- Email: [email protected]
Spatial variability of monthly and annual rainfall data over Southern Tunisia
Atmospheric Research 93 (2009) 832–839
Contents lists available at ScienceDirect
Atmospheric Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a t m o s
Spatial variability of monthly and annual rainfall data over Southern Tunisia Manel Ellouze a,1, Chafai Azri b,2, Habib Abida b,⁎ a b
Faculty of Science, Road Soukra BP 1171, 3000 Sfax, Tunisia Department of Earth Sciences, Faculty of Science, Road Soukra BP 1171, 3000 Sfax, Tunisia
a r t i c l e
i n f o
Article history: Received 16 October 2008 Received in revised form 5 March 2009 Accepted 17 April 2009 Keywords: Southern Tunisia Rainfall Principal Component Analysis Representation quality Multiple regression
a b s t r a c t Spatial and temporal variability of rainfall characteristics in southern Tunisia are monitored. Performance is evaluated through descriptive and statistical analysis of continuous monthly and annual rainfall data over the period extending from 1930 to 2000. Principal Component Analysis (PCA), representation quality and multiple regression methods are carried out on the rainfall data, recorded in twelve stations, to find out the nature of rainfall distribution and the dominant variables related to its variability. A varimax rotation with Kaiser normalization was used. Applied to the monthly series data, three principal components (PCs) are found to be significant, explaining 69% of the total variance. Rainfall variability is shown to be dependent on seasonal conditions. The longitude presents the best quality of representation, followed closely by winter and fall rainfall. Spatial patterns of shorter rainfall series (annual) are governed mainly by topography and coastal influence. The first three PCs contribute by 90% of the total variance and their loadings indicate that annual rainfall is significant over the south-eastern costal area. Four regions are delineated based on the projection over the factorial plane, showing the influence of topography and seasonality on annual rainfall variability in southern Tunisia. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Quantitative evaluation of the spatial distribution of rainfall is required for a number of applications including water resources management, hydrologic modelling, flood forecasting using, rainfall–runoff relationship, hydrometeorologic network design, water balance computations, soil moisture modelling for crop production and irrigation scheduling etc. Among the hydrometeorological variables, rainfall is the most difficult to predict or simulate due to its inherent variability in time and space, especially for arid regions (Guenni and Hutchinson, 1998; Kipkorior, 2002). Detailed studies of spatial rainfall patterns and temporal variability provide vital information about the influence of meteorological and topographical factors. In arid regions, it is crucial to study the influence of the climate and the degree of
⁎ Corresponding author. Tel.: +216 98952472; fax: +216 74274437. E-mail addresses: [email protected] (M. Ellouze), [email protected] (C. Azri), [email protected] (H. Abida). 1 Tel.: +216 98 510 385; fax: +216 74274437. 2 Tel.: +216 98595067; fax: +216 74274437. 0169-8095/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2009.04.005
aridity on the rainfall variability. These studies were based mainly on statistical techniques. Time-series of annual rainfall, number of rainy-days per year and monthly rainfall of 20 stations were analyzed to assess climate variability in arid and semi-arid regions of Iran (Modarres and Rodrigues da Silva, 2007). Increasing and decreasing monthly rainfall trends were found over large continuous areas in the study region. These trends were statistically significant mostly during the winter and spring seasons, suggesting a seasonal movement of rainfall concentration. Results also showed that there is no significant climate variability in the arid and semi-arid environments of Iran. Studies of spatial rainfall variability also involve the use of the dominant component extraction technique. The method is known as Principal Component Analysis (PCA), or the closely related empirical orthogonal function analysis (EOF; Wilks, 1995). This technique focuses on second-order statistics, by reducing the correlation of the extracted components while at the same time maximizing the variance (in a least squares sense) of successive principal components. Component extraction techniques have been used in a variety of climate studies to (1) reduce the dimension of large datasets, and
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
(2) aid in the identification and interpretation of significant ‘modes’ of climate variability. There are many examples in the literature where this technique has been applied to climate datasets, and this has assisted in the identification of a wide range of climate phenomena, such as the Interdecadal Pacific Oscillation (IPO; Zhang et al., 1997), the Indian Ocean Dipole (IOD; Saji et al., 1999), and the Artic Oscillation (AO; Thompson and Wallace, 1998). Recent studies have been carried out based on PCA techniques such as those by Webster et al. (1998), Compagnucci et al. (2001), Penarrocha et al. (2002; Valencia), Mohapatra et al. (2003; India), Lana et al. (2004; Spain), Bordi et al. (2004; China) and Tosic (2004; Serbia). Chambers (2003) explored rainfall variability and trends within the State of South Australia over the past century in an attempt to group geographical areas with similar rainfall patterns over the long term. Using Principal Component Analysis and Cluster Analysis, new divisions were proposed. Annual and monthly rainfall data and time series data from the Principal Component Analysis were used to look for the existence of linear and non-linear trends in the rainfall time series. Spatial comparisons revealed that many of the statistically significant (increasing) trends in rainfall occurred in the southeast of the State. Changes in the relationship
833
between rainfall in South Australia and the Southern Oscillation Index were also discussed. More recently, Singh (2006) used the Principal Component Analysis (PCA) to determine the dominant rainfall patterns from rainfall records over India. The PCA is carried out on the rainfall data to find out the nature of rainfall distribution and percentage of variance is estimated. The first principal component explains 55.5% of the variance and exhibits factor of one positive value throughout the Indian subcontinent. The analysis identifies the spatial and temporal characteristics of possible physical significance. The first study of the different aspects of temporal and spatial variability of rainfall in Tunisia was presented by Berndtsson (1987). Long-term trends were shown to follow a general pattern of consecutive dry or wet periods of 5 to 30 years. The author proved, using a cross correlation function, that spatial patterns of shorter rainfall series (annual, monthly) are governed mainly by topography and coastal influence. In the present study statistical methods such as Principal Component Analysis (PCA), representation quality and multiple regression were used to determine the dominant rainfall patterns from rainfall records over Southern Tunisia. Pattern characteristics of seasonal rainfall are studied for 12 stations, evenly distributed over the study zone. The PCA is carried out
Fig. 1. Study area.
834
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
on the rainfall data to find out the nature of rainfall distribution and the percentage of variance.
the variation of the quality parameters in the selected model were also determined.
