
Research Article


Improved Estimation of the Mean Rainfall and Rainfallrunoff Modeling to a Station with High Rainfall (Tabou) in Southwestern Côte D'ivoire 

T.A. Goula Bi,
V. Fadika
and
G.E. Soro



ABSTRACT

The annual rainfall series of Tabou remained stationary over the period 19222004 with the application of the segmentation test. However, a decrease of 10% over the 1990s is noted. The 199398 deficit sequence which is at the origin of this decline seamless stationarity is characterized by observations of average deficits of 30, 31 and 44% of the months of heavy rainfall in May, June and November. Also for the months of December, January and March of the long dry season with rainfall amounts recorded decreases of 36, 44 and 38% compared to the period 19221992. Estimates of monthly rainfall in Tabou over the period 20002002 with the usual stations are less effective than those conducted by kriging and inverse distance which improve on average 26122% in the month and, thanks to increased density in rainfall stations. The introduction of these estimates obtained by spatial interpolation instead of rainfall depths known in proportions of 19, 39 and 58% as the input data is supported by the model GR2M in calibration and validation phases. Unlike those from the arithmetic mean that cause decreases in 921% of the coefficients of Nash which amplified in validation from 9 to 48% depending on the size of their proportions in the rain input.





Received: October 08, 2010;
Accepted: December 18, 2010;
Published: January 22, 2011


INTRODUCTION
Climate variability is usually an effect of natural environmental conditions
(Refsgaard et al., 1989). It describes the fluctuation
of the seasonal or annual climatic parameters in relation to the multiannual
mean of reference (Servat et al., 1999). Tropical
Africa is characterized by high rainfall variability. Several authors have highlighted
it including the detection of breaks in its temporal evolution. The period late
1960searly 1970s is that which sees a decrease in rainfall in the majority
of stations in West Africa (Hubert et al., 1998;
Savane et al., 2001; Le
Barbe et al., 2002; L’Hote et al.,
2002; Paturel et al., 2004; Lay
and Galle, 2005; Goula et al., 2009). This
similarity of behavior of annual rainfall at the regional level shows the organization
of the cumulative rainfall variability in tropical annual homogeneous spatial
structures whose size is important in the tropics and subtropics. Hence the
observation that the main factors involved in the genesis of rainfall anomalies
are of regional or global scale. The modifications of the climate in Africa
are strongly related to certain modes dominating the interannual variability
of the thermal fields of the oceans (Janicot et al.,
1998; Fontaine et al., 1999). Thus, the existence
of significant relations is noted between the thermic anomalies of the tropical
Atlantic Ocean and certain regional interannual evolutions of precipitations
in Côte d’Ivoire (Bigot et al., 2002,
2005). Like the cooling of the temperatures of ocean
surfaces in the Gulf of Guinea in May, at the beginning of the great rain season,
which precedes a rise by precipitations on the littoral of the Côte d’Ivoire
(Kouadio et al., 2002). However areas because
of certain factors such as the importance of vegetation cover or topography
does not always follow the regional climatic variations (Moron,
1996). The coastal region of Tabou in the Southwestern Côte d'Ivoire
subject to the direct influence of the West African monsoon, where rainfall
is significant, seems to have this feature. Its annual pluviometry remained
surplus during the decades 1970 and 1980 in spite of the general dryness in
West Africa (Fadika et al., 2008). The penetration
of flow of trade winds strongly humidified coming from the southern hemisphere
which this zone undergoes is under the influence of the displacement of the
zone of intertropical convergence (Lebel et al.,
2003; Sultan and Janicot, 2004).
The objective of this study was to estimate rainfall in the Tabou area by spatial
interpolation using data from a neighboring area and to determine the effect
of errors in the series of rain on the effectiveness and the robustness of a
rainfallrunoff model. We begin first by showing the rainfall characteristics
of Tabou in the context of decreasing rainfall in West Africa. Then estimates
by interpolation of rain at Tabou station will be done using data from an adjacent
area which has a good density of rainfall stations. Finally, we will determine
the influence of previous estimates of rainfall data on the calibration and
validation of rainfallrunoff GR2M model.
