<figure><img src="image_1.png" /></figure>

HAL
open science

# Multiscale Impacts of Anthropogenic and Climate Changes on Tropical and Mediterranean Hydrology

Luc Descroix, Gil Mahe, Alain Laraque, Olivier Ribolzi, Guillaume Lacombe

<figure><img src="image_2.png" /></figure>

## To cite this version:

Luc Descroix, Gil Mahe, Alain Laraque, Olivier Ribolzi, Guillaume Lacombe. Multiscale Impacts of Anthropogenic and Climate Changes on Tropical and Mediterranean Hydrology. Water, pp.372, 2021, 10.3390/books978-3-0365-1237-2 . ird-04154829

HAL Id: ird-04154829

https://ird.hal.science/ird-04154829

Submitted on 7 Jul 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
<figure><img src="image_3.png" /></figure>

water

Multiscale Impacts
of Anthropogenic
and Climate
Changes on Tropical
and Mediterranean
Hydrology

Edited by

Luc Descroix, Gil Mahé, Alain Laraque, Olivier Ribolzi and
Guillaume Lacombe

Printed Edition of the Special Issue Published in *Water*
Multiscale Impacts of Anthropogenic
and Climate Changes on Tropical and
Mediterranean Hydrology
<figure><img src="image_4.png" /></figure>
Multiscale Impacts of Anthropogenic
and Climate Changes on Tropical and
Mediterranean Hydrology

Editors

Luc Descroix

Gil Mahé

Alain Laraque

Olivier Ribolzi

Guillaume Lacombe

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

<figure><img src="image_5.png" /></figure>
Editors

Luc Descroix
IRD, UMR PALOC (Patrimoines
Locaux, Environnement et
Globalisation)
IRD/MNHN, Paris
France

Gil Mahé
IRD, UMR HSM IRD/
Univ Montpellier,
France

Alain Laraque
IRD, UMR GET
IRD/CNRS/CNES/UPS
France

Olivier Ribolzi
IRD, UMR GET
IRD/CNRS/CNES/UPS
France

Guillaume Lacombe
CIRAD, UMR G-EAU
Institut Agronomique et
Vétérinaire Hassan II
Morocco

Editorial Office

MDPI
St. Alban-Anlage 66
4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Water* (ISSN 2073-4441) (available at: https://www.mdpi.com/journal/water/special_issues/Tropical_Mediterranean_Hydrology).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

Last Name, A.A.; Last Name, B.B.; Last Name, C.C. Article Title. *Journal Name Year, Volume Number, Page Range*.

ISBN 978-3-0365-1236-5 (Hbk)

ISBN 978-3-0365-1237-2 (PDF)

Cover image courtesy of Alain Laraque.

It depicts the Canal Casiquiare in Venezuela, South America.

© 2021 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.
# Contents

<table><tr><td>About the Editors</td><td>vii</td></tr><tr><td>Gil Mahé, Luc Descroix, Alain Laraque, Olivier Ribolzi and Guillaume Lacombe<br>Special Issue "Multiscale Impacts of Anthropogenic and Climate Changes on Tropical and Mediterranean Hydrology"<br>Reprinted from: Water 2021, 13, 491, doi:10.3390/w13040491</td><td>1</td></tr><tr><td>Jean-Claude Bader, Honoré Dacosta and Jean-Christophe Pouget<br>Seasonal Variations of the Depletion Factor during Recession Periods in the Senegal, Gambia and Niger Watersheds<br>Reprinted from: Water 2020, 12, 2520, doi:10.3390/w12092520</td><td>9</td></tr><tr><td>Ernest Amoussou, Hervé Awoye, Henri S. Totin Vodounon, Salomon Obahoundje, Pierre Camberlin, Arona Diedhiou, Kouakou Kouadio, Gil Mahé, Constant Hound énou and Michel Boko<br>Climate and Extreme Rainfall Events in the Mono River Basin (West Africa): Investigating Future Changes with Regional Climate Models<br>Reprinted from: Water 2020, 12, 833, doi:10.3390/w12030833</td><td>33</td></tr><tr><td>Luc Descroix, Bakary Faty, Sylvie Paméla Manga, Ange Bouramanding Diedhiou, Laurent A. Lambert, Safietou Soumaré, Julien Andrieu, Andrew Ogilvie, Ababacar Fall, Gil Mahé, Fatoumata Binta Sombily Diallo, Amirou Diallo, Kadiatou Diallo, Jean Albergel, Bachir Alkali Tanimoun, Ilia Amadou, Jean-Claude Bader, Aliou Barry, Ansoumana Bodian, Yves Boulvert, Nadine Braquet, Jean-Louis Couture, Honoré Dacosta, Gwenaelle Dejacquelot, Mahamadou Diakité, Kourahoye Diallo, Eugenia Gallese, Luc Ferry, Lamine Konaté, Bernadette Nka Nnomo, Jean-Claude Olivry, Didier Orange, Yaya Sakho, Saly Sambou and Jean-Pierre Vandervaere<br>Are the Fouta Djallon Highlands Still the Water Tower of West Africa?<br>Reprinted from: Water 2020, 12, 2968, doi:10.3390/w12112968</td><td>61</td></tr><tr><td>Mustafa Utku Yilmaz and Bihrat Onoz<br>A Comparative Study of Statistical Methods for Daily Streamflow Estimation at Ungauged Basins in Turkey<br>Reprinted from: Water 2020, 12, 459, doi:10.3390/w12020459</td><td>93</td></tr><tr><td>Radouane Hout, Véronique Maleval, Gil Mahe, Eric Rouvellac, Rémi Crouzevialle and Fabien Cerbelaud<br>UAV and LiDAR Data in the Service of Bank Gully Erosion Measurement in Rambla de Algeciras Lakeshore<br>Reprinted from: Water 2020, 12, 2748, doi:10.3390/w12102748</td><td>115</td></tr><tr><td>Layheang Song, Laurie Boithias, Oloth Sengtaheuanghoung, Chantha Oeurng, Christian Valentin, Bounthan Souksavath, Phabvilay Sounyafong, Anneke de Rouw, Bounsamay Soulileuth, Norbert Silvera, Bounchanh Lattanavongkot, Alain Pierret and Olivier Ribolzi<br>Understory Limits Surface Runoff and Soil Loss in Teak Tree Plantations of Northern Lao PDR<br>Reprinted from: Water 2020, 12, 2327, doi:10.3390/w12092327</td><td>143</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>Mohamed Abdellah Ezzaouini, Gil Mahé, Ilias Kacimi and Abdelaziz Zerouali<br>Comparison of the MUSLE Model and Two Years of Solid Transport Measurement, in the Bouregreg Basin, and Impact on the Sedimentation in the Sidi Mohamed Ben Abdellah Reservoir, Morocco<br>Reprinted from: Water 2020, 12, 1882, doi:10.3390/w12071882</td>
      <td>167</td>
    </tr>
    <tr>
      <td>Valentin Brice Ebodé, Gil Mahé, Jean Guy Dzana and Joseph Armathé Amougou<br>Anthropization and Climate Change: Impact on the Discharges of Forest Watersheds in Central Africa<br>Reprinted from: Water 2020, 12, 2718, doi:10.3390/w12102718</td>
      <td>195</td>
    </tr>
    <tr>
      <td>Xing Ma, Guillaume Lacombe, Rhett Harrison, Jianchu Xu and Meine van Noordwijk<br>Expanding Rubber Plantations in Southern China: Evidence for Hydrological Impacts<br>Reprinted from: Water 2019, 11, 651, doi:10.3390/w11040651</td>
      <td>219</td>
    </tr>
    <tr>
      <td>Ansoumana Bodian, Lamine Diop, Geremy Panthou, Honoré Dacosta, Abdoulaye Deme, Alain Dezetter, Pape Malick Ndiaye, Ibrahima Diouf and Théo Vischel<br>Recent Trend in Hydroclimatic Conditions in the Senegal River Basin<br>Reprinted from: Water 2020, 12, 436, doi:10.3390/w12020436</td>
      <td>235</td>
    </tr>
    <tr>
      <td>Yonca Cavus and Hafzullah Aksoy<br>Spatial Drought Characterization for Seyhan River Basin in the Mediterranean Region of Turkey<br>Reprinted from: Water 2019, 11, 1331, doi:10.3390/w11071331</td>
      <td>247</td>
    </tr>
    <tr>
      <td>Claudine Dieulin, Gil Mahé, Jean-Emmanuel Paturel, Soundouss Ejjiyar, Yves Tramblay, Nathalie Rouché and Bouabid EL Mansouri<br>A New 60-Year 1940/1999 Monthly-Gridded Rainfall Data Set for Africa<br>Reprinted from: Water 2019, 11, 387, doi:10.3390/w11020387</td>
      <td>265</td>
    </tr>
    <tr>
      <td>Alain Laraque, Guy D. Moukandi N'kaya, Didier Orange, Raphael Tshimanga, Jean Marie Tshitenge, Gil Mahé, Cyriaque R. Nguimalet, Mark A. Trigg, Santiago Yepez and Georges Gulemvuga<br>Recent Budget of Hydroclimatology and Hydrosedimentology of the Congo River in Central Africa<br>Reprinted from: Water 2020, 12, 2613, doi:10.3390/w12092613</td>
      <td>283</td>
    </tr>
    <tr>
      <td>Alain Laraque, Jose Luis Lopez, Santiago Yepez and Paul Georgescu<br>Water and Sediment Budget of Casiquiare Channel Linking Orinoco and Amazon Catchments, Venezuela<br>Reprinted from: Water 2019, 11, 2068, doi:10.3390/w11102068</td>
      <td>319</td>
    </tr>
    <tr>
      <td>Luc Descroix, Yancouba Sané, Mamadou Thior, Sylvie-Paméla Manga, Boubacar Demba Ba, Joseph Mingou, Victor Mendy, Saloum Coly, Arame Dièye, Alexandre Badiane, Marie-Jeanne Senghor, Ange-Bouramanding Diedhiou, Djiby Sow, Yasmin Bouaita, Safietou Soumaré, Awa Diop, Bakary Faty, Bamol Ali Sow, Eric Machu, Jean-Pierre Montoroi, Julien Andrieu and Jean-Pierre Vandervaere<br>Inverse Estuaries in West Africa: Evidence of the Rainfall Recovery?<br>Reprinted from: Water 2020, 12, 647, doi:10.3390/w12030647</td>
      <td>337</td>
    </tr>
  </tbody>
</table>
## About the Editors

**Luc Descroix** is a hydrologist of IRD (Institut de Recherche pour le Développement, the French Research Institute for Sustainable Development, Marseille, France). His lab PALOC (Patrimoines Locaux, Environnement et Globalisation) is located in the Muséum National d'Histoire Naturelle, in Paris, France. L Descroix defended his PhD in geography at Lyon (France) Université Lumière, and he holds his HDR (the degree to become senior researcher in Europe) in hydrology at Grenoble, France, Université Joseph Fourier. His research focuses on the impact of land use and climate changes on the water cycle, through the evolution of water resources (streamflows, groundwater, ponds and lakes, wetlands, soil water, etc.), soil water holding capacity and river recession coefficients. He is also very interested in the role of trees in the field, in the cities, in the societies and their impact on local and regional climates.

**Gil Mahé** is a research director at the Institute of Research for Development. He has worked on the hydrology and climatology of Africa for more than three decades and spent many years working in cooperation with national and international institutions in many African countries. He has studied hydroclimatic variability and its impact on river regimes and water resources, and the impact of human activities on the environment. He also studied erosion and solid transport and the alteration of the sediment transport by dams. He leads the FRIEND-Water program of UNESCO/IHP and he is the president of the International Commission of Surface Waters of the International Association of Hydrological Sciences.

**Alain Laraque** is a potamologist at the French National Research Institute for Sustainable Development. For more than three decades, he has been studying the main hydrosystems (Amazon, Congo, Orinoco) that converge in the Intertropical Atlantic Ocean, with the study of their hydroclimatic, hydrosedimentological, geochemical and geodynamic functioning, as well as the anthropic impacts (dams, etc.). He also has experience in hydro-saline processes within hill reservoirs in semi-arid environments.

**Olivier Ribolzi** is a research director at the Institute of Research for Sustainable Development (IRD) in the field of hydro-geochemistry, having gained over 20 years of experience in conducting and coordinating interdisciplinary research in IRD, mainly in Southeast Asia, West Africa and the Mediterranean region. His main research interests include the effect of land use/land use change on the hydro-biogeochemical response of headwater catchments, soil erosion and sediment yield, groundwater-stream water interactions, and the occurrence/spread of contaminants. His publishing credits include more than 70 articles in refereed journals.

**Guillaume Lacombe** is a researcher in hydrology and agricultural water management at CIRAD (French agricultural research and international cooperation organization). He has authored more than 25 peer-reviewed journal articles, assessing how human activities alter the spatial and temporal variability of water resources over multiple scales, in order to improve the efficiency and sustainability of water uses. Geographic focuses include developing countries in Asia and Africa, where he has been collaborating with research for development organizations and universities.
<figure><img src="image_6.png" /></figure>
Editorial

# Special Issue “Multiscale Impacts of Anthropogenic and Climate Changes on Tropical and Mediterranean Hydrology”

Gil Mahé<fnref n="1" />, Luc Descroix 2,3,*, Alain Laraque 4, Olivier Ribolzi 5 and Guillaume Lacombe 6

<figure><img src="image_7.png" /></figure>

check for
updates

**Citation:** Mahé, G.; Descroix, L.; Laraque, A.; Ribolzi, O.; Lacombe, G. Special Issue “Multiscale Impacts of Anthropogenic and Climate Changes on Tropical and Mediterranean Hydrology”. *Water* **2021**, *13*, 491. https://doi.org/10.3390/w13040491

Received: 14 January 2021

Accepted: 8 February 2021

Published: 14 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

<figure><img src="image_8.png" /></figure>

Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).

## 1. Introduction

Most tropical and Mediterranean areas, landscapes, soils, and territories are experiencing new vulnerabilities, facing global warming [1] and accelerating changes in land-use in all kinds of ecosystems [2]. Long droughts, dry spells, rainfall intensification, and an increase in the number of storms and cyclones make agriculture as well as land management and water and sediment control more difficult. In many regions, the population increase is too strong to allow cropping and rural activities to easily reach Boserupian behavior. The intensification of the climatic cycle induced by global warming commonly leads to an acceleration of the hydrological cycle, increasing the occurrence of flooding, inundation, as well as droughts and water shortages [3,4]. Human actions and overall rural activity can strongly modify water runoff and infiltration, then water balance, by increasing infiltration and buffering the water cycle, or on the contrary, by reducing the soil permeability, increasing runoff, and accelerating the water cycle [5–7]. Rural practices are commonly suspected to decrease the soil water-holding capacity. This could lead to a rise in flooding occurrence and intensity downstream, and could cause an edaphic drought even in areas where no climatic drought is observed.

These kinds of changes influence hydrology and erosion/sedimentation processes, with implications for various risks: food insecurity, natural disasters (landslides, flood damage), water shortages, and pathogenic contaminations. The accelerating pace of these environmental changes leaves limited time for adaptation. While the need for “climate change adaptation” is recognized, there is also a need for land-use change adaptation and a better assessment of contamination risks [8]. To date, there is limited understanding of the processes linking land-use management to these risks.

There is a need to understand causal chains of processes, from land-use, vegetation structure, soil, erosion, hydrological connectivity (surface and subsurface) infiltration, and their related risks in order to better manage these risks and reduce them [9]. Multi-scale approaches are relevant because there are multi-scale impacts; micro-plots and hillslopes are relevant to understanding processes controlling soil detachment and the partition of rainfall into surface and subsurface flow in relation with interacting land-use and soil surface dynamics. At the watershed level, local dynamics translate into risks of hydrological extremes, erosion, and contamination, threatening downstream ecosystems, infrastructures, and populations [10].

<footnote n="1">¹ IRD HSM, Case MSE, Université Montpellier, 300 avenue Emile Jeanbrau, 34090 Montpellier, France; gilmahe@hotmail.com</footnote>

<footnote n="2">² UMR PALOC IRD/MNHN/Sorbonne Université, Museum National d'Histoire Naturelle, 75231 Paris, France</footnote>

<footnote n="3">³ LMI PATEO, UGB, St. Louis 46024, Senegal</footnote>

<footnote n="4">⁴ Géosciences Environnement Toulouse, Université de Toulouse, CNES, CNRS, IRD, UPS, 31400 Toulouse, France; alain.laraque@ird.fr</footnote>

<footnote n="5">5 Géosciences Environnement Toulouse, Université de Toulouse, CNES, CNRS, IRD, UPS, 31400 Toulouse, France; olivier.ribolzi@ird.fr</footnote>

<footnote n="6">⁶ CIRAD, UMR G-EAU, Université Montpellier, AgroParisTech, CIRAD, INRAE, Institut Agro, IRD, 34398 Montpellier, France; guillaume.lacombe@cirad.fr</footnote>

<footnote>* Correspondence: luc.descroix@ird.fr</footnote>
## 2. Spatial and Temporal Scales

This Special Issue presents results of studies from many different parts of the world, mainly from Africa and Europe, including the Mediterranean area, Asia [11,12], and South America [13]. The papers showcase studies under equatorial, tropical humid, semi-arid, and Mediterranean climate. All spatial scales are investigated, from the very local scale of gullies in Spain [14] to the largest rivers of the world, the Amazon and Orinoco rivers in South America [13] and Congo River in Central Africa [15]. The whole African continent is also the topic of the paper of Dieulin et al. [16] (2020), presenting a new continental monthly rainfall dataset at the half-degree square scale covering the years 1940 to 1999, computed only from observations from ground-based stations. Many time scales are also investigated, from daily events [17,18] to interannual variability [15,16].

The topics studied cover a large panel of hydrological questions. Many of them deal with the study of time series variability, rainfall [16], discharges [19,20], sediment transport [11–13,21], recession coefficient [22,23], climate change impacts [17,24], or anthropogenic impacts [2,11,20,21]. Drought is also a topic of notable interest in Mediterranean and tropical areas [23–25].

This Special Issue includes several papers dealing with topics at the continental or subcontinental scale. The quality of rainfall data is, for instance, of very high importance to improve the efficiency of hydrological modeling through calibration/validation experiments. The HydroSciences Montpellier Laboratory (HSM) has a long experience in collecting and managing hydro-climatological data. Dieulin et al. [16] present the results of several years of studies to elaborate a reference dataset in order to build monthly rainfall grids over the African continent over a period of 60 years (1940–1999). The large quantity of data collected (about 7000 measurement points) allowed for interpolation using only ground-based observed data, with no statistical use of a reference period. The mean annual grid was compared to the Climate Research Unit (CRU) grid with HSM_SIEREM data (database HydroSciences Montpellier_Système d'Information Environnementales pour les Ressources en Eau et leur Modélisation) being closer to the observed rain gauge values. The statistical tests, computed on the observed and gridded data, detected a rupture in the rainfall regime around 1979/1980, at the scale of the whole continent, which seems in line with some results in different parts of Africa (North Africa [21]; Congo basin in Central Africa [15]). At the monthly time scale, the most widely observed signal over the period of 1940–1999 was a significant decrease of the austral rainy season between March and May, which has not been previously well documented.

## 3. Hydrosedimentary Regimes of the Three Largest Rivers of the World

Laraque et al. [13,15] also deal with very large scales, as they cover the three largest rivers of the world by discharge value, all located in equatorial-tropical areas, the Amazon and Orinoco rivers in South America and Congo River in Central Africa. These papers highlight low-documented areas. In South America, the study is focused on the very curious and much unknown Casiquiare Canal, linking both the giant Orinoco and Amazon rivers, investigated during a dedicated international expedition in 2000 [13]. The results presented for the Congo River cover more than one century of measurements and represent the most recently documented synthesis on the Congo River water, with an investigation of dissolved and suspended matters fluxes [15]. In the flat basin of the Congo River, the absence of mountain chains and the extent of its coverage by dense rainforest explains how chemical weathering (10.6 t km⁻² year⁻¹ of total dissolved solids) slightly predominates physical erosion (9.3 t km⁻² year⁻¹ of total suspended solids), followed by organic production (4.5 t km⁻² year⁻¹ of dissolved organic carbon). As the interannual mean discharges are similar, it can be assumed that these interannual averages of material fluxes, calculated over the longest period (2006–2017) of monthly monitoring of its sedimentology and bio-physical-chemistry, are therefore representative of the flow record available since 1902 (with the exception of the wet decade of 1960). Without neglecting the indispensable in situ work, the contributions of remote sensing and numerical modelling should be
increasingly used to try to circumvent the dramatic lack of field data that persists in this
basin.

Regarding the South American rivers, the aim is to present a review and synthesis of the hydrological and sedimentological knowledge of the world's longest natural defluence, the Casiquiare channel, including its first hydrosedimentary, which was conducted 9–12 September 2000 at the bifurcation and mouth during the expedition 'Humboldt-Amazonia 2000'. This fluvial system connects the two largest river of South America and the main conclusions of this study explain why the Casiquiare can be qualificated of a 'cameleon' channel which is taking a significant proportion of flow (20% to 30%) from the Upper Orinoco basin to the Amazon basin.

4. Climatic or Anthropogenic Impacts on River Regimes

In several studies, authors search for the possible origin, climatic or anthropogenic, of the interannual variability observed in the times series of rainfall and discharges. In Central Africa, Ebodé et al. [20] study the impact of anthropization and climate change on two forested watersheds (of Ntem and Nyong) in the south of the country, under equatorial and sub-equatorial climates. The results of this study show that in Central Africa, annual discharges have decreased significantly since the 1970s, and yet the decline in annual rainfall does not become significant until the 2000s. The discharges of the rainy seasons (spring and autumn) recorded the most important changes, following variations in the rainfall patterns of the dry seasons (winter and summer) that preceded them. Winters experienced a significant decrease in precipitation between the 1970s and 1990s, which caused a drop in spring flows. Their rise, which began in the 2000s, is also accompanied by an increase in spring flows, which nevertheless seems to have been very moderated in the case of the Nyong. Conversely, between the 1970s and 1990s, there was a joint increase in summer rainfall and autumn flows. A decrease in summer rainfall was noted since the 2000s, and is also noticeable in autumn flows. Maximum flows have remained constant on the Nyong despite the slight drop in rainfall. This seems to be a consequence of changes in land-use patterns (diminution of forest and increases in the amount of impervious areas). The decrease in maximum flows noted on the Ntem could be linked to the slight drop in precipitation during the rainy season that generates it. Natural factors, such as the general decrease in precipitation during the winter and the reduction in the area occupied by water bodies, could justify the decrease in minimum flows observed in the two watersheds.

Amoussou et al. [17] study the impact of climate change from regional climate model outputs on extreme rainfall events for the Mono River, between Benin and Togo. This research characterizes the future changes in extreme rainfall and air temperature from observational datasets and regional climate models (RCMs) that were used to analyze climatic variations in space and time and fit a generalized extreme value (GEV) model to investigate the extreme rainfalls and their return periods. The authors show that the annual maxima of daily precipitation is expected to increase by 2050 and could be of benefit to the ecosystem services and socioeconomic activities in the Mono River basin, but could also be a threat due to unpredictable consequences of more extreme events.

Bodian et al. [18] investigate the recent trend of hydroclimatic variables in the Senegal River basin based on 36 rain gauge stations and three hydrometric stations not influenced by hydraulic structures. They concentrate on the description of insight views regarding the consequences of the changes in rainfall regimes on the hydrological characteristics of several stations of the Senegal River over several decades. The Mann–Kendall and Pettitt's tests were applied for the annual rainfall time series from 1940 to 2013 to detect the shift and the general trend of the annual rainfall. In addition, trends of the average annual flow rate (AAFR), maximum daily flow (MADF), and low flow rate (LFR) were evaluated before and after annual rainfall shift.
**5. Changes in Hydrological Cycle and Water Quality**

Descroix et al. [24] explore the evolution of the salinity in the inverse estuaries of two Senegalese rivers in West Africa since the end of the 1968–1993 drought. The results show that in both estuaries, the mean water salinity values have markedly decreased since the end of the drought. However, the Saloum estuary remains a totally inverse estuary, while for the Casamance River, the estuarine turbidity maximum (ETM) is the location of the salinity maximum, and it moves according to the seasons. The West African mangroves are among the few in the world that have been markedly increasing since the beginning of the 1990s and the end of the peak of the dry period in West Africa, as mangrove growth is favored by the relative salinity reduction in this area.

