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Since the 90s, several studies were conducted to evaluate the predictability of the Sahelian rainy season and propose seasonal rainfall forecasts to help stakeholders to take the adequate decisions to adapt with the predicted situation. Unfortunately, two decades later, the forecasting skills remains low and forecasts have a limited value for decision making while the population is still suffering from rainfall interannual variability: this shows the limit of commonly used predictors and forecast approaches for this region. Thus, this paper developed and tested new predictors and new approaches to predict the upcoming seasonal rainfall amount over the Sirba watershed. Predictors selected through a linear correlation analysis were further processed using combined linear methods to identify those having high predictive power. Seasonal rainfall was forecasted using a set of linear and non-linear models. An average lag time up to eight months was obtained for all models. It is found that the combined linear methods performed better than non-linear, possibly because non-linear models require larger and better datasets for calibration. The R 2 , Nash and Hit rate score are OPEN ACCESS Climate 2015, 3 728 respectively 0.53, 0.52, and 68% for the combined linear approach; and 0.46, 0.45, 61% for non-linear principal component analysis.
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Climate 2015, 3, 727-752; doi:10.3390/cli3030727
ISSN 2225-1154
Linear and Non-Linear Approaches for Statistical Seasonal
Rainfall Forecast in the Sirba Watershed Region (SAHEL)
Abdouramane Gado Djibo
1, 2,*
, Harouna Karambiri
, Ousmane Seidou
, Ketvara Sittichok
Nathalie Philippon
, Jean Emmanuel Paturel
and Hadiza Moussa Saley
International Institute for Water and Environmental Engineering (2iE), 01 BP 594,
Ouagadougou 01, Burkina Faso; E-Mail:
Department of Civil Engineering, University of Ottawa, Ottawa, ON K1N 6N5, Canada;
E-Mails: (O.S.); (K.S.)
Centre de Recherches de Climatologie, UMR6282 Biogéosciences CNRS, Université de
Bourgogne, Dijon 21000, France; E-Mail:
Institut de Recherche pour le Développement (IRD), Abidjan 08 BP 3800, Côte d’Ivoire;
Centre Africain d’Études Supérieures en Gestion (CESAG), Dakar BP 3802, Ségal;
* Author to whom correspondence should be addressed; E-Mail:;
Tel.: +00226-7195-2188.
Received: 19 June 2015 / Accepted: 1 September 2015 / Published: 14 September 2015
Abstract: Since the 90s, several studies were conducted to evaluate the predictability of the
Sahelian rainy season and propose seasonal rainfall forecasts to help stakeholders to take the
adequate decisions to adapt with the predicted situation. Unfortunately, two decades later,
the forecasting skills remains low and forecasts have a limited value for decision making
while the population is still suffering from rainfall interannual variability: this shows the
limit of commonly used predictors and forecast approaches for this region. Thus, this paper
developed and tested new predictors and new approaches to predict the upcoming seasonal
rainfall amount over the Sirba watershed. Predictors selected through a linear correlation
analysis were further processed using combined linear methods to identify those having high
predictive power. Seasonal rainfall was forecasted using a set of linear and non-linear models.
An average lag time up to eight months was obtained for all models. It is found that the
combined linear methods performed better than non-linear, possibly because non-linear
models require larger and better datasets for calibration. The R
, Nash and Hit rate score are
Climate 2015, 3 728
respectively 0.53, 0.52, and 68% for the combined linear approach; and 0.46, 0.45, 61% for
non-linear principal component analysis.
Keywords: rainfall forecasting; neural network; non-linear principal component analysis;
Sirba basin; West African monsoon; air temperature
1. Introduction
The summer rainfall of semi-arid regions of the world is known for its unreliability, which has a large
impact on the continental hydrological cycle, water resources and food security. The Sahel, extending across
Africa from the Atlantic Ocean to 30°E and from 12 to 17°N is the largest area of these regions, recording
between 200 and 800 mm/year from north to south, ~80% of the rain being recorded in JulySeptember the
cool rainy season. Temperature in this region ranges from approximately 18 to 36 °C. The recurrent droughts
and subsequent famines that struck the Sahel in the 1970s (19721974), and the 1980s (19831985) and
make it unique at the global scale led the scientific community to investigate possible mechanisms
responsible for these dramatic events and to develop forecasting models to help coping with such
phenomena. This area experienced severe droughts almost every two to three years. The devastate
drought in 2012 affected more than 18 million people in nine countries with food insecurity, high grain
prices and environmental degradation. This 2012 crisis came after the severe drought in 2010 [118].
The Sahelian rainfall pattern is season dependent and is directly related to the West African
Monsoon (WAM).
Although, the WAMs dynamic is better understood nowadays, the main challenge with regards to its
variability and predictability comes from its varying teleconnections. A teleconnection is the linkage of
climate variables between two different areas, which may be close or far to each other [19,20].
Teleconnections between Sahelian rainfall and the oceanic basins have changed quickly much since the
60s: the tropical Atlantic had the strongest influence during the years 6070, then the equatorial Pacific
(El Nino/Southern Oscillation) during the 8090s, and the Mediterranean now [2125]. Thus, the
absence of well-established predictors that can be used to predict seasonal rainfall as well as streamflow in
the Sahel partly explains why forecasts at all scales in the Sahel are tricky. Many studies attempted to forecast
Sahelian seasonal rainfall and streamflow for the purpose to overcome the droughts impacts [4,7,2633].
Unfortunately, most of these works focused on only sea surface temperatures (SST) over
years [24,3436]. Nevertheless, few studies attempted to use the atmospheric dynamics for carrying out
seasonal forecasts. This prediction relies on the explicit simulation of major atmospheric
processes [3744]. Garric et al. [42] used the ARPEGE atmospheric model forced by SST anomalies
and multivariate linear regression using SST and rainfall predictors observed before the monsoon season.
They showed that the ARPEGE model did not give better seasonal rainfall predictions than simple
regression systems.
Thus, the objective of this paper is to develop a method that would identify new skillful predictors
for seasonal rainfall in the Sahel, and to compare a set of linear models to non-linear ones for forecasting
JAS (July to September) rainfall amounts. This would provide the community with actionable seasonal
Climate 2015, 3 729
information that would constitutes a major tool for farmers, decision makers and water resources
managers in this region.
For such purpose, a pool of predictors is built by analyzing the physical influence on the WAM. Each
predictor is tested as an input to a linear rainfall forecasting model as in [4]. At the end of the process,
an optimal lag time and an optimal season are obtained to extract the predictor. Retained predictors are
afterward also tested in new developed non-linear models. Finally, the forecast skills of the two groups
of models are discussed.
2. Review of the Main Drivers of the Sahelian Rainfall Variability
In West Africa, the rainfall pattern is firmly related to the seasonal movement of the inter-tropical
convergence zone (ITCZ) and consequently to the development of the WAM circulation [45].
The SST constitutes a key factor in the variability of the WAM and therefore the Sahelian precipitations
as shown in several studies [12,34,37,4648]. The tropical Atlantic Ocean is considered as the principal
source of moisture for West Africa. Its impact on the WAM system was shown since 1970s when the
Sahelian rainfall deficit was associated to colder SST in the north tropical Atlantic and warmer SST in the
south and at the equator which promotes a southernmost ITCZ than the normal. These results were confirmed,
and then extended to longer time scales by many studies [13,4952]. However, Janicot et al. [53] noticed
that the relationship between Sahelian rainfall and Atlantic SSTs considerably decreased to a point to be
statistically not significant during the dry period (i.e., post 1970). This teleconnection changed from
Atlantic SST to the SST over eastern and center Equatorial Pacific, in agreement with the work of [54].
