Lagrangian mixed layer modeling of the western equatorial Pacific

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. C2, PAGES 2523-2541, FEBRUARY 15, 1995

Lagrangian mixed layer modeling of the western equatorial Pacific

Toshiaki Shinoda

Joint Institute for Marine and Atmospheric Research, University of Hawaii, Honolulu

Roger Lukas Joint Institute for Marine and Atmospheric Research and Department of Oceanography University of Hawaii, Honolulu

Abstract. Processes that control the upper ocean thermohaline structure in the western equatorial Pacific are examined using a Lagrangian mixed layer model. The one-dimensional bulk mixed layer model of Garwood (1977) is integrated along the trajectories derived from a nonlinear 1« layer reduced gravity model forced with actual wind fields. The Global Precipitation Climatology Project (GPCP) data are used to estimate surface freshwater fluxes for the mixed layer model. The wind stress data

1

which forced the 1• layer model are used for the mixed layer model. The model was run for the period 1987-1988. This simple model is able to simulate the isothermal layer below the mixed layer in the western Pacific warm pool and its variation. The subduction mechanism hypothesized by Lukas and Lindstrom (1991) is evident in the model results. During periods of strong South Equatorial Current, the warm and salty mixed layer waters in the central Pacific are subducted below the fresh shallow mixed layer in the western Pacific. However, this subduction mechanism is not evident when upwelling Rossby waves reach the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific due to episodes of strong wind and light precipitation associated with the E1 Nifio-Southern Oscillation. Comparison of the results between the Lagrangian mixed layer model and a locally forced Eulerian mixed layer model indicated that horizontal advection of salty waters from the central Pacific strongly affects the upper ocean salinity variation in the western Pacific, and that this advection is necessary to maintain the upper ocean thermohaline structure in this region.

1. Introduction

Until recently, it was generally accepted that the mixed layer depth is approximately 100 m in the western equatorial Pacific from the frequently cited equatorial temperature section [Colin et al., 1971]. However, the data from the Western Equatorial Pacific Ocean Circulation Study (WEP- OCS) cruises of 1985-1986 [Lindstrom et al., 1987] show that the mixed layer in this region is much shallower than previously thought.

Lukas and Lindstrom [1991] investigated the mixed layer structure in the western Pacific by the analyses of conduc- tivity-temperature-depth (CTD) data from two of the WEP- OCS cruises. They show that the mixed layer is relatively shallow due to the large net surface freshwater flux and to the light winds that prevail in this region. They also show that a nearly isothermal layer separates the bottom of the mixed layer from the top of the thermocline, referred to as the "barrier layer." The existence of this barrier layer is important because there can be no heat flux at the base of the mixed layer if there is no vertical temperature gradient below. Using the WEPOCS data, Godfrey and Lindstrom [1989] suggested that this thermohaline structure affects the

Copyright 1995 by the American Geophysical Union.

Paper number 94JC02486. 0148-0227/95/94 J C-02486505.00

heat budget in this region. These results suggest the importance of studying the space and time variation of the thermohaline structure in the western Pacific upper ocean.

Sprintall and Tomczak [1992] analyzed the climatological temperature and salinity data compiled by Levitus [ 1982] and described the geographical distribution of the barrier layer. They confirmed the importance of heavy local precipitation in the western Pacific which was previously indicated by Lukas and Lindstrom [1991]. However, other important processes were not discussed.

Delcroix et al. [1992] described the barrier layer thickness variation along 165øE using CTD data from 21 cruises during 1984-1988. Using the high vertical resolution data sets, they confirmed the existence of a barrier layer in the warm pool as far east as 165øE. Prominent interannual variation in the

barrier layer was shown. They suggested the importance of various processes such as the variation of the South Equa- torial Current (SEC) and surface forcing. However, they did not show how these processes control the upper ocean structure in this region.

Sprintall and McPhaden [1994] demonstrated strong time variability of the barrier layer for the period November 1988 to August 1991 using the mooring measurement data at 0 ø, 165øE. Their study indicated that the upper ocean structure in this region is characterized by two distinct climatic regimes evident during this period.

2523

2524 SHINODA AND LUKAS: LAGRANGIAN MIXED LAYER MODELING

Table 1. Hydrographic Observations Along 165øE

Cruise Origin Date

US-PRC 2 SOA-WHOI Dec. 13-15, 1986 SURTROPAC 7 ORSTOM Jan. 15-16, 1987 SURTROPAC 8 ORSTOM July 8-9, 1987 PROPPAC 1 ORSTOM Sept. 14-16, 1987 US-PRC 3 SOA-WHOI Oct. 20, 1987 SURTROPAC 9 ORSTOM Jan. 21-22, 1988 PROPPAC 2 ORSTOM April 2-3, 1988 US-PRC 4 SOA-WHOI May 21-22, 1988 SURTROPAC 10 ORSTOM June 19-20, 1988 PROPPAC 3 ORSTOM Sept. 17-18, 1988 US-PRC 5 SOA-WHOI Nov. 15-16, 1988 SURTROPAC 11 ORSTOM Jan. 11-12, 1989

US-PRC, U.S.-People's Republic of China Joint Program on Air-Sea Interaction Studies in the tropical western Pacific; SOA, State Oceanic Administration, Qingdao and Guangzhou, PRC; WHOI, Woods Hole Oceanographic Institution; SURTROPAC, Surveilence Trans-Oceanique du Pacifique; ORSTOM, Institut Francais de Recherche Scientifique pour le Developpment en Co- operation in Noumea, New Caledonia; PROPPAC, Production Pelagique dans le Pacifique.

Chen and Rothstein [1991] examined the short timescale response of the upper layer in the western equatorial Pacific using the one-dimensional turbulent closure model of Me#or and Yamada [1982]. They show that a barrier layer can be created when a shallow mixed layer is formed by heavy precipitation after strong westerly wind bursts occur. The model was run for only 10 days, and longer timescale processes were not discussed. Also, their study did not address the effect of horizontal advection on the upper ocean structure in this region.

The principal aim of this study is to understand the role of horizontal advection in the variation of the thermohaline

structure in the western equatorial Pacific upper ocean. Interannual variations provide the main motivation and thus are the focus of this study.

A specific question that we will address in this study is, How is the barrier layer maintained? The following mechanism for the maintenance of the barrier layer has been hypothesized by Lukas and Lindstrom [1991].

As in the model of Atlantic Ocean 18øC water formation by Woods and Barkman [ 1986], we believe that mixed layer waters formed in the near-equatorial region in the vicinity of the international date line are subducted below the extremely light surface waters of the western Pacific as they are moved westward in the South Equatorial Current (SEC).

definition proposed by Cushman-Roisin [1987] has thus been adopted.

Subduction is the process by which mixed-layer convergence and/or retreat leave formerly turbulent fluid to become part of the underlying stratum.

Note that the process seen in the Lagrangian mixed layer model of Woods and Barkman [1986] is subduction accord- ing to the above definition, since it does not require vertical shear.

To answer the question mentioned earlier, an attempt was made to simulate the observations using a one-dimensional mixed layer model in a Lagrangian framework. The trajectory of the upper water column is calculated using the output

1

velocity field of a 1• layer reduced gravity model. The hypothesized subduction mechanism is tested by examining the processes in the model results. This simple model success- fully simulated major features of the upper ocean structure in this region, and the subduction mechanism is evident in the model results. The results of the Lagrangian model are compared with the results of a locally forced Eulerian model. The effect of horizontal advection on the upper ocean thermohaline structure in the western Pacific is discussed.

Since a major assumption of the model is that there is no vertical shear throughout the water column, the effect of shear cannot be examined in this study. The model was run only in an area where vertical shear is generally weak. However, vertical shear may s•r0ngly affect the upper ocean structure near the equator. This will be discussed briefly using the published results of observations and modeling.

A further attempt was made to examine how the mixed layer temperature variation is controlled by various processes. The mixed layer temperature of the model is roughly consistent with the observations, and important processes are identified. However, a robust conclusion about the mixed layer temperature variation could not be obtained because of the importance of short timescale variation and the uncertainty of the surface forcing.

This paper is organized as follows. Section 2 presents observations that will be compared with the results of mixed layer models. In section 3 the results of the Lagrangian mixed layer modeling are presented, and the processes that control the variation of the upper ocean structure are discussed. In section 4 the results of the locally forced Eulerian mixed layer model are compared with the results of the Lagrangian model. A discussion of the results is presented in section 5. Finally, the conclusions are stated in section 6.

In this manner, the warm and salty water below the fresh mixed layer in the western Pacific is maintained because mixed layer waters in the central Pacific are saltier and of nearly the same temperature as in the western Pacific.

The specific objective of this study is to test the subduction mechanism hypothesized by Lukas and Lindstrom [1991] using a simple mixed layer model. The mixed layer model is studied in a Lagrangian framework, since horizontal advection and surface mixing are both important in the subduction mechanism.

Subduction is a term that has been used recently in physical oceanography, and its definition is still somewhat ambiguous. Yet, a specific definition of subduction is necessary for the use of the term in this study. The following

2. Observations

In this section, hydrographic observations which are compared with results of the Lagrangian mixed layer model and the locally forced Eulerian mixed layer model are briefly discussed.

CTD data used in this study are listed in Table 1. These data are described in a paper by Delcroix et al. [1992].

Figures l a and lb show the time series of CTD temperature and salinity profiles averaged over 4øS-7øS along 165øE during 1987-1988. This latitudinal range is chosen because the vertical shear in this region is generally weak (Figure 2), and the major assumption of the Lagrangian mixed layer model is that there is no vertical shear throughout the water

SHINODA AND LUKAS: LAGRANGIAN MIXED LAYER MODELING 2525

o

50

100

150

200

Temperature 165E 4S-7S a

1987 I • 1988

Salinity 165E 4S-7S b

ø I 50

200 '/•' "' """2"•' I" ' ' '' '' '•' '" I 1987 1988

Time (year)

Figure 1. Time series of (a) temperature and (b) salinity along 165øE between 4øS and 7øS from CTD observation during 1987-1988. Dashed lines indicate the mixed layer depth. Triangles indicate time of cruises.

column. Dashed lines indicate the mixed layer depth. A density gradient criterion of 0.01 kg/m 4 is used for the estimation of the mixed layer depth [Lukas and Lindstrom, 1991]. To eliminate the very short timescale shallow mixed layer due to an occasional near-surface salinity gradient associated with heavy rain, data obtained from depths less than 10 m are not used for determination of the mixed layer depth [Delcroix et al., 1992]. Note that the data have limited temporal resolution and are aliased.

The large interannual variation of the upper ocean structure in the western equatorial Pacific is seen. The mixed layer was shallow during 1987 and the first half of 1988 and then became deep in mid-1988. The top of the thermocline is shallow during 1987, and it became deep in 1988. The barrier layer is seen during early 1987, the first half of 1988, and late 1988. Strong salinity stratification is evident in the upper 50 m. The mixed layer salinity is more than 34 practical salinity

units (psu) most of the time, and the salinity below the mixed layer is much higher than the mixed layer salinity.

3. Lagrangian Mixed Layer Modeling

A Lagrangian mixed layer model was used to simulate the Atlantic 18øC water formation by Woods and Barkman [1986]. The model simulated the nearly isothermal layer, which is formed by the subduction of the well-mixed water beneath the seasonal boundary layer.

Because horizontal advection and surface mixing are both important in the subduction mechanism hypothesized by Lukas and Lindstrom [1991], the mixed layer model in a Lagrangian framework is useful for the present study. In this section, the Lagrangian mixed layer model is used to examine the hypothesized subduction mechanism.


1984-1986 Mean Measured Zonal Current (cm/s) ref. 600db

20S 15S

If r>,

"•,• ========================

5N 1ON

Latitude

Figure 2. Reference section of measured zonal current at 165øE, calculated from the 1984-1986 SURTROPAC cruises [after Delcroix et al., 1992]. The contour interval is 10 cm/s; shaded areas denote westward flows. Currents are relative to 600 dbar. The mean 23.5cr t isopycnal is denoted by the heavy dashed line.

3.1. Method

The one-dimensional bulk mixed layer model of Garwood [1977] is integrated along the trajectory derived from the

Naval Research Laboratory (NRL) 1E layer reduced gravity model [Hurlburt et al., 1992; Walcraft, 1991; Kindle and Phoebus, 1995]. The trajectory simulation is explained in Appendix A, and the mixed layer model and model constants

used in this study are presented in Appendix B. The 1E layer model is explained in Appendix C.

Since only monthly wind data are available, the model based on the turbulent kinetic energy budget is appropriate for the present study. The shear instability model [e.g., Price et al., 1986] is useful only if short timescale wind data are available because the mean current shear due to inertial

oscillations causes mixing in the model. The mixed layer model includes the effects of vertical

advection as a parameter. The vertical velocity is zero at the surface, and it varies linearly with depth in the mixed layer [Muller et al., 1984]. The vertical velocity below the mixed layer is assumed to be constant, and the velocity at the bottom of the mixed layer is given by

W_h(t ) = Dhr/Dt (1) 1

where h r is the upper layer thickness of the 1• layer model. This vertical velocity formulation is inconsistent with the

vertical velocity profile of the 1• layer reduced gravity model. However, observations suggest that the use of the profile is appropriate for this study [Bryden and Brady, 1989; Halpern et al., 1989; Delcroix et al., 1992]. For instance, Bryden and Brady [1989] estimated the vertical velocity profile using the current meter data in the equatorial Pacific. The results indicated that the maximum vertical velocity is found around 70-m depth and gradually decreases below this depth [Bryden and Brady, 1989, Figure 4]. The temperature variation of the upper ocean in the western equatorial Pacific during 1986-1989 shows that the thickness of the upper sharp

thermocline below 70 m is almost constant during 1987-1988 when strong upwelling and downwelling occurred [Delcroix et al., 1992, Figure 11]. This suggests that the vertical velocity below 70 m in the upper ocean is almost constant.

The upper layer thickness of the 1• layer model in the western and central equatorial Pacific is about 180-200 m most of the time (Figure 5). Thus the vertical velocity profile used in this study seems to be similar to the profile in the real ocean in comparison with the profile that is consistent with

the 1• layer model (linearly depth dependent in the upper layer of the 1E layer model and constant below).

Since temperature and salinity profiles at the initial location and time are not available, the climatological seasonal data compiled by Levitus [1982] are used. Since only data at standard depths are available, cubic splines are used to interpolate data to each grid point of the mixed layer model.

The monthly wind stress data that were used to force the

1• layer model are also used to estimate the surface momentum flux for the mixed layer model. The hybrid wind stress data sets were created at NRL (J. Kindle, personal communication, 1994) by adding monthly averaged anomalies of the European Center for Medium-Range Weather Forecasts (ECMWF) 1000-mbar wind analyses to the Hellerman and Rosenstein [1983] wind stress climatology. A constant value of the drag coefficient 1.7 x 10 -3 is used. The spatial resolution of the wind stress data is 1 ø in latitude and 1.4 ø in

longitude. : The Global Precipitation Climatology Project (GPCP [Ar-

kin and Ardanuy, 1989]) data are used to estimate surface freshwater fluxes. GPCP data provide the 5-day accumulated rainfall estimated for the area of 2.5 ø longitude x 2.5 ø latitude. Precipitation is estimated by a simple cloud-top temperature thresholding algorithm using infrared data from geostationary and polar-orbiting satellites. Details of the estimation method from the satellite data are explained by Janowiak and Arkin [ 1991].


The latent and sensible heat fluxes at the surface and

evaporation are estimated using the observed wind stress data, along with monthly climatological specific humidity and air temperature [Esbensen and Kushnir, 1981]. Sea surface temperature of the mixed layer model at each time step is used for the flux calculations. Since winds are often weak in the western equatorial Pacific, the parameterization by Liu et al. [1979] is used. This method includes the dynamics of the interfacial sublayers on both sides of the air-sea interface where molecular constraints on transports are important. The increase of bulk exchange coefficient at low wind speed under unstable conditions is predicted by the method. Bradley et al. [1991] concluded that the bulk coef- ficients for the sensible heat and water vapor derived from their direct measurements of latent and sensible heat flux

during May 1988 in the western equatorial Pacific agree well with predictions of the model by Liu et al. [1979].

Incoming solar radiation data along the trajectories during the period of this study are not available. A linear relationship between precipitation rate and fractional cloudiness of high cloud is suggested using the satellite IR brightness data during the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE) [Arkin, 1979; Albright et al., 1985]. Since cloud data from all heights are necessary to calculate the incoming solar radiation, the relationship between rainfall and cloudiness is examined using the monthly climatological cloudiness data [Esbensen and Kush- nir, 1982] and GPCP data in the western and central Pacific (125øE-130øW, 12øN-12øS). Average precipitation of each month during 1986-1989 from GPCP data is used. The following formula is obtained by least squares fit:

C = 0.0039361Pr + 0.46960 (2)

where C is the cloudiness and P r is the 5-day accumulated rainfall in millimeters. In this manner, the interannual variation of incoming solar radiation can be roughly included. The monthly cloudiness in the western and central equatorial Pacific is more than 0.5 most of the time [Esbensen and Kushnir, 1981].

The formula given by $eckel and Beaudry [1973] is used for the daily averaged short-wave solar radiation under clear-sky conditions. The formula is valid between latitude 20øS and 40øN [$eckel and Beaudry, 1973]. The cloud correction formula by Reed [ 1977] is used for the calculation of incoming solar radiation. Godfrey et al. [1991] tested the various empirical formulae of the surface heat flux by comparing with the measurements in the western equatorial Pacific during May 1988. They concluded that Reed's formula performed best for the short-wave radiation.

The sea surface albedo was taken to be a constant 6%

[Payne, 1972]. Payne [1972] showed that the average value of the surface albedo is approximately constant for low latitudes.

The net long-wave radiation is calculated using the formula originally suggested by Brunt [1932] and modified by Berliand and Berliand [1952] (cited by Budyko [1974]). Godfrey et al. [1991] also concluded that this formula for long-wave radiation best agrees with observations in the western equatorial Pacific. Monthly climatological sea level pressure data [Esbensen and Kushnir, 1981] are used for the calculation.

All components of the surface forcing at daily successive positions obtained by trajectory simulation are estimated.

Table 2. Data Used for the Estimation of Surface

Forcings

Surface Forcing Data

Precipitation GPCP data Surface wind Forcing of the 13 layer model (monthly mean) Latent heat flux Monthly climatological specific humidity

[Esbensen and Kushnir, 1981] SST of mixed layer model Monthly mean wind

Evaporation Monthly climatological specific humidity [Esbensen and Kushnir, 1981]

SST of mixed layer model Monthly mean wind

Sensible heat flux Monthly climatological air temperature [Esbensen and Kushnir, 1981]

SST of mixed layer model Monthly mean wind

Incoming solar Relation between monthly climatological radiation cloudiness [Esbensen and Kushnir, 1981] and

GPCP data

Long-wave Monthly climatological sea level pressure radiation [Esbensen•and Kushnir, 1981]

SST of mixed layer model ,

Monthly dlimatological specific humidity [Esbensen and Kushnir, 1981]

Monthly climatological air temperature [Esbensen and Kushnir, 1981]

Relation between monthly climatological cloudiness [Esbensen and Kushnir, 1981] and GPCP data

Linear interpolation in space and time is used to calculate the forcing at daily positions along the trajectory. Data used for the estimation of surface forcings are listed in Table 2.

Upper layer thickness along the trajectory is calculated to estimate the vertical velocity in (1). Four-point Lagrangian interpolation in time and 16-point Lagrangian interpolation in space are used to obtain the values at successive daily positions.

Artificial mixing in the 1F layer model is included to avoid surfacing of the interface when the upper layer thickness becomes less than 75 m. If this mixing occurs, the vertical velocity formulation of (1) is not appropriate. Thus the trajectory in which the upper layer thickness becomes less than 75 m is not used for the integration of the mixed layer model. This happens in only one out of 168 trajectories calculated in this study (the trajectory that reached 165øE, 5øS in October 1987).

3.2. Results

Integrations of the mixed layer model were carried out for the time period 1987-1988 to compare with the observations that show the large interannual variation of the upper ocean structure in the western equatorial Pacific.

The major assumption of this model is that there is no vertical shear throughout the water column. Because of this assumption, the model is applicable to a limited area. Figure 2 shows the average zonal current at 165øE during 1984-1986 measured by profiling current meter [Delcroix et al., 1992]. Because interannual variability of the atmosphere and ocean in this region was relatively small during this period, this velocity section is considered to be representative of the mean current structure of this region [Delcroix et al., 1992]. Strong vertical shears exist in the latitudinal range of 5øN - 3øS in this region (Figure 2). The vertical shear is small


Zonal Transport 165E 2.75S-7.25S

15

lO

5

o

-10 -15

-25

-30 1986 1987 1988

Time (year)

b 20

SEC Transport 165E (Upper 300 db)

-20

-40

-80

-12½ 1986 1987 1988

Time (year)

Figure 3. l(a) Zonal transport through 165øE, 2.75øS-7.25øS from the 1• layer model during 1986-1988. (b) SEC transport estima?ted by Delcroix et al. [1992].

between 4øS and 8øS. In this study, the results of calculations along the trajectories that reach the area 165øE, 4øS-7øS will be discussed, since it is possible to compare with the large number of CTD profiles that have been made there in recent years [Delcroix et al., 1992].

Figure 3a shows the zonal current transport through

165øE, 2.75øS-7.25øS from the 17 layer model output. The area corresponds to the SEC region. The Equatorial Under- current (EUC) region is omitted because there is no EUC in

the 17 layer model. In mