A non-stationary model for reconstruction of historical annual 3 runoff on tropical catchments under increasing urbanization 4 ( Yaoundé , Cameroon ) 5 6

Supplementary Material 1 2 A non-stationary model for reconstruction of historical annual 3 runoff on tropical catchments under increasing urbanization 4 (Yaoundé, Cameroon) 5 6 Camille Jourdan, Valérie Borrell-Estupina, David Sebag, Jean-Jacques Braun, Jean-Pierre Bedimo 7 Bedimo, François Colin, Armand Crabit, Alain Fezeu, Cécile Llovel, Jules Rémy Ndam Ngoupayou, 8 Benjamin Ngounou Ngatcha, Sandra Van-Exter, Eric Servat, Roger Moussa 9 10 1 OSU OREME, Univ Montpellier, Montpellier, France 11 2 LISAH, Univ Montpellier, INRA, IRD, SupAgro, Montpellier, France 12 3 HSM, Univ Montpellier, CNRS, IRD, Montpellier, France 13 4 Normandie Univ, UNIROUEN, UNICAEN, CNRS, M2C, Rouen, France 14 5 GET, CNRS, IRD, University of Toulouse, Toulouse, France 15 6 Institut de Recherches Géologiques et Minières, Centre de Recherches Hydrologiques, Yaoundé, Cameroon 16 7 French National Research Institute for Development (IRD), Yaoundé, Cameroon 17 8 WSP France, Toulouse, France 18 9 Laboratoire de Géologie de l’ingénieur et d’Altérologie, Département des Sciences de la Terre et de l’Univers, 19 Faculté des Sciences, Université de Yaoundé I, BP 812, Yaoundé, Cameroun 20 10 Department of Earth Sciences, Faculty of Sciences, University of Ngaoundéré, Ngaoundere, Cameroon 21 11 GM, Univ Montpellier, CNRS, Université des Antilles, Montpellier, France 22 † deacesed 23


Introduction
The link between the hydrological cycle and human societies has been strong with changes and intensification of these interactions over time (Koutsoyiannis, 2013;McMillan et al., 2016).In response to the imperative to include human increasing impacts as integral to hydrological research, the International Association of Hydrological Sciences (IAHS) launched the hydrological decade (2013-2022) with theme "Panta Rhei: Change in Hydrology and Society".Due to rapid and complex anthropic changes, the IAHS emphasize the necessity to improve the capability of decision maker and water resources stakeholders to make predictions of hydrological dynamics and support sustainable societal development in a changing environment (Montanari et al., 2013).
Quantifying and understanding past changes in hydrological processes are necessary to suggest reliable future predictions of hydrological signatures.Reconstructing past data and predicting annual, monthly and daily hydrographs in a changing environment, and especially on poorly gauged catchments with sparse data, remains a challenge for hydrological science.
Long-term hydrological modelling requires integrating the impact of global changes in terms of climate, land-use and infrastructures.Nowadays, urban areas represent only 2 % of the total surface of the Earth but concentrate more than 50 % of world population, cities count close to four billions people, this figure was multiplied by five since 1950 (Janicot et al., 2015).This huge urbanization rate combined with a demographic explosion is especially significant in the inter-tropical regions where most of developing countries and numerous in development megalopolis are located (UNDESA, 2017).For example, population in Africa is projected to reach 2.5 billion people by 2050 with about 55 % living in urban areas (Güneralp et al., 2017).Hence in this context, the impact of land-use changes on runoff, especially in urban and peri-urban zones, seems to override rainfall changes impacts.
Empirical, conceptual, probabilistic and physically-based models can be used to simulate the impact on runoff of global changes.Conceptual models such as HBV (Bergström and Singh, 1995), GR1A, GR2M or GR5J (Mouelhi, 2003;Mouelhi et al., 2006;Le Moine, 2008) or physically-based models as MIKE-SHE (Abbott et al., 1986) were applied to assess global changes impacts on hydrology.On tropical climate, such models were applied at the local scale (Giertz et al., 2006), the mesoscale (Beck et al., 2013;Wagner et al., 2013;Yira et al., 2016) or large scale catchments (Genwei, 1999;Zhou et al., 2010) at daily, monthly or annual time steps.All these models require accurate information about the basin physiographic characteristics, long series of rainfall-runoff data, climate and land-use changes data; moreover an adequate calibration/validation strategy must be undertaken in order to take into account the spatio-temporal evolution of some parameters.However, on basins with sparse data at various time steps (e.g.only monthly rainfall available on a given period), and in the absence of continuous long series rainfall-runoff data, simple modelling approaches must be adapted for reconstructing annual runoff taking into account available sparse historical data and information on climate and land-use changes.
For that, empirical approaches in non-dimensional spaces were largely used since Turc (1954) and Budyko (1974) which were largely applied, analysed and extended the last decade (Zhou et al., 2015; see a synthesis in Moussa and Lhomme, 2016).Ponce and Shetty (1995) developed an original annual rainfall-runoff model based on a formulation similar to the one developed in the Soil Conservation Service method (SCS, 1956;Mishra and Singh, 2013), and Sivapalan et al. (2011) extended this approach to model different components of the water cycle at the annual scale.However, all these models generally don't take into account changes in climate and land-use.Hence, there is a need to develop simple parsimonious approaches modelling for annual runoff taking into account non-stationarity due to land-use long term evolution, and adapted to basins with sparse data.
In most of developing countries, environmental monitoring as precipitation and streamflow are often limited.
This data-sparse condition results of a poor knowledge of basin climatology and hydrological signatures, such as annual runoff.Even for areas faced with recurring high water management issues, most of national organizations do not have resources to purchase and maintain the necessary instrumentation for field monitoring (Hughes et al., 2015).The availability of continuous and long term data sets of runoff varies dramatically throughout the world (Kundzewicz et al., 2007).Prediction in ungauged basins (PUB) approaches are tools to cope with this data-sparse context (Blöschl, 2013) and are based on regionalization of hydrological characteristics by spatial proximity or geomorphological similarities from donor to target catchments (Parajka et al., 2013;Salinas et al., 2013).However, recently development of soft monitoring (Crabit et al., 2011) and crowdsourced hydrology (Lowry and Fienen, 2013;Le Coz et al., 2016;Mazzoleni et al., 2017) gave encouraging results.To cope with the lack of long-term observation (rainfall-runoff) on catchment faced to land-use changes a solution is to set up a dedicated short-term instrumentation on catchment faced to various land-use states associated with a best valorisation of historical database.This methodology lets to observe hydrological processes of catchments characterized by various states of land-use and under various climatic contexts.
The scope of this paper is to develop a combined approach of data acquisition and the development of a new semi-distributed model taking into account land-use changes to reconstruct and predict annual runoff on a catchment exposed to high urban increase.The data acquisition step implies (1) to deploy a complementary and dedicated short-term and multi-scale space hydro-meteorological network, (2) to analyse the most recent global land-use products with adapted time and space resolution and (3) to maximize the valorisation of historical studies for the evaluation of catchment characteristics (land-use, topography, soils map) and some environment variables The model is based on mathematical relationship between precipitation P and runoff R similar that proposed by Ponce and Shetty (1995) and Sivapalan et al. (2011) for applications at the annual scale on the basis of the SCS equations (Mishra and Singh, 2003).P ranges between Pn and Px which respectively correspond to the minimal and the maximal precipitation values over a large historical period of the main study catchment.Applications were conducted in tropical basins where R is not nil.Therefore, in order to simplify, we use a simple second order polynomial relationship between R and P such as (Fig. 1): and the annual runoff coefficient: where and  are empirical parameters which can be linked to catchment properties (e.g.topography, soil, landuse).
The first hypothesis is that the annual volume VO at the outlet of the main catchment is the sum of the annual volumes Vi on each sub-catchment Ti (Fig. 2b): where n is the number of sub-catchments and i is the index representing a sub-catchment noted Ti.We define the annual runoff Ri on each sub-catchment Ti as: where Ai is the area of Ti and AO is the area of the whole catchment with: Consequently the annual runoff RO of the whole catchment is defined as: The second hypothesis presumes that the runoff coefficient R / P and the annual runoff R are only functions of P and an "hydrological index" noted I with fP, I) and R = g(P, I) similar to the SCS approach used in Ponce and Shetty (1995) and Sivapalan et al. (2011).As for the curve numbers CN in the Soil Conservation Service method (Mishra and Singh, 2003), the index I characterizes topography, soil and land-use of the basin, and enables to take into account land-use evolution through time: I is considered low for permeable soils and/or low urbanization areas producing low runoff, and I is considered high for impermeable soils and/or high urbanization areas producing high runoff.The index I is an empirical indicator and can be defined as a linear combination of several components Ci.As for the CN method, in this study we choose the following three