Going further inside the hydrological cycle, Descroix et al. [23] discuss the recent dynamics of the Fouta Djallon's hydrological functioning. The evolution of the runoff and depletion coefficients are analyzed as well as their correlations with the rainfall and vegetation cover. The latter is described at three different space scales and with different methods. Twenty-five years after the end of the 1968–1993 major drought, annual discharges continue to slowly increase, nearly reaching the long-term average, as natural reservoirs which were emptied to sustain streamflows during the drought have been replenishing since the 1990s, explaining the slow increase in discharges. However, another important trend has been detected since the beginning of the drought, namely the increase in the depletion coefficient of some of the Fouta Djallon upper basins, as a consequence of the reduction in the soil water-holding capacity. After observing that this increase and subsequent decrease in the depletion coefficient is localized in parts of the Upper Niger basin and the Konkouré basin, this paper identifies the factors possibly linked with the basins' storage capacity trends. Two pieces of “good news” are highlighted: first, the densely populated areas of the summit plateau are also shown to be the ones where vegetation cover is not threatened and where the ecological intensification of rural activities is ancient; second, most of the river basins providing the Sahel with freshwater have recovered the discharge and soil water-holding capacity levels that they had before the drought.

Bader et al. [22] develops a methodology to compare the evolution of the runoff and depletion coefficients in the Senegal Niger and Gambia rivers. The seasonal flow recession observed at 54 gauging stations in these basins from 1950 to 2016 is represented by empirical and usual conceptual models that express the daily depletion factor (K). Compared to conventional conceptual models, an empirical model representing K as a polynomial of the decimal logarithm of discharge (Q) is shown to provide better representations of K and better discharge forecasting at horizons from 1 to 120 days for most stations. The relationship between specific discharge (Qs) and K, not monotonous, is highly homogeneous in some sub-basins but differs significantly between the Senegal and Gambia basins on the one hand and the Niger basin on the other.

Concerning the Mediterranean, three studies deal with complementary topics: rainfall, runoff, and erosion.

Cavus and Aksoy [25] study the spatial drought characterization for the Seyhan River in Turkey, investigating the spatial and temporal characteristics of drought using standardized precipitation index and different spatialization techniques. They primarily use the standardized precipitation index (SPI) from monthly precipitation data at a 12-month time scale for 19 meteorological stations scattered over the river basin. The drought with the highest severity in each year is defined as the critical drought of the year. Frequency analysis was applied on the critical drought to determine the best-fit probability distribution function by using the total probability theorem. The sole frequency analysis is insufficient in drought studies unless it is numerically related to other factors, such as the severity, duration, and intensity. Yilmaz et al. [19] use statistical methods for daily streamflow estimation at ungauged basins in Turkey. The single donor station drainage area ratio (DAR) method, the multiple-donor stations drainage area ratio (MDAR) method, the inverse similarity weighted (ISW) method, and its variations with three different power parameters (1, 2, and 3) are applied to the two main sub-basins of the Euphrates basin
in Turkey to estimate daily streamflow data. Each station in each basin is considered in turn as the target station where there are no streamflow data. Their results show that MDAR and ISW give improved performance compared to DAR for estimating the daily streamflow for seven out of eight target stations in the Middle Euphrates basin and for four out of seven target stations in the Upper Euphrates basin. Higher Nash-Sutcliffe Efficiency (NSE) values for both MDAR and ISW are mostly obtained with the three most physically similar donor stations in the Middle Euphrates basin and with the two most physically similar donor stations in the Upper Euphrates basin. Hout et al. [14] use lidar data to survey the evolution of the morphology of gullies on the slopes of a lake in semi-arid southern Spain. Due to the nature of the geological formations at the lakeshore level, gully erosion is very high and leads to silting up of the dam. This study was conducted to estimate the sediment input from the bank gullies. The combination of two configurations of nadir and oblique photography allowed the authors to obtain a complete high-resolution modeling of complex bank gullies with overhangs. They develop a complex methodology to allow erosion to be quantified between two dates at the gully scale. The results reveal significant lakeshore erosion activity by bank gullies, since the annual inflow from the banks is estimated at $39 \text{ t ha}^{-1} \text{ year}^{-1}$.

## 6. Erosion, Land Cover, and Land Use

Three more papers investigate erosion surveys and their relationships with land cover and land use. Two of these studies use spatial data to retrieve land-cover characteristics.

In northern Laos (Song et al. [12]), the replacement of traditional crops by tree plantations, such as teak trees, has led to a dramatic increase in floods and soil loss and to the degradation of basic soil ecosystem services, such as water filtration by soil, fertility maintenance, etc. The authors [12] hypothesized that conserving understory under teak trees would protect soil, limit surface runoff, and help reduce soil erosion. It is shown that teak planting does not have an anti-erosive power at all; this land cover shows the highest runoff coefficient and soil loss, associated with the highest crusting rate; this is due to the kinetic energy of rain drops falling from the broad leaves of the tall teak trees down to bare soil, devoid of plant residues, thus leading to severe soil surface crusting and soil detachment. Hence, teak tree plantation owners could divide soil loss by 14 by keeping understory, such as broom grass, within teak tree plantations. Overall, promoting understory, such as broom grass, in teak tree plantations would (1) limit surface runoff and improve soil infiltrability, thus increasing the soil water stock available for both root absorption and groundwater recharge, and (2) mitigate soil loss while favoring soil fertility conservation.

Ma et al. [11] study the hydrological impacts of expanding rubber plantations on a watershed of 100 km² in the Xishuangbanna prefecture, Yunnan Province, China. The influence of land-cover change on streamflow recorded since 1992 was isolated from that of rainfall variability using cross-simulation matrices produced with the monthly lumped conceptual water balance model GR2M. Their results indicate a statistically significant reduction in wet and dry season streamflow from 1992 to 2002, followed by an insignificant increase until 2006. Analysis of satellite images from 1992, 2002, 2007, and 2010 shows a gradual increase in the areal percentage of rubber tree plantations at the watershed scale. However, there were marked heterogeneities in land conversions (between forest, farmland, grassland, and rubber tree plantations), and in their distribution across elevations and slopes, among the studied periods. Possible effects of this heterogeneity on hydrological processes, controlled mainly by infiltration and evapotranspiration, are discussed in light of the hydrological changes observed over the study period. The authors suggest pathways to improve the eco-hydrological functionalities of rubber tree plantations, particularly those enhancing dry-season base flow, and recommend how to monitor them.

In Morocco, North Africa, Ezzaouini et al. [21] assess the sediment inputs into the dam's lake on the Bouregreg River. They apply the Modified Universal Soil Loss Equation (MUSLE) model to predict solid transport, calibrated by two years of solid transport
measurements from four main gauging stations at the entrance of the Sidi Mohamed Ben Abdellah dam. The application of the MUSLE on the basin demonstrated relatively small differences between the measured values and those expected for the calibrated version; these differences are, for the non-calibrated version, +5% and +102% for the years 2016/2017 and 2017/2018, respectively, and between −33% and +34% for the calibrated version. Furthermore, the measured and modeled volumes that do not exceed $1.78 \times 10^6 \text{ m}^3/\text{year}^{-1}$ remain well below the dam's siltation rate of $9.49 \times 10^6 \text{ m}^3/\text{year}^{-1}$, obtained from a continuous bathymetry survey, which means that only 18% of the dam's sediment comes from upstream. This seems very low because it is calculated from only two years. The main hypothesis that is formulated is that the majority of the sediments of the dam most probably come from the erosion of its banks.

## 7. Concluding Remarks

This Special Issue shows the great interest of the scientific community in investigating how to characterize the environmental impact of anthropogenic and climatic changes, and also determining which is the main source of changes depending on the regional situations and thematic issues. This first issue might lead to following issues on more specific topics, according to, for instance, the 23 unsolved problems in hydrology [26], or future issues that are focused on different regional areas. Future issues on this topic might also focus more on water resources challenges in urban tropical and Mediterranean areas, which constitute increasing shares of the populations in these areas. These densely populated areas are also often localized near the coast, which brings up specific concerns about the coastal damages caused by human interventions (such as dams and irrigations) and sea level rising on the inland water cycle [27]. The impact of global warming and the increasing occurrence of extreme events on runoff generation and discharge dynamics must also be addressed in the future. Changes in the water-holding capacity of soil (at the point scale) and basins (at the regional scale) will impact river regimes through the evolution of runoff and recession coefficients as indexes of these major possible dynamics.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Tramblay, Y.; Koutroulis, A.; Samaniego, L.; Vicente-Serrano, S.M.; Volaire, F.; Boone, A.; Le Page, M.; Carmen Llasat, M.; Albergel, C.; Burak, S.; et al. Challenges for drought assessment in the mediterranean region under future climate scenarios. *Earth Sci. Rev.* **2020**, *210*, 103348. [CrossRef]

2. Song, X.P.; Hansen, M.C.; Stehman, S.V.; Potapov, P.V.; Tyukania, A.; Vermote, E.F.; Townshend, J.R. Global land change from 1982 to 2016. *Nature* **2018**, *560*, 639–643. [CrossRef]

3. Eccles, R.; Zhang, H.; Hamilton, D. A review of the effects of climate change on riverine flooding in subtropical and tropical regions. *J. Water Clim. Chang.* **2019**, *10*, 687–707. [CrossRef]

4. Tramblay, Y.; Llasat, M.C.; Randin, C.; Coppola, E. Climate change impacts on water resources in the Mediterranean. *Reg. Environ. Chang.* **2020**, *20*, 83. [CrossRef]

5. Mahé, G.; Dray, A.; Paturel, J.E.; Crès, A.; Koné, F.; Manga, M.; Crès, F.N.; Djoukam, J.; Maïga, A.H.; Ouédraogo, M.; et al. Climatic and anthropogenic impacts on the flow regime of the Nakambe River in Burkina. In *Bridging the Gap between Research and Practice, Proceedings of the Fourth International FRIEND Conference, Cape Town, South Africa, 18–22 March 2002*; Van Lannen, H., Demuth, S., Eds.; IAHS Publ. 274; IAHS Publications: Oxfordshire, UK, 2002; pp. 69–76. Available online: https://iahs.info/uploads/dms/12264.14-Mahe-et-al.--F28--pp.-69-76-revised.pdf (accessed on 22 March 2020).

6. Descroix, L.; Guichard, F.; Grippa, M.; Lambert, L.; Panthou, J.; Mahe, G.; Gal, L.; Dardel, C.; Quantin, G.; Kergoat, L.; et al. Surface hydrology evolution in the Sahelo-Sudanian stripe: An updated review. *Water* **2018**, *10*, 748. [CrossRef]

7. Ribolzi, O.; Evrard, O.; Huon, S.; Rouw, A.; De Silvera, N.; Latsachack, O.; Soulileuth, B.; Lefèvre, I.; Pierret, A. From shifting cultivation to teak plantation: Effect on overland flow and sediment yield in a montane tropical catchment. *Sci. Rep.* **2017**, *12*, 1–12. [CrossRef]

8. Toteu, S.F.; Mahé, G.; Moritz, R.; Tracek, O.; Davies, T.C.; Ramasamy, J. Environmental, health and social legacies of mining activities in Sub-Saharan Africa. *J. Geochem. Explor.* **2020**, *209*. [CrossRef]

9. Lacombe, G.; Valentin, C.; Sounyafong, P.; Rouw, A.; De Soulileuth, B.; Silvera, N.; Pierret, A.; Sengtaheuanghoug, O.; Ribolzi, O. 2018. Linking crop structure, throughfall, soil surface conditions, runoff and soil detachment: 10 land uses analyzed in Northern Laos. *Sci. Total Environ.* **2017**, *616–617*, 1330–1338. [CrossRef]
10. Morán-Ordóñez, A.; Duane, A.; Gil-Tena, A.; De Cáceres, M.; Aquilué, N.; Guerra, C.; Geijzendorffer, I.R.; Fortin, M.-J.; Brotons, L. Future impact of climate extremes in the Mediterranean: Soil erosion projections when fire and extreme rainfall meet. *Land Degrad. Dev.* **2020**, *31*, 3040–3054. [CrossRef]

11. Ma, X.; Lacombe, G.; Harrison, R.; Xu, J.; van Noordwijk, M. Expanding Rubber Plantations in Southern China: Evidence for Hydrological Impacts. *Water* **2019**, *11*, 651. [CrossRef]

12. Song, L.; Boithias, L.; Sengtaheuanghoung, O.; Oeurng, C.; Valentin, C.; Souksavath, B.; Sounyafong, P.; de Rouw, A.; Soulileuth, B.; Silvera, N.; et al. Understory Limits Surface Runoff and Soil Loss in Teak Tree Plantations of Northern Lao PDR. *Water* **2020**, *12*, 2327. [CrossRef]

13. Laraque, A.; Lopez, J.; Yepez, S.; Georgescu, P. Water and Sediment Budget of Casiquiare Channel Linking Orinoco and Amazon Catchments, Venezuela. *Water* **2019**, *11*, 2068. [CrossRef]

14. Hout, R.; Maleval, V.; Mahe, G.; Rouvellac, E.; Crouzevialle, R.; Cerbelaud, F. UAV and LiDAR Data in the Service of Bank Gully Erosion Measurement in Rambla de Algeciras Lakeshore. *Water* **2020**, *12*, 2748. [CrossRef]

15. Laraque, A.; Moukandi N’kaya, G.; Orange, D.; Tshimanga, R.; Tshitenge, J.; Mahé, G.; Nguimalet, C.; Trigg, M.; Yepez, S.; Gulemvuga, G. Recent Budget of Hydroclimatology and Hydrosedimentology of the Congo River in Central Africa. *Water* **2020**, *12*, 2613. [CrossRef]

16. Dieulin, C.; Mahé, G.; Paturel, J.; Ejjiyar, S.; Tramblay, Y.; Rouché, N.; EL Mansouri, B. A New 60-Year 1940/1999 Monthly-Gridded Rainfall Data Set for Africa. *Water* **2019**, *11*, 387. [CrossRef]

17. Amoussou, E.; Awoye, H.; Totin Vodounon, H.; Obahoundje, S.; Camberlin, P.; Diedhiou, A.; Kouadio, K.; Mahé, G.; Houndénou, C.; Boko, M. Climate and Extreme Rainfall Events in the Mono River Basin (West Africa): Investigating Future Changes with Regional Climate Models. *Water* **2020**, *12*, 833. [CrossRef]

18. Bodian, A.; Diop, L.; Panthou, G.; Dacosta, H.; Deme, A.; Dezetter, A.; Ndiaye, P.; Diouf, I.; Vischel, T. Recent Trend in Hydroclimatic Conditions in the Senegal River Basin. *Water* **2020**, *12*, 436. [CrossRef]

19. Yilmaz, M.; Onoz, B. A Comparative Study of Statistical Methods for Daily Streamflow Estimation at Ungauged Basins in Turkey. *Water* **2020**, *12*, 459. [CrossRef]

20. Ebodé, V.; Mahé, G.; Dzana, J.; Amougou, J. Anthropization and Climate Change: Impact on the Discharges of Forest Watersheds in Central Africa. *Water* **2020**, *12*, 2718. [CrossRef]

21. Ezzaouini, M.; Mahé, G.; Kacimi, I.; Zerouali, A. Comparison of the MUSLE Model and Two Years of Solid Transport Measurement, in the Bouregreg Basin, and Impact on the Sedimentation in the Sidi Mohamed Ben Abdellah Reservoir, Morocco. *Water* **2020**, *12*, 1882. [CrossRef]

22. Bader, J.; Dacosta, H.; Pouget, J. Seasonal Variations of the Depletion Factor during Recession Periods in the Senegal, Gambia and Niger Watersheds. *Water* **2020**, *12*, 2520. [CrossRef]

23. Descroix, L.; Faty, B.; Manga, S.; Diedhiou, A.; Lambert, L.A.; Soumaré, S.; Andrieu, J.; Ogilvie, A.; Fall, A.; Mahé, G.; et al. Are the Fouta Djallon Highlands Still the Water Tower of West Africa? *Water* **2020**, *12*, 2968. [CrossRef]

24. Descroix, L.; Sané, Y.; Thior, M.; Manga, S.; Ba, B.; Mingou, J.; Mendy, V.; Coly, S.; Dièye, A.; Badiane, A.; et al. Inverse Estuaries in West Africa: Evidence of the Rainfall Recovery? *Water* **2020**, *12*, 647. [CrossRef]

25. Cavus, Y.; Aksoy, H. Spatial Drought Characterization for Seyhan River Basin in the Mediterranean Region of Turkey. *Water* **2019**, *11*, 1331. [CrossRef]

26. Blöschl, G.; Bierkens, M.F.; Chambel, A.; Cudennec, C.; Destouni, G.; Fiori, A.; Kirchner, J.W.; McDonnell, J.J.; Savenije, H.H.; Sivapalan, M.; et al. Twenty-three unsolved problems in hydrology (UPH)—A community perspective. *Hydrol. Sci. J.* **2019**, *64*, 1141–1158. [CrossRef]

27. Hzami, A.; Heggy, E.; Amrouni, O.; Mahe, G.; Maanan, M.; Abdeljaouad, S. Alarming coastal vulnerability of the deltaic and sandy beaches of North Africa. *Nat. Sci. Rep.* **2021**, *11*, 2320. [CrossRef] [PubMed]
<figure><img src="image_9.png" /></figure>
Article

# Seasonal Variations of the Depletion Factor during Recession Periods in the Senegal, Gambia and Niger Watersheds

Jean-Claude Bader ¹*, Honoré Dacosta ² and Jean-Christophe Pouget ¹

¹ G-EAU, IRD (AgroParisTech, Cirad, IRSTEA, MontpellierSupAgro, Univ Montpellier), BP5095, 34196 Montpellier, France; jean-christophe.pouget@ird.fr

² Département de Géographie, FLSH-UCAD, BP 5005 Dakar-Fann, Senegal; honore.dacosta@ucad.edu.sn

* Correspondence: jean-claude.bader@ird.fr

Received: 17 July 2020; Accepted: 29 August 2020; Published: 9 September 2020

**Abstract:** The daily depletion factor K describes the discharge decrease of rivers only fed by groundwater in the absence of rainfall. In the Senegal, Gambia and Niger river basins in West Africa, the flow recession can exceed 6 months and the precise knowledge of K thus allows discharge forecasts to be made over several months, and is hence potentially interesting for hydraulic structure managers. Seasonal flow recession observed at 54 gauging stations in these basins from 1950 to 2016 is represented by empirical and usual conceptual models that express K. Compared to conventional conceptual models, an empirical model representing K as a polynomial of the decimal logarithm of discharge Q gives better representations of K and better discharge forecasting at horizons from 1 to 120 days for most stations. The relationship between specific discharge Qs and K, not monotonous, is highly homogeneous in some sub-basins but differs significantly between the Senegal and Gambia basins on the one hand and the Niger basin on the other. The relationship K(Q) evolves slightly between three successive periods, with values of K generally lower (meaning faster discharge decrease) in the intermediate period centered on the years 1970–1980. These climate-related interannual variations are much smaller than the seasonal variations of K.

**Keywords:** flow recession model; discharge forecast; Senegal River; Gambia River; Niger River

# 1. Introduction

## 1.1. Background, Context

According to [1], “the decrease of discharge corresponding to the emptying of groundwater without any precipitation is called the flow recession of a river”. This stream flow regime has been the subject of numerous studies, including reviews [2,3].

According to these authors, the flow recession concerns “all natural storages feeding the stream, including unsaturated grounds and lakes”. Among the oldest works, [4] established the differential equation governing the discharge of an aquifer in a homogeneous ground. This author derives two conceptual models that give the discharge rate of the groundwater into a river under certain boundary conditions. The first, which is the most widely used recession model [1,5], is described as linear [2]. Assuming a thick aquifer whose free surface is close to the horizontal, it expresses the discharge Q at time T as a function of discharge Q₀ at time T₀, with a constant α characteristic of the ground and the dimensions of the aquifer and dependent on the unit of time (but independent of T₀), or with a constant K equal to e⁻$^{α}$, called “depletion factor” [6]:

$$Q(T) = Q_0 e^{-\alpha(T-T_0)} = Q_0 K^{(T-T_0)}. \quad (1)$$
The second model proposed by [4], described as non-linear [2], assumes a groundwater table limited by an impermeable horizontal bottom and vertical wall, draining into the watercourse at its base. It is expressed in this way, with a constant $\sigma_0$ characteristic of the soil and the dimensions of the aquifer and depending on both the unit of time T and the initial time $T_0$:

$$Q(T) = Q_0/(1 + \sigma_0(T - T_0))^2. \qquad (2)$$

According to [5], the relationship (1) first applied by [7] is generally referred to as the “Maillet formula”, while the relationship (2), used by [8] for African rivers, is generally referred to as the “Tison formula”.

Reference [9] shows that these two formulas are particular cases of a more general conceptual model ($Q = ZV^m$) that represents the emptying of a reservoir under the assumption of a discharge Q proportional to a certain m power of the remaining water volume V, with a proportionality constant Z. This author finds the Maillet equation (1) with m equal to 1, his model then representing the emptying of a vertical cylinder by a porous plug at its base [1]. When m is different from 1, he obtains the following result where $V_0$ is the volume remaining at time $T_0$:

$$Q(T) = Q_0/(1 + \sigma_0(T - T_0))^n, \qquad (3)$$

$$n = m/(m-1), \qquad (4)$$

$$\sigma_0 = (m-1)Q_0/V_0. \qquad (5)$$

with $m = 2$, the “Coutagne equation” (3) gives the Tison equation (2) and represents the emptying of a vertical cylindrical reservoir by a parabolic spillway with a vertical axis [10].

Some authors propose the empirical addition of a constant term W to Maillet’s equation [11–15], to Tison’s equation (Maillet, in [4]) or to that of Coutagne [9,16]. The relationships thus obtained are called here “generalized Maillet equation” (6) and “generalized Coutagne equation” (7):

$$Q(T) = W + (Q_0 - W)e^{-\alpha(T - T_0)}, \qquad (6)$$

$$Q(T) = W + (Q_0 - W)/(1 + \sigma_0(T - T_0))^n. \qquad (7)$$

in these relationships, the parameters $\alpha$ and $\sigma_0$ depend on the time unit and $\sigma_0$ also depends on the initial time $T_0$, which can be set arbitrarily. With the relationship (6), the recession can be represented indifferently from the flow rates $Q_A$ and $Q_B$ at the initial times $T_A$ and $T_B$ if the relationship (8) is respected. With the relationship (7), $Q_A$ and $Q_B$ at the initial times $T_A$ and $T_B$, associated with $\sigma_A$ and $\sigma_B$, must verify the relationship (9).

$$Q_B = W + (Q_A - W)e^{-\alpha(T_B - T_A)}, \qquad (8)$$

$$\sigma_B = \sigma_A / (1 + \sigma_A(T_B - T_A)) = \sigma_A ((Q_B - W) / (Q_A - W))^{1/n}. \qquad (9)$$

Relationship (10) is a particular case of the generalized Coutagne equation obtained after changing the variable by translation over time. It is used in different forms with the parameters $\lambda$, $\mu$ and $r$ by some authors [13,17–21]:

$$Q(T) = \mu + \lambda/T^r. \qquad (10)$$

Reference [22] proposes an empirical adaptation of the Maillet formula, by a change of variable with a power function over time. So the “Horton formula”, sometimes referred to as the double exponential [2], is expressed as follows with the parameters $\beta$ and $p$:

$$Q(T) = Q_0 e^{-\beta(T - T_0)^p}. \qquad (11)$$
Finally, recession is often represented by the sum of Maillet formulas [4,6,23–26] or Maillet formulas and Tison formulas [27].

