JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C9, 3297, doi: /2002jc001745, 2003

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C9, 3297, doi: /2002jc001745, 2003 Three-dimensional analysis of temperature and salinity in the equatorial Pacific using a variational method with vertical coupled temperature-salinity empirical orthogonal function modes Y. Fujii and M. Kamachi Oceanographic Research Department, Meteorological Research Institute, Tsukuba, Ibaraki, Japan Received 15 December 2002; revised 9 June 2003; accepted 12 June 2003; published 17 September [1] A method of analyzing salinity, as well as temperature, is adopted in the equatorial Pacific. It is a three-dimensional variational method with vertical coupled temperaturesalinity empirical orthogonal function modes. The salinity field is estimated from temperature observation alone such that the surface dynamic height calculated from the estimation has realistic variability compared with TOPEX/Poseidon (T/P) altimetry data. Using T/P altimetry data with temperature observation further improves the analysis of the salinity field. The comparison with the in situ salinity data showed that the salinity fields were analyzed successfully with temperature and T/P observation data alone especially in the western equatorial Pacific, although there are some difficulties in analyzing salinity in the eastern equatorial Pacific and the surface mixed layer. These results convince us that the analysis salinity field has its own reliability even where no salinity observation exists. We also confirm that interannual variabilities of the nearsurface salinity field and the barrier layer in the period of in the analyses are consistent with former studies. The fresh water is confined to the west, sea surface salinity in the central equatorial Pacific is relatively high, and a thick barrier layer develops in the western equatorial Pacific during La Niña periods. The fresh water spreads to the central equatorial Pacific, and the thick barrier layer moves to the east during El Niño periods. The correlation between near-surface temperature and the barrier layer thickness is also confirmed. The analysis fields presented here are quite adequate to study the salinity interannual variability. INDEX TERMS: 4231 Oceanography: General: Equatorial oceanography; 4215 Oceanography: General: Climate and interannual variability (3309); 4522 Oceanography: Physical: El Niño; 4556 Oceanography: Physical: Sea level variations; KEYWORDS: ENSO, equatorial Pacific, freshwater pool, barrier layer, 3DVAR, coupled T-S EOF Citation: Fujii, Y., and M. Kamachi, Three-dimensional analysis of temperature and salinity in the equatorial Pacific using a variational method with vertical coupled temperature-salinity empirical orthogonal function modes, J. Geophys. Res., 108(C9), 3297, doi: /2002jc001745, Introduction [2] The salinity field has great variability in the equatorial Pacific. In terms of the sea surface salinity (SSS) field, a freshwater pool is in the western equatorial Pacific, and lowsalinity water (<34.5 psu) accumulates there. In contrast, there is high-salinity water (>35.0) related to the South Pacific Tropical Water (SPTW) south of the equator and east of the date line. A salinity front forms between the fresh and salty water masses. The front is sharp and travels long distance in a short time. Hénin et al. [1998] reported that the salinity gradient in the front was more than 1.5 psu over 200 km, and that the front travelled more than 3000 km in a Copyright 2003 by the American Geophysical Union /03/2002JC few months. In their estimation, the speed of the displacement was in the range of cm s 1. Recently, oceanographers have focused on this displacement of the salinity front. The front is located in the Eastern Warm Pool Convergence Zone (EWPCZ) [e.g., Picaut et al., 1996, 2001]. EWPCZ denotes the eastern edge of the warm water pool in the western equatorial Pacific. The displacement of this front is mainly related to the advection by surface currents [Delcroix and Picaut, 1998]. The currents are not only driven by local winds but also affected by equatorial Kelvin and Rossby waves. Picaut et al. [1997] insisted that the displacement affected the position of the atmospheric convective zone and tightly connected to the El Niño-Southern Oscillation (ENSO) mechanism. The EWPCZ is not easy to detect from the temperature field. Therefore the salinity front is important information for analyzing the position of EWPCZ. 13-1