Calibration, validation, reconstruction procedure
The annual rainfall-runoff model developed herein is calibrated using data from donor catchments (noted D) historical information, and from the dedicated short-term instrumentation.Donors could be catchments or subcatchments inside or near to the main study catchment (Fig. 2a).
where   ̂ is the simulated annual runoff and   j the observed annual runoff for the main study catchment; n the number of the evaluated year and j the index corresponding to a given year. ̂, is the simulated annual runoff for target i for the evaluated year j and Ri,j the observed annual for target i for the evaluated year j.In order to evaluate the robustness of the model, a sensitivity analysis is conducted on the impact of the number of donor catchments used establishing the rules of the hydrologic index I.Finally, the performance of the developed model is compared to a classical annual runoff model generally applied under stationary conditions (i.e. the GR1A model based on the Turc (1954) equation; Mouelhi, 2003).
3 Study site

Oro-hydrography and climate
The Mefou River is a tributary of the Nyong.The Mefou catchment at Nsimalen (421 km²) includes the capital city of Cameroon, Yaoundé (Fig. 3a).The upstream part of the basin (70 km²) is controlled by the Mopfou dam built in 1969 planned to provide about one third of the drinking water to the Yaoundé urban area (100,000 m 3 .day - ).
The catchment is hilly (peaks at 1000 m a.s.l) with important wetland areas (around 700 m a.s.l) at the downstream parts (Fig. 3a).The Mefou River is 35 km length from the Mopfou dam to Nsimalen.The main tributaries of the Mefou is the Mfoundi which drains the most urbanized parts of the whole catchment (Fig. 3a).
The river channel slope ranges between 1 ‰ and 5 ‰ causing frequent floods in the lowlands.Canalization of the upstream Mfoundi and its tributaries were undertaken since 2002 in order to reduce floods in the urbanized zone.
The landform of the South Cameroon Plateau corresponds to the dismantling of an old iron crust undergoing more humid climatic conditions (Bilong et al., 1992;Beauvais, 1999;Bitom et al., 2004).This multi-convex landform is composed of rather closely spaced hilly compartments, typically of few hundred metres in diameter, separated by flat swampy valleys of variable stretch from 50 to 500 m width (Bitom et al., 2004).We used the slope index SI of Roche (Roche, 1963)  March to June, short dry season from July to August, short rainy season from September to November, and long dry season from December to February.The hydrological year is defined from March to February.Ikounga (1978) has estimated the potential evapotranspiration PET between 900 mm (Sunken Colorado pan) to 1200 mm (Thornthwaite method).Supplementary Material (Sect.2, Fig. S1) shows the mean monthly precipitation, temperature and PET.

Soil and land-use
The regolith is developed on a granito-gneissic basement.Ferralsol (laterite) regolith is developed on the hillslopes while in the swampy valleys, it is topped with bleached hydromorphic soils developed on colluvium and river alluvium (Bachelier, 1959;Braun et al., 2005;Braun et al., 2012).In the region of Yaoundé, Humbel and Pellier (1969) calculated a soil surface permeability between 20 and 70 cm.h - up the hill, and 200 cm.h - near the swampy valleys.These values of permeability are very high and limit the surface runoff, especially in swampy valleys.The clay amount is generally higher at the top of the hills than at the bottom.In the field experiment we conducted in 2017, we measured in the region of Yaoundé the soil surface permeability by a simplified Beerkan method (Bagarello et al., 2014) and obtained values ranging between 2 and 125 cm.h -1 which are comparable to the values given by Humbel and Pellier (1969).Humbel and Pellier (1969) also showed that for both types of soil, the surface permeability decreases quickly with the depth until an impermeable layer facilitating lateral flow.In this study we use the proportion of hydromorphic soil (HS) to characterize the soil component of the hydrological index I for donor and target catchments (see Sect. 5.1).
The administrative urban area of Urban Community of Yaoundé (CUY) covers nowadays about 297 km².As most part of the Nyong basin (Olivry, 1979), the Mefou catchment was originally mainly covered by humid tropical forest.The study area is faced to major land-use changes due to human activities mainly urbanization and agriculture (see more details in Supplementary Material, Sect.3).Population in Yaoundé has increased from 90,000 in 1960 (Franqueville, 1968)  The impact of these land-use changes on hydrological processes is not yet quantified on the Mefou catchment.The urbanization of the Mefou catchment also impacts both groundwater and river water quality due to domestic and industrial untreated wastewater from urban areas but also contamination by peri-urban agriculture.
For example, Branchet et al. (2018) recently shows high Diuron® concentration on surface water that frequently exceeded the European water quality guideline.These growing issues of water management drive the removal of wetlands in lowlands impacting their ecosystem services as the natural purification of water (Daily, 1997;Russo, 2013).

