too weak to protect them [112]. During the prolonged and extreme drought from 2020 to 2023, wildlife in the Amboseli Ecosystem experienced severe starvation and significant mortality (Figs CK–CN and CU–DO in S1 File). Similarly, numerous livestock suffered from starvation and considerable mortality (Figs CO–CT in S1 File). S1 File provides additional details on wildlife mortality due to starvation, poaching and game control during the 1973-1974 drought in the Athi-Kaputiei Ecosystem, located in Kenya’s Kajiado County.
Drought increases predation risk for and poaching of wild herbivores
Severe droughts also elevate predation risk for wildlife, as malnutrition renders them lethargic and less capable of evading predators and poachers seeking subsistence meat and trophies. Excessive drought conditions over prolonged periods in particular increase the incentive and ease of poaching wildlife. Not surprisingly, poaching activities spike during drought years, driven by local communities’ desperation and struggle to survive in the wake of crop failures and famine. Drought-driven hunger also forces wildlife into human settlements, often inhabited by poachers, leading to increased wildlife mortality and human-wildlife conflicts. The poaching surge not only threatens the survival prospects of already stressed wildlife populations but also complicates conservation efforts, requiring more stringent and expensive anti-poaching measures. For instance, the extreme drought conditions in 1961 caused severe hunger, making it one of the worst years on record for poaching in Kenya. Overall, poachers killed 139 rhinos (Diceros bicornis) in Kenya during the drought of 1961 [101]. Notably, the Masai of Kenya’s Narok and Kajiado districts experienced famine due to the loss of their livestock during the 1960–1961 drought. The drought caused a significant increase in the spearing of rhinos for their horns throughout Kenya’s Kajiado District in 1961, with 40 rhinos killed, including 11 inside the Amboseli Game Reserve [101]. Poaching was also especially serious in the Northern Frontier District of Kenya in 1943, a severe drought year [113].
The near-complete failure of rains can force pastoralists and their livestock to concentrate along permanent rivers, resulting in considerable human casualties and livestock losses, primarily due to carnivore attacks, such as those by hyenas (Crocuta crocuta) [105, 106]. For example, during the 1953 drought wildlife concentrated in large numbers along the Mara River, leading to one of the worst wildlife casualties of the century due to weakened body condition and heightened predation [98, 99]. Moreover, drought accompanied by locust outbreak in 1938–1939 caused crops and grazing to wither and forced wildlife to concentrate around the few remaining streams and water points, making wildlife to fall easy prey for poachers using snares, pits, spears and poisoned arrows [108, 114]. Also, during the severe drought and rinderpest outbreak from 1881–1882, the rivers on the Kenya Mau dried up. Only the Mara River retained water, forming a series of pools where thousands of wildlife gathered and subsequently perished. Similar extreme droughts affected the Mara in 1933–1934 and 1961 [115]. Wildlife also encroach on agricultural areas during droughts, causing serious crop depredations. This damage is bitterly resented by local communities, inciting reprisals and further escalating human-wildlife conflicts [92–96, 116, 117]. This antagonism hinders conservation initiatives, as local support wanes in the face of continual losses and threats to human livelihoods, especially during such stressful times.
The physical challenges faced by wildlife during droughts are exacerbated by the increased risk of becoming trapped in mud or water wells as they search for water. Many trapped wildlife die because they are too weak to extricate themselves again. For example, six rhinos died this way at Laisamis in Kenya’s Marsabit District in 1933, several buffalo (Syncerus caffer) died from getting bogged in the small Crater Lake near Marsabit in Kenya and being too weak to get out in 1933 and elephants got frequently trapped in liquid mud during the severe droughts [92–94, 99, 118, 119].
Droughts interact with land use to accentuate wildlife mortality
Severe droughts, compounded by continuous overgrazing, shrinking open range for wildlife and pastoralists, permanent settlements, pasture degradation and land fragmentation by fences, lead to significant wildlife and livestock mortality. For instance, in 1960, a severe drought across most of Kenya resulted in the deaths of over 80 rhinos in Tsavo National Park alone [100]. Moreover, in Kajiado District, extensive overgrazing by cattle over many years left little forage during times of stress, leading to the starvation of thousands of cattle (numbers reduced from 500,000 to 200,000) and many hundreds of wildlife, including zebra, wildebeest, Coke’s hartebeest (Alcelaphus buselaphus cokei), and Thomson’s gazelle by the end of 1960 [100]. Browsers such as Grant’s gazelle (Nanger granti) and eland suffered less, as they could rely on vegetation other than grass and moved out of the Athi-Kaputiei Ecosystem [101].