The most commonly used conceptual models to represent recession, listed by [3,28], can all be represented by the generalized Maillet (6), generalized Coutagne (7) or Horton (11) formulas, or by combinations of these formulas. The calibration of these conceptual or empirical models is usually based on the analysis of certain relationships in observed data, using either a graphical or least squares method. These relationships, sometimes interpreted as envelope curves to distinguish the origin of the flows (slow variable feeding by the aquifers and more rapid variable feeding for the other origins), are as follows:

* Relationship between $Q(T)$ and $Q(T + dT)$: correlation method. With $dT = 1$ day, [29] uses this mean relationship as an empirical recession curve, and [30] represents the upper envelope curve by a line passing through the origin, whose slope corresponds to the depletion factor $K$ of the Maillet equation (1). With $dT = 5$ days, [31] represents the mean relationship by a line passing through the origin, whose slope corresponds to $K^5$.

* Relationships between $T$ and $\text{Log}(Q)$ established for different recession sequences. Reference [32] uses these relationships and interprets their slope in each point as $-\alpha$ (Maillet's formula). He derives an empirical model giving $\alpha$ as a function of $Q$ and $T$. Ref. [33] set the Maillet formula by representing the relationships obtained for the different sequences by linear relationships, whose common slope corresponds to $-\alpha$.

* Relationship between $\text{Log}(Q)$ and $\text{Log}(-dQ/dT)$. Refs. [34,35] represent the low envelope curve of this relationship by sections of linear functions, whose slope and ordinate at the origin correspond respectively to $(n + 1)/n$ and $\text{Log}(n\sigma_0Q_0^{-1/n})$, where $n$ and $\sigma_0$ are the parameters of the Coutagne equation (3). The 3/2 slope obtained for low flows gives $n = 2$, according to the Tison equation (2). Reference [36] obtains an average relationship with a slope close to 1, according to the Maillet equation (1).

* Relationship between $Q$ and $-dQ/dT$. For different periods varying in distance from the beginning of recession, [37] represent the upper and lower envelopes of this relationship by lines passing through the origin, whose slope corresponds to the $\alpha$ parameter of the Maillet equation (1). These authors find that $\alpha$ is not very variable for low envelopes associated with baseflow from groundwater, while it decreases over time for high envelopes.

Each of the above methods, therefore, consists in representing, generally by one or more lines, a relationship between a primary variable ($Q(T)$, $T$, $\text{Log}(Q)$ or $Q$) and a secondary variable ($Q(T + dT)$, $\text{Log}(Q)$, $\text{Log}(-dQ/dT)$ or $-dQ/dT$). This can be problematic for rivers in West Africa, where $Q$ and $-dQ/dT$ can decrease by several orders of magnitude during recession sequences spread over several months. Any elementary function adjusted to $Q$ or $-dQ/dT$ by the least squares method can then lead to very large relative errors for the lowest values of $Q(T + dT)$ or $-dQ/dT$. Conversely, adjusting a function on logarithms of $Q$ or $-dQ/dT$ can be unfavorable and allow large relative errors for the highest values of $Q$ or $-dQ/dT$.

The method used by [5,38], derived from the correlation method, does not have these disadvantages. From the mean $Q_m$ of observed discharge, these authors calibrate the Maillet equation by calculating the ratio $Q_m(T + dT)/Q_m(T)$, interpreted as $K^{dT}$. They deduce $K$ from the resulting ratios calculated for different $dT$ values.

To study the flow recession on the Senegal River basin in West Africa, reference [39] uses a quite similar method to the previous one. Instead of $Q_m(T + dT)/Q_m(T)$, they calculate for $dT = 1$ day the daily values of $Q(T + dT)/Q(T)$ that corresponds to the daily depletion factor $K$ of the Maillet formula. Despite their wide dispersion between 0.5 and 1, the values obtained show an average seasonal evolution that can be represented by an empirical function of time $T$, which is counted from an origin set at the same date each year. This function represents $K$ with the same accuracy for very different discharges, which is an advantage over the methods mentioned above. For most of the
stations analyzed, K does not vary monotonously with T: from a low value at the beginning of recession, K increases to a maximum value and then decreases rapidly until the end of recession. Among the commonly used conceptual models, only the generalized Coutagne model (7), used with a negative W, makes it possible to represent such a variation of K (for a demonstration see text S1).

## 1.2. Objectives of the Project

This study, which is an extension of the work of [39], focuses on the depletion factor K in the Senegal, Gambia and Niger river basins in West Africa. Precise knowledge of K, always situated between 0 and 1 by definition, is of interest for two main reasons:

* The knowledge of groundwater, since K describes the recharge of the river flow by the groundwater in the absence of rainfall. A high K coefficient, close to 1, corresponds to a slow decrease in the discharge, thanks to important contributions from the water tables. Conversely, a low K coefficient corresponds to a rapid decrease in the flow of rivers, with little discharge supply from groundwater. K thus characterizes the capacity of groundwater to supply rivers. This capacity depends both on geological and pedological characteristics (transmissivity, storage, permeability) and on the abundance of previous rainfall inputs to the basin.

* The forecasting of discharge during recession periods, which can extend more than 6 months in the region. Flow forecasts can, therefore, be made over very long horizons of several months, which can be of great interest to managers of hydraulic structures such as dams.

For 54 stations located in the Senegal, Gambia and Niger river basins, we model the flow recession of rivers from observed values of the daily depletion factor K over the period 1950–2016. In addition to the most frequently used Maillet model (K constant), other models are tested to describe seasonal variations of K as a function of time T or discharge Q, using formulas whose form is empirical or imposed by the generalized Coutagne equation (7). We compare the performance of the different models in representing K and in forecasting discharge Q at all possible forecast horizons during the recession sequences enabled by the models. Finally, we compare seasonal variations and interannual variations of K.

The following sections present the method, data, results and conclusions of the study. All dates are expressed in day/month/year.

# 2. Materials and Methods

## 2.1. Methods

### 2.1.1. Observed Values of the Daily Depletion Factor K

According to equation (1), the daily depletion factor K(T) is equal to Q(T + 1)/Q(T) with T expressed in days. But to limit their dispersion, its values are calculated over 3 consecutive days from the flows observed at times T − 1 and T + 2:

$$K(T) = (Q(T + 2)/Q(T - 1))^{1/3}. \qquad (12)$$

Only the values K(T) based on flows Q(T − 1) and Q(T + 2) belonging to the same recession sequence are retained, with T verifying the following 3 conditions:

* C1: times T − 2 to T + 2 fall within the usual recession period, which starts and ends on invariable dates T1 and T2, expressed in days/months;

* C2: between times T − 2 and T + 2, the discharge is known at a daily time step with no missing data and decreases in the broad sense, meaning that Q(T + k) ≤ Q(T + k − 1) for all integer numbers k between − 1 and 2;

* C3: the discharge Q(T + 2) is greater than a minimum threshold Qthr arbitrarily set at 0.1 m$^3$.s$^{-1}$.
2.1.2. Analyses Performed

We tested 5 models to represent the depletion factor K:

* The Maillet's conceptual model (model 0). This model was chosen because it is the most often used model of recession.

* An empirical model representing K as a function of time (model 1).

* An empirical model representing K as a function of discharge (model 2).

* The generalized Coutagne conceptual model. This model was chosen because it is the only usual conceptual model capable of representing the non-monotonic evolution of K observed in the Senegal River basin during the recession period (see above). The generalized Coutagne model is used to represent K as a function of time (model 3) or as a function of discharge (model 4).

For each station, we represent the seasonal variations of K(T) with these five models calibrated using the least squares method:

* model 0: average Km of the observed values of K(T), constant value compatible with the Maillet formula;

* model 1: empirical polynomial function f of the delay D(T) elapsed between the initial time T₀ (invariable, expressed in day/month) and T, defined with parameters A₁ to A₆ by:

$$K = f(D) = \sum_{i=0}^{i=6} (A_i \times D^i); \qquad (13)$$

* model 2: empirical function g of the discharge Q(T), polynomial of the decimal logarithm of Q defined with parameters B1 to B6 by:

$$K = g(Q) = \sum_{i=0}^{i=6} (B_i \times (\log Q)^i); \qquad (14)$$

* model 3: function fb of the delay D(T), verifying with the parameters Q₀, W, σ₀ and n the relationship (15) imposed by the generalized Coutagne formula:

$$K = fb(D) = \frac{W + (Q_0 - W)(1 + \sigma_0 + \sigma_0 D)^{-n}}{W + (Q_0 - W)(1 + \sigma_0 D)^{-n}}; \qquad (15)$$

* model 4: function gb of the discharge Q(T), verifying with the parameters Q₀, W, σ₀ and n the relationship (16) imposed by the generalized Coutagne formula:

$$K = gb(Q) = \frac{W + (Q_0 - W)\left(\left(\frac{Q_0 - W}{Q - W}\right)^{1/n} + \sigma_0\right)^{-n}}{Q}. \qquad (16)$$

Calibrated on all the N observed values of K, each of these models makes it possible to represent hydrographs Q(T) that differ between different recession periods by homothety for models 0, 1 and 3 and by time translation for models 0, 2 and 4 (for a demonstration see Text S2). The models are classified according to the Nash and Sutcliffe efficiency coefficient C<sub>NSE0</sub> relative to the N modeled K values (C<sub>NSE0</sub> = 0 for model 0 based on the Maillet formula), with R<sub>a</sub> rank ranging from 1 for maximum C<sub>NSE0</sub> to 5 for minimum C<sub>NSE0</sub>. The models' ability to forecast recession flows is then evaluated for all entire H forecast horizons between 1 and 120 days.

Let a sequence of uninterrupted recession be limited by the times T<sub>b</sub> - 2 and T<sub>b</sub> + N<sub>p</sub> + 1, during which conditions C1 to C3 are checked for any T between T<sub>b</sub> and T<sub>b</sub> + N<sub>p</sub> - 1. These conditions make it possible to calculate N<sub>p</sub> observed values of K with equation (12) between the times T<sub>b</sub> and T<sub>b</sub> + N - 1, and also to calculate N<sub>p</sub> × (N<sub>p</sub> + 1)/2 forecasted discharges over the sequence with each recession model: N<sub>p</sub> values are forecast on a first sub sequence at times T<sub>b</sub> + 1 to T<sub>b</sub> + N<sub>p</sub> from the discharge
observed at time $T_b$, for horizons $H$ from 1 to $N_p$ days; $N_p - 1$ values are forecast on a second sub sequence at times $T_b + 2$ to $T_b + N_p$ from the discharge observed at time $T_b + 1$, for horizons $H$ from 1 to $N_p - 1$ days; a value is predicted on a $N_p$th sub sequence at time $T_b + N_p$ from the discharge observed at time $T_b + N_p - 1$, for a horizon of 1 day. For each sub sequence, each forecast discharge is calculated with the recession model applied to the previous day's discharge (observed for the first of the sub sequence and forecast for the following ones).

The accuracy of the forecast discharges is evaluated as follows: for each horizon $H$, using the relative standard error $R_{rmse}$ (ratio between the standard error $S_e$ and the average $Q_m$ of the corresponding observed flows) and the Nash and Sutcliffe efficiency coefficient $C_{NSE1}$ for the $N_e$ values forecast at horizon $H$ over all the recession periods defined above; using the $C_{NSE2}$ for the $N_t$ values predicted at the different horizons (with $N_t = \sum_{H=1}^{H=120} N_e$).

## 2.2. Data

The data used are the average daily discharges observed under natural conditions between 1950 and 2016 at 54 gauging stations (Tables 1–3 and Figure 1) located in the upper basins of the Senegal River (up to Kaédi), the Gambia River (in Senegal, upstream of Gouloumbo) and the Niger River (in Mali, up to Ansongo). These data come from the former ORSTOM/IRD databases developed and enriched through various projects [39–43], often carried out in partnership with data-producing or -managing organizations (Direction Nationale de l'Hydraulique du Mali, Organisation pour la Mise en Valeur du fleuve Gambie, Organisation pour la Mise en Valeur du fleuve Sénégal, Service de Gestion et de Planification des Ressources en Eau du Sénégal).

<table><caption>**Table 1.** Senegal basin-list of stations analyzed, with their catchment area and mean specific discharge $Q_{sm}$ over the period 1970–1979.</caption><thead><tr><th>Sub-Basin</th><th>River</th><th>Station</th><th>Rank</th><th>Long. (° W)</th><th>Lat. (° N)</th><th>Area (km²)</th><th>Q<sub>sm</sub> l·s<sup>-1</sup>·km<sup>-1</sup></th></tr></thead><tbody><tr><td>High Bafing</td><td>Bafing</td><td>Pont km17</td><td>1</td><td>12°09'</td><td>10°29'</td><td>18</td><td>17.45</td></tr><tr><td>High Bafing</td><td>Samenta</td><td>Doureko</td><td>2</td><td>11°42'</td><td>11°18'</td><td>225</td><td>17.38</td></tr><tr><td>High Bafing</td><td>Kioma</td><td>Teliko</td><td>3</td><td>11°53'</td><td>11°22'</td><td>360</td><td>17.34</td></tr><tr><td>High Bafing</td><td>Kioma</td><td>Salouma</td><td>4</td><td>11°42'</td><td>11°17'</td><td>775</td><td>15.96</td></tr><tr><td>High Bafing</td><td>Téné</td><td>Bebele</td><td>5</td><td>11°49'</td><td>11°01'</td><td>3470</td><td>17.59</td></tr><tr><td>High Bafing</td><td>Bafing</td><td>Balabori</td><td>6</td><td>11°22'</td><td>11°18'</td><td>11,600</td><td>13.29</td></tr><tr><td>Bafing</td><td>Bafing</td><td>Boureya</td><td>7</td><td>10°44'</td><td>11°45'</td><td>14,800</td><td>12.77</td></tr><tr><td>Bafing</td><td>Bafing</td><td>Daka Saidou</td><td>8</td><td>10°37'</td><td>11°57'</td><td>15,700</td><td>12.50</td></tr><tr><td>Bafing</td><td>Bafing</td><td>Makana</td><td>9</td><td>10°17'</td><td>12°33'</td><td>22,000</td><td>10.44</td></tr><tr><td>Bafing</td><td>Bafing</td><td>Soukoutali</td><td>10</td><td>10°25'</td><td>13°12'</td><td>27,800</td><td>9.11</td></tr><tr><td>Bafing</td><td>Bafing</td><td>Dibia</td><td>11</td><td>10°48'</td><td>13°14'</td><td>33,500</td><td>7.74</td></tr><tr><td>Faleme</td><td>Faleme</td><td>Moussala</td><td>12</td><td>11°18'</td><td>12°31'</td><td>3103</td><td>10.04</td></tr><tr><td>Faleme</td><td>Faleme</td><td>Fadougou</td><td>13</td><td>11°23'</td><td>12°31'</td><td>9300</td><td>5.75</td></tr><tr><td>Faleme</td><td>Faleme</td><td>Gourbassy</td><td>14</td><td>11°38'</td><td>13°24'</td><td>17,100</td><td>5.01</td></tr><tr><td>Faleme</td><td>Faleme</td><td>Kidira</td><td>15</td><td>12°13'</td><td>14°27'</td><td>28,900</td><td>3.61</td></tr><tr><td>Bakoye</td><td>Bakoye</td><td>Toukoto</td><td>16</td><td>09°53'</td><td>13°27'</td><td>16,500</td><td>2.94</td></tr><tr><td>Bakoye</td><td>Baoule</td><td>Siramakana</td><td>17</td><td>09°53'</td><td>13°35'</td><td>59,500</td><td>0.56</td></tr><tr><td>Bakoye</td><td>Bakoye</td><td>Oualia</td><td>18</td><td>10°23'</td><td>13°36'</td><td>84,700</td><td>1.05</td></tr><tr><td>Bakoye</td><td>Bakoye</td><td>Kalé</td><td>19</td><td>10°39'</td><td>13°43'</td><td>85,600</td><td>1.05</td></tr><tr><td>Senegal</td><td>Senegal</td><td>Galougo</td><td>20</td><td>11°03'</td><td>13°51'</td><td>128,400</td><td>2.79</td></tr><tr><td>Senegal</td><td>Senegal</td><td>Gouina</td><td>21</td><td>11°06'</td><td>14°00'</td><td>128,600</td><td>2.83</td></tr><tr><td>Senegal</td><td>Senegal</td><td>Kayes</td><td>22</td><td>11°27'</td><td>14°27'</td><td>157,400</td><td>2.32</td></tr><tr><td>Senegal</td><td>Senegal</td><td>Bakel</td><td>23</td><td>12°27'</td><td>14°54'</td><td>218,000</td><td>2.36</td></tr><tr><td>Senegal</td><td>Senegal</td><td>Matam</td><td>24</td><td>13°15'</td><td>15°39'</td><td>230,000</td><td>1.99</td></tr><tr><td>Senegal</td><td>Senegal</td><td>Kaédi</td><td>25</td><td>13°30'</td><td>16°08'</td><td>253,000</td><td>1.53</td></tr></tbody></table>
<table><caption>**Table 2.** Gambia basin—list of stations analyzed, with their catchment area and mean specific discharge $Q_{sm}$ over the period 1970–1979.</caption><thead><tr><th>Sub-Basin</th><th>River</th><th>Station</th><th>Rank</th><th>Long. (° W)</th><th>Lat. (° N)</th><th>Area (km²)</th><th>Q<sub>sm</sub> l·s<sup>-1</sup>km<sup>-1</sup></th></tr></thead><tbody><tr><td>tributaries</td><td>Sili</td><td>pont routier</td><td>26</td><td>12°16'</td><td>13°32'</td><td>90</td><td>9.12</td></tr><tr><td>tributaries</td><td>Diarha</td><td>pont routier</td><td>27</td><td>12°37'</td><td>12°36'</td><td>760</td><td>10.00</td></tr><tr><td>tributaries</td><td>Tiokoye</td><td>pont routier</td><td>28</td><td>12°32'</td><td>12°34'</td><td>950</td><td>9.41</td></tr><tr><td>tributaries</td><td>Diaguery</td><td>pont routier</td><td>29</td><td>12°05'</td><td>12°38'</td><td>1010</td><td>7.52</td></tr><tr><td>tributaries</td><td>Niokolokoba</td><td>pont routier</td><td>30</td><td>12°44'</td><td>13°04'</td><td>3000</td><td>2.65</td></tr><tr><td>tributaries</td><td>Koulountou</td><td>Gué (parc)</td><td>31</td><td>13°29'</td><td>12°47</td><td>5350</td><td>4.88</td></tr><tr><td>tributaries</td><td>Koulountou</td><td>Missira Gounasse</td><td>32</td><td>13°37'</td><td>13°12'</td><td>6200</td><td>5.13</td></tr><tr><td>Gambia</td><td>Gambia</td><td>Kedougou</td><td>33</td><td>12°11'</td><td>12°33'</td><td>7550</td><td>10.69</td></tr><tr><td>Gambia</td><td>Gambia</td><td>Mako</td><td>34</td><td>12°21'</td><td>12°52'</td><td>10,450</td><td>8.86</td></tr><tr><td>Gambia</td><td>Gambia</td><td>Simenti</td><td>35</td><td>13°18'</td><td>13°02'</td><td>20,500</td><td>6.42</td></tr><tr><td>Gambia</td><td>Gambia</td><td>Wassadou amont</td><td>36</td><td>13°22'</td><td>13°21'</td><td>21,200</td><td>6.20</td></tr><tr><td>Gambia</td><td>Gambia</td><td>Wassadou aval</td><td>37</td><td>13°23'</td><td>13°21'</td><td>33,500</td><td>3.96</td></tr></tbody></table>

<table><caption>**Table 3.** Niger basin—list of stations analyzed, with their catchment area and mean specific discharge $Q_{sm}$ over the period 1970–1979.</caption><thead><tr><th>Sub-Basin</th><th>River</th><th>Station</th><th>Rank</th><th>Long. (° W)</th><th>Lat. (° N)</th><th>Area (km²)</th><th>Q<sub>sm</sub> l·s<sup>-1</sup>km<sup>-1</sup></th></tr></thead><tbody><tr><td>High Niger</td><td>Sankarani</td><td>Selingue</td><td>38</td><td>08°13'</td><td>11°38'</td><td>34,200</td><td>9.51</td></tr><tr><td>High Niger</td><td>Niger</td><td>Banankoro</td><td>39</td><td>08°40'</td><td>11°41'</td><td>70,740</td><td>12.72</td></tr><tr><td>High Niger</td><td>Niger</td><td>Koulikouro</td><td>40</td><td>07°33'</td><td>12°51'</td><td>120,000</td><td>10.60</td></tr><tr><td>High Niger</td><td>Niger</td><td>Ke Macina</td><td>41</td><td>05°21'</td><td>13°58'</td><td>141,000</td><td>8.41</td></tr><tr><td>Bani</td><td>Degou</td><td>Manankoro</td><td>42</td><td>07°27'</td><td>10°27'</td><td>1550</td><td>5.52</td></tr><tr><td>Bani</td><td>Banifing</td><td>Kolondieba</td><td>43</td><td>06°51'</td><td>11°03'</td><td>3050</td><td>3.36</td></tr><tr><td>Bani</td><td>Baoulé</td><td>Madina Diassa</td><td>44</td><td>07°40'</td><td>10°47'</td><td>7880</td><td>6.60</td></tr><tr><td>Bani</td><td>Baoulé</td><td>Dioila</td><td>45</td><td>06°48'</td><td>12°31</td><td>32,500</td><td>3.25</td></tr><tr><td>Bani</td><td>Bani</td><td>Douna</td><td>46</td><td>05°54'</td><td>13°12'</td><td>101,600</td><td>2.73</td></tr><tr><td>Bani</td><td>Bani</td><td>Beneny Kegny</td><td>47</td><td>04°54'</td><td>13°23'</td><td>116,000</td><td>2.47</td></tr><tr><td>Bani</td><td>Bani</td><td>Sofara</td><td>48</td><td>04°05'</td><td>14°05'</td><td>125,400</td><td>1.96</td></tr><tr><td>Niger</td><td>Niger</td><td>Mopti</td><td>49</td><td>04°12'</td><td>14°30'</td><td>281,600</td><td>3.00</td></tr><tr><td>Niger</td><td>Niger</td><td>Akka</td><td>50</td><td>04°14'</td><td>15°24'</td><td>-</td><td>-</td></tr><tr><td>Niger</td><td>Niger</td><td>Diré</td><td>51</td><td>03°23'</td><td>16°16'</td><td>-</td><td>-</td></tr><tr><td>Niger</td><td>Niger</td><td>Koryoumé</td><td>52</td><td>03°01'</td><td>16°40'</td><td>-</td><td>-</td></tr><tr><td>Niger</td><td>Niger</td><td>Tossaye</td><td>53</td><td>00°35'</td><td>16°57'</td><td>-</td><td>-</td></tr><tr><td>Niger</td><td>Niger</td><td>Ansongo</td><td>54</td><td>-00°30'</td><td>15°40'</td><td>-</td><td>-</td></tr></tbody></table>

Among the discharges obtained by translating the levels observed at the stations, all the reconstructed values are excluded from the analyses of the recession regime. Data influenced by large reservoir dams upstream (at Soukoutali and downstream from 1987 on the Senegal basin (Manantali dam); at Sélingué and downstream from 1981 on the Niger basin (Sélingué dam)) are also excluded.

The stations analyzed control basins whose area ranges from 18 to more than 280,000 km². Their mean interannual specific discharges $Q_{sm}$ (calculated by integrating certain reconstituted values) vary between 0.56 and 17.59 l·s⁻¹·km⁻² (Tables 1–3). The study, therefore, concerns very diverse stations, for which the data also cover the study period in a very variable way (varying numbers of missing observations).

The annual peak flood in the region occurs generally in mid September, except in the Inner Niger Delta (DIN) and downstream, where the flood mainly formed upstream spreads very slowly (Figure 2). The general decrease in flow occurs then and persists until the arrival of flows caused by the following monsoon, usually in May or June or even in July downstream of the DIN. The origin $T_0$ of the times is therefore set to the previous 15 September for all stations and the $T_1$ and $T_2$ start and end dates of the usual recession period are set to 15 September and 31 May, respectively, except for the following stations:
* $T_1$ = 15 October and $T_2$ = 30 June for Akka on Niger (rank 50), due to the slower spread of flows as they pass the DIN;

* $T_1$ = 15 November and $T_2$ = 31 July for Diré, Koryoumé, Tossaye and Ansongo on Niger (ranks 51 to 54), for the same reasons as Akka;

* $T_1$ = 15 September and $T_2$ = 30 April for Moussala and Siramakana in the Senegal watershed (ranks 12 and 17), Diaguery and Niokolokoba in the Gambia watershed (ranks 29 and 30) and Manankoro in the Niger watershed (rank 42), where the discharge ceases each year before the end of April.

