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  • View in gallery

    Domain of analysis.

  • View in gallery

    Monthly percentages of 2° boxes inanalysis region containing SST data.

  • View in gallery

    A comparison of the 3.5σ and 4.5σ trimmings of extreme outliers in the COADS SST in the analysis region. The number of observations retained each month is plotted for each trimming as obtained from the COADS.

  • View in gallery

    The estimated bias in SST measurements. The monthly spatial averages of SST are in red (only 1 out of every 4 months is plotted for clarity). Other lines are as labeled: the monthly SST averages are smoothed with a 14 yr plus 1 month running mean. The straight lines represent the biases of the different time periods. Also shown are the monthly SST averages with the estimated bucket bias removed before smoothing.

  • View in gallery

    The normalized residual (small-scale variance of the test bed divided by the variance of the complete test bed rT/σB) for varying number of modes. Two different months from the reconstruction are shown. The minimum (black diamond) gives the number of modes for the reconstruction of the month being examined.

  • View in gallery

    (a) EOF-1 (40% of the variance) and (b) EOF-2 (10% of the variance) of the OI SST are normalized by the largest absolute value in each. (c) and (d) The time series for EOF-1 (fm1) from the monthly least squares fit to COADS SST when the reconstruction is possible. ENSO extremes are indicated by black filling between the curve and ±0.5°C. Each “∼” denotes the first extreme ENSO year of the Kiladis and Diaz (1989) determination of warm (red) and cold (blue) ENSO events. The negative SOI smoothed with three 1–2–1 Hanning windows is pink. (e) and (f) The monthly time series for EOF-2 (fm2). Blanks indicate the mode was not used in the reconstruction.

  • View in gallery

    As in Fig. 6 but for modes 3 and 4, with 7.3% and 3.6% of the variance, respectively.

  • View in gallery

    The modulus of the Morlet wavelet transform of (a) the time series for the first EOF (fm1) and (b) the extended SOI from Allan et al. (1991). Colors indicate amplitude: black indicates zero and white the maximum, as indicated by the color bar.

  • View in gallery

    The number of spatial EOF patterns, Nm, usedin reconstruction of the monthly SST.

  • View in gallery

    A comparison of two raw COADS fields with the Reynolds and Smith (1995) climatology removed. Empty grid boxes are shown in black. (a) Good data coverage with data in 84% of the oceanic grid boxes; (c) poor coverage with data in only 12%. This is the smallest amount of data in any COADS field during the data sparse 1940s. Fields (b) and (d) are reconstructions of these fields using a fit of the first few EOFs from OI SST. The number of EOFs used in each fit is noted in the margin.

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Reconstruction of Monthly SST in the Tropical Pacific Ocean during 1868–1993Using Adaptive Climate Basis Functions

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  • 1 Center for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida
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Abstract

An EOF-based reconstruction of monthly SST anomaly fields is calculated for the years 1868–1993 in the tropical Pacific Ocean. The EOFs are computed from optimally interpolated SST anomaly fields from November 1981 to October 1995 from the same region. These are used as a functional basis set for projecting SST anomalies from the Comprehensive Ocean–Atmosphere Data Set (COADS) to produce a smooth, spatially complete reconstruction. The optimal number of EOF modes for each month’s reconstruction is chosen using large-scale error analysis: a modern subset of the COADS SST is subsampled according to the distribution of observations in the historical month being reconstructed, forming a testbed on which to evaluate the reconstruction based on a variable number of modes. The test bed is least squares fit to the basis EOFs. The difference fields between the reconstruction and a smoothed version of the test bed is found. The total variance of difference fields (residual) is minimized with respect to the number of EOF modes. Additionally, the residual is not allowed to be greater than the total variance of the large-scale features of the test bed. The number of modes used in each monthly reconstruction increases with the spatial coverage of observations.

The time series associated with the first EOF mode is a new ENSO index. There is general agreement of warm and cold ENSO events between this new index and those determined by the SOI as well as those described in previous studies. A wavelet analysis of the new index reveals its spectral evolution from 1870 to 1992 is similar to that of the SOI. Most of the energy at periods less than 10 yr is concentrated in the 3–8-yr range in bursts typically lasting 5–10 yr. Previous reconstruction studies also show agreement with this new ENSO index as measured by the timing and amplitude of premodern El Niño events.

* Current affiliation: University of South Florida, St. Petersburg, Florida.

Corresponding author address: S. D. Meyers, Department of Marine Science, University of South Florida, 140 Seventh Ave. South, St. Petersburg, FL 33701-5001.

Email: meyers@stommel.marine.usf.edu

Abstract

An EOF-based reconstruction of monthly SST anomaly fields is calculated for the years 1868–1993 in the tropical Pacific Ocean. The EOFs are computed from optimally interpolated SST anomaly fields from November 1981 to October 1995 from the same region. These are used as a functional basis set for projecting SST anomalies from the Comprehensive Ocean–Atmosphere Data Set (COADS) to produce a smooth, spatially complete reconstruction. The optimal number of EOF modes for each month’s reconstruction is chosen using large-scale error analysis: a modern subset of the COADS SST is subsampled according to the distribution of observations in the historical month being reconstructed, forming a testbed on which to evaluate the reconstruction based on a variable number of modes. The test bed is least squares fit to the basis EOFs. The difference fields between the reconstruction and a smoothed version of the test bed is found. The total variance of difference fields (residual) is minimized with respect to the number of EOF modes. Additionally, the residual is not allowed to be greater than the total variance of the large-scale features of the test bed. The number of modes used in each monthly reconstruction increases with the spatial coverage of observations.