As well, from August 1960 to September 1961, extreme drought led to the starvation of 282 rhinos in Tsavo National Park, exacerbated by vegetation damage caused by an apparent overpopulation of elephants [101]. The 1951 drought, caused by the failure of rainfall in the first quarter of the year, left the vicinity of the Sabenna wells in the Lorian Swamp in Kenya’s Garissa District strewn with the bodies of dead and dying livestock due to thirst and starvation, with at least 11 elephants also dying of thirst [118].
The drought of 1961 was the worst in 50 years, coupled with Kenya-wide invasion of army worms and followed by unprecedented floods starting in September 1961 [101]. Consequently, high wildlife and livestock mortality continued in Kajiado District from 1960 to 1961. Despite the drought conditions affecting the Mara region similarly, fewer livestock deaths and no wildlife deaths were recorded there, thanks to less damage to vegetative cover from overgrazing [101].
Droughts lead to an increase followed by a decrease in carnivores
While droughts can initially boost carnivore populations due to increased availability of carcasses, the subsequent decline in prey leads to starvation among predators. Notably, the 1960–1961 drought and subsequent flood losses resulted in a dramatic rise in the numbers of lions (Panthera leo), hyenas, and jackals (Canis spp.) in Kenya. This was particularly evident in Kajiado District, where hyenas fed on the carcasses of dying livestock throughout the day [120]. However, by April 1962, as cattle deaths ceased, the carnivores faced starvation due to the lack of available food [120]. Notably, hyenas faced starvation and became unusually bold in their search for food. In the outskirts of Nairobi, dustbins were raided, garden hoses chewed, and even rear reflectors were eaten off cars. In remote areas, their actions were more severe, with manyattas (pastoralist settlements) regularly raided, cattle taken, and on at least two occasions, small children dragged out and killed. In response, the Game Department launched an intensive campaign, resulting in the killing of 1,176, hyenas, including 633 in Kajiado District and the rest in Narok District and parts of the Northern Province, where livestock losses were severe [120].
Heavy rainfall has both negative and positive effects on wildlife.
Conversely to droughts, heavy rains and subsequent floods, while replenishing water sources, can also cause wildlife drownings and habitat destruction. The aftermath of such events often leaves wildlife populations fragmented and struggling to recover, further stressing conservation efforts. Heavy rains and floods therefore significantly impact wildlife, creating both opportunities and threats. During heavy rains, water pans and waterholes fill up, providing wildlife with more drinking places [118, 121, 122]. In 1961, floods filled Amboseli Lake in Amboseli National Park from bank to bank, while Lake Victoria and most Rift Valley lakes in Kenya saw rising water levels, creating new fertile shallows beneficial to ducks and other water birds [123].
However, floods can be severely detrimental to wildlife. In 1961, many habitats near the Kenyan coast were submerged, displacing or drowning the resident population of topi (Damaliscus lunatus jimela) and Hunter’s hartebeest (Beatragus hunteri) [101]. Floods also sweep wildlife away in swollen rivers, as happened with elephants, topi, and zebra in the Tana River during the exceptional rains of 1951 [118]. Flash floods in the Northern Frontier District (N.F.D) drowned at least 13 elephants, 12 rhinos, and 6 giraffes (Giraffa camelopardalis), while similar incidents occurred in the Mara region and the Tana River [101]. Animals like giraffes, particularly in Kenya’s Kitui, Isiolo, Samburu, Marsabit, and Wajir districts, often got stuck in mud, with as many as 20 giraffe carcasses seen in a single week in Wajir District in 1961 [101]. Additionally, 14 rhinos drowned during the late 1961 floods [101].
Heavy rainfall after droughts can kill wildlife
Heavy rains following a severe drought can result in significant mortality among weakened wildlife and cattle. The sudden abundance of young grass can further endanger and kill more weakened animals [124]. For instance, thousands of Coke’s hartebeest died from starvation and cold on Kenya’s Athi-Kaputiei Plains when heavy rains fell during April 12–13, 1918, following a prolonged drought [121–122]. Additionally, sudden severe temperature changes following the onset of rains can be fatal, as evidenced by the deaths of young elephants in Marsabit Forest in 1933 due to a drastic weather shift [92–94]. Many antelope species and livestock, already weakened by severe drought, also succumb to the cold and wet conditions brought by the first heavy rains [125].
