ANALYSIS OF ANNUAL RAINFALL DATA BY MARKOVIAN APPROACH IN THE LOBO WATERSHED (WEST-CENTER OF CÔTE D’IVOIRE)

VAMI HERMANN N’GUESSAN BI1,2, MARC YOUAN TA1,2, FABRICE BLANCHARD ALLECHY1, FABRICE ASSA YAPI1, ALIOUNE BADRA KONE2, KOUADIO AFFIAN1,2 ABSTRACT. The rainfall deficit has become remarkable in recent decades in Côte d’Ivoire in general and particularly in the Lobo watershed. The objective of this study is to analyze rain behaviour using weather generator MulGETS based on first order Markov chains to two states. Daily data from 1984 to 2013 from 17 stations were used to predict daily precipitation data for the period 2021 to 2050. The results obtained show that the probability of having two successive dry years or two successive wet years is higher over the entire study area for the period 1984-2013. For the period 2021 to 2050, the probability of having two successive dry years and two successive wet years will be higher over the entire basin and in the south, center and north respectively. The probability of a wet year followed by a dry year will be higher in the south, west, northwest and north of the basin. The probability of a dry year followed by a wet year will be relatively high in the north, center and southwest of the basin.


INTRODUCTION
Climate change is one of the greatest challenges facing humanity in the 21 st century. West Africa is one of the most vulnerable regions in the world to climate change, which is now a potentially major threat to the environment, water resources and sustainable development (Koumassi et al., 2014). Climate change causes several natural phenomena (flooding, drought, desertification) 7 It covers the departments of Daloa, Issia, Vavoua and Zoukougbeu; the far north belongs to the department of Séguéla; while it overflows into the south, on that of Soubré. The climate of the basin is characterized by two types of climate: the attenuated equatorial transition climate (Baoule climate with two seasons) observed in the northern half of the basin and the equatorial transition climate (attiéen climate with four seasons) observed in the extreme south. Its relief is like a peneplain whose altitude varies between 160 m and 480 m (Avenard, 1971). It is monotonous as a whole with singularities in places. Two main types of relief share the basin: plains at altitudes ranging from 160 to 240 m, located in the south of the basin, and plateaus at altitudes of 240 m and 320 m occupying most of the basin (Yao, 2014). The Lobo river basin is located in the Guinean domain and belongs to the mesophilic sector with forest areas suitable for agriculture. It is mainly composed of highly or moderately desaturated modal reworked ferrallitic soils with overburden from schists and granites (Perraud, 1971).

Data
The data consist mainly of daily precipitation data from seventeen (17) weather stations covering the study area over a period from 1984 to 2013 (30 years). They come from the Climate Prediction System Reanalysis Centre (CFSR) available on the website: https://globalweather.tamu.edu/#pubs. They were used as a reference for forecasting daily data from 2021 to 2050.

Software
The software used is of several types: -XLSTAT 2016 was used to store and statistically process rainfall data; -Matlab 2014 for the forecasting of daily precipitation data and Markovian modelling.

MulGETS model
Multi-site weather Generator of École de Technologie Supérieure (MulGETS) was developed by Chen et al, 2012. It is a stochastic time generator that generates climate data that is statistically similar to data observed at several sites. MulGETS is an extension of a single-site weather generator WeaGETS (Weather Generator of École de Technologie Supérieure) that is suitable for small watersheds where a single station can be used to represent the entire watershed (Chen et al, 2012). It uses a first-order linear autoregressive model to generate temperature and a multi-gamma distribution (a combination of several gamma distributions) and a multi-exponential distribution to generate daily precipitation amounts. However, Chen et al (2012) indicated that the gamma distribution is generally the most widely used because it is more efficient compared to the exponential distribution. This time generator was used to predict precipitation data in this study. Details of this time generator are known from the work of

First order Markov
Several studies have focused on precipitation analysis from Markov chains (Benzerti and Habaieb, 2001;Cazacioc and Cipu, 2004;Chèze and Jourdain, 2003;Meddi and Meddi, 2009; N'guessan Bi et al, 2014) because they describe precipitation echoes well. We apply it on an annual scale to determine or predict the probability of having a dry year after a dry year or not. This process expresses conditional probabilities of moving from the previous day's status (previous year) to the current year's status. To do this, we used the Markov chain method (Arnaud, 1985). Markov chains take into account the link between successive years; indeed, the rainfall in year k depends on the state of past years. This model will be of the first order if the rain in year k depends only on the previous year, i.e. the closest past of the state. It will be of order h if the rain of year k depends on the k -1, k -2, ..., k -h past years. Thus, the state of year k only depends on the state of year k -1 for the first order Markov. The first order Markov chain is introduced by a probability (equation 1): and we note (equation 2): where Pij is the i th element of the j th column of the transition matrix of the Markov chain. These probabilities were calculated using the following relationship

Markovian first-order model for the period 1984-2013
The results of the first-order Markov matrix for the seventeen stations for the period 1984 to 2013 are shown in Table 1.  79  21  80  20  S5  75  25  77  23  S6  81  19  85  15  S7  94  06  92  08  S8  93  07  100  00  S9  93  07  100  00  S10  93  07  100  00  S11  86  14  93  07  S12  93  07  93  07  S13  79  21  80  20  S14  86  14  93  07  S15  88  13  85  15  S16  79  21  80  20  S17  81  19  85  15 The results of the transition matrix for the period 1984 to 2013 show that: -for the period 1984 to 2013 the probability varies from 0 to 100% to have a dry year regardless of the year of departure (dry or wet) for the seventeen stations; -the probability of having a wet year followed by a dry year (P-S) is low (it varies from 7% to 31%) over the entire basin; -to have a dry year followed by a wet year (S-P), the probability is also low (7% to 31%) on most stations but it is nil for stations S8, S9 and S10 located in the center of the Lobo watershed; -the probability of having two successive dry years (S-S) is very high for the seventeen stations (it is between 69% and 100%); -for two successive wet years (P-P), the probability is also higher (between 69% and 94%) over the entire study area.