2. Methodology
3. Study area and data used
The PCA method involves the transformation of a greater number of unorthogonal variables into smaller number of orthogonal variables, which present common causes of their changes. It can therefore reduce the dimensionality of a problem by replacing the measured variables and the intercorrelated variables by using a smaller number of uncorrelated variables. This can be useful in reducing the amount of basic data to be processed. Depending on the data, it is possible to interpret the orthogonal functions in terms of some underlying physical processes. Castell (1966) proposed a method of retaining significant factors in PCA. Similar methods have been used by Ogallo (1988, 1989) and Basalirwa et al. (1995) for East Africa and Tanzania respectively. In the present work, data presented in the form of monthly and annual precipitation were first used to compute the coefficients of variation (CV), coefficients of skewness (CS) and coefficients of kurtosis (Ck). Statistical methods were later applied to complete and refine the analysis. They especially included linear correlations and multiple regression analysis. A representation quality of the parameters (positions in the factorial plane) was also performed. Statistical analysis was performed using the STATITCF (1987). Significant factors were retained based on the method proposed by Castell (1966). The representation quality of a parameter is identified by a coefficient, which explains its position in the selected factorial plane. It is given by the sum of the squares of the correlation coefficients between each parameter and the factorial axis of the considered plane (Dutot et al., 1983):
The method described above was applied to southern Tunisia basin. Most of the watershed is composed of plains, with altitudes varying between 4 and 600 m. The average altitude is 200 m and rarely exceeds 300 m. Southern Tunisia basin is characterized by a stretched form and a poorly developed stream network (Fig. 1). The climate is characterized by mild rainy winters and hot dry summers. The dry and wet periods are more or less clearly distinguishable all over southern Tunisia. This division, however, seems to become less clear with increasing distance from the Mediterranean coast and decreasing latitude (Branigan and Jarrett, 1969). The rainy season starts in September and ends in May. The main annual rain volume, however, falls between October and January. The rains falling in other months during the rainy season are more erratic and occur with less probability. The relative weakness of rains, as well as their irregularity are accentuated by an evaporation attributed to strong temperatures and dry and often violent winds. The North eastern air masses generate stormy rains while the contribution of the Saharan air masses to the seasonal rains remains typical of the spring. They provoke on the coastline generally insignificant rains. These disruptions are bound to the Saharan front, which separates a mass of hot air of tropical origin from a mass of cold air of continental or maritime origin. In summer, the driest season, the region is subjected to the continental air flux coming from the south and the southwest. The region is also subjected to marine influences as it is bordered by the Mediterranean Sea in the east. Rainfall data of twelve stations were used to evaluate rainfall variability in arid zones throughout southern Tunisia (Table 1). These stations were selected because they are evenly spread throughout the study region and they have continuous rainfall records extending over a period of 70 years. The data set which include annual and monthly rainfall, were obtained from the publications of the Tunisian Ministry of Agriculture and Water Resources. The rainfall data series need to be independent, random, homogeneous, and without trends. These characteristics were verified by four nonparametric tests using the Consolidated Frequency Analysis (CFA) package of Environment Canada (Pilon and Harvey, 1994). All data sets passed the four nonparametric
Q LTð jÞ =
n X
2
ri ð jÞ
ð1Þ
i=1
Where: QLT (j) is the representation quality of the parameter j (‰); ri is the correlation coefficient between the parameter j and the factorial axis and n is the number of considered factorial axes. Multiple regressions were also used to select parameters that significantly affect the variability of rainfall distribution and analyze the relationships between the identified variables. Relative contributions of each independent variable to Table 1 Characteristics of the rainfall stations and their corresponding time series.
Station number Station name Latitude Longitude Altitude (m) Min. rainfall (mm) Mean rainfall (mm) Max. rainfall (mm) SD
CV
CS
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12
0.52 0.41 0.52 0.41 0.57 0.48 0.60 0.56 0.47 0.58 0.55 0.63
1.26 4.56 0.21 2.35 2.29 10.70 0.57 3.62 1.68 7.84 0.45 3.21 1.23 4.31 1.37 5.21 1.67 7.74 1.83 7.37 1.39 4.77 2.07 8.18
Gabes Metlaoui Mednine Gafsa Tataouine Tozeur Matmata Zarzis Redeyef Maknassy B. Guerdane Remeda
37.65 38.13 37.04 38.25 36.58 37.69 37.27 37.22 38.21 38.42 36.82 35.90
8.62 6.70 9.07 7.18 9.02 6.46 8.50 9.75 6.46 8.04 9.87 8.97
4 202 125 300 240 45 441 11 586 278 12 300
39.3 12.1 36.4 36.1 25.7 15.8 29.3 28.7 49.9 41.3 44.8 8.4
189 124 152 161 127 98 215 217 138 199 181 87
534 262 550 390 484 259 692 684 434 689 520 323
98.9 50.9 79.6 65.8 71.6 46.9 129 120 65.5 115 99.6 55
Ck
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
tests at the 1% level of significance. The mean annual precipitation is 158 mm, ranging between more than 200 mm, recorded in the coastal sector (station 6) and less than 90 mm, recorded in the north west. These averages are subject to very wide annual fluctuations (1 to 12). 4. Results and discussion Statistics of annual rainfall data such as the coefficient of variation (CV), coefficient of skewness (CS) and coefficient of kurtosis (Ck) are presented in Table 1. The mean values of CV, CS and Ck for the study region are 53%, 1.34 and 5.82, respectively. CV values are generally higher than 50%, except for stations 6, 4, 2 and 9 (Tozeur, Gafsa, Metlaoui and Redeyef respectively) which are located in the northwest of the study area. The highest values of the coefficient of kurtosis were found for Mednine and Remeda (stations 3 and 12 respectively). All the stations showed a high degree of peakedness which is quite different from that of a normal distribution. CV values decline from the south-east to the north-west, with a maximum value of 0.63 in the Remeda station. In general, CV slightly decreases, CS remains constant and Ck slightly increases with an increase in annual rainfall (Modarres and Rodrigues da Silva, 2007). There was a mixture of increase and decrease of rainfall trends widespread throughout the study area. This result suggests that the rainfall trends may be attributed to local changes in the rainfall regime rather than the large-scale patterns of atmospheric circulation. To refine the preliminary analysis and identify the principal factors affecting rainfall characteristics and the principal sources of its variation, a multivariable analysis of data was performed using the STATITCF statistical software
835
package (1987). Statistical analysis especially included PCA, representation quality and multiple regression related to monthly and annual rainfall. A total of 8 variables were considered, namely annual rainfall (P), latitude (LAT), longitude (LON), altitude (ALT), and the seasonal rainfall for the winter, autumn, spring and summer seasons (WIN, AUT, SPR and SUM respectively).
