1. Introduction
Since the start of the Tropical Ocean Global Atmosphere (TOGA) program, there has been substantial progress in forecasting the El Niño–Southern Oscillation (ENSO; e.g., Latif et al. 1998). Numerical models are now able to perform considerably better than persistence in forecasting standard ENSO indices at lead times of 6–12 months. Given this progress, operational ENSO prediction systems have been established at weather forecast centers such as the National Centers for Environmental Prediction (NCEP). In such systems, the initial state of the atmosphere is taken from an operational weather analysis while oceanic observations are used to estimate the ocean state through ocean data assimilation. Of course, such forecast tools are in constant development, evolving as our understanding of climate physics improves and as the number and kind of observations used to determine the initial conditions changes.
The major components of the ocean observing system for ENSO prediction are the Tropical Atmosphere Ocean (TAO) array of moored buoys, the Volunteer Observing Ship expendable bathythermograph program, and satellite observations of sea surface temperature (SST) and sea level as observed by the TOPEX/Poseidon satellite altimeter [T/P; see McPhaden et al. (1998) for details]. Recent experiments with an ocean data assimilation system designed to correct temperature have revealed large discrepancies between different ocean analyses and between the analyses and observations depending on whether T/P sea level data are assimilated (Ji et al. 2000). The origin of these differences is believed to be related to the uncorrected salinity field in the ocean model. The use of sea level in an assimilation system that corrects only the temperature field neglects the fact that sea level is determined by salinity as well as temperature. In the western tropical Pacific Ocean, the influence of salinity on sea level variability is strong enough to be detectable by an altimeter (Delcroix et al. 1987; Maes 1998). This would suggest that to get an estimate of the ocean state that captures the correct relationships among temperature, salinity, and sea level, the assimilation system must correct both temperature and salinity. The expectation is that a more accurate and consistent estimate of the ocean initial conditions in the western tropical Pacific, where we expect to find precursors of ENSO events, would lead to improved predictions.
Any effort to correct the salinity field through data assimilation must confront the current scarcity of direct observations of salinity. While there are efforts now under way to increase the rate of measurement of sea surface salinity (SSS) by employing satellites (Lagerloef et al. 1995) and volunteer commercial vessels (Delcroix and Hénin 1991; Hénin and Grelet 1996; Hénin et al. 1998) and of subsurface salinity by equipping autonomous drifting floats with salinity sensors (Davis et al. 1992), the salinity field is likely to remain poorly sampled for some time to come. In the subsurface, some efforts are also in progress, in particular for the western Pacific Ocean using the TAO array infrastructure (Cronin and McPhaden 1998). Nevertheless, it is therefore worthwhile, especially for operational needs, to consider indirect methods for determining the salinity field. If temperature observations are available, a simple approach would be to construct a salinity profile based on the local correlation between temperature and salinity (T–S relation) derived from climatological data (Stommel 1947). For this method to work well the T–S relation must be relatively stable. Moreover, it assumes that the depth of the mixed layer is the same for both temperature and salinity, an assumption that does not hold up everywhere: it fails, for example, in the western tropical Pacific Ocean (Lukas and Lindstrom 1991). Complicating the matter further, Donguy (1994) and Ando and McPhaden (1997) have shown for the same part of the ocean that the relationship between the mixed layers for temperature and salinity varies at the ENSO timescale. To deal with the variability of the T–S relation near the surface, extensions to this simple method have been developed that make use of additional fields such as SSS (Kessler and Taft 1987), or sea level and SSS (Vossepoel et al. 1999). These methods, however, do not take into account the deep variability of the salinity field, which may be important at ENSO timescales.
In the present study, we will present another approach to reconstructing the vertical profile of salinity. In this method, a linear combination of predetermined, coupled modes of temperature and salinity are fitted to the available data in a weighted, least-squares sense. The weights, in principle, represent inverses of the data error variances, where the errors in this context should include the representativeness of the data relative to the time and space scales of the profiles we are trying to reconstruct. In practice, the weights have been determined empirically during the process of tuning the method, taking care that they remain within sensible bounds. We have applied the method in the western tropical Pacific Ocean along 165°E where we have been able to take advantage of a reasonably large set of conductivity–temperature–depth (CTD) data as well as the TOGA–TAO array.