A rainy season with below average rainfall in West Africa is usually associated to a warm period of
El Niño-Southern Oscillation (ENSO). Janicot et al. [55] explained this link by a strengthening of the
Walker circulation and a weakening of both the monsoon and the southern cell of the Hadley circulation.
This situation leads to an increase in trade winds over the northern tropical Atlantic and a reduction in
the water vapor in West Africa. Recently, a teleconnection with the Mediterranean Sea has been
highlighted [5658]. It seems to impact the WAM system in addition to the Atlantic and Pacific [58].
Rowell [56] found that the influence of temperature anomalies in the Mediterranean on the Sahel (for
19471996) is of a similar magnitude with that in the Pacific. From numerical simulations, he showed
that a warm Mediterranean sea promotes excess rainfall in the Sahel. Additionally, Gaetani et al. [57]
pointed out that a positive precipitation response to warmer than average conditions in the Mediterranean
Sea is found in the Sudano-Sahelian belt in August to September.
Several recent papers analyzed the interactions of the different oceanic basins and the resulting impact
on the Sahelian rainfall variability. Shaman and Tziperman [59] found that the interannual rainfall
variability over the Mediterranean region is related to ENSO variability in the eastern Pacific via an
eastward-propagating atmospheric stationary barotropic Rossby-wave train. Moreover,
Lopez-Parages et al. [60] explained how the teleconnection with the ENSO appears modulated by
multidecadal oscillations of the SST over the Atlantic and Pacific basins.
With regards to the role of the land surface on the Sahelian rainfall variability, Webster et al. [61]
indicated that the use of the moist static energy (MSE) (its three components: sensitive, latent and potential)
could improve the rainfall forecasts in the Sahel. They argued that the variation in temperature between
the ocean and the continent is responsible for the monsoon circulation; and this circulation is even better
Climate 2015, 3 730
explained when the moisture gradient is considered. Eltahir [62], Philippon and Fontaine [63], Hall and
Peyrillé [64] highlighted the role of these gradients on the dynamics of WAM and the Sahelian rainfall
variability. Zheng and Eltahir [65] found that a change in vegetation (e.g., deforestation) on the Guinean
coast has a direct substantial impact on atmospheric dynamics associated with the monsoon circulation
through MSE gradients. Thus, some authors such as Wang and Eltahir [66] suggested the inclusion of
vegetation dynamics in the modeling exercises as it constitutes an important process for simulating
Sahelian rainfall variability. In addition, while testing the impact of vegetation in rainfall variability
simulation, Zeng et al. [67] found that the decadal variability is best reproduced when interactive
vegetation is added to the model. The role of soil moisture on West African rainfall event is also
addressed in some studies [62,68]. These authors emphasized that a positive anomaly of soil moisture
would strengthen the monsoon circulation through a modification of MSE gradients.
Douville et al. [69], Douville [70], and Douville [71] found that any reduction in soil moisture in
ARPEGE is associated with low intensities of precipitations. Thus, based on these results they concluded
that soil moisture contributes to the interannual variability of rainfall in the Sahel.
It therefore appears that the climate in West Africa (predominantly in the Sahel) is determined by
interactions between global processes (e.g., sea surface temperatures) and regional processes (e.g.,
physiographic characteristics). The use of parameters related to these processes in seasonal rainfall
forecasting models would generate more skillful forecasts for the Sahel.
3. Materials and Methods
3.1. Study Area
The study area considered in this work is the Sirba watershed. This watershed, shared by Burkina Faso
and Niger, is situated between latitudes 12°55'54"S14°23'30"N and longitudes 1°27'W23'42''E with
an area of 38,750 km
(Figure 1) [72]. This choice is motivated by the fact that the Sirba basin is central
in the Sahel region, and there are many climate stations inside and around the basin that have been
collecting climate data daily for more than 40 years. Another reason is that, locally, the Sirba tributary
plays an important role in the hydrological regime of the Niger river at Niamey, as it participates in its
Sudanian flood in September. The Sirba extends over three sub-climate zones based on the amount of
rainfall decreasing from south to north: a southern Sudanian zone with mean annual rainfall between
700 and 800 mm, a northern Sudanian zone with mean annual rainfall ranging from 550 to 650 mm and
a Sahelian zone with mean annual rainfall of 300 to 500 mm [73]. The largest quantities of rainfall are
observed during the months of July to September (JAS), regardless of the climate zone. The climate is
generally characterized by the presence of two seasons: a dry season (October to April) due to the
Harmattan (dry wind) and a rainy season (May to September) influenced by the WAM (wet wind). The
hydrographic network is relatively dense and consists of three main tributaries (Sirba, Faga and Yeli) as
well as some water reservoirs from dams [71]. Based on the description of the rainfall pattern, the
hydrological regime in the Sirba watershed is of Sahelian type, as it is characterized by non-sustainable
flows with an exoreic operation pattern. At the upper bed of the Sirba, there is a series of depressions
with intermittent flow. However some sections of the Sirba reaches have water constantly during the
wettest years. Its vegetation formation is thorny, lightly-wooded savannah.
Climate 2015, 3 731
Figure 1. Sirba watershed and observation stations.
3.2. Climate and Atmospheric Data
Climate data used in this study include rainfall and atmospheric data. In situ daily rainfall data span
the period 19602008, and are obtained from national meteorological offices of Burkina Faso and Niger.
Five of these stations are located within the watershed while the remaining six stations are located at
most 25 km from the watershed boundary (Figure 1). The Thiessen polygon method is a standard method
widely used to calculate average areal precipitation [74]. It was implemented to estimate average rainfall
over the watershed from the 11 rainfall time series (Table 1). Though there is a lack of good climate data
throughout African Sahel, only a few gaps were found in these records, and they do not alter the quality.
The in situ rainfall time series have less than 10% missing data as this ratio varies from 0 to 7% for all
11 stations over the period. Moreover, monthly precipitation time series of Climatic Research Unit (CRU
TS 3.21 0.5° global) with a spatial resolution of 0.5° × 0.5° and defined on latitudes 10°N15°N, longitudes
WE are used. They are sourced from the British Atmospheric Data Centre (BADC, and span the period 19012012 [75].
The atmospheric data considered are Sea Level Pressure (SLP), Sea Surface Temperature (SST),
Relative Humidity (RHUM), Air Temperature (AirTemp), Meridional Wind (VWND), and Zonal Wind
(UWND). These variables are monthly NCEP-DOE Reanalysis data sourced from the National Oceanic
and Atmospheric Administration (NOAA: except the SST data series (NOAA
NCDC ERSST version3b sst) obtained from the IRI data library (International Research Institute for
Climate and Society: [76]. These data span from January 1979 to August
Climate 2015, 3 732
2013, except for SST data which cover the period January 1960 to December 2013. The relationship of
these predictors with the WAM is briefly described in the following paragraphs.
Table 1. Specifics of rainfall stations.
Station number
Station name
(degrees: °)
Burkina Faso
Burkina Faso
Burkina Faso
Burkina Faso
Burkina Faso
Burkina Faso
Burkina Faso
(a) Zonal Wind and Meridional Wind
Gallée et al. [77] have highlighted the importance of the meridian gradient of MSE on the movement
of the ITCZ northward. According to their studies, MSE led the WAM and creates an environment
favorable for deep convection over the Sahel. Thus, the spread of WAM to north is associated with
strong gradient of MSE in the lower layers, the convergence result in the triggering of convection over
the Sahel. These authors emphasized the relationship between the WAM, precipitation, the MSE, the
meridian wind and sensible and latent heat in the Sahel. The strong north-south gradient (weak) of the
meridian wind seems to be the result of a strong south-north gradient (weak) of MSE. The first maximum
MSE gradient develops, followed by the maximum meridian wind. Then the MSE meridian gradient
leads meridian wind speed and precipitation to a secondary maximum. In general, changes in
precipitation appear to be a consequence of MSE with a major role of the meridian wind.
