# Impact of Climate Variability on Rainfall Characteristics in the Semi-Arid Shashe Catchment (Botswana) from 1981–2050

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Study Area Description

#### 2.3. Data Sets

#### 2.4. Rainfall Projections

#### 2.5. Trend Analysis

#### 2.5.1. Mann-Kendall Test

_{j}and x

_{i}are annual values in years j and i, j > i, respectively. The ordered time series from i = 1, 2, ………n − 1 and x

_{j}, which is ranked from j = I + 1, 2, ………. n is evaluated by comparing subsequent data values. When the current time data value is higher than the data value of the previous period, the S statistical value is increased by 1. Contrariwise, S value is decreased by 1. According to [63,64] is normally distributed when n ≥ 8 having mean:

_{i}is the amount of data in the tied group, and m is the number of groups of tied ranks. The Mann-Kendall standardized test statistic Z is computed by:

_{1−α/2}at a significance level α [65].

**H**

_{0}**(null hypothesis).**

**H**

_{A}**(alternative hypothesis).**

_{α}/2, 0.025 is 1.96. That is, if |Z| is less than 1.96, the trend is invalid; therefore, reject the null hypothesis.

#### 2.5.2. Sen’s Slope Estimator

#### 2.5.3. Innovative Trend Analysis (ITA) Method

- (i)
- the x
_{1}, x_{2}, x_{3}, … x_{n}time series is split into two halves, {S_{(1,2/2)}} and {S_{(1,2/2)}}.$${S}_{1,\frac{n}{2}}=\left\{{x}_{1},{x}_{1},{x}_{1}\dots ,{x}_{\frac{n}{2}}\right\}$$$$\left\{{S}_{2,\frac{n}{2}}\right\}=\{{x}_{\frac{n}{2}+1},{x}_{\frac{n}{2}+2},{x}_{1}\dots ,{x}_{n}\}$$ - (ii)
- Sort elements of each series from the smallest to the largest$$\left\{{t}_{1}\right\}=\left\{min\left({s}_{1,n/2}\right),\dots ,{s}_{1},\dots max\left({s}_{1,n/2}\right)\right\}(1in/2)$$$$\left\{{t}_{2}\right\}=\left\{min\left({s}_{2,n/2}\right),\dots ,{s}_{1},\dots max\left({s}_{2,n/2}\right)\right\}(1jn/2)$$
- (iii)
- The slope of the trend is then calculated using [46]:$$s=\frac{2\left({\overline{y}}_{2}-{\overline{y}}_{1}\right)}{n}$$

#### 2.6. L-Moments—Regional Frequency Analysis

_{1}, λ

_{2}, λ

_{3}and λ

_{4}are L-moments of probability weighted moments as:

_{1}, λ

_{2}, λ

_{3}and λ

_{4}represent the parameters related to location, scale, shape and peakedness, respectively. The most useful quantities for summarizing probability distributions of the L-moments are location (λ

_{1}), and scale (λ

_{2}), which are used to define L-moment ratios as [79]:

_{2}), L-skewness (τ

_{3}) and L-kurtosis (τ

_{4}) are given as 0 ≤ τ

_{2}< 1, −1 < τ

_{3}< 1 and −1 < τ

_{4}< 1 respectively.

#### 2.6.1. Discordancy and Heterogeneity Measure

- Discordancy measure

_{3}), and the L-Kurtosis (or τ

_{4}) are the three L-moment statistic ratios used to measure discordancy in a data sample. Their sample estimates are denoted by t, t

_{3}, and t

_{4}. In a group of sites, L-moments identifies those sites that are inconsistent or in agreement with the whole group. The discordancy measure is defined by [69] as:

_{i}is the discordancy measure for site i, N is the number of sites in the group, superscript T is the transposition of a vector or matrix, u

_{i}is a vector containing the ${t}^{\left(i\right)},{t}_{3}{}^{\left(i\right)}\mathrm{and}{t}_{4}{}^{\left(i\right)}$ values denoting coefficients of variation, skewness, and kurtosis, respectively in a 3-dimension space for site i. The 3 × 1 vector u

_{i}is expressed as:

_{i}value exceeds the critical value D

_{crit}, which depends on N, the number of sites within region R. [69] has noted that for N = 10, the discordant value should not exceed 2.491.

- Heterogeneity measure

_{i}and sample L-moment ratios denoted by t

^{(i)}, t

_{3}

^{(i)}, and t

_{4}

^{(i)}. The regional average L-CV, L-skewness, and L-kurtosis is denoted by t

^{R}, t

_{3}

^{R}, and t

_{4}

^{R}. The weighted proportionally is then defined by [69]:

_{sim}for a region with N sites. The simulated homogeneous regions have the same record length and assessed in a series of Monte Carlo simulation trials [69]. From the simulations, N

_{sim}of the weighted standard deviation V, the mean $\widehat{\mu}v$ and standard deviation $\widehat{\sigma}v$ are determined. The mean $\widehat{\mu}v$ is defined by:

_{SIM}values of V

_{l}and it is defined by:

#### 2.6.2. Choice of a Frequency Distribution

^{DIST}for each distribution is then expressed as:

^{DIST}goodness-of-fit measure selects a distribution that gives the closest estimate as observed data. The best-fit model is judged by the difference between L-kurtosis ${t}_{4}^{DIST}$ of the fitted distribution and the L-kurtosis ${t}_{4}^{R}$ of the regional average. The standard deviation ${\sigma}_{4}$ of ${t}_{4}^{R}$ is obtained through repeated simulations of a kappa region with the same number of sites and record lengths as the observed data. The bias of the simulated region is attained from the same simulations as ${\sigma}_{4}$ and it is calculated by:

_{sim}is the number of realizations for sites with N sites and m is a simulation. The standard deviation ${\sigma}_{4}$ of ${t}_{4}^{R}$:

#### 2.6.3. Estimation of the Quantiles

^{th}repetition. Let M be the number of simulations, ${Q}_{i}\left(F\right)$ implies the true growth curve of a site i, then the relative RMSE of the estimated regional growth curve at a site i can be computed by:

## 3. Results

#### 3.1. Rainfall Projections

#### 3.2. Total Annual Rainfall Projections

#### 3.3. Model Validation

#### 3.4. Mann-Kendall, Sen’s Slope, and the Innovative Trends Analysis of Annual Total Rainfall for the Shashe Catchment

#### 3.5. Mann-Kendall, Sen’s Slope and the Innovative Trends Analysis of Annual Maximum Rainfall for the Shashe Catchment

#### 3.6. Sample L-Moment Test Statistics for Sites in the Region

#### 3.7. Heterogeneity Measure for the Region

#### 3.8. Goodness-of-Fit Statistical Measure and Parameter Estimates for Distributions

^{DIST}goodness-of-fit measure selects a distribution that gives the closest estimate as observed data. A region is considered homogeneous if ${Z}^{DIST}$ if it is close to zero and it is acceptable of $\left|{Z}^{DIST}\right|\le 1.64$. The results in Table 11 indicate that Generalized logistics is the only best-fit distribution for observed and under-climate projections. All other distributions have a Z-Value greater than 1.64; hence not fit for further analysis. Parameters estimates for the best fit Generalized Logistic distribution were determined as indicated in Table 12.

#### 3.9. Estimation of the Quantiles

## 4. Discussion

## 5. Conclusions

- The LARS-WG statistical downscaling model performed well, with over 95% of datasets having a p-value greater than the 0.05 critical value using the Chi-square and t-test. This indicates that this model is capable of generating future rainfall datasets which have the same statistical properties as the observed datasets.
- There are inconsistencies between observed and projected trends in both trend detection methods.
- Overall results indicate an increasing trend in annual total rainfall for over 70% of gauging stations by a range between 0.1 mm to 8 mm per year for both observed and projected rainfall scenarios.
- The trend of annual maximum rainfall is decreasing for 60% of gauging stations for observed and under RCP 4.5, while 80% of the stations show an increasing trend under RCP 2.6 and RCP 8.5 with high inconsistencies between observed and projected rainfall. The increase and decrease are between −1 mm and 1 mm per year.
- As per the L-Moment analysis, the catchment has shown to be homogeneous as there is no discordant site in the region and the Generalized Logistic distribution was found to be the best-fit distribution for both observed and under climate projection data.
- Spatial coverage of a 100-year rainfall between 151–180 mm will be 81% based on observed data and 87% based on projected data under RCP 2.6 scenario when it happens. A 200-year rainfall that ranges between 196–240 mm under RCP 4.5 and 8.5 have high spatial coverage, at least 90%.
- Another notable observation is that rainfall increases from the west and northwest towards the east and northeastern parts of the catchment.

## 6. Future Outlooks

- Generally, there are inconsistencies in the trend detection methods. Therefore, future studies may consider applying modified versions of the time series data by Trend Free Prewhitening (TFPW), Block Bootstrapping (BBS), Bias Corrected Prewhitening, Prewhitening (PW) and Variance Correction Approach by calculating effective sample size.
- Semi-arid basins are highly variable and subject to uncertainties in modeling hydro-climatic systems. Machine learning-based downscaling techniques and climate projections are suggested for future research as these approaches can learn non-linear patterns such as climate change.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**General Circulation Models (GCMs) from Coupled Model Inter-comparison Project Phase 5 (CMIP5) were used in rainfall projections in this study.

Model Name | Model Country | Model Agency |
---|---|---|

ACCESS1_3 | Australia | Commonwealth Scientific and Industrial Research Organisation, Australia), and BOM (Bureau of Meteorology, Australia) |

bcc-csm1-1 | China | Beijing Climate Center, China Meteorological Administration |

BNU-ESM | China | College of Global Change and Earth System Science, Beijing Normal University, China |

CanESM2 | Canada | Canadian Centre for Climate Modeling and Analysis |

CMCC_CM | Italy | Centro Euro-Mediterraneo per I Cambiamenti Climatici |

CNRM-CM5 | France | National Centre of Meteorological Research, France |

CSIRO-Mk3-6-0 | Australia | Commonwealth Scientific and Industrial Research Organization/Queensland Climate Change Centre of Excellence, Australia |

EC_EARTH | Sweden | EC-EARTH consortium |

GFDL-ESM2M | USA | NOAA Geophysical Fluid Dynamics Laboratory, USA |

HadGEM2-ES | United Kingdom | Met Office Hadley Center, UK |

inmcm4 | Russia | Institute for Numerical Mathematics, Russia |

IPSL-CM5A-MR | France | Institut Pierre Simon Laplace, France |

MIROC5 | Japan | Atmosphere and Ocean Research Institute (The University of Tokyo), National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology |

MIROC-ESM | Japan | Japan Agency for Marine-Earth Science and Technology, Atmosphere and Ocean Research Institute (The University of Tokyo), and National Institute for Environmental Studies |

MIROC-ESM-CHEM | Japan | Japan Agency for Marine-Earth Science and Technology, Atmosphere and Ocean Research Institute (The University of Tokyo), and National Institute for Environmental Studies |

MRI-CGCM3 | Japan | Meteorological Research Institute, Japan |

NorESM1-M | Norway | Norwegian Climate Center, Norway |

NCAR_CCSM4 | USA | National Center of Atmospheric Research, USA |

**Figure A1.**Typical rainfall projections using General Circulation Models (GCMs) from Coupled Model Inter-comparison Project Phase 5 (CMIP5) for the ten gauging stations in the Shashe catchment.

## Appendix B

**Table A2.**Accuracy assessment for the Long Ashton Research Station Weather Generator (LARS-WG) used in rainfall projections in this study.