Droughts make wildlife more susceptible to diseases and pathogens
Droughts also compromise wildlife health by lowering body condition through malnutrition, making them more susceptible to diseases and pathogens to which they may be more immune under favourable circumstances [92–94, 125–129]. Outbreaks of diseases such as anthrax, rinderpest, and parasitic infections often coincide with droughts, leading to significant wildlife mortality and undermining conservation efforts and biodiversity. For instance, lungworm infestations caused the deaths of hundreds of zebra, Coke’s hartebeest, Grant’s and Thomson’s gazelles on the Athi-Kaputiei Plains of Kenya during prolonged droughts in the early 20th century [92–94, 125, 126, 128, 129]. Similarly, the severe drought of 1950 resulted in widespread rinderpest among buffalo and eland in various districts of Kenya [98, 99, 101, 104, 118]. Furthermore, hyena, jackals and hunting dogs (Lycaon pictus) also suffered from a severe outbreak of distemper causing a very great decrease in numbers all over Kenya during the 1907–1908 drought [127]. During a very severe outbreak of rinderpest amongst the Masai in 1890–1891 wildebeest, Coke’s hartebeest, buffalo, eland and cattle died [89].
Droughts shrink the area of wetlands critical for herbivores during droughts
Persistent droughts can significantly reduce the area of wetlands, such as permanent swamps, crucial for buffering wildlife against droughts. In 1911, a severe drought dried up the papyrus swamps of the Mara River, affecting the region across the Kenya-Tanzania border [115]. The permanent Lorian Swamp in Kenya’s Garissa County shrank from 150 km² in 1913 to about 39 km² in 1962, and further to 8 km² by 1990 [130], with adverse consequences for wild and domestic herbivores. The drought of 1921 caused many springs and permanent waterholes to dry up in Kenya [124]. During the great drought of 1951, the Lorian Swamp completely dried up and remained without water until at least August 1952 [97, 118]. In October 1955, the wells at Ijara, also in Garissa District, dried up for the first time in recorded history due to unusually low rainfall in the Garissa and Kitui Districts [99, 119].
Heavy rainfall increases the risk and intensity of fires
Sustained heavy rainfall can significantly heighten the risk and intensity of fires in savannas. In 1962 and 1963, unusually heavy rains led to luxuriant grass growth, which, once dried, ignited and caused the entire Masai Mara Game Reserve to burn in early September 1963, severely damaging woody growth [123]. Similarly, in April and May 1978, heavy rainfall caused considerable flooding of the Mara and Ewaso Nyiro Rivers. By June 1978, almost three-quarters of the reserve burned due to the abundant grass biomass produced by the rains [131].
Rainfall governs seasonal dispersal and migratory wildlife movements
Rainfall patterns play a crucial role in governing wildlife movements, including seasonal dispersal and migrations. Exceptional and prolonged droughts, such as the one experienced in Kenya in 1925, force wildlife to migrate in search of food and water [116]. During periods of low rainfall, like those prevailing in Kenya in 1947–1949, 1953 and 1955, the annual wildebeest and zebra migrations on the Loita Plains in the Mara Ecosystem were minimal [98, 99, 104, 119]. Conversely, heavy rainfall in Narok District in 1951 led to large migrations of wildebeest and zebra to the Loita Plains [118].
Extreme drought in 1961 caused unprecedented wildlife movements in many parts of Kenya [101]. In 1961, the migratory wildebeest and zebra departed earlier from the Mara Loita Plains due to failure of the long rains [101]. The lush conditions following good rainfall in 1962 and 1963 enabled elephants to wander far from their usual home ranges, with sightings in areas where they had not been recorded for decades [123]. Similarly, the abnormal rainfall patterns in 1909 and 1910 altered the usual migration patterns of zebra and Thomson’s gazelle in Kenya’s Rift Valley [129, 132].