<figure><img src="image_10.png" /><figcaption>**Figure 1.** Hydrographic networks of the Senegal River upstream of Kaédi, Gambia upstream of Gouloumbo and Niger upstream of Ansongo, based on the maps of [40] for Senegal, [41] for Niger and [42] for Gambia.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 2.** Median annual hydrographs for Senegal at Bakel (rank 23), Gambia at Wassadou upstream (rank 36), Niger at Koulikouro (rank 40) and Niger at Diré (rank 51) over the period 1970–1979.</figcaption></figure>
3. Results

3.1. Calibration of Models Representing K

3.1.1. Results for Daka Saidou Station

This station has the largest number (N = 10,966) of observed values of K (mean: K_m = 0.9714). The average evolution of K as a function of D (growth from September to the beginning of February and then decline until the end of May, Figure 3) is better represented by model 1 than by model 3 (C<sub>NSE0</sub> = 0.347 and 0.296 respectively). Similarly, the mean evolution of K as a function of Q is better represented by model 2 than by model 4 (C<sub>NSE0</sub> = 0.392 and 0.335 respectively): K increases strongly as a function of Q under low flows; under Q greater than about 25 m<sup>3</sup>·s<sup>-1</sup>, K decreases as a function of Q until the highest flows are reached (Figure 4).

<figure><img src="image_12.png" /><figcaption>**Figure 3.** Relationship between *D* (time elapsed since 15 September) and *K* at Daka Saidou on the Bafing (row 8; *N* = 10,966 observed values from 5 october 1952 to 20 october 2016; *C*<sub>NSE0</sub> = 0.347 for model 1 with *K* = *f*(*D*), *C*<sub>NSE0</sub> = 0.296 for model 3 with *K* = *fb*(*D*)).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 4.** Relationship between discharge Q and K at Daka Saidou on the Bafing (row 8; 10,966 points observed from 5 october 1952 to 20 october 2016; C<sub>NSE0</sub> =0.392 for model 2 with K = g(Q); C<sub>NSE0</sub> = 0.335 for model 4 with K = gb(Q)), with abscissa in logarithmic values on the left (a) and natural values on the right (b).</figcaption></figure>

3.1.2. Results for All Stations

For the calibration of functions *f* and *g* of models 1 and 2, the degree of the polynomial of *D* or
log(*Q*) is generally limited to 3. However, a higher degree (between 4 and 6) is used to improve the
calibration for 30% of the stations for *f* and 41% for *g*, mainly for the Niger basin. To set the functions
$f_b$ and $g_b$ of models 3 and 4, a superior limit of 10 is imposed on parameter *n* and $Q_0$ is arbitrarily set to the highest discharge *Q* associated with observed *K* (with no effect on the quality of the model, see above: relation (9)).

The parameters of the different models calibrated for each station are given in the Supplementary Materials (Tables S1–S3 for models 0 to 2 and Table S4 for models 3 and 4), with the $C_{NSEO}$ of calibration, the $R_a$ classification rows and the extremities of the calibration domains ($D_{min}$ and $D_{max}$ for *f* and $f_b$ and $Q_{min}$ and $Q_{max}$ for *g* and $g_b$). Figure 5 compares model performance in describing the observed values of *K*. For the average of their rank $R_a$ over all stations, indicated in brackets, the models rank from best to worst as follows: model 2 (1.2), model 1 (2.3), model 4 (2.9), model 3 (3.9) and model 0 (4.6). The best results are obtained with model 2 for 81% of the stations, with model 1 for 13% of the stations, with model 3 for 4% of the stations and with model 4 for 2% of the stations. The results of the two best models are detailed below.

<figure><img src="image_14.png" /><figcaption>**Figure 5.** Efficiency coefficient $C_{NSEO}$ and number *N* of calibration of models 1 to 4 describing *K* as a function of *D* or *Q*, for each station analyzed.</figcaption></figure>

### 3.1.3. Results for Model 1, Describing K as an Empirical Function of D

For most stations in the Senegal and Gambia basins (Figure 6a–g), the evolution of *K* as a function of time *D* elapsed since 15 September is large and very close to that observed at Daka Saidou: *K* increases as a function of *D* for 3 to 5 months from mid September on, then decreases until the end of May. Most downstream stations (ranks 23 to 25 for Senegal; 32 and 35 to 37 for Gambia) are characterized by smaller amplitude of *K* variations and some differences at the beginning and end of the recession.

Compared to the above stations, those in the Niger Basin have very different seasonal variations of *K*, with smaller amplitude (Figure 6h–j): *K* decreases with *D* for about 2 months from a very high value at the beginning of the recession period, and then changes relatively little for most stations.

### 3.1.4. Results for Model 2, Describing K as an Empirical Function of Q

For most stations in the Senegal and Gambia (Figure S1) basins, the functions $K = g(Q)$ are similar to those of Daka Saidou, as shown in Figures 7a–e and 8a,b, where discharge *Q* on the abscissa is mostly replaced by specific discharge $Q_s$ (flow divided by catchment area) to facilitate readability. Under low flows, *K* increases rapidly with $Q_s$. Under higher flows, *K* gradually decreases as a function of $Q_s$ with curves often quite close to each other at most stations in the same sub basin such as Bafing, Falémé and Senegal (Figure 7b,c,e). As an exception to these general trends, there is an additional inflection and growth of the function $g(Q)$ under the highest flow rates, at the following stations: Siramakana and Niokolokoba (ranges 17 and 30) that drain the northernmost and, therefore, least watered, sub basins among the stations analyzed in the Senegal and Gambia basins respectively; Bakel, Matam and Kaedi (ranges 23 to 25) in the Senegal basin and Missira Gonasse, Simenti, Wassadou upstream and Wassadou downstream (ranges 32 and 35 to 37) in the Gambia basin, the most downstream stations in these basins.
<figure><img src="image_15.png" /><figcaption>**Figure 6.** Model 1 representing *K* as a function of the time *D* elapsed since the previous 15 September (*K* = *f*(*D*)) at the 54 stations located in the Senegal, Gambia and Niger basins, by sub-basins: High Bafing (a); Bafing (b); Faleme (c); Bakoye (d); Senegal (e); Gambia tributaries (f); Gambia (g); High Niger (h); Bani (i); Niger (j).</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Figure 7.** Model 2 representing *K* as a function of the specific discharge *Q*<sub>s</sub> at the 25 stations located in the Senegal basin (relations *K* = *g*(*Q*)), with abscissa in logarithmic values on the left (index 1) and natural values on the right (index 2), by sub-basins: High Bafing (**a1**,**a2**), Bafing (**b1**,**b2**), Faleme (**c1**,**c2**), Bakoye (**d1**,**d2**), Senegal (**e1**,**e2**).</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Figure 8.** Model 2 representing K as a function of the specific discharge Qs or the discharge Q at stations 26 to 54 in the Gambia and Niger basins (relations K = g(Q)), with abscissa in logarithmic values on the left (index 1) and natural values on the right (index 2), by sub-basins: Gambia tributaries (**a1**, **a2**), Gambia (**b1**, **b2**), High Niger (**c1**, **c2**), Bani (**d1**, **d2**), Niger (**e1**, **e2**).</figcaption></figure>

For stations in the Niger Basin (Figure S2 and Figure 8c-e), the K = g(Q) functions differ significantly from previous ones with a smaller amplitude of variation and a reverse direction of variation (except
under low flows). For four stations (rows 43, 49, 50 and 52), the *K* rate increases as a function of discharge over the entire tidal range. For the other stations, *K* generally increases as a function of discharge at low water, slightly decreases at medium water and increases at high water.

## 3.2. Performance of the Recession Models in Forecasting Discharge

### 3.2.1. Calculation Details

For each station, the discharge chronicle used to calculate the observed *K* rates is also used to evaluate the discharge forecasts made with the different recession models, at all entire *H* horizons between 1 and 120 days. For model 0 characterized by a constant *K* rate characteristic of each station, we use the value *K*₀ which maximizes the overall *C*<sub>NSE2</sub> of the *N*<sub>t</sub> forecasts calculated at the different horizons *H*. This optimal rate *K*₀ differs slightly from the average *K*<sub>m</sub> of the observed *K* rates (Figure 9; Table S1). But the differences observed between basins are identical with *K*₀ and *K*<sub>m</sub>, with a distribution function that is low for the Gambia, intermediate for Senegal and high for Niger. The *K*₀ value is particularly low for Siramakana and Niokolokoba stations (ranges 17 and 30), mentioned above for their relations *K* = *g*(*Q*).

<figure><img src="image_18.png" /><figcaption>**Figure 9.** Mean *K*<sub>m</sub> of *K* observed and optimal value *K*<sub>0</sub> maximizing the efficiency coefficient *C*<sub>NSE2</sub> of the *N*<sub>t</sub> discharge forecasts made with model 0 (Maillet) at horizons *H* between 1 and 120 days.</figcaption></figure>

The discharge forecasts calculated with models 1 to 4 are performed for *D* and *Q* values within their calibration ranges. For some stations (mainly in the Niger basin), however, the function *g* tends to overestimate *K* under the highest flows, with values very close to or slightly higher than 1. The application range of *g* under high water for these stations is therefore reduced, with a limit *Q*<sub>lim</sub> lower than *Q*<sub>max</sub> (Table S3). In this case, model 2 is applied with a value *g*(*Q*<sub>lim</sub>) for all flows above *Q*<sub>lim</sub>.

### 3.2.2. Results for All Forecasting Horizons

Unlike parameter *K*₀ of model 0, the parameters of models 1 to 4 are not optimized to maximize the overall *C*<sub>NSE2</sub> from forecasts to different forecast horizons, but simply based on observed values of *K*. Notwithstanding, these models perform better (higher *C*<sub>NSE2</sub>) than model 0 for most stations, except models 3 and 4 in the Niger basin (Figure 10). The number of stations for which a model gives the best results (maximum *C*<sub>NSE2</sub>) is 3, 10, 40, 0 and 1 for models 0 to 5 respectively, whose average rankings based on *C*<sub>NSE2</sub> are 3.8, 2.4, 1.4, 4.3 and 3.1. Overall, model 2 is, therefore, the best for flow forecasts at different horizons *H* between 1 and 120 days.
<figure><img src="image_19.png" /><figcaption>**Figure 10.** $C_{\text{NSE2}}$ efficiency coefficient and number $N_t$ of the discharge forecasts made with the different K models (optimal $K_0$ value or D or Q functions) at all H horizons between 1 and 120 days.</figcaption></figure>

### 3.2.3. Results for Each Forecasting Horizon

For all models, the accuracy of flow forecasts, expressed by $C_{\text{NSE1}}$, tends to decrease with time horizon $H$, as shown in Figure 11 for Daka Saidou station and Figures S3 and S4 for Kedougou and Mopti. For Daka Saidou, the superiority of models 1 and 2 over the others is verified for each horizon.

<figure><img src="image_20.png" /><figcaption>**Figure 11.** Performance of models in forecasting discharge during recession periods at Daka Saidou on the Bafing, according to the forecast horizon.</figcaption></figure>

The following result shows that model 2 provides the best overall forecasts for all stations for each forecast horizon: for each horizon $H$ between 1 and 120 days, the average for the different stations of the relative standard error $R_{\text{rmse}}$ is always lower with model 2 than with the other models (Figure 12). The advantage of model 2 increases with the forecast horizon, since compared to model 0, it gives a lower average $R_{\text{rmse}}$ value of 15% to 30% for each horizon between 1 and 30 days, 30% to 36% for each horizon between 31 and 60 days and 36% to 41% for each horizon between 61 and 120 days.

The values of the Nash and Sutcliffe coefficient $C_{\text{NSE1}}$ and the relative standard error $R_{\text{rmse}}$ for flow forecasting at each station are given for all $H$ horizon multiples of 5 days in Supplementary Materials (Tables S5 and S6).

Example: Forecasting of $N_e = 3082$ discharge values at horizon $H = 70$ days gives $C_{\text{NSE1}}$ equal to 0.165, 0.798, 0.769, 0.654 and 0.647 with models 0, 1, 2, 3 and 4, respectively
<figure><img src="image_21.png" /><figcaption>**Figure 12.** Average model performance in forecasting discharge at all stations, according to the forecast horizon *H* (average of the relative standard error *R*<sub>rmse</sub>, calculated on the *N*<sub>s</sub> stations for which the number *N*<sub>e</sub> of discharge forecasts at horizon *H* is greater than 1).</figcaption></figure>

3.3. *Interannual Evolution of the Recession Regime*

3.3.1. Results for Daka Saidou Station

For each station, model 2, based on all available data from 1950 to 2016, represents the observed values of *K* with some errors. For most stations, the chronological accumulation *C*<sub>e</sub> of these errors does not vary randomly according to the chronological rank *R*<sub>c</sub>. On the contrary, *C*<sub>e</sub> shows fairly clear overall slope breaks under low flows, high flows or all flows as the case may be. However, the slope d*C*<sub>e</sub>/d*R*<sub>c</sub> of *C*<sub>e</sub> is equal to the error of the model. When fairly regular over a certain period, this slope then corresponds to a systematic error of the model, which justifies a particular calibration of the model in this period. For the Daka Saidou station, for example (Figure 13), the overall slope of *C*<sub>e</sub>(*R*<sub>c</sub>) under high flows, initially negative (*K* is generally underestimated by the model), increases significantly and even becomes positive from about March 1976 (*K* is strongly overestimated), then decreases while remaining positive from about December 1994 (*K* is overestimated). The model can, therefore, be calibrated over three periods 1 to 3 (October 1952 to February 1976; March 1976 to November 1994; December 1994 to October 2016) to better represent *K*. The three curves *K* = *g*(*Q*) obtained differ quite clearly under high flows, with the lowest values obtained in period 2 and the highest in period 1 (Figure 14). However, their general shape remains identical to that of the average model based on all the data.
<figure><img src="image_22.png" /><figcaption>**Figure 13.** Chronological evolution of the cumulative error C<sub>e</sub> of model 2 with respect to the *N* = 10,966 observed values of *K* on the Bafing at Daka Saidou, for low flows with frequency of exceedance between 0.5 and 0.99 (**a**), high flows with frequency between 0.01 and 0.5 (**b**), and all flows except extreme flows, with frequency between 0.01 and 0.99 (**c**).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 14.** Model 2 representing *K* as a function of discharge *Q*, calibrated on successive periods 1 to 3 and on the overall period, for the Bafing at Daka Saidou (station 8), with abscissa in logarithmic values on the left (**a**) and natural values on the right (**b**).</figcaption></figure>
### 3.3.2. Results for All Stations

By reproducing this analysis of the cumulative errors $C_e(R_c)$ for each station, we obtain the following results (Figure 15):

* for 44 stations, a transition between period 1 and 2 can be detected by $C_e(R_c)$ overall change in slope under high flows (38 stations) or low flows (6 stations). Except for the station of rank 1, for which data are lacking, this transition can be dated between March 1968 and March 1983, depending on the station. For 39 of these 44 stations, the transition from period 1 to period 2 corresponds to an increase in errors in the average model and therefore a decrease in $K$ observed for the same $Q$, like for Daka Saidou;

* for 26 stations, a transition between period 2 and 3 can be detected by a change in $C_e(R_c)$ slope under high flows (25 stations) or under low flows (1 station). Except for stations 29 to 31, for which data are lacking, this transition can be dated between March 1988 and December 1994, depending on the station. For these 26 stations, the transition from period 2 to period 3 corresponds to a decrease in the errors of the average model and therefore to an increase in $K$ observed for the same $Q$, like for Daka Saidou;

* the following results are observed for the average $K_m$ of the observed values of $K$ (Table S1): $K_m$ decreases by an average of 1.2% between periods 1 and 2 and increases by an average of 0.8% between periods 2 and 3. This evolution of $K_m$ is observed at all stations with rare exceptions. With $\alpha = -\text{Log}(K)$ according to equation (1), these average changes in $K$ over all the stations correspond to an average increase of $0.0120 \, d^{-1}$ between periods 1 and 2 and a decrease of $0.0080 \, d^{-1}$ between periods 2 and 3 for the parameter $\alpha$ generally used with the Maillet formula. This evolution of $\alpha$ between periods 1 and 2 is consistent with the results presented by [44,45] for several basins of West and Central Africa, [46] for the Niger River and [47] for the Bani.

<figure><img src="image_24.png" /><figcaption>**Figure 15.** Division of the data series into successive periods for each station, based on the dates of change in the overall slope of the time accumulation $C_e$ of the model 2 error.</figcaption></figure>

For each station, model 2 is finally calibrated successively on the three periods 1, 2 and 3, defined from the transition dates determined above for the stations concerned. For the other stations, these
dates are arbitrarily fixed (or specified for stations 1 and 29 to 31) from the dates determined at neighboring stations: the transition between periods 1 and 2 for 8 stations (ranks 1, 4 to 7, 11, 37 and 54); the transition between periods 2 and 3 for 9 stations (ranks 4 to 7, 12, 27 and 29 to 31).

For each station, as for Daka Saidou (Figure 14), the general shape of the $g(Q)$ curves set over successive periods is identical to that of the average model set over all the data (see Figures S5 and S6 for examples). The main differences already noted between basins on the $g(Q)$ curves set on all the data are, therefore, found over each period 1 to 3, in particular for the $g(Q)$ slope on most of the upper part of the tidal range: mainly negative in the Senegal and Gambia basins and positive in the Niger basin.

For all stations, the amplitude of variation of the average function $g(Q)$ over its field of application is much greater than the offsets observed between functions $g(Q)$ set over successive periods. On average for all stations, this amplitude $\max(g(Q)) - \min(g(Q))$ represents 13% of the average observed rate $K_m$ over all the data. It is much higher than the differences observed between the average $K_m$ values calculated over periods 1 and 2 (Figure 16). The seasonal variations of $K_m$, therefore, appear to be much greater than its interannual variations

<figure><img src="image_25.png" /><figcaption>**Figure 16.** Mean $K_m$ of $K$ observed over each period 1 and 2 and minimum and maximum values of $K$ modeled as a function of discharge (model $K = g(Q)$ calibrated on all observations).</figcaption></figure>

## 4. Discussion

For the representation of the daily depletion factor $K$ and the discharge forecasting at horizons 1 to 120 days during recession regimes over the Senegal, Gambia and Niger basins, empirical models 1 ($K = f(D)$) and 2 ($K = g(Q)$) give better overall results than conceptual models based on the Maillet (model 0) and generalized Coutagne (models 3 and 4) formula. The best (model 2) represents $K$ by a polynomial of the decimal logarithm of the discharge $Q$, with a Nash and Sutcliffe $C_{NSEO}$ coefficient varying between 0.04 and 0.83 (mean 0.37, median 0.37) compared to the observed values of $K$ over the 1950–2016 period. Compared to the most frequently used Maillet formula, it improves flow forecasting with an average 30% to 41% decrease of relative standard error $R_{rmse}$, for each forecast horizon $H$ between 31 and 120 days.

Model 2 shows a fairly homogeneous relationship over some areas or sub-basins (Bafing, Falémé, Senegal, Upper Niger) between the specific discharge $Q_s$ and $K$. On average over each basin, according to this model, $K$ evolves during the recession period as follows:

* In the Senegal and Gambia basins, $K$ is generally quite low at the beginning of the recession (between 0.80 and 0.95 under the highest discharges $Q$). It then increases over time ($K(Q)$ decreasing) to reach a fairly high value (between 0.96 and 0.98), for a specific flow rate $Q_s$ between 0.3 and $2 \cdot 10^{-1} \cdot \text{km}^{-2}$ depending on the sub-basin concerned, before decreasing ($K(Q)$ strongly increasing) until the end of the recession. The downstream stations are characterized by a decrease of $K$ at the beginning of the recession ($K(Q)$ increasing), from very high values, close to 1 under the highest flows;

* In the Niger basin, $K$ is generally very high at the beginning of the recession (higher than 0.975 under the highest flows). It then decreases ($K(Q)$ slightly increases) to a value greater than 0.95,
reached for a specific discharge $Q_s$ between 7 and 17 l·s⁻¹·km⁻² upstream of the Inner Delta or for a discharge Q of about 133 m³·s⁻¹ for stations downstream. Then, K evolves relatively little according to the flow and in a variable way according to the station, until the end of the recession.

The basins also differ in the $K_0$ value of K which optimizes discharge forecasts at horizons 1 to 120 days with the model 0 (Maillet formula). Overall, $K_0$ is quite low in the Gambia basin (average = 0.934; median = 0.941), medium in the Senegal basin (average = 0.955; median = 0.960) and quite high in the Niger basin (average = 0.972; median = 0.972). These differences may be related to the geological and soil characteristics of the three basins, but also to the rainfall regime. Indeed, the Gambia basin, which has the least rainfall in its upstream part according to [48], has the fastest drying up, while the Niger basin, which has the most rainfall according to [48], has the slowest drying up.

Finally, for most stations, the analysis of the chronological accumulation of errors on K with model 2 shows successive periods that differ slightly for model calibration. According to the available data, for each station we identified two or three periods with transition dates ranging from 1968 to 1983 between periods 1 and 2 and from 1988 to 1994 between periods 2 and 3. Generally, the average $K_m$ of K observed decreases between periods 1 and 2 and increases between periods 2 and 3. The faster depletion during period 2 is probably related to a decrease in groundwater reserves, as a result of reduced rainfall in West Africa during this period [48,49]. Over each period, the function $K = g(Q)$ differs slightly from the average function based on all the data. However, the differences between periods are much smaller than the amplitude of variation of $g(Q)$ over its field of application. On average for all stations, seasonal variations of K represent 13% of the average observed $K_m$ rate (15% for Senegal; 15% for Gambia; 9% for Niger), while interannual variations of $K_m$ are only about 1% between successive periods 1 and 2. For each basin, the seasonal variations of the daily depletion factor K are, therefore, much greater than its climate-related interannual variations.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4441/12/9/2520/s1: mathematical demonstrations (Texts S1 and S2) and detailed results (Tables S1–S6 and Figures S1–S6) for interested readers. However, this material is not essential for the understanding of the article. A list of variables and parameters used is given in the Abbreviations.

**Author Contributions:** conceptualization, J.-C.B.; data curation, J.-C.B.; formal analysis, J.-C.B.; investigation, J.-C.B., H.D., J.-C.P.; methodology, J.-C.B.; project administration, J.-C.B.; resources, J.-C.B.; software, J.-C.B.; supervision, J.-C.B.; validation, J.-C.B., H.D., J.-C.P.; visualization, J.-C.B., H.D., J.-C.P.; writing—original draft, J.-C.B.; writing—review & editing, J.-C.B., H.D., J.-C.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** the authors declare no conflict of interest.