Masunga | Mathangwane | Jackalas 2 | ||||||||||||||||

Month | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value |

J | 0.105 | 0.999 | 1.58 | 0.118 | 1.63 | 0.104 | 0.156 | 0.92 | −1.491 | 0.14 | 1.241 | 0.468 | 0.075 | 1 | 0.863 | 0.391 | 3.315 | 0.001 |

F | 0.097 | 1 | 0.839 | 0.403 | 1.629 | 0.104 | 0.202 | 0.685 | 0.311 | 0.756 | 1.232 | 0.484 | 0.055 | 1 | −0.341 | 0.734 | 1.201 | 0.585 |

M | 0.115 | 0.996 | −2.074 | 0.041 | 2.303 | 0.008 | 0.085 | 1 | −1.574 | 0.119 | 2.634 | 0.002 | 0.037 | 1 | 0.563 | 0.575 | 1.849 | 0.072 |

A | 0.207 | 0.655 | −0.673 | 0.503 | 1.159 | 0.634 | 0.138 | 0.971 | −0.85 | 0.398 | 1.672 | 0.096 | 0.042 | 1 | −0.522 | 0.604 | 1.382 | 0.34 |

M | 0.348 | 0.096 | −0.841 | 0.402 | 1.913 | 0.037 | 0.258 | 0.373 | 1.004 | 0.318 | 2.872 | 0.001 | 0.054 | 1 | 0.039 | 0.969 | 1.921 | 0.056 |

J | 0.304 | 0.196 | 1.337 | 0.185 | 5.899 | 0 | 0.096 | 1 | 0.432 | 0.667 | 2.304 | 0.006 | 0.162 | 0.897 | −1.76 | 0.083 | 1.009 | 0.991 |

J | 0.522 | 0.002 | 0.205 | 0.838 | 1.356 | 0.308 | 0.254 | 0.393 | 0.567 | 0.572 | 8.054 | 0 | 0.052 | 1 | 0.339 | 0.735 | 1.064 | 0.846 |

A | 0 | 1 | −0.316 | 0.753 | 3.283 | 0 | 0.192 | 0.744 | −0.58 | 0.563 | 1.239 | 0.473 | 0.05 | 1 | −1.268 | 0.209 | 1.062 | 0.85 |

S | 0.131 | 0.982 | −1.98 | 0.051 | 6.867 | 0 | 0.19 | 0.755 | 0.663 | 0.509 | 1.934 | 0.028 | 0.113 | 0.997 | 0.519 | 0.606 | 1.878 | 0.065 |

O | 0.251 | 0.407 | 0.422 | 0.674 | 1.309 | 0.383 | 0.152 | 0.934 | 0.631 | 0.53 | 1.165 | 0.607 | 0.045 | 1 | 1.409 | 0.163 | 1.654 | 0.139 |

N | 0.156 | 0.92 | −0.654 | 0.515 | 1.637 | 0.111 | 0.137 | 0.972 | −1.041 | 0.301 | 2.089 | 0.018 | 0.031 | 1 | −0.32 | 0.75 | 1.465 | 0.261 |

D | 0.109 | 0.998 | 1.629 | 0.107 | 1.423 | 0.238 | 0.151 | 0.937 | −0.579 | 0.564 | 1.198 | 0.56 | 0.043 | 1 | −0.479 | 0.633 | 1.445 | 0.278 |

Matsiloje | Ramokgwebana | Senyawe | ||||||||||||||||

Month | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value |

J | 0.123 | 0.991 | 0.265 | 0.792 | 1.671 | 0.097 | 0.121 | 0.993 | −0.475 | 0.636 | 1.474 | 0.208 | 0.143 | 0.959 | −1.794 | 0.076 | 1.559 | 0.151 |

F | 0.133 | 0.979 | −0.069 | 0.945 | 1.335 | 0.348 | 0.082 | 1 | −1.695 | 0.094 | 2.051 | 0.021 | 0.114 | 0.997 | −0.635 | 0.527 | 1.587 | 0.135 |

M | 0.119 | 0.994 | 0.717 | 0.475 | 1.215 | 0.514 | 0.125 | 0.989 | −1.065 | 0.29 | 1.55 | 0.156 | 0.235 | 0.492 | −0.214 | 0.831 | 1.072 | 0.81 |

A | 0.168 | 0.87 | 0.59 | 0.557 | 1.238 | 0.474 | 0.217 | 0.595 | −0.253 | 0.801 | 1.576 | 0.14 | 0.286 | 0.256 | −0.921 | 0.36 | 3.59 | 0 |

M | 0.174 | 0.842 | 0.818 | 0.415 | 1.596 | 0.119 | 0.266 | 0.337 | −0.968 | 0.336 | 1.591 | 0.132 | 0.299 | 0.212 | −0.464 | 0.644 | 2.777 | 0.001 |

J | 0.305 | 0.193 | 0.59 | 0.557 | 2.036 | 0.018 | 0.291 | 0.238 | −1.021 | 0.31 | 1.298 | 0.398 | 0.092 | 1 | −0.663 | 0.509 | 3.397 | 0 |

J | 0.609 | 0 | −0.612 | 0.542 | 1.311 | 0.379 | 0.338 | 0.113 | −1.506 | 0.136 | 12.318 | 0 | 0.15 | 0.94 | 0.325 | 0.746 | 5.527 | 0 |

A | 0 | 1 | −1.154 | 0.252 | 3.077 | 0 | 0.645 | 0 | −1.477 | 0.143 | 1.883 | 0.041 | 0.367 | 0.068 | −0.616 | 0.54 | 1.337 | 0.347 |

S | 0.217 | 0.595 | −0.809 | 0.421 | 3.325 | 0 | 0.295 | 0.225 | −2.654 | 0.009 | 4.304 | 0 | 0.311 | 0.176 | −1.179 | 0.241 | 1.288 | 0.412 |

O | 0.144 | 0.957 | 0.655 | 0.514 | 1.06 | 0.856 | 0.142 | 0.962 | −1.024 | 0.309 | 1.76 | 0.068 | 0.172 | 0.851 | 0.367 | 0.715 | 1.199 | 0.558 |

N | 0.138 | 0.971 | 0.229 | 0.82 | 1.921 | 0.035 | 0.138 | 0.971 | −0.531 | 0.597 | 2.595 | 0.002 | 0.059 | 1 | −0.583 | 0.562 | 2.276 | 0.008 |

D | 0.127 | 0.987 | −0.006 | 0.995 | 1.008 | 0.972 | 0.083 | 1 | 0.166 | 0.869 | 1.971 | 0.029 | 0.062 | 1 | −0.655 | 0.514 | 1.38 | 0.296 |

Sebina | Siviya | Tonota | ||||||||||||||||

Month | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value | KS Statistic | p-Value | t-Test | p-Value | f-Test | p-Value |