During droughts, many species, such as eland, move to forests and woodlands where grass remains green longer [124] due to protection from direct solar radiation. Conversely, forest-dwelling animals, such as elephants and buffalo, emerge more openly during heavy rains due to the wet conditions in the forest and the cooler temperatures [99, 118, 119]. In dry years, like 1954 and 1955 in Kenya, hippos (Hippopotamus amphibius) and other wildlife travel considerable distances in search of grazing [98, 99, 119]. The migratory patterns of wildebeest in 1974 were also affected by varying rainfall, with early arrivals in the Mara and a second arrival in August and September due to the dry conditions in Tanzania’s Serengeti [115].
Climate variability affects wildlife breeding patterns
Climate variability significantly affects wildlife breeding patterns in savannas, including the timing, synchronization and prolificacy of calving [30, 31, 42]. Extended droughts suppress reproduction, leading to reduced birth rates and weakened populations. Drought can reduce calving in ungulates by reducing milk availability for the young and green grass for weaning, increasing mortality of the young. Droughts can also debilitate adults rendering them unable to mate or fertilize successfully and leading to no calf or only few calves being born at the normal calving times [120]. Conversely, periods of abundant rainfall can boost breeding but may also increase mortality due to diseases and predation in lush conditions. Such fluctuations create unpredictable population dynamics, complicating conservation efforts [98, 99, 104, 124, 129, 131].
Poor rains can delay whereas good rains can advance the onset and enhance calving success in savanna ungulates [98, 99, 124, 131]. So, droughts can delay the onset of calving until favourable rains and vegetation growth resume [129, 133]. For example, zebra and wildebeest have most of their young during the long rains (April-May), whereas topi drop most of their calves during the short rains (October-November) in Narok District and Nairobi National Park in Kenya [118]. However, they typically fail to calve or lose most of their calves during droughts. For instance, the virtual failure of three successive rains resulted in extreme drought conditions during the first nine months of 1961 throughout Kenya and the loss of almost the entire year’s crop of wildebeest calves in the Athi-Kaputiei Ecosystem in 1961 [101]. Consequently, in October 1962, wildebeest younger than two years numbered no more than 50, compared to the usual 4000 animals expected to survive to that date in the Athi-Kaputiei Ecosystem at the time. But losses were less severe in the adjacent Narok District which experienced a normal calving season due to less damage from overgrazing by domestic livestock [120], indicating that land use intensity accentuates the deleterious effects of droughts on wildlife breeding. By November 1962, large numbers of calves were born in both the Athi-Kaputiei and Masai Mara ecosystems, with an extremely successful calving season resulting in 90% of females producing young. This peak was sharper in Athi-Kaputiei than in the Mara [120]. This pattern did not repeat in 1963, as wildebeest in both ecosystems reverted to the normal breeding pattern, calving in February-March, despite the Mara region experiencing unusually heavy and prolonged rains in 1963 [123]. Similarly, most birds in Kenya breed during the heavy rains when cover is thick and food is abundant, so increasing irregularity in rainfall makes it difficult for birds to adaptively time their breeding period [104].
Topi also exhibit marked birth peaks, though less sharp than those of wildebeest. In 1962, topi in the Masai Mara dropped most of their calves earlier in September-October instead of the usual October-November [120]. In 1964, widespread and good rainfall created excellent conditions for wildlife. The first topi calf was noted in Narok District on 5 July, 1964, and excellent calving continued throughout the year. Wildebeest began calving on 30 October, 1964, and continued throughout November and December [134]. Moreover, drought suppresses or delays breeding in many other ungulates such as Thomson’s gazelle, topi, Coke’s hartebeest, warthog (Pharcocoerus africana), impala (Aepycerus melampus) and zebra and the animals that breed during droughts lose both body condition and many calves [98, 99, 124, 131].
The timing and success or prolificacy of calving in ungulates in East African savannas are closely tied to local climatic patterns, with significant fluctuations observed in response to drought and abnormal weather conditions. In general, favourable rainfall conditions lead to successful and widespread calving with sharper birth peaks whereas droughts can severely suppress calving success by reducing available resources, weakening potential mates and causing significant mortality among young ungulates. For example, wildebeest show a sharp peak in their calving season in East Africa, occurring just before the onset of the long rains, but there is a tendency for calving to start earlier in the south and later in the north, reflecting the earlier onset of rainfall in the south [120]. Topi populations on the north-eastern shores of Lake Turkana in Kenya had a very successful calving season in 1963, with all calves born within a few days of one another at the beginning of February, eight months earlier than the peak calving time of the Mara population, indicating adaptation to local climatic or vegetational conditions [123].
