256 JOURNAL OF APPLIED METEOROLOGY VOLUME 44 Wavelet Analysis of Variability, Teleconnectivity, and Predictability of the September–November East African Rainfall DAVISON MWALE AND THIAN YEW GAN Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada (Manuscript received 2 October 2003, in final form 10 July 2004) ABSTRACT By applying wavelet analysis and wavelet principal component analysis (WPCA) to individual wavelet- scale power and scale-averaged wavelet power, homogeneous zones of rainfall variability and predictability were objectively identified for September–November (SON) rainfall in East Africa (EA). Teleconnections between the SON rainfall and the Indian Ocean and South Atlantic Ocean sea surface temperatures (SST) were also established for the period 1950–97. Excluding the Great Rift Valley, located along the western boundaries of Tanzania and Uganda, and Mount Kilimanjaro in northeastern Tanzania, EA was found to exhibit a single leading mode of spatial and temporal variability. WPCA revealed that EA suffered a consistent decrease in the SON rainfall from 1962 to 1997, resulting in 12 droughts between 1965 and 1997. Using SST predictors identified in the April–June season from the Indian and South Atlantic Oceans, the prediction skill achieved for the SON (one-season lead time) season by the nonlinear model known as artificial neural network calibrated by a genetic algorithm (ANN-GA) was high [Pearson correlation ␳ ranged between 0.65 and 0.9, Hansen–Kuipers (HK) scores ranged between 0.2 and 0.8, and root-mean- square errors (rmse) ranged between 0.4 and 0.75 of the standardized precipitation], but that achieved by the linear canonical correlation analysis model was relatively modest (␳ between 0.25 and 0.55, HK score between Ϫ0.05 and 0.3, and rmse between 0.4 and 1.2 of the standardized precipitation). 1. Introduction ability than the MAM rainfall, with one flood in 1961 and another in 1997 (Philippon et al. 2002) and 12 East Africa (EA), which consists of Kenya, Uganda, droughts between 1965 and 1997 (Ntale 2001), whereas and Tanzania (Fig. 1), has two main rainy seasons: Sep- there was only one recorded failure in the MAM rain- tember–November (SON) and March–May (MAM). fall, which occurred in 1984 (Ntale 2001). Several investigators have studied the spatial and tem- Even though the spatial variability and temporal poral characteristics of EA seasonal rainfall and its as- variability of the SON rainfall have been documented sociations with sea surface temperature (SST) varia- and linked to external forcings such as SST and sea tions in the surrounding oceans (e.g., Ogallo 1989; level pressure, it is still a challenge to try to predict the Basalirwa 1995; Mutai et al. 1998; Basalirwa et al. 1999; SON rainfall accurately (e.g., Ntale et al. 2003). The Ntale et al. 2003). There is a general consensus that the deficiency in prediction skill has been observed in other spatial and temporal variabilities of EA rainfall are parts of the world, especially in the last two decades complex, and, as such, EA has previously been divided (Hastenrath 1995; Webster et al. 2002; Zebiak 2003) into 6–26 homogenous zones of rainfall variability (e.g., and has been attributed to nonstationarity in climate Ogallo 1989; Ntale 2001). The spatial inhomogeneities (Landman et al. 2001), nonlinearity in the interaction of of rainfall variability are attributed to the complex to- climate elements (Barnston et al. 1994), failure to iden- pography, the effects of inland lakes, the seasonal mi- tify robust predictor data (Singh et al. 1995), and the gration of the intertropical convergence zone (ITCZ), inadequacy of prediction models (Webster et al. 2002). and the influence of Indian Ocean SST variations The frequent drought episodes in the latter half of (Ntale 2001). In the last four decades, it has been found the twentieth century and two floods (in 1961 and 1997) that the SON rainfall exhibited greater temporal vari- are good examples of the nonstationary character of the SON rainfall of EA. In addition, previous work by Potts (1971), Rodhe and Virji (1976), and Ropelewski and Corresponding author address: Dr. Thian Yew Gan, Dept. of Halpert (1987) found oscillatory peaks in EA rainfall of Civil and Environmental Engineering, 220 Civil Electrical Engi- neering Bldg., University of Alberta, Edmonton, AB T6B 2G7, 2–8 yr. Because of nonstationarity, the temporal reso- Canada. lution of these oscillations is unknown. Therefore, to E-mail:[email protected] investigate the SON rainfall variability and its relation- © 2005 American Meteorological Society Unauthenticated | Downloaded 09/23/21 07:45 PM UTC FEBRUARY 2005 MWALE AND GAN 257 explore teleconnectivity between rainfall fields in EA and SST in the Indian and South Atlantic Oceans, 3) and, on the basis of SST predictor fields identified from objective 2, to use a linear statistical model (CCA) and a nonlinear model [artificial neural net- work calibrated by a genetic algorithm (ANN-GA)] to predict SON rainfall of EA at one-season lead time. The rest of the paper is organized as follows: Section 2 presents the data and methods used in the analysis. The dominant modes and variability of the SON rain- fall are identified and analyzed in section 3. Relation- ships between EA rainfall variability and the Indian and South Atlantic Ocean SST variability are identified and discussed in section 4. The models used to predict the SON rainfall are presented in section 5. The SON rainfall season is predicted in section 6 using SST data selected from the Indian and Atlantic Oceans. The summary, conclusions, and future work are presented in section 7. 2. Data and methods a. Data FIG. 1. Map showing the study location, East Africa (Uganda, Monthly rainfall data (1950–97) from 21 grid loca- Kenya, and Tanzania), and the Indian and Atlantic Oceans. tions at a resolution of 2.5° ϫ 3.75° latitude–longitude were extracted for EA over 2°N–12°S and 30°–43°E (Fig. 1). The rainfall data are part of a monthly precipi- ship to other climatic elements such as SST, it has be- tation dataset for land areas worldwide from 1900 to come imperative to analyze the events irregularly dis- 1998 provided by the Met Office (UKMO). These data tributed in time that depict nonstationary power. This were constructed from station datasets averaged onto paper attempts to solve the problem of nonstationarity 2.5° ϫ 3.75° grids using Thiessen polygon weights. The by using wavelet analysis and wavelet-based empirical quality control of the data is described in Hulme (1994). orthogonal function analysis (WEOF), also known in Monthly SST anomaly grid data at 5° ϫ 5° latitude– this paper as wavelet principal component analysis longitude resolution were extracted from the Indian (WPCA). Furthermore, because the relationship be- Ocean (20°N–40°S, 40°–105°E; Fig. 1). The SST tween rainfall and SST is nonlinear (e.g., Landman and datasets were 48 yr long (1950–97) and were trans- Mason 1999), this study also proposes to teleconnect formed into seasonal and annual data by computing the SON rainfall to SST using a nonlinear prediction 3-month averages [January–March (JFM), April–June model, the artificial neural network (ANN). The results (AMJ), July–September (JAS), and October–Decem- from the nonlinear prediction model are compared with ber (OND)] and 12-month averages, respectively. The the linear canonical correlation analysis (CCA) model. SST dataset is part of the UKMO historical SST6 data Efforts to improve climate prediction will have eco- (MOHSST6), a historical global dataset of mean nomic significance, because agriculture (both rain fed monthly global SST anomalies with respect to the 1961– and irrigated) and water resources are inextricably 90 normals. linked to the timing and amount of rainfall. Because there is a clear need to explore longer lead times for b. Methods predicting seasonal rainfall in EA and to continuously monitor prediction relationships, the objectives of this 1) WAVELET ANALYSIS study are as follows: The wavelet transform of a real signal X(t) with re- ⌿ 1) to identify and analyze the spatial, temporal, and spect to a mother wavelet is a convolution integral frequency variability of the dominant oscillations of given as the rainfall fields of EA using wavelet analysis and 1 T t Ϫ b WEOF, W͑b, a͒ ϭ ͵ X͑t͒⌿*ͩ ͪ dt, ͑1͒ 2) to use the information obtained from objective 1 to ͌a 0 a Unauthenticated | Downloaded 09/23/21 07:45 PM UTC 258 JOURNAL OF APPLIED METEOROLOGY VOLUME 44 where ⌿* is the complex conjugate of ⌿, t is time, T is distinguish EOF of raw data from EOF performed on the total length of the time series, and W(b, a)isa the wavelet spectra SAWP, the latter is called wavelet wavelet spectrum, a matrix of energy coefficients of the empirical orthogonal function analysis or wavelet prin- decomposed time series at each scale a and time b. The cipal components analysis and their corresponding PCs magnitude of the wavelet spectrum coefficients shows are referred to as wavelet principal components how well the wavelet matches with the time series. At (WPCs). The WPCs obtained from SAWP are inter- each scale, the wavelet spectrum coefficients also depict preted as frequency-compacted energy variability, and the amplitude of a time series. In a rainfall or SST time they also indicate the magnitude of events of time series series, power at each scale will therefore be a good averaged from various scales. measure of the magnitude of the rainfall or SST anoma- An important decision in EOF is to select an appro- lies. In addition to power at individual scales, power priate number of PCs that most strongly capture the over a range of scales [the scale-averaged wavelet joint variability of the original data, without discarding power (SAWP), which represents the mean variance of important information carried in the original data.