J | 0.237 | 0.481 | −0.289 | 0.774 | 1.148 | 0.641 | 0.062 | 1 | 1.257 | 0.212 | 1.307 | 0.37 | 0.065 | 1 | −0.14 | 0.889 | 1.334 | 0.335 |

F | 0.181 | 0.805 | 0.504 | 0.616 | 1.095 | 0.772 | 0.064 | 1 | −0.793 | 0.43 | 1.046 | 0.874 | 0.103 | 0.999 | −2.057 | 0.043 | 1.455 | 0.224 |

M | 0.174 | 0.842 | 0.071 | 0.944 | 1.141 | 0.656 | 0.138 | 0.971 | −0.744 | 0.459 | 2.253 | 0.009 | 0.086 | 1 | −0.996 | 0.322 | 2.784 | 0.001 |

A | 0.209 | 0.643 | 2.344 | 0.021 | 2.391 | 0.004 | 0.217 | 0.595 | 1.032 | 0.305 | 1.537 | 0.152 | 0.116 | 0.996 | 0.739 | 0.462 | 1.205 | 0.531 |

M | 0.217 | 0.595 | −0.595 | 0.553 | 1.408 | 0.267 | 0.289 | 0.245 | 1.573 | 0.119 | 18.752 | 0 | 0.261 | 0.359 | 0.002 | 0.998 | 1.156 | 0.624 |

J | 0.218 | 0.589 | 0.627 | 0.532 | 6.305 | 0 | 0.309 | 0.182 | 0.442 | 0.659 | 1.384 | 0.292 | 0.522 | 0.002 | 0.659 | 0.511 | 3.842 | 0 |

J | 0.217 | 0.595 | −0.295 | 0.769 | 1.211 | 0.536 | 0.419 | 0.024 | 0.923 | 0.358 | 22.504 | 0 | 0.609 | 0 | 0.934 | 0.353 | 18.33 | 0 |

A | 0.261 | 0.359 | −0.588 | 0.558 | 1.417 | 0.258 | 0.506 | 0.003 | 1.195 | 0.235 | 490.881 | 0 | 0.696 | 0 | −1.333 | 0.186 | 2.457 | 0.004 |

S | 0.348 | 0.096 | −0.53 | 0.598 | 2.638 | 0.002 | 0.244 | 0.443 | 0.25 | 0.803 | 2.813 | 0.001 | 0.261 | 0.359 | −1.223 | 0.225 | 3.975 | 0 |

O | 0.229 | 0.526 | 0.92 | 0.36 | 1.124 | 0.692 | 0.169 | 0.866 | −0.391 | 0.697 | 3.918 | 0 | 0.066 | 1 | −1.055 | 0.294 | 1.803 | 0.057 |

N | 0.215 | 0.607 | 0 | 1 | 1.334 | 0.35 | 0.154 | 0.927 | 1.5 | 0.137 | 1.796 | 0.059 | 0.093 | 1 | −0.527 | 0.599 | 1.034 | 0.92 |

D | 0.125 | 0.989 | −0.59 | 0.557 | 1.778 | 0.063 | 0.086 | 1 | −0.034 | 0.973 | 1.055 | 0.867 | 0.124 | 0.99 | −0.024 | 0.981 | 1.277 | 0.412 |

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**Figure 1.**Maps showing the location of the study area. (

**a**) The base map of Botswana shows the location of the Shashe catchment and (

**b**) the distribution of rainfall gauging stations within the catchment.

**Figure 8.**Annual variation trend of observed total rainfall for ten stations in Shashe catchment determined using the ITA method.

**Figure 9.**Annual variation of total rainfall trend projected under RCP2.6 climate scenario for ten stations in Shashe catchment determined using the ITA method.

**Figure 10.**Annual variation of total rainfall trend projected under RCP 4.5 climate scenario for ten stations in Shashe catchment determined using the ITA method.

**Figure 11.**Annual variation of total rainfall trend projected under RCP 8.5 climate scenario for ten stations in Shashe catchment determined using the ITA method.

**Figure 12.**The annual variation of the annual maximum rainfall trend from 1981–2020 for ten stations in the Shashe catchment was determined using the ITA method.

**Figure 13.**Annual variation of annual maximum rainfall trend projected under RCP 2.6 climate scenario from 1981–2050 for ten stations in Shashe catchment determined using the ITA method.

**Figure 14.**Annual variation of maximum rainfall trend projected under RCP 4.5 climate scenario from 1981–2050 for ten stations in Shashe catchment determined using the ITA method.

**Figure 15.**Annual variation of annual maximum rainfall trend projected under RCP 8.5 climate scenario from 1981–2050 for ten stations in Shashe catchment determined using the ITA method.

**Figure 16.**Maps of spatial rainfall distribution at: (

**a**) 10–year, (

**b**) 50–year and (

**c**) 100–year recurrence intervals in the study area for the 1981–2020 study period.

**Figure 17.**Maps of spatial rainfall distribution under RCP 2.6 climate scenario at 10–year, 50–year, 100–year, 150–year and 200–year recurrence intervals.

**Figure 18.**Maps of spatial rainfall distribution under RCP 4.5 climate scenario at 10–year, 50–year, 100–year, 150–year and 200–year recurrence interval.

**Figure 19.**Maps of spatial rainfall distribution under RCP 8.5 climate scenario at: (

**a**) 10–year, (

**b**) 50–year, (

**c**) 100–year, (

**d**) 150–year and (

**e**) 200–year recurrence intervals.

**Table 1.**Rainfall gauging stations, their geographic location and length of record years (Source: Department of Meteorological Services (DMS), Botswana).

Station Name | Longitude | Latitude | Observed Years |
---|---|---|---|

Francistown | 27.502515 | −21.16636 | 1981–2020 |

Jackalas No 2 | 27.680671 | −20.954196 | 1981–2020 |

Masunga | 27.445115 | −20.620707 | 1981–2020 |

Mathangwane | 27.32 | −20.98 | 1981–2020 |

Matsiloje | 27.88544 | −21.299711 | 1981–2020 |

Ramokgwebana | 27.64629 | −20.587204 | 1981–2020 |

Sebina | 27.219551 | −20.830506 | 1981–2020 |

Senyawe | 27.688029 | −20.779341 | 1981–2020 |

Siviya | 27.675744 | −20.857003 | 1981–2020 |

Tonota | 27.463376 | −21.437833 | 1981–2020 |

**Table 2.**Performance of LARS-WG statistical downscaling model using the Chi-square, t-test and f-test statistics alongside their p-values.