MATERIALS AND METHODS Presentation of the study area: The study area is composed of the Tabou area and an area of the Dodo River basin (Fig. 1) is part of the coastal zone of Côte d'Ivoire. The climate is of equatorial type with four seasons, two rainy seasons and two dry seasons. The evergreen forest and plains where the altitude does not exceed 200 meters characterize vegetation and terrain in southern Côte d' Ivoire. The coastline stretches over 500 km is composed in its Western half of rocky cliffs to the west of Sassandra and sandy clay to Cape Palmas (Liberia border). In fact, there are highly desaturated lateritic soils which cover much of southern Côte d'Ivoire. The drainage of the west coast consists of small rivers of which the most important are Tabou, Dodo, Nero and San Pedro.
Data rainfall: The monthly rainfall depth of Tabou precipitation station
19222004 and those of eighteen stations (HK1, HK2, HK3, KO1, KO2, KO3, SG1,
SG2, SG3, BC1, BC2, BC3, DL1, DL2, DL3, KT1, KT2, KT3) from 2000 to 2002 belonging
to the neighboring basin of the river Dodo are used (Fig. 1).
This data was derived from the National Meteorology office and of a private
company. In addition, Monthly potential evapotranspiration from 1977 to 2003
of Tabou Station are available as well as the mean monthly discharge of the
river Tabou to its oufall Yaka Station (810 km^{2}) from 1963 to 2004.
Methods:
Stationarity of annual rainfall serie: The segmentation procedure (Hubert
et al., 1998) is somehow a stationarity test whose null hypothesis
is: The series of interest is stationary. If the time series being tested is
not homogeneous (stationary), it is cut into as many subsets homogeneous as
possible. The Scheffe (1959) allows determining the optimal
segmentation and stopping the segmentation process with a significance level
of 1%. The segmentation is applied with the Khrono Stat software.
Interannual variability of rain: The centered and reduced variable is the variation with the mutiannual mean of rainfall depth for one year on the standard deviation of the series. It highlights the surplus, deficit or normal character one year and therefore the fluctuation of annual rainfall. Seasonal variations: The objective of this part is to identify possible changes in the distribution of monthly rainfall totals with the decrease in annual rainfall.
Influence of errors in input data on the calibration and validation of the
GR2M model: In this section, the objective is to determine the influence
of errors in the series of rain on the calibration and validation of the GR2M
(modèle du Génie Rural with 2 Monthly parameters (Mouelhi
et al., 2006) Model parameters.
 Fig. 1: 
Location of the study area 
 Fig. 2: 
Squares interpolation of rainfall including station and Taboo:
Eighteen news other (a) and normal two stations (b) 
In this context, systematic errors (for overestimation and/or underestimation
of rainfall) are intentionally introduced in the series of monthly rainfall
amounts over the period January 2000 to December 2002 (36 months). Estimated
rainfall by interpolation and arithmetic mean form the series of pseudomonthly
rainfall amounts. The kriging and inverse distance methods, which are two strong
methods (Baillargeon, 2005) are used for interpolation
of rain to the Tabou station. For this, the interpolation square (1356 km^{2})
includes eighteen other stations in the basin of the Dodo, that is to say a
station for 71 km^{2} (Fig. 2a). The estimates of
rain per arithmetic mean are based on the data traditionally available in this
zone i.e., those of San Pedro and Sassandra. Indeed, the stations eighteen located
in the basin of the Dodo belong to a private entity. So, the users confronted
with gaps in the Tabou series typically use these two stations, which is a station
for 2862 km^{2} (Fig. 2b).