The zonal and Meridian winds play a very important role in the flow in the middle and upper
troposphere. Indeed, in the middle and upper troposphere, the zonal wind profile is dominated by three
jets: AEJ (African East Jet), TEJ (Tropical East Jet) and WSJ (West South Jet). AEJ is at the level of
600 hPa and TEJ at 200 hPa. These two jets, which are located above the Sahel and Guinea, are important
for the atmospheric dynamics in West Africa. The variation of these winds regulates the position of the
AEJ, which, in turn, explains why during wet years (dry) for the Sahel [68,78]. Grist and Nicholson [79]
showed evidence of AEJ above the Sahel (10°N to 15°N). JET looks very bound to the African monsoon.
Indeed, through the Walker circulation, the intensity of the jet effect of the monsoon which forms the
lower part of the cell [80]. Sultan [81] shows that the jet's installation date is a good indicator of the
development of the monsoon. Finally, Nicholson and Grist [82] suggested that the jet is a response to
precipitation but is not a cause of the variability of rainfall.
Climate 2015, 3 733
(b) Air Temperature
The impact of Air temperature on the WAM occurs through a link with atmospheric dynamics over
West Africa. According to Fontaine et al. [83], the air temperature at two meters presents its maximum
before the wet period (during the month of May) because of the maximum exposure at the top of the
atmosphere and is followed by a maximum equivalent potential temperature (Ɵe) in August because of the
maximum of the zenith angle of the sun. Ɵe in the lower troposphere is equivalent to MSE whose transport
is due to the circulation of large-scale (the Hadley). But Flaounas et al. [84] and Guiavarch et al. [85] like
other studies have clearly shown the relationship between this surface energy and WAM. Thus, it appears
that the relationship between air temperature and the WAM is not a direct link but rather a role on the
dynamics of WAM in terms of anomalies reflections in atmospheric circulation like Hadley types.
(c) SST
Several studies have analyzed the relationship between WAM and SSTs. Coëtlogon et al. [86] studied
the link between WAM and the contrast between SST and the temperature at the coast of Guinea.
According to their results, from spring to summer, a band of cold water settles between Ecuador and the
coast of Guinea and enhances the temperature gradient at the surface meridian. This causes the
acceleration of the WAM which then moves further north. The appearance of this band of cold water is
attributed to the process of recovery in deep and cold ocean masses “upwelling”, mostly due to surface
winds. Thus, the acceleration of WAM resulted from a positive feedback system since the acceleration
intensifies upwelling increasing itself from WAM that spreads further north. Moreover, Peyrillé and
Lafore [87] developed a two-dimensional idealized model to reproduce the monsoon system in West
Africa. Their study reveals the importance of SST in the Mediterranean. The lack of moisture transport
or transport by zonal eddies above the African continent requires forcing external moisture advection in
the Mediterranean to get realistic monsoon in West Africa. Thus, they show that warm SST in the
Mediterranean entails strengthening moisture advection in the lower layers. SST of West Mediterranean
seems to have a stronger impact on the variability of precipitation in the Gulf of Guinea (Sahel) [88].
Several studies suggested some links between the variability of SST during the season of coastal rain
and precipitation, especially through the installation of the equatorial upwelling. Gu and Adler [89]
describe, using satellite observations and reanalysis, the seasonal evolution of the tropical Atlantic. They
show that, in the Gulf of Guinea, convection is modulated by seasonal forcing of the ocean and the SST
gradient meridian. In addition, it was shown that the Pacific Ocean [34], the Atlantic Ocean [90], the
Mediterranean [88] as well as the phenomenon El Niño-Southern Oscillation [10] generate atmospheric
disturbances and, in this way, affect the African monsoon.
(d) SLP
A climatological analysis by Baldi et al. [91] suggests that the West Africa monsoon influence the
central-western [92,93]. Using NCEP/NCAR global reanalysis [91] analyzed in detail the events
characterizing summer 2002 over Mediterranean, Europe and North Atlantic, in particular the anomalous
SST and Sea Level Pressure (SLP) fields relatively to the mean climate patterns Mediterranean summer,
and specifically the SLP (weakly), the temperature and the rainfall. They also found that the overall
Climate 2015, 3 734
pattern of the WAM changed in July, when a lower pressure developed from Iceland to central
Mediterranean along a northwest to south-east axis, with anomalously high pressures in the south-west
and north-east. Moreover, the summer average SLP field was similar to the pattern observed in July. The
surface air temperature field over Mediterranean closely follows the sea level pressure patterns in summer
(e.g., Maheras and Kutiel, [94]). They also run sensitivity analysis which shows how the SST anomalies can
produce quantitatively significant anomalies in the sea level pressure patterns over North Sahel (positive).
(e) RHUM
The interaction between the flows of heat from the surface of ground water and in the atmosphere has
been studied by Lafore [95] and Fontaine et al. [88] over the period 19792001. Four phases of the ITCZ
(inter tropical convergence zone) were identified: early March, mid-April, May and late June
(establishment of WAM). These phases appear to be sensitive to the relative humidity of last year. The
interaction between these phases is as follows: positive anomalies in this humidity entail an increase in
the humidity of the atmosphere, and the convergence of humidity flux- and a decrease in surface albedo.
Therefore, the net solar radiation is strengthened on the surface but the air temperature in the lower
layers decreases. Net radiation on the surface increases as well as the flow of heat to the atmosphere.
This process results in the strengthening of MSE in the lower layers and the strengthening of the
circulation of WAM. On the other hand, Fontaine et al. [83] showed that in the three regions in West
Africa (Guinea, N10°N, Sudan 10°N15°N, the Sahel 15°N20°N), the convergence integrated
moisture flux in the entire atmospheric column is significantly correlated with the precipitation at
different scales. It is interesting that in the Sahel, unlike the rest of West Africa, the relationship between
precipitation and soil evaporation (consequently the RUM) in the Sahel is almost linear. Moreover,
Broman et al. [96] performed A K-means cluster analysis to identify spatially coherent regions of relative
humidity variability during the two periods over West African Sahel. They found that correlating the
cluster indices with large-scale circulation and SSTs indicates that the land-ocean temperature gradient
and the corresponding circulation, tropical Atlantic sea surface temperatures (SSTs), and to a somewhat
lesser extent tropical Pacific SSTs all play a role in modulating the timing of the monsoon season relative
humidity onset and retreat.
Thus, it is clear that the RUM is a link because it is connected to the mainland that can exert forcing on
the atmospheric dynamics through which it is a reflection of abnormalities in the circulation of WAM.
From the above explanation, it is clear that despite that the atmosphere has no inertia the predictors
(SLP, AirTemp, and RUM) are connected either to the ocean or continent that can have a forcing on
atmospheric dynamics and they are the reflections of anomalies in the atmospheric circulation types
Hadley or Walker. Other predictors are related to the Pacific or the Mediterranean to the tropical Atlantic.
Table 2 summarizes the atmospheric data and their geographical locations.
3.3. Selection of Predictors and Optimal Lag Time
Monthly CRU precipitation time series cover an area larger than the extent of the Sirba basin. They
were initially used as predictand for selecting a pool of potential predictors having a known relationship
with the WAM, and to avoid those with no effect on the monsoon dynamics.