This paper is organized in the following way. In section 2, we will discuss the different datasets used to illustrate the method and to cross validate the results. In section 3, we will present the method. In section 4, we will examine a reconstruction of salinity variability using temperature data from the TAO array and provide some evidence that the method is able to give consistent reconstructions of temperature, salinity, and dynamic height. In section 5, we will conclude with a discussion of the results.
2. Data
a. The 1984–92 CTD dataset
The CTD casts were collected by several independent research programs that conducted oceanographic cruises along 165°E, mainly during the TOGA period. These data have been compiled and provided to us by the SURTROPAC team of ORSTOM-Nouméa. The meridional interval between casts is typically 1°, but it is reduced to ½° within the equatorial band (3°N–3°S). Detailed information on the data, data processing, and other applications can be found in Delcroix et al. (1992) and in Gouriou and Toole (1993). These data are used to compute the coupled modes of temperature and salinity variability. The full set of 778 profiles within the 10°S/10°N band along 165°E has been subsampled within 1° of each TAO mooring location and deviations from the local averages are computed in a manner similar to that described by Maes (1999).
b. The temperature profiles from the TAO array
The temperature data from the TAO array are collected and made available by the National Oceanic and Atmospheric Administration (NOAA) Pacific Marine Environmental Laboratory (Internet address: http://www.pmel.noaa.gov/toga-tao). The data locations along 165°E are at 8°N, 5°N, 2°N, the equator, 2°S, 5°S, and 8°S, and at several depths from the surface down to 500 m. A complete description of the array components and of the technical and historical background is given by McPhaden et al. (1998). Some of the time series began in 1985 but the complete array along 165°E was not available before the beginning of the 1990s. At any location some data may be missing for periods of 1 day up to several weeks due to instrument failure or mooring loss. The data used in the present study are daily averages of temperature and the uncertainty in these values due to instrumental error is small. However, our goal is to reconstruct salinity profiles representative of ENSO timescales and thus the weighting used in the least squares fitting procedure should reflect the uncertainty of using daily data as a measure of variability at longer timescales. Finally, the method uses deviations of temperature from the mean and these are constructed relative to the 1986–96 period.
c. Validation datasets
The present method computes coupled modes of temperature and salinity variability from CTD profiles. Once the modes have been determined, the goal is to reconstruct the salinity field using temperature data without further resort to direct observations of salinity itself. Three datasets are used for validation.
The original CTD measurements from which the modes were computed are used first to check for consistency. In other words, when the modes are fitted only to the temperature profiles, are the salinity profiles reconstructed with good accuracy?
Next, the monthly SSS analyses produced by Reynolds et al. (1998) are used in an independent check. These analyses are based on bucket and thermosalinograph measurements collected by the ORSTOM (Delcroix and Hénin 1991; Hénin and Grelet 1996; Hénin et al. 1998). We use the analysis that is an optimal interpolation of SSS anomalies starting from a first guess of zero. The total deviation field is then determined by adding to this a modified climatological seasonal cycle of Levitus et al. (1994). The climatology has been locally smoothed to reduce month-to-month noise by fitting mean, annual, and semiannual harmonics to the monthly fields. The resulting anomaly is then smoothed by applying a 3-month running mean and averaging to a 2.5° grid, so this estimate will be useful only for examining the low-frequency variability of SSS reproduced by the method.
A third check, which is also independent, is made by comparing dynamic height computed from the reconstructed temperature and salinity profiles with sea level observations from the Geosat and T/P altimeters. These observations are expressed as time series of sea level deviations with respect to a given time period, averaged at 1° lat intervals along the satellite track. The data processing is discussed by Miller and Cheney (1990) and by Cheney et al. (1994) for the Geosat and T/P missions, respectively. Only the more accurate T/P data will be used in quantitative comparisons. The T/P deviations are relative to the January 1993 through December 1995 period. Here the word deviations refers to departures from the overall mean for the period, whereas the word anomalies would refer to departures from the monthly means for the period.