Historical sparse data
Precipitation measurements are available at a monthly time step at two historical raingauges (Fig. 3a): P1 from 1930 to 2017, and P2 from 1955 to 1978.The correlation coefficient for the common period between both stations at the annual time step is 0.74.A long-term reference precipitation dataset was calculated using the mean of P1 and P2 when data from both stations are available, and from P1 for the remaining periods.
Daily runoff measurements at the Mefou catchment outlet at Nsimalen started in 1963 but with long periods of gaps.Annual runoff is available for only 29 years (1964-1977, 1979, 1982-1986, 2005-2011 and 2017), and ranges between 250 mm and 850 mm.Annual runoff coefficient ranges between 0.21 and 0.48.
Few studies are available on the hydrology of Yaoundé, and most of them date before the 80 th .They particularly focused on water balance at monthly and annual scales: on the Mefou river (Lefèvre, 1966;SNEC, 1969;Olivry, 1979), on the Mfoundi (Srang, 1972;Nguemou, 2008), and on sites downstream Nsimalen (Ikounga, 1978).From these studies, we retain six historical donors (noted DH; Fig. 4a), and Table 1 presents their characteristics: area between 24 and 235 km², period of observation, annual precipitation P between 1640 and 1930 mm, annual runoff R between 392 and 1340 mm, and annual runoff coefficient  between 0.22 and 0.77.
Under the hypothesis that the storage annual variation is nil, we estimate an annual evapotranspiration AET = P -R which ranges between 400 and 1400 mm.Information relative to precipitation measurements are well documented in the historical studies previously cited.Note that the donor DH6 is located out of the Mefou catchment but quite close from Yaoundé area (40 km) and presents a similar topography, soil and land-use conditions of the Mefou catchment (Ikounga, 1978).These donors cover different land-use states: e.g.forestry natural cover for DH4 and DH6 (U < 1%) and highly urbanized cover for DH3 (U > 75%).
Other historical studies of smaller (< 10km²) and larger (> 5000 km²) catchments in Nyong basins in natural land-use context give P between 1420 and 1730 mm, R between 392 and 530 mm,  between 0.18 and 0.

Dedicated short-term multi-scale instrumentation (03/2017-02/2018)
In order to complete historical data, we undertook dense spatial rainfall-runoff instrumentation during one hydrological year (03/2017-02/2018).Eleven daily time step raingauges were installed in order to study the spatial variability of precipitation (Fig. 4a).The choice of limnimetric stations location was determined by the position of the main confluences, by the position of historical limnimetric stations, and the need to measure runoff from basins with different degrees of urbanization (Fig. 4a).This instrumentation provides six additional experimental donors (noted DI) with different ranges of heterogeneities in terms of area, land-use, topography and soil (Table 1).The limnimetric station DI1 is located downstream the dam and enables to measure the outflow from the reservoir at 100 ± 25 mm.yr -1 .The lack of measurements of the outflow value until 2017-2018 makes this results the first assessment of the dam impact on Mefou water budget.The donor DI4 corresponds to the intermediate basin between DI3 and DI2.Table 1 presents their characteristics: area between 21 and 120 km², P between 1620 and 1715 mm, R between 712 and 1250 mm,  between 0.40 and 0.76 and AET between 405 and 908 mm.Annual precipitation on these donors DI are of the same order as for historical donors DH while runoff and runoff coefficients are generally higher for catchments with higher urbanization rate.

Main characteristics of the donor catchments
The Mefou catchment originally covers by dense tropical forest includes the most part of the city of Yaoundé.
The urban area started growing since 1960 (1 % of the total basin area) to currently reach about 30-35 % of the basin area with an impervious area estimated to 15 %.The forest cover has vanished of more than 50 % since 1980 with a huge conversion of the primary forest into secondary and degraded forests.Nowadays, the forests cover about 40 % of the Mefou at Nsimalen.The various sources cited in Sect.3.2 showed a growth of agricultural areas around the urban area of Yaoundé, with cropland and grassland covers around 30 % of the catchment area in 2015.
The catchment can be considered as peri-urban due to the noticeable urbanization and the development of agricultural activities observed in lowlands and outskirts.However, the south-west part and the area drained by the Mopfou dam in upstream remain slightly affected by urbanization.
Combining historical studies and dedicated short-term instrumentation 2017-2018, we have 12 donor catchments, 6 from historical studies (DH) and 6 from the instrumentation (DI) presenting various topographic, soil and land-use characteristics; the area ranges between 21 and 235 km², P ranges between 1620 to 1930 mm, R between 390 and 1340 mm, between 0.22 and 0.77 and AET between 400 mm to 1400 mm.SI varies from 6.7 % to 13.5 %, HS varies from 0 to 44 % and U varies from 0 to 83 % over donor catchments of the study area.We

Precipitation
The model needs as input the precipitation P which has to be calculated on both donor and target catchments (Fig. 4).For donors, precipitation information are well documented in corresponding studies or issue of dedicated short-term instrumentation (Table 1).For targets, we used the long-term historical raingauges and the spatially short-term information (1968( -1969( from SNEC (1969)), and 2017-2018 from the short-term instrumentation) to construct historical precipitation database for each target.

Temporal variability of precipitation
First, we study long-term precipitation trends  over the Mefou catchment from historical raingauges P1 and P2.The average precipitation is 1580 mm (Pm) and the minimal and maximal annual precipitation are respectively Pn = 1050 mm and Px = 2200 mm.Values of Pn and Px set the limit of availability of the developed model for the study catchment.Fig. 5a shows no significant trends of annual precipitation over the period, but we observe a succession of humid (1960-1970, 1980-1990, and 2006-2013) and dry (1935-1950, 1970-1980, and 1990-2000) periods.At the seasonal scale we observe some changes in amount of precipitation: i) no change during the first wet season (March to June) (Fig. 5b); ii) during the first dry season (July and August), increase of the mean precipitation from 100 to 220 mm (+120 %) on the period 1930 to 2015 (Fig. 5c); iii) during the second wet season (September to November) slight increase from 700 to 760 mm (+9 % ; Fig. 5d); iv) during the second dry season (December to February) decrease from 110 to 80 mm (-28 %; Fig. 5e).This historical precipitation database is used to construct the database precipitation for target catchments.Results shows also that there is no a clear changes on annual precipitation between 1930 and 2015, and consequently the trend of annual runoff coefficient increase can be related mainly to catchment change and particularly to the increase of urbanized areas.

Spatial variability of precipitation
Second, we study the spatial distribution of annual precipitation over the Mefou catchment.Due to the lack of spatial information for the historical period, a precipitation weight wTi is assigned to a target catchment Ti such as: where P is the mean annual precipitation on the Mefou catchment from the historical database and PTi the mean annual precipitation on Ti.The term wTi = PTi/P can be both calculated using historical data (Figs.6a and 6c) and the instrumentation 2017-2018 (Figs.6b and 6d).For both cases, we obtain comparable and retain wT1 = wT3 = wT5 = wT6 = wT7 = 1 for respectively T1, T3, T4, T5, T6 and T7; wT2 = 1.05 for T2 is slightly high due to the high values of P; wT4 = wT8 = 0.95 for T4 and T8.

Relationship between annual runoff coefficient and precipitation
Third we study the relationship between the annual runoff coefficient and P for three stations in nearlysteady land-use states (Fig. For topography CT, the slope index SI of Roche (Roche, 1963) is calculated for donors (Table 1) and targets from SRTM (2014).We define: CT = 0 for SI < 7 %; CT = 0.5 for 7 % ≤ SI ≤ 12 %; CT = 1 for SI > 12 %.
For soil condition CS, the lack of accurate soil maps over the catchment constrains us to define indirectly soil condition heterogeneities over the catchment.Historical studies of soil characteristics (Bachelier, 1959;Pellier, 1969;Humbel and Pellier, 1969) are used to define soil classes depending on the altitude and the slope derived from the SRTM 2014.For that, we calculate the area of lowlands (altitude < 730 m) with low slopes (< 7 %) corresponding to hydromorphic yellow soil characterized by lower rate in clay and higher surface permeability.The proportion of hydromorphic soil (HS) on each catchment is used to estimate the classes of CS (see for donors Table 1, and for targets: CS = 0 for HS > 15 %; CS = 0.5 for 2 % ≤ HS ≤ 15 %; CS = 1 for HS < 2 %. For land-use component CLC, historical references and global products (summarized in Table 2) are used to characterize land-use of donors and the evolution of target land-use over past-period with available data (1930, 1950, 1980, 2000, and 2017) and future scenario (2030).In order to integrate the main land-use signature, we define six classes for CLC according to urban area proportion of (U; see for donors Table 1, and for targets the Supplementary Material, Table S3): CLC = 0 for U < 1 %; CLC = 0.2 for 1 < U < 5 %; CLC = 0.4 for 5 < U < 20 %;  3 and for targets in Table 4.

5.2
Relationship between annual runoff  and CT, CS and CLC for donors DH4, DH5 and DH6 correspond to forested areas (CLC = 0) whereas DI5 and DH3 have high rates of urbanization (CLC = 1, Table 3).For these basins, precipitation presents a low range of variation between 1645 and 1810 mm.These results show the significant impact of land-use conditions on runoff, but topography and soil condition could explain complex hydrological responses.Consequently when calculating the index I, we will give a higher weight to the component CLC in comparison to CT and CS.

5.3
The weights T, S and LC From data analysis (Sect.5.2), we showed that the impact of land-use change on runoff is higher than the impact of soil and topography.Consequently, we affect higher weight for LC, with LC > T and LC > S.

5.4
Introducing I in the model structure In the following, we choose a simple linear relationship between I and Eq.14; Fig. 9) which leads that the value of 1 is constant and similar for all values of I. We observe that the impact of land-use change (represented by I) on annual runoff (2) is higher than the impact of precipitation change (1), with 1 = 0.15 (Fig. 7), 2 = 0.60 (Fig. 9) and 1 << 2.We consider a reference precipitation   =   +

2
, and let  be the runoff coefficient calculated by the linear regression adjusted from donors under precipitation near of PR (1625 mm).Then  is calculated as the sum of   and a factor G taking into account the impact of precipitation: Introducing Eq. ( 14) and ( 16) into Eq.( 15), we obtain very simple second order polynomial relationship between R and P (Eq.17 similar to Eq. 1) and a linear relationship between  and P (Eq.18 similar to Eq. 2), and with  = ( In summary, the model needs the precipitation P as input and the three parameters a, b and 1 characterizing the relationship between  and I.These three parameters can be calibrated using data from donor catchments.-to study the spatial hydrological functioning of the basin on eight target sub-catchments and calculate the water balance during the short instrumentation period 2017-2018 (Sect.6.2).
-to reconstruct the hydrograph at the Mefou at Nsimalen and on the eight sub-catchments for the historical period 1930-2017 and to simulate the impact of future scenarios of land use and urbanization (Sect.6.3).

Sensitivity analysis, calibration, validation and model comparison
Applications were conducted on the period 1930-2017, using precipitation data on P1 and P2, to reconstruct annual runoff for all eight target sub-catchments and the whole Mefou catchment at Nsimalen.Predictions for the impact assessment of future land-use scenario on annual runoff were then also made.In the application, we distinguish two cases, before and after the dam construction (1970).Before 1970, the catchment T1 (controlled area of the dam location) is considered as other catchments (R depends of I and P).After 1970, the simulated R of T1 corresponds to the proportion of precipitation discharged measured during the short-term instrumented period (= 0.05 to 0.15; see Table 1 for DI1 and Sect.3.4).
From data analysis in Sect.4.3 (Fig. 7), we retain 1 = 0.15.We run a sensitivity analysis on the remaining two parameters a and b (adjusted from the regression DaIb with I calculated using Eq.13 with T = 1/9 and S = 1/9, LC = 7/9) for different sets of donor catchments.We run the model for n = 6, 8, 9 and 10 donors (see Table 1 and Sect.3.3 and 3.4).In each run, we select randomly 30 sets of n donors, and in order to have a wide range of variation of I, we add a constrain that for at least one point we have I < 0.3 and for at least one point we have I > 0.7.The model output is given by Eq. 1 to 6 at the Mefou at Nsimalen, and the model is evaluated using the three criteria RMSE (Eq.8) and r² (Eq.9) and  ̅ (Eq.11) for the 29 observed years (see Sect.The semi-distributed model results were also compared to the stationary lumped annual runoff model GR1A (Mouelhi, 2003) using the same calibration and validation procedure.GR1A is used to compare with a stationary approach of the catchment characteristics.Results are shown on Fig. 12 with performance for GR1A significantly lower with RMSE = 126 mm, r² = 0.43 and  ̅ =19 % for calibration and RMSE = 128 mm, r² = 0.42 and  ̅ = 22 % for validation over the both same periods at Mefou catchment scale.As the GR1A was calibrated using alternate years on the whole period, we observe that GR1A slightly overestimate the runoff for the period 1963-1980 (with low impact of urbanization), and underestimates runoff for the period 2011-2017 (with high impacts of urbanization)

Annual water balance on the instrumented period 2017-2018
The rainfall-runoff data from the short-term instrumentation 2017-2018 enables to measure the contribution of the catchments T1, T2, T3 and T6 of the Mefou catchment at Nsimalen.However, the target sub-catchments T4, T5, T7 and T8 were not gauged.Table 5 gives the values of P, R, AET, and the contribution of each sub-catchment Ki, corresponding to runoff volume of sub-catchment Vi divided by the volume at Nsimalen VO (with Ki = Vi / VO).
P ranges between 1580 and 1715 mm, R between 100 and 1325 mm, AET between 320 and 1260 mm, between 0.21 and 0.76 and K between 2.5 to 18.5 %.We can classify the eight target catchments into four categories according to land-use: i) controlled by the dam, T1; ii) urbanized T5, T6 and T7; iii) peri-urban T2, T3 and T8; iv) natural basins T4.
The first category concerns the sub-catchment T1 controlled by the dam.The annual discharge R1 measured at the outlet of the dam is 100 mm +/-25 mm, corresponding to a contribution K1 = 2.5 % on the total volume at Nsimalen.
The second category corresponds to sub-catchments firstly faced to urbanization during the study period.We For the second category (T5, T6, T7), an increasing trend of R is observed very early among the whole period for T5 and T6 which are nowadays the most urbanized target of the Mefou catchment following by T7. Between the two periods (1950-1980) and (1987-2017),  ̅ increases from 45 % for T5 to 79 % for T6, ̅ increases between 50 % for T5 to 85 % for T6.Q5 increases of 37 % for T5 to 74 % for T7 and Q95 increases of 47 % for T5 to 82 % for T6.
For the third category (T2, T3, and T8), classified as peri-urban catchments, sub-catchments are characterized by an increasing R more delayed compared to catchments of the first category.Current changes are deeply modifying these catchments for the last decade and the urbanization processes will be certainly higher than on other sub-catchments in the near-future due to the current extension of the urban area.Between the two periods,  ̅ increases of 25 % for T3 to 62 % for T8.Q5 increases of 30 % for T2 and T8 but decreases from of 26 % for T3 whereas the Q95 increases for the three catchments, from 48 % for T3 to 69 % for T8.Land-use changes were significant only since 2000 for T3, and impact on R is moderate compared to the two other catchments.
For the fourth category (T4), T4 was not impacted by urbanisation, ̅ is unchanged (0.20) and differences of  ̅ are only drived by  ̅ difference of -5% (from 1625 mm to 1550 mm) and impact mainly low flows (-26 % for Q5).No major changes were observed in this area until nowadays, but in development projects and urban area extension will certainly impact T4 in near-future.
At the Mefou scale and for the same two periods, we observe an increase of  ̅ of 27% (from 409 to 518 mm), an increase of ̅ of 31 % (from 0.25 to 0.33), an increase of Q95 of 29% (from 650 to 840 mm) and nearly no changes for Q5 (from 280 mm to 273 mm).The impact of land-use changes is clear on annual runoff but driest years are much less impacted than wettest years.
In order to quantify only the impact of land-use changes on annual runoff, we applied a constant precipitation of 1580 mm (mean precipitation over the period) for the period 1930-2017 (Fig. 13).Until 1980, the impact of land-use changes seems quite limited, with an increase of 110 mm of R (+ 30%).However, between 1980 and 2017, the increase of R and under the same precipitation condition seems quite relevant with an increase of 53% (from 455 to 700 mm and from 0.29 to 0.44).These hydrological changes are associated with a huge increasing of urban areas from 38 km² over the whole catchment to 130 km² over the same period.
We observe an increase of R and of 85 % (from 455 to 840 mm and from 0.29 to 0.53) between 1980 and 2030.
Even if this scenario is fictive, it is quite reliable due to the dynamic of land-use changes observed these few decades and knowing the most recent projection of population of Yaoundé.
In tropical context, few studies evaluated the impact of land-use conversion from natural to urbanized area.
Most of the studies quantified the impact of conversion from forest or shrub cover into cropland (Gessess et al., 2015;Yira et al., 2016) or forest regeneration (Beck et al., 2013).

Conclusion
Urbanization impacts drastically the water cycle, and this phenomenon will intensify in the future for most tropical regions due to huge population growth and rural exodus.These impacts are complex and not yet quantified especially in tropical area presenting sparse hydrological data.This work is part of the theme Panta Rhei of the IAHS, and aims to study the impact of land-use change, especially due to urbanization, on annual runoff on the tropical mesoscale catchment of the Mefou, Yaoundé, Cameroon.
The methodology combines the processing of historical sparse hydrological data and a dedicated short-term instrumentation (2017-2018) in order to get heterogeneous set of catchments in terms of land-use.Data analysis shows that there is no significant trend on annual precipitation for the last 90 years.However, the analysis of historical precipitation/runoff data on different catchments with different land-uses show an increase of the annual runoff coefficient due to urbanization from 22 % on natural basins to 77 % on urbanized basins.
A simple semi-distributed annual runoff model was developed taking into account non-stationarity due to land-use changes.The model is based on a similar approach as proposed by Ponce and Shetty (1995)  for catchment faced to urbanization (Braud et al., 2013;White and Greer, 2006;Barron et al., 2003).
The coupled experimental-modelling approach proposed herein opens promising perspectives regarding the           for 1930, 1950, 1980, 2000, 2017 and scenario for 2030 (see references of land-use sources in Table 2).Q95 and Q5 for 1950-1980 and 1987-2017 for the eight sub-catchments and the whole catchment. ̅ : Mean annual simulated runoff for a period of 30 years (1950-1980 and 1987-2017) r² : Coefficient of determination (Eq.9)

(
abbreviations.The Supplementary Material gives additional information on data sets. components: topographic component (CT) such as slope classes impacting runoff, and soil component (CS) such as permeability classes and land-use component (CLC) such as urbanization classes.Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.i is the weight attributed to component i and m the number of components including in the hydrological index.If m is equal to 1, the hydrological index I is based on only one component, for example the land-use characteristics (CLC) if this descriptor is considered as the main factor changing in time.We note In and Ix respectively the lowest and the highest values of I over the catchment dataset used to construct the model.Therefore, for a given rainfall P, R increases when I increases; for a given index I, R increases when P increases.For a given value of I the runoff coefficient  increases when the rainfall increases from Pn to Px.Let n,I and x,I be the corresponding values of  for Pn and Px respectively.Let 1 = x,I -n,I as shown in Fig. 1a.For a given value of P, the runoff coefficient  increases when I increases from In to Ix.Let n,P and x,P be the corresponding values of  for In and Ix respectively.Let 2 = x,P -n,P as shown in Fig. 1a.As we have a linear relationship between P and Fig.1a, the value of 2 is constant and similar for all values of P. In order to calculate 2, we need data on different catchments and periods with the same value of P but with different values of I ranging between In and Ix.The annual runoff model proposed herein uses a simple relationship R = f(P, I) as shown in Fig. 1b.The domain of application of the model is for the precipitation P ∈ [Pn, Px] and the hydrological index I ∈ [In, Ix].The model needs as input the precipitation P which has to be calculated on each sub-catchment Ti (see an application in Sect.4).The model needs also the definition of the hydrological index I which is time variable and enables to take into account land-use changes and non-stationary relationships between R and P. The definition of the rules to construct the components Ci and the weights i of I (Eq.7) are obtained from data analysis on the study site as shown later in Sect. 5.
to 3.65 million in 2017 (UNDESA, 2017) with an annual growth rate of 5.7 % per year between 1987 and 2005 according to the Central Office of Cameroonian Population Study and Census.This huge demographic change is characterized by an important expansion of the urban area Fig.3band the increase of population density(Bopda, 2003).In the opposite, forest and wetlands areas decreased, and were generally replaced by agricultural and urban areas as shown in Fig.3cwith the land-use classification over the Mefou catchment from the land cover product of the European Space Agency available for Africa (ESA-CCI LC) for the year 2016.Moffo (2017) analysed a set of aerial photography in 1956 and estimated that the impervious areas covered 3.5 km², less than 1 % of the Mefou catchment area.We used ESA-CCI LC and OpenStreetMap® 2015 layers to calculate impervious areas of around 64 km² (15 %) in 2016.Ebodé (2017) used Landsat images to study the evolution of land-use from 1978 to 2015.He noticed at the Mefou catchment until the Nyong confluence (basin area of 802 km², approximately two times the Mefou basin area at Nsimalen) a decrease of 160 km² of the total forest cover, with specifically a decrease of 60 % of the primary forest area from 235 km² in 1978 to 94 km² in 2015, a decrease of 73 % for swampy forest from 206 km² to 57 km², and an increase of 60 % in degraded and secondary forest from 223 km² to 353 km².For the Mefou at Nsimalen, Ebodé (2017) estimated that the agricultural Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.area increased from 10 km² (3.5 % of the catchment area) in 1978 to 28 km² (10 %) in 2015, and that the urban area (integrating impervious surfaces) increased from 45 km² (11 %) in 1978 to 151 km² (36 %) in 2015.We used the proportion of urban area U over donor and target catchments to characterize the land-use component of the hydrological index.
observe that  can vary widely for the same catchment function of the land-use: e.g. from 0.33-0.4for DH1 (U = 5 %) and DH2 to 0.77 for DH3 (U > 75 %).All the observed data on the study site are analysed to understand Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.hydrological processes of the catchments faced to land-use changes in order to identify rules defining the hydrological index I on donors and apply it on targets for the period 1930-2017.

Figures
Figures 6a and 6bshow the mean annual precipitation for respectively the hydrologic years1968 -1969     (SNEC, 1969) )  and 2017-2018 (dedicated short-term instrumentation), the only historical years with available dense spatially measured precipitation.For 1968-1969, P varies over the Mefou catchment between 1400 mm to 2000 mm with an average of 1780 mm.For 2017-2018, P varies between 1400 and 2100 mm with an average of 1640 mm.The hydrological year 7): the Mefou at Nsimalen on the period 1964-1984 with a low impact of land-use evolution in comparison to the period 1984-2015, the Mefou at Etoa natural forested basin on the period 1967-1983, and the semi-urbanized Mfoundi on the period 1969-1971.Both the Mefou at Etoa and Mfoundi are subcatchments of the Mefou at Nsimalen.For the Mefou at Nsimalen, we adjusted a linear relationship between and P;  increases from n,P = 0.2 corresponding to Pn = 1050 mm to x,P = 0.35 corresponding to Px = 200 mm; this gives 1 = x,P -n,P = 0.15.For the Mefou at Etoa,  = 0.15 for P = 1330 mm and  = 0.30 for P = 2200 mm; both values of  for the Mefou at Etoa are inferior than those observed on the Mefou at Nsimalen for similar values of precipitation, showing the impact of land-use with low annual runoff coefficient on natural basins.For the Mfoundi,  = 0.33 for P = 1640 mm and  = 0.40 for P = 1930 mm; both values of  for the Mfoundi are superior than those observed on the Mefou at Nsimalen for similar values of precipitation, showing the impact of land-use with high annual runoff coefficient on semi-urbanized basins.In summary, we obtain approximately similar values of 1 = 0.15 on the Mefou at Nsimalen, but also on the natural Etoa catchment(1967)(1968)(1969)(1970)(1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983) and on the in-urbanization Mfoundi upstream catchment(1969)(1970).These three catchments have three different values of the hydrological index I, but with I considered constant on the presented periods.Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License. 5 The hydrological index I This section analyses the hydrological and physiographic data in order to define the rules for constructing the hydrological index I calculated as a linear combination of three components:  =     +     +     , (13) where CT is the topography component, CS the soil component, CLC the land-use component, T the weight of CT, S the weight of CS, and LC the weight of CLC.5.1 The components CT, CS and CLC Heterogeneities of topography, soil condition and land-use variability in space and time observed on the study area (Sect.3) lead us to propose classification rules to highlight the main features of catchments and to define the three components CT, CS, and CLC of the hydrological index I using cartographical data.All three components range between 0 and 1; when any of the terms (CT, CS and CLC) increase,  increases.The topography (CT) and soil condition (CS) are considered stable over the time contrary to land-use (CLC) faced to major changes.
= 0.6 for 20 < U < 50 %; CLC = 0.8 for 50 < U < 70 %; CLC = 1 for U > 70 %.Different trends of land-use changes are observed for the 8 target sub-catchments (Fig.8).From 1930 to 1950, the whole main catchment is considered to be mostly cover by originally forest (CLC = 0 for all the targets).Development of urbanization impacted first the Mfoundi sub-catchments from 1960 to 1980 (T5, T6 and T7) especially T5.Nowadays, these subcatchments reach a maximum of urbanization for T5 and T6 (CLC = 1).T2 and T8 faced to major changes since 1980 with intensification since 2000.Nowadays, the urbanization process do not get the entire area of these catchments.The urbanization continue and will be amplified in these surrounding areas due to the lack of space in the most urbanized part of Yaoundé (T5, T6 and T7).T1, T3 and T4 are the last sub-catchments impacted by urbanization; a high proportion of these catchments have forest or wetland covers.We propose a fictive but plausible scenario of land-use for 2030, regarding to the current expansion of the urban area and the perspective of future population Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.estimation for Yaoundé (from 3.6 million in 2017 to 6.7 million in 2035; UNDESA, 2017).We suppose a high development of urbanization for T2 and T8 (CLC from 0.6 in 2017 to 0.8 in 2030) and in a lesser extent a development of urbanization over the south part of the basin (T4 with CLC from 0 in 2017 to 0.4 in 2030).Values of CT, CS and CLC are presented for donors in Table

DH4,
DH5 and DH6 present low values of annual runoff coefficient with  varying from 0.22 to 0.25.DI5 and DH3 present very highvalues of runoff with  = 0.76 and 0.77.For catchments with intermediate levels of urbanization (DI2, DI3, DI4, DI6, DH1, DH2), runoff ranges between those observed in the two previous cases with ranging between 0.33 and 0.54.Analysis of  for donors DI2 and DI6 presenting the same value of CLC (0.6) but extreme values of CT and CS (DI2 is located in the hilly part of the Mefou catchment whereas DI6 present high portion of lowlands) enables to quantify the impact of CS and CT on .For the period September-December, DI6 presents runoff coefficient of 0.40 which is significantly lower than the value of 0.53 observed for DI2 on the same period.Differences observed are quite clear in term of runoff with for DI4 runoff value up to 160 mm in October against 95 mm for DI6 (see Supplementary Material, Sect.5).
the values of I for donors and Fig. 10 gives the temporal evolution of I from 1930 until now for targets.Note that in 2017, the values of I are particularly high for the target catchments T5, T6 and T7 on the Mfoundi basin due to high urbanization.In contrast, some target catchments such as T1 and T4 are or not impacted nowadays by urbanization and presents very low values of I. Finally, the target catchments T2, T3, and T8 are currently faced to the most important land-use change and have intermediate values of I.
value of I (Fig.9): for P = Pn, we have G = -1/2 and consequently = Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.6 Applications The model presented in Sect. 2 is function of precipitation P and the hydrological index I.Precipitation was calculated on the target sub-catchments using historical precipitation dataset and the relationships established in Sect. 4. The hydrological index I is defined in Sect. 5 and presented in Fig. 10 for target catchments for the period 1930 -2030.First a sensitivity analysis was conducted and the calibrated parameters a, b of the model are discussed (Sect.6.1).Then two applications were conducted on the Mefou at Nsimalen subdivided into eight target sub-catchments (Fig. 4.b) in order: 3.3).For n = 6, 8, 9 or the 10 donors, we observe a low impact of the number of donors on the calibrated parameters (a and b) and the three performance criteria with a = 0.68 +/-0.02,b = 0.12+/-0.01,RMSE = 101+/-1 mm, r² = 0.66, and  ̅ = 15 % (see Supplementary Material, Sect.6).The low variability of the average of parameters a and b from n = 8 lead us to select 8 donors by keeping the last two donors for validation.In order to get a model adapted to various states of urbanization, the calibration and validation dataset at the Mefou catchment scale should include periods of low and high urbanization rate.Observed annual runoff at the Mefou at Nsimalen are used in alternate years for calibration (15 years) and validation (14 years).From the sensitivity analysis, we calibrate a and b, choosing the set of 8 from 10 donors giving the lowest values of RMSE Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.on the 15 years calibrated period.We use the 9 donors DH2, DH3, DH4, DH6, DI2, DI3, DI4, DI5 and DI6.We obtain a = 0.74; b = 0.12 with performance criteria RMSE = 70 mm, r² = 0.79 and  ̅ = 11 %.Figure9presents the linear regression for the calibrated parameters and Fig.11shows the abacus  = g(P,I) for these parameters.In the abacus, we plotted the donor catchments by specifying the corresponding estimation of I in parenthesis to compare with the model.We also plotted the points of Etoa for the period 1967-1983 characterized by a stationarity value of I (0.11) but with a wide range of P (1320 to 2150 mm).The validation is made at two levels.First, the two remaining donor catchments DH3 and DI2 are used to validate; we obtain   3 = +8 % (+105 mm) and   3 = +12 % (+110 mm).Second, at the Mefou at Nsimalen for the remaining 14 years; we obtain RMSE = 123 mm, r² = 0.60, and  ̅ = 18 %.
Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.More studies of annual runoff urbanization impacts have been lead in temperate or Mediterranean climate (see Supplementary Material, Sect.7), Braud et al. (2013) observed a significate increases of quick-flow and decrease of inter-flow and base-flow in urbanization context on the Yzeron catchment (150 km²).Through modelling, Beighley et al. (2003) estimated for Atascadera Creek (P = 610 mm) an increase of R of more than 80 mm (+115 %) for 8 % to 38 % of urban area and an increases of R of 150 mm (+215 %) from 8 % to 52 % of urban area.
and uses a hydrological index I characterizing soil, topography and land-use.From data analysis on donor catchments, empirical rules were established to calculate I, and the model parameters.The model can be represented by simple abacus giving relationships between the annual precipitation P, the annual runoff R and the hydrological index I.The non-stationarity of the model is characterized by the hydrological index I which is time variable depending on land-use evolution.Applications were first done on target sub-catchments of the Mefou basin in order to calculate the annual water balance for catchments with different land-uses.Results show that that the Mfoundi catchment, integrating the three more urbanized sub-catchments, contributes near to 40 % of the Mefou catchment at Nsimalen despite covering only 23 % of the basin.On the opposite, the natural sub-catchment T4, not yet impacted by urbanization, contributes to only 9 % but covers 18 % of the Mefou catchment.The second result is the reconstruction of historical annual runoff from 1930-2017 for the Mefou catchment at Nsimalen with satisfying performance in a poorly-gauged context (RMSE = 99 mm; r² = 0.68;  ̅ = 14.5 %) compared to the commonly used stationary annual model (GR1A).The mean values of P, R, , Q5 and Q95 over the two periods of 30 years before and during the urbanized processes show changes at both the sub-catchment scale and the whole Mefou scale: for a decrease of about 50 % of the forest area and an increase from 8 % to 35 % of the urban area between 1980 and nowadays, we observe an increase of 53 % of R (and ) for the Mefou catchment at Nsimalen.The Future scenario of land-use Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.proposed leads to an increase of R and  of 85 % between 1980 and 2030.The observed and simulated values for heterogeneous land-use characteristics are in line with other studies which observed an increasing of annual runoff

Figure 1 .
Figure 1.The model general relationships between annual precipitation P, annual runoff R, annual runoff coefficient  and the hydrological index I.(a) Relationship between  and P with  = AP+B for different ranges of I; (b) Relationship between R and P with R = AP²+BP for different ranges of I. Pn: minimum P; Px: maximum P; In: minimum I; Ix: maximum I.The point in each graph is an example of annual runoff coefficient and annual runoff estimation for a precipitation P and an hydrological index I.

Figure 3 .
Figure 3.The Mefou catchment at Nsimalen: (a) Location, channel network and topography.(b) Urban areas evolution from 1956 to 2018 from historical photography (Moffo, 2011) and satellite images (Google Earth ®) (c) Land-use extracted from the product Land Cover for Africa of European Space Agency (ESA-LC), based on one year Sentinel-2A observations from December 2015 to December 2016.

Figure 4 .
Figure 4.The Mefou catchment: (a) Location of raingauges and limnimetric stations on donor catchments (NB: the donor DH6 is located outside of the Mefou basin at 40 km south-west); (b) target catchments.

Figure 5 .
Figure 5. Annual and seasonal precipitation: (a) Annual precipitation from 1930 to 2015 from historical raingauge P1 (Mvan Airport).(b) Precipitation during the wet season I March to June.(c) Precipitation during the dry season I July to August.(d) Precipitation during the wet season II September to November.(e) Precipitation during dry season II December to February.

Figure 7 .
Figure 7. Relationship between the annual runoff coefficient  and the annual precipitation P on three stations (Nsimalen, Mfoundi and Etoa; see the location on Fig. 3.a) for periods before 1985 with low impact of urbanization.

Figure 9 .
Figure 9. Linear relationship between the hydrological index I and the annual runoff coefficient  based on donor catchments (Table1).The term 1 represents the variation of for a given value of I and for a large range of precipitation P with Pn < P < Px.The term 2 represents the variation of for a given value of P and for a large range of I with In < I < Ix.

Figure 10 .
Figure 10.Evolution of the hydrological index I over time for target catchments for the period 1930 -2030.The points correspond to the dates where references of land-use sources are available (Table2and Fig.8).

Figure 11 .
Figure 11.Abacus obtained from the model calibrated parameters for the relationship between annual runoff coefficient  and the annual precipitation P for different values of the hydrological index I.Each point corresponds to donor catchment; the value of the calculated hydrological index I (Table3) is indicated into brackets.Crosses (+) correspond to available information at Etoa station between 1967 and 1983 for an unchanged hydrological index I estimated to 0.11.

Figure 12 .*
Figure 12.Annual runoff simulated on the 8 target catchments (T1 to T8) and on the Mefou catchment at Nsimalen for the period 1930-2017 (dark line with grey uncertainty range due to precipitation +/-10 % and hydrological index I +/-15 % estimation).The black points indicate the observed values on Nsimalen.The simulation with GR1A is presented with a dashed line.
equation: = AP + B [ -] Ai : Area of target sub-catchment i [ L² ] AO : Area of the whole catchment [ L² ] a : Parameter of the model in   =  +  [ -] equation: = AP + B [ -] b : Second parameter of the model in   =  +  [ -] Ci : Component i of the hydrological index [ -] CLC : Land-use component of the hydrological index I [ -] CS : Soil component of the hydrological index I [ -] CT : Topographic component of the hydrological index I [ -] of I [ -] Ix : Minimum value of I [ -] Ki : Contribution of sub-catchment i to the whole catchment (Ki = Vi / VO) [ -] Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.target catchment i (Eq.12) [L] Px : Maximal annual precipitation over the historical database [L]  ̅ : Mean annual precipitation for a period of 30 years (1950-1980 and 1987-2017) P1 : Annual precipitation at historical raingauge P1 [ L ] to the 5 th -percentile over a period of 30 years [ L ] Q95 : Annual runoff corresponding to the 95 th -percentile over a period of 30 years [ L ]
calibration of the model parameters and the second one for the validation.The dataset used for the calibration must include data from different ranges of precipitation Pn < P < Px and land-use characterized by the Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.The RMSE, the r², the normalised error (E) and the mean normalised absolute error ( ̅ ) criteria functions are used to assess and compare simulation performance: hydrological index In < I < Ix.
evaluation of annual runoff in catchments under changes.Nowadays, development of low cost monitoring sensors and crowdsourced sciences open opportunities to get more easily data to calibrate and validate models.In changing context, the development of coupled non-stationary modelling and dedicated instrumentation can be useful to improve the capability of stakeholders to make predictions of the hydrological dynamics of tropical peri-urban catchments.Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.

Table 5 .
Calculated values (either from observation or from model simulation as indicated) of R, AET, and K 822 for each target catchments and for the whole Mefou catchment at Nsimalen taking into account +/-10 % 823 uncertainty on P and +/-15 % I for the hydrological year 2017-2018.824 Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-116Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 May 2019 c Author(s) 2019.CC BY 4.0 License.

Table 6 .
Mean values of P, R, , and percentile