4.1. Monthly rainfall The Principal Component Analysis (PCA) applied to all data (monthly rainfall) resulted essentially in three principal components. A varimax rotation with Kaiser normalization was used for all 70 years data sets of the twelve stations. The threshold of significance considered for p b 0.05 is equal to 0.23 after a test of Student (n = 70). The significant correlations between selected parameters (variables) and these components represent approximately 68% of the total variance. The first, second and third PCs explained 29%, 26% and 13% of the total variance respectively. The projection, over the (1 × 2) factorial plane (presenting 56% of inertia), of all selected variables and individuals shows three distinct data groups (Fig. 2): - Group 1, represented positively along axis 1, is composed of rainfall and seasonal downpours of winter, autumn and spring. These variables are highly inter-correlated. - Group 2, represented positively along axis 2, is formed by the variables latitude, altitude and summer rainfall. - Group 3, represented positively and negatively along axis 2 and 1 respectively, is characterized by the longitude.
Fig. 2. Projection of individuals in the (1 × 2) factorial plane (monthly rainfall).
836
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
Table 2 Representation qualities (QLT) of the selected parameters with respect to the first two principal axes (monthly rainfall). Parameter
Latitude Longitude Altitude Fall rainfall Winter rainfall Spring rainfall Summer rainfall
Factor 1
Factor 2
Factorial plane (1 × 2)
r21
r22
QLT⁎
1.8 148.6 49.7 405.5 488 304.9 7.7
682 652 316.1 0.1 7.6 76.8 348.2
683.8 800.6 365.8 405.6 495.6 381.7 355.9
⁎The threshold of significance = 400 for p b 0.05 and n = 790.
These distinct groups clearly show that rainfall distribution is more related to longitude and seasonality than altitude and latitude. This could be explained by the irregularity of
rainfall and the climate changes from a season to another. In fact, the region receives a small amount of rainfall, which largely varies in time and space compared to northern and coastal regions (Branigan and Jarrett, 1969). On the other hand, southern Tunisia is mainly a plane region, where rainfall variability is more governed by the Mediterranean Sea proximity. Rainfall increases continuously from the west (continent) to the east (coast line), implying an important effect of longitude. In order to better examine the effect of the load of each parameter, the quality of representation (over the 1 × 2 factorial plane) of the selected parameters was checked (Table 2). This exercise showed that the latitude and longitude are associated with the best quality of representation (683.8 and 800.6 respectively). Furthermore, they represent the most predominant and significant variables. Moreover, fall and winter rainfall,
Fig. 3. Maps of distribution of loadings of the three dominant PC modes (annual rainfall).
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
with representation quality values greater than 400, can be considered as significant variables. Monthly rainfall data was correlated with all independent variables. A multiple regression method was used to evaluate the effect of the aforementioned parameters on rainfall in all selected stations. The rainfall frequency variability DP is given by: ΔP = 0:0001 LAT − 0:0001 LON + AUT + WIN + SPR + SUM − 0:0023
ð2Þ
The obtained regression model suggests, by the coefficient of determination (R2 = 0.99), that the rainfall frequency variation is dependent on the majority of the selected parameters. The contribution's rates of latitude and longitude are insignificant (1% of the variance). These two parameters are disregarded and the model is modified: ΔP = AUT + WIN + SPR + SUM
ð3Þ
The percentage of variance in precipitation change may be explained by 36% of the fall rainfall AUT, followed very closely by that of winter WIN (33%). The spring rainfall SPR provided 27% of the variance of monthly rainfall, while summer rain (SUM) contributed only by 3% to the total variation. Therefore, monthly rainfall frequency variation in southern Tunisia is based on seasonality and climate changes, while spatial influence is insignificant. An analysis of rain seasonal distributions carried out in the study zone showed frequent downpours during the fall and winter seasons and scarce light rainfall events in the rest of the year (Abou-Hadid, 2006). The author also proved that the dry period extends from April to
837
August, with an important inter and intra-annual variability of rainfall. 4.2. Annual rainfall This analysis seeks to identify the dominant independent components of seasonal rainfall data from a number of point locations spread over Southern Tunisia, with the presumption that these PCs will be related to the two main sources of rainfall variability. However, with a large number of observations (790, considering temporal and spatial variation of rainfall), no relationship between any of the stations was found. The PCA exercise is repeated based on the annual values of the same eight variables (P, LAT, ALT, LON, WIN, AUT, SPR, and SUM) for the twelve selected stations. The contributions of the first, second and third PCs to the total variance are 68%, 14% and 8%, respectively. The individual contributions to the total variation from the fourth component are relatively low, and the corresponding eigenvalue decreases from 7 to nearly 0 between the third and fourth PCs. Therefore, we consider the first three PCs to describe the major patterns of the geographical variability in the mean annual rainfall data series and explain the corresponding temporal aspects of this variability. The first three PCs contributed 90% to the total variance and the corresponding eigenvalue is greater than 1.5. The correlation matrix was computed to identify the variables that contribute significantly to the variance of the selected PCs (Fig. 3). The threshold of significance considered for p b 0.05 is equal to 0.55 after a test of Student (n = 12). The first PC reveals a pattern showing significantly positive
Fig. 4. Delineation of statistical regions based on the projection of annual individuals in the (1 × 2) factorial plane.