## Abbreviations

List of Variables and Parameters

<table><tr><td>A<sub>i</sub> (d<sup>-i</sup>)</td><td>with i integer between 0 and 6: model 1 parameters (K = f(D)), polynomial coefficients of D</td></tr><tr><td>B<sub>i</sub> (-)</td><td>with i integer between 0 and 6: model 2 parameters (K = g(Q)), polynomial coefficients of log(Q)</td></tr><tr><td>C<sub>e</sub> (-)</td><td>chronological accumulation of model 2 errors in relation to observed values of K</td></tr><tr><td>C<sub>NSEO</sub> (-)</td><td>Nash and Sutcliffe model efficiency coefficient, equal to 1-((standard error)/(standard deviation))<sup>2</sup>, for the modeling of K</td></tr><tr><td>C<sub>NSE1</sub> (-)</td><td>Nash and Sutcliffe model efficiency coefficient, for the forecast of Q at a given horizon H</td></tr><tr><td>C<sub>NSE2</sub> (-)</td><td>Nash and Sutcliffe model efficiency coefficient, for the forecast of Q at all horizons H</td></tr><tr><td>D (d)</td><td>period elapsed since the previous 15 September</td></tr><tr><td>D<sub>max</sub> (d)</td><td>upper limit of the calibration range of the function f(D)</td></tr><tr><td>D<sub>min</sub> (d)</td><td>lower limit of the calibration range of the function f(D)</td></tr><tr><td>f (-)</td><td>relationship giving K as a function of D (model 1, empirical)</td></tr><tr><td>f<sub>b</sub> (-)</td><td>relationship giving K as a function of D (model 3, based on the generalized Coutagne formula)</td></tr></table>
<table>
  <tr>
    <td>g (-)</td>
    <td>relationship giving K as a function of Q (model 2, empirical)</td>
  </tr>
  <tr>
    <td>g<sub>b</sub> (-)</td>
    <td>relationship giving K as a function of Q (model 4, based on the generalized Coutagne formula)</td>
  </tr>
  <tr>
    <td>H (d)</td>
    <td>horizon of discharge forecast</td>
  </tr>
  <tr>
    <td>i (-)</td>
    <td>rank of a recession sequence</td>
  </tr>
  <tr>
    <td>j (-)</td>
    <td>rank of a recession sequence</td>
  </tr>
  <tr>
    <td>K (-)</td>
    <td>daily discharge depletion factor, between 0 (end of flow) and 1 (flow constancy)</td>
  </tr>
  <tr>
    <td>K<sub>0</sub> (-)</td>
    <td>optimal constant value of K, maximizing the C<sub>NSE2</sub> of the N<sub>t</sub> forecast discharges with the recession model 0 at all H horizons between 1 and 120 days</td>
  </tr>
  <tr>
    <td>K<sub>m</sub> (-)</td>
    <td>average of the N observed values of K</td>
  </tr>
  <tr>
    <td>Log (-)</td>
    <td>neperian logarithm</td>
  </tr>
  <tr>
    <td>log (-)</td>
    <td>decimal logarithm</td>
  </tr>
  <tr>
    <td>m (-)</td>
    <td>positive exponent of volume V, used in the Coutagne theory</td>
  </tr>
  <tr>
    <td>n (-)</td>
    <td>positive exponent of time in the Coutagne formula</td>
  </tr>
  <tr>
    <td>N (-)</td>
    <td>number of observed values of K</td>
  </tr>
  <tr>
    <td>N<sub>e</sub> (-)</td>
    <td>number of discharge values forecast by recession model, for a given forecast horizon H</td>
  </tr>
  <tr>
    <td>N<sub>s</sub> (-)</td>
    <td>number of stations for which N<sub>e</sub> is greater than 1</td>
  </tr>
  <tr>
    <td>N<sub>t</sub> (-)</td>
    <td>number of discharge values forecast per recession model, for all forecast horizons H between 1 and 120 days</td>
  </tr>
  <tr>
    <td>p (-)</td>
    <td>positive exponent of time used in the Horton formula</td>
  </tr>
  <tr>
    <td>P (-)</td>
    <td>percentage of stations, between 0 (no stations) and 100 (all stations)</td>
  </tr>
  <tr>
    <td>Q (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>discharge</td>
  </tr>
  <tr>
    <td>Q<sub>A</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>discharge at time T<sub>A</sub></td>
  </tr>
  <tr>
    <td>Q<sub>B</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>discharge at time T<sub>B</sub></td>
  </tr>
  <tr>
    <td>Q<sub>lim</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>upper limit of the application range of function g(Q)</td>
  </tr>
  <tr>
    <td>Q<sub>m</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>average of observed discharges</td>
  </tr>
  <tr>
    <td>Q<sub>max</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>upper limit of the calibration range of function g(Q)</td>
  </tr>
  <tr>
    <td>Q<sub>min</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>lower limit of the calibration range of function g(Q)</td>
  </tr>
  <tr>
    <td>Q<sub>0</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>discharge at the beginning of a recession sequence</td>
  </tr>
  <tr>
    <td>Q<sub>s</sub> (l·s<sup>-1</sup>·km<sup>-2</sup>)</td>
    <td>specific discharge (discharge per unit of drained area)</td>
  </tr>
  <tr>
    <td>Q<sub>sm</sub> (l·s<sup>-1</sup>·km<sup>-2</sup>)</td>
    <td>mean interannual specific discharge</td>
  </tr>
  <tr>
    <td>Q<sub>thr</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>minimum discharge required to account for the observed values of K</td>
  </tr>
  <tr>
    <td>r (-)</td>
    <td>exponent of time used in the Otnes model</td>
  </tr>
  <tr>
    <td>R<sub>a</sub></td>
    <td>rank of a recession model for a given station, between 1 for the best (maximum C<sub>NSE</sub>) and 5 for the worst (minimum C<sub>NSE</sub>)</td>
  </tr>
  <tr>
    <td>R<sub>c</sub></td>
    <td>chronological rank of K modeled</td>
  </tr>
  <tr>
    <td>R<sub>rmse</sub></td>
    <td>relative standard error of the discharges forecast per recession model, for a given time horizon</td>
  </tr>
  <tr>
    <td>S (-)</td>
    <td>homothety slope between hydrographs of distinct recession sequences</td>
  </tr>
  <tr>
    <td>S<sub>e</sub> (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>standard error of the discharge forecasts calculated by a recession model, for a given horizon H</td>
  </tr>
  <tr>
    <td>T (d)</td>
    <td>time</td>
  </tr>
  <tr>
    <td>T<sub>A</sub> (d)</td>
    <td>initial time</td>
  </tr>
  <tr>
    <td>T<sub>B</sub> (d)</td>
    <td>initial time</td>
  </tr>
  <tr>
    <td>T<sub>b</sub> (d)</td>
    <td>date of the oldest K observed during an uninterrupted sequence of recession</td>
  </tr>
  <tr>
    <td>T<sub>r</sub> (d)</td>
    <td>time translation duration</td>
  </tr>
  <tr>
    <td>T<sub>0</sub> (d)</td>
    <td>initial time, used in the Maillet and Tison formulas</td>
  </tr>
  <tr>
    <td>T<sub>1</sub> (d)</td>
    <td>usual start date of the recession period, expressed in "dd/mm" format</td>
  </tr>
  <tr>
    <td>T<sub>2</sub> (d)</td>
    <td>usual end date of the recession period, expressed in "dd/mm" format</td>
  </tr>
  <tr>
    <td>V (m<sup>3</sup>)</td>
    <td>remaining water volume in a reservoir used in the Coutagne theory</td>
  </tr>
  <tr>
    <td>W (m<sup>3</sup>·s<sup>-1</sup>)</td>
    <td>constant used in the generalized Maillet and generalized Coutagne formulas. If positive, it is the theoretical value of the discharge reached after an infinite time during a recession phase</td>
  </tr>
  <tr>
    <td>Z (m<sup>3</sup>(1<sup>-m</sup>)·s<sup>-1</sup>)</td>
    <td>proportionality constant between Q and V<sup>m</sup> in the Coutagne theory</td>
  </tr>
  <tr>
    <td>α (d<sup>-1</sup>)</td>
    <td>positive recession coefficient, used in the Maillet formula (exponential form)</td>
  </tr>
</table>
<table>
   <tr>
    <td>
     β (d<sup>-p</sup>)
    </td>
    <td>
     positive recession coefficient, used in the Horton formula
    </td>
   </tr>
   <tr>
    <td>
     λ (m<sup>3</sup>·s<sup>-1</sup>·d<sup>p</sup>)
    </td>
    <td>
     parameter used in the Otnes model
    </td>
   </tr>
   <tr>
    <td>
     μ (m<sup>3</sup>·s<sup>-1</sup>)
    </td>
    <td>
     parameter used in the Otnes model
    </td>
   </tr>
   <tr>
    <td>
     σ<sub>0</sub> (d<sup>-1</sup>)
    </td>
    <td>
     positive recession coefficient, used in the Tison and Coutagne formulas
    </td>
   </tr>
  </table>

References

1. Roche, M. *Hydrologie de Surface*; Gauthier-Villars/ORSTOM: Paris, France, 1963; p. 430.

2. Hall, F.R. Base Flow Recessions—A review. *Water Resour. Res.* **1968**, *4*, 973–983. [CrossRef]

3. Tallaksen, L.M. A Review of Baseflow Recesslon Analysis. J. Hydrol. **1995**, *165*, 349–370. [CrossRef]

4. Boussinesq, J. Recherches théoriques sur l'écoulement des nappes d'eau infiltrées dans le sol et sur le débit des sources. J. Math. Pure Appl. **1904**, *10*, 5–78.

5. Lang, C. Etiages et Tarissements: Vers Quelles Modélisations ? L'approche Conceptuelle et L'analyse Statistique en Réponse à la Diversité Spatiale des Ecoulements en Etiage des Cours d'eau de l'Est Français; Thèse de l'université Paul Verlaine de Metz: Metz, France, 2007. Available online: https://tel.archives-ouvertes.fr/tel-00534656/document (accessed on 3 January 2014).

6. Barnes, B.S. The structure of discharge-recession curves. Trans. Am. Geophys Union **1939**, *20*, 721–725. [CrossRef]

7. Maillet, E. Essai d'hydraulique Souterraine et Fluviale; Herman, A., Ed.; Libraire Sci. Hall: Paris, France, 1905.

8. Tison, G. Courbe de Tarissement, Coefficient D'écoulement et Perméabilité du Bassin; Mém. A.I.H.S.: Helsinki, Finland, 1960; pp. 229–243.

9. Coutagne, A. Meteorologie et Hydrologie. Etude Générale des Variations de Débit en Fonction des Facteurs qui les Conditionnent. 2me Partie. Les Variations de Débit en Période non Influencée par les Précipitations. Le Débit D'infiltration (Correlations Fluviales Internes); La Houille Blanche: Grenoble, France, 1948; pp. 416–436. Available online: https://www.shf-lhb.org/articles/lhb/pdf/1948/07/lhb1948053.pdf (accessed on 24 June 2019).

10. Carlier, M. *Hydraulique Générale et Appliquée*; Eyrolles: Paris, France, 1972; p. 565.

11. Thomson, S.H. Hydrologic conditions in the chalk at Compton, West-Sussex. Trans. Inst. Water Eng. **1921**, *26*, 228–261.

12. Wicht, C.L. Determination of the effects of watershed-management on mountain streams. Trans. Am. Geophys. Union **1943**, *24*, 594–606. [CrossRef]

13. Toebes, C.; Strang, D.D. On recession curves, 1-Recession equations. J. Hydrol. NZ **1964**, *3*, 2–15.

14. Radczuk, L.; Szarska, O. Use of the flow recession curve for the estimation of conditions of river supply by underground water. IAHS Publ. **1989**, *187*, 67–74.

15. Clausen, B. Modelling streamflow recession in two Danish streams. Nord. Hydrol. **1992**, *23*, 73–88. [CrossRef]

16. Padilla, A.; Pulido-Bosh, A.; Mangin, A. Relative importance of baseflow and quickflow from hydrographs of karst spring. Ground Water **1994**, *32*, 267–277. [CrossRef]

17. Otnes, J. Uregulerte elvers vassføring i tørrværsperioder. Nor. Geogr. Tidsskr. **1953**, *14*, 210–218. [CrossRef]

18. Otnes, J. Tørrværskurven. In *Hydrologi i Praksis*; Otnes, J., Ræstad, E., Eds.; Ingeniørforlaget: Oslo, Norway, 1978; pp. 227–233.

19. Gjørsvik, O.G. Grosetbekken. En Vurdering av Vannbalansen; NVE Rep. 2, Part I, 1970; Norwegian Water and Energy Admin: Oslo, Norway, 1970.

20. Andersen, T. En Undersøkelse av Grunnvannsmagasinet i et Representativt Høyfjellsområde. Master's Thesis, University of Oslo, Oslo, Norway, 1972.

21. Tjomsland, T.; Ruud, E.; Nordseth, K. The physiographic influence on recession runoff in small Norwegian rivers. Nord. Hydrol. **1978**, *9*, 17–30. [CrossRef]

22. Horton, R.E. The role of infiltration in the hydrologic cycle. Trans. Am. Geophys. Union **1933**, *14*, 446–460. [CrossRef]

23. Werner, P.W.; Sundquist, K.J. On the groundwater recession curve for large watersheds. IAHS Publ. **1951**, *33*, 202–212.

24. Pereira, L.S.; Keller, H.M. Recession characteristics of small mountain basins, derivation of master recession curves and optimization of recession parameters. IAHS Publ. **1982**, *138*, 243–255.

25. Nutbrown, D.A. Normal mode analysis of the linear equation of groundwater flow. Water Resour. Res. **1975**, *11*, 979–987. [CrossRef]
26. Petras, I. An approach to the mathematical expression of recession curves. *Water S. Afr.* **1986**, *12*, 145–150.

27. Ishihara, T.; Takagi, F. A study of the variation of low flow. *Disaster Prev. Res. Inst. Kyoto Univ. Bull.* **1965**, *15*, 75–98.

28. Dewandel, B.; Lachassagne, P.; Bakalowicz, M.; Weng, P.; Al-Malki, A. Evaluation of aquifer thickness by analysing recession hydrographs. Application to the Oman ophiolite hard-rock aquifer. *J. Hydrol.* **2003**, *274*, 248–269. [CrossRef]

29. Langbein, W.B. Some channel-storage studies and their application to the determination of infiltration. *Trans. Am. Geophys. Union* **1938**, *19*, 435–445. [CrossRef]

30. Knisel, W.G. Baseflow recession analysis for comparison of drainage basin and geology. *J. Geophys. Res.* **1963**, *68*, 3649–3653. [CrossRef]

31. Lebaut, S. *L'apport de l'analyse et de la Modélisation Hydrologiques de Bassins Versants Dans la Connaissance du Fonctionnement d'un Aquifère: Les Grès d'Ardenne-Luxembourg*; Thèse de l'université de Metz: Metz, France, 2000. Available online: http://docnum.univ-lorraine.fr/public/UPV-M/Theses/2000/Lebaut-Sebastien.LMZ0010.pdf (accessed on 2 October 2019).

32. Federer, C.A. Forest transpiration greatly speeds streamflow recession. *Water Resour. Res.* **1973**, *9*, 1599–1604. [CrossRef]

33. Bako, M.D.; Hunt, D.N. Derivation of baseflow recession constant using computer and numerical analysis. *Hydrol. Sci. J.* **1988**, *33*, 357–367. [CrossRef]

34. Brutsaert, W.; Nieber, J.L. Regionalized drought flow hydrographs from a mature glaciated plateau. *Water Resour. Res.* **1977**, *13*, 637–643. [CrossRef]

35. Troch, P.A.; De Troch, P.; Brutsaert, W. Effective water table depth to describe initial conditions prior to storm rainfall in humid regions. *Water Resour. Res.* **1993**, *29*, 427–434. [CrossRef]

36. Vogel, R.M.; Kroll, C.N. Regional geohydrologic-geomorphic relationships for the estimation of low flow statistics. *Water Resour. Res.* **1992**, *28*, 2451–2458. [CrossRef]

37. Zecharias, Y.B.; Brutsaert, W. Recession characteristics of groundwater outflow and base flow from mountainous watersheds. *Water Resour. Res.* **1988**, *24*, 1651–1658. [CrossRef]

38. Lang, C.; Gilles, E. Une méthode d'analyse du tarissement des cours d'eau pour la prévision des débits d'étiage. *Norois* **2006**, *201*, 31–43. [CrossRef]

39. Bader, J.C.; Cauchy, S.; Duffar, L.; Saura, P. *Monographie Hydrologique du Fleuve Sénégal: De L'origine des Mesures Jusqu'en 2011*; Bader, J.C., Ed.; IRD: Marseille, France, 2015; pp. 79–920, ISBN 978-2-7099-1885-5.

40. Rochette, C.; Camus, H.; Danuc, R.; Pereira-Barreto, S. *Le Bassin du Fleuve Senegal. Monographies Hydrologiques*, 1; ORSTOM: Paris, France, 1974; p. 440, ISBN 2-7099-0344-X.

41. Brunet-Moret, Y.; Chaperon, P.; Lamagat, J.P.; Molinier, M. *Monographie Hydrologique du Fleuve Niger*; Monographies hydrologiques, 8; ORSTOM: Paris, France, 1986; pp. 402–510.

42. Lamagat, J.P.; Albergel, J.; Bouchez, J.M.; Descroix, L. *Monographie Hydrologique du Fleuve Gambie*; ORSTOM, OMVG: Dakar, Sénégal, 1990; p. 247.

43. Vauchel, P.; Guiguen, N.; Gomis, D.; Konaté, L. *Appui Institutionnel Aux Brigades Régionales du Ministère de L'hydraulique: Rapports D'avancement de Septembre 1998 à Septembre 2000*; IRD, SGPRE: Dakar, Sénégal, 2000; p. 88.

44. Olivry, J.C. *Etudes Régionales Sur Les Basses Eaux, Les Effets Durables du Déficit des Précipitations Sur Les Etiages et Les Tarissements en Afrique de L'ouest et du Centre*; XIIèmes journées hydrologiques de l'ORSTOM: Montpellier, France, 1996.

45. Bricquet, J.P.; Bamba, F.; Mahé, G.; Toure, M.; Olivry, J.C. Evolution récente des ressources en eau de l'Afrique atlantique. *Revue des Sciences de l'eau* **1997**, *3*, 321–337. [CrossRef]

46. Bricquet, J.P.; Mahé, G.; Bamba, F.; Olivry, J.C. Changements climatiques récents et modification du régime hydrologique du fleuve Niger à Koulikouro (Mali). *L'hydrologie Tropicale: Géoscience et Outil Pour le Développement*. 1995, Volume 238. Available online: https://books.google.fr/books?hl=fr&lr=&id=azUCAebIN-YC&oi=fnd&pg=PA157&dq=46.%09Bricquet,+J.P.%3B+Mah% C3%A99,+G.%3B+Bamba,+F.%3B+Olivry,+J.C.+Changements+climatiques+r%C3%A9cents+et+modification+du+r%C3%A9gime+hydrologique+du+fleuve+Niger++% C3%A0+Koulikouro+(Mali)&ots=MXLgArm6vz&sig=QUNj1kfsu8aHq4b-ivKMTMR0eIl#v=onepage&q&f=false (accessed on 8 June 2020).
47. Mahé, G.; Olivry, J.C.; Dessouassi, R.; Orange, D.; Bamba, F.; Servat, E. Relations eaux de surface-eaux souterraines d'une rivière tropicale au Mali. C.R. Acad. Sci. **2000**, *330*, 689-692. [CrossRef]

48. L'Hôte, Y.; Mahé, G. *Afrique de L'ouest et Centrale: Précipitations Moyennes Annuelles (Période 1951-1989)*; ORSTOM: Paris, France, 1996. Available online: https://horizon/documentation.ird.fr/exl-doc/pleins_textes/divers16-08/010058020.pdf (accessed on 24 August 2020).

49. Descroix, L.; Diongue, N.A.; Panthou, G.; Bodian, A.; Sane, Y.; Dacosta, H.; Malam, A.M.; Vandervaere, J.-P.; Quantin, G. Evolution récente de la pluviométrie en Afrique de l'ouest à travers deux régions: La Sénégambie et le bassin du Niger moyen. *Climatologie* **2015**, *12*, 25-43. [CrossRef]

<figure><img src="image_26.png" /></figure>

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Article

# Climate and Extreme Rainfall Events in the Mono River Basin (West Africa): Investigating Future Changes with Regional Climate Models

Ernest Amoussou 1,2,3,4,*, Hervé Awoye 5,6, Henri S. Totin Vodounon 1,2, Salomon Obahoundje 3, Pierre Camberlin 4, Arona Diedhiou 3,7, Kouakou Kouadio 3,8,9, Gil Mahé 10, Constant Houndénou 2 and Michel Boko 2

Received: 28 November 2019; Accepted: 21 January 2020; Published: 16 March 2020

**Abstract:** This study characterizes the future changes in extreme rainfall and air temperature in the Mono river basin where the main economic activity is weather dependent and local populations are highly vulnerable to natural hazards, including flood inundations. Daily precipitation and temperature from observational datasets and Regional Climate Models (RCMs) output from REMO, RegCM, HadRM3, and RCA were used to analyze climatic variations in space and time, and fit a GEV model to investigate the extreme rainfalls and their return periods. The results indicate that the realism of the simulated climate in this domain is mainly controlled by the choice of the RCMs. These RCMs projected a 1 to 1.5 °C temperature increase by 2050 while the projected trends for cumulated precipitation are null or very moderate and diverge among models. Contrasting results were obtained for the intense rainfall events, with RegCM and HadRM3 pointing to a significant increase in the intensity of extreme rainfall events. The GEV model is well suited for the prediction of heavy rainfall events although there are uncertainties beyond the 90th percentile. The annual maxima of daily precipitation will also increase by 2050 and could be of benefit to the ecosystem services and socioeconomic activities in the Mono river basin but could also be a threat.

**Keywords:** Mono basin; extreme rainfall events; ENSEMBLE; regional climate models

<footnote n="1">1 Département de Géographie et Aménagement du Territoire, Université de Parakou, Parakou BP 123, Benin; sourouhenri@yahoo.fr</footnote>

<footnote n="2">2 Laboratoire Pierre PAGNEY, Climat, Eau, Ecosystème et Développement (LACEEDE), Université d'Abomey-Calavi, Cotonou 03 BP1122, Benin; constant500@yahoo.fr (C.H.); bokomichel@gmail.com (M.B.)</footnote>

<footnote n="3">3 African Centre of Excellence on Climate Change, Biodiversity and Sustainable Development, Université Félix Houphouët Boigny (UFHB), 22 B.P. 582 Abidjan 22, Cote D'Ivoire; obahoundjes@yahoo.com (S.O.); arona.diedhiou@ird.fr (A.D.); kk.kouadio@yahoo.fr (K.K.)</footnote>

<footnote n="4">4 Centre de Recherches de Climatologie (CRC), Biogéosciences, Université de Bourgogne, 6 boulevard Gabriel, F-21000 Dijon, France; camber@u-bourgogne.fr</footnote>

<footnote n="5">5 Laboratoire d'Hydraulique et de Maîtrise de l'Eau (LHME), Université d'Abomey-Calavi, Cotonou 01 BP 526, Benin; herve.awoye@gmail.com</footnote>

<footnote n="6">6 Department of Geography, University of Calgary, Calgary, AB T2N 1N4, Canada</footnote>

<footnote n="7">7 Institute of Research for Development IRD, CNRS, Grenoble INP, IGE, University Grenoble Alpes, F-38000 Grenoble, France</footnote>

<footnote n="8">8 Laboratory of Atmosphere Physics and Fluid Mechanics, UFHB, 22 BP 582 Abidjan 22, Cote D'Ivoire</footnote>

<footnote n="9">9 Geophysical Station of Lamto (GSL), N'Douci BP 31, Cote D'Ivoire</footnote>

<footnote n="10">10 IRD, Laboratoire HydroSciences de Montpellier, Université de Montpellier 2, Case courrier MSE, Place Eugène Bataillon, 34095 Montpellier CEDEX 5, France; gil.mahe@ird.fr</footnote>

<footnote>* Correspondence: ernestamoussou@gmail.com; Tel.: +229-95064746</footnote>
# 1. Introduction

Climate change represents the latest in a series of environmental drivers of human conflict that have been identified in recent decades, following others, including drought, desertification, land degradation, failing water supplies, deforestation, fisheries depletion, and even ozone depletion [1]. Extreme hydroclimatic events, such as heavy rainfall, floods, and droughts, have detrimental effects on local populations and their socioeconomic environment. With the projected increase in the atmospheric greenhouse gases concentration, it is important to investigate the future evolution of the frequency and intensity of these extreme events [2–4]. In this respect, sub-Saharan Africa is greatly concerned because the populations are highly vulnerable and hydroclimatic phenomena are responsible for the majority of the reported victims of the natural hazards the region has experienced [5]. In the Gulf of Guinea, the Mono river basin, which extends over Benin and Togo, is influenced by two types of climate: A subequatorial climate in the south and a tropical wet climate over the rest of the watershed to the north. This climatic pattern is constrained by the seasonal shift of the Intertropical Convergence zone and associated lower and upper tropospheric flows over West Africa [2]. Interannual variations of these features as well as short-term rainfall and temperature variations result in a succession of drought and flood events. With ongoing global warming, we may experience an increase in rainfall intensity in the watershed [6]. Indeed, previous studies reported more frequent extreme rainfall events in many regions of the world and predicted increases in the future flood frequency in the West African Sahel [4,7].

The climate degradation could generate conflicts of water resource usage mainly in the transboundary basins. As most West African basins are trans-boundaries, this could be a source of conflict among different sectors of water users [8,9]. Brown and Crawford [10] proved that climate change has increased the conflict risk in trans-boundaries river basins like Volta shared by Burkina and Ghana. Additionally, as West African sub-Saharan agriculture systems are mainly rainfed agriculture systems, then any change or variation in rainfall could affect the production, and consequently lead to food insecurity. Moreover, the increase in temperature could accelerate the evaporative loss, and thus increase water competition [11–13].

Climate change impacts were previously assessed using raw simulations from global climate models (GCMs), which operate at coarse spatial resolutions ranging from 150 to 400 km [14–17]. Thus, the information generated by these models does not always match ground observations because GCMs do not explicitly consider the spatial heterogeneity of land surface conditions [18]. In addition, these models impose limits on the representation of certain atmospheric phenomena (e.g., mesoscale processes, localized orographic ascendancy, etc.) [18,19]. The expected changes derived from GCM simulations should be considered with caution for climate impact and adaptation studies [3,20]. A more convenient way of assessing climate change impact on water resources, ecosystems, and agriculture is to use global climate model projections downscaled at a finer scale [21–24]. Many statistical approaches are used to downscale the coarse resolution GCM simulations and better account for the local or regional effects of topography, land use, and other forcings [3,17,25,26]. An alternative to statistical downscaling is dynamical downscaling with regional climate models (RCMs). With their higher spatial resolution as compared to GCMs, RCMs account for greater topographic diversity and more localized atmospheric dynamics [27]. Their ability to reproduce the main characteristics of hydro-climatological dynamics during extreme rainfall events has been demonstrated [28]. This good performance is mainly due to the higher spatial resolution of RCMs that better match the spatial scales at which mesoscale convective processes occur [29]. Despite these improvements, we still need to validate the RCM simulations before using them for climate change impact studies because they still feature systematic biases, which vary substantially from one model to another.

The aims of this paper were to assess the historical and future changes in key climatic variables (e.g., near-surface air temperature and precipitation, extreme rainfall) in the Mono river basin and derive conclusions regarding their impact on flood dynamics in the watershed upstream of the hydroelectric dam of Nangbéto. The RCM simulations over West Africa developed in the frame of the European
project ENSEMBLES, CMIP5, and CORDEX-Africa. We assessed the performance of four RCMs to reproduce the mean air temperature, precipitation, and extreme rainfall events. An analysis of the changes in these climatic variables over 2028–2050 as projected by each RCM is presented, with an emphasis on the frequency and intensity of daily rainfall events. The selected RCMs were driven by two GCMs in order to assess the robustness of the simulations and the role of large and regional scales in the model differences. However, for this typical work, it was applied to a small watershed scale, like the Mono river basin.

This work is structured as follows: The study area is described followed by the used data; the statistical methods used for data analysis are presented as well; next, the results focus on the relevance of climatic fields and regimes simulated by the selected RCMs, the expected changes in mean near-surface air temperature, mean precipitation, the frequency and return periods of extreme rainfall events, and their potential impacts on the catchment hydrology and; finally, the results are discussed and some perspectives are highlighted.

## 2. Study Area

The Mono river basin is in West Africa and extends over 560 km from the north to the south [2]. This transboundary watershed covers 15,680 km² and is shared by Benin and Togo (Figure 1). This watershed is home to the Nangbéto hydroelectric dam that has been providing electricity to Benin and Togo since September 1987. As this hydroelectric dam is modifying the hydrology of the river, the main part of this study will focus on the Mono river basin upstream of the dam.

This watershed is patterned in the south by floodplains and plateaus, and higher landforms in the north and north-west, e.g., the Atakora Mountains with a height of 800 m and their southern extensions that are the Togo mountains.

Precipitation in Togo and Benin is constrained by the organization of the atmospheric circulation over West Africa as a whole, i.e., both that of the lower layers (humid monsoon flow from the southwest, and dry Harmattan flow from the northeast) and the flow of air in the lower troposphere and upper atmosphere (respectively African Easterly Jet (AEJ) and Tropical Easterly Jet (TEJ)) [2]. At the scale of the Mono river basin, this circulation is strongly linked to the energy gradients between the coastal plain and the Gulf of Guinea. The precipitations are also modulated by the interaction of the southwesterly humid monsoon flow and the landforms in the northwestern part of the watershed. The average annual precipitation ranges from 900 mm in the southeast, i.e., in the plains along the dry diagonal in the south of Togo, to 1200 mm in the northwestern uplands. There are two climatic domains in the basin: The subequatorial domain in the southern part of the basin with two rainy and two dry seasons and the tropical domain in the northern part with one rainy season and one dry season.

The hydrological regime is of a humid tropical type and consistent with the tropical climate that governs it. The uneven distribution of precipitation combined with heavy rainfall events over very short periods leads to recurring flooding events. These phenomena are aggravated by the increase in surface runoff due to land cover degradation [30]. As a result, the local population or riparian and their properties and livelihoods are more vulnerable than the population living upstream of the basin as evidenced by the severe floods of the past 12 years in the lower valley of the Mono river basin.
<figure><img src="image_27.png" /><figcaption>**Figure 1.** Location of the rainfall (blue triangles) and hydrometric stations (red dots) in the Mono river basin between Benin and Togo.</figcaption></figure>

# 3. Materials and Methods

## 3.1. *Observational Climate Data*

We used daily rainfall data from 14 rain gauge stations located in the Mono river basin and its close vicinity, and daily near-surface air temperature from two meteorological stations, namely the Bohicon and Nangbéro stations. Those observed data were used to select the closest model to the
observation (reality) for projection. Thus, the model closest to the reality was used. The data cover a 50-year period (1961–2010) and are provided by the Agency for the Air Navigation Safety in Africa and Madagascar (ASECNA) in Cotonou—Benin, the Direction de la Météorologie Nationale (DMN) of Togo, the Climatology Research Centre (CRC) of the University of Bourgogne in France, and the Global Historical Climate Network (GHCN, [31]).

We compared the gauged rainfall data with the gridded data from the RCM models. The rain-gauge data were spatially interpolated to a 0.5° resolution upstream of the Nangbéto hydro-electric dam using an ordinary kriging block (Figure 1). A climatological variogram was considered and an adjustment was made to a spherical variogram [22]. The range parameter of the adjusted model is 65 km and indicates the average distance of precipitation decorrelation between two stations. In contrast, the arithmetic mean of the two observed air temperature stations data was made and then used to compare to the model dataset.

In order to describe the climates that prevail in West Africa and compare them with the RCM simulations, gridded monthly data of precipitation and near-surface air temperature from 3 additional datasets were extracted over the region extending over 5–14° N and 1.2–3° E. These sets of data covering the years from 1988 to 2009 at a 0.5° spatial resolution are the GPCP Global Precipitation Climatology Project data [32], the near-surface air temperature data from CRU (Climatic Research Unit, [33]). The CRU data is chosen based on its multidiscipline application, namely in applied climatology, biogeochemical modelling, hydrology, and agricultural meteorology domains [33] and its performance [34].

## 3.2. Data from Regional Climate Models

Precipitation and near-surface air temperature data from the selected four RCMs developed in the framework of the ENSEMBLES European project [35] are listed in Table 1. They are extracted from the AMMA-ENSEMBLES database [17]. These RCMs simulations are centered on West Africa (19.8° S–35.2° N and 35.2° W–31.2° E), have a horizontal resolution of 50 km, and cover the period 1951–2050 (1980–2050 for the ICTP model). These RCMs simulations are driven by two CMIP3 global climate models (GCMs), namely ECHAM5 for MPI and ICTP models and HadCM3 for HC (METO) and SMHI models, following the IPCC A1B scenario. We used these RCM simulations at a daily time step for a region extending over 5–14° N and 1.2° W–3° E. METO and SMHI simulations follow a 360-day calendar. The 18-year period spanning 1988–2005 was used for the comparison of the precipitation, and air temperature RCMs data with observations (GPCP for precipitation and CRU for temperature) were considered for the air temperature.

<table><caption>Table 1. Selected models.</caption><thead><tr><th rowspan="2">Model Number</th><th colspan="2">Regional Climate Model (RCM)</th><th colspan="2">Driving Global Climate Model (GCM)</th></tr><tr><th>RCM</th><th>Modeling Agency</th><th>GCM</th><th>Modeling Agency</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center;">CORDEX</td></tr><tr><td>(1)</td><td>REMO</td><td>GERICS</td><td>CM5A-LR</td><td>IPSL</td></tr><tr><td>(2)</td><td>RegCM4-3</td><td>ICTP</td><td>MPI-ESM-MR</td><td>MPI-M</td></tr><tr><td>(3)</td><td>REMO</td><td>MPI-CSC</td><td>MPI-ESM-LR</td><td>MPI-M</td></tr><tr><td>(4)</td><td>SMHI</td><td>RCA4</td><td>CNRM-CERFACS</td><td>CNRM-CM5</td></tr><tr><td>(5)</td><td>SMHI</td><td>RCA4</td><td>CM5A-MR</td><td>IPSL</td></tr><tr><td>(6)</td><td>SMHI</td><td>RCA4</td><td>MPI-ESM-LR</td><td>MPI-M</td></tr><tr><td colspan="5" style="text-align: center;">CMIP5</td></tr><tr><td>(7)</td><td></td><td></td><td>CM5</td><td>CNRM</td></tr><tr><td>(8)</td><td></td><td></td><td>CM5A-LR</td><td>IPSL</td></tr><tr><td>(9)</td><td></td><td></td><td>CM5A-MR</td><td>IPSL</td></tr><tr><td>(10)</td><td></td><td></td><td>ESM-LR</td><td>MPI</td></tr><tr><td>(11)</td><td></td><td></td><td>ESM-MR</td><td>MPI</td></tr></tbody></table>
<table><caption>Table 1. *Cont.*</caption><thead><tr><th rowspan="3">Model Number</th><th colspan="2">Regional Climate Model (RCM)</th><th colspan="2">Driving Global Climate Model (GCM)</th></tr><tr><th>RCM</th><th>Modeling Agency</th><th>GCM</th><th>Modeling Agency</th></tr><tr><th colspan="2">AMMA-ENSEMBLES</th><th colspan="2">Scenario</th></tr></thead><tbody><tr><td>(12)</td><td>RegCM3</td><td>ICTP</td><td>ECHAM5</td><td>A1B</td></tr><tr><td>(13)</td><td>HIRHAM</td><td>METNO</td><td>HadCM3</td><td>A1B</td></tr><tr><td>(14)</td><td>REMO</td><td>MPI-M</td><td>ECHAM</td><td>A1B</td></tr><tr><td>(15)</td><td>RCA</td><td>SMHI</td><td>HadCM3</td><td>A1B</td></tr></tbody></table>

NB: MPI-M—Max Planck Institute of Meteorology; MPI-CSC—Climate Service Center, Max Planck Institute for Meteorology; ICTP—International Centre for Theoretical Physics; SMHI—Swedish Meteorological and Hydrological Institute; CNRM—Centre National de Recherches Météorologiques; REMO—Regional Climate Model; RegCM—Regional Climate Model; RCA—Rossby Centre regional atmospheric model; GERICS—Climate Service Center Germany; HadCM3—Hadley Centre Coupled Model.

It is important to note that for the next step, International Centre for Theoretical Physics will be called (ICT); Swedish Meteorological and Hydrological Institute by SMH; Max Planck Institute of Meteorology by MPI, and Hadley Centre Coupled Model by METO.

We extracted the CORDEX, CMIP5, and AMMA-ENSEMBLES outputs over the Mono river basin at the outlet of Nangbéto, computed the spatial ensemble averages of each data type, and compared them with the interpolated (observed) data. Since the streamflow gauge data recorded are only available over 1988–2010, we used the period 1988 to 2010 (23 years) as the reference period and the period 2028 to 2050 (23 years) as the scenario period.

### 3.3. Statistical Methods

Observed and simulated climate data were analyzed for the sub-region and the Mono river basin itself. At the sub-regional scale, seasonal average maps were used to compare simulated precipitation and mean air temperature fields with the observational data over 1988–2010, and to assess the projected future changes for 2028–2050. The RCM whose outputs in the reference period is closer to observations can be considered for future projection.

At the catchment scale, the observed and simulated climate data were also spatially averaged and statistically processed. First, monthly averages of rainfall and air temperature were computed to describe the ability of the regional climate models to reproduce the present-day climatic regimes and to assess the projected future changes (2028–2050). The average frequency of the number of rainy days (i.e., a day with a rainfall amount higher than 1 mm) in each grid point in the Mono river basin was also computed. The contribution of the different classes of daily rainfall intensity to the total precipitation recorded on average in the watershed was determined from the calculation of deciles. The 99th percentile is usually used to characterize the extreme events [36–39]. This is the reason why the 99th percentile is used to assess the importance of heavy rains in the basin.

Observed hydroclimatic series do not always meet the assumption of data stationarity [40,41]. This is often the case for extreme rainfall and flood discharge. In the literature, some scholars [42,43] have suggested describing the distribution of extreme values with three different types of probability distribution for extreme order statistics while others [44–47] suggested using a generalized extreme value (GEV) distribution, which combines the three types of Fisher–Tippett extreme value distributions [48]. The GEV parameters use the generalized maximum likelihood (GML) method, which includes an additional constraint on the shape parameter to eliminate potentially invalid values of this parameter based on Tramblay et al.’s [4] study.

In this study, we used a GEV distribution to characterize extreme events. In the case of non-stationarity, the GEV parameters are not constant but are dependent on time or other covariates. To avoid having a value of zero for the scale parameter, $\alpha t$, we considered the parameterization as $\phi t = \log(\alpha t)$ and thus restricted our analysis to linear dependencies [49]. However, many other types of dependencies can be linearized [41,44,48,50].
The return periods of a GEV model are defined by the cumulative distribution function (CDF), F(x), or the probability density function (PDF), f(x), hat are given by the formula:

$$F(x) = \text{Pr}[X \le x] \text{ and } f(x) = \frac{dF(x)}{dx}, \qquad (1)$$

where Pr is the probability of the occurrence of an event and X stands for the random variable, which in this case is a series of annual daily maxima of rainfall. The quantile value, Q_T, is a magnitude of the extreme event that has a probability of 1/T and can be exceeded by a single event. A return period, T, associated with a quantile value, Q_T, was adapted from Stedinger et al.’s [51] equation and can be expressed as:

$$T = \frac{1}{[1 - F(Q_T)]} \qquad (2)$$

The selection of the best GEV model adjustment was made by using the deviance test, which is based on the log-likelihood [20].

# 4. Results and Discussion

## 4.1. Spatial Distribution of the Annual Rainfall and Air Temperature for Three Datasets

Figures 2 and 3 present the ensemble average annual rainfall and mean air temperature for the historical period 1988–2005 (first column) and change between the reanalysis (GPCP) and models in (second column) the historical period as well as the projected changes for 2028–2050 (third column).

The spatial distribution of the observed rainfall (1988–2005 annual rainfall average, GPCP data) in the Mono river basin and surrounding areas is presented in Figure 2d. The observed rainfall pattern shows a diagonal axis of a high rainfall amount (over 1320 mm per year) from south-west to north-east along with the Togo and Atakora mountain ranges. A strong decrease in rainfall is also shown in the north towards the Sahelian zone (<600 mm/year). The GPCP reanalysis data captures the observed precipitation gradient over West Africa well [52] and this finding agrees with the study of Ntajal et al. [49] in Mono basin.

The ensemble averages were computed for CMIP5 and RCP8.5 for CORDEX. The CORDEX (Figure 2c) and CMIP5 (Figure 2b) display a greater rainfall estimation in the historical period compared to the AMMA-Ensemble (Figure 2a) and GPCP (Figure 2d), especially at the southern part. The validation made (second column of Figure 2) exhibits that CMIP5 and CORDEX overestimate the rainfall, which is about 340 mm/year. Nevertheless, the AMMA-Ensemble gives an estimation closer to the reanalysis (±20 mm/year).

There is a projected general decrease varying by 16 to 32 mm in the annual total precipitation. For instance, the CMIP5 model presents a decrease of about 24 mm and less than 24 mm, respectively, in the central and southern parts of the basin while the CORDEX estimates a decrease between 24 and 32 mm in the central and southern part of the basin. Nevertheless, in the northern part of the basin, an increase in the annual total precipitation of around 16 mm and in the range of 16 to 24 mm for the CMIP5 and CORDEX models, respectively, is projected. Finally, the AMMA-ENSEMBLES displays a decrease in the projection change ranging from 0 to 32 mm/year.

The temperature gradient was well shown by all the datasets, which increase in the northern direction (first column of Figure 3). The observed mean air temperature extracted from Climate Research Unit (CRU) varies slightly, with a maximum of 29.5 °C in the far north (the Sahel in Niger) and a minimum of 26 °C in altitude on the Togolese ridge (Figure 3d). The AMMA-Ensemble and CORDEX data give an underestimation of the temperature ranging from 0 to 1 °C while the CMIP5 presents an underestimation between 1 and 2 °C (second column of Figure 3) and the lowest rise is given by AMMA-ENSEMBLES. Unlike the rainfall, there is a very good agreement in the projected changes (increase) of air temperature from the AMMA-Ensemble, CMIP5, and CORDEX dataset.
The warming is expected to vary between 1.4 °C in the south to 1.8 °C towards the north. However, AMMA-ENSEMBLES gives the lowest projected changes among all the models (third column).

The performance of CORDEX RCMs in simulating the spatial distribution of the main precipitation and temperature features as well as the occurrence of other physical phenomena over West Africa was demonstrated by Gbobaniyi et al. [53]. Diallo et al. [54] also showed the importance of the ensemble mean of multiple models. They proved that the RCMs-GCMs alone are biased and these biases are reduced by averaging all RCM simulations, suggesting that multi-model RCM ensembles based on different driving GCMs help to compensate systematic errors from both the nested and the driving models [54]. This justified the use of multiple models. According to IPCC assessment reports, the temperature is projected to increase over West Africa for the end of the 21st century from the global climate simulation range between 3 and 6 °C above the late 20th century baseline depending on the emission scenario [55]. However, they also revealed that the onset and length of precipitation could also change.

<figure><img src="image_28.png" /><figcaption>**Figure 2.** Ensemble average annual mean rainfall for 1988–2005 (first column), validation (second column over 1988–2005 period), and the projected changes with respect to the period 2028–2050 (third column).</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>**Figure 3.** Ensemble average annual mean temperature for 1988–2005 (first column), validation (second column over 1988–2005 period), and the projected changes with respect to the period 2028–2050 (third column).</figcaption></figure>

AMMA-ENSEMBLES data permits a better understanding of the processes underlying the West-African Monsoon (WAM) [56]. It provides and advances an understanding of the atmospheric processes over West Africa [57]. AMMA data were used in climate change assessment in the region. The finding of the current study is in accordance with Angelina et al.'s [58] study on the river Niger basin West Africa. They confirmed that all RCMs of AMMA-ENSEMBLES experiment displays an increase in air temperature while there was no consensus among them in precipitation variables.

## 4.2. Spatial Distribution of the Averaged Annual Precipitation and Air Temperature for AMMA-ENSEMBLES Models

An analysis of Figure 4 shows the simulated AMMA-ENSEMBLES model’s precipitation dataset. The total annual precipitation data for the reference period (1988–2010 in the first raw) and projected period (2028–2050 in the second raw) and the changes in projection in the third raw are presented in Figure 4 for the MPI, METO, SMH, and ICT models. The total annual precipitation over the basin varies from 1200 to 1800 mm/year whatever the model. The total annual precipitation simulated in the reference period (1988–2010) ranges from 600 to 1800 mm while the observed annual precipitation
is between 680 and 1640 mm over the chosen window. The spatial distribution of precipitation is almost similar in the reference period and the scenario period (2028–2050). In the south, a diagonal band of relatively low rainfall (<1000 mm/year) follows the Ghanaian-Togolese coast in relation to the difffluence of the monsoon winds and the seasonal rise of coastal cold water. However, we noted minor discrepancies, especially in the number of rainy days, as shown in Table 2, for METO and SMH. MPI and ICT simulate the same number of rainy days in the reference period and the scenario or projection period. By comparing it to the reference period (1988–2010) data, the models METO and SMH project a reduction in rainfall amounts during the projection period (2028–2050) by 2% and 4%, respectively [55]. In contrast, the fifth IPCC assessment reports a slight increase in precipitation over West Africa. Nevertheless, they could not be able to show any trend in precipitation in this zone.

<figure><img src="image_30.png" /><figcaption>**Figure 4.** Spatial variation of the mean annual precipitation in the Mono river basin and surrounding areas as modeled by the four Regional Climate Models (RCMs). Upper panels: 1988–2010 reference period; Middle panels: 2028–2050 projection period; Bottom panels: variation between the reference and the scenario periods (%).</figcaption></figure>
<table><caption>**Table 2.** Percentage (%) of the number of rainy days (>1 mm).</caption><thead><tr><th>RCMs</th><th>Ref_1988-2010</th><th>Proj_2028-2050</th></tr></thead><tbody><tr><td>MPI</td><td>42</td><td>42</td></tr><tr><td>METO</td><td>63</td><td>62</td></tr><tr><td>SMH</td><td>47</td><td>45</td></tr><tr><td>ICT</td><td>48</td><td>48</td></tr></tbody></table>

An analysis of the variations between the two periods shows moderate but contrasting changes from one model to the others, and across the domain. METO and ICT have projected a slight increase in rainfall ranging between 2% and 5% by 2050. Meanwhile, MPI projection shows no rainfall change whereas SMH has projected a strong rainfall deficit amounting up to 15% to 20% by 2050 in the south of the Mono river basin. These precipitation changes are associated with an increase in air temperature. This result is in accordance with the IPCC report [55] over the West Africa region. The same conclusion was made by Sylla et al. [59].

Figure 5 shows for the Mono river basin and surrounding areas, the spatial distribution of the simulated mean air temperature. It came out that the spatial distribution of the mean air temperature is well reproduced by the RCMs although most of these RCMs, especially SMH, underestimate the values. MPI simulates temperature variations closer to the observations and a much better spatial distribution. However, MPI still overestimates the average minimum air temperature (e.g., 27.5 °C on average for the whole catchment area) compared to the observed data (26.5 °C).

An analysis of Figure 5 for air temperature changes between the projection and reference periods confirms warming of a 1 °C magnitude order whatever the model. This fairly corroborates the 1.22 °C temperature increase obtained with the historical data and is also in good agreement with the SRES-A1B scenario. METO is the only RCM that projected a warming of more than 1.5 °C by 2050 all over the region, except on the coast of the Gulf of Guinea. Thus, the control of the large-scale driver is key to reproducing an accurate simulation of these dry zone features whose origin is mainly related to ocean-atmosphere interactions along the Ghana-Togo coast [60]. This finding agrees with some previous studies in West Africa. For instance, Sylla et al. [59] reported a gradual warming spatial variable reaching 0.5 °C per decade in recent years over West Africa, with a recovery from drought conditions. However, the amount of total annual precipitation of this recent decade is still lower compared with the decade before the 1970s' and 1980s' drought episodes [61,62]. Moreover, they also confirmed the increasing trend in the projected air temperature, and this could be in the range of 1.5 to 6.5 °C depending on the emission scenario. Furthermore, the projection of precipitation is with a lot of uncertainties. The West Africa region could experience change in the range of ±30% in the future associated with more intense extremes in the future climate but to a lesser extent [55,59].
<figure><img src="image_31.png" /><figcaption>**Figure 5.** Spatial variation of the annual mean air temperature in the Mono river basin and surrounding areas as simulated by the four RCMs. Up: 1988–2010 reference period (in °C); Middle: 2028–2050 projection period (in °C); Down: variation between the reference and projection periods.</figcaption></figure>

### 4.3. Average Rainfall and Temperature Regimes in the Mono River Basin at the Nangbéto Outlet

Figure 6 shows the average rainfall and air temperature regimes in the Mono river basin upstream of Nangbéto as observed and modeled by the four RCMs.
<figure><img src="image_32.png" /><figcaption>**Figure 6.** Comparison of the observed and simulated rainfall (mm/day) and air temperature (°C) regimes in the Mono river basin at the Nangbéto outlet (1988–2010 average).</figcaption></figure>

As shown in Figure 6, the four RCMs reproduce the seasonal cycle of precipitation well. This has been proven earlier by some previous works in the region [54,57,63]. In the middle of the rainy season, MPI, SMH, and ICT overestimated the rainfall amounts while they also underestimated the rainfall amounts in January–February, which corresponds to the dry season. The smallest biases were obtained with ICT, thus making ICT the model that best replicated the rainfall regime of this watershed.

In most cases, the RCMs satisfactorily reproduce the temperature seasonality in the watershed. The simulated temperature values are underestimated, except MPI, which overestimates these values from April to July. These biases can significantly influence hydrological impact simulations as they will lead to an under(over)estimation of the high streamflow because of an under(over)estimation of the evaporative loss.

Figure 7 reveals the annual cycle of precipitation simulated by the RCMs for the reference period (1988–2010) and the projection period (2028–2050). For SMH, a moderate decrease in the rainfall regime is shown, especially from March to September. SMH fails to reproduce the observed rainfall regime. The other RCMs rarely show a significant decrease, except METO from June to August. A Fisher's test indicates that the changes of the rainfall regime between the reference and projection periods are not statistically significant at a 95% confidence level. Therefore, we assume that only small changes are to be expected in the hydrological regimes by 2050.
<figure><img src="image_33.png" /><figcaption>**Figure 7.** Regional climate models (RCMs) projection of monthly average precipitation (mm/day, 2028–2050) and comparison to the reference period (1988–2010).</figcaption></figure>

Figure 8 reveals that the four RCMs projected an increase of the air temperature by 2050. This could amplify the evaporative loss in the future and potentially induce a decrease in surface runoff. This warming is relatively uniform throughout the year and ranges between +1 and +1.5 °C (a little beyond this range for METO) in accordance with some previous studies [55,59].

<figure><img src="image_34.png" /><figcaption>**Figure 8.** Projection of the monthly near-surface mean air temperature (2028–2050) and comparison to the reference period (1988–2010) for the four RCMs.</figcaption></figure>

Overall, there is a good fit between the seasonal cycles of precipitation and air temperature simulated by the four RCMs, but some of these models still feature biases. The precipitation biases are more dependent on the RCM than the driving GCM. Sylla et al. made the same conclusion [54,59] over West Africa. Indeed, the strongest overestimations of rainfall during the monsoon seasons were obtained with the MPI and SMH experiments. These RCMs were not driven by the same GCM
(ECHAM5 for MPI and HadCM3 for SMH). In addition, both ICT and MPI are forced by ECHAM5 but the ICT simulates a more realistic annual precipitation cycle than MPI. Thus, the projection biases originate from both the RCMs and their driven GCMs.

4.4. Frequency Analysis of Rainfall Distribution in the Mono River Basin

The cumulative frequency of daily rainfall intensity according to the four RCMs is illustrated in Figure 9. This figure compares the distributions of rainfall intensity between observations and the RCM simulations in the reference period, and between the RCM simulations in the reference and projection periods. For most RCMs, the sill of the cumulative daily distribution is obtained after 200 days, except METO, for which the sill is obtained after 250 days. For SMH and ICT, the distribution of daily rainfall frequencies agreed well with the observations, with many days recording less than 20 mm, and a number of wet days (about 200) similar to the observations. METO shows many wet days with a very high number of medium intensity days (5–10 mm). By contrast, the MPI model underestimates precipitation occurrence, especially for intensity values around 5 to 15 mm/day. The study of Tossou et al. [64] also provides a characterization and analysis of rainfall variability in the Mono river watershed complex.

<figure><img src="image_35.png" /><figcaption>**Figure 9.** Cumulative distributions of daily precipitation from the four RCMs and comparison to observations (interpolated rainfall field). Cumul. Freq. Number Days = cumulative frequency of the number of days. NB: The empirical cumulative frequency of the number of rainfall days consists of adding up the sum of the number of days with more than 1 mm of rain.</figcaption></figure>
In the projection period, the four RCMs projected a similar distribution of precipitation in the study area as in the reference period, except the SMH model, for which a small change in the distribution of precipitation is displayed, i.e., a slightly reduced number of rain days beyond 10 mm. This close relationship between the distributions from simulations and observations is consistent with previous findings [3,21,27,46,65,66] and confirms that the RCMs satisfactorily reproduced rainfall at a local scale as stated by Amoussou [2] and other works [4,6,67].

A detailed analysis was performed to overcome the bias challenges regarding the number of rainy days and to better describe the future changes in rainfall distribution. We computed the deciles of the observed daily rainfall and examined for each RCM the contribution of these 10 rainfall classes to the total rainfall as shown by López-Moreno and Beniston [27] in their study on the evolution of rainfall intensity in the Pyrenees. The computation was made for both the reference period (1988–2010) and the projection period (2028–2050). This approach helps to quantify the evolution of the influence of precipitation belonging to different classes of the frequency distribution [27,68–71].

Figure 10 displays for the Mono river basin at the outlet of Nangbóthe the rainfall distribution from the four RCMs according to the thresholds of the 10 quantiles as obtained from the observations. The threshold values are provided at the bottom of Figure 10.

<figure><img src="image_36.png" /><figcaption>**Figure 10.** Comparison of the contribution of the 10 classes of quantile of daily precipitation defined from observations (interpolated rainfall field) to total precipitation under present-day and future climates (SRES-A1B scenario) (left), and changes between the reference and projection periods (right).</figcaption></figure>
Figure 10 indicates that apart from SMH, all RCMs underestimate the distribution of rainfall quantiles, especially the contribution of low rainfall (first four quantiles). This reveals an underestimation of the frequency of low rainfall. For the fifth decile to the eighth decile, the MPI and SMH simulations are close to the observed values. Meanwhile, both ICT and METO overestimate the rainfall in the basin, but this overestimation is stronger with METO. ICT and METO also underestimate the heavy rains (Q9 and Q10), unlike SMH and MPI, which simulate an increase of the daily rainfall (Q10) in the Mono river basin. Between the projection period (2028–2050) and the reference period (1988–2010), the analysis shows a relatively stable distribution of rainfall for most rainfall quantiles from MPI and ICT. For SMH, a strong decrease is found in the contribution of rainfall from the fifth quantile. Meanwhile, an increase of the contribution of the high rainfall intensities to the total rainfall is expected with METO.

### 4.5. Analysis of Extreme Precipitation under Present Day and Future Climates

The hydrological and societal importance of high-intensity rainfall coupled with the disparities between the RCMs regarding the reproduction of the 10th decile of daily rainfall (Q10 > 15 mm) led us to investigate the 99th percentile of daily rainfall in order to better understand the dynamics of heavy rainfall in the Mono river basin. We also analyzed the 5-day cumulative rainfall that likely contributes to flood generation downstream of the basin. Recurrent flood events were experienced in recent years in the Mono river basin [40] because of the high risk of soil saturation that induces a fast runoff. Table 3 displays the 99th percentile of precipitation for the reference and projection periods (1988–2010 and 2028–2050).

<table><caption>**Table 3.** 99th percentile values of daily precipitation in the Mono river basin.</caption><thead><tr><th>Precipitation (mm)</th><th>Hist</th><th>MPI</th><th>METO</th><th>SMH</th><th>ICT</th></tr></thead><tbody><tr><td rowspan="2">99th percentile</td><td rowspan="2">29.92</td><td colspan="4"><strong>Ref_1988-2010</strong></td></tr><tr><td>86.66</td><td>17.98</td><td>75.22</td><td>31.32</td></tr><tr><td rowspan="2">99th percentile</td><td rowspan="2">-</td><td colspan="4"><strong>Proj_2028-2050</strong></td></tr><tr><td>85.70</td><td>19.36</td><td>71.39</td><td>38.11</td></tr></tbody></table>

Ref = reference period for observations and RCM simulations; Proj = Projection period for the RCMs.

The values in Table 3 show that in the reference period, about 30 mm/day of rainfall is equivalent to the 99th percentile in this basin, i.e., the highest 1% of the precipitation days according to the historical data. This recorded heavy rainfall intensity followed or preceded by rainy days could trigger catastrophic floods in the Mono river basin.

ICT simulation of heavy rainfall is the closest to observations. METO underestimated the heavy rainfall whereas SMH and MPI largely overestimated these rainfall extremes. A 99th percentile greater than 75 mm/day is too high for a catchment of 15,680 km². However, this is not excluded because the rainfall of a year can precipitate in almost a day, as was the case in Ouagadougou (Burkina-Faso) in 2009 with nearly 290 mm.

In simulation as in projection, the ICT model simulates the heavy rains, but MPI and SMH overestimate them while the low rains are recorded by METO. With the reference data used, the MPI model especially simulates the very heavy rainfall the best, as well as projection periods. In both the reference and projection periods, the evolution is almost identical whatever the climate model [72,73].

In order to comprehend the seasonal distribution of these heavy rains, we also computed per month the 99th percentile of daily rainfall (Figure 11).
<figure><img src="image_37.png" /><figcaption>**Figure 11.** Monthly variation of the 99th percentiles of daily precipitation in the Mono river basin. Top panel: comparison between observation and simulation during the reference period. Bottom panels: comparison between the reference and the projection periods.</figcaption></figure>

The distribution of the 99th percentiles of daily rainfall shows that all RCMs underestimated the heavy rainfall from November to February (dry season). However, MPI overestimated the heavy rainfall in February and November while SMH overestimated only that of November in the dry season. The high rainfall observed in December and January is only sporadic because the occurrence of rainfall events during the dry season is extremely rare. SMH and MPI also overestimated the rainfall intensity in the core rainy season months (a maximum of 65 mm in September for MPI). This hinders a realistic estimation of the hydrological risks.
In the projection period, we will focus on ICT simulations and to a lesser extent on METO simulations as these two climate models stand out as being the most realistic for simulating heavy rainfall events in the basin. For these two climate models, the heavy rainfall intensities obtained in the projection period are close to those of the reference period even if an increase is noticeable in many months. ICT shows a sharp one-off increase of rainfall intensity in March. However, SMH and MPI predicted a slight decrease in the intensity of the heavy rainfall events from February to August and from August to October, respectively, but these two climate models are the least realistic for the simulation of the heavy rainfall intensities.

The monthly variation of the 99th percentile rainfall maxima shows that the most intense heavy rainfall events occur at the core of the rainy season. However, the so-called dry months sometimes record strong rainfall. Therefore, an analysis of the return periods of the heavy rainfall events can help to better understand the distribution and occurrence of the extreme events in the Mono river basin, and the occurrence of high streamflow in the basin upstream of the dam, and the resulting floods. This result agrees with the study of Kodja [74] in the Ouémé river basin, which is located in the same climatic zone as our study basin.

4.6. *Analysis of the Return Periods of Rainfall Extreme Using a GEV Model*

The annual maxima of daily rainfall in the Mono river basin upstream of the outlet of Nangbéto (observed and simulated values) were adjusted to a generalized extreme value (GEV) distribution. The values of the three parameters, namely k, sigma (ζ), and mu (μ) of the GEV distribution (Figure 12), show a similarity between the observed and simulated data for the sigma and mu parameters but strong differences for the k parameter, where K refers to the shape parameter, sigma the scale parameter, and mu stands for the location parameter [75]. Nevertheless, these three parameters were always positive (for observations and simulations in the reference and projection periods) (Figure 12), thus pointing to a Frechet distribution (extreme value distribution type II).

<figure><img src="image_38.png" /><figcaption>**Figure 12.** Temporal evolution of the three parameters (k, sigma, mu) of the Generalized Extreme Value (GEV) distribution for different sets of data.</figcaption></figure>

Furthermore, when $k > 0$, the GEV distribution is the type II, or Frechet, extreme value distribution. The variance of GEV is not finite when $k \ge 1/2$. The GEV distribution has positive density only for values of X, such that $k \times (X-mu)/sigma > -1$ [75].
Figure 13 shows the evolution of the annual maxima of observed daily rainfall. The analysis reveals a strong increase in the annual maximum of daily precipitation that is statistically significant at the 95% confidence level. The frequency of high streamflow is not increasing, and this could be explained by the increase in temperature, which induces more evapotranspiration and thus compensates for the impact on high streamflow. This has also been proved by Ntajal et al. [49] downstream of the Mono river basin. However, an in-depth analysis is still needed to prove this assumption because, in principle, very high streamflow is sometimes generated from rapid runoff in response to water excess in soil with a low retention capacity [41,71,76]. This occurs in a very short time period, during which the increase of the evaporative demand is not really a constraint.

<figure><img src="image_39.png" /><figcaption>**Figure 13.** Interannual variation of the daily rainfall maxima from 1988 to 2010 in the Mono river basin at the outlet of Nangbéto.</figcaption></figure>

This result is consistent with the evolution of discharge maxima flowing into the Nangbéto dam from 1988 to 2010, which pointed to an increase of the annual maxima, which is significant at *p* = 0.0185 according to a Mann–Kendall test [41,77,78].

Figure 14 compares the distributions of the quantiles of daily rainfall maxima observed over 23 years (1988–2010) to those adjusted by the GEV.

<figure><img src="image_40.png" /><figcaption>**Figure 14.** Comparison of the annual maxima of the quantiles of observed and simulated rainfall with a GEV model.</figcaption></figure>
The annual maxima of daily rainfall are well adjusted to the GEV distribution. The analysis of the return periods of the extreme rainfall events, as displayed in Figure 15, shows that the rainfall events of an intensity higher than 40 mm are likely to occur at a recurrence interval of about 5 years.

<figure><img src="image_41.png" /><figcaption>**Figure 15.** Estimation of the return periods of the annual maxima of rainfall events (mm). The circle represents the observed values over 23 years (1988–2010) and the blue curves refer to the confidence level.</figcaption></figure>

The uncertainty of the rainfall events occurring in a 50-year recurrence interval is higher because of the short length of the available time series and the trend shown in Figure 13.

Table 4 presents the return periods for the annual maxima of the daily rainfall simulated with ICT, which stands out as the best of the four models for the reproduction of intense rainfall. The rarest and thus most intense rainfall events remain poorly simulated, as illustrated by the divergence of the 10-day recurrence values (45 mm in the observations, 77 mm in the model). Nevertheless, the projections show a strong increase in rainfall intensities for all return periods described in Table 4. The daily precipitation increases with the return period in the basin, which is in accordance with Ntajal et al.'s [49] and Kodja's [74] studies in the Mono and Ouémé basins, respectively. Ntajal et al. [49] compared the return period at the annual time scale and showed that GEV gives overestimation than the Goodrich exponential distribution model. This could also justify the overestimation of the model.

<table><caption>**Table 4.** Annual daily precipitation (mm) for different return periods in the Mono river basin.</caption><thead><tr><td>Return Periods (Years)</td><td>Hist</td><td>ICT_Ref</td><td>ICT_Proj</td></tr></thead><tbody><tr><td>1</td><td>32.5</td><td>40</td><td>90</td></tr><tr><td>2</td><td>35</td><td>48</td><td>100</td></tr><tr><td>5</td><td>40</td><td>52.5</td><td>120</td></tr><tr><td>10</td><td>45</td><td>77</td><td>200</td></tr><tr><td>20</td><td>47.5</td><td>89</td><td>289</td></tr></tbody></table>

This could induce high magnitude floods, which may pose a critical risk of flood inundation and thus cause damages with severe economic and societal consequences in the lower valley of the Mono river basin. Considering these return periods, the amounts of heavy rains projected are alarming. This confirms the increase in intense rainfall events predicted by the regional climate models.
**5. Conclusions**

The comparative analysis of different regional climate models simulating air temperature and precipitation in the Mono river basin and the West African sub-region leads to three major conclusions regarding their ability to reproduce the present-day climate.

First, apart from the few exceptions noted below, the realism of the simulated climate is more controlled by the regional climate model (RCM) than the driven global climate model (GCM). For the same forcing GCM (ECHAM5 or HadCM3 in this study), the precipitation fields are substantially different from one RCM to the others used for the dynamical downscaling. This strong model sensitivity may arise from the RCM structure (model approximations) or from the choice of parameterization techniques made to run each model (e.g., convective scheme).

Second, though the seasonal cycles of air temperature and precipitation are well reproduced by the RCMs, most of them still feature systematic errors related to the magnitude of these variations. In general, the selected RCMs underestimate air temperature in the range 1–3 °C for the Mono river basin. Two RCMs largely overestimate rainfall (by a factor of 1.5 to 2) during the rainy season. This overestimation is due to very high rainfall intensities that could not be compensated by the underestimation of the number of rainy days. The most realistic models regarding the reproduction of the actual seasonal cycle are those that simulate both the frequency of rainfall events and the average intensity of daily rainfall well (ICT and to a lesser extent METO). Finally, almost all RCMs introduced bias with respect to the spatial variation of the climatic variables being analyzed. The north–south gradients of precipitation between the Sahel and the Guinean regions are well reproduced by all RCMs, except METO, although the simulated values for precipitation are not always correct. There are also errors in the southern part of the Guinean region regarding the reproduction of the drought band diagonally stretching from southern Ghana to southern Benin (Dahomey Gap). It was not reproduced by the RCMs forced with ECHAM5 GCM at their boundaries (MPI and ICT).

Third, and this is implicitly derived from the conclusion above, the hierarchy of RCMs in terms of the quality of their simulations differs according to the climate variable considered. For example, MPI tends to offer the most accurate reproduction of air temperature (especially their spatial distribution) and ICT is the most realistic for the precipitation patterns. This conclusion still needs to be taken with caution because though ICT satisfactorily reproduces the rainfall regimes and the frequency distribution of the rainfall events, the spatial distribution of the average annual precipitation is better simulated by the SMH model. Indeed, ICT fails to reproduce the relative dryness of the Ghanaian-Togolese coast in the south of the Guinean region. As well, ICT still features bias regarding the reproduction of the return periods of the annual rainfall maxima, for which it overestimated the frequency despite its good performance for the reproduction of the distribution of daily rainfall. Thus, we conclude that the choice of an appropriate RCM should be based on the research objectives, especially for impact studies.

Though these conclusions call for caution in using climate model simulations to assess future climate change in the sub-region, some lessons can nevertheless be drawn. The four RCMs unanimously project a +1 to +1.5 °C temperature increase in the sub-region by 2028–2050 as compared to the 1988–2010 reference period. The projected trends for cumulated precipitation are null or very moderate and diverge from one RCM to the others. Only SMH projected a significant decrease of precipitation in the Mono river basin. The simulations of the intense rainfall events (99th percentiles) also display contrasted results, but the two regional climate models that better reproduce these extreme rainfall events in the reference period have also unanimously projected a significant increase in their intensity by 2028–2050.

For the intense rainfall events, the Mono river basin at the outlet of Nangbéto recorded between 1988 and 2010 a significant increase in the intensity of the maximum daily rainfall averaged over the watershed, and this increase may be a risk factor. The heaviest rainfall events (99th percentile) occur mainly during the months of July to September, with a peak in September. This fits well with the discharge peaks in the basin. Thus, the intense rainfall events recorded in the tropical domain of the
basin could lead to probable risks of flood inundations in the lower valley of the Mono river basin due to an overflow of the river.

The ICT simulations were the closest to the observations in terms of the reproduction of the cumulated precipitation and frequency distribution of daily rainfall. ICT is thus more robust for the analysis of the intense rainfall events and thereby flood forecasting in the Mono river basin. The estimation of extreme rainfall events using ICT showed stability except for the rainfall events occurring in October–November, which slightly increase. The adjusted GEV model satisfactorily predicted the heavy rainfall events, but there are uncertainties beyond the 90th percentile. The adjustment of a Weibull-type GEV distribution is well suited here for the prediction of extreme rainfall events (shape parameter of the GEV distribution = 0), although it is heavy-tailed at the 99th percentile.

The annual maxima of daily precipitation are increasing. Therefore, the impact of heavy rainfall events on discharge will increase under climate change conditions. This knowledge is important to develop an early warning system for the Mono river basin for the sustainability of the ecosystems. This calls for further research to better understand the physical mechanisms underlying the changes in extreme precipitation events and thus improve climate model simulations for short- and medium-term use. Moreover, for future study, a bias correction could be done for those datasets before quantifying the magnitudes of changes due to their coarser resolution.

**Author Contributions:** E.A. conducted this research. Conceptualization: E.A., A.D., H.A., S.O., P.C. and H.S.T.V.; Methodology and modelling and data processing: E.A., H.A., H.S.T.V., A.D., K.K.; Writing—Original Draft Preparation, E.A., H.A., H.S.T.V., S.O., A.D., M.B., G.M., C.H.; Writing—Review and Editing, P.C., G.M., C.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** The APC was funded by les universités des auteurs ayant contribué à la reduction des coûts de publications.

**Acknowledgments:** The authors thank the reviewers for their comments which improve the quality of the manuscript. We thank the Climatology Research Center (CRC) of Dijon (France) for providing us AMMA-Ensemble data. We thank LAPA-MF -African Centre of Excellence on Climate Change, Biodiversity and Sustainable Development, the Institute of Research for Development (IRD, France) and Institute of Geosciences for Environment (IGE, University Grenoble Alpes) for providing the facility (the Regional Climate Modelling Platform) to perform this study at the University Félix Houphouët Boigny (Abidjan, Côte d'Ivoire).

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Brown, O.L.I.; Hammill, A.; Mcleman, R. Climate change as the 'new' security threat: Implications for Africa. *Int. Aff.* **2007**, *83*, 1141–1154. [CrossRef]

2. Amoussou, E. Variabilité Pluviométrique et Dynamique Hydro-Sédimentaire du Bassin Versant du Complexe Fluvio-Lagunaire Mono-Ahémé-Couffo (Afrique de l'ouest). Ph.D. Thesis, Université de Bourgogne, Dijon, France, January 2010.

3. Mladjic, B.; Sushama, L.; Khaliq, M.N.; Laprise, R.; Caya, D.; Roy, R. Canadian RCM projected changes to extreme precipitation characteristics over Canada. *J. Clim.* **2011**, *24*, 2565–2584. [CrossRef]

4. Tramblay, Y.; Amoussou, E.; Dorigo, W.; Mahé, G. Flood risk under future climate in data sparse regions: Linking extreme value models and flood generating processes. *J. Hydrol.* **2014**, *519*, 549–558. [CrossRef]

5. Dilley, M.; Chen, R.S.; Deichmann, U.; Lerner-Lam, A.L.; Arnold, M. *Natural Disaster Hotspots: A Global Risk Analysis*; World Bank: Washington, DC, USA, 2005; Volume 7.

6. Crétat, J.; Vizy, E.K.; Cook, K.H. How well are daily intense rainfall events captured by current climate models over Africa? *Clim. Dyn.* **2014**, *42*, 2691–2711. [CrossRef]

7. Panthou, G.; Lebel, T.; Vischel, T.; Quantin, G.; Sane, Y.; Ba, A.; Ndiaye, O.; Diongue-Niang, A.; Diopkane, M. Rainfall intensification in tropical semi-arid regions: The Sahelian case. *Environ. Res. Letts.* **2018**, *13*, 064013. [CrossRef]
8. Niasse, M.; Coalition, I.L. Climate-Induced Water Conflict Risks in West Africa: Recognizing and Coping with Increasing Climate Impacts on Shared Watercourses. In *Human Security and Climate Change*; PRIO, CICERO and GECHS: Asker, Norway, 2005; pp. 21–23. Available online: https://www.researchgate.net/profile/Madiodio_Niasse/publication/237699436_Climate-Induced_Water_Conflict_Risks_in_West_Africa_Recognizing_and_Coping_with_Increasing_Climate_Impacts_on_Shared_Watercourses/links/5440fe550cf2a76a3cc60e7c.pdf (accessed on 1 January 2019).

9. Loughlin, J.O.; Witmer, F.D.W.; Linke, A.M.; Laing, A.; Gettelman, A.; Dudhia, J. Climate variability and confluence risk in East. *Proc. Natl. Acad. Sci. USA* **2012**, *109*, 18344–18349.