2 13-2 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS [3] The salinity front is also related to the barrier layer [Lukas and Lindstrom, 1991] formation at the equatorial Pacific [Vialard and Delecluse, 1998]. The barrier layer forms in the warm water pool under the fresh water. In the barrier layer, the temperature is homogeneous, but salinity increases with depth. The layer therefore has density stratification by salinity. The formation of the barrier layer makes the density mixed layer at the surface shallower than the thermocline, and prevents cold water under the thermocline from mixing with warm water in the mixed layer. The barrier layer can therefore affect sea surface temperature (SST) [see Ando and McPhaden, 1997]. The barrier layer, also, confines the effect of the westerly wind burst to the shallow surface mixed layer and induces the fresh equatorial jet [Roemmich et al., 1994]. Vialard and Delecluse [1998] pointed out the barrier layer could play an essential role in onsets of El Niño. Hence understanding the variability of the barrier layer distribution is important for studying the ENSO mechanism. [4] Many oceanographers have studied the salinity field in the equatorial Pacific with observed data. The studies, however, used only climatology [e.g., Johnson and McPhaden, 2000], a surface field [e.g., Hénin et al., 1998], or the fields of some limited sections [e.g., Johnson and McPhaden, 2000], because the available salinity data were very limited. Other studies used composite fields during El Niño or La Niña periods [e.g., Ando and McPhaden, 1997]. In their works, the three-dimensional interannual variability of the salinity field was rarely discussed, because there was no reliable data set of three-dimensional salinity fields in a period of the interannual timescale. Studies using ocean general circulation models (OGCMs) began to reveal the salinity variability of the entire equatorial Pacific [e.g., Vialard et al., 2002]. Those studies, however, have somewhat unreliable in terms of forcing at the atmosphere-ocean boundary and the parameterization of sub-grid-scale ocean physics. We should therefore confirm the salinity variability with the three-dimensional data set produced from observation data. [5] Ocean assimilation systems have been expected to produce that kind of data set. Assimilation systems have been adopted at operational centers such as the National Centers for Environment Prediction (NCEP), European Centre for Medium-Range Weather Forecasts (ECMWF), and the Japan Meteorological Agency (JMA). Most of them, however, correct the model temperature field alone and rely on model equations in terms of the salinity field [e.g., Smith et al., 1991; Ji et al., 1995; Behringer et al., 1998]. Ji et al. [2000] pointed out that the salinity variability in the equatorial Pacific was not expressed adequately without salinity correction in their assimilation system and that the salinity correction was also important for effectively assimilating sea surface height (SSH) observation. [6] In order to correct a model salinity field, some oceanographers are developing methods of salinity analysis with a few salinity observation [e.g., Troccoli and Haines, 1999; Vossepoel et al., 1999; Vossepoel and Behringer, 2000; Maes and Behringer, 2000; Fujii and Kamachi, 2003a]. In particular, Maes and Behringer [2000] and Fujii and Kamachi [2003a] used vertical coupled temperature-salinity (T-S) empirical orthogonal function (EOF) modes. The vertical correlations among temperature and salinity at each depth were explained by the EOF modes in their method. Although their method was adopted for estimating only one-dimensional vertical temperature and salinity profiles, salinity profiles were effectively estimated from temperature and SSH observations without salinity observation. This was because the EOF modes effectively represented the coupled variability of temperature and salinity fields. [7] In this study, we adopted a variational method with the vertical coupled T-S EOF modes for estimating threedimensional temperature and salinity fields in the equatorial Pacific (20 S 20 N, 110 E 70 W) without an OGCM. This method was originally examined in onedimensional estimations by Maes and Behringer [2000] in the equatorial Pacific and Fujii and Kamachi [2003a] in the western North Pacific, and extended to three-dimensional analysis by Fujii and Kamachi [2003b]. The method was improved in order to express the spatial variability of the coupled T-S relation, and the nonlinear equation calculating sea surface dynamic height (SDH) from temperature and salinity is adopted without linearization. EOF modes are calculated with observed profiles in the area of 15 S 15 N, 110 E 70 W. The nonlinear constraints for avoiding density inversion and higher temperature than surface at the near-surface layer are also adopted. The analysis results are validated with TOPEX/Poseidon (T/P) altimetry data and in situ salinity data. We also examined the interannual variabilities of the near-surface salinity field and the barrier layer in the equatorial Pacific with the analysis result and confirmed they are consistent with former studies. [8] This paper is organized as follows. The analysis method is described in section 2. The variability of analysis temperature fields is presented in section 3. The analysis salinity fields are validated with observation data in section 4. Interannual variability of the near-surface salinity field is examined in section 5. The feature of the barrier layer is examined in section 6. Results are summarized in section Analysis Method 2.1. Analysis Scheme [9] In this study, we analyzed monthly temperature and salinity fields in the horizontal area of 20 S 20 N, 110 E 70 W, with 1 grid spacing. The analysis levels are 0, 10, 20, 30, 50, 75, 100, 125, 150, 200, 250, 300, 400, 500, 600, 700, 800, 900, and 1000 m. The analysis method is based on Maes and Behringer [2000] and Fujii and Kamachi [2003a, 2003b]. It is a three-dimensional variational (3DVAR) method adopting vertical coupled T-S EOF modes as the control variables. [10] We first partitioned the analysis area in the same manner as Hoteit and Pham [2001] and Fukumori [2002] into seven regions as shown in Figure 1. T-S EOF modes were calculated for each region and its amplitudes were adopted as the control variables. It is noted that there are overlapping areas. These overlapping areas are required to connect the seven regions smoothly. Further explanation will be shown later.