3. Methodology
a. Predetermined vertical structures
The method begins with the computation of characteristic vertical structures of temperature and salinity. These are represented by coupled empirical orthogonal functions (EOFs) of temperature and salinity. Past studies of dynamical processes in the vertical have used EOFs based on a variety of datasets from time series recorded at individual moorings (Hayes and Halpern 1984; McPhaden 1996), to CTD profiles collected on regional cruises (Mercier and Colin de Verdière 1985; Gavart and De Mey 1997), to datasets assembled to represent whole basins (Fukumori and Wunsch 1991). Vertical EOFs also represent an efficient tool for reducing the order of the problem of data assimilation into numerical ocean models, particularly in its application to altimetry [see DeMey (1997) for a review].
Coupled EOFs of temperature and salinity are computed at each TAO mooring site using only the CTD profiles collected within ±1° lat of that location. The number of profiles used at each position is listed in Table 1; with the exception of the site at 8°N these numbers range between 90 and 110. The modes are computed from the deviations of the temperature and salinity profiles relative to the 1984–92 period. Because we are interested in their respective contribution to the density field, we scale the temperature profiles by the coefficient of thermal expansion and the salinity profiles by the coefficient of saline contraction (Maes 1999). Thus, the EOFs are the eigenmodes of the covariance matrix calculated from the scaled profiles. The structures of the first six modes at 2°S are shown in Fig. 1; the structures at the other mooring locations are similar. The largest amplitudes for these modes occur in the thermocline (halocline) or at the surface, while amplitudes below 300 m are uniformly small. Table 1 lists the number of modes (six or seven) retained at each location for the remainder of this study and the cumulative variance in temperature and salinity that they can explain (typically in excess of 80%). In a separate study, Maes (1999) has shown that the rms difference between dynamic height computed from the original data and the dynamic height reconstructed from the first several modes ranges from 1 to 3 dyn cm between the equator and the subtropics.
b. Minimization method
In the cost functional, the first term expresses the proximity of the modal reconstruction to the observed temperature data. The second term provides a constraint on the salinity part of the modes in the absence of salinity observations. Through the selection of the weight, ws, this term controls how much the reconstructed salinity deviations will depart from zero or, in other words, how close the total reconstructed salinity will be to its climatological mean value. Such constraint is necessary, in principle, because the temperature and salinity modes are coupled and applying a constraint to both variables is necessary. In practice, if the second term is neglected the resulting salinity reconstructions may take on unreasonable values.
The weights, wt(k), should reflect the uncertainty in the observed temperature deviations and could be set equal to the inverse of the error variance, scaled by α2. On the other hand the weights, ws(k), should reflect the full variability of the salinity deviations, not just the uncertainty, and could be set equal to the inverse of the estimated variance of that variability, scaled by β2. In practice, the weights were tuned somewhat as we experimented with the method, but care was taken so that they remain within reasonable bounds. For this study we have used 0.5°C and 1.0°C as estimates of the standard deviations of the uncertainty in the surface and subsurface temperature deviations and 0.6 psu as an estimate of the standard deviation of the variability in the deviations of salinity. With these choices the ratio of the weights, wt(k = 0)/wt(k > 0)/ws(k), is 4/1/1.
The minimization is obtained by solving the system of linear equations, which results from setting ∂F/∂cn = 0. Because we retain only the dominant modes for the reconstruction, the number of equations is small (n < 10) and the computational burden is slight. Next, we consider the results and their validation through comparisons with independent data.
4. Results
In the present study, we fit the vertical EOF modes computed from the CTD profiles to temperature deviations computed from measurements made with the TAO array at 165°E. One immediate difficulty is that the method works with deviations relative to a mean period. The mean profiles of temperature from the TAO and the CTD data are not identical, mainly due to sampling differences. There is no obvious solution to this problem. Simply using the mean profile from one source or the other is not satisfactory: on the one hand, the CTD mean profiles could be aliased by undersampling, while on the other hand, the TAO array cannot provide a mean salinity profile. The deviations of the TAO temperature profiles have been expressed as departure from the 1986–96 mean period in the 〈2°N–2°S〉 band, and from the 1990–96 mean period elsewhere.
