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- 3. Frequency Domain Multi Taper Method-Singular Value Decomposition (MTM-SVD) Approach
| Joint Spatio-Temporal Variability of Global Sea-Surface Temperatures and Global Palmer Drought Severity Index Values
Somkiat Apipattanavis Office of Research and Development, Royal Irrigation Department, Nonthaburi, Thailand Gregory J. McCabe U.S. Geological Survey, Denver, Colorado, United States Balaji Rajagopalan Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado, United States Co-operative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, United States Subhrendu Gangopadhyay Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado, United States Co-operative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, United States AMEC Earth and Environmental, Boulder, Colorado, United States Corresponding author: Gregory J. McCabe U.S. Geological Survey Denver Federal Center MS 412 Denver, Colorado 80225 phone: 303-236-7278 fax: 303-236-5034 email: gmccabe@usgs.gov
Gregory J. McCabe U.S. Geological Survey, Denver, Colorado, United States Balaji Rajagopalan Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado, United States Co-operative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, United States Subhrendu Gangopadhyay Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado, United States Co-operative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, United States AMEC Earth and Environmental, Boulder, Colorado, United States Abstract
Dominant modes of individual and joint variability in global sea-surface temperatures (SST) and global Palmer Drought Severity Index (PDSI) values for the 20th century are identified through a multivariate frequency domain singular value decomposition. This analysis indicates that a secular trend and variability related to the El Nino Southern Oscillation (ENSO) are the dominant modes of variance shared among the global data sets. An additional significant frequency, multidecadal variability, is identified for the Northern Hemisphere. This multidecadal frequency appears to be related to the Atlantic Multidecadal Oscillation (AMO). These few frequencies explain both the spatial and temporal variability of global SSTs and PDSI values. 1. Introduction A number of changes in the global climate system have been attributed to increasing global temperatures resulting from anthropogenically supplied greenhouse gases (IPCC, 2007). To appropriately attribute climate changes to global warming it is necessary to understand the primary modes of global climate variability and to separate climate trends from natural climate variability (Ghil and Vautard, 1991; Mann and Park, 1996). Dai et al. (1997) examined the variability of global precipitation using a dataset of gridded (2.5 degree by 2.5 degree) monthly precipitation for the period 1900-1988. In their study, the first empirical orthogonal function (EOF) of the precipitation data indicated an El Nino/Southern Oscillation (ENSO) - related pattern and the second EOF reflected a linear trend in global precipitation. The trends in precipitation were primarily increases in North America, mid- to high-latitude Eurasia, Argentina, and Australia. Dai et al. (1997) reported that this pattern of trends in precipitation was consistent with precipitation changes projected by general circulation model (GCM) experiments of future climate changes in response to increasing atmospheric concentrations of carbon dioxide. In another study, Dai et al. (2004) examined the variability of global annual Palmer Drought Severity Index (PDSI) values using principal components analysis. Similar to the study of global precipitation, Dai et al (2004) reported that the first two principal components of global annual PDSI are related to long-term trends and the ENSO. However, for the analysis of the PDSI data, the first principal component reflected long-term trends in PDSI and the second component reflected ENSO variability. Long-term trends in PDSI represented more of the variability in the PDSI data than in precipitation data likely because PDSI values also include the effects of long-term trends in temperature. McCabe and Palecki (2006) used principal components analysis and singular value decomposition (SVD) to examine primary modes of global PDSI and sea-surface temperature (SST) variability on decadal to multidecadal (D2M) time scales. Results indicated two principal modes of D2M variability. The first mode of D2M variability is related to the Pacific Decadal Oscillation (PDO), Indian Ocean SSTs, and an index of ENSO, while the second mode is related to the Atlantic Multidecadal Oscillation (AMO).
