ISSN 0001-4338, Izvestiya, Atmospheric and Oceanic Physics, 2016, Vol. 52, No. 5, pp. 550–559. © Pleiades Publishing, Ltd., 2016. Original Russian Text © V.I. Kuzin, A.S. Lobanov, 2016, published in Izvestiya Rossiiskoi Akademii Nauk, Fizika Atmosfery i Okeana, 2016, Vol. 52, No. 5, pp. 618–627.
Analysis of Variations in the Surface Temperature of Tropical and Northern Pacific Ocean V. I. Kuzin* and A. S. Lobanov Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 6, Novosibirsk, 630090 Russia *e-mail:
[email protected] Received October 29, 2015; in final form, January 11, 2016
Abstract⎯Studies on the analysis of the Pacific Ocean surface temperature are presented based on the data of the NCEP/NCAR reanalysis. Two methods are used in the work. The first is a classical analysis of the empirical orthogonal functions (EOFs) that makes it possible to identify the El Niño and La Niña phenomena in tropics. In this case, the anomalies of the ocean surface temperature (OST) are reconstructed during these events with quite high accuracy when using several first EOFs. In contrast, at the time between these events, more harmonics are required for the reconstruction. The OST variability in the middle and high latitudes cannot be identified highly accurately based on this approach, since it is considerably weaker than a strong signal in tropics. This signal was detected by the method of cluster analysis. The results show that, in addition to the signal in tropics, there are well-pronounced quasi-decadal signals between the eastern and western Pacific, as well as in the region of the Kuroshio continuation and in the subpolar gyre that can be identified with Pacific decadal oscillations (PDOs). Keywords: Pacific Ocean, variability of temperature, sea surface, empirical orthogonal functions, cluster analysis DOI: 10.1134/S0001433816050091
INTRODUCTION The Pacific Ocean is a source of climate variability that has a large impact on atmospheric processes on the Earth. The El Niño–Southern Oscillation (ENSO), the strongest signal, is the interannual variability of the ocean surface temperature (OST) in the tropical Pacific Ocean, which affects the climate not only on the regional but also on the global level [1, 2]. At the same time, in the tropical, medium, and high latitudes, there is a quasi-decadal signal, the so-called Pacific decadal oscillations (PDOs), which exerts an influence on the atmospheric processes over the Pacific Ocean and North America [3–9]. The physical mechanisms that control these processes were analyzed based on numerical modeling. These studies are described in [5, 10] and others. The line of research on numerical modeling of the ocean dynamics was established and developed by А.S. Sarkisyan in [11, 12]. It is also of interest to continue the detailed analysis of the variability of the Pacific Ocean surface temperature (OST) by the methods of statistical processing. For the World Ocean these studies were conducted earlier in [2, 7–9, 13]. Our work continues them. We used two methods for the analysis. The first one is a classical EOF analysis to identify the El Niño and La Niña phenomena in tropics. However, the OST variability
in the middle and high latitudes cannot be detected quite accurately, since it is much weaker than the strong signal in the tropics. We used the method of cluster analysis to identify those signals. This allowed us to classify the data of the OST in the Pacific Ocean basin and to define the interacting zones in the Pacific Ocean. The results show that, in addition to the signal in tropics, there are also well-defined quasi-decadal signals in the eastern and western Pacific Ocean, as well as in the region of the Kuroshio continuation in the subpolar zone. ANALYSIS BASED ON THE EMPIRICAL ORTHOGONAL FUNCTIONS At the first stage of the studies, the empirical orthogonal functions (EOFs) were analyzed for the period of 1948–2003 based on the classical approach of computing eigenvalues and eigenvectors from the covariance matrix of the monthly average data with a 1° resolution in latitude and longitude. The data were selected from the NCEP/NCAR renanalysis [14]. The Pacific Ocean region taken for analysis represents a spherical trapezium (122.5° E–70.5° W, 29.5° S– 60.5° N]. In this case, the data contain 11569 points in space and 668 steps in time.
550
ANALYSIS OF VARIATIONS IN THE SURFACE TEMPERATURE
551
120 100 80 60 40 20 0 2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Fig. 1. Eigenvalues for the values starting from the second one. The first value equal to 2465 is seasonal variations.