a. Determining the number of modes
We begin by determining the number of modes to retain in the reconstruction. We base the decision on the overall goodness of fit, as measured by the rms residual between the reconstructed and observed temperature deviations. Figure 2 shows these rms residuals for the surface and subsurface (as given by the TAO moorings) as a function of the number of modes retained. Increasing the number of modes in the reconstruction will obviously decrease the residuals, but there are two distinct jumps: one between modes 2 and 3 and the other between modes 5 and 6. When 6 or more modes are retained the rms residual at the surface is less than 0.1°C and for the rest of the profile it falls below 0.5°C. These values are well below the overall rms variability of the temperature. For the remainder of this study we will consider reconstructions of temperature and salinity profiles based typically on six modes. Table 1 lists the specific numbers for each of the TAO locations along 165°E. Note that seven modes are retained at the equator and that they explain less of the variance than six modes explain at sites off the equator; the need for additional modes to capture the equatorial variability is consistent with a study by Dewitte et al. (1999) based on dynamical modes.
b. Comparison with CTD data
A comparison of the TAO-based reconstructions with the CTD profiles is not an entirely independent check because the modes were originally computed from that data. Nevertheless, the full set of reconstructed profiles was subsampled to select those that correspond in time and location with the CTD profiles. There were 11 or more corresponding profiles at the TAO sites between 5°N and 5°S and comparisons were made at those locations. Table 2 lists the rms errors between the reconstructed and CTD profiles at the surface and for the 100–300-m depth range. One should note that the surface values are also representative of the upper layers (i.e., 100 m or less). In general, the rms differences in SSS are about 0.3 psu at the surface and less than 0.1 psu for the subsurface salinity. Rms differences for the temperature are 0.25°C and 0.6°C for the surface and subsurface, respectively. The number of samples in these statistics is relatively small and they might not be stable. For example, the largest rms SSS difference (0.5 psu at 2°N) is mainly the result of a few large differences between the reconstruction and the CTD data at the end of the 1989. These errors are also similar to the errors reported by Maes (1999). In any case, the rms differences listed in Table 2 are less than the total variability of the observed salinity as shown in Figs. 3 and 4a.
Figure 3 shows the reconstruction of SSS and the original values from the CTD at each location. It is clear that the SSS reconstruction is reasonable. The differences may be due in part to the neglect of higher modes in fitting the data and also in part to the coupled nature of the modes such that errors in the fit to temperature will be projected onto the salinity reconstruction. Nevertheless, although the TAO-based SSS reconstruction exhibits some high-frequency variability that is difficult to interpret [see Cronin and McPhaden (1998) for more details], it is clear from Fig. 3 that the low-frequency variability that would be relevant to ENSO is captured by the present method.
Figure 4 shows the rms variability of the CTD salinity and reconstructed salinity as a function of depth and latitude. To include as much data as possible in these estimates we used the period 1984–92 for the CTD data and the period 1986–97 for the reconstruction. The rms structures for the CTD dataset has been discussed in some detail by Delcroix and Picaut (1998). Hereafter we focus only on the ability of the method to reproduce these observed patterns. The overall distribution of the salinity variability is similar for the two datasets with larger values (>0.5 psu) occurring in the equatorial surface waters. North of 4°N, the variability in the reconstructed salinity is stronger between 50 and 100 m than it is above 50 m. This feature is not nearly so well identified in the CTD salinity although there is a suggestion of it north of 8°N. This difference may be related to the strong seasonal cycle present in the reconstruction that is associated with the latitudinal displacement of the intertropical convergence zone. As the oceanographic cruises usually took place twice a year, we suspect that this part of the salinity variability has been largely missed by the CTD data. Below 100 m, the variability in both datasets is less than 0.2 psu, except in the Southern Hemisphere where values larger than 0.2 psu occur near 200 m at the depth of the main halocline. This signal is particularly interesting because it is difficult to obtain it with a T–S relationship (Femke Vossepoel 1998, personal communication), and because it is related to the dynamic height signal reported by Ji et al. (2000). Figure 5 shows the time series at 165°E–8°S of the deep salinity deviations (100–300 m) reconstructed by the method for the 1993–98 period. Even if the number of CTD data is relatively small, it is obvious that the variability reproduced is quite similar. In particular, there is a strong positive signal starting by mid-1995 to the end of 1997 with a maximum amplitude of 0.2 psu in 1996. It will be shown that the related signal in sea surface height is not negligible (see the discussion and Fig. 9).
