Analysis of extreme rainfall in Oti River Basin (West Africa)


 Understanding how extreme rainfall is changing locally is a useful step in the implementation of efficient adaptation strategies to negative impacts of climate change. This study aims to analyze extreme rainfall over the middle Oti River Basin. Ten moderate extreme precipitation indices as well as heavy rainfall of higher return periods (25, 50, 75, and 100 years) were calculated using observed daily data from 1921 to 2018. In addition, Mann–Kendall and Sen's slope tests were used for trend analysis. The results showed decreasing trends in most of the heavy rainfall indices while the dry spell index exhibited a rising trend in a large portion of the study area. The occurrence of heavy rainfall of higher return periods has slightly decreased in a large part of the study area. Also, analysis of the annual maximum rainfall revealed that the generalized extreme value is the most appropriate three-parameter frequency distribution for predicting extreme rainfall in the Oti River Basin. The novelty of this study lies in the combination of both descriptive indices and extreme value theory in the analysis of extreme rainfall in a data-scarce river basin. The results are useful for water resources management in this area.


INTRODUCTION
Anthropogenic climate change is now evident. The global warning accelerates the evapotranspiration process which further alters the rainfall regime due to the increased capacity of the atmosphere to hold moisture according to the Clausius-Clapeyron relationship. Thus, the frequency and intensity of extreme natural events are expected to change under climate change in many regions of the world including West Africa and the need of information to manage the risk related to climate extremes is increasing (Klein et al. ). These changes may not be uniform across the globe due to differences in local or regional atmospheric circulation patterns and the high level of spatio-temporal variation in rainfall. Rainfall in West Africa is controlled by the seasonal variation in the geographical position of the Intertropical Convergence Zone (ITCZ) which is the most important meteorological phenomenon in the region (Nicholson ). The ITCZ appears at the ascending branch of atmospheric Hadley cells. In boreal winter, the ITCZ is situated around 5 S on the Tropical Atlantic and the continent is dry. Then, it moves to the north, following the northward migration of the maximum of received solar radiation energy. The ITCZ reaches its most northern position in August between 10 N and 12 N before retreating to the south. As a consequence, areas located north of the 8th parallel experience only one rainy season while those situated south of this parallel are characterized by two rainy seasons (Nicholson ). During the last decades, rainfall in West Africa had been characterized by a pronounced variability over a range of temporal scales (Nicholson ). Increase in extreme rainfall could contribute to more floods or droughts in some regions with severe impacts on human life and socio-economic activities. For instance, many West African countries have experienced severe drought since the late 1960s, and the 1980s were the driest decade of the century in this region (Nicholson ). In contrast, the Oti River Basin (ORB) experienced damaging flood events in 1998, 2007, 2008, 2010, and 2018  Specifically, this study aims at (i) examining the spatio-temporal changes in extreme rainfall indices, (ii) identifying the best probability distribution to predict extreme rainfall, and (iii) analyzing trend in rainfall of higher return periods in the study area.

Study area
The Oti River Basin is a sub-basin of the Volta Basin in West Africa. It is a transboundary river basin shared by four countries, namely, Togo, Ghana, Burkina Faso, and Benin.  (Table 1). These data were subjected to two types of quality control. First, the freely available software Rclimdex 1.0 (Zhang & Yang ) was used to detect errors caused by data pre-processing. Some unrealistic data such as daily rainfall greater than 500 mm were found and replaced by missing values. After this step, the time series were tested for homogeneity in order to identify artificial shift in the collected data using the R package RHtests_dlyPrcp developed for the homogenization of daily precipitation data (Wang & Feng ).
Some change points were detected in the daily rainfall data and the adjustments were made using the meanadjusted algorithm (Wang et al. ). Second, the mean annual maximum (AMAX) rainfall of 17 meteorological stations were screened for discordancy in a regional frequency analysis process using a test proposed by Hosking & Wallis (). The discordancy measure (Di) is a statistic test based on the difference between the L-moment ratios of a site and the mean L-moment ratios of a group of sites. The critical value of Di depends on the number of sites (N) in a given group. For N ! 15, Di should be less or equal to 3 for a site to be used in a regional frequency analysis. In this study, no discordant site from the whole group has been observed ( Table 1).

Calculation of descriptive extreme rainfall indices
Ten extreme precipitation indices were selected among the list of 27 climate extreme indices that have been developed i. CDD (consecutive dry days) ¼ largest number of consecutive days with no precipitation (days) ii. CWD (consecutive wet days) ¼ highest number of consecutive days with precipitation !1 mm (days) iii. PRCPTOT (annual total wet-day precipitation) ¼ annual total precipitation from days with precipitation !1 mm (mm) iv. Rx1day (maximum 1-day precipitation) ¼ annual maximum 1 day precipitation v. Rx5day (maximum 5-day precipitation amount) ¼ monthly maximum consecutive 5-day precipitation (mm) vi. R10 (number of heavy precipitation days) ¼ annual count when precipitation !10 mm (days) vii. R20 (number of very heavy precipitation days) ¼ annual count when precipitation !20 mm (days) viii. R95p (very wet days) ¼ annual total precipitation when daily precipitation >95th percentile (mm) ix. R99p (extremely wet days) ¼ annual total precipitation when daily precipitation >99th percentile (mm) x. SDII (simple daily intensity index) ¼ the ratio of annual total precipitation to the number of wet days (mm/day).

Estimation of extreme rainfall quantiles
A limitation of the descriptive indices is their focus on moderate extreme events which occur many times every year rather than rare extreme events associated with high return periods. Hence, extreme value theory is used in this study in order to analyze the trend of rare rainfall events such as the ones of 25-, 50-, 75-, and 100-year return periods too. This will enable a holistic trend analysis of extreme rainfall in the ORB. The methodology used to estimate extreme rainfall quantiles is an index storm regional frequency analysis based on L-moments of annual maximum rainfall, which was introduced by Hosking & Wallis (). This approach is suitable for short samples of data, as is the case in the present study, and assumes that sites from a homogeneous region have the same probability distribution apart from the mean of site data which represents the scaling factor of this site. Thus, this method requires testing the homogeneity of the proposed region and selecting the best frequency distribution.

Homogeneity test
The aim of this homogeneity test in a regional frequency analysis is to estimate the level of homogeneity in a group  Table 2.
Originally, an H value of 1.0 was suggested to decide if a group is homogeneous or not. However, according to Hosking & Wallis (), the threshold for rejection of the hypothesis of homogeneity at a significance level of 10% is H ¼ 1.28. Based on the latter criterion, the study area is considered as a homogeneous region.

Selection of the best frequency distribution
Many goodness-of-fit methods have been developed for selecting the most appropriate frequency distribution of sample data, among which, are the quantile-quantile plots, the Kolmogrov-Smirnov, Cramer-von Mises, Anderson-Darling tests, as well as those based on L-moment statistics.
In the present study, the Z-statistic (Z Dist ) which was introduced by Hosking & Wallis () was used to identify the best frequency distribution. This statistic evaluates the difference between the theoretical L-kurtosis of the fitted three parameters' distribution and the regional average Lkurtosis of the observed data. This test is defined in Equation (1) as follows: where D ist refers to a particular distribution, τ Dist 4 is the L-kurtosis of the selected distribution, t R 4 is the regional weighted average of sample L-kurtosis, B 4 and σ 4 are, respectively, the bias of t R 4 and the standard deviation of sample L-kurtosis. The fit of the distribution is considered satisfactory if the absolute value of Z for a candidate distribution is less or equal to 1.64 (Hosking & Wallis ).
After the homogeneity test, the hypothesis of fitting the generalized extreme value (GEV), the generalized Pareto (GPA), and Pearson type III distributions to AMAX rainfall of the study area was made. The values of the Z Dist were À0.96, À2.81, and À7.50, respectively, for the GEV, Pearson type III, and GPA distributions indicating that the GEV is the most robust of the three parameters' probability distribution for estimating extreme rainfall quantile in the middle portion of the ORB.

Estimation of the parameters and quantiles for GEV distribution
The quantile function of the GEV distribution is given by Equations (2) and (3): where, α, ε, k are, respectively, the scale, location, and shape parameters of the distributions. T is the return period and q R is the regional growth curve.
The estimated values of α, ϵ, k are, respectively, 0.23, 0.85, and À0.04. The rainfall associated with 25À, 50À, 75À and 100-year return periods at each of the meteorological stations The MK trend test is a non-parametric method which does not require the data to follow a specific distribution.
It has both the advantage of being robust to the presence of outliers in the time series and is less sensitive to inhomogeneous data. In order to carry out a MK test, the differences between later observed values and those from earlier time periods are computed. Hence, the test statistic, S, is estimated using the formulae given by Equations (4) and (5): x j and x k are data values at times j and k, respectively, while n is the number of data points. For n < 10, the value of |S| is compared to the theoretical distribution of S derived by Mann and Kendall. In the cases where n > 10, the standard normal variable Z is calculated by: where VAR (S) ¼ n(n À 1)(2n þ 5) À P q p¼1 t p (t p À 1)(2t p þ 5) 18 (7) q is the number of tied groups while tp is the number of data Then, Sen's slope estimator is the median of these N values of Qi:

Uncertainty assessment
Uncertainty in trend results is vital to give insight into the confidence that can be attributed to the analyses To investigate uncertainties in trend results, the root mean square error (RMSE) and the confidence intervals (CI) of the mean trend magnitude were computed using the same approaches as in Burgan & Aksoy () and Helsel et al.
(), respectively, for the RMSE and the CI: were computed using the qt function in R software.

Trends in descriptive extreme indices during 1921-2018
The computed extreme rainfall indices for each selected meteorological station were plotted with the trends and some of the graphs are provided in the Supplementary materials. Table 3  stations with a significant trend. In order to explore the spatial patterns of the trends over the whole study area, the trends were interpolated using inverse distance weighted (IDW) method in a geographic information system (GIS) software and the results are shown in Figures 2 and 3.
As shown in Table 3, only the consecutive dry day index had positive trends for more than half of the stations (88%).
Trends in heavy rainfall of higher return periods Table 4 and Figure 4 show, respectively, the summary of the     Comparison with previous studies Moreover, Panthou et al. () showed an increase in the proportion of annual rainfall associated with extreme rainfall from 17% in 1970-1990 to 19% in 1991-2000 and to 21% in 2001-2010   increasing dry spells could lead to crop failure and reduction in food consumption which could cause childhood malnutrition. In addition, meteorological droughts have negative effects on water quantity and quality resulting in health issues such as diarrhea and hydroelectric power shortage due to lack of water in dams. Meteorological droughts can also be responsible for loss of biodiversity. Therefore, there is a need to implement integrated drought management strategies in order to reduce the adverse impacts of drought on local communities. In this context, future research on how climate change will impact extreme hydrometeorogical events, such as drought in the study area, is of a great importance.

ACKNOWLEDGEMENTS
The authors are grateful to the editor and the three anonymous reviewers for their useful comments and suggestions. We would like to thank the national meteorological services of Benin, Ghana, and Togo for providing the rainfall data. The authors declare no conflicts of interests.

DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.