Francistown | ||||||
---|---|---|---|---|---|---|

Month | Chi-Square | p-Value | t-Test | p-Value | f-Test | p-Value |

Jan | 0.147 | 0.949 | −0.323 | 0.747 | 1.182 | 0.59 |

Feb | 0.131 | 0.982 | 0.034 | 0.973 | 1.829 | 0.045 |

Mar | 0.122 | 0.992 | −0.416 | 0.679 | 1.551 | 0.155 |

Apr | 0.166 | 0.879 | −1.175 | 0.243 | 2.363 | 0.006 |

May | 0.21 | 0.637 | 0.154 | 0.878 | 1.527 | 0.158 |

Jun | 0.217 | 0.595 | −0.122 | 0.903 | 1.837 | 0.043 |

Jul | 0.218 | 0.589 | −0.086 | 0.932 | 1.346 | 0.321 |

Aug | 0.304 | 0.196 | −0.318 | 0.752 | 1.143 | 0.652 |

Sep | 0.402 | 0.035 | −0.775 | 0.44 | 1.507 | 0.183 |

Oct | 0.135 | 0.976 | −0.656 | 0.513 | 1.035 | 0.918 |

Nov | 0.159 | 0.909 | 0.245 | 0.807 | 1.077 | 0.8 |

Dec | 0.139 | 0.969 | 0.79 | 0.431 | 1.442 | 0.221 |

**Table 3.**The trend for total annual rainfall for observed and projected rainfall under RCP 2.6, 4.5 and RCP 8.5 climate scenarios between 1981–2050 for gauging stations in the Shashe Catchment based on Mann-Kendall, Sen’s Slope, and the Innovative Trends Analysis.

Location | Francistown | Jackalas_2 | Masunga | Mathangwane | Matsiloje | Ramokgwebana | Sebina | Senyawe | Siviya | Tonota | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MK | Tau | Observed | −0.146 | 0.1490 | 0.0500 | −0.0295 | 0.2560 | −0.0282 | 0.2850 | 0.1900 | 0.1820 | 0.0744 |

RCP 2.6 | 0.3140 | 0.3130 | 0.0150 | 0.2500 | 0.1060 | 0.4350 | 0.1440 | 0.3110 | 0.0370 | 0.1520 | ||

RCP 4.5 | 0.2170 | 0.1880 | 0.0090 | 0.2410 | 0.0820 | 0.3180 | 0.0090 | 0.3300 | −0.046 | 0.2240 | ||

RCP 8.5 | 0.3040 | 0.3290 | 0.0090 | 0.2060 | 0.1110 | 0.4100 | 0.1190 | 0.2030 | −0.034 | 0.0860 | ||

p-Value | Observed | 0.1880 | 0.1803 | 0.6579 | 0.7887 | 0.0204 | 0.8067 | 0.0100 | 0.0868 | 0.1004 | 0.5066 | |

RCP 2.6 | 0.0000 | 0.0000 | 0.8590 | 0.0020 | 0.1940 | 0.0000 | 0.0790 | 0.0000 | 0.6560 | 0.0640 | ||

RCP 4.5 | 0.0080 | 0.0220 | 0.9150 | 0.0030 | 0.3160 | 0.0000 | 0.9190 | 0.0000 | 0.5770 | 0.0060 | ||

RCP 8.5 | 0.0000 | 0.0000 | 0.9150 | 0.0120 | 0.1770 | 0.0000 | 0.1470 | 0.0130 | 0.6850 | 0.2960 | ||

Z-Value | Observed | −1.317 | 1.3399 | 0.4428 | −0.2680 | 2.3186 | −0.2447 | 2.5749 | 1.7127 | 1.6428 | 0.6641 | |

RCP 2.6 | 3.8430 | 3.8230 | 0.1770 | 3.0520 | 1.2980 | 5.3230 | 1.7540 | 3.8020 | 0.4460 | 1.8560 | ||

RCP 4.5 | 2.6570 | 2.2920 | 0.1060 | 2.9400 | 1.0040 | 3.8830 | 0.1010 | 4.0350 | −0.558 | 2.7380 | ||

RCP 8.5 | 3.7110 | 4.0250 | 0.1060 | 2.5150 | 1.3490 | 5.0090 | 1.4500 | 2.4840 | −0.406 | 1.0440 | ||

Sen’s slope (mm) | Observed | −2.674 | 3.6746 | 0.7000 | −1.0075 | 6.8493 | −0.2739 | 8.0434 | 3.8553 | 6.2331 | 1.1792 | |

RCP 2.6 | 3.2740 | 3.6820 | 0.2530 | 4.0430 | 1.2920 | 6.6550 | 2.1740 | 3.9670 | 0.5790 | 1.7890 | ||

RCP 4.5 | 2.0150 | 2.0690 | 0.1000 | 3.5410 | 0.9270 | 3.7470 | 0.0850 | 4.3630 | −0.732 | 2.7750 | ||

RCP 8.5 | 3.1650 | 3.8970 | 0.1000 | 2.9610 | 1.2490 | 5.4530 | 1.6740 | 2.4320 | −0.490 | 0.8460 | ||

ITA | Trend Slope | Observed | −6.170 | 0.4925 | 0.1756 | −3.2842 | 7.0208 | −1.7894 | 4.6660 | 1.2116 | 2.4522 | 0.5364 |

RCP 2.6 | 2.8984 | 3.4833 | −0.683 | 4.9125 | 1.6544 | 6.7938 | 3.1353 | 5.7210 | 0.2693 | 1.5975 | ||

RCP 4.5 | 1.8362 | 2.0448 | −0.993 | 4.1429 | 1.3623 | 3.9288 | 0.9489 | 6.0135 | −0.909 | 2.7171 | ||

RCP 8.5 | 3.2081 | 3.9058 | −0.994 | 3.5784 | 1.8418 | 6.0658 | 2.4074 | 4.2460 | −0.878 | 0.6100 | ||

Trend Indicator | Observed | −2.789 | 0.2324 | 0.0750 | −1.5943 | 4.0217 | −1.0141 | 2.0337 | 0.5972 | 1.0589 | 0.3046 | |

RCP 2.6 | 2.6338 | 2.9300 | −0.508 | 4.5229 | 1.5111 | 6.9732 | 2.3825 | 4.9476 | 0.1969 | 1.5508 | ||

RCP 4.5 | 1.6686 | 1.7200 | −0.739 | 3.8143 | 1.2443 | 4.0326 | 0.7210 | 5.2006 | −0.664 | 2.6377 | ||

RCP 8.5 | 2.9153 | 3.2854 | −0.740 | 3.2946 | 1.6823 | 6.2260 | 1.8294 | 3.6719 | −0.642 | 0.5922 |

**Table 4.**The trend for annual maximum rainfall and magnitude of trend between 1981–2020 for gauging stations in the study area.