Climate 2015, 3 735
Table 2. Description of atmospheric data.
Reference Data
Spatial coverage
Regions of the
Sea level pressures (SLP)
2.5° × 2.5° grid
Atlantic ocean
1979/01/01 to
Air temperature
2.5° × 2.5° grid
Pacific ocean
1979/01/01 to
Meridional wind
2.5° × 2.5° grid
Sahel (Easterly jet)
1979/01/01 to
Zonal wind (UWND)
2.5° × 2.5° grid
Sahel (Easterly jet)
1979/01/01 to
Relative humidity
2.5° × 2.5° grid
1979/01/01 to
Sea surface temperature
ERSST version3b
× grid
Atlantic ocean
1854/01/01 to
Climatic research unit
rainfall (CRU)
0.5° × 0.5° grid
January 1901 to
December 2012
These monthly precipitations time series were averaged over the season JulySeptember (JAS), which
is the core of the rainy season in the Sahel. As a preliminary test, different time periods 19602010,
19702010, 19802010, 19902010, 20002010 are considered to check the most favorable periods in
terms of signals within the pool of potential predictors. The reason for testing these sub-periods resulted
from the previously mentioned studies (Section 2) which showed that the teleconnections of the Sahelian
rainfall have evolved since the 60s. Based on these defined periods, 13 groups (with 89 sub-components)
of predictors were considered for the preliminary test to check the presence of significant correlations
(R > 0.5) between each predictor and CRU rainfall.
After this first selection which relies on the CRU precipitations dataset as predictand, predictors were
selected using the in situ rainfall (from rain gauge stations) as predictand. This selection is done using
the method developed in [4]. This method was employed to link the observed rainfall and each predictor
through some statistical techniques. The candidate predictor was aggregated over all possible time
windows (where a time window's length in months is an integer) during the 18 months prior to the rainy
season onset and each of the obtained time series was used as an explanatory variable in a linear model
having the seasonal rainfall on the Sirba watershed as explained variable.
The choice of the period over which the predictor is averaged will impact the performance of the
forecast. Since the best period is not known a priori, predictor data sets were aggregated over various
periods with different lengths and different start dates. The periods were restricted to start at the
Climate 2015, 3 736
beginning of a calendar month and finish at the end of a calendar month. The beginning of a period has
to be later or equal to January 1st of the previous year (year Y-1, where Y is the year containing the
rainy season for which the forecast is issued).
The end of the period must be prior or equal to June 30th of year Y. Figure 2 shows how time windows
were systematically generated. The upper bar indicates all months starting from January of the previous
year (year Y-1) to June of the year the forecast is issued (year Y). In the first run, for example, only the
predictor of January (Y-1) was selected to use as a predictor. Predictor averaged over January-February
(Y-1) was used as a predictor in the second run. This process was iterated at one-month increments until
June (Y) was reached as the end of the period. The process was repeated until the beginning and the end
of the periods were June (Y).
For each time window, a linear model linking the predictor averaged over that time window and
seasonal rainfall on the Sirba was built as follows:
(a) For each year Y that the predictor was available,
(i) The predictor of year Y-1 was removed from the predictor grid;
(ii) The rainfall of year Y was removed from the rainfall data set;
(iii) A coefficient of correlation (R) is used to screen the remaining predictor data: a
correlation analysis between the predictor at each grid point and the rainfall was
computed and its level of significance (P-value <0.05) was assessed. Once the
correlation was not significant, the grid point was discarded. The remaining grid points
were then ordered decreasingly;
(iv) Afterward, a principal component analysis (PCA) was applied on the retained
predictor gridded data from the previous step to reduce the number of predictors;
(v) Since PCA gave rise to more sets of new predictor data, a stepwise regression (5%
confidence interval) was used to keep only grid points with high predictive power;
(vi) A linear regression was fitted between the predictors and precipitation time series;
(vii) The fitted linear regression was used to simulate the rainfall of year Y. If predictor and
rainfall were in the same year (Year Y), only predictor and rainfall time series for that
year were removed in the first step.
(b) Then, the coefficient of determination (R
), Nash-Sutcliffe coefficient (Nash), and Hit-Rate scores
(HIT) were computed to estimate the model's performance.
Figure 2. Predictor averaging periods (Adapted from Sittichok et al. [4]).
Climate 2015, 3 737
In summary, all predictors were selected according to their physical link with the WAM based on the
hypothesis that only predictors having dynamical link with the WAM seem to give good forecast skills.
Each of these predictors was screened through simple correlation test to find its link with the CRU
rainfall data defined over a region covering more than the Sirba watershed. The main criteria used to
find either the predictor should be retained or rejected is the correlation coefficient (R) that has to be
greater or equal to 0.5 (i.e., p-value < 0.05). The CRU rainfall was used at this stage for the purpose to
have a good assessment of all possible predictors having impact on the WAM. The retained predictors
were further screened based on in situ rainfall using the approach explained previously and summarized
in Figure 2. All these steps were summarized in the new flowchart of Figure 3. It should be noted that
the figures provided were based on leave-one out cross validation (LOOV) which was also used is
selecting the predictor. The LOOV was used due to the small length of data used.
The first three (3) best predictors in terms of high Nash values were used to test the performance of
the two sets of methods (linear approach and non-linear approach).
3.4. Linear Approach
Several linear methods are applied successively for selecting the predictors and developing the
seasonal rainfall forecast models. They include: correlation analysis, principal component analysis
(PCA), stepwise regression, linear regression, and cross validation.
They were used to perform three successive tasks: predictor selection; predictor dimension reduction
and linear regression. The first application discarded meaningless predictors from the original data set
using the coefficient of correlation as criteria of selection. At this stage, the correlation coefficient
between the predictor at each grid point and the rainfall on the Sirba watershed was calculated and its
level of significance (p-value < 0.05) was tested. When the correlation was not significant, the grid point
was discarded. The remaining grid points were then decreasingly ordered according to the correlation
p-value. Only the best grid points were included in the analysis. Afterward, PCA was applied on the
retained predictors to reduce their number. A forward stepwise regression method (5% confidence
interval threshold) was then applied to keep predictors having only a significant predictive power.
It should be noted that a leave-one-out cross validation was used in the model application to avoid
the bias which might occur during the development of empirical equations using statistical models.
3.5. Non-Linear Approach
Two non-linear methods were tested for each of the three best predictors selected based on the
correlation analysis. The description of these methods and how they are applied is detailed in the next
paragraphs. The R
, Nash, and HIT were calculated to estimate the model’s performance.
3.5.1. Non-Linear Principal Component Analysis
The non-linear principal component analysis (NLPCA) algorithm developed by [97] is generally
considered as a non-linear generalization of standard linear PCA and was successfully applied in
atmospheric and oceanic sciences [98102]. The principal components (PCs) are generalized from
straight lines to curves, thus the NLPCA helps to extract PCs either linear or not. This could improve
Climate 2015, 3 738
seasonal rainfall forecast skills because it is well known that most of atmospheric/climate relationships
are not linear as always assumed. Each predictor was first screened using R
before being fed into the
NLPCA. However, due to the high computational time of NLPCA the number of PCs is narrowed in
considering only the three best PCs in the process. Figure 4 presents the entire process of the NLPCA
seasonal forecast model. More details on the way NLPCA model works and its difference with the
ordinary PCA can be found in Scholz et al. [97].
Figure 3. Steps for the selection of predictors.
Pool of predictors
with physical link
on West African
monsoon dynamic
CRU Monthly
rainfall covering
West African Sahel
p-value <0.05
Pool of retained
(Sirba basin)
Screening of
Approach of
Sittichok et al [4]
Ranking of good
Climate 2015, 3 739
Figure 4. Developed non-linear statistical approach for rainfall forecast.