140 120 100 80 60 40 20 0 –20 –40 –60
60 50 140
0 10
40
60
30
60 80
60
20 20
10 0 0
–10 –20
–20
–40
140
160
180
160
140
120
100
80
Fig. 2. EOF-1 harmonic. Seasonal variations.
The EOF analysis was performed with an excluded climate constituent that was obtained by averaging the data with respect to the time at each point of the region. The climate constituent corresponds to the data from the Levitus atlas [15]. The EOF calculations show that the maximum contribution of 89% to the OST (Fig. 1) is made by the first harmonic (Fig. 2) representing seasonal oscillations. The second harmonic with a contribution of 4.7% (Fig. 3) illustrates a typical distribution of the OST during the El Niño and La Niña events. The temporal variations are shown in Fig. 3b. The positive values of the curve correspond to the El Niño period and the negative ones correspond to the La Niña phenomenon. The period under study is characterized by the following clearly pronounced events of the El Niño warm phase in 1957, 1963, 1973, 1982, 1987, and 1997 and the La Niña cold phase in 1966, 1972, 1976, and 1988. The third harmonic with IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
the contribution of 1.9% (Fig. 4) describes a negative correlation of variability in the subtropical and the circumpolar zones. The fourth and fifths harmonics contribute less and cause variations in the central, tropical, and subtropical zones and in the zone of the Kuroshio continuation. At the next stage of the studies, we examine the possibility of reconstructing the OST anomalies for the different periods by using the reduced EOF sets. The share of the EOF harmonics in the presentation of the OST anomalies at the point (110° W, 0.5° S) is shown in Fig. 5 for the various periods. It is seen that, during the extreme El Niño and La Niña events (December 1982, July 1988, and November 1997), the share of the first harmonics in the OST anomalies significantly prevails, while in the intermediate periods, such as September 1984, the contribution of the higher harmonics is greater. This leads to the fact that Vol. 52
No. 5
2016
552
KUZIN, LOBANOV
(а) 35 30 25 20 15 10 5 0 –5 –10 –15
60 15
50
10 5
40 –10
20
10
30
0
10 15
20
30
15
5
0
35
–10
20 5
–20 –5
140
160
180
160
140
120
100
80
(b) 0.15 0.10 0.05 0 –0.05 –0.10
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Fig. 3. EOF-2 harmonic. Interannual variations (the El Niño and La Niña events).
25
5
10
50
30 15
25
60
15
40
20
5 0
15
30 –10
20
5
–10
10
10
–5
0
0
–5
5
–20
–5
0 15
0
–10
5
–15
10
140
160
180
160
140
120
100
–10
80
Fig. 4. EOF-3 harmonic. Variability in subtropical and subpolar zones.
the results obtained from reconstructing the OST anomalies in the different periods of the Pacific Ocean climate state differ considerably. During the extreme El Niño and La Niña events, the anomalous
field is reconstructed with excluded seasonal oscillations at quite high accuracy based on the first harmonics. At the same time, during the intermediate periods (September 1984), a sufficiently adequate
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 52
No. 5
2016
ANALYSIS OF VARIATIONS IN THE SURFACE TEMPERATURE
(а)
(c)
(b)
553
(d)
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0
20 40 60 80 100 0
20 40 60 80 100 0
20 40 60 80 100 0
20 40 60 80 100
Fig. 5. Share of EOF harmonics in the OST anomalous field in the different periods: (a) December 1982, (b) September 1984, (c) July 1988, and (d) November 1997.