Conclusions
The univariate patterns produced several interesting insights. The Greater Mara-Serengeti Ecosystem experiences recurrent severe droughts and erratic wet conditions and recorded a substantial rise in temperatures over six decades. The monthly minimum temperature showed a striking increase, while the trends in maximum temperature were more subdued. Notably, monthly minimum temperatures increased by 4.2°C during wet seasons and 3.3°C in dry seasons, while maximum temperatures also increased, though with greater variability. Rainfall showed quasi-periodic oscillations with cycle periods of between 2.5 and 5.3 years. The SOI showed no evident trend and was generally stable. The IOD increased persistently and significantly and had a stochastic cycle period of about 4.1 to 5.5 years. The bivariate and multivariate patterns also yielded several key findings. These include negative correlations between wet and dry season rainfall, marked by opposing oscillations, and consistent increases in IOD and temperature trends, with notable correlations among them. The SOI and IOD trends were negatively correlated and influenced rainfall patterns. Rainfall trends were often correlated more strongly with IOD than with SOI variations. The models also identified many significant structural breaks and outliers in the series. The multivariate models provided many subtle additional insights. These insights provide a comprehensive understanding of the complex interplay between rainfall, temperature, SOI and IOD across the region. They have important implications for a predictive understanding, designing and managing strategies to mitigate diverse climate change impacts on ecosystems, biodiversity, and human wellbeing.
Overall, the consequences of climate change and variability for wildlife conservation are complex and severe. Droughts exacerbate resource competition, increase wildlife mortality rates from starvation and disease, heighten predation risks, intensify human-wildlife conflicts, delay the onset and reduce the prolificity of calving and shrink wetlands. Conversely, periods of heavy rainfall, while beneficial in some respects, can lead to habitat destruction and increased mortality due to environmental changes. Addressing these challenges requires comprehensive and adaptive conservation strategies that enhance resilience by considering the intricate and interconnected interplay between climate change, variability, wildlife behaviour, and human activities. Only through such holistic approaches can the long-term resilience and sustainability of wildlife populations and the overall health of their critical ecosystems be ensured.
Supporting information
S1 File. Supplementary figures (Figs A–CT) and supplementary tables (Tables A—U).
https://doi.org/10.1371/journal.pclm.0000388.s001
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S1 Text. SAS Program codes for fitting UCMs and SSMs.
https://doi.org/10.1371/journal.pclm.0000388.s002
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S2 Text. SAS Program codes for fitting UCMs and SSMs.
https://doi.org/10.1371/journal.pclm.0000388.s003
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S1 Data. The monthly Southern Oscillation Index (SOI) (NINA34, 5N-5S 170W-120W, HadISST, Anomaly from 1981–2010.
https://psl.noaa.gov/gcos_wgsp/Timeseries/Nino34/units=degC) for January 1870 to May 2024. Available from: https://psl.noaa.gov/gcos_wgsp/Timeseries/Data/nino34.long.anom.data.
https://doi.org/10.1371/journal.pclm.0000388.s005
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S2 Data. The monthly Indian Ocean Dipole Mode Index (IOD) (IOD WEST, HadISST1.1 created using SST anomaly area, 10S:10N, 50E-70E area averaged.
Timeseries output created at NOAA PSL. https://psl.noaa.gov/gcos_wgsp/timeseries/DMI Preliminary) for January 1870 to January 2024. Available from: https://psl.noaa.gov/gcos_wgsp/Timeseries/Data/dmiwest.had.long.data.
https://doi.org/10.1371/journal.pclm.0000388.s006
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S3 Data. The monthly average (of daily records) minimum and maximum surface air temperature in degrees celsius at Narok Town Meteorological Station for the period January 1960 to May 2024.
Most of the temperature values, including for 1970–1974, were cross-checked against the original paper records at the Kenya Meteorological Department.
https://doi.org/10.1371/journal.pclm.0000388.s007
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S4 Data. Total monthly (Month1(Jan) to Month12 (Dec)) rainfall in milimeters for Narok Town Meteorological Station from April 1913 to May 2024.