3.5.2. Feedforward Neural Network
The feedforward neural network (FFNN) is just tested in this work because to show its performance
which is somehow poor. For more details on this method, the reader can refer to [103109].
4. Results and Discussions
4.1. Selected Predictors and Lag Time Period
In the preliminary setting of a pool of predictors, the synchronous correlations between
predictors-predictand (i.e., correlations between rainfall and predictors averaged over JAS period) have
revealed the presence of the largest correlations for the period 19702010. Thus, it was used as the
reference study period. For instance, Figure 5 presents the correlation between rainfall and SLP over this
time period with a lag time of three months between the two variables.
During the second step dedicated to selecting the predictors, the time window (or season) which yielded
the best Nash coefficient (and therefore the optimal lag time) was determined. Tables 35 summarize the
final selected predictors used to forecast seasonal rainfall using combined linear methods, NLPCA and
FFNN, respectively. It is obvious that for all models the best predictors according to the forecast skills
are AirTemp, RHUM and SLP. In addition, the lag time (eight months lead time on average) obtained
for most predictors is large enough to develop early warning systems for the decision makers and
socio-economic actors about the issue of the forthcoming rainy season.
Climate 2015, 3 740
4.2. Seasonal Rainfall Forecast
The performance of the combined linear models showed that AirTemp (from Pacific Tropical North),
RHUM (from Mediterranean East) and SLP (from Atlantic tropical South) are the best predictors with
respective Nash coefficients of 0.53, 0.52 and 0.46 (see Table 3). They have also the best coefficients of
determination (53%, 58%, 48%) and Hit rate scores (67.9%, 64.3%, 60.7%), respectively. While SST
(from Atlantic Ocean) obtained 0.34, 43%, and 58.5% as Nash, R
and Hit rate scores, respectively.
These results from the predictors AirTemp, RHUM, and SLP seem to be better than those obtained
in [4] who used linear methods to forecast seasonal rainfall in the same area based on Pacific and Atlantic
SSTs as predictor. They obtained 0.45, 0.38 and 66.67% respectively for R
, Nash, and Hit rate score.
Figures 6 and 7 present the observed and simulated seasonal rainfall for combined linear models.
Figure 5. Correlation map between seasonal precipitation and sea level pressure (Da Silva
analysis, sea).
Climate 2015, 3 741
Table 3. Combined linear methods for seasonal rainfall forecast.
Nash coef.
Best period
Lag period
Sea Level Pressure (SLP) at 1000hPa
Relative Humidity (RHUM) at 1000hPa
8 months
Air Temperature (AirTemp) at 1000hPa
7 months
Meridional Wind (VWND) at 1000hPa
8 months
Zonal Wind
(UWND) at 1000hPa
7 months
Sea surface temperature (SST)
12 months
(**) M1=1:12 (January to December); M2=M1:18 (considered month of M1 to the next coming June)
(*) NMAX: number of best grid points retained after screening the predictor grid based on R
Table 4. Seasonal rainfall forecast model skills using non-linear principal component
analysis (NLPCA).
Lag time Period
Sea Level Pressure (SLP) at 1000hPa
9 months
Relative Humidity (RHUM) at 1000hPa
7 months
Air Temperature (AirTemp) at 1000hPa
8 months
Table 5. Feedforward neural network (FFNN) model (single predictor) output for Sirba
seasonal rainfall forecast.
HIT score (%)
Lag time (months)
For the NLPCA model, the issued seasonal forecast skills can be judged satisfactory regarding the
short study period considered, because non-linear models need longer study periods to over perform the
linear ones. Results showed that the predictor AirTemp (R
: 0.46; Nash: 0.45; HIT: 60.7%) was the best,
and then followed by RHUM and SLP, respectively. It was also found that this method provides a to larger
lag time compared to combined non-linear methods despite of its relative low forecast skills. Table 4
presents the model performance and the lag time, while Figure 8 illustrates some of the rainfall forecast
obtained from the NLCPA model using, respectively, the predictors AirTemp and RHUM.
Overall, the set of linear models performs better than the non-linear ones. This suggests that there is less
benefit using non-linear methods when dealing with small samples, as found in previous studies [27,96,102].
Climate 2015, 3 742
Figure 6. Combined linear model for seasonal rainfall forecast using SLP (upper panel) and
RHUM (lower panel).
1975 1980 1985 1990 1995 2000 2005 2010
Rainfall (mm)
Combined Linear seasonal rainfall forecast model using SLP
Observed rainfall
Forecasted rainfall
1975 1980 1985 1990 1995 2000 2005 2010
Rainfall (mm)
Combined Linear seasonal rainfall forecast model using RHUM
Observed rainfall
Forecasted rainfall
Climate 2015, 3 743
Figure 7. Combined linear model for seasonal rainfall forecast using AirTemp (upper panel)
and SST (lower panel).
1975 1980 1985 1990 1995 2000 2005 2010
Rainfall (mm)
Combined Linear seasonal rainfall forecast model using AirTemp
Observed rainfall
Forecasted rainfall
1975 1980 1985 1990 1995 2000 2005 2010
Rainfall (mm)
Combined Linear seasonal rainfall forecast model using SST
Observed rainfall
Forecasted rainfall
Climate 2015, 3 744
Figure 8. NLPCA seasonal rainfall forecast model using AirTemp (upper panel) and RHUM
(lower panel).
1975 1980 1985 1990 1995 2000 2005 2010
Rainfall (mm)
NLPCA seasonal rainfall forecast model using AirTemp
1975 1980 1985 1990 1995 2000 2005 2010
Rainfall (mm)
NLPCA seasonal rainfall forecast model using RHUM
Climate 2015, 3 745
5. Conclusions
Two non-linear methods and a combined linear approach were used to forecast JAS (July to September)
rainfall on the Sirba watershed, West Africa. Predictors were first screened using a series of steps to isolate
those having the highest predictive power. At the end of the process three predictors, air temperature (from
Pacific Tropical North), sea level pressure (from Atlantic Tropical South) and relative humidity (from
Mediterranean East) were retained and tested as inputs for seasonal rainfall forecasting models. Forecast
performances were compared using R
, Nash and HIT. Results showed that the combined linear approach
performed better than the non-linear models. The best forecasts were obtained using air temperature as
predictor (R
= 53%; Nash = 0.53; HIT = 67.9%; Lead-time = 7 months). The next best model uses relative
humidity as predictor (R
= 58%; Nash = 0.52; HIT = 64.3%, Lead-time = eight months). Nonlinear
Principal Component Analysis (NLPCA) was the best non-linear method while FFNN performed poorly.
These new predictors found in this study could lead to better forecasts of seasonal rainfall over West
Africa, an issue which has challenged forecasters over many years. This paper also helped understanding
that non-linear methods could also be used instead of the usual linear methods. The specificity of this
work is the use of other predictors rather than the SST which gave acceptable results than the SST.
However, the limit of the approach resides on the small length of data used. Therefore, to generalize the
results for other scientists, it is recommended that during the forecast a Sahelian global index must be
constructed using CRU data while examining its correlation with the index of the watershed and the skill
of models. As a future step of this work, a multi-model approach will be used to compare the resulting
skills to that of the best model.
The authors would like to thank the International Research Initiative on Adaptation to Climate
Change (IRIACC) program through the International Development Research Center (Canada) for
funding this research.
Author Contributions
Abdouramane Gado Djibo developed the models, performed analyses and wrote the paper.