Markovian first-order model for the period 2021-2050
The results of the first-order Markov matrix for the seventeen stations for the period 2021 to 2050 are shown in Table 2.
-the probability of having a wet year followed by a dry year (P-S) will be higher (50% to 64%) in the South of the basin (Grand-Zattry), in the West (Zoukougbeu), in the North-West (Pélezi) and in the North (Vavoua) than in the Centre of the basin (38% to 47%) in Daloa; -to have a dry year followed by a wet year (S-P), the probability will be higher (50% to 57%) in the north (Seguela), in the centre (Daloa), in the southwest of the basin, and will decrease (27% to 44%) towards the southeast (Saiga) and the south of the basin (Great zattry); -the probability of having two successive dry years will be higher (50% to 72%) for the majority of stations but relatively lower (43% to 47%) for stations S10, S14 and S15 located north of Vavoua and Pélezi and northeast; -if a year is wet, the probability of a wet year (P-P) will be higher (50% to 64%) in the south (Issia), southeast (Saiga), center (Daloa) and north (Séguéla) of the basin.

Discussion
This study consists of the analysis of annual rainfall in the Lobo catchment area located in the western central part of Côte d'Ivoire. The precipitation data used in this study are obtained from the National Environmental Prediction Centre's (CFSR) climate prediction system reanalysis repository. The CFSR was designed and executed as a coupled atmosphere-ocean-land-sea ice system surface to provide the best estimate of the state of these coupled domains during this period. Mo et al, 2011; Najafi et al, 2012; Dile and Srinivasan, 2014 have conducted several studies with CFSR data and indicate their validity. According to Fuka et al (2013) these data have the advantage of better reflecting the rainfall event measured by satellites. His studies on the use of reanalysis of the climate prediction system as meteorological input data for watershed models have shown that CFSR data can be reliably applied to watershed modelling in various hydroclimatic regimes and other watersheds. The work of Saleh (2000) in the northern upper part of the Bosque River watershed reached the same conclusion. The methodological approach is based on the use of Markov chains, widely used for precipitation analysis (Chèze and Jourdain, 2003;Cazacioc and Cipu, 2004), which describe daily precipitation fields well. They have the advantage of taking into account the memory effect. The work of Stern et al (2006) and N'Guessan Bi (2014) came to the same conclusion. The MulGETS first-order Markov model, which uses a first-order linear autoregressive model and a multi-gamma distribution (more efficient compared to the exponential distribution according to Chen et al., 2012), was selected to adequately generate the daily precipitation data. These results are consistent with the work of Brissette et al (2007) and Chen et al (2014). This study shows that the probability of having two successive dry years or two successive wet years is higher over the entire study area for the period 1984-2013. These results are similar to the work of Lazri et al (2007), Meddi and Meddi (2009) and Meledje et al (2015). Indeed, in their studies on the analysis of rainfall and the occurrence of drought, Lazri et al (2007) showed that in the "Sea" zone, the probability of having a non-precipitating state after a non-precipitating state is higher than in the "Land" zone. On the other hand, the probability of having a precipitating state following a precipitating state is higher in the "Land" zone than in the "Sea" zone. Meddi and Meddi (2009) in northwest Algeria have shown that the probability of a dry year being followed by a dry year is higher in the west (Habra-Sig, Ghriss, Sidi bel Abbes and Maghnia plains) and the probability of having two successive non-drying years is high for all stations. Meledje et al (2015) indicate that the probability of having two successive dry years is higher in the northern part of the transboundary Bia river basin between Côte d'Ivoire and Ghana. For the period 2021 to 2050, the probability of having two successive dry years and two successive wet years will be higher over the entire basin and in the south, centre and north respectively. The probability of a wet year followed by a dry year will be higher in the south, west, northwest and north of the basin. The probability of a dry year followed by a wet year will be relatively high in the north, centre and southwest of the basin. These results may be explained by the fact that annual rainfall amounts will be decreasing over the entire study area and that the highest rainfall amounts will be observed in the central and southwestern part of the Lobo watershed.

CONCLUSION
The application of first-order Markov has made it possible to determine the probability of occurrence of annual precipitation in the Lobo watershed. Thus, the probability of having two successive dry years or two successive wet years is higher over the entire study area for the period 1984-2013. For the period 2021 to 2050, the probability of having two successive dry years and two successive wet years will be higher over the entire basin and in the south, centre and north respectively. The probability of a wet year followed by a dry year will be higher in the south, west, northwest and north of the basin. The probability of a dry year followed by a wet year will be relatively high in the north, centre and southwest of the basin. All these results show that precipitation is well described by Markov chains over the entire Lobo watershed. They can help to find strategies to fight drought and floods.