3 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS 13-3 Figure 1. Analysis area and seven partitioned regions. Analysis area is partitioned by the colored solid lines. A set of EOF modes was calculated from the averaged statistics in the area surrounded by the same colored dashed line for each partitioned region. [11] The cost function J (w) is defined as follows: JðwÞ ¼ 1 X 2 m X l w T m;l B 1 m w m;l þ 1 2 ðh i x y i Þþ 1 X 2a 2 j X ðh i x y i i 2þ h j ðþ h x o 1 j Þ T R 1 i 2 C 2 rðþ x þ 1 ½ 2 C T ðþ x Š 2 : ð1þ where w is the vector of the control variables, and w m,l is the partial vector of w whose elements are amplitudes of the lth mode in the mth region. In this analysis, 12 dominant modes were adopted as control variables in each region. The matrix B m denotes the background (first-guess) covariance matrix in the mth region. The vector y i denotes the ith observation profile of temperature and salinity data and h o j the jth TOPEX/Poseidon (T/P) altimetry data. The vector x = Gw + x f is the state vector of temperature and salinity, where G denotes the transformation from the control variables w to deviations of gridded temperature and salinity from their first-guess x f. The matrix H i denotes horizontal interpolation for acquiring the values equivalent to the observed profile data, and h j is the nonlinear operator that includes calculation of SDH from gridded temperature and salinity data and interpolation. The matrix R i is the observation error covariance matrix for the ith observation profile. The coefficient a means the root mean square error of T/P altimetry data. The fourth and fifth terms on the right hand side are constraints for avoiding density inversion and higher temperature at the near-surface layer than at the surface, respectively, and C r and C T are defined as follows: X C r ¼ 1=b r p C T ¼ ð1=b T Þ X p X k X k D r p;k r p;kþ1 ; ð2þ DT p;k T p;0 ; ð3þ where r p,k and T p,k denote the density and temperature at the pth grid point and kth layer (k = 0: surface), and b r and b T are coefficients deciding the strength of the constraints. D is the following nonlinear function: D(x) = 0 when x < 0, and D(x) =x when x > 0. The density is calculated according to the formula of United Nations Educational, Scientific, and Cultural Organization [1981]. It should be noted that the terms are weak constraints, they do not perfectly avoid density inversion or higher temperature at the layer near the surface than at the surface, although they reduce the possibility and extent. In this study, we adopted b r = 0.02 (kg m 3 ) and b T = 1.0 ( C). [12] The vertical temperature and salinity profiles at the pth horizontal grid, x p, are reconstructed from EOF mode amplitudes as follows: X x p ¼ S p w m;p U m m;p w m;p þ x f p m where S p is the standard deviations of temperature and salinity from their first-guess, w m,p is a weight coefficient of each region (m is the index of regions), U m is the matrix constituted by dominant EOF modes, m,p is the diagonal matrix whose elements are the singular values of the EOF modes, w m,p is a mode amplitude vector of each region, and x f p is the first-guess of the profiles. The weight coefficients 2 w m,p satisfy m w m,p = 1, avoiding the loss or gain of total variances for each control variable by the area partition. The square of w m,p varies linearly from 0 to 1 along longitudes and latitudes in overlapping areas. [13] The calculation of SDH in the nonlinear operator h j is implemented as follows: h ¼ 1 r s Z zm 0 ð4þ r 0 ðt; S; pþdz; ð5þ where h is the difference of SDH from a reference state; r s is the surface density; z m is the reference depth; r 0 is the difference of the density from the reference state; z denotes the vertical coordinate; and T, S and p denote temperature, salinity and pressure. We chose 0 C and 35 psu as the reference state, and 1000 m as the reference depth, which is the same depth as the deepest analysis depth. [14] It is noted that correlations among control variables of the same mode in the same region are considered, that is, B m is non-diagonal matrix. We adopted the Gaussian function as the horizontal correlation. The e-folding scale is 10 along longitudes and 5 along latitudes. We chose the longer scale along longitudes than that along latitudes because the zonal scale of variability in the equatorial Pacific is much larger than the meridional scale [see Derber and Rosati, 1989; Kuragano and Kamachi, 2000]. The correlations between control variables in different regions, as well as between different modes, are not counted. This means that the observed information does not propagate out of the regions where the observation was located. The analysis field would have a gap at the boundary of the regions if the overlapping areas did not exist. This is why overlapping areas are required.

4 13-4 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS Table 1. Table of the Observation Data Adopted in Each Analysis Temperature T/P Altimetry Salinity Experiment 1 adopted not adopted not adopted Experiment 2 adopted adopted not adopted Experiment 3 adopted adopted adopted Experiment 4 adopted not adopted adopted [15] The gradient of the cost function is written as follows: g ¼ X X B 1 m w m;l þ G X T H T i R 1 i ðh i x y i Þ m l i þ 1 X a 2 GT h * j ðþ x h j ðxþ h o j j þ G T C * r ðþc x r ðxþþg T C * T ðþc x T ðþ: x where h* j, C* r and C* T are the adjoint codes of the nonlinear operators h j, C r, and C T, respectively. It should be noted that the gradient is a nonlinear function of w, and that the calculation of g requires inversion of the non-diagonal matrix B m. The method of Derber and Rosati [1989] is often adopted in order to avoid inversion of a non-diagonal background error covariance matrix in oceanography. However, the method is not available for nonlinear cost functions. Because of this difficulty, the nonlinearity between temperature/salinity and SDH is often ignored and the additional nonlinear constraints have never been adopted. In this study, the preconditioned quasi-newton method of Fujii and Kamachi [2003b] is adopted. Their ð6þ method can minimize a nonlinear cost function without inversion of a non-diagonal background error covariance matrix in variational analyses, and is therefore a powerful tool for such a case where some sophisticated constraints are required as in the 3DVAR analysis of this study. The effects of nonlinear constraints are shown in the Appendix Data [16] We adopted the monthly climatology of Kuragano and Kamachi [1997] as the first-guess fields, and EOF modes and other statistics were calculated using the observed temperature and salinity profile data in the World Ocean Database 2001 (WOD01) [Conkright et al., 2002]. We calculated statistics for each 5 5 box at first and then obtained statistics of each region by averaging the 5 5 box statistics in the area surrounded by dashed lines in Figure 1. The data out of the 15 S 15 N band and in Indonesian archipelago were excluded because we sought to obtain EOF modes expressing properly the variability of the equatorial Pacific. It should also be noted that the analysis area is narrower than the region where the EOF modes are adopted. This is for reducing the effect that specific regional characteristics are smoothed by the averaging and eventually become undistinguishable in the EOF modes. The method of calculating statistics was according to Fujii and Kamachi [2003b]. [17] We implemented the four kinds of analyses with different input data (Table 1) in the period of when TOPEX/Poseidon (T/P) altimetry data were available. Temperature and salinity observations were corrected from Figure 2. Vertical profiles of the first five vertical coupled T-S EOF modes in the area surrounded by the yellow dashed line in Figure 1. The percentage of each mode is noted on the top of each profile.