Nathalie Philippon, Ousmane Seidou, Harouna Karambiri, Hadiza Moussa Saley, Ketvara Sittichok and
Jean Emmanuel Paturel contributed to analysis and interpretation of results. Nathalie Philippon,
Ousmane Seidou, and Ketvara Sittichok proofread the manuscript and contributed to answer
reviewers’ comments.
Conflicts of Interest
The authors declare no conflict of interest.
Climate 2015, 3 746
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© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article
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... Indeed, interannual rainfall has seen important changes in the last five decades. Severe drought in the 1970s and 1980s brought famine and humanitarian crisis in the region [2][3][4]. While at the break of the current century, Samimi et al. [5] observed intense rainfall in 2007, equivalent to values with a return period of 1200 years. ...
... SST is the main variable in the rainfall forecast [2,13]. In the forecast models, the Tropical Atlantic (70 • W, 20 • E, 20 • S, 40 • N) was used as the predictor variable of the linear, polynomial, and exponential models. ...
... It is known that the Atlantic Ocean is the main source of humidity for West Africa [2,13], but it is necessary to know which region is better tele-connected between ocean-atmospheric variables and WAM. In addition, it is important to find the optimal time lag between the variables and the WAM. ...
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The high variability of rainfall in the Sahel region causes droughts and floods that affect millions of people every year. Several rainfall forecasting models have been proposed, but the results still need to be improved. In this study, linear, polynomial, and exponential models are developed to forecast rainfall in the Bani and Senegal River basins. All three models use Atlantic sea surface temperature (SST). A fourth algorithm using stepwise regression was also developed for the precipitation estimates over these two basins. The stepwise regression algorithm uses SST with covariates, mean sea level pressure (MSLP), relative humidity (RHUM), and five El Niño indices. The explanatory variables SST, RHUM, and MSLP were selected based on principal component analysis (PCA) and cluster analysis to find the homogeneous region of the Atlantic with the greatest predictive ability. PERSIANN-CDR rainfall data were used as the dependent variable. Models were developed for each pixel of 0.25° × 0.25° spatial resolution. The second-order polynomial model with a lag of about 11 months outperforms all other models and explains 87% of the variance in precipitation over the two watersheds. Nash–Sutcliffe efficiency (NSE) values were between 0.751 and 0.926 for the Bani River basin and from 0.175 to 0.915 for the Senegal River basin, for which the lowest values are found in the driest area (Sahara). Results showed that the North Atlantic SST shows a more robust teleconnection with precipitation dynamics in both basins.
... Multivariate statistical techniques have been widely used in environmental sciences, especially in hydrology. These include studies by Singh (2006), Mourato et al. (2009), Darand and Daneshvar (2014), Manatsa and Mukwada (2015), Djibo et al. (2015), among others. The largest commonly applied techniques are principal component analysis (PCA), discriminant analysis (DA), factor analysis (FA), cluster analysis (CA), hierarchical clustering analysis (HCA) and multiple linear regression (MLR). ...
... Multiple linear regressions are used to predict the value of a variable depending on the values of two or more explanatory variables by fitting a linear equation to observed data. Djibo et al. (2015) developed nonlinear and linear models to forecast seasonal precipitation in West Africa (Watershed of Sirba). The joined linear approach was found to be more suitable than the nonlinear approach. ...
... Several linear methods are appropriately tested to choose the predictors and develop rainfall forecasting models (Djibo et al., 2015). Probabilistic models which combine more than one independent variable are named multiple regressions (Chifurira & Chikobvu, 2014). ...
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Precipitation is the principal component of the hydrologic cycle. This study examines the spatial and temporal rainfall variability in Gabes Catchment (southeastern Tunisia) by analyzing annual precipitation data in nine stations during the period extending from 1977 to 2015. Several multivariate statistical tools, essentially principal component analysis (PCA), hierarchical clustering analysis and multiple linear regression, are used to characterize spatial variability of rainfall and identify its major controlling factors. PCA resulted in four principal components explaining 70% of the total variance. Stations were clustered into three different groups based on topography, the proximity to the Mediterranean Sea, continentality and seasonality. Hierarchical clustering, applying Ward method, classified variables into two groups. A multiple regression model including 13 variables was developed, representing a suitable tool for predicting precipitation of the different stations spread throughout Gabes Catchment. The proposed model displays acceptable efficiency with an absolute prediction error of approximately 87%.
... Multiple studies have reported complexities associated with flow forecasting, driven by the natural complexity, nonlinearity, and randomness of river systems (Smith et al., 2007). In order to reduce the number of predictors, different linear or non-linear Feature Selection Algorithms (FSAs) such as Pearson's correlation analysis (Pca) (Djibo et al., 2015), Recursive Feature Elimination (RFE) (Ferreira et al., 2021), and Bayesian networks (BN) (Das et al., 2022) are commonly used. In terms of ML algorithm calibration, the optimization of hyperparameters has a significant impact on the performance of ML models (Szczepanek, 2022). ...
... It has been commonly observed that the forecasting capability of non-linear modelling approaches (e.g. ANN) are better than the linear modelling techniques in predicting seasonal rainfall (Adamowski et al. 2012;Mekanik et al. 2013;Djibo et al. 2015;Rasel et al. 2016a, b;Hossain et al. 2020a). Nevertheless, most of the seasonal rainfall predictive models considered only two independent variables in developing the linear models (Mekanik et al. 2013;Rasel et al. 2016a, b;Hossain et al. 2018bHossain et al. , 2020a. ...
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Precipitation is one of the most intrinsic resources for manifold industrial activities all over Western Australia; consequently, immaculate rainfall prediction is indispensable for flood mitigation as well as water resources management. This study investigated the performance of artificial neural networks (ANN) and Linear multiple regression (LMR) analysis to forecast long-term seasonal spring rainfall in Western Australia, using lagged El Nino Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) as potential climatic phenomena. The ANN was developed in the form of multilayer perceptron using Levenberg–Marquardt algorithm and subsequently LMR was used with statistical significance for future spring rainfall forecast. The total climatic dataset has been divided into calibration and testing phases to determine the efficacy of the developed models. Different statistical skill tests such as root mean square error (RMSE), mean absolute error (MAE), and Willmott index of agreement ‘ d ’ were used to assess the efficacy of LMR and ANN modelling. In general, LMR has lower MAE and RMSE values as compared to ANN for most of the stations during calibration and testing periods, whereas ANN models performed better than LMR models based on ‘ d ’ values. The overall statistical analysis paradigm suggests the efficacy of LMR over ANN models for rainfall forecasting using more climatic variables. As a result, the developed LMR model, incorporated with lagged global climate indices, will facilitate the adequate preparedness for the risks associated with potential droughts in the study region.
... These types of soil have good humidity and moisture level required for most of the crops. Rainfall is also an important factor for crop health [6,7]. Each crop may have different water requirement. ...