The time series associated with the first EOF mode is a new ENSO index. There is general agreement of warm and cold ENSO events between this new index and those determined by the SOI as well as those described in previous studies. A wavelet analysis of the new index reveals its spectral evolution from 1870 to 1992 is similar to that of the SOI. Most of the energy at periods less than 10 yr is concentrated in the 3–8-yr range in bursts typically lasting 5–10 yr. Previous reconstruction studies also show agreement with this new ENSO index as measured by the timing and amplitude of premodern El Niño events.

* Current affiliation: University of South Florida, St. Petersburg, Florida.

Corresponding author address: S. D. Meyers, Department of Marine Science, University of South Florida, 140 Seventh Ave. South, St. Petersburg, FL 33701-5001.

Email: meyers@stommel.marine.usf.edu

1. Introduction

The El Niño–Southern Oscillation (ENSO) is the dominant interannual climate anomaly in the tropical Pacific Ocean. ENSO creates large variations in sea surface temperature (SST) in the eastern tropical Pacific and in the overlying atmospheric circulation, as measured by the Southern Oscillation index (SOI). ENSO is the primary source of interannual climate variability around much of the globe (Kiladis and Diaz 1989; Diaz and Markgraf 1992; Richards and O’Brien 1996; Ropelewski and Halpert 1996) and can have economic impacts totaling billions of dollars per event (Adams et al. 1995; Glantz 1996; Solow et al. 1998). Historical records aid understanding of this major climatic cycle.

SST and SOI are two useful indicators of the ENSO state, though SOI is relatively noisy because it is based on the difference of two point measurements (the surface atmospheric pressure at Tahiti, and at Darwin, Australia). SST indices are typically spatially averaged quantities and therefore contain reduced observational noise. Changes in SST associated with ENSO are driven by the dynamics of oceanic Kelvin waves (Wyrtki 1974;Busalacchi and O’Brien 1981). A series of downwelling Kelvin waves, triggered by relaxation of the trade winds, moves from west to east across the equatorial Pacific Ocean. SST anomalies increase in the eastern tropical Pacific because downwelling inhibits the deep cold waters from mixing with the upper warmer waters. A sufficiently warm SST anomaly around the equatorial Pacific is called an El Niño state, defined (Sittel 1994) as at least six consecutive months of SST anomalies greater than 0.5°C. Other definitions are discussed by Trenberth (1997).

The other extreme of the ENSO cycle is El Viejo (sometimes called La Niña). It is driven by upwelling Kelvin waves triggered by increased trade winds. The Kelvin wave raises the thermocline and results in cold SST anomalies. There is no general agreement on the designation of cold events (Bradley 1987; Kiladis and Diaz 1989; Meyers and O’Brien 1995). Therefore, we use a symmetric definition, that is, colder than 0.5°C for at least 6 months.

Observations of SST in the tropical Pacific are spatially sparse, especially prior to the 1950s, and therefore have limited utility for ENSO research. Most of the observations are reported by “ships of opportunity” operating in commercial lanes and by ocean buoys, so vast stretches of the ocean are unsampled or undersampled. Our work is aimed at generating spatially complete 2° × 2° monthly reconstructions of SST fields in the tropical Pacific. The period for the reconstruction is from the late 1860s to the early 1990s.

The reconstruction is accomplished by first computing empirical orthogonal functions (EOFs) from SST anomalies of the Reynolds and Smith (1994) optimally interpolated (OI) monthly SST fields from November 1981 to October 1995. It is assumed these EOFs typify the patterns of tropical Pacific SST in the Comprehensive Ocean–Atmosphere Data Set (COADS) record. Historical monthly median SST records in each 2° × 2° box from the COADS monthly summaries are least squares fitted to a subset of the large variance EOFs.

Others have used a similar technique. Shriver and O’Brien (1995) reconstructed surface wind stress in the tropical Pacific. Their approach used a weight function dependent on the number of observations in each grid box. They also selected the average number of high variance EOFs that are statistically distinct from white noise as the set of basis functions for the least squares fit. Smith et al. (1996) reconstructed global and regional SST from 1950–92. They tried several sets of basis functions, starting with the first five EOF modes, and included an increasing number (5, 13, 20, 24, 30) of EOFs in each new basis. (“Basis” refers to the collection of EOF modes selected for any particular reconstruction.) Using cross validation they found a functional basis set containing the first 24 modes to be optimal. Kaplan et al. (1997) used a combined EOF and Kalman filter approach to reconstruct Atlantic SST. They modeled the SST as a Markov process and selected the number of modes (30) that minimized the relative error of the model. Results of their technique were used by Kaplan et al. (1998) and Cane et al. (1997) to analyze global SST and its trend.

Smith et al. (1998) made a reconstruction of tropical Pacific SST using a technique very similar to ours, though their projection was upon increments of SST anomalies. They also used a process known as “screening regression” to eliminate unsupported modes. This is a measure of the variance of each spatial EOF captured by the sampling of each COADS field. If the captured variance was too low, the mode was eliminated from the reconstruction.