description of the anomalies requires more than 60 decomposed harmonics (the pictures of the reconstructed fields are not provided). This means that, in these periods, the Pacific OST is mostly determined by the climate state and the seasonal variation and the anomalies result from the more complicated internal processes. Here, the reconstruction accuracy of the OST anomalies in the middle and high latitudes is rather low, since it is much weaker than a strong signal in tropics. This does not allow us to identify the typical formations in these latitudes. This fact initiated the use of the second approach to the OST analysis, cluster analysis. CLUSTER ANALYSIS A cluster analysis is a method of integrating the data into classes (clusters) according to the criterion of correlation between the spatial-temporal points [16, 17]. For the analysis we used the above-indicated monthly NCEP/NCAR data with 1° resolution at the seasonal variation and excluding the climate state [14]. The method of cluster analysis makes it possible to solve the following problems: (1) classify the objects with respect to the main features of these objects, (2) test the hypotheses on the origination of a definite IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
structure in the set of objects, and (3) develop a new classification for the weakly studied events in order to establish relations in the set and to introduce a particular structure in it. SPATIAL CLASSIFICATION It is required to divide the set of implemented time series that are normalized to standard deviation into a certain number of subsets (classes) so that each sample belongs to a particular class. All classes should consist of rather “close” samples that are well correlated with each other. The Euclidean distance between the time series or their correlation coefficient is taken as a measure of closeness for them. For each class, the “center” of the class can be determined as a point where each point from the class is correlated with it better than with other points. The next step in this procedure is so-called “cleaning.” A certain correlation level is selected in the classes (e.g., 0.7), all points below which are excluded in each class. As a result, the region is divided into a number of subregions (clusters) consisting of the points for which each center would represent a temporal variation in this class. The relations between the classes can be studied by analyzing the degree of Vol. 52
No. 5
2016
554
KUZIN, LOBANOV
60
40
20 1 2 0
–20 150
160
110
Fig. 6. Distribution of two spatial classes.
correlation between their centers. Thus, when a distance measure is determined in such a way and when a number of classes is assigned, the problem of classification is reduced to the problem of finding the centers of the classes, which, in turn, is reduced to minimizing a certain functional [16]. In general, this problem is rather complicated; however, the introduction of an intermediate functional can lead its solution to the recursive procedure. The spatial classification was performed to the level of ten classes. The first step consisted of the formation of two classes. Figure 6 presents the spatial distribution of these classes that separate the Pacific Ocean into the eastern and western sectors. The western segment (the first class) is considerably expanded in the subtropical zones in the both Northern and Southern hemispheres, while the eastern segment (the second
class) is broader in the tropical and subpolar zones. This spatial distribution of the classes fully conforms to the pattern of the OST anomalies during the Pacific Decadal Oscillation (PDO) [4]. In this case, the western and eastern segments of the Pacific are negatively correlated (Fig. 7). By analyzing the temporal distribution of the behavior of classes (Fig. 8), we can identify a cold (from 1948 until 1977) and a warm (from 1978 until recently) phase that are known in the published literature [18]. According to the estimates of climate researchers, the warm phase of the PDO leads to warming in tropics and the Alaska region and cooling in the eastern United States [19]. The pattern of the temporal behavior of the second class also contains the El Niño and La Niña periods. To continue our analysis, we chose ten classes (Fig. 9). It is seen that several classes are identified in the tropical zone, in the eastern zone of upwelling, and in the subtropical and subpolar zones. Our correlation analysis for the centers of the classes provides an evidently high correlation between classes 2 and 7 in the tropical zone (0.79); a positive correlation between tropics and the eastern zone of the coastal upwelling (0.42); and a weak negative correlation between the eastern tropics and the region of the Kuroshio continuation (–0.32), class 3. Figure 10 presents the temporal behavior of the center from class 7 in the eastern tropical segment of the Pacific Ocean. The maximum values correspond to the El Niño periods in 1957, 1964, 1972, 1982, 1987, and 1997. The negative values are the La Niña events corresponding to the periods in 1950, 1955, 1968, 1973, 1975, 1988, and 1999. Figure 10 also shows the results for the short-time Fourier analysis. The windows had the following ranges: 1–5 years, 5–10 years, and equal to or greater than 10 years. The interannual variations are recorded. The spectral analysis (Fig. 11) demonstrates the peaks during the periods of 21, 4.5,
0.15 0.10
1 2
0.05 0 –0.05 –0.10 1948 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997
Fig. 7. Temporal behavior of the first and second classes. Moving averaging for five months. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 52
No. 5
2016
ANALYSIS OF VARIATIONS IN THE SURFACE TEMPERATURE
0.15
555
Center 2 Avg.
0.10 0.05 0 –0.05
–0.10 1948 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 Fig. 8. Periods of the cold and warm phases for class 2.