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Today, farmers are suffering from the low yield of crops. Though right crop selection is the main boosting key to maximize crop yield by doing soil analysis and considering metrological factors, the lack of knowledge about soil fertility and crop selection is the main reason for low crop production. In the changed current climate, the farmers having primitive knowledge about conventional farming are facing challenges about making sagacious decisions on crop selection. The selection of the same crop in every seasonal cycle makes the low soil fertility. This study is aimed at making an efficient and accurate system using IoT devices and machine learning (ML) algorithms that can correctly select a crop for maximal yield. Such a system is reliable as compared to the old laboratory testing manual systems, which bear the chances of human errors. Correct selection of a crop is predominantly a priority in agricultural arena. As a contribution, we propose an ML-based model, Smart Crop Selection (SCS), which is based on data of metrological and soil factors. These factors include nitrogen, phosphorus, potassium, CO2, pH, EC, temperature, humidity of soil, and rainfall. Existing IoT-based systems are not efficient as compared to our proposed model due to limited consideration of these factors. In the proposed model, real-time sensory data is sent to Firebase cloud for analysis. Its results are also visualized on the Android app. SCS ensembles the following five ML algorithms to increase performance and accuracy: Decision tree, SVM, KNN, Random Forest, and Gaussian Naïve Bayes. For rainfall prediction, a dataset containing historical data of the last fifteen years is acquired from Bahawalpur Agricultural Department. This dataset and an ML algorithm, Multiple Linear Regression leverages prediction of the rainfall in future, a much-desired information for the health of any crop. The Root Mean Square Error of the rain fall prediction model is 0.3%, which is quite promising. The SCS model is trained for 11 crops’ prediction, while its accuracy is 97% to 98%.
... The rainfall patterns are linked to the movement of the intertropical convergence zone (ITCZ) and are characterized by high seasonal and interannual variabilities. The mean annual rainfall depth varies from North to South between 200 and 800 mm (Djibo et al., 2015), whereas mean maximum temperature ranges between 36 and 42 • C. Populations in the Sahel mostly live in rural areas, and their economy mainly depends on rain-fed agriculture and livestock farming. The recurrent droughts caused by seasonal and inter-annual irregularities of rainfall in this region have negatively affected people's standard of living. ...
A composite drought index (CDI) was developed for seasonal drought monitoring at 1 km² resolution over the West African Sahel (WAS). The CDI was derived from remote sensing data, mainly, the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS), normalized difference vegetation index (NDVI) and land surface temperature (LST) from the Terra/MODIS satellite. The weights of these input variables were estimated using a combined entropy method and weighted Euclidian distance. The CHIRPS resulted with the highest weight (mean = 0.74) followed by the NDVI (mean = 0.243) and the LST (mean = 0.016). The CDI was found to be well correlated with the standardized precipitation index (SPI) and the standardized precipitation evapotranspiration index (SPEI)—computed from station data. However, the CDI showed a better sensitivity for drought detection following a comparison of drought classes. The suitability of the CDI for agricultural drought monitoring was validated by its good correlation with crop production data, namely maize, millet and sorghum with a Pearson r in the range of 0.29–0.56, 0.40–0.81 and 0.57–0.71, respectively. Finally, a drought database was generated for the WAS, enabling the extraction of drought characteristics at a given location using its geographic coordinates.
... Most of the available research study prefer to the use of non-linear modelling approaches in excess of linear modelling techniques for the precise projection of long-term seasonal rainfall [4,5]. However, some of the researchers found better predictability of combined linear models over non-linear models [6]. The statement was obtained using the small length of data. ...
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Generalised extreme value distribution (GEVD) remains the commonly employed technique for investigating the probability of occurrence of extreme events for given recurrence of intervals. However, the application of the GEV distribution requires the estimation of its three parameters. There are different methods presented in the literature to determine the parameters of the GEVD. Different methods have been adopted by different researchers in determining the three parameters. This paper investigates the comparison of the commonly used methods to estimate the GEVD parameters. The maximum likelihood estimation (MLE), generalised maximum likelihood estimation (GMLE) and L-moments methods were considered in this study. The analysis was performed using the monthly extreme rainfall of Tasmania, Australia. The GEVD was fitted to four different data sets using the three parameters estimation techniques. The outcomes of the analysis suggest that parameters estimation techniques have negligible impact on the magnitude of the parameters. However, length of the data series has minor impact on the parameters value of different parameters estimation techniques.
... Most of the available literature prefer to the use of non-linear modelling approaches in excess of linear modelling techniques for the precise projection of long-term seasonal rainfall (Mekanik et al. 2013;Hossain et al. 2020a). However, some of the researchers found better predictability of combined linear models over non-linear models (Djibo et al. 2015). The statement was obtained using the small length of data. ...
Full-text available
The application of generalised extreme value distribution (GEVD) requires the estimation of three parameters. Different researchers adopted different techniques for the estimation of the GEVD parameters and no standard comparison amongst those methods are available. This paper investigates the comparison of the commonly used GEVD parameters’ estimations for extreme rainfall modelling. The maximum likelihood estimation, generalised maximum likelihood estimation, Bayesian and L-moments methods were considered in this study to compare the magnitude of the GEVD parameters and the corresponding return level estimations. The analysis was performed using the monthly and yearly extreme rainfall of Tasmania, Australia. The GEVD was fitted to four different data sets using the four parameters estimation techniques. Estimated return levels of the GEVD for all the estimation techniques were compared with the return levels provided by the Australian Rainfall and Runoff (ARR), which is the national guideline for Australian rainfall and flood studies. The outcomes of the analysis suggest that the L-moments method is the better estimator of the return levels when comparing the ARR provided return levels.
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Drought is a prolonged dry period that has a serious impact on health, agriculture, economies, energy, and the environment. Thus, there have been numerous attempts to make this phenomenon more predictable for preventing the aforementioned effects. The present study aims to determine the best combination of input data sets and predict the Standardized Precipitation Evapotranspiration Index (SPEI) in 1,6, and 12-month time scales using Artificial Intelligence (AI) models (Multilayer Perceptron Neural Network (MLPNN), Support Vector Regression (SVR), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Ensemble Decision Tree (EDT)), which all models are hybridized with a wavelet transformation at three synoptic stations named Ardebil, Khalkhal, and Moghan. To this end, monthly lags of precipitation, temperature, and SPEI were used in northwestern Iran from 1987 to 2018. The methods were classified into single parameter and multiparameter, and each sub-method was designed based on a combination of the parameters. Moreover, Autocorrelation Function (ACF), Partial Autocorrelation Function (PACF), Effective Factor Elimination Technique (EFET), and Feature Scaling (FS) were used to determine the best lags of parameters. In this regard, Root Mean Square Error (RMSE), Correlation Coefficient (CC), and Nash–Sutcliffe Efficiency Index (NSE) were used as the statistical criteria to assess AI models, methods, and sub-methods. The results revealed that the sub-method (D) with W-MLPNN in the 1-month and 6-month time scales and the sub-method (D, P, T) with W-SVR in the 12-month time scale were the best models and sub-methods of this area, respectively. Moreover, based on the results, the efficiency of the AI was enhanced in longer time scales (more than the 6th month) and the longer the time scale, the more the number of lags (under the 6th month) in input data is decreased. Graphical Abstract
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The relation between sunspots and rainfall patterns is still obscure in Africa, especially for Sudan and South Sudan. This research explores the response of rainfall to solar activity in eastern regions of Africa, with a case study in Sudan and South Sudan. Rainfall varies with time; therefore, skillful monitoring, predicting, and early warning of rainfall events is indispensable. Severe climatic events, such as droughts and floods, are critical factors in planning and managing all socioeconomic activities. Similar trends for the sunspot activity (sunspot number and sunspot groups) changes and rainfall variations for different stations in East Africa during the years 1910–2018 were not found. Correlation analysis carried out for the above period indicated a weak negative correlation between the total rainfall and the average number of sunspots over the long-term scale for selected stations in Sudan and South Sudan. The overall result of the paper indicated no significant relationship between sunspot numbers and rainfall in temporal and spatial scales in Sudan and South Sudan. HIGHLIGHTS This paper analyzed the rainfall variability of Sudan and South Sudan.; Many statistical measures were employed to evaluate the rainfall trend.; The paper specified the link between sunspot numbers and groups with rainfall variability.; The paper assessed the impact of climate change on rainfall annually and seasonally.;
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Study region: The Sirba watershed, Niger and Burkina Faso countries, West Africa. Study focus: Water resources management in the Sahel region, West Africa, is extremely difficult because of high inter-annual rainfall variability. Unexpected floods and droughts often lead to severe humanitarian crises. Seasonal rainfall forecasting is one possible way to increase resilience to climate variability by providing information in advance about the amount of rainfall expected in each upcoming rainy season. Rainfall forecasting models often arbitrarily assume that rainfall is linked to predictors by a multiple linear regression with parameters that are independent of time and of predictor magnitude. Two probabilistic methods based on change point detection that allow the relationship to change according to time or rainfall magnitude were developed in this paper using normalized Bayes factors. Each method uses one of the following predictors: sea level pressure, air temperature and relative humidity. Method M1 allows for change in model parameters according to annual rainfall magnitude, while M2 allows for changes in model parameters with time. M1 and M2 were compared to the classical linear model with constant parameters (M3) and to the climatology (M4). New hydrological insights for the region: The model that allows a change in the predictor–predictand relationship according to rainfall amplitude (M1) and uses air temperature as predictor is the best model for seasonal rainfall forecasting in the study area.