5 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS 13-5 Figure 3. Time-longitude sections of (a) SST anomaly ( C) and (b) m depth-averaged temperature anomaly ( C) at the equator in the period of in experiment 3. the WOD01, the Global Temperature-Salinity Profile Program (GTSPP) database [Hamilton, 1994], and the data of the TAO/TRITON array [Hayes et al., 1991; McPhaden et al., 1998; Kuroda, 2002]. As T/P altimetry data, we adopted the anomaly data of Kuragano and Shibata [1997] after adding them to the mean SDH of experiment 4. The observation data are combined by averaging when more than one profile or T/P observation are available in the same box in the same month before employed in the analyses EOF Modes [18] Vertical coupled T-S EOF modes form an essential part of the analysis method in this study. Therefore we will discuss the EOF modes in the area surrounded by the yellow dashed line (Figure 1) in this subsection. It is not easy to explain what physical variation they represent because the EOF modes are calculated on the basis of statistical theory. Maes [1999] had previously shown and discussed the EOF modes in this region. However, the EOF modes used here are not similar to that of Maes [1999]. This difference is caused by the difference of the methods used for normalizing each variable that constitutes the modes. Maes [1999] used the same normalizing factors among temperature/salinity at all depths. In contrast, each variable at each depth is normalized with its standard deviation in this study. Although our method is suitable for effectively using the observed information, relations between the physics and EOF modes calculated in the method seem to be less clear (Figure 2). [19] The first EOF mode represents the first baroclinic mode, that is, the vertical displacement of whole water column, which agrees with the first mode of Maes [1999]. This mode has anomalies of the same sign for the temperature and salinity at the layers deeper than 200 m because their means decrease monotonically at such depths [see Maes, 1999; Fujii and Kamachi, 2003a]. The near-surface feature of this mode is a bit complex and seems to represent the variability away from the equator. The mode represents that an upward (downward) displacement tends to confine (relax) the thermocline, which is denoted by the different signs between depths above and below 100 m. The upward displacement often coincides with the decrease of nearsurface salinity in El Niño period by the intensification of Intertropical Convergence Zone (ITCZ). Also, a sharp thermocline tends to coincide with the low near-surface salinity. This mode represents the complicatedly coupled variability of these variations. [20] The second mode also appears to represent the first baroclinic mode but seems to be coupled with the nearsurface variability at the equator. In this mode, the upward (downward) mode is coupled with relaxing (confining) the thermocline and high- (low-) salinity anomaly. Because the low-salinity anomaly tends to promote the barrier layer formation, this mode seems to represent the close relationship between downwelling Kelvin waves and the barrier layer formation. This relationship is discussed in section 6. [21] The third mode mainly represents the second baroclinic mode. That is, the variation caused by vertical displacement whose direction changes at around 300 m depth. The temperature anomaly of the layer deeper than 300 m depth is not clear because the decrease of the mean temper-

6 13-6 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS Figure 4. Depth-longitude sections of temperature ( C, contour lines, 1 C interval) and salinity (psu, color shaded) at the equator in experiment 3: (a) December 1997 (El Niño) and (b) December 1998 (La Niña). The black lines denote (upper) MLD and (lower) ILD. ature with depth is small under the thermocline around the equator. This mode also denotes the coupled variation of warm temperature and high-salinity anomalies. In the La Niña period, the fresh water retreating to the west often coincides with the thermocline deepening related to the warm water accommodation in the western Pacific [e.g., Kuroda and McPhaden, 1993]. The third mode includes this variability. [22] The higher modes represent more complicated variabilities. It should be noted that the modes of this region have many coincidences with the modes of other regions, although there are modes that are dominant only in the western equatorial Pacific (e.g., the third mode). Specifically, a mode similar to the second mode can be found from the EOF modes of all regions. This suggests a close relationship between downwelling Kelvin waves and the barrier layer formation in the whole equatorial Pacific, as will be discussed in section Temperature Field [23] In this section, we confirm that the analysis temperature fields correctly express the interannual variability related to ENSO cycles. Figures 3a and 3b show the variabilities of sea surface temperature (SST) and m depth-averaged temperature at the equator in a timelongitude section in experiment 3. The SST variability is consistent with the analysis of Reynolds and Snith [1994], and warm (cold) anomalies related to El Niño (La Niña) are well analyzed. The anomalies propagating from west to east related to equatorial Kelvin waves are clearly expressed in Figure 3b. The variability of the heat content along the equator is thus consistent with other studies [e.g., McPhaden et al., 1998; McPhaden, 1999; Vialard et al., 2001]. [24] We have shown the temperature and salinity fields at the equator in an El Niño and a La Niña periods with the mixed layer depths (MLD) and the isothermal layer depth (ILD) in Figure 4. MLD and ILD are calculated in the same manner as Vialard and Delecluse [1998]: ILD (MLD) is the depth where temperature (density) is T lower (r higher) than the surface, where T =0.5 C and r = (@r/@t) T. This is suitable for low vertical resolution data. In the La Niña period (Figure 4b), warm water (>28 C) can be seen at the western region and surface water at the eastern region is cold. The thermocline is deep (shallow) in the west (east) and declines from the east to the west. In contrast, the warm water (>28 C) spreads to the eastern boundary at the surface, and the thermocline becomes almost flat in the El Niño period (Figure 4a). The temperature fields of the analysis thus satisfactorily represent the features of El Niño and La Niña events. 4. Validation With Observation Data 4.1. Validation With T/P Data [25] In this section, the accuracy and reliability of the analysis salinity fields are validated with observation data.