EOF projection was used by Rayner et al. (1996) as a gap-filling tool for generating complete Global Sea-Ice and Sea Surface Temperature (GISST) fields. The newer version considered below (GISST3.0) differs from Rayner et al. (1996) in that the eigenvector reconstructions before 1981 are combined with the original SST data where available (D. E. Parker 1998, personal communication), and GISST3.0 uses a variable number of modes.

Here, the number of modes is chosen using a new statistical test, large-scale error analysis (LSEA), that is well suited to the present task of SST reconstruction. The misfit of the reconstructed field to a smoothed test bed field is minimized with respect to the number of modes. The final result is an SST record that is spatially smoother and lower in variance than raw observations. Additionally, the amplitude of the first EOF mode (the primary ENSO mode) is a new ENSO index based solely on in situ SST. During the months where the reconstruction was possible, the extremes of the time series for EOF-1 are in general agreement with those found in the SOI, and with the listing of ENSO events by Kiladis and Diaz (1989), even during years where there is very little data. There is also good agreement with reconstructed ENSO indices created by Kaplan et al. (1998, hereafter K98), Smith et al. (1998) (S98), and from GISST3.0.

The following section presents the observational SST data taken from both COADS and Reynolds and Smith (1994). The third section discusses the removal of instrumental bias, the EOF projection technique used for reconstructing the historical monthly SST fields, and large-scale error analysis. The fourth section presents the four modes with the largest variance, discussing their spatial structure and temporal behavior. The time series for the first mode is shown to be a reasonable ENSO indicator. Wavelet analysis of this mode is used to examine the spectral evolution of ENSO. The final section summarizes the results and compares the El Niño events in the reconstruction to those found in previous SST reconstruction efforts.

2. Data

a. COADS SST

The COADS (Slutz et al. 1985; Woodruff et al. 1987) contains data gathered at the surface of the oceans amalgamated from many smaller compilations of ship and buoy observations. (Satellite measurements are excluded, because they are only intermittently available for the last 20 yr and they suffer bias problems.) Ship and buoy observations that deviate too strongly from climatology are excluded by a trimming process discussed below. Remaining observations are binned in 2° × 2° boxes for each month. The resulting fields are the monthly medians of SST in our domain (Fig. 1) from 1868 through 1993.

COADS grid boxes with high data density tend to be clustered along shipping lanes, leaving large data voids in between. Many grid boxes therefore do not contain data, particularly in the early years (Fig. 2). Only a few percent of the 2° monthly fields in the 1870s have SST values. In the following two decades, there is about 10% coverage. For 1900–13, each monthly field has 15% coverage, but the percentage drops to near 3% in the next 3 yr, because of the effects of World War I on shipping. In the 1920s each field returns to around 15% coverage, and in the 1930s each field has close to 25%. During World War II (WW II) and the Communist Revolution in China in the 1940s, the number of 2° boxes containing SST measurements is frequently driven below 15%. From the late 1940s through 1950 the typical percentage increases from 20% to 40%. From the 1950s through the 1960s the percentage increases to around 80% where it remains through 1993.

After 1965 the COADS SST has smaller patches without data; however, the measurement errors become larger, because a high number of the observations were reported through the Global Telecommunications System. Such satellite transmitted reports are frequently garbled (Woodruff et al. 1987). Trimming extreme outliers eliminates the worst of the garbled data, but unrealistic variability remains, mostly at the small scale.

Prior to 1980, data included in the COADS SST undergo a trimming process in three separate periods: before 1910, 1910–49, and 1950–79. For each of the three periods, a monthly climatology is computed and the standard deviation, σ, is estimated for each location. (These climatologies should not be confused with the climatology used for calculating SST anomalies below.) Values more than ±3.5σ away from the climatology are rejected (Slutz et al. 1985).

After 1980, the 1950–79 COADS climatology and standard deviation are used for the trimming process. However, removing measurements beyond 3.5σ eliminates many realistic reports during the 1982–83 El Niño. Thus, for the period beginning in 1980 another version of COADS with 4.5σ trimming is used in our analysis. This trimming is believed to accept more of the realistic reports during the El Niño without accepting too many additional unrealistic reports.

The difference in the number of reports accepted by the two trimming criteria changes in time (Fig. 3). In 1986 the number of reports ⩽4.5σ in our domain increases whereas the number of reports ⩽3.5σ begins a steady decline. The increase coincides with the introduction of the moored array of data buoys in the Tropical Ocean Global Atmosphere–Tropical Atmosphere Ocean (TOGA-TAO) program (Hayes et al. 1991). Between 700 and 800 observations per month are expected from each buoy. The increase of 4.5σ reports is therefore expected. The 3.5σ data has a strong downward trend from 1.8 × 104 reports per month in 1980 to about 104 reports per month in 1993. This suggests that the 3.5σ trimming is rejecting increasing amounts of accurate data that is accepted by the 4.5σ trimming. Thus we use the COADS 4.5σ trimmed data for the period starting with 1980.

There is an additional problem in the COADS SST data related to changes in instrumentation. Prior to 1942, temperature was usually measured by placing a thermometer in a bucket of water taken from the sea surface. Evaporative cooling caused a cold bias in such measurements. Folland and Parker (1995) made an extensive analysis of bucket bias in SST, using numerical models that describe how buckets of seawater cool after they are lifted out of the ocean. Many assumptions about influences such as wind velocities and time of exposure to the wind are included in their analysis of bias in the Meteorological Office historical SST, though their results are not sensitive to these assumptions.