Location | Francistown | Jackalas_2 | Masunga | Mathangwane | Matsiloje | Ramokgwebana | Sebina | Senyawe | Siviya | Tonota | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MK | Tau | Observed | −0.148 | −0.189 | −0.213 | 0.347 | −0.0064 | −0.0488 | −0.353 | 0.158 | 0.0758 | 0.165 |

RCP 2.6 | 0.0840 | 0.1290 | 0.0680 | 0.2560 | 0.0740 | 0.1120 | 0.0980 | 0.2950 | 0.0350 | 0.2810 | ||

RCP 4.5 | −0.0120 | 0.0200 | −0.0180 | 0.1670 | −0.0090 | 0.0700 | 0.0320 | 0.2150 | −0.1080 | 0.1950 | ||

RCP 8.5 | 0.1180 | 0.0990 | −0.0180 | 0.2250 | 0.0790 | 0.1150 | 0.0970 | 0.2780 | −0.1310 | 0.2860 | ||

p-Value | Observed | 0.1841 | 0.0889 | 0.05448 | 0.00172 | 0.9628 | 0.6664 | 0.00141 | 0.1552 | 0.4991 | 0.1388 | |

RCP 2.6 | 0.3080 | 0.1150 | 0.4120 | 0.0020 | 0.3700 | 0.1710 | 0.2340 | 0.0000 | 0.6700 | 0.0010 | ||

RCP 4.5 | 0.8830 | 0.8120 | 0.8310 | 0.0420 | 0.9150 | 0.3940 | 0.6960 | 0.0090 | 0.1890 | 0.0170 | ||

RCP 8.5 | 0.1480 | 0.2260 | 0.8310 | 0.0060 | 0.3380 | 0.1620 | 0.2380 | 0.0010 | 0.1100 | 0.0000 | ||

Z-Value | Observed | −1.3283 | −1.7015 | −1.9230 | 3.1351 | −0.0466 | −0.4312 | −3.1926 | 1.4215 | 0.6759 | 1.4804 | |

RCP 2.6 | 1.0190 | 1.5770 | 0.8210 | 3.1230 | 0.8970 | 1.3690 | 1.1910 | 3.6050 | 0.4260 | 3.4270 | ||

RCP 4.5 | −0.1470 | 0.2380 | −0.2130 | 2.0380 | −0.1060 | 0.8520 | 0.3900 | 2.6310 | −1.3130 | 2.3830 | ||

RCP 8.5 | 1.4450 | 1.2120 | −0.2130 | 2.7480 | 0.9580 | 1.3990 | 1.4450 | 3.4020 | −1.5970 | 3.4980 | ||

Sen’s slope (mm) | Observed | −0.3082 | −0.5848 | −0.6093 | 0.9264 | −0.0033 | −0.1708 | −0.9999 | 0.5929 | 0.3097 | 0.4771 | |

RCP 2.6 | 0.1300 | 0.2300 | 0.1100 | 0.4200 | 0.1100 | 0.2300 | 0.2100 | 0.7000 | 0.0500 | 0.5100 | ||

RCP 4.5 | −0.0100 | 0.0200 | −0.0200 | 0.2300 | −0.0100 | 0.1300 | 0.0500 | 0.5000 | −0.1500 | 0.3100 | ||

RCP 8.5 | 0.1800 | 0.1800 | −0.0200 | 0.3600 | 0.1500 | 0.2400 | 0.2000 | 0.6600 | −0.1900 | 0.5000 | ||

ITA | Trend Slope | Observed | −0.2528 | −0.6325 | −0.4372 | −0.0059 | 0.0217 | 0.2370 | −0.9505 | 0.1585 | −0.0055 | 0.6580 |

RCP 2.6 | 0.0734 | 0.1744 | 0.0657 | 0.3644 | −0.0617 | 0.4134 | 0.1150 | 0.8456 | 0.1357 | 0.3832 | ||

RCP 4.5 | −0.1306 | −0.0803 | −0.0741 | 0.1639 | −0.2092 | 0.1024 | −0.0774 | 0.5350 | −0.0994 | 0.1963 | ||

RCP 8.5 | 0.0596 | −0.0684 | 0.1798 | 0.2808 | 0.0416 | 0.2476 | 0.0895 | 0.7160 | −0.1884 | 0.4177 | ||

Trend Indicator | Observed | −0.7626 | −1.9312 | −1.7288 | −0.0207 | 0.0722 | 0.7566 | −3.0449 | 0.4434 | −0.0160 | 2.4564 | |

RCP 2.6 | 0.3926 | 0.9922 | 0.4610 | 2.3519 | −0.3388 | 2.1159 | 0.6937 | 4.1425 | 0.7045 | 2.1903 | ||

RCP 4.5 | −0.6987 | −0.4566 | −0.5199 | 1.0582 | −1.1483 | 0.5243 | −0.4664 | 2.6210 | −0.5164 | 1.1219 | ||

RCP 8.5 | 0.3187 | −0.4798 | 1.0228 | 1.8127 | 0.2286 | 1.2675 | 0.5397 | 3.5077 | −0.9781 | 2.3872 |

Gauging Station | Record Length | Annual Maximum (mm) | L-CV (t) | L-Skewness (t3) | L-Kurtosis (t4) | Discordancy Measure (DI) |
---|---|---|---|---|---|---|