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Daily precipitation data from 31 Senegalese stations spanning the period from 1950 to 2007 were used to examine the inter-annual variations of seven rainfall indices: the annual mean precipitation (MEAN); the annual standard deviation of daily precipitation (STD); the frequency of wet days (PRCP1); the maximum number of consecutive dry days (CDD); the greatest 3-day total of rainfall (R3D); the wet day precipitation intensity (SDII); and the 90th percentile of rain day precipitation (Prec90p). The indices were spatially averaged over three agroclimatic regions in Senegal. Trends in the averaged indices time series were assessed using both visual examination and a modified version of the Mann-Kendall test (MM-K). Initially negative significant trends in all seven indices suggest gradually drier conditions over the three agroclimatic regions between 1950 and 1980. In contrast, no significant trends or even positive significant trends were observed from the mid-1980s to 2007. The MM-K test was applied to all available data (1950-2007) and the period spanning from 1971 to 2000.
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The ability of various statistical techniques to forecast the Jul-August-September (JAS) total rainfall and monthly streamflow in the Sirba watershed (in West Africa) was tested in this paper. First, multiple linear regression was used to link predictors derived from the Atlantic and Pacific sea surface temperature (SST) to JAS rainfall in the watershed up to 18 months ahead; then, daily precipitation was generated using temporal disaggregation; and finally, a rainfall-runoff model was used to generate future hydrographs. Different combinations of lag times and time windows on which SSTs were averaged were considered. Model performance was assessed using the Nash-Sutcliffe coefficient (Ef), the coefficient of determination (R2) and a three-category hit score (H). The best results were achieved using the Pacific Ocean SST averaged over the March-June period of the year before the rainy season and led to a performance of R2 = 0.458, Ef = 0.387 and H = 66.67% for JAS total rainfall and R2 = 0.552, Ef = 0.487 and H = 73.28% for monthly streamflow.
Pre-monsoon principal components (PCs) of circulation fields covering the South Asian subcontinent were used as predictors for all-India summer monsoon rainfall (AISMR) over the period 1958-1993. Predictive skill of non-linear neural network models and linear multiple regression models was compared using a bootstrap-based resampling procedure. Monsoon precursor signals represented by PCs were investigated and comparisons made with a recent observational and general circulation modelling study. Pre-monsoon PCs of the 200 hPa geopotential height field in May formed a compact, interpretable, and significant set of predictors for AISMR. Predictive skill was comparable to or better than that reported in prior modelling studies, each of which used optimized sets of regional and global predictors. No improvement was noted when using data from multiple atmospheric levels, and skill at lead times more than 1 month prior to monsoon onset in June was poor. For May predictors there were only small differences in skill between the neural network and multiple regression models, although the neural network results at longer lead times tended to be better than those shown by multiple regression. Interestingly, the 850 hPa PCs in January showed a maximum in predictive skill that was only evident in the neural network model results. The strength of this relationship suggests that further investigation into the use of January 850 hPa predictors for the long-range forecasting of AISMR is warranted. Copyright (C) 1999 Royal Meteorological Society.
A brief history and current practiceReasons for forecast verification and its benefitsTypes of forecast and verification dataScores, skill and valueData quality and other practical considerationsSummary
Available online: http:/ / water/ about/ publications/ document/ dynamic_seasonal_streamflow_forecasting.pdf.
[1] The present study offers for the first time the validation of decadal prediction systems upon the West African monsoon (WAM) variability. The ENSEMBLES multimodel and perturbed parameter decadal reforecasts are used to assess multiyear prediction skill for the dominant WAM precipitation regimes. Thus, the focus of the assessment is on time scales longer than seasonal to interannual. To retain lower-frequency predictability (interannual to decadal), a 4 year average is applied, which indeed has been shown to remove most of the interannual variability that is unpredictable beyond 1 year in dynamical forecasting (e.g., El Niño–Southern Oscillation). First, the decadal hindcasts are analyzed to assess forecast skill of Guinean and Sahelian area-averaged rainfall indices. Findings suggest that there is no significant skill in predicting these rainfall indices, probably due to the distinctive representations of deep tropical convection in each forecast system. This is further addressed by computing and comparing the leading modes of WAM variability in the ENSEMBLES decadal reforecasts against observations. Results show that while in the observations, global warming has an important role, in the forecast systems, the Atlantic Ocean is the main player. The Atlantic Niño represents the leading forcing for the simulated Guinean precipitation. Sea surface temperature (SST) anomalies associated with the simulated Sahelian precipitation project onto the Atlantic multidecadal variability (AMV), in which the subtropical branch shows consistency across the forecast systems. No significant skill has been found, however, to predict these WAM precipitation modes, although the Sahelian pattern presents systematic positive correlation scores and lower root mean square errors along the whole forecast range. This is reflected in a tendency for reproducing the Sahel dry period around the 1980s. Likewise, the good performance across the models in simulating the relationship between the leading rainfall modes and the surrounding SST forcings points out encouraging prospects for decadal forecasting. Previous studies show multiyear prediction skill of the AMV in the ENSEMBLES decadal reforecasts. Here the skill of the Atlantic-3 SST index is discussed.
Rainfall in the Sahel region of Africa is prone to large interannual variability, and it has exhibited a recent multidecadal drying trend. The well-documented social impacts of this variability have motivated numerous efforts at seasonal precipitation prediction, many of which employ statistical techniques that forecast Sahelian precipitation as a function of large-scale indices of surface air temperature (SAT) anomalies, sea surface temperature (SST), surface pressure, and other variables. These statistical models have demonstrated some skill, but nearly all have adopted conventional statistical modeling techniques-most commonly generalized linear models-to associate predictor fields with precipitation anomalies. Here, the results of an artificial neural network (ANN) machine-learning algorithm applied to predict summertime (July-September) Sahel rainfall anomalies using indices of springtime (April-June) SST and SAT anomalies for the period 1900-2011 are presented. Principal component analysis was used to remove multicollinearity between predictor variables. Predictive accuracy was assessed using repeated k-fold random holdout and leave-one-out cross-validation methods. It was found that the ANN achieved predictive accuracy superior to that of eight alternative statistical methods tested in this study, and it was also superior to that of previously published predictive models of summertime Sahel precipitation. Analysis of partial dependence plots indicates that ANN skill is derived primarily from the ability to capture nonlinear influences that multiple major modes of large-scale variability have on Sahelian precipitation. These results point to the value of ANN techniques for seasonal precipitation prediction in the Sahel.