They estimated the bias in the tropical Pacific to be −0.1°C to −0.2°C for wooden buckets and −0.4°C to −0.6°C for canvas buckets. Both types of buckets were commonly used, so the COADS SST is calculated from reports that have a mixture of these biases, making bias removal difficult. With the advent of World War II it became dangerous for a ship to have nightime illumination, such as that needed to read a thermometer. In late 1941, many ships had instrumentation installed to read SST by measuring the temperature of engine cooling water at the intake. Since then the impact of bucket biases has been minimal, though biases from engine intake may have been introduced.

b. OI data and climatology

The OI SST fields, as discussed by Reynolds and Smith (1994), are computed in weekly fields from November 1981 to the present with 1° resolution and global coverage. The fields combine both in situ and satellite data in a way that deals with the distinctly different problems of both types of information. For in situ data, weekly 1° compilations have many grid boxes of missing data. Similar compilations of satellite data from the Advanced Very High Resolution Radiometer (AVHRR) have nearly complete coverage. Calculation of SST from satellite soundings involves the use of simple atmospheric correction models to adjust for atmospheric effects. The primary limitation is the AVHRR’s inability to retrieve SST through clouds and other unmodeled atmospheric obstacles such as volcanic dust. Unmodeled attenuation processes vary with location, leaving spatially dependent biases in the final SST product. In the OI data, both in situ and AVHRR data are merged to minimize the impact of both the AVHRR biases and the scarcity of in situ data. Before any computation, the OI data is interpolated to the 2° × 2° COADS grid.

The OI climatology has abnormally warm features, because of the extreme El Niño event of 1982–83 and the anomalously warm 1990s. Therefore, the hybrid climatology of Reynolds and Smith (1995) combining 1959–79 in situ data at the large scale and the OI climatology at the smaller scales is removed from the OI measurements and EOFs are calculated from the resulting anomalies.

3. Method

a. Bias correction

Before the COADS data can be projected onto the EOFs, the instrumental bias of the measurements must be removed. For each monthly field a single number is used to represent the bias over the entire domain. Though differences between the bias due to wooden versus canvas buckets are about 0.4°C (and generally increasing) in Folland and Parker (1995), this type of instrument-dependent spatial variability is dealt with differently in our analysis. We also ignore any spatial variability of bucket corrections. The dominant modes have large spatial scales and long timescales, so smaller-scale variability is not retained in the reconstruction.

The average COADS SST anomaly in our domain is shown in Fig. 4. The data have strong oscillations on timescales of a few years or less. These are generally taken to be natural variability. However, the two sudden shifts in the mean temperature in 1906 and near the beginning of 1940 are assumed to result from an instrumental change. The bias is modeled as the average of the SST anomaly in three time intervals: (I) May 1880–April 1906 (−0.33°C); (II) May 1906–January 1940 (−0.66°C); and (III) February 1940–September 1941 (−0.46°C). The bias for I is subtracted from the COADS anomaly fields from 1868 through April 1906. The early years were not included in computing the bias, because there was not enough data in those fields. The biases for intervals II and III are subtracted from COADS anomaly fields for their respective period. Interval III is an extremely short step because the values in that period are not as strongly negative as those of II and because III is intermediate between the absence of bias and the most strongly biased step.

The EOF basis functions are derived from a 14-yr dataset, so they best represent variations at this or shorter timescales. After the bias removal, a 14 yr plus 1 month (169 month) running mean of the spatially averaged anomaly is removed from the COADS anomaly fields. The smoothing is only done over the spatial average, not at each individual point. Long-term variations with spatial scales smaller than the domain size, such as those captured in the EOF analysis, are preserved. The final monthly COADS SST anomalies are projected onto the EOFs of the OI data using a least squares fit. After reassembly of the EOF projections the running mean can be restored.

b. Mode calculation

The 2° OI data (Reynolds and Smith 1994) at each grid point in the region xn(tm), n = 1, . . . , N (=2247), at time tm, m = 1, . . . , NT (=1512), are put into an NT × N data matrix R. The eigenvectors (temporal EOFs) of the covariance matrix M = RRT describe how the spatial cross correlation of the OI data varies in time. The eigenvectors are placed in the columns of matrix J with one eigenvector in each column: (IλRRT)J = O, where λ is the vector of eigenvalues. The matrix of associated spatial patterns is computed by projecting the OI data matrix onto the temporal EOFs, K = RTJ. The direct calculation of spatial EOF modes is thus avoided (von Storch and Hannoschöck 1984) for computational efficiency. Each spatial EOF mode and the corresponding temporal EOF have the same eigenvalue, which indicates how much of the OI data’s variance is represented by the space–time pair of EOFs. The spatial EOFs are ordered by variance (eigenvalue) from the EOF containing the most variance to the one containing the least. The OI SST anomaly field is the sum over products of the spatial EOF modes and temporal modes.
i1520-0493-127-7-1599-e1

Through the remainder of this article, the modes are ordered according to variance, with mode k = 1 indicating the highest variance mode.

c. Historical reconstruction

The historical SST anomaly fields are reconstructed by a least squares fit of existing COADS SST anomaly data to the EOFs derived above. The reconstructed anomaly is given by
i1520-0493-127-7-1599-e2
where f is the time series associated with the kth spatial mode, and α is a functional of value zero or one, described below. The variable number of modes used in the reconstruction is Nm ⩽ min(NT, N). The full historical reconstruction is Tanom plus the running mean and the climatology.