In a number of studies, variability in global sea-surface temperatures (SSTs) have been shown to be a significant driving force of hydro-climate variability (Fontaine and Janicot, 1996; Enfield and Alfaro, 1999; Rodwell et al., 1999; Enfield et al., 2001; Nicholson et al., 2001; Giannini et al., 2003; Gray et al., 2003; Sutton and Hodson, 2003; Hidalgo, 2004; McCabe et al., 2004; Shabbar and Skinner; 2004; Schubert et al., 2004; Seager et al., 2005; Sutton and Hodson, 2005; McCabe and Palecki, 2006). These studies have shown the large influence of tropical Pacific Ocean SSTs (i.e. El Nino and La Nina events) on hydro-climate across the globe. More recently, several of these studies have shown substantial associations between North Atlantic SSTs and global hydro-climate, particularly on D2M time scales (McCabe and Palecki, 2006; Dong et al., 2006; Dima and Lohman, 2007). In this study we examine the joint spatio-temporal variability between global annual PDSI values and global annual sea-surface temperatures (SSTs). The PDSI data were chosen to represent land-based climate variability and SSTs were chosen to represent the large-scale climate variability forcing at interannual and interdecadal time scales. We use a nonparametric spectral domain technique called the Multi Taper Method – Singular Value Decomposition (MTM-SVD) on this joint data set (Mann and Park, 1996). This method aims to identify dominant modes (i.e., frequencies) of variability that are jointly shared by the two fields and subsequently, spatial and temporal patterns of these identified frequencies are reconstructed. This method is data driven and is unaffected by trends and other aliasing problems that commonly constrain the traditional time and frequency domain techniques. The dominant patterns will provide increased understanding of the low-frequency modes of variability, in particular, of the land-surface conditions that are important for long-term drought monitoring and mitigation efforts. A brief description of the data is provided, followed by the description of the MTM-SVD methodology. The identified space-time modes of variability will be described and discussed in the results section. 2. DataThe Palmer Drought Severity Index (PDSI) is a well known representation of meteorological drought, including the simultaneous and lagged effects of both precipitation and air temperature anomalies on a simplified representation of soil moisture content (Palmer, 1965). Although there are known short comings inherent in the PDSI (Alley, 1984), it has simple data requirements compared to more complex soil-moisture models. PDSI is also widely used by the water-resources engineering and science community as an important practical indicator of basin soil moisture state (e.g., dry, normal, wet, etc.). Dai et al. (2004) have developed a data set of gridded 2.5o x 2.5o (2.5 degrees of latitude by 2.5 degrees of longitude) monthly PDSI values for the global land surface for the period 1870 through 2003. The needed precipitation data follows from the work of Chen et al. (2002) for the 1948-2003 period and Dai et al. (1997) for the 1870-1947 period. An adjustment was made to place the two data sets on a compatible scale. Dai et al. (2004) applied step-change homogenization corrections to a small percentage of the original precipitation time series prior to gridding the data. The required temperature data were gridded by Jones and Moberg (2003) at a coarser 5o x 5o resolution, and the station temperature time series used were subjected to a variety of homogenization techniques by their sources. The monthly PDSI data were averaged to compute annual PDSI values. For grid cells with missing monthly data within a year, the annual value was not computed and designated as missing. Only 2.5-degree by 2.5-degree grid cells with complete annual data for the 1925 through 2003 period (1341 grid cells, Figure 1a) were used for the analysis in this paper. The time period chosen provided a reasonable compromise between length of record and completeness of spatial coverage. Sea surface temperature (SST) variability is strongly related to global climate variability (Diaz and Markgraf, 2000; Mantua and Hare, 2002; Hoerling and Kumar, 2003; McCabe et al., 2004). Previous research indicates that SSTs over large areas vary simultaneously under preferred spatial modes and time scales (Kawamura, 1994; Enfield and Mestas-Nuñez, 1999; Mestas-Nuñez and Enfield, 1999). In some of these studies, global-scale signals were removed prior to variability analysis, including trends and ENSO signals. For the analysis in this paper, 5º x 5º resolution grid cell SST data with complete annual records for 1925-2003 (1207 cells, Figure 1b) were extracted from the Kaplan extended SST data set of monthly SSTs (Kaplan et al., 1998). The annual values were computed as 12-month averages of the monthly SSTs. 3. Frequency Domain Multi Taper Method-Singular Value Decomposition (MTM-SVD) ApproachRobust diagnosis of the key low-frequency modes of large-scale climate entails capturing the coherent space-time variations across multiple climate state variables. Traditional time-domain decomposition approaches for univariate and multivariate data provide useful details on the broad-scale patterns of variability. However, these approaches lack the ability to isolate narrow-band frequency domain structure (Mann and Park, 1994; 1996). Detailed methodology development and examples of the MTM-SVD methodology can be found in Thomson (1982); Mann and Park (1994, 1996); Lees and Park (1995). Here, we describe the MTM-SVD methodology for decomposing the individual and joint global SST and PDSI data sets into few frequencies to identify the significant modes of variability. The method relies on the assumption that climate modes are narrow band and evolve in a noise background that varies smoothly across the frequencies. Subsequently, spectral domain equivalents of each grid point are computed based on the multi-taper spectral analysis (Thomson, 1982; Park et al., 1987). The output of the discrete Fourier transform of an N-point data series  at grid location m is the complex-valued eigen-spectrum at discrete frequency f,  , as
 (1)
where t is the sampling interval (1 year in this application), with  being the kth member of the orthogonal sequence of p-prolate Slepian tapers (Lees and Park, 1995), k = 1,…, K, K is a small subset of orthogonal Slepian tapers ; m = 1,…, M are the number of time series used for the analysis, and N is the length of each time series. Lees and Park (1995) provides an excellent description and necessary computer codes for estimating the p-prolate Slepian tapers. In the p-prolate Slepian tapers p is the “time-bandwidth” product and it scales the spectral information in a frequency band of half-bandwidth  , where fR = 1/(Nt) is the Rayleigh frequency. Also, because the Slepian tapers are derived using eigen decomposition, the usual question of how many eigen vectors/tapers (i.e. the choice of K) to retain to explain a large fraction of the total variance remains. The level of compromise between the variance and frequency resolution of the Fourier transform depends on the choice of K. Mann and Park (1994) suggest p = 2 and K = 3 as a reasonable compromise between frequency resolution and also providing sufficient degrees of freedom for signal-noise decomposition. For each frequency point to be resolved by this analysis, a M K matrix Directory: ~balajir ~balajir -> Atlantic basin tropical cyclones: risk assessment using climate indicators Download 6.42 Mb. Share with your friends:
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