7 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS 13-7 Figure 5. Validation using SDH (cm) field in experiment 1. Horizontal fields of (a) the error of the firstguess SSH, (b) the error of the SSH calculated from the analysis temperature and the first-guess salinity, (c) the error of the SSH calculated from the analysis temperature and salinity, and (d) Figure 5b minus 5c.

8 13-8 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS Figure 6. Vertical profiles of the RMSEs of salinity (psu) in the area of (a) 5 S 5 N, 150 E 170 W, (b) 5 S 5 N, W, and (c) 5 15 N, 130 E 160 W in the period of Black, first guess; green, experiment 1; blue, experiment 2; and red, experiment 3. We start the validation by comparing the analyzed SDH in experiment 1 and T/P altimetry data. Since T/P data were not adopted in experiment 1, they are independent data here. It is also noted that SSH includes the information of temperature and salinity at all depths. We can therefore guess the accuracy of whole analyzed interior salinity and temperature fields by this comparison. It should be noted that the correspondence of the analyzed SDH with the T/P altimetry does not mean that the variations of temperature/salinity at each depth are correctly distributed. We adopted the gridded data of T/P altimetry provided by Kuragano and Kamachi [2000] as the reference. The comparison is implemented in terms of the anomaly fields of SSH and SDH from their mean states. [26] Figure 5a illustrates the error of the first guess (i.e., monthly climatology) referred to T/P altimetry data. This implies interannual variability plus variability on a timescale shorter than one year because the first-guess field includes the annual variability. This figure is consistent with the equatorial seesaw pattern of SSH anomaly related to ENSO cycles [see Picaut and Busalacchi, 2001; Picaut et al., 2002]. The equatorial Kelvin wave pattern, which has a peak at the equator, is dominant in the central and eastern equatorial Pacific. In contrast, the equatorial Rossby wave pattern, which has two peaks at the south and north of the equator, is seen at the western equatorial Pacific. It is also noted that there is a region where the error of the first-guess field is relatively small at the center of the seesaw pattern (i.e., in the western equatorial Pacific from 150 E to the date line). The variability of the thermocline depth is relatively small in that region. [27] Figure 5b depicts the error of the SDH field calculated from the analysis temperature and the first-guess salinity (i.e., monthly climatology). This error field is equivalent to that when only temperature is analyzed. The error in the central and eastern equatorial Pacific related to equatorial Kelvin waves is almost removed by the temperature analysis. This means that the TAO/TRITON array effectively detects the ENSO signal in the equatorial Pacific. The variability related to the equatorial Rossby waves in the western equatorial Pacific is also effectively expressed. The small errors of SSH imply that the analysis temperature field is reasonably reliable. Relatively large errors (>6 cm), however, remain in the western edge of the equatorial Pacific and between 160 E 180 in the southern hemisphere. The salinity variability affects the SSH variability in these regions. An error larger than 7 cm remains near the Middle American coast. Small-scale variability is dominant in this region because of effects of the California current and the wind through the valleys in Middle America. It is difficult to express the smallscale variability from limited data, and EOF modes more suitable for the variability are required. There are also large errors in the area north of 15 N and west of 160 W. This area was not the target of this experiment and the variability there was not considered sufficiently when EOF modes were calculated (see subsection 2.2). [28] Figure 5c presents the error calculated from the analysis temperature and salinity, and Figure 5d shows the difference, Figure 5b minus 5c. This difference expresses the improvement of the SSH field by the analysis of the salinity field. The SSH field is improved by the salinity analysis in almost all areas. This improvement implies that the salinity field is analyzed properly. The expression of salinity in particular is effectively improved in the western equatorial Pacific between 150 E 170 W where the firstguess error in Figure 5a is small. In this area, the temperature variability is not so large, as mentioned before. However, the salinity front at the eastern edge of the freshwater pool travels through the region and the salinity variability near the surface is large. The salinity variability is therefore one of the main causes of the SSH variability in this area as reported by Maes [1998]. Analyzing the salinity field accurately is required in order to express the SSH variability accurately in this area. The improved salinity expression in this area, implied by the improved SSH expression, is desirable since the salinity variability here is important because of the remarkable phenomena such as the salinity front and the barrier layer. The SSH field is also improved in the south of 10 S