The number of spatial EOFs in the reconstruction (Nm) is chosen as follows. Each monthly SST anomaly field from 1868 to 1993 is analyzed separately. The spatial sampling distribution, X(m), of the month being analyzed is imposed on each field of a test bed of the SST dataset. These subsampled test bed fields are least squares fit to the spatial EOFs, and the large-scale error is minimized with respect to the number of basis modes. This is now explained in greater detail.

The COADS SST anomaly fields in the 1970s are used as the test bed for evaluating each reconstruction. The 1970s are chosen for several reasons. Each field in the 1970s is nearly complete, with data in about 80% of the grid boxes. The 1970s are independent of the EOF basis since the EOF modes are computed for data only in the 1980s and early 1990s. Additionally, 1970s data contain small-scale noise similar to what is found in any COADS field, though not identical due to errors in the reporting system. Both the effect of noise and the data distribution are therefore included in the selection process.

The 1970s fields are not spatially complete fields, though the data gaps are small. Before subsampling, data-void regions are filled with an average of data in the neighboring grid boxes. Each average includes the six grid boxes that are zonally, meridionally, and temporally adjacent to the grid box that lacks a value. This is a trilinear interpolation over the two spatial and one temporal dimensions and is done repeatedly until the field converges within the regions that were originally empty.

The EOF modes are orthogonal over the full domain of analysis; that is,
i1520-0493-127-7-1599-e3
where δjk is the Kroenecker delta function and Aj is the norm of the jth spatial mode. When the modes are subsampled over X(m), they lose their orthogonality and a nonorthogonal least squares fit must be used for the projection. The error between the reconstruction of month m and any month of the test bed is
i1520-0493-127-7-1599-e4
where p is the number of modes being tested, M is the number of spatial points in the mth month in the field X(m)n, Ek is the kth spatial EOF mode (the subsampled kth column of K), B is a month of the test bed data, and gkm is the unknown weight for mode k. Minimizing emp with respect to gkm implies for each mode k,
i1520-0493-127-7-1599-e5
Without the subsampling, (3) would hold and the inner summation would reduce to a delta function. The least squares projection is therefore a solution of the matrix equation ETEg = ETb, where E is the matrix of subsampled spatial EOFs Ek(X(m)); b is the vector of SST anomaly data B; and g is the resulting vector of least squares coefficients. The reconstruction of the complete (not subsampled) monthly anomaly field of the test bed is then Kg.
Reconstruction using a least squares fit by definition minimizes the error over the points containing data regardless of how many EOFs are used in the reconstruction. Using a progressively higher number of modes can only decrease the error. Therefore, (4) cannot be used to evaluate the reconstruction and the choice of basis functions. To evaluate the quality of the reconstruction of B(x, t), it is necessary to use a test different than mean-squared differences. LSEA is therefore chosen that examines problems associated with both the data distribution and noise reduction. That is, it explicitly chooses the number of modes that minimizes that variance in the misfit to the large scales (≳2000 km). A smoothed version of the fully sampled test bed (generated with eight passes of a 1–2–1 Hanning filter applied in both the zonal and meridional directions) is subtracted from its reconstruction. The total residual
i1520-0493-127-7-1599-eq1
where Tp is the temperature reconstruction based on p EOF modes, B is the smoothed test bed, and NB is the number of months in the test bed, is examined for increasing p until the first minimum of rT is found. The number of modes Nm in (2) equals p at this minimum. Two examples of this minimization are shown in Fig. 5.
The ratio rT/σB, where σB is the total variance of the smoothed test bed
i1520-0493-127-7-1599-eq2
gives a number that is less than one if the residual contains less variance than the large scales of the test bed. In this case the reconstruction is accepted and αm = 1 in (2). If rTσ−1B ≥ 1, the entire reconstruction for that month is rejected, αm = 0, leaving only the climatology (and running mean) in the reconstruction. This latter condition occurs mostly in the early years, indicated by missing values for the time series of the first EOF in Fig. 6.

Once an optimal number of modes is determined the SST anomalies of the month under consideration are fit to the EOFs using an equation of the form (5), with the test bed data B replaced by the individual monthly summary. Additionally, the time series f from (2) replaces g in (5). This completes the calculation of the reconstructed SST anomalies in the tropical Pacific Ocean following the addition of the climatology and running mean.

4. Results

a. First mode

The spatial structure of the first four EOF modes of the SST anomaly are shown in Figs. 6a,b and Figs. 7a,b. The first mode, representing the ENSO cycle, contains 40.0% of the variance in the OI. This mode is comprised of a large, quasi-elliptical maximum in the central and eastern Pacific. There is also a relatively small region of strong variation extending southward from the equator along the South American coast. The strongest component of the second mode is in this same small region, but with sign opposite to the first mode. The third mode has almost a bipolar structure, with a maximum along the central equator and a maximum of opposite sign south of the equator near Peru and Chile. The fourth mode has multiple poles of positive and negative sign.

The time series for modes 1 through 4 are shown (where a reconstruction was possible) in Figs. 6c–f and Figs. 7c–f. The first mode is used almost continuously from 1868 to 1993. Strong positive values indicate warm El Niño states and strong negative values indicate cold El Viejo states. These events correspond well with those found in previous retrospective studies, as discussed in the next section. Also see Table 1.