60 50 3
40
8
30 5
1
4
20 8
10 9
2
0
7 –10
10 1
–20
6 140
160
180
160
140
120
100
80
Fig. 9. Distribution of ten classes in the spatial classification.
and 3.5 years. The peak with a period of 21 years conforms to the Pacific quasi-decadal oscillation; however, due to the short length of the series, it cannot be statistically sufficiently representative. At the same time, in Fig. 10 the Fourier harmonic with a period of more than 10 years yields consistent results with respect to the occurrence of a cold and a warm phase of the PDO before and after 1977. It is also of interest to study the behavior of the classes in subpolar regions, because these zones are negatively correlated with tropics. The time variation for the center of class 3 is also represented by interannual and quasi-decadal variations. The analysis of the oscillation spectra (Fig. 12) in this region shows the IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
occurrence of interannual harmonics with periods of 21, 12, 5, and 3.5 years. TIME CLASSIFICATION If we represent the information on the OST as spatial maps made up of the points corresponding to the time steps, i.e., we replace the temporal and spatial variables and classify the data set with respect to the time, this problem will have the same mathematical type as the previous one. In this case, the set of maps for the OST spatial distribution is divided into a number of classes (clusters) consisting of the “most typical” maps. Figure 13 presents six temporal classes. The Vol. 52
No. 5
2016
556
KUZIN, LOBANOV
0.20 0.15 0.10
1 2
0.05 0
3
–0.05 –0.10 –0.15
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Fig. 10. Temporal behavior of the center for class 7 (the tropical zone) and the results of the short-time Fourier analysis with the following ranges of the windows: (1) 1–5 years, (2) 5–10 years, and (3) equal to or greater than 10 years.
0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 21
4.5 3.5
Fig. 11. Variability spectrum for class 7. The variation periods of 21, 4.5, and 3.5 years are identified.
0.030 0.025 0.020 0.015 0.010 0.005 0 21 12
5
3.5
1
Fig. 12. Variability spectrum for class 3 (the Kuroshio continuation). The variation periods of 21, 12, 5, and 3.5 years are identified. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 52
No. 5
2016
ANALYSIS OF VARIATIONS IN THE SURFACE TEMPERATURE
557
60 1 0 – –0. 01
0
0.0 1
20
0.01
0.0
0
0.01
5
0.02
6
.01
–0 –0.03 .0 0 2
–0
–
+ 0.0@
1 0.0
0
0.02
– .01 0 – 0. –0.03 02 .01 –0
–0
+ 0.01
0
0.01
0.0 0.01 2 +
.01
–0
.01 –0.01
150
0
–
–0
–20
0.01
0.01
–
– 3 .0 –0.03 –0
0
0
0
0 0
0
40 20
4 0.03 0.0 + 0.02 3 1 0 . 0 0
+ 1 0 .
–20 60
3
–0.02 –
0
0
0
20
2 .02 0.0 –0
40
0.01 0 – –0.02 –00.01 .01
0
0.01
0
+
.01 –0 –0.02 –
4
–20 60
–0.01 0
0 0.01 0.02 0.03 +
0
0.01 +
0.01
02 0.
0
40
2
–0 – .01
160
110
150
160
110
Fig. 13. Six classes in the OST temporal classification.
first and the second ones show the El Niño and La Niña events, respectively. Classes 3 and 4 describe an OST decrease and increase in the region of the Kuroshio continuation. Clusters 5 and 6 describe the episodes of an OST decrease in the subpolar and subtropical gyres, respectively.
during the extreme El Niño and La Niña events, the processes in the middle and high latitudes are also interrelated with the tropical processes.
It is also of interest to study the relations between tropical, subtropical, and subpolar zones based on the temporal behavior of the classes obtained. Figure 14 illustrates the time variation of the center for class 7 from the spatial classification. The numbers below designate the numbers of the temporal classification class that prevail in the given period. It is seen that, in addition to the direct impact of the temporal classes
The analysis of the EOF data made it possible to identify and reconstruct the interannual OST signal in the tropical Pacific Ocean based on the first harmonics. This indicates that the anomalies during the extreme tropical events are determined by the first harmonics and that the processes forming the anomalies during the intermediate periods can even be more complicated. The variability of the OST anomalies in
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
CONCLUSIONS
Vol. 52
No. 5
2016
558
KUZIN, LOBANOV
0.15 0.10 0.05 0 –0.05 –0.10 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 5544222222211442251122222222221111155555555522242244444222211554442235511111222222211112222222222221165
0.15 0.10 0.05 0 –0.05 –0.10 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0
1
2
3
4
3331111666111336611111333332222361111111222333444444111116611666661666333661111122222222444444444116
Fig. 14. Temporal behavior for class 7 in the spatial classification. The numbers below designate what class of the temporal classification dominates in the particular period.