c. Comparison with independent SSS
A comparison of the SSS variability in the present reconstruction with the variability in the independent analysis of Reynolds et al. (1998) is shown in Fig. 6 for the 1986–97 period. At the ENSO period, both analyses show similar features with large positive deviations in 1988–89 and in 1996, and large negative deviations in 1987 and in the 1992–94 period. These features are well correlated with the Southern Oscillation index (SOI), which gives an integrated idea of the ENSO conditions. The reconstruction is also able to reproduce the seasonal cycle in the Northern Hemisphere, within 5°–10°N, in agreement with climatological evidence (Delcroix and Henin 1991). However, Fig. 6 indicates clearly that the SSS variability in the reconstruction is strongly confined between 4°N and 4°S, while this is not the case for the Reynolds et al. (1998) analysis. It is suspected that these differences may be due to the heavy smoothing in the Reynolds et al. (1998) analysis made necessary by the scarcity of SSS observations. Referring back to Figs. 3 and 4, it can be seen that for the CTD data as for the reconstructed data the strongest SSS variability is confined to the equatorial band.
d. Comparison with sea level
Independent satellite observations of sea level variability provide another means for checking the reconstructed temperature and salinity. In the Tropics, the variability of the dynamic height may be compared to the sea level given by an altimeter as both the barotropic signal and the variability below 600 m can be neglected (Chao and Fu 1995; Picaut et al. 1995). This check is important because there is no constraint on the dynamic height in the minimization.
Figure 7 shows the sea level deviations along 165°E as given by the Geosat (1986–88) and T/P (1992–97) altimeters and by the dynamic height deviations computed from the reconstruction of the temperature and salinity fields from TAO profiles (1986–97). The agreement among the different time series is generally good (the correlation coefficients are larger than 0.8), and the reproduced variability is in phase with the low-frequency ENSO variability as represented by the SOI index. In particular, strong minima occur in 1987 and in 1997 associated with the mature phase of the El Niño event, characterized also by a low value of the SOI. On the other hand, between 1995 and the beginning of 1997, the western Pacific shows generally positive deviations in sea level that are largest in the subtropics.
We next make a closer comparison between the variability in the reconstructed dynamic height and the variability in T/P sea level. Because our interest here is in the low-frequency variability of the ocean, the T/P time series has been smoothed by a 60-day hanning filter. The time series for the filtered T/P sea level deviations and dynamic height reconstruction are shown in Fig. 8 at the TAO sites along 165°E. Summary statistics are listed in Table 3. Correlations between the time series are generally high with correlation coefficients better than 0.8 and the rms differences range between 2.5 and 3.8 cm. Overall the standard deviations for the two kinds of time series are similar, although the standard deviations for the T/P data show a more distinct minimum at the equator. To explain some of the residual differences, we offer two possibilities. First, because only six modes have been retained as the basis for the reconstructions, any variability represented by higher modes will be lost. Second, the modes have been computed from CTD data for the period 1984–92 and they may not representative of all of the possible variability outside of that time period. This may well be the situation during the big drop in sea level at the end of 1997, when the T/P sea level is systematically lower than the dynamic height. More observations, however, would be required to verify whether the structure of the EOFs would change significantly during this period, characterized by some of the strongest changes ever reported.
5. Discussion
In this study we began with the idea that the variability of temperature and salinity in the ocean are sufficiently coupled so that given observations of the temperature field, all or part of the salinity field might be reproduced. The idea, of course, is not new; climatological T–S relationships have been used for this purpose for some time. However, we have taken the idea a step further; instead of representing the relationship between temperature and salinity at any location with a single profile of temperature versus salinity, we have represented the deviations of temperature and salinity from their means as a set of coupled vertical empirical orthogonal functions. These functions then form the basis for a weighted least-squares procedure that reconstructs salinity profiles from observed temperature profiles. The main advantage of our approach is that it does not consider a fixed T–S relationship in time but allows different combinations between the dominant modes. This depends on the observed features (which are reconstructed), and thus takes into account the observed variability in time. However, for the method to be useful there must be adequate observations from which to compute EOFs that capture the timescales of interest, which, in the present case, are seasonal to interannual. The representation of such variability by a few modes extracted from a relatively short dataset (i.e., the CTD) suggests several potential problems. The first concerns the stability of the modes. Different tests show that the vertical structures were robust, and due to the large interannual variability associated with the ENSO events in part. The second concerns the extension of the present method to different parts of the tropical Pacific Ocean. Preliminary results indicate that the density of the CTD data is sufficient to determine the vertical modes. Nevertheless, the determination of the modes in the other regions of the global ocean may be more critical and will certainly deserve more attention.