New information regarding interdecadal variations of the ENSO cycle (Wang 1995) is revealed. For example, the 1870s show a prolonged cool state, whereas the period 1895 to 1905 experienced a sequence of four large El Niño events, reminiscent of the prolonged warm state in the early 1990s. The 1930s showed relatively weak ENSO activity. The 1877/78 and 1888/89 El Niño events are comparable in magnitude to the 1982/83 El Niño, widely accepted as a milestone event in the modern record. (Table 2 shows the 1877 event to be weaker than the 1888 event due to a 5-month filter.) Such strong events appear to be relatively infrequent. The 1970s have a negative average value, due to a sequence of cold events. This sequence is related to the “climate shift” at the higher latitudes of the North Pacific Ocean (Meyers et al. 1996). A similar sequence of cold events, though relatively weak, also occurs in the 1940s.

The interannual variability can be more accurately examined using wavelet analysis (Grossman and Morlet 1984; Meyer and Ryan 1993; Meyers et al. 1993). The Morlet wavelet projection of the monthly time series for EOF-1 and the extended SOI (Ropelewski and Jones 1987; Allan et al. 1991) are shown in Fig. 8. A similar analysis of SST or SOI can be found in Mak (1995), Wang and Wang (1996), and Kestin et al. (1998).

The annual cycle is removed from both the SOI and EOF-1 time series, so only interannual to decadal variations are examined. The wavelet scale is converted to Fourier period using the projection of Meyers et al. (1993). A wavelength λ projects maximum energy onto a Morlet wavelet scale a as
i1520-0493-127-7-1599-e6
where kc (=5) is an adjustable parameter of the Morlet wavelet. The largest structure in both transforms (Fig. 8) is the 3–9-yr band around 1905–20. The period of this signal decreases with time, starting with maximum energy near the 7–8-yr band. For EOF-1, the amplitude drops to a 6-yr period, while simultaneously picking up energy in the 3–4-yr band. The SOI has a smoother decline to a 3–4-yr period. The secondary peaks largely agree, though there are some differences in period and relative magnitude.

Two important differences occur near 1940 and following 1970. The warm event of 1940/41 is present in the EOF time series, but the interannual variability in the 1940s is weak. The modulus peak during this time is about half the maximum of the peak in the late 1910s. In contrast, the SOI shows a peak in the 1940s about 80% of the 1910s maximum. Both transforms show 6-yr variability in the 1950s, 2–4-yr cycles in the early 1970s, and 3–5-yr cycles in the 1980s, with some differences in duration and spectral evolution. In the EOF time series, the magnitude of the 1970s peak is comparable to the 1940s peak; whereas in the SOI the 1970s is 80% of the large maximum. The 4-yr cycle in the 1980s is about 15% larger than the 1940s peak in the EOF time series, as opposed to being 86% of the 1940s peak in the SOI. Around 1890 there is a 3–4-yr variation in both transforms, but the EOF time series lack the 4-yr peak around 1880 that is present in the SOI.

b. Higher modes

The second EOF basis mode, containing 10.8% of the OI variance, is not always justified. It is rarely used in years before 1880, in the mid-1890s, and 1910s. In later years it is used almost continuously. This mode is not associated with ENSO because of its emphasis on near-coastal and nonequatorial variations. Modes 3 and 4, 7.3% and 3.6% of the OI variance, respectively, are essentially unused before the early 1920s, but are selected almost continuously after 1925. The maximum amplitudes of these modes, given by the product of the time series and the eigenfunction, are less than half that for modes 1 and 2, and thus contribute relatively less to the behavior of the final SST fields. Neither of these modes is associated with ENSO, though mode 3 does contain a strong equatorial component. Higher modes generally contain higher wavenumber components and contribute even lower amounts of variance to the reconstruction.

The total number of modes justified by large-scale error analysis is indicated in Fig. 9. Until about 1925 the typical number of modes that are determined to be useful is generally less than 10 and is sometimes zero. The 1930s are able to support between 10 and 20 modes, followed by a drop during WWII. In all the years after 1950 our technique used over 20 modes for projection, with a final plateau attained in the 1960s between 40 and 50 modes. This variation is roughly proportional to the spatial coverage of the observations (Fig. 2). As the coverage increases, more details of the SST field are revealed and a greater number of EOF modes are able to accurately represent the field without overfitting.

c. Examples of reconstruction

Two illustrative examples of the final SST monthly reconstruction are shown in Fig. 10. The first is a relatively recent sample from September 1970, when most (about 80%) of the grid boxes contain measurements. The sampling bias toward shipping lanes in the raw data can be seen in a radiating pattern extending, for example, from Hawaii. The level of instrumental noise at scales of the grid box is comparable to the magnitude of the large-scale pattern. A general trend toward positive anomalies can be seen in the east equatorial region. In this case 47 EOF modes are used for reconstruction of the SST. Choosing this limited number of modes eliminates the small-scale noise present in the raw anomaly data. The empty grid boxes are filled and the large-scale pattern is revealed.

The second case is from a sparse month (about 10% coverage), November 1941, near the end of an El Niño. Only a few measurements along ship tracks were taken during this month; the initial measurement field is almost empty. Little can be said regarding the large-scale or ENSO condition from the raw data. The projection onto a few EOFS, in this case seven, yields a spatially complete field with a physically realistic structure concentrated around the equatorial region. The first example with 47 modes, contains more off-equatorial structure. The technique presented above recreates the SST field with realistic spatial and temporal structure, even in observation-sparse months.