Francistown | 40 | 63.76 | 0.2171 | 0.2868 | 0.1748 | 1.84 |

Jackalas_2 | 40 | 59.18 | 0.2223 | 0.0259 | 0.1368 | 1.11 |

Masunga | 40 | 46.20 | 0.2654 | 0.1306 | 0.1464 | 0.29 |

Mathangwane | 40 | 56.73 | 0.3274 | 0.3982 | 0.397 | 1.64 |

Matsiloje | 40 | 60.38 | 0.286 | 0.1522 | 0.2502 | 0.9 |

Ramokgwebana | 40 | 65.02 | 0.2649 | 0.2832 | 0.2607 | 0.41 |

Sebina | 40 | 52.93 | 0.3713 | 0.3264 | 0.2405 | 2.2 |

Senyawe | 40 | 73.08 | 0.3189 | 0.3163 | 0.2787 | 0.3 |

Siviya | 40 | 68.69 | 0.2222 | 0.0412 | 0.0755 | 0.84 |

Tonota | 40 | 60.16 | 0.2552 | 0.2146 | 0.1493 | 0.46 |

Gauging Station | Record Length | Annual Maximum | L-CV (t) | L-Skewness (t3) | L-Kurtosis (t4) | Discordancy Measure (DI) |
---|---|---|---|---|---|---|

Francistown | 70 | 66.72 | 0.2007 | 0.2479 | 0.1501 | 1.95 |

Jackalas_2 | 70 | 64.57 | 0.2035 | 0.0832 | 0.1823 | 0.66 |

Masunga | 70 | 50.14 | 0.2463 | 0.0648 | 0.1471 | 0.58 |

Mathangwane | 70 | 60.60 | 0.2944 | 0.3653 | 0.3646 | 1.85 |

Matsiloje | 70 | 62.67 | 0.2388 | 0.1245 | 0.2312 | 0.66 |

Ramokgwebana | 70 | 75.61 | 0.3101 | 0.3742 | 0.2655 | 0.78 |

Sebina | 70 | 60.06 | 0.319 | 0.2254 | 0.2208 | 1.15 |

Senyawe | 70 | 86.24 | 0.3017 | 0.2901 | 0.2111 | 0.62 |

Siviya | 70 | 69.78 | 0.1888 | −0.0279 | 0.0942 | 0.99 |

Tonota | 70 | 67.94 | 0.2309 | 0.1472 | 0.1049 | 0.75 |

Gauging Station | Record Length | Annual Maximum | L-CV (t) | L-Skewness (t3) | L-Kurtosis (t4) | Discordancy Measure (DI) |
---|---|---|---|---|---|---|

Francistown | 70 | 63.15 | 0.1894 | 0.2351 | 0.1351 | 1.96 |

Jackalas_2 | 70 | 60.12 | 0.1965 | 0.0597 | 0.1533 | 0.69 |

Masunga | 70 | 47.81 | 0.2464 | 0.1085 | 0.1727 | 0.5 |

Mathangwane | 70 | 57.10 | 0.2921 | 0.3719 | 0.3803 | 2.14 |

Matsiloje | 70 | 60.09 | 0.2369 | 0.1448 | 0.2591 | 0.89 |

Ramokgwebana | 70 | 70.17 | 0.2875 | 0.3246 | 0.2441 | 0.51 |

Sebina | 70 | 56.69 | 0.3177 | 0.2566 | 0.2443 | 1.13 |

Senyawe | 70 | 80.81 | 0.2936 | 0.2726 | 0.1903 | 0.85 |

Siviya | 70 | 65.67 | 0.1931 | 0.0373 | 0.1214 | 0.79 |

Tonota | 70 | 64.67 | 0.2303 | 0.1898 | 0.1275 | 0.53 |

Gauging Station | Record Length | Annual Maximum | L-CV (t) | L-Skewness (t3) | L-Kurtosis (t4) | Discordancy Measure (DI) |
---|---|---|---|---|---|---|

Francistown | 70 | 66.48 | 0.1888 | 0.2068 | 0.1385 | 1.84 |

Jackalas_2 | 70 | 64.67 | 0.2172 | 0.1221 | 0.175 | 0.4 |

Masunga | 70 | 47.81 | 0.2464 | 0.1085 | 0.1727 | 0.58 |

Mathangwane | 70 | 59.14 | 0.2908 | 0.3589 | 0.3762 | 2.34 |

Matsiloje | 70 | 64.48 | 0.2479 | 0.1406 | 0.2218 | 0.66 |

Ramokgwebana | 70 | 72.71 | 0.2909 | 0.3306 | 0.2545 | 0.81 |

Sebina | 70 | 59.61 | 0.3159 | 0.2307 | 0.2261 | 1.16 |

Senyawe | 70 | 83.97 | 0.293 | 0.2579 | 0.1844 | 0.98 |

Siviya | 70 | 64.11 | 0.1982 | 0.0767 | 0.1297 | 0.72 |

Tonota | 70 | 68.54 | 0.2333 | 0.1584 | 0.1237 | 0.5 |

**Table 9.**The regional average L-moment ratios for records between 1981–2020 and under RCP 2.6, 4.5 and RCP 8.5 climate scenarios.

L-CV (t) | L-Skewness (t_{3}) | L-Kurtosis (t_{4}) | |
---|---|---|---|

1981–2000 | 0.2751 | 0.2175 | 0.211 |

RCP 2.6 | 0.2534 | 0.1895 | 0.1972 |

RCP 4.5 | 0.2483 | 0.2001 | 0.2028 |

RCP 8.5 | 0.2523 | 0.1991 | 0.2003 |

**Table 10.**Heterogeneity measure for the region for records between 1981–2020 and under RCP 2.6, 4.5 and RCP 8.5 climate scenarios.