subtropics and subpolar regions is blocked by a strong tropical signal. The analysis of the temporal-spatial distribution of the clusters allowed us to classify the typical structures in the variability of the Pacific OST and establish the relations between the western and eastern, as well as subtropical and subpolar, regions. During the analysis we detected a signal of quasi-decadal variability in the tropical, subpolar, and subtropical zones of the Pacific Ocean that may be the PDO signal manifestation. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 14-05-00730. REFERENCES 1. H. F. Diaz and V. Markgraf, El Niño and the Southern Oscillation: Multiscale Variability and Global and Regional Impacts (Cambridge University Press, Cambridge, 2000). 2. M. J. McPhaden, “El Niño and La Niña: Causes and global consequences. The Earth system: Physical and chemical dimensions of global environmental change,” in Encyclopedia of Global Environmental Change (2003), Vol. 1, pp. 353–370.
3. F. Biondi, A. Gershunov, and D. R. Cayan, “North Pacific decadal climate variability since 1961,” Geophys. Res. Lett. 1, 5–10 (2001). 4. N. J. Mantua, R. S. Hare, Y. Zhang, et al., “A Pacific interdecadal climate oscillation with impacts on salmon production,” Bull. Am. Meteorol. Soc. 78 (6), 1069–1079 (1997). 5. E. N. Curchitser, D. B. Haidvogel, A. J. Hermann, et al., “Multi-scale modeling of the North Pacific Ocean: Assessment and analysis of simulated basinscale variability (1996–2003),” J. Geophys. Res. 110, C11021 (2005). doi 10.1029/2005JC002902 6. K. Stahl, R. Dan Moore, and I. G. Mckendry, “The role of synoptic-scale circulation in the linkage between large-scale ocean–atmosphere indices and winter surface climate in British Columbia, Canada,” Int. J. Climatol. 26 (4), 541–560 (2006). 7. R. Krishnan and M. Sugi, “Pacific decadal oscillation and variability of the Indian summer monsoon rainfall,” Clim. Dyn. 21, 233–242 (2003). 8. A. Montecinos, S. Purca, and O. Pizarro, “Interannual-to-interdecadal sea surface temperature variability along the western coast of South America,” Geophys. Res. Lett. 30 (11), 1570 (2003). 9. M. J. Salinger, J. A. Renwick, and A. B. Mullan, “Interdecadal Pacific oscillation and south Pacific climate,” Int. J. Climatol. 21, 1705–1721 (2001). 10. V. I. Kuzin and V. M. Moiseev, “Analysis of the results of diagnostic and adaptation calculations in the north-
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 52
No. 5
2016
ANALYSIS OF VARIATIONS IN THE SURFACE TEMPERATURE
11.
12. 13.
14. 15.
ern part of the Pacific Ocean,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 32 (5), 680–689 (1995). A. S. Sarkisyan, Basics of the Theory and Computation of Oceanic Currents (Gidrometeoizdat, Leningrad, 1966) [in Russian]. A. S. Sarkisyan and J. E. Sündermann, Modelling Ocean Climate Variablity (Springer, Rotterdam, 2009). V. V. Efimov, A. V. Prusov, and M. V. Shokurov, “Patterns of interannual variability defined by a cluster analysis and their relation with ENSO,” Q. J. R. Meteorol. Soc. 121, 1651–1679 (1995). NCEP/NCAR Dataset. http://dss.ucar.edu/datasets/ds090.0/docs/papers/Tchng. S. Levitus, World Ocean Atlas 1994 (NOAA, 1994), Vol. 5.
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
559
16. R. Xu and D. Wunsch II, “Survey of clustering algorithms,” IEEE Trans. Neural Networks 16, 645–678 (2005). 17. V. V. Efimov, A. V. Prusov, and M. V. Shokurov, “Classification of interannual anomalies in ocean surface temperature,” Okeanologiya 35 (4), 505–513 (1995). 18. A. J. Miller, D. R. Cayan, T. P. Barnett, et al., “The 1976–77 climate shift of the Pacific Ocean,” Oceanography 7, 21–26 (1994). 19. J. Fei-Fei, “A theory of interdecadal climate variability of the North Pacific ocean–atmosphere system,” J. Clim. 10 (8), 1821–1835 (1997).
Translated by L. Mukhortova
Vol. 52
No. 5
2016