5. Discussion and summary

The mode reconstruction technique is superior to a traditional interpolative reconstruction using smoothing or a polynomial fit, which would lose accuracy in the data-void regions. The modal technique also suffers due to regions of sparse observations, since the fit of each spatially complete mode is biased toward regions with high concentrations of data. However, the spatial modes contain more realistic spatial structure that is not introduced using interpolative methods.

Smith et al. (1996) and Smith et al. (1998) also used the OI SST data to generate an EOF basis. The former projected onto the 2° COADS and the latter projected onto an updated version of the 5° GOSTA SST (Bottomley et al. 1990). Kaplan et al. (1998) also projected their EOF functions onto GOSTA SST, and from which they generated their basis functions. Here, a version of the COADS SST is used with the spatially average bias removed from different time intervals. This largely eliminates multidecadal variations and focuses the results onto the ENSO (interannual) to decadal timescales.

Anomalies of the COADS SST are computed in several steps. First, the Reynolds and Smith (1995) climatology is removed from the COADS. Then, instrumental bias as represented by a series of step-functions was subtracted (Fig. 4). Last, a 14 yr plus 1 month running mean is removed. Once the EOFs are generated, SST anomalies in the tropical Pacific Ocean are projected onto the variable basis set of EOF functions to produce a collection of SST fields from 1868 to 1993.

Our technique, LSEA, for choosing the variable EOF basis is fundamentally different from others who used a fixed number of modes (Smith et al. 1996; Rayner et al. 1996; Kaplan et al. 1998). The number of modes in our reconstruction is allowed to vary with time. A mode selection criterion is used based on a statistical analysis of a known dataset: the misfit to the large-scale field of a test bed (the entire 1970s) of COADS SST anomalies is minimized. Smith et al. (1998) also used a variable number of modes; their selection criterion was based on the location of the observations with respect to the loading of their EOF spatial functions. The GISST3.0 reconstruction used a variable number of modes based on a combination of objective and subjective criteria (N. Rayner 1998, personal communication).

It is unclear which reconstruction method is more accurate. On one hand, allowing the number of modes to vary might introduce undesired temporal noise (which might be decreased using an appropriate temporal filter). On the other hand, fixing the number of modes forces the acceptance of unsupported modes, possibly introducing errors into the reconstructed spatial patterns due to overfitting.

Once the modes are selected they are least squares fit to the SST anomaly data (5). The resulting coefficients fmk in (2) form time series that represent the strength of each mode k in month m. The time series from the largest variance EOF corresponds to an ENSO index. Most of the ENSO extremes indicated by the SOI and EOF-1 are coincident (Figs. 6c,d). The linear correlation of the SOI with the EOF-1 index is −0.7 after a 5-month running mean is applied to each time series. Even in the 1880s, when very few data are available, there is general agreement between the extremes. There are occasional disagreements of phase, such as in 1907/08, as well as relative amplitude, such as in 1890. Most of the differences exist in the years prior to 1920. A wavelet analysis quantifies the variations of the ENSO cycle (Fig. 8).

Kiladis and Diaz (1989) list starting years of ENSO events based on a composite of the SOI and eastern equatorial Pacific SST. All their El Niño events are associated with positive values of the time series for the first EOF (fm1), though not every positive peak of fm1 is associated with their warm events. Many of their cold events are associated with negative fm1, but there are several instances where the cold events of Kiladis and Diaz (1989) do not obviously coincide with negative fm1. The reason for these discrepencies is not clear. There may be differences due to their choice of indices, or by a failure of our technique to work in the data-poor times of the late 1800s and early 1900s. Table 1 lists the ENSO events using the time series for EOF-1, those listed by Kiladis and Diaz (1989), and by Quinn et al. (1978, hereafter Q78).

The ENSO index created here is similar to the Niño3.4 indices created by K98, S98, and GISST3.0 (Table 2), with a few months difference in the timing of some events (e.g., 1868, 1891). Additionally, there are significant differences in the relative magnitudes of many of the ENSO extremes. (Table 2 uses normalized indices because each index is based on different datasets and is with respect to different climatologies.) There is greater consistency between our EOF-1 index and that of K98 and GISST3.0, than between S98 and the other reconstructions. Nearly all the premodern warm events detected by our method are also detected by K98 and GISST3.0. An exception is the 1913 event, which does not have a distinct maximum in the reconstruction of K98. The El Niño events of 1940 and 1941 are also points of disagreement. The EOF-1 index shows the 1940 event to be much weaker than the 1982/83 event and the 1941 event to be of moderate strength. In contrast, the K98 index indicates both are strong events and the GISST3.0 indicates the 1940 and 1941 events are strong and moderate, respectively. S98 indicates both events had moderate strength.

Assessing the accuracy of the different techniques is confounded by the lack of sufficient objective data in the pre-WWII era. One of the few efforts to quantify the ENSO cycle in these early years was done by Q78. All the warm events indicated by EOF-1 are found in the Q78 analysis. The K98 analysis misses the 1913 event and S98 and GISST3.0 both appear to miss two events. None of the analyses suggest 1891 was nearly as strong as indicated by Q78.