10. Brown, O.; Crawford, A. Climate change: A new threat to stability in West Africa? Evidence from Ghana and Burkina Faso Climate change: A new threat to stability in West Africa? Evidence from Ghana and Burkina Faso. *Afr. Secur. Stud.* **2010**, *17*, 39–57. [CrossRef]

11. Collier, P.; Conway, G.; Venables, T. Climate change and Africa. *Oxf. Rev. Econ. Policy* **2008**, *24*, 337–353. [CrossRef]

12. Oyebande, L. Climate Change Impact on Water Resources at the Transboundary Level in West Africa: The Cases of the Senegal, Niger and Volta Basins. *Open Hydrol. J.* **2013**, *4*, 163–172. [CrossRef]

13. Barbe, L. Rainfall Variability in West Africa during the Years 1950–1990. *J. Clim.* **2002**, *15*, 187–202. [CrossRef]

14. Dezetter, A.; Servat, E.; Paturel, J.E.; Mahé, G.; Dieulin, C. Using general circulation model outputs to assess impacts of climate change on runoff for large hydrological catchments in West Africa Using general circulation model outputs to assess impacts of climate change on runoff for large hydrological catchments. *Hydrol. Sci. J.* **2009**, *6667*, 1.

15. Houghton, J.T.; Ding, Y.D.; Griggs, D.J.; Noguer, M.; van der Linden, P.J.; Dai, X.; Maskell, K.; Johnson, C.A. *Climate Change 2001: The Scientific Basis*; The Press Syndicate of the University of Cambridge: Cambridge, UK, 2001.

16. IPCC (Intergovernmental Panel on Climate Change). Summary for Policymakers. In *Climate Change 2007: The Physical Science Basis*; Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change; Solomon, S., Qin, M.M., Chen, M.M.Z., Averyt, K.B., Tignor, M., Miller, H.L., Eds.; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2007; pp. 1–18.

17. Paeth, H.; Hall, N.M.; Gaertner, M.A.; Alonso, M.D.; Moumouni, S.; Polcher, J.; Ruti, P.M.; Fink, A.H.; Gosset, M.; Lebel, T.; et al. Progress in regional downscaling of West African precipitation Progress in regional downscaling of west African precipitation. *Atmos. Sci. Lett.* **2016**, *12*, 75–82. [CrossRef]

18. Louis, J.-F. A Parametric Model of Vertical Fluxes in the atmosphere. *Bound. Layer Meteorol.* **1979**, *17*, 187–202. [CrossRef]

19. Dayan, U.; Nissen, K.; Ulbrich, U. Review Article: Atmospheric conditions inducing extreme precipitation over the eastern and western Mediterranean. *Nat. Hazards Earth Syst. Sci.* **2015**, *15*, 2525–2544. [CrossRef]

20. Katz, R.W.; Parlange, M.B.; Naveau, P. Statistics of extremes in hydrology. *Adv. Water Ressour.* **2002**, *25*, 1287–1304. [CrossRef]

21. Fowler, H.J.; Blenkinsop, S.; Tebaldi, C. Linking climate change modelling to impacts studies: Recent advances in downscaling techniques for hydrological. *Int. J. Climatol.* **2007**, *27*, 1547–1578. [CrossRef]

22. Lebel, T.; le Barbé, L.; Delclaux, F.; Polcher, J. From GCM scales to hydrological scales: Rainfall variability in West Africa. *Stoch. Environ. Res. Risk Assess.* **2000**, *14*, 275–295. [CrossRef]

23. Paeth, H.; Scholten, A.; Friederichs, P.; Hense, A. Uncertainties in climate change prediction: El Niño-Southern Oscillation and monsoons. *Glob. Planet. Chang.* **2008**, *60*, 265–288. [CrossRef]

24. Camberlin, P.; Fauchereau, N.; Gabriel, S. Empirical predictability study of October–December East African rainfall. *Q. J. R. Meteorol. Soc.* **2002**, *128*, 2239–2256.

25. Girmes, H.; Robin, P. Improving Seasonal Forecasting in the Low Latitudes. *Mon. Weather Rev.* **2006**, *134*, 1859–1879.

26. Paeth, H.; Diederich, M. Postprocessing of simulated precipitation for impact research in West Africa. Part II: A weather generator for daily data. *Clim. Dyn.* **2011**, *36*, 1337–1348. [CrossRef]

27. López-Moreno, J.I.; Beniston, M. Daily precipitation intensity projected for the 21st century: Seasonal changes over the Pyrenees. *Theor. Appl. Climatol.* **2009**, *95*, 375–384. [CrossRef]

28. Olume, V. Hydrological Processes in Regional Climate Model Simulations of the Central United States Flood of June–July 1993. *J. Hydrometeorol.* **2003**, *4*, 584–598.
29. Fowler, H.J.; Ekström, M.; Kilsby, C.G.; Jones, P.D. New estimates of future changes in extreme rainfall across the UK using regional climate model integrations. 1. Assessment of control climate. *J. Hydrol.* **2005**, *300*, 212–233. [CrossRef]

30. Dee, D.P.; Uppala, S.M.; Simmons, A.J.; Berrisford, P.; Poli, P.; Kobayashi, S.; Andrae, U.; Balmaseda, M.A.; Balsamo, G.; Bauer, D.P.; et al. The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. *Q. J. R. Meteorol. Soc.* **2011**, *137*, 553–597. [CrossRef]

31. Vose, R.S.; Schmoyer, R.L.; Steurer, P.M.; Peterson, T.C.; Heim, R.; Karl, T.R.; Eischeid, J.K. *The Global Historical Climatology Network: Long-Term Monthly Temperature, Precipitation, Sea Level Pressure, and Station Pressure Data*; Oak Ridge National Lab., TN (United States). Carbon Dioxide Information Analysis Center: Washington, DC, USA, 1992.

32. Pendergrass Angeline, The Climate Data Guide: GPCP (Monthly): Global Precipitation Climatology Project, National Center for Atmospheric Research Staff (Eds.), Last Modified 02 July 2016. 2016. Available online: https://climatedataguide.ucar.edu/climate-data/gpcp-monthly-global-precipitation-climatology-project. (accessed on 2 January 2018).

33. New, M.; Lister, D.; Hulme, M.; Makin, I. A high-resolution data set of surface climate over global land areas. *Clim. Res.* **2002**, *21*, 1–25. [CrossRef]

34. Simmons, A.J.; Jones, P.D.; Bechtold, V.C.; Beljaars, A.C.M.; Ka, P.W. Comparison of trends and low-frequency variability in CRU, ERA-40, and NCEP/NCAR analyses of surface air temperature. *J. Geophys. Res.* **2004**, *109*, 1–18. [CrossRef]

35. Hewitt, C.D.; Griggs, D.J. Ensembles-based predictions of climate changes and their impacts. *Eos* **2004**, *85*, 566. [CrossRef]

36. Shahid, S. Trends in extreme rainfall events of Bangladesh. *Theor. Appl. Climatol.* **2011**, *104*, 489–499. [CrossRef]

37. Sciences, E.; Carolina, N.; Columbia, B.; Sciences, E.; Carolina, N. Avoiding Inhomogeneity in Percentile-Based Indices of Temperature Extremes. *J. Clim.* **2005**, *18*, 1641–1651.

38. Villarini, G.; Scoccimarro, E.; Gualdi, S. Projections of heavy rainfall over the central United States based on CMIP5 models. *Atmos. Sci. Lett.* **2013**, *14*, 200–205. [CrossRef]

39. Zolina, O.; Simmer, C.; Belyaev, K.; Kapala, A.; Gulev, S. Improving Estimates of Heavy and Extreme Precipitation Using Daily Records from European Rain Gauges. *J. Hydrometeorol.* **2009**, *10*, 701–716. [CrossRef]

40. Amoussou, E.; Camberlin, P.; Totin, V.S.H.; Pérard, J. Événements hydroclimatiques et risque d'inondation au sud-ouest du Bénin. In Proceedings of the 24ème colloque de l'Association Internationale de Climatologie, Rovereto, Italy, 6–10 September 2011; p. 2010.

41. Amoussou, E.; Tramblay, Y.; Totin, H.S.V.; Mahé, G. Dynamique et modélisation des crues dans le bassin du Mono à Nangbéto (Togo/Bénin). *Hydrol. Sci. J.* **2014**, *59*, 2060–2071. [CrossRef]

42. Fisher, R.A.; Tippett, L.H.C. Limiting forms of the frequency distribution in the largest particle size and smallest member of a sample. *Proc. Camb. Phil. Soc.* **1928**, *24*, 180–190. [CrossRef]

43. Nelder, J.A.; Mead, R. Nelder1965.pdf. *Comput. J.* **1965**, *7*, 308–313. [CrossRef]

44. Coles, S. *An Introduction to Statistical Modeling of Extreme Values*; Springer: London, UK, 2011; Volume 208.

45. Chu, P.S.; Zhao, X.; Ruan, Y.; Grubbs, M. Extreme rainfall events in the Hawaiian Islands. *J. Appl. Meteorol. Climatol.* **2009**, *48*, 502–516. [CrossRef]

46. Cunnane, C. *Statistical Distributions for Flood Frequency Analysis*; WMO Operational Hydrolofy report no. 33; the Secretariat of the Word Meteorological Organization: Geneva, Switzerland, 1989; pp. 581–582.

47. Jenkinson, A.F. The frequency distribution of the annual maximum (or minimum) values of meteorological elements. *Q. J. R. Meteorol. Soc.* **1955**, *81*, 158–171. [CrossRef]

48. El Adlouni, S.; Quarda, T.B.M.J. Comparaison des méthodes d'estimation des paramètres du modèle GEV non stationnaire. *Rev. des Sci. l'Eau* **2008**, *21*, 35–50. [CrossRef]

49. Ntajal, J.; Lamptey, B.L.; Mianikpo, J.; Kpotivi, W.K. R Ainfall T Rends and F Lood F Requency a Nalyses in the L Ower M Ono R Iver B Asin in T Ogo, W Est a Frica. *Int. J. Adv. Res.* **2016**, *4*, 1–11.

50. Davison, A. *Bootstrap Methods and their Application, no. 1*; Cambridge University Press: Cambridge, UK, 1997.

51. Stedinger, J.R.; Vogel, R.M.; Foufoula-Georgiou, E. Frequency Analysis of Extreme Events. In *Handbook of Hydrology*; Maidment, D.D.M.-H., Ed.; McGraw-Hill: New York, NY, USA, 1993; p. 68.
52. Lamptey, B.L. Comparison of gridded multisatellite rainfall estimates with gridded gauge rainfall over West Africa. *J. Appl. Meteorol. Climatol.* **2008**, *47*, 185–205. [CrossRef]

53. Gbobaniyi, E.; Sarr, A.; Sylla, M.B.; Diallo, I.; Lennard, C.; Dosio, A.; Dhiédiou, A.; Kamga, A.; Klutse, N.A.; Hewitson, B.; et al. Climatology, annual cycle and interannual variability of precipitation and temperature in CORDEX simulations over West Africa. *Int. J. Climatol.* **2014**, *34*, 2241–2257. [CrossRef]

54. Diallo, I.; Sylla, M.B.; Giorgi, F.; Gaye, A.T.; Camara, M. Multimodel GCM-RCM ensemble-based projections of temperature and precipitation over West Africa for the Early 21st Century. *Int. J. Geophys.* **2012**, *2012*. [CrossRef]

55. Riede, J.O.; Posada, R.; Fink, A.H.; Kaspar, F. What's on the 5th IPCC Report for West Africa? In *Adaptation to Climate Change and Variability in Rural West Africa*; Springer: Cham, Switzerland, 2016; pp. 7–23.

56. Ruti, P.M.; Williams, J.E.; Hourdin, F.; Guichard, F.; Boone, A.; Van Velthoven, P.; Favot, F.; Musat, I.; Rummukainen, M.; Domínguez, M.; et al. The West African climate system: A review of the AMMA model inter-comparison initiatives. *Atmos. Sci. Lett.* **2011**, *12*, 116–122. [CrossRef]

57. Lafore, J.P.; Flamant, C.; Giraud, V.; Guichard, F.; Knippertz, P.; Mahfouf, J.F.; Mascart, P.; Williams, E.R. Introduction to the AMMA Special Issue on 'Advances in understanding atmospheric processes over West Africa through the AMMA field campaign'. *Q. J. R. Meteorol. Soc.* **2010**, *136*, 2–7. [CrossRef]

58. Angelina, A.; Djibo, A.G.; Seidou, O.; Sanda, I.S.; Sittichok, K. Modifications du régime d'écoulement du fleuve Niger à Koulikoro sous changement climatique. *Hydrol. Sci. J.* **2015**, *60*, 1709–1723. [CrossRef]

59. Sylla, M.B.; Nikiema, P.M.; Gibba, P.; Kebe, I.; Klutse, N.A.B. Climate Change over West Africa: Recent Trends and Future Projections. In *Adaptation to Climate Change and Variability in Rural West Africa*; Yaro, J.A., Hesselberg, J., Eds.; Springer International Publishing: Berlin, Germany, 2016; pp. 1–244.

60. Mahe, G. Mémoire Habilitation à Diriger des Recherches Variabilité pluie-débit en Afrique de l'Ouest et Centrale au 20ème siècle: Changements Hydro-Climatiques, Occupation du sol et Modélisation Hydrologique Université des Sciences et Techniques Gil Mahé. HDR Dissertation, Université des Sciences et Techniques Montpellier, Montpellier, France, 2015.

61. Yabi, I.; Afouda, F. Extreme rainfall years in Benin (West Africa). *Quat. Int.* **2012**, *262*, 39–43. [CrossRef]

62. Kasei, R.; Diekkrüger, B.; Leemhuis, C. Drought frequency in the Volta basin of West Africa. *Sustain. Sci.* **2010**, *5*, 89–97. [CrossRef]

63. Hourdin, F.; Musat, I.; Guichard, F.S.; Ruti, P.M.; Favot, F.; Filiberti, M.A.; Pham, M.; Grandpeix, J.Y.; Polcher, J.; Marquet, P.; et al. Amma-Model intercomparison project. *Bull. Am. Meteorol. Soc.* **2010**, *91*, 95–104. [CrossRef]

64. Tossou, E.M.; Ndiaye, M.L.; Traore, V.B.; Sambou, H.; Kelome, N.C.; SY, B.A.; Diaw, A.T. Characterisation and Analysis of Rainfall Variability in the Mono-Couffo River Watershed Complex, Benin (West Africa). *Resour. Environ.* **2017**, *7*, 13–29.

65. Fowler, H.J.; Wilby, R.L. Detecting changes in seasonal precipitation extremes using regional climate model projections: Implications for managing fluvial flood risk. *Water Resour. Res.* **2010**, *46*, 1–17. [CrossRef]

66. Frei, C.; Scho, R.; Fukutome, S.; Vidale, P.L. Future change of precipitation extremes in Europe: Intercomparison of scenarios from regional climate models. *J. Geophys. Res.* **2006**, *111*. [CrossRef]

67. Beniston, M.; Stephenson, D.B.; Christensen, O.B.; Ferro, C.A.; Frei, C.; Goyette, S.; Halsnaes, K.; Holt, T.; Jylhä, K.; Koffi, B.; et al. Future extreme events in European climate: An exploration of regional climate model projections. *Clim. Chang.* **2007**, *81*, 71–95. [CrossRef]

68. Burn, D.H. The use of resampling for estimating confidence intervals for single site and pooled frequency analysis/Utilisation d' un rééchantillonnage pour l' estimation des intervalles de confiance lors d' analyses fréquentielles mono et multi-site intervals f. *Hydrol. Sci. Sci. Hydrol.* **2003**, *48*, 25–38. [CrossRef]

69. Caya, D.; Laprise, R. A semi-implicit semi-Lagrangian regional climate model: The Canadian RCM. *Mon. Weather Rev.* **1999**, *127*, 341–362. [CrossRef]

70. Hall, M.J.; Van den Boogaard, H.F.; Fernando, R.C.; Mynett, A.E. The construction of confidence intervals for frequency analysis using resampling techniques to cite this version: HAL Id: Hal-00304907 The construction of confidence intervals for frequency analysis using resampling techniques. *Hydrol. Earth Syst. Sci.* **2004**, *8*, 235–246. [CrossRef]

71. Sylla, M.B.; Gaye, A.T.; Jenkins, G.S. On the fine-scale topography regulating changes in atmospheric hydrological cycle and extreme rainfall over West Africa in a regional limate model projections. *Int. J. Geophys.* **2012**. [CrossRef]
72. Ekström, M.; Fowler, H.J.; Kilsby, C.G.; Jones, P.D. New estimates of future changes in extreme rainfall across the UK using regional climate model integrations. 2. Future estimates and use in impact studies. *J. Hydrol.* **2005**, *300*, 234–251. [CrossRef]

73. Emori, S.; Hasegawa, A.; Suzuki, T.; Dairaku, K. Validation, parameterization dependence, and future projection of daily precipitation simulated with a high-resolution atmospheric GCM. *Geophys. Res. Lett.* **2005**, *32*, 1–4. [CrossRef]

74. Kodja, D.J. Indicateurs des Évènements Hydroclimatiques Extrêmes dans le Bassin Versant de l'Ouémé à l'exutoire de Bonou en Afrique de l'Ouest. Ph.D. Dissertation, Université of Montpellier, Montpellier, France, 2018.

75. Embrechts, P.; Klüppelberg, C.; Mikosch, T.; Emberchts, P.; Klüppelberg, C.; Mikosch, T. Modelling Extremal Events. In *Statistical Methods for Extremal Events*; Springer: Berlin/Heidelberg, Germany; New York, NY, USA; London, UK; Paris, France; Tokyo, Japan; Hong Kong, China; Barcelona, Spain; Budapest, Hungary, 1997; pp. 283–370.

76. Zwiers, F.W.; Kharin, V.V. Changes in the Extremes of the Climate Simulated by CCC GCM2 under CO₂ Doubling. *J. Clim.* **1998**, *2*, 2200–2222. [CrossRef]

77. Amoussou, E.; Camberlin, P.; Mahe, G. Impact de la variabilité climatique et du barrage Nangbéto sur l'hydrologie du système Mono-Couffo (Afrique de l'Ouest). *Hydrol. Sci. J.* **2012**, *57*, 805–817.

78. Kendall, M.; Stuart, A. *Analysis Multivariate*; Griffin, C., Ed.; Charles Griffin & Company Ltd.: London, UK, 1975.

<figure><img src="image_42.png" /></figure>

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
<figure><img src="image_43.png" /></figure>
Article

Are the Fouta Djallon Highlands Still the Water Tower of West Africa?

Luc Descroix <fnref n="1" />,<fnref n="2" />,*, Bakary Faty <fnref n="3" />, Sylvie Paméla Manga <fnref n="2" />,<fnref n="4" />,<fnref n="5" />, Ange Bouramanding Diedhiou <fnref n="6" />,
Laurent A. Lambert <fnref n="7" />, Safietou Soumaré <fnref n="2" />,<fnref n="8" />,<fnref n="9" />, Julien Andrieu <fnref n="1" />,<fnref n="9" />, Andrew Ogilvie <fnref n="10" />,
Ababacar Fall <fnref n="8" />, Gil Mahé <fnref n="11" />, Fatoumata Binta Sombily Diallo <fnref n="12" />, Amirou Diallo <fnref n="12" />,
Kadiatou Diallo <fnref n="13" />, Jean Albergel <fnref n="14" />, Bachir Alkali Tanimoun <fnref n="15" />, Ilia Amadou <fnref n="15" />,
Jean-Claude Bader <fnref n="16" />, Aliou Barry <fnref n="17" />, Ansoumana Bodian <fnref n="18" />, Yves Boulvert <fnref n="19" />, Nadine Braquet <fnref n="20" />,
Jean-Louis Couture <fnref n="21" />, Honoré Dacosta <fnref n="22" />, Gwenaelle Dejacquelot ²³, Mahamadou Diakité ²⁴,
Kourahoye Diallo ²⁵, Eugenia Gallese ²³, Luc Ferry <fnref n="20" />, Lamine Konaté ²⁶,
Bernadette Nka Nnomo ²⁷, Jean-Claude Olivry <fnref n="19" />, Didier Orange ²⁸, Yaya Sakho ²⁹,
Saly Sambou <fnref n="22" /> and Jean-Pierre Vandervaere ³⁰

<footnote n="1">¹ Museum National d'Histoire Naturelle, UMR PALOC IRD/MNHN/Sorbonne Université, 75231 Paris, France; Julien.ANDRIEU@univ-cotedazur.fr</footnote>

<footnote n="2">2 LMI PATEO, UGB, St Louis 46024, Senegal; s.manga4555@zig.univ.sn (S.P.M.); s.soumare913@zig.univ.sn (S.S.)</footnote>

<footnote n="3">3 Direction de la Gestion et de la Planification des Ressources en Eau (DGPRE), Dakar 12500, Senegal; bakaryfaty@gmail.com</footnote>

<footnote n="4">4 Département de Géographie, Université Assane Seck de Ziguinchor, Ziguinchor 27000, Senegal</footnote>

<footnote n="5">5 UFR des Sciences Humaines et Sociales, Université de Lorraine, 54015 Nancy, France</footnote>

<footnote n="6">6 Master SPIBES/WABES Project (Centre d'Excellence sur les CC) Bingerville, Université Félix Houphouët Boigny, 582 Abidjan 22, Côte d'Ivoire; bouramanding@gmail.com</footnote>

<footnote n="7">7 Doha Institute for Graduate Studies, BP 200592 Doha, Qatar; llambert@qu.edu.qa</footnote>

<footnote n="8">8 Ecole Polytechnique de Thiès, Laboratoire des Sciences et Techniques de l'Eau et de l'Environnement, LaSTEE, Thiès BP A10, Senegal; afall@ept.sn</footnote>

<footnote n="9">9 ESPACE, Université Côte d'Azur, 06204 Nice, France</footnote>

<footnote n="10">10 UMR G-EAU, IRD (AgroParisTech, Cirad, INRAE, MontpellierSupAgro, University of Montpellier), Dakar 12500, Senegal; andrew.ogilvie@ird.fr</footnote>

<footnote n="11">11 IRD HSM, Case MSE, Université Montpellier, 300 avenue Emile Jeanbrau, 34090 Montpellier, France; gilmahe@hotmail.com</footnote>

<footnote n="12">12 CERE Centre d'Etudes et de Recherches sur l'Environnement, UGANC Conakry, Conakry 001, Guinea; binetasombily@yahoo.fr (F.B.S.D.); damirou2013@gmail.com (A.D.)</footnote>

<footnote n="13">13 Institut Universitaire des Hautes Etudes IUHEG, Conakry et GEOPROSPECT, Conakry 001, Guinea; Kadiatoudiallo5459@gmail.com</footnote>

<footnote n="14">14 Montpellier SupAgro, UMR LISAH, IRD, INRA, University of Montpellier, 34090 Montpellier, France; jean.albergel@ird.fr</footnote>

<footnote n="15">15 NBA (ABN) Niger Basin Authority, Niamey 8000, Niger; balkaly83@gmail.com (B.A.T.); i_amadou@yahoo.fr (I.A.)</footnote>

<footnote n="16">16 UMR G-EAU, IRD (AgroParisTech, Cirad, INRAE, MontpellierSupAgro, Univ Montpellier), Univ Montpellier, 34196 Montpellier, France; jean-claude.bader@ird.fr</footnote>

<footnote n="17">17 Direction Nationale de l'Hydraulique, Conakry 001, Guinea; barryaliou55@yahoo.fr</footnote>

<footnote n="18">18 Laboratoire Leïdi "Dynamique des Territoires et Développement", Université Gaston Berger (UGB), BP 234-Saint Louis 46024, Senegal; ansoumana.bodian@ugb.edu.sn</footnote>

<footnote n="19">19 Senior Investigator of IRD; yj.boulvert@gmail.com (Y.B.); jean-claude.olivry@wanadoo.fr (J.-C.O.)</footnote>

<footnote n="20">20 UMR G-EAU, IRD (AgroParisTech, Cirad, INRAE, MontpellierSupAgro, Univ Montpellier), Conakry 001, Guinea; nadine.braquet@ird.fr (N.B.); luc.ferry3435@gmail.com (L.F.)</footnote>

<footnote n="21">21 Independent Consultant, 34980 Combaillaux, France; jean-louis.couture@wanadoo.fr</footnote>

<footnote n="22">22 Département de Géographie, Faculté des Lettres et Sciences Humaines, Université Cheikh Anta Diop, Dakar 12500, Senegal; honore.dacosta@ucad.edu.sn (H.D.); sambousaly@gmail.com (S.S.)</footnote>