9 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS 13-9 Figure 7. Same as Figure 6 but for the correlation coefficients of a salinity analysis increment to the deviation of the observed value from the first guess; the black line for the first-guess is omitted. between 170 E 130 W and the north of 10 N, west of 160 W. In these regions, the thermocline broadens more than in the region near the equator. The salinity decreases with depth as well as temperature in the lower part of the broad thermocline. Baroclinic waves displace water mass vertically around the thermocline [e.g., Cushman-Roisin, 1994]. This displacement causes a salinity anomaly as well as a temperature anomaly. The salinity anomaly caused by the baroclinic waves seems to be analyzed properly in our analysis, improving the SSH field in these regions. A part of the eastern equatorial Pacific SSH field is not improved by the salinity analysis. This may be because the coupling of near-surface temperature and salinity variability is not tight because the near-surface salinity is much affected by precipitation. This problem is retained for future works Validation With in Situ Salinity Data [29] In this subsection, we will show improvement of the salinity field by T/P data adopted with temperature observation data in experiment 2. For this purpose, we adopted in situ salinity observation data as a reference. It should be noted that the salinity observation data are independent data as they were not adopted in experiment 2. [30] Figure 6 shows the vertical profiles of root mean square errors (RMSE) in the western equatorial (5 S 5 N, 150 E 170 W), the eastern equatorial (5 S 5 N, 170 E 90 W), and the northern subtropical (5 15 N, 130 E 160 W) regions. Figures 7 and 8 also show the vertical profiles of correlation and regression coefficients of salinity increments to the deviations of observed values from the first guess in the same regions. CTD and profiling float data in WOD01 are adopted as the reference as well as the profile data in GTSPP in which more than 15 available values are reported. The profiles observed in the period of [31] Figure 6a implies that temperature data effectively reduce the first-guess salinity errors in the layers above 100 m and between m in the western equatorial region in experiment 1. The correlation in Figure 7a exceeds Figure 8. Same as Figure 7 but for the regression coefficients.

10 13-10 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS 0.8 in the layer above 50 m, and the regression in Figure 8a implies the amplitude of the salinity variation near the surface is almost fully recovered. Employing T/P altimetry data in experiment 2 further reduces the RMSE errors near the surface. The correlation coefficients increase at the layer above 200 m. The regression coefficients of experiment 2 are higher than those of experiment 1. This indicates the amplitude of variation is recovered more effectively although the variation near the surface is overestimated, as indicated by the coefficients being greater than 1. Employing T/P altimetry data thus effectively improves near-surface salinity variability in this region. The displacement of the salinity front at the edge of the fresh water caused a large variability of near-surface salinity here, and the variability affects the SSH field as discussed before. This also means that the SSH variability has information of the salinity variability. The salinity field is therefore improved by the T/P altimetry data. This result is consistent with other studies [e.g., Troccoli and Haines, 1999; Maes and Behringer, 2000; Vossepoel and Behringer, 2000]. The analyses of experiments 1 and 2 seem to make almost no improvement of the salinity field at 100 and 125 m depths in this region. The unsatisfactory result is related to the vertical displacement of the salinity maximum related to SPTW. This cause will be discussed later. [32] Figure 6b demonstrates that only a small improvement by the analyses can be seen in the eastern equatorial region when the salinity observation is not employed (experiments 1 and 2). The salinity variation near the surface is slightly improved by employing T/P altimetry. At the northern tropical region, RMSEs near the surface are smaller than the first guess in experiment 1, and employing T/P altimetry further reduces it in experiment 2, although neither analyses is satisfactory at layers below 150 m (Figure 6c). The correlation and regression coefficients denote the same tendency. [33] Figure 9 presents the time series of observed SSS at three observation points of the TAO/TRITON array with the analyzed SSS in the experiments. The estimation of experiment 1 at equator, 165 E (Figure 9a) expresses the interannual variability: low salinity in 1993, salinity increase in 1994, the high-salinity period between 1995 and 1996, the low-salinity period related to the El Niño, and the increase after the El Niño. The amplitudes of the variability are, however, underestimated in experiment 1. The amplitude is better recovered in experiment 2 than in experiment 1: low salinity in 1993, high salinity in , and low salinity at the onset of El Niño are better estimated. The higher correlation in experiment 2 than in experiment 1 also suggests the effectiveness of employing T/P altimetry data in the analysis. The figures of the other points (5 N, 165 E and 5 S, 180 ) exhibit the same tendency. [34] Figure 10 illustrates the temperature and salinity analysis fields of the vertical section at 165 E in October 1997 and October 1999 in experiment 2 with the fields of the same section in the same period observed by Ryofumaru, the observation vessel of JMA. MLD and ILD are also shown. The large-scale features of the temperature fields are well reconstructed in both periods because the temperature observation is directly employed to correct the first-guess fields. The large-scale features of salinity fields Figure 9. Time series of observed and analyzed SSS (psu) at (a) equator, 165 E, (b) 5 N, 165 E, and (c) 5 S, 180 in the period of Black, observation; green, experiment 1; blue, experiment 2; and red, experiment 3. The correlation of each analyzed SSS with the observed SSS is also denoted.

11 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS (a) Observation. Oct (b) Observation. Oct (c) Analysis. Oct (d) Analysis. Oct Figure 10. The comparison of temperature ( C, contour lines), salinity (psu, color shaded) fields and MLD and ILD (black lines) in the depth-longitude section at 165 E: (a) observation fields of October 1997, (b) observation fields of October 1999, (c) analysis fields of October 1997 in experiment 2, and (d) analysis fields of October 1999 in experiment 2. also correspond well. The thermocline is shallow and flat between 2 10 N in October 1997, which keeps ILD shallower than 50 m and the barrier layer between MLD and ILD thin. The salinity maximum is also elevated to about 80 m depth following the thermocline. The highsalinity water (>35.0 psu) related to SPTW reaches further north than its usual position in this period. In contrast, the thermocline is pushed down around 5 N in October 1999, accompanied by the deepening of the salinity maximum to about 140 m depth. ILD becomes deeper than in 1997, and a thick barrier layer forms there. The salinity near the surface around the equator is high because of upwelling. The high

12 13-12 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS Figure 11. Horizontal analysis fields of SSS (psu) in experiment 3: (a) December 1997 (El Niño) and (b) December 1998 (La Niña). salinity related to SPTW does not intrude to the north, although the water around the thermocline at the equator is saltier than in October The low-salinity water related to North Pacific Intermediate Water (NPIW), which comes from the north under the thermocline, has a weaker influence than the El Niño period. These tendencies are analyzed in experiment 2. [35] Figure 10 however reveals shortcomings of the analysis. First, salinity at the salinity maximum is higher than the observation. In particular, salinity exceeding 35.2 psu is analyzed around 80 m depth between 4 and 9 N in October This shortcoming is also revealed in Figures 6a, 7a, and 8a. Variations of the salinity maximum are difficult to analyze for the following reason. EOF modes represent the relatively high salinity at the layer right above the salinity maximum when the depth of the maximum becomes shallow. If the depth varies significantly, the highsalinity anomaly at the layer will be overestimated. This shortcoming may be improved by refining statistics. Actually, adopting more EOF modes relaxes the problem, although the variability of near-surface salinity in the western equatorial Pacific is less recovered. Another shortcoming is the expression of the deep mixed layer near the equator and the north of 10 N during the La Niña period. The first-guess field of salinity has salinity stratification near the surface in both regions, and it still remains in the analysis field. The tendency of high salinity at the equator in October 1999 is detected but underestimated, as well as the north of 10 N. Thus the analysis fields have shortcomings in terms of small-scale variability, which have to be overcome in future works. However, the salinity fields presented in this study are quite adequate to study interannual largescale variabilities as confirmed further in the next section. 5. Variability of Near-Surface Salinity [36] In this section, we will confirm that the variability of the equatorial Pacific near-surface salinity field analyzed in this study is consistent with results of former studies. Figure 11 presents the distribution of SSS in December 1997 and December 1998 in experiment 3. The former is the mature phase of an El Niño, and the later is the mature phase of a La Niña. There is a high-salinity area (>34.8 psu) in the southern hemisphere east of the date line, related to the formation area of SPTW. The high-salinity area is extended to the northern hemisphere through the central equatorial Pacific during the La Niña period. This high salinity is advected to the north under the Ekman layer in the southern hemisphere and upwells near the equator where the surface Ekman current diverges. Therefore surface water at the equator gets saltier while it is advected to the west by the South Equatorial Current (SEC). The high-salinity zone is extended to 160 E at the equator in Figure 11b. This is caused by the SEC and the upwelling due to the divergence of the Ekman drift [e.g., Kuroda and McPhaden, 1993; Delcroix and Picaut, 1998]. In contrast, a low-salinity area exists under the ITCZ and South Pacific Convergence Zone (SPCZ). In Figure 11b, SSS under SPCZ is extraordinarily

13 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS Figure 12. Time-longitude sections of SSS (psu) at the equator in the period of in (a) experiment 1, (b) experiment 2, and (c) experiment 3. low. SPCZ was intensified by the strong easterly trade wind in the La Niña period. The low SSS is due to this intensification. Between the high salinity and the freshwater pool, there is the salinity front that is the eastern edge of the freshwater pool. Delcroix and Picaut [1998] chose the 35.0 psu contour as the position of the salinity front because of its high 1-month lag correlation coefficient with the Southern Oscillation Index (SOI). We choose the 34.8 psu contour because of the large gradient of the salinity field around it in the analyses. The front is displaced to the west from the mean position during the La Niña period (Figure 11b). During the El Niño period (Figure 11a) the salinity under the ITCZ is lower than usual because of the intensification of ITCZ. The high salinity of SPTW is confined to the south of the equator, and the SSS at the equator is lower than its mean state. The front of the freshwater pool at the equator is also displaced to the east from the mean position (at 165 W). Similar salinity changes have been associated with the weakening of the SEC and the rest of the upwelling at the equator because of the disappearance of the easterly wind [e.g., Vialard et al., 2002]. The westerly wind burst can also drive the eastward displacement of the fresh water. [37] The salinity fields of the equatorial section in the same time frame in experiment 3 are shown in Figure 4 with the temperature fields, MLD and ILD. In December 1998 (Figure 4b: the La Niña period), the high salinity (>35.0 psu) related to SPTW reaches the surface between 180 and 145 W. This implies that there is upwelling caused by the divergence of the Ekman drift there. The shallowness of the salinity maximum related to SPTW accompanies the thermocline elevation in the eastern equatorial Pacific (east of 130 W). The salinity front between the fresh water and the salty water in the central equatorial Pacific forms around 160 E and the salty water subducts and is advected to the west under the fresh water. This salty water forms a barrier layer at m depth. In December 1997 (Figure 4a: the El Niño period), the salinity front reaches 165 W. The layer of high salinity deepens with the deepening of the thermocline in the eastern equatorial Pacific, and another low-salinity water reaches 140 W from the east. The highsalinity water (>35.0 psu) hardly upwells at this time because the easterly trade wind has nearly ceased. These variations related to the ENSO cycles are consistent with former studies [e.g., Delcroix et al., 1996; Picaut et al., 1996]. [38] Figure 12 presents the variabilities of the SSS fields at the equator in a longitude-time section in experiments 1, 2, and 3. The displacement of the salinity front at the eastern edge of the freshwater pool is clearly shown by the 34.8 psu contour (black line) in the result of experiment 3 (Figure 12c). In 1993, the salinity front is around the date line, and the high-sss area related to the equatorial upwelling (>35.1 psu) is smaller than usual. Although the front moves to 160 E and the high-sss area spreads temporarily at the beginning of 1994, the salinity front retreats to the date line and the high-sss area disappears in the second half of Between 1995 and the beginning of 1997, SSS is high in the central equatorial Pacific and the salinity front is located around 160 E. The high-salinity area spreads to 120 W before the onset of the El Niño. The salinity front moved to 160 W, and the high-salinity area (>35.1 psu) almost disappeared in the El Niño period. After the El Niño, the salinity front retreated to around 160 E and SSS at the central equatorial Pacific increased again. The variabilities of the salinity front position and the area of high salinity related to the equatorial upwelling correspond well with other studies [e.g., Delcroix and McPhaden, 2002; Vialard et al., 2002].

14 13-14 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS Figure 13. Horizontal field of Mean BLT (m) in the period of in experiment 3. [39] The disappearance of the high-salinity water (>35.1 psu) is analyzed with temperature observation alone in experiment 1 (Figure 12c), as well as the variability of the salinity front position. However, the T/P altimetry data are required in order to satisfactorily recover the amplitudes of those interannual variabilities. There is no serious difference between the results of experiments 2 and 3. The small amount of salinity data is one reason for this correspondence. Another is that the analysis without salinity data successfully expresses the variability found in salinity observation data. This correspondence means that the analysis field in experiment 3 has its own reliability even where no salinity observation exists. 6. Barrier Layer [40] In this section, we will discuss the barrier layer by examining the field of the barrier layer thickness (BLT) of the analysis fields in experiment 3. The mean BLT field in experiment 3 is shown in Figure 13. This coincides well with the equivalent figure of Ando and McPhaden [1997]. The thick barrier layer exists at the western equatorial Figure 14. Horizontal fields of BLT (m) in experiment 3: (a) December 1997 (El Niño) and (b) December 1998 (La Niña).

15 FUJII AND KAMACHI: EQUATORIAL PACIFIC THREE-DIMENSIONAL ANALYSIS Figure 15. Time-longitude section of (a) BLT (m) and (b) 0 50 m depth-averaged temperature ( C) at the equator in the period of in experiment 3. Pacific. The layer tends to develop more south of the equator than north of the equator. The mean BLT is relatively small around the equator east of the dateline, and large mean BLT areas are extended to the east south of 5 S and between 3 7 N. These features are consistent with Ando and McPhaden [1997]. [41] The thick BLT area in this study, however, is more to west than in the study by Ando and McPhaden [1997]. One of the reasons for this difference is the different manner of calculating BLT (Ando and McPhaden [1997] adopted T = 0.05 C and r =0.01kgm 4 ). As a result, the analyzed ILD is deeper in our study. We also insist that the peak at equator, 170 E of the mean BLT field of Ando and McPhaden [1997] is doubtful and may be because of a shortage of data in this area. The salinity front often exists west of 170 E at the equator and the equatorial upwelling seems to occur frequently at this point. The mean BLT should therefore be smaller there than west of 160 E at the equator that always locates west of the salinity front and a thick barrier layer forms except for El Niño periods, although a thick barrier layer can form at 170 E when the salinity front exists just east of there. There is also a relatively thick barrier layer area east of the Philippines in this study, which did not exist in the figure of Ando and McPhaden [1997]. This difference is because our analyses have difficulty expressing mixed layer in this area as has been discussed in Subsection 4.2: our method tends to analyze the mixed layer as relatively shallow here. [42] The BLT fields in the El Niño (December 1997) and La Niña (December 1998) periods are depicted in Figure 14. During the La Niña period, a thick barrier layer forms west of 160 E between 5 S 5 N and the large BLT area (>20 m) extends to 170 W north of the equator and to 160 W south of the equator. It should be noted that BLT is relatively small at the equator east of 165 E. In contrast, there is no robust barrier layer in the western equatorial Pacific and the thick barrier layer forms east of 150 W between 10 S 5 N in the El Niño period. [43] This tendency can also be seen in the time-longitude section of BLT at the equator, Figure 15a. The area of the thick barrier layer is confined to the western equatorial Pacific in La Niña periods (i.e., and ). At the beginning of the El Niño (i.e., 1997), the barrier layer travels to the east and almost disappears in the mature phase of El Niño (i.e., beginning of 1998). This tendency agrees with the study of Ando and McPhaden [1997]. The displacement of the thick barrier layer accompanied with the displacement of the salinity front and the fresh water (Figure 12c). The thick barrier layer usually exists west of salinity front and moves with it. These displacements are partly because of the eastward advection by the fresh equatorial jet [see, Delcroix and Picaut, 1998]. The similarity of BLT variability at the beginning of the El Niño period to the subsurface temperature anomaly propagation in Figure 3 also implies that the barrier layer displacement is related to downwelling Kelvin waves. This relationship is also represented by the EOF modes discussed in Subsection 2.3 (Figure 2). Downwelling Kelvin waves not only push the thermocline down but also create a convergence zone east of the wave. This convergence