We have specified the weights used in the minimization based on very simple estimates of the errors in temperature and the variability in salinity. Likewise, we took a simple approach in determining the number of modes retained in the analysis. This was simply to repeat the analysis, increasing each time the number of modes, until the residual error in the fit to temperature fell below a specified level. The level of the residual error was chosen to ensure that the reconstructed temperature variability could resolve the ENSO signal. A more careful and complicated approach could be taken with respect to these issues and it might provide some benefit, but for the purpose of demonstrating the method, our simple approach has been adequate.
We have tested the method in the western equatorial Pacific Ocean, a region where there is evidence that the variability of salinity plays an important role in the variability of sea level. This is also a region where the ability to accurately estimate the ocean state has important ramifications for short-range climate forecasting. As a practical matter we chose a section at 165°E, between 8°N and 8°S, where there are a relatively large number of CTD casts of known high quality and long time series of temperature profiles from the TAO array. In this location, the method has been successful in reconstructing the variability of salinity at annual to ENSO timescales. We have demonstrated this directly through comparisons with independent analyses of SSS and indirectly through comparisons with independent satellite observations of sea level.
These comparisons demonstrate that the present estimate is consistent, especially between the resulting dynamic height and the T/P variabilities. The evidence provided here shows that the differences revealed by Ji et al. (2000) are due to the neglect of the salinity variability. The full impact of the salinity field along 165°E for the 1986–97 period may be addressed from Fig. 9. This figure shows the difference between the reconstructed dynamic height anomaly and a second computation, in which reconstructed temperature profiles are retained while estimated salinity profiles are replaced by mean profile. Here, the mean salinity profiles are the temporally averaged over the 1984–92 period from the CTD dataset but retain their changes with latitude. These differences are in agreement with similar results reported by Maes (1998). In the equatorial band, the salinity impact in well correlated with the SSS changes (Fig. 6) and corresponds to a signal trapped in the mixed layer (figure not shown). In the south, the surface changes are not sufficient to explain completely the differences. The variations from +5 dyn cm in 1992 to −5 dyn cm in 1996 are also due to the variability of the subsurface high-salinity tongue (revealed by the large rms between 150 and 250 m in Figs. 4 and 5). This signal exhibits a pronounced variability at the interannual timescales in agreement with the results reported by Kessler (1999).
The work presented here is a beginning and it can be extended in a number of ways. First, there is the question as to whether the historical database of temperature and salinity profiles is adequate for computing the EOFs in many other areas, thus permitting a global application of the method. Second, the cost function used in the minimization could be modified to include other constraints. For example, satellite observations of sea level could be included as a constraint on the dynamic height computed from the reconstructed temperature and salinity. Finally, the method suggests an indirect way of correcting salinity in ocean data assimilation systems when ample observations of temperature and sea level are available but salinity observations are scarce. Work on all of these issues is currently under way.
Acknowledgments
The authors want to thank the different data providers, namely Christian Hénin and the SURTROPAC team (ORSTOM-IRD), Robert Cheney (NOAA LAS), and Michael McPhaden and the TAO group (NOAA PMEL). The illustrations in this study have been made with the Plot-Plus graphics software (many thanks to its author D. W. Denbo). Results of this research, vertical profiles of temperature and salinity along 165°E, are available to the oceanographic community by request. For more information, please contact the authors. This research was supported in part by an appointment to the National Centers for Environmental Prediction, administered by the University Corporation for Atmospheric Research.
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Characteristics of the modes along 165°E retained for the fit to the TAO temperature profiles. The EOF computation is based CTD casts within approximately ±1° lat of the TAO buoys.
Estimations of the rms difference between TAO-based reconstructions and CTD measurements of temperature and salinity for the 1986–92 period. Units are in °C for temperature and in psu for salinity. Data in common means observations from both TAO and CTD were present at the same date.
Standard deviations of T/P data and reconstructed dynamic height, correlation coefficients, rms differences, and number of data used to determine these differences at the different TAO moorings along 165°E. Data in common means observations from both TAO and CTD were present at the same date.