The Nash coefficient varies consecutive to each of these changes compared to those obtained with the real rainfall amounts will determine the influence of errors in the rainfall depths input on the performance (efficiency and robustness) of the GR2M model. RESULTS AND DISCUSSION
Stationarity of the annual series of rainfall: Applying the segmentation
test to annual rainfall totals of Tabou shows that this serie is stationary
over the period 19222004. The stationarity ruptures observed in general in
West Africa in the period late 1960 early 1970s (Hubert
et al., 1998; Servat et al., 1999;
Paturel et al., 2004) indicating a decrease in
rainfall do not appear in Tabou. The rupture indicating a change of average,
that lets think that pluviometry is relatively remained abundant in the zone
of Tabou. The Tabou area is wetter as it benefits from its position at the extreme
western coast of which the provision is more perpendicular to the monsoon winds
just like the eastern end of the Ivorian coast (Aubreville,
1949 cited in Eldin, 1971). The series of Taboo is
different from those of other longterm stations of Southwestern Côte
d'Ivoire as Grabo and Sassandra where ruptures are noted (Fadika
et al., 2008). The rupture detected in 1995, by Goula
et al. (2009), on shorter series of this station (19501997), proves
to be therefore not significant with the lengthening of the series (19222004).
It could simply reflect the observation of a short deficit sequence.
Interannual fluctuation and per decade: The annual rainfall totals vary
greatly from one year to another. So the estate of more than three years of
deficits, for example, appears only three times in the series, the sequence
196467, 197477 and 199398 (Fig. 3a). The latter is most
important, thus the rainfall in the decade 199099 also recorded the largest
deficit (10%) compared to the multiannual mean (Fig. 3b).
However, this deficit is lower than the average of 2025% recorded in the humid
zone of West Africa (Paturel et al. 1997; Servat
et al., 1999). The absence of deficit phase of the late 1960s to
early 1970s explains also that of stationarity breaks in this period in the
annual series of Tabou.
Thus, the 1970 is in excess of 2% compared to the multiannual mean as the
1980s (5%). While the latter has seen, in general, an increased incidence of
low annual rainfall in West Africa, (Ardoin, 2004). Through
cons, the 1990s drought, which affects rainfall for the first time with the
emergence of six consecutive years of deficits from 1993 to 1998. Not to the
point of talking about rupture, the excess of 2% of the rainfall in the early
2000s confirmed (Fig. 3b).
Change of seasons: Averages of monthly rainfall totals over the period
of study (19222004) and the phases that we consider to be wet or deficit make
it possible to see time variation of the season (Fig. 4).
 Fig. 3: 
Interannual (a) and decennial (b) variability of the rain
at the station of Tabou 
 Fig. 4: 
Changes in periods of wet seasons and deficit 
Thus, the distribution of rainfall is organized in two rainy seasons alternating
with two dry seasons. The big rainy season stood from April to July, the short
dry season in August, the short rains from September to November and the long
dry season from December to March. This distribution is also that of the wet
period 192297 also remains the same during the deficit phases: 199398 and
surplus: 19992004 but with decreases or increases in certain monthly rainfall
depths. Thus, the decrease in total annual rainfall during the 199398 is characterized
by the months of high rainfall and long dry season. For example 131 and 168
mm less for May and June of the big rainy season, 26, 32 and 88 mm less for
September, October and November of the short rainy season and 50, 22 and 34
mm less for months December, January and March of the long dry season.
 Fig. 5: 
Average absolute errors committed by estimating Monthly Rainfall
depths at Tabou Station 20002002 by the methods of the arithmetic mean
(ARI), Kriging (KRI) and the inverse distance (IDW) 
Servat et al. (1999) have also noted in regions
of West Africa, a decrease of rainfall recorded outside the rainy season. This
marks a strengthening of the dry season, which contributes at the same time,
lower annual precipitation and the clear perception of corruption by the people.
The decrease in rainfall during the rainy season in the deficit period was
due a reduction in the number of rainy days (Houdenou and
Hernandez, 1998; Lay and Galle, 2005) a relative
drop in the number of rainfall events (Tapsoba et al.,
2002) and reduced the frequency of heavy precipitation (Assani,
1999). The increase in annual rainfall from 1999 to 2004 also saw one of
those months with almost the same order as during the previous wet phase (19221997).