There is only moderate consistency between the strength of the reconstructed events and the Q78 index. For example, the 1877 event, given a level 4 by Q78, is found to be strong in several of the reconstructions. The level 4 event in 1891 is found to be very weak in all the reconstructions. On average, the weakest El Niño events (level 2 of Q78) have the lowest normalized value of reconstructed SST (Table 3). However, all reconstructions give the same value for the level 3 and level 4 events, within one standard deviation. This disagreement could be due to biases in the datafields used for the reconstruction or due to uncertainties in the Q78 index. Further analysis of the accuracy of the reconstructions will be pursued in a later article.

Another method for understanding long-term ENSO variability is explored by Caron and O’Brien (1998). They created a synthetic time series based on the spectrum of the temporal functions for the first few EOF modes. This yielded spatially complete monthly SST fields of arbitrary duration. However, they cannot match their results to any particular year, since the technique involved randomization of phase. The synthetic temperature fields of Caron and O’Brien (1998) might serve as a database for testing the various reconstruction techniques (as suggested by an anonymous reviewer). Those fields are spatially complete. Subsampling a hundred or more years of the synthetic SST according to patterns found in COADS would allow direct testing of the various reconstruction schemes on realistic data.

Acknowledgments

The Center for Ocean–Atmosphere Prediction Studies received its base support from the Secretary of the Navy Chair awarded to J.J.O. by the Office of Naval Research, from NOAA-OGP for TOGA, and from the oceanography section of NASA Headquarters. Thanks to Tom Smith and Nick Rayner for providing Niño3.4 indices. Thanks to Drs. David Legler and Mark Bourassa for their help with the manuscript.

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Fig. 1.
Fig. 1.

Domain of analysis.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 2.
Fig. 2.

Monthly percentages of 2° boxes inanalysis region containing SST data.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 3.
Fig. 3.

A comparison of the 3.5σ and 4.5σ trimmings of extreme outliers in the COADS SST in the analysis region. The number of observations retained each month is plotted for each trimming as obtained from the COADS.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 4.
Fig. 4.

The estimated bias in SST measurements. The monthly spatial averages of SST are in red (only 1 out of every 4 months is plotted for clarity). Other lines are as labeled: the monthly SST averages are smoothed with a 14 yr plus 1 month running mean. The straight lines represent the biases of the different time periods. Also shown are the monthly SST averages with the estimated bucket bias removed before smoothing.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 5.
Fig. 5.

The normalized residual (small-scale variance of the test bed divided by the variance of the complete test bed rT/σB) for varying number of modes. Two different months from the reconstruction are shown. The minimum (black diamond) gives the number of modes for the reconstruction of the month being examined.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 6.
Fig. 6.

(a) EOF-1 (40% of the variance) and (b) EOF-2 (10% of the variance) of the OI SST are normalized by the largest absolute value in each. (c) and (d) The time series for EOF-1 (fm1) from the monthly least squares fit to COADS SST when the reconstruction is possible. ENSO extremes are indicated by black filling between the curve and ±0.5°C. Each “∼” denotes the first extreme ENSO year of the Kiladis and Diaz (1989) determination of warm (red) and cold (blue) ENSO events. The negative SOI smoothed with three 1–2–1 Hanning windows is pink. (e) and (f) The monthly time series for EOF-2 (fm2). Blanks indicate the mode was not used in the reconstruction.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 7.
Fig. 7.

As in Fig. 6 but for modes 3 and 4, with 7.3% and 3.6% of the variance, respectively.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 8.
Fig. 8.

The modulus of the Morlet wavelet transform of (a) the time series for the first EOF (fm1) and (b) the extended SOI from Allan et al. (1991). Colors indicate amplitude: black indicates zero and white the maximum, as indicated by the color bar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 9.
Fig. 9.

The number of spatial EOF patterns, Nm, usedin reconstruction of the monthly SST.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Fig. 10.
Fig. 10.

A comparison of two raw COADS fields with the Reynolds and Smith (1995) climatology removed. Empty grid boxes are shown in black. (a) Good data coverage with data in 84% of the oceanic grid boxes; (c) poor coverage with data in only 12%. This is the smallest amount of data in any COADS field during the data sparse 1940s. Fields (b) and (d) are reconstructions of these fields using a fit of the first few EOFs from OI SST. The number of EOFs used in each fit is noted in the margin.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1599:ROMSIT>2.0.CO;2

Table 1.

Starting years of warm and cold ENSO events. This study defines a warm (cold) event as at least consecutive months of +0.5°C (−0.5°C) of the time series of EOF-1 after smoothing with a 5-month running mean. The second and third columns list the events from Kiladis and Diaz (1989) (KD89) and Quinn et al. (1978) (Q78), respectively. The fourth and fifth columns list cold events from this study and from Kiladis and Diza (1989), respectively.

Table 1.
Table 2.

Comparison of the El Niño events before the modern era from Quinn et al. (1978) (Q78, their Table 1) and the different long-term SST reconstructions. Year the events started, month/year of maximum index value, and relative magnitude of the maximum are shown. Each index is normalized such that the 1982/83 peak is 1.0. Our index is the timeseries of EOF-1. The Niño3.4 indices are from Kaplan et al. (1998) (K98, via WWW), Smith et al. (1998) (S98), and GISST3.0. A 5-month running smoother has been applied to all indices. NM indicates no maximum, but with relative amplitudes above 0.2. The dash indicates no maximum and vales are ⩽0.2.

Table 2.
Table 3.

Average and standard deviation of peak El Niño intensities from Table 2 compared to Quinn et al. (1978).

Table 3.
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