The rainfall values were verified against the original monthly paper cards at the Kenya Meteorological Department.
https://doi.org/10.1371/journal.pclm.0000388.s008
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S5 Data. The combined total monthly rainfall, average monthly minimum and maximum temperatures, monthly SOI and IOD data set for Narok Town.
https://doi.org/10.1371/journal.pclm.0000388.s009
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S6 Data. The total monthly rainfall in milimeters (Rain) for 15 rain gauges located within or near (Cottars Camp later renamed Siana Springs) the Masai Mara National Reserve for the period January 1965 to August 2020.
Predicted is the model predicted rainfall. Rain_imp is the measured rain (Rain) and imputed (predicted) missing values.
https://doi.org/10.1371/journal.pclm.0000388.s010
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S7 Data. The combined total monthly rainfall, monthly SOI and IOD data set for Masai Mara.
https://doi.org/10.1371/journal.pclm.0000388.s011
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S8 Data. The total monthly rainfall in milimiters (rain) for Seronera Research Station in Serengeti National Park in Tanzania for the period January 1980 to December 2015.
Rain_imp are the measured rainfall records and imputed missing values. The rainfall values were not checked against original paper records because these were unavaiable.
https://doi.org/10.1371/journal.pclm.0000388.s012
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S9 Data. The combined total monthly rainfall, monthly SOI and IOD data set for Seronera in Serengeti National Park in Tanzania.
https://doi.org/10.1371/journal.pclm.0000388.s013
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S10 Data. The total monthly rainfall in milimiters (rain) for Ngorongoro Crater in Tanzania for the period January 1963 to December 2014.
Rain_imp are the measured rainfall records and imputed missing values. Only some of the rainfall values were checked against original paper records because not all the original records were avaiable.
https://doi.org/10.1371/journal.pclm.0000388.s014
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S11 Data. The combined total monthly rainfall, monthly SOI and IOD data set for Ngorongoro Crater in Tanzania.
https://doi.org/10.1371/journal.pclm.0000388.s015
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S12 Data. The total monthly rainfall averaged over all 5 × 5 km grids in Narok County of Kenya based on blended station-satellite rainfall data (rain) and on rainfall data predicted by a spatio-temporal hierarchical Bayesian model (rain_Bayes provided in Mukhopadhyay S, Ogutu J O, Bartzke G, Dublin HT, Piepho HP.
Modelling spatio-temporal variation in sparse rainfall data using a hierarchical Bayesian regression model. Journal of Agricultural, Biological and Environmental Statistics. 2019 Jun 15; 24(2): 369–393). Min (minimum) and max (maximum) are the average monthly temperatures based on blended Station-Satellite data. The NOAA and SPOT Normalized Difference Vegetation Index (NDVI) (minimum, maximum, mean, range and standard deviation) averaged over the 5 × 5 km grid in Narok County. Rain_1 to Rain_6 are lagged rainfall values whereas rain_Bayes_1 to rain_Bayes_6 are lagged rain_Bayes values.
https://doi.org/10.1371/journal.pclm.0000388.s016
(XLSX)
Acknowledgments
We thank the Kenya Meteorological Department (KMD), Prof. Kay E. Holekamp (Michigan State University), the World Wildlife Fund for Nature (WWF) and Friends of Conservation (FOC) for providing the rainfall data. The MMEMP was designed and supervised by Dr. Holly T. Dublin, supported by Professor A.R.E. Sinclair (University of British Columbia), and executed by Messrs. Paul Chara (July 1989–1992), John Naiyoma (1989–1993), Alex Obara (1995–1997) and Charles Matankory (1991–2003). Nina Bhola also contributed to data collection. We are greatly indebted to Ms Christine Mahonga for her patience and support in making the rainfall data available and coordinating the verification of the rainfall data at KMD. We thank Mr. Alex Lijodi for his assistance in verifying the rainfall, minimum and maximum temperature data for the Narok Meteorological Station. Many other individuals and organizations, too many to list individually, also helped in various ways over the last 40 years. We are grateful to Mr. Gordon O. Ojwang (Directorate of Resource Surveys and Remote Sensing of Kenya) for his assistance in acquiring the rainfall data for Narok for 1970–2014 from the KMD. Chris Shitote helped with extracting and processing the Chirps rainfall and temperature data for Narok County.
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