838
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
loadings of the annual rainfall for the south eastern and north eastern parts of the study area (Fig. 3). The second PC yields significantly positive loadings over most of the northern zone, while the south eastern region is less important in comparison to the first principal component. The third PC reveals an interesting pattern with significant loadings in a south direction along the study area. Thus, the variability of annual rainfall is usually significant along the southeastern coastal part as indicated by the dominantly positive loadings of the three PCs over that area compared to other areas. The projection, over the (1 × 2) factorial plane of all annual selected variables and individuals, leads to the division of the study area into four sub-regions (Fig. 4). These sub-regions are delineated by regrouping stations, statistically correlated on the factorial plane (1 × 2). Regions R I and R II reflect the influence of topography. In fact, they are characterized by relatively high altitudes, ranging between 125 and 300 m. Compared to the three remaining zones rainfall variation is more important for region R III. It is important to note at this stage that, this delineation confirms the above results showing that rainfall variation in southern Tunisia is based on topography and seasonal characteristics. Moreover, this delineation proves the importance of rainfall variation over the coastline (R III), confirmed by the positive loadings (Fig 3). 5. Conclusion This study investigated rainfall variability in southern Tunisia by analyzing monthly and annual rainfall data recorded in twelve stations. The PCA analysis, using a varimax rotation with Kaiser normalization, was applied to monthly series data and resulted essentially in three principal components, describing approximately 68% of the total variance. Three distinct groups were identified, showing that rainfall distribution was more related to longitude and seasonality than altitude and latitude. This result was confirmed by the regression model, which revealed that monthly rainfall is based on seasonality and climate changes. As for annual rainfall, the first three principal components (PCs) contributed 90% to the total variance and the corresponding eigenvalue exceeds 1.5. The positive loadings of these PCs over the southeastern coastal area indicated that the annual rainfall variability is significant. The study area was divided into four sub-regions based on the projection over the factorial plane. The obtained delineation confirmed the influence of topography and seasonality on rainfall distribution in southern Tunisia. 6. List of symbols ALT AO AUT Ck CS Cv EOF IOD IOP LAT LON
altitude Artic oscillation autumn rainfall coefficient of kurtosis coefficient of skewness coefficient of variation empirical orthogonal function Indian Ocean dipole interdecadal pacific oscillation latitude longitude
P PCA PCs QLT SD SPR SUM WIN DP
rainfall depth principal component analysis principal components representation quality standard deviation spring rainfall summer rainfall winter rainfall rainfall variability
Acknowledgments Data used in this study were provided by the Tunisian Ministry of Agriculture and Water Resources. The collaboration of Mr. Saadaoui of the Water Resources Division and Mr. Ben Younes, engineer in the Tunisian Institute of Research (INRAT) are gratefully acknowledged. References Abou-Hadid, A.F., 2006. Assessment of impacts, adaptation, and vulnerability to climate change in North Africa: food production and water resources. A Final Report Submitted to Assessments of Impacts and Adaptations to Climate Change (AIACC), Project No. AF 90. The International START Secretariat 2000 Florida Avenue, NW Washington, DC 20009 USA. Basalirwa, C.P.K., et al., 1995. The climatological zones of Tanzania based on rainfall characteristics. Water Resources Engineering Research Report, University of Dar-es-Salaam. Berndtsson, R., 1987. Spatial and temporal variability of rainfall and potential evaporation in Tunisia. The Influence of Climate Change and Climatic Variability on the Hydrologie Regime and Water Resources (Proceedings of the Vancouver Symposium, August 1987). IAHS Publ. no. 168. Bordi, I., Fraedrich, K., Jiang, J.M., Sutera, A., 2004. Spatio-temporal variability of dry and wet period in eastern China. Theoretical and Applied Climatology 79 (1–2), 81–91. Branigan, J.J., Jarrett, H.R., 1969. The Mediterranean Lands. Macdonald and Evans, London. Castell, R.B., 1966. The Scree test for the number of factors. Multivariate Behavioral Research 1, 245–276. Chambers, L.E., 2003. South Australian rainfall variability and trends. BMRC RESEARCH REPORT NO. 92, Commonwealth of Australia, Published by the Bureau of Meteorology. Compagnucci, Rose H., Araneo, Diego, Canziani, Pablo, O., 2001. Principal sequence pattern analysis: a new approach to classifying the evolution of atmospheric system. International Journal of Climatology 21 (2), 197–217. Dutot, A.L., Elichegaray, C., Vie le sage, R., 1983. Application de L'analyse des correspondences à l'étude de la composition physico-chimique de l'aérosol urbain. Atmospheric Environment 17 (1), 73–78. Guenni, L., Hutchinson, M.F., 1998. Spatial interpolation of the parameters of a rainfall model from ground based data. Journal of Hydrology 212–213, 335–347. Kipkorior, E.C., 2002. Analysis of rainfall climate on the Njemps Flats, Baringo District, Kenya. Journal of Arid Environments 50, 445–458. Lana, X., Martinez, M.D., Serra, C., Burgueno, 2004. Spatial and temporal variability of the daily rainfall regime in Catalonia (northeastern Spain), 1950–2000. International Journal of Climatology 24 (5), 613–641. Modarres, Reza, Rodrigues da Silva, V.P., 2007. Rainfall trends in arid and semi-arid regions of Iran. Journal of Arid Environments 70, 344–355. Mohapatra, M., Mohanty, U.C., Behera, S., 2003. Spatial variability of daily rainfall over Orissa, India, during the southwest summer monsoon season. International Journal of Climatology 23 (15), 1867–1887. Ogallo, L.A., 1988. The spatial and temporal clusters of the East African Seasonal Rainfall anomalies derived from Principal component analysis. Journal of Climatology 6, 1–23. Ogallo, L.A., 1989. The spatial and temporal patterns of East African Seasonal Rainfall derived from Principal component analysis. Journal of Climatology 9, 145–167. Penarrocha, D., Estrela, M.J., Mullon, M., 2002. Classification of daily rainfall patterns in a Mediterranean area with extreme intensity levels: the Valencia region. International Journal of Climatology 22 (6), 677–695. Pilon, P.J., Harvey, K.D., 1994. Consolidated Frequency Analysis Package. Environment Canada, Ottawa, Qntario, Canada.
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839 Saji, N.H., Goswami, B.N., Vinayachandran, P.N., Yamagata, T., 1999. A dipole mode in the tropical Indian Ocean. Nature 401, 360–363. Singh, C.V., 2006. Pattern characteristics of Indian monsoon rainfall using principal component analysis (PCA). Elsevier Atmospheric Research 79, 317–326. STATITCF package, 1987. Services des Etudes statistiques de l'I.T.C.F. Thompson, D.W.J., Wallace, J.M., 1998. The arctic oscillation signature in the wintertime geopotential height and temperature fields. Geophysical Research Letters 25, 1297–1300. Tosic, I., 2004. Spatial and temporal variability of winter and summer precipitation over Serbia and Montenegra. Theoretical and Applied Climatology 77 (1–2), 47–56.
839
Webster, P.J., Magana, V.O., Palmer, T.N., Shukla, J., Tomas, R.A., Yanai, M., Yasunari, T., 1998. Monsoon: process, predictability and the prospectus for prediction. Journal of Geophysical Research 103 (C7), 14451–14510. Wilks, D.S., 1995. Statistical Methods in Atmospheric Sciences. Academic Press, San Diego. Zhang, Y., Wallace, J.M., Battisti, D.S., 1997. ENSOlike interdecadal variability: 1900–93. Journal of Climate 10 (5), 1004–1020.
Contents lists available at ScienceDirect
Atmospheric Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a t m o s
Spatial variability of monthly and annual rainfall data over Southern Tunisia Manel Ellouze a,1, Chafai Azri b,2, Habib Abida b,⁎ a b
Faculty of Science, Road Soukra BP 1171, 3000 Sfax, Tunisia Department of Earth Sciences, Faculty of Science, Road Soukra BP 1171, 3000 Sfax, Tunisia
a r t i c l e
i n f o
Article history: Received 16 October 2008 Received in revised form 5 March 2009 Accepted 17 April 2009 Keywords: Southern Tunisia Rainfall Principal Component Analysis Representation quality Multiple regression
a b s t r a c t Spatial and temporal variability of rainfall characteristics in southern Tunisia are monitored. Performance is evaluated through descriptive and statistical analysis of continuous monthly and annual rainfall data over the period extending from 1930 to 2000. Principal Component Analysis (PCA), representation quality and multiple regression methods are carried out on the rainfall data, recorded in twelve stations, to find out the nature of rainfall distribution and the dominant variables related to its variability. A varimax rotation with Kaiser normalization was used. Applied to the monthly series data, three principal components (PCs) are found to be significant, explaining 69% of the total variance. Rainfall variability is shown to be dependent on seasonal conditions. The longitude presents the best quality of representation, followed closely by winter and fall rainfall. Spatial patterns of shorter rainfall series (annual) are governed mainly by topography and coastal influence. The first three PCs contribute by 90% of the total variance and their loadings indicate that annual rainfall is significant over the south-eastern costal area. Four regions are delineated based on the projection over the factorial plane, showing the influence of topography and seasonality on annual rainfall variability in southern Tunisia. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Quantitative evaluation of the spatial distribution of rainfall is required for a number of applications including water resources management, hydrologic modelling, flood forecasting using, rainfall–runoff relationship, hydrometeorologic network design, water balance computations, soil moisture modelling for crop production and irrigation scheduling etc. Among the hydrometeorological variables, rainfall is the most difficult to predict or simulate due to its inherent variability in time and space, especially for arid regions (Guenni and Hutchinson, 1998; Kipkorior, 2002). Detailed studies of spatial rainfall patterns and temporal variability provide vital information about the influence of meteorological and topographical factors. In arid regions, it is crucial to study the influence of the climate and the degree of
⁎ Corresponding author. Tel.: +216 98952472; fax: +216 74274437. E-mail addresses: [email protected] (M. Ellouze), [email protected] (C. Azri), [email protected] (H. Abida). 1 Tel.: +216 98 510 385; fax: +216 74274437. 2 Tel.: +216 98595067; fax: +216 74274437. 0169-8095/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2009.04.005
aridity on the rainfall variability. These studies were based mainly on statistical techniques. Time-series of annual rainfall, number of rainy-days per year and monthly rainfall of 20 stations were analyzed to assess climate variability in arid and semi-arid regions of Iran (Modarres and Rodrigues da Silva, 2007). Increasing and decreasing monthly rainfall trends were found over large continuous areas in the study region. These trends were statistically significant mostly during the winter and spring seasons, suggesting a seasonal movement of rainfall concentration. Results also showed that there is no significant climate variability in the arid and semi-arid environments of Iran. Studies of spatial rainfall variability also involve the use of the dominant component extraction technique. The method is known as Principal Component Analysis (PCA), or the closely related empirical orthogonal function analysis (EOF; Wilks, 1995). This technique focuses on second-order statistics, by reducing the correlation of the extracted components while at the same time maximizing the variance (in a least squares sense) of successive principal components. Component extraction techniques have been used in a variety of climate studies to (1) reduce the dimension of large datasets, and
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
(2) aid in the identification and interpretation of significant ‘modes’ of climate variability. There are many examples in the literature where this technique has been applied to climate datasets, and this has assisted in the identification of a wide range of climate phenomena, such as the Interdecadal Pacific Oscillation (IPO; Zhang et al., 1997), the Indian Ocean Dipole (IOD; Saji et al., 1999), and the Artic Oscillation (AO; Thompson and Wallace, 1998). Recent studies have been carried out based on PCA techniques such as those by Webster et al. (1998), Compagnucci et al. (2001), Penarrocha et al. (2002; Valencia), Mohapatra et al. (2003; India), Lana et al. (2004; Spain), Bordi et al. (2004; China) and Tosic (2004; Serbia). Chambers (2003) explored rainfall variability and trends within the State of South Australia over the past century in an attempt to group geographical areas with similar rainfall patterns over the long term. Using Principal Component Analysis and Cluster Analysis, new divisions were proposed. Annual and monthly rainfall data and time series data from the Principal Component Analysis were used to look for the existence of linear and non-linear trends in the rainfall time series. Spatial comparisons revealed that many of the statistically significant (increasing) trends in rainfall occurred in the southeast of the State. Changes in the relationship
833
between rainfall in South Australia and the Southern Oscillation Index were also discussed. More recently, Singh (2006) used the Principal Component Analysis (PCA) to determine the dominant rainfall patterns from rainfall records over India. The PCA is carried out on the rainfall data to find out the nature of rainfall distribution and percentage of variance is estimated. The first principal component explains 55.5% of the variance and exhibits factor of one positive value throughout the Indian subcontinent. The analysis identifies the spatial and temporal characteristics of possible physical significance. The first study of the different aspects of temporal and spatial variability of rainfall in Tunisia was presented by Berndtsson (1987). Long-term trends were shown to follow a general pattern of consecutive dry or wet periods of 5 to 30 years. The author proved, using a cross correlation function, that spatial patterns of shorter rainfall series (annual, monthly) are governed mainly by topography and coastal influence. In the present study statistical methods such as Principal Component Analysis (PCA), representation quality and multiple regression were used to determine the dominant rainfall patterns from rainfall records over Southern Tunisia. Pattern characteristics of seasonal rainfall are studied for 12 stations, evenly distributed over the study zone. The PCA is carried out
Fig. 1. Study area.
834
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
on the rainfall data to find out the nature of rainfall distribution and the percentage of variance.
the variation of the quality parameters in the selected model were also determined.
2. Methodology
3. Study area and data used
The PCA method involves the transformation of a greater number of unorthogonal variables into smaller number of orthogonal variables, which present common causes of their changes. It can therefore reduce the dimensionality of a problem by replacing the measured variables and the intercorrelated variables by using a smaller number of uncorrelated variables. This can be useful in reducing the amount of basic data to be processed. Depending on the data, it is possible to interpret the orthogonal functions in terms of some underlying physical processes. Castell (1966) proposed a method of retaining significant factors in PCA. Similar methods have been used by Ogallo (1988, 1989) and Basalirwa et al. (1995) for East Africa and Tanzania respectively. In the present work, data presented in the form of monthly and annual precipitation were first used to compute the coefficients of variation (CV), coefficients of skewness (CS) and coefficients of kurtosis (Ck). Statistical methods were later applied to complete and refine the analysis. They especially included linear correlations and multiple regression analysis. A representation quality of the parameters (positions in the factorial plane) was also performed. Statistical analysis was performed using the STATITCF (1987). Significant factors were retained based on the method proposed by Castell (1966). The representation quality of a parameter is identified by a coefficient, which explains its position in the selected factorial plane. It is given by the sum of the squares of the correlation coefficients between each parameter and the factorial axis of the considered plane (Dutot et al., 1983):
The method described above was applied to southern Tunisia basin. Most of the watershed is composed of plains, with altitudes varying between 4 and 600 m. The average altitude is 200 m and rarely exceeds 300 m. Southern Tunisia basin is characterized by a stretched form and a poorly developed stream network (Fig. 1). The climate is characterized by mild rainy winters and hot dry summers. The dry and wet periods are more or less clearly distinguishable all over southern Tunisia. This division, however, seems to become less clear with increasing distance from the Mediterranean coast and decreasing latitude (Branigan and Jarrett, 1969). The rainy season starts in September and ends in May. The main annual rain volume, however, falls between October and January. The rains falling in other months during the rainy season are more erratic and occur with less probability. The relative weakness of rains, as well as their irregularity are accentuated by an evaporation attributed to strong temperatures and dry and often violent winds. The North eastern air masses generate stormy rains while the contribution of the Saharan air masses to the seasonal rains remains typical of the spring. They provoke on the coastline generally insignificant rains. These disruptions are bound to the Saharan front, which separates a mass of hot air of tropical origin from a mass of cold air of continental or maritime origin. In summer, the driest season, the region is subjected to the continental air flux coming from the south and the southwest. The region is also subjected to marine influences as it is bordered by the Mediterranean Sea in the east. Rainfall data of twelve stations were used to evaluate rainfall variability in arid zones throughout southern Tunisia (Table 1). These stations were selected because they are evenly spread throughout the study region and they have continuous rainfall records extending over a period of 70 years. The data set which include annual and monthly rainfall, were obtained from the publications of the Tunisian Ministry of Agriculture and Water Resources. The rainfall data series need to be independent, random, homogeneous, and without trends. These characteristics were verified by four nonparametric tests using the Consolidated Frequency Analysis (CFA) package of Environment Canada (Pilon and Harvey, 1994). All data sets passed the four nonparametric
Q LTð jÞ =
n X
2
ri ð jÞ
ð1Þ
i=1
Where: QLT (j) is the representation quality of the parameter j (‰); ri is the correlation coefficient between the parameter j and the factorial axis and n is the number of considered factorial axes. Multiple regressions were also used to select parameters that significantly affect the variability of rainfall distribution and analyze the relationships between the identified variables. Relative contributions of each independent variable to Table 1 Characteristics of the rainfall stations and their corresponding time series.
Station number Station name Latitude Longitude Altitude (m) Min. rainfall (mm) Mean rainfall (mm) Max. rainfall (mm) SD
CV
CS
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12
0.52 0.41 0.52 0.41 0.57 0.48 0.60 0.56 0.47 0.58 0.55 0.63
1.26 4.56 0.21 2.35 2.29 10.70 0.57 3.62 1.68 7.84 0.45 3.21 1.23 4.31 1.37 5.21 1.67 7.74 1.83 7.37 1.39 4.77 2.07 8.18
Gabes Metlaoui Mednine Gafsa Tataouine Tozeur Matmata Zarzis Redeyef Maknassy B. Guerdane Remeda
37.65 38.13 37.04 38.25 36.58 37.69 37.27 37.22 38.21 38.42 36.82 35.90
8.62 6.70 9.07 7.18 9.02 6.46 8.50 9.75 6.46 8.04 9.87 8.97
4 202 125 300 240 45 441 11 586 278 12 300
39.3 12.1 36.4 36.1 25.7 15.8 29.3 28.7 49.9 41.3 44.8 8.4
189 124 152 161 127 98 215 217 138 199 181 87
534 262 550 390 484 259 692 684 434 689 520 323
98.9 50.9 79.6 65.8 71.6 46.9 129 120 65.5 115 99.6 55
Ck
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
tests at the 1% level of significance. The mean annual precipitation is 158 mm, ranging between more than 200 mm, recorded in the coastal sector (station 6) and less than 90 mm, recorded in the north west. These averages are subject to very wide annual fluctuations (1 to 12). 4. Results and discussion Statistics of annual rainfall data such as the coefficient of variation (CV), coefficient of skewness (CS) and coefficient of kurtosis (Ck) are presented in Table 1. The mean values of CV, CS and Ck for the study region are 53%, 1.34 and 5.82, respectively. CV values are generally higher than 50%, except for stations 6, 4, 2 and 9 (Tozeur, Gafsa, Metlaoui and Redeyef respectively) which are located in the northwest of the study area. The highest values of the coefficient of kurtosis were found for Mednine and Remeda (stations 3 and 12 respectively). All the stations showed a high degree of peakedness which is quite different from that of a normal distribution. CV values decline from the south-east to the north-west, with a maximum value of 0.63 in the Remeda station. In general, CV slightly decreases, CS remains constant and Ck slightly increases with an increase in annual rainfall (Modarres and Rodrigues da Silva, 2007). There was a mixture of increase and decrease of rainfall trends widespread throughout the study area. This result suggests that the rainfall trends may be attributed to local changes in the rainfall regime rather than the large-scale patterns of atmospheric circulation. To refine the preliminary analysis and identify the principal factors affecting rainfall characteristics and the principal sources of its variation, a multivariable analysis of data was performed using the STATITCF statistical software
835
package (1987). Statistical analysis especially included PCA, representation quality and multiple regression related to monthly and annual rainfall. A total of 8 variables were considered, namely annual rainfall (P), latitude (LAT), longitude (LON), altitude (ALT), and the seasonal rainfall for the winter, autumn, spring and summer seasons (WIN, AUT, SPR and SUM respectively).
4.1. Monthly rainfall The Principal Component Analysis (PCA) applied to all data (monthly rainfall) resulted essentially in three principal components. A varimax rotation with Kaiser normalization was used for all 70 years data sets of the twelve stations. The threshold of significance considered for p b 0.05 is equal to 0.23 after a test of Student (n = 70). The significant correlations between selected parameters (variables) and these components represent approximately 68% of the total variance. The first, second and third PCs explained 29%, 26% and 13% of the total variance respectively. The projection, over the (1 × 2) factorial plane (presenting 56% of inertia), of all selected variables and individuals shows three distinct data groups (Fig. 2): - Group 1, represented positively along axis 1, is composed of rainfall and seasonal downpours of winter, autumn and spring. These variables are highly inter-correlated. - Group 2, represented positively along axis 2, is formed by the variables latitude, altitude and summer rainfall. - Group 3, represented positively and negatively along axis 2 and 1 respectively, is characterized by the longitude.
Fig. 2. Projection of individuals in the (1 × 2) factorial plane (monthly rainfall).
836
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
Table 2 Representation qualities (QLT) of the selected parameters with respect to the first two principal axes (monthly rainfall). Parameter
Latitude Longitude Altitude Fall rainfall Winter rainfall Spring rainfall Summer rainfall
Factor 1
Factor 2
Factorial plane (1 × 2)
r21
r22
QLT⁎
1.8 148.6 49.7 405.5 488 304.9 7.7
682 652 316.1 0.1 7.6 76.8 348.2
683.8 800.6 365.8 405.6 495.6 381.7 355.9
⁎The threshold of significance = 400 for p b 0.05 and n = 790.
These distinct groups clearly show that rainfall distribution is more related to longitude and seasonality than altitude and latitude. This could be explained by the irregularity of
rainfall and the climate changes from a season to another. In fact, the region receives a small amount of rainfall, which largely varies in time and space compared to northern and coastal regions (Branigan and Jarrett, 1969). On the other hand, southern Tunisia is mainly a plane region, where rainfall variability is more governed by the Mediterranean Sea proximity. Rainfall increases continuously from the west (continent) to the east (coast line), implying an important effect of longitude. In order to better examine the effect of the load of each parameter, the quality of representation (over the 1 × 2 factorial plane) of the selected parameters was checked (Table 2). This exercise showed that the latitude and longitude are associated with the best quality of representation (683.8 and 800.6 respectively). Furthermore, they represent the most predominant and significant variables. Moreover, fall and winter rainfall,
Fig. 3. Maps of distribution of loadings of the three dominant PC modes (annual rainfall).
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
with representation quality values greater than 400, can be considered as significant variables. Monthly rainfall data was correlated with all independent variables. A multiple regression method was used to evaluate the effect of the aforementioned parameters on rainfall in all selected stations. The rainfall frequency variability DP is given by: ΔP = 0:0001 LAT − 0:0001 LON + AUT + WIN + SPR + SUM − 0:0023
ð2Þ
The obtained regression model suggests, by the coefficient of determination (R2 = 0.99), that the rainfall frequency variation is dependent on the majority of the selected parameters. The contribution's rates of latitude and longitude are insignificant (1% of the variance). These two parameters are disregarded and the model is modified: ΔP = AUT + WIN + SPR + SUM
ð3Þ
The percentage of variance in precipitation change may be explained by 36% of the fall rainfall AUT, followed very closely by that of winter WIN (33%). The spring rainfall SPR provided 27% of the variance of monthly rainfall, while summer rain (SUM) contributed only by 3% to the total variation. Therefore, monthly rainfall frequency variation in southern Tunisia is based on seasonality and climate changes, while spatial influence is insignificant. An analysis of rain seasonal distributions carried out in the study zone showed frequent downpours during the fall and winter seasons and scarce light rainfall events in the rest of the year (Abou-Hadid, 2006). The author also proved that the dry period extends from April to
837
August, with an important inter and intra-annual variability of rainfall. 4.2. Annual rainfall This analysis seeks to identify the dominant independent components of seasonal rainfall data from a number of point locations spread over Southern Tunisia, with the presumption that these PCs will be related to the two main sources of rainfall variability. However, with a large number of observations (790, considering temporal and spatial variation of rainfall), no relationship between any of the stations was found. The PCA exercise is repeated based on the annual values of the same eight variables (P, LAT, ALT, LON, WIN, AUT, SPR, and SUM) for the twelve selected stations. The contributions of the first, second and third PCs to the total variance are 68%, 14% and 8%, respectively. The individual contributions to the total variation from the fourth component are relatively low, and the corresponding eigenvalue decreases from 7 to nearly 0 between the third and fourth PCs. Therefore, we consider the first three PCs to describe the major patterns of the geographical variability in the mean annual rainfall data series and explain the corresponding temporal aspects of this variability. The first three PCs contributed 90% to the total variance and the corresponding eigenvalue is greater than 1.5. The correlation matrix was computed to identify the variables that contribute significantly to the variance of the selected PCs (Fig. 3). The threshold of significance considered for p b 0.05 is equal to 0.55 after a test of Student (n = 12). The first PC reveals a pattern showing significantly positive
Fig. 4. Delineation of statistical regions based on the projection of annual individuals in the (1 × 2) factorial plane.