1981–2020 | RCP 2.6 | RCP 4.5 | RCP 8.5 | |
---|---|---|---|---|

Observed s.d. of L-skew/L-kurtosis distance | 0.1327 | 0.1316 | 0.118 | 0.101 |

Sim. mean of s.d. of L-skew/L-kurtosis distance | 0.1046 | 0.0768 | 0.0781 | 0.079 |

Sim. s.d. of s.d. of L-skew/L-kurtosis distance | 0.0244 | 0.0165 | 0.0179 | 0.0174 |

Heterogeneity measure H [3] | 1.15 | 3.31 | 2.23 | 1.26 |

Probability Distributions | 1981–2020 | RCP 2.6 | RCP 4.5 | RCP 8.5 |
---|---|---|---|---|

Gen. logistic | −0.64 * | −0.26 * | −0.48 * | −0.23 * |

Gen. extreme value | −1.94 | −2.23 | −2.36 | −2.09 |

Gen. normal | −2.35 | −2.62 | −2.8 | −2.53 |

Pearson type III | −3.14 | −3.47 | −3.73 | −3.43 |

Gen. Pareto | −5.05 | −6.73 | −6.72 | −6.4 |

**Table 12.**Parameter estimates for Generalised Logistic distribution accepted at 0.90 confidence level.

L-CV (t) | L-Skewness (t3) | L-Kurtosis (t4) | |
---|---|---|---|

1981–2020 | 0.9038 | 0.2542 | −0.2175 |

RCP 2.6 | 0.9224 | 0.2387 | −0.1895 |

RCP 4.5 | 0.9199 | 0.2323 | −0.2001 |

RCP 8.5 | 0.919 | 0.2361 | −0.1991 |

**Table 13.**Areal change in rainfall distribution at 10–year, 50–year and 100–year recurrence intervals in the study area for the 1981–2020 study period.

Rainfall (mm) | 10–Year Area (km^{2}) | 50–Year Area (km^{2}) | 100–Year Area (km^{2}) | |||
---|---|---|---|---|---|---|

61–75 | 11 | |||||

76–90 | 1434 | (99%) | ||||

91–105 | 6095 | |||||

106–120 | 76 | 87 | ||||

121–135 | 960 | 5 | ||||

136–150 | 4468 | (86%) | 231 | |||

151–165 | 2095 | 1584 | (81%) | |||

166–180 | 6 | 4661 | ||||

181–195 | 1128 | |||||

196–210 | 7 |

**Table 14.**Areal change in rainfall distribution under RCP 2.6 climate scenario at 10–year, 50–year, 100–year, 150–year and 200–year recurrence intervals.

Rainfall (mm) | 10–Year Area (km^{2}) | 50–Year Area (km^{2}) | 100–Year Area (km^{2}) | 150–Year Area (km^{2}) | 200–Year Area (km^{2}) | |||||
---|---|---|---|---|---|---|---|---|---|---|

76–90 | 271 | |||||||||

91–105 | 6013 | (96%) | ||||||||

106–120 | 1334 | 55 | ||||||||

121–135 | 346 | 9 | ||||||||

136–150 | 3663 | (92%) | 199 | 34 | ||||||

151–165 | 3396 | 1504 | (87%) | 205 | 87 | |||||

166–180 | 156 | 5120 | 1537 | (82%) | 252 | |||||

181–195 | 688 | 4764 | 1996 | (89%) | ||||||

196–210 | 96 | 933 | 4776 | |||||||

211–225 | 143 | 389 | ||||||||

226–240 | 116 |

**Table 15.**Areal change in rainfall distribution under RCP 4.5 climate scenario at 10–year, 50–year, 100–year, 150–year and 200–year recurrence intervals.

Rainfall (mm) | 10–Year Area (km^{2}) | 50–Year Area (km^{2}) | 100–Year Area (km^{2}) | 150–Year Area (km^{2}) | 200–Year Area (km^{2}) | |||||
---|---|---|---|---|---|---|---|---|---|---|

76–90 | 6 | |||||||||

91–105 | 1162 | (97%) | ||||||||

106–120 | 6293 | |||||||||

121–135 | 155 | 167 | ||||||||

136–150 | 1985 | (94%) | 84 | |||||||

151–165 | 5190 | 392 | 120 | 12 | ||||||

166–180 | 274 | 3494 | (92%) | 422 | 190 | |||||

181–195 | 3500 | 3376 | (91%) | 1246 | ||||||

196–210 | 146 | 3517 | 3913 | (79%) | ||||||

211–225 | 181 | 2121 | ||||||||

226–240 | 134 |

**Table 16.**Areal change in rainfall distribution under RCP 8.5 climate scenario at 10–year, 50–year, 100–year, 150–year and 200–year recurrence intervals.

Rainfall (mm) | 10–Year Area (km^{2}) | 50–Year Area (km^{2}) | 100–Year Area (km^{2}) | 150–Year Area (km^{2}) | 200–Year Area (km^{2}) | |||||
---|---|---|---|---|---|---|---|---|---|---|

76–90 | 466 | |||||||||

91–105 | 6231 | (94%) | ||||||||

106–120 | 919 | |||||||||

121–135 | 123 | |||||||||

136–150 | 501 | 59 | ||||||||

151–165 | 3438 | (91%) | 255 | 87 | ||||||

166–180 | 3520 | 1819 | (83%) | 259 | 146 | |||||

181–195 | 34 | 4524 | 1755 | 331 | ||||||

196–210 | 951 | 4034 | (92%) | 2110 | (82%) | |||||

211–225 | 8 | 1442 | 4173 | |||||||

226–240 | 39 | 820 |

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## Share and Cite

**MDPI and ACS Style**

Matenge, R.G.; Parida, B.P.; Letshwenyo, M.W.; Ditalelo, G.
Impact of Climate Variability on Rainfall Characteristics in the Semi-Arid Shashe Catchment (Botswana) from 1981–2050. *Earth* **2023**, *4*, 398-441.
https://doi.org/10.3390/earth4020022

**AMA Style**

Matenge RG, Parida BP, Letshwenyo MW, Ditalelo G.
Impact of Climate Variability on Rainfall Characteristics in the Semi-Arid Shashe Catchment (Botswana) from 1981–2050. *Earth*. 2023; 4(2):398-441.
https://doi.org/10.3390/earth4020022

**Chicago/Turabian Style**

Matenge, Ronny G., Bhagabat P. Parida, Moatlhodi W. Letshwenyo, and Gofetamang Ditalelo.
2023. "Impact of Climate Variability on Rainfall Characteristics in the Semi-Arid Shashe Catchment (Botswana) from 1981–2050" *Earth* 4, no. 2: 398-441.
https://doi.org/10.3390/earth4020022