Comparison of the estimate of rain with the arithmetic mean and the spatial
interpolation: Using three different methods to estimate the known values
of monthly rainfall at Tabou station 20002002 let’s show the absolute
mean errors committed (Fig. 5). Both interpolation methods
give similar results which are better than those of the arithmetic mean. This
difference is accentuated during the months of heavy rainfall (May, June). Errors
introduced in the data by using the arithmetic mean filling corrected for 26122%
by using kriging and 27131% by the IDW is an average of 47% for both methods
interpolation. These results were expected since the estimation with kriging
takes into account the structure of spatial dependence of data (Baillargeon,
2005). While the arithmetic uses mean values of specific only two surrounding
stations at some distance, so that there are three stations on 8587 km^{2}.
Similarly, estimates at any point using the IDW are highly dependent on values
of the three nearest points.
 Fig. 6: 
Changes in coefficient of Nash with the replacement in the
data input, 12, 24 and 36 months, with rainfall amounts by estimated by
the arithmetic mean (ARI), Kriging (KRI) and inverse distance (IDW) 
Thus, the presence of nineteen stations over 1356 km^{2} which is a
much higher density than the previous one has favored these results. This confirms
the assumption that errors in estimating basin rain increases with decreasing
density of rainfall network (Robinson, 2005). Indeed,
over the network is denser, it will likely capture the local intensity have
significant weight in the final value of the basin rain (Bourqui,
2008).
Influence of estimates of rain on the calibration and validation of the
GR2M model:
Calibration: The model calibration GR2M over 19982003 gives 44.2
as the coefficient of Nash. Variations in this ratio with the realization of
substitutions of input rainfall amounts of 12, 24 and 36 months in the period
20002002 by others estimated provide evidence of the effectiveness of the GR2M
model (Fig. 6). The effectiveness of the model drops for all
three methods with increasing the length of new data.
These 12, 24 and 36 months respectively represent the proportions of 19, 39
and 58% for 62 months of monthly heights used as input data for calibration.
The initial coefficient of Nash (44.2) shows a greater decrease with the rains
from the arithmetic mean for which the gaps vary on average from 4 to 9.3 is
from9 to21%. For cons the Nash coefficient varies less with the rain from
kriging and IDW: 0.6 to 2.1 as deviations is from1 to5%. These findings corroborate
those of Ardoin (2004) which also noted deterioration
in the Nash criterion with relative errors in precipitation. Although variations
of Nash from65 to203% with relative errors of ± 30% rainfall is far
superior to ours.
 Fig. 7: 
Hydrographs obtained after GR2M model calibration over the
period January 1982April 1987 
This decrease Nash highlights the influence of network density on the effectiveness
of a model. Uncertainties due to a poor estimation of the rain because of the
low density of rain gauges are translated into a bad estimate (Bourqui,
2008). In fact, increasing the density of rain would lead to improved stability
of the vectors of model parameters (Duncan et al.,
1993; Anctil et al., 2006; Andreassian
et al., 2001). In addition, they would adjust to errors in input
data of precipitation with which models are effective (Troutman,
1983; Bell and Moore, 2000; Andreassian
et al., 2001).). But this adaptability of models to errors in input
data which depends on their structures is possible until a certain point and
walk with those type as systematic over estimation or underestimation of rain
(Oudin et al., 2006). It is this type of error
that which has been committed with the estimates of the arithmetic mean, of
kriging and inverse distance of our work. We deduce that the GR2M model could
adapt to systematic errors introduced in the input data by kriging and IDW.
But less than those caused by the arithmetic mean.
Validation: The GR2M model calibration over the period 19821987 gives 79.2 as the coefficient of Nash. The almost similar evolution of the flows simulated and observed confirms the good results of the GR2M model over this period (Fig. 7). The use, over this period, of the parameters obtained during the calibration phase in 19982003 produced a lower coefficient of Nash (66.2).
What causes the decrease of the coefficient of determination between series
of observed and simulated flows from 0.76 to 0.54 (Fig. 8a,
b). The calibration parameters obtained after made data substitutions
in the previous section allows also appreciating the change in the robustness
of the GR2M model. Indeed, by calculating the differences between the new coefficients
of Nash and the first is to say 66.2 the Fig. 9 is obtained.