838
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839
loadings of the annual rainfall for the south eastern and north eastern parts of the study area (Fig. 3). The second PC yields significantly positive loadings over most of the northern zone, while the south eastern region is less important in comparison to the first principal component. The third PC reveals an interesting pattern with significant loadings in a south direction along the study area. Thus, the variability of annual rainfall is usually significant along the southeastern coastal part as indicated by the dominantly positive loadings of the three PCs over that area compared to other areas. The projection, over the (1 × 2) factorial plane of all annual selected variables and individuals, leads to the division of the study area into four sub-regions (Fig. 4). These sub-regions are delineated by regrouping stations, statistically correlated on the factorial plane (1 × 2). Regions R I and R II reflect the influence of topography. In fact, they are characterized by relatively high altitudes, ranging between 125 and 300 m. Compared to the three remaining zones rainfall variation is more important for region R III. It is important to note at this stage that, this delineation confirms the above results showing that rainfall variation in southern Tunisia is based on topography and seasonal characteristics. Moreover, this delineation proves the importance of rainfall variation over the coastline (R III), confirmed by the positive loadings (Fig 3). 5. Conclusion This study investigated rainfall variability in southern Tunisia by analyzing monthly and annual rainfall data recorded in twelve stations. The PCA analysis, using a varimax rotation with Kaiser normalization, was applied to monthly series data and resulted essentially in three principal components, describing approximately 68% of the total variance. Three distinct groups were identified, showing that rainfall distribution was more related to longitude and seasonality than altitude and latitude. This result was confirmed by the regression model, which revealed that monthly rainfall is based on seasonality and climate changes. As for annual rainfall, the first three principal components (PCs) contributed 90% to the total variance and the corresponding eigenvalue exceeds 1.5. The positive loadings of these PCs over the southeastern coastal area indicated that the annual rainfall variability is significant. The study area was divided into four sub-regions based on the projection over the factorial plane. The obtained delineation confirmed the influence of topography and seasonality on rainfall distribution in southern Tunisia. 6. List of symbols ALT AO AUT Ck CS Cv EOF IOD IOP LAT LON
altitude Artic oscillation autumn rainfall coefficient of kurtosis coefficient of skewness coefficient of variation empirical orthogonal function Indian Ocean dipole interdecadal pacific oscillation latitude longitude
P PCA PCs QLT SD SPR SUM WIN DP
rainfall depth principal component analysis principal components representation quality standard deviation spring rainfall summer rainfall winter rainfall rainfall variability
Acknowledgments Data used in this study were provided by the Tunisian Ministry of Agriculture and Water Resources. The collaboration of Mr. Saadaoui of the Water Resources Division and Mr. Ben Younes, engineer in the Tunisian Institute of Research (INRAT) are gratefully acknowledged. References Abou-Hadid, A.F., 2006. Assessment of impacts, adaptation, and vulnerability to climate change in North Africa: food production and water resources. A Final Report Submitted to Assessments of Impacts and Adaptations to Climate Change (AIACC), Project No. AF 90. The International START Secretariat 2000 Florida Avenue, NW Washington, DC 20009 USA. Basalirwa, C.P.K., et al., 1995. The climatological zones of Tanzania based on rainfall characteristics. Water Resources Engineering Research Report, University of Dar-es-Salaam. Berndtsson, R., 1987. Spatial and temporal variability of rainfall and potential evaporation in Tunisia. The Influence of Climate Change and Climatic Variability on the Hydrologie Regime and Water Resources (Proceedings of the Vancouver Symposium, August 1987). IAHS Publ. no. 168. Bordi, I., Fraedrich, K., Jiang, J.M., Sutera, A., 2004. Spatio-temporal variability of dry and wet period in eastern China. Theoretical and Applied Climatology 79 (1–2), 81–91. Branigan, J.J., Jarrett, H.R., 1969. The Mediterranean Lands. Macdonald and Evans, London. Castell, R.B., 1966. The Scree test for the number of factors. Multivariate Behavioral Research 1, 245–276. Chambers, L.E., 2003. South Australian rainfall variability and trends. BMRC RESEARCH REPORT NO. 92, Commonwealth of Australia, Published by the Bureau of Meteorology. Compagnucci, Rose H., Araneo, Diego, Canziani, Pablo, O., 2001. Principal sequence pattern analysis: a new approach to classifying the evolution of atmospheric system. International Journal of Climatology 21 (2), 197–217. Dutot, A.L., Elichegaray, C., Vie le sage, R., 1983. Application de L'analyse des correspondences à l'étude de la composition physico-chimique de l'aérosol urbain. Atmospheric Environment 17 (1), 73–78. Guenni, L., Hutchinson, M.F., 1998. Spatial interpolation of the parameters of a rainfall model from ground based data. Journal of Hydrology 212–213, 335–347. Kipkorior, E.C., 2002. Analysis of rainfall climate on the Njemps Flats, Baringo District, Kenya. Journal of Arid Environments 50, 445–458. Lana, X., Martinez, M.D., Serra, C., Burgueno, 2004. Spatial and temporal variability of the daily rainfall regime in Catalonia (northeastern Spain), 1950–2000. International Journal of Climatology 24 (5), 613–641. Modarres, Reza, Rodrigues da Silva, V.P., 2007. Rainfall trends in arid and semi-arid regions of Iran. Journal of Arid Environments 70, 344–355. Mohapatra, M., Mohanty, U.C., Behera, S., 2003. Spatial variability of daily rainfall over Orissa, India, during the southwest summer monsoon season. International Journal of Climatology 23 (15), 1867–1887. Ogallo, L.A., 1988. The spatial and temporal clusters of the East African Seasonal Rainfall anomalies derived from Principal component analysis. Journal of Climatology 6, 1–23. Ogallo, L.A., 1989. The spatial and temporal patterns of East African Seasonal Rainfall derived from Principal component analysis. Journal of Climatology 9, 145–167. Penarrocha, D., Estrela, M.J., Mullon, M., 2002. Classification of daily rainfall patterns in a Mediterranean area with extreme intensity levels: the Valencia region. International Journal of Climatology 22 (6), 677–695. Pilon, P.J., Harvey, K.D., 1994. Consolidated Frequency Analysis Package. Environment Canada, Ottawa, Qntario, Canada.
M. Ellouze et al. / Atmospheric Research 93 (2009) 832–839 Saji, N.H., Goswami, B.N., Vinayachandran, P.N., Yamagata, T., 1999. A dipole mode in the tropical Indian Ocean. Nature 401, 360–363. Singh, C.V., 2006. Pattern characteristics of Indian monsoon rainfall using principal component analysis (PCA). Elsevier Atmospheric Research 79, 317–326. STATITCF package, 1987. Services des Etudes statistiques de l'I.T.C.F. Thompson, D.W.J., Wallace, J.M., 1998. The arctic oscillation signature in the wintertime geopotential height and temperature fields. Geophysical Research Letters 25, 1297–1300. Tosic, I., 2004. Spatial and temporal variability of winter and summer precipitation over Serbia and Montenegra. Theoretical and Applied Climatology 77 (1–2), 47–56.
839
Webster, P.J., Magana, V.O., Palmer, T.N., Shukla, J., Tomas, R.A., Yanai, M., Yasunari, T., 1998. Monsoon: process, predictability and the prospectus for prediction. Journal of Geophysical Research 103 (C7), 14451–14510. Wilks, D.S., 1995. Statistical Methods in Atmospheric Sciences. Academic Press, San Diego. Zhang, Y., Wallace, J.M., Battisti, D.S., 1997. ENSOlike interdecadal variability: 1900–93. Journal of Climate 10 (5), 1004–1020.