It appears clearly with the three methods that the new Nash coefficients vary
more than the old with the length of the integrated rainfall estimates.
 Fig. 8: 
Flow rates observed and simulated during the GR2M model calibration
over the period January 1982April 1987 (a) and during the validation of
parameters for the period January 1998April 2003 on the previous phase
(b) 
Also, as during the calibration, the parameters obtained with data containing
values estimated by the arithmetic mean produce the lowest Nash. Hence larger
variations of 632 or 9 to48% which are much higher than those that give the
other two methods. Indeed, the coefficients of Nash slightly increased and decreased,
respectively from 0.3 to 0.9 for kriging and 0.9 to 3 for IDW. This provides
variations of 01% for kriging and1 to5% for the inverse distance. Thus, the
adaptation of GR2M model to the errors introduced into the input rains by the
krigeage and the IDW is confirmed since they practically does not influence
the process of validation of the parameters obtained on another phase.
 Fig. 9: 
Variation of Nash coefficients after validation of parameters
obtained after the GR2M model calibration with data estimated over the period
20002002, the arithmetic mean (ARI), Kriging (KRI) and the inverse of distance
(IDW) 
Similarly, the difficulty in integrating those coming from the estimates by
arithmetic mean of which the effect is accentuated during the validation especially
with the length of the new data Ardoin (2004) also noted,
with different basins of West Africa, an amplification of the initial error
by the GR2M model as well in overestimated as in underestimation. In total,
the filling of gaps, of monthly rainfall amounts, made by arithmetic mean values
for neighboring stations available are not reliable as input to simulate rainfallrunoff.
And this, especially if their length is more than 19% of the total rainfall
input.
CONCLUSION The station of Tabou recorded an important rainfall as benefiting from its position at the extreme southwestern Côte d'Ivoire. The annual rainfall series of this station also has the peculiarity to have remained stationary from 1922 to 2004 in a general context of decrease in total annual rainfall since the late 1960s in wet Africa. It was not until the 1990s to record a first deficit sequence of five years from 1993 to 1998 thus where the largest deficit displayed by 10% this decade. This relative decline in annual rainfall over the period 19931998 is characterized by lower contribution to annual total of month of heavy rainfall compare to phase 19221992. Thus, the months of May and June ot the big rainy season have, on average, respectively 131 and 168 mm in less as 26, 32 and 83 mm less for September, October and November of the short rainy season. A strengthening of the long dry season also appears with decreases of 36, 44 and 38 mm of rainfall deph mean of December, January and March. The interpolation of rainfall by kriging and inverse distance highlights the reduction of estimation errors with increasing density gauges. Indeed, these two methods allows while based on a catchment area of eighteen gauges 350 km^{2} respectively to improve, according to the month of 26122 and 27131% with an average of 47% for the both, the estimates made by the arithmetic mean of the observed rainfall at Sassandra and San Pedro, which are normally available. The introduction of these estimates of monthly rainfall of these three methods in proportions of 1958% (1236 months) in the input data from 2000 to 2002 reduced the effectiveness of the model with a decrease of Nash coefficient from 4 to 9.3 for the arithmetic mean. But the GR2M model is less sensitive to estimates of kriging and IDW, with only 0.6 to 2 drops of the Nash criterion. The validation of the parameters coming from the chock with the rains obtained by arithmetic mean causes an amplification of the fall of the coefficient of Nash from 6 to 32.Validation of parameters from calibration with rainfall obtained by arithmetic mean causes an amplification of the fall of Nash coefficient from 6 to 32. While those of interpolation methods generate light decreases of the Nash coefficient from 0.3 to 3. In sum, Tabou serie notwithstanding the importance of its rainfall from the rest of Southwestern Côte d'Ivoire may suffer fillers with estimates from spatial interpolation of data from the vicinity of a fairly good density. These new rain could consist up to 58% of monthly rainfall input is reliable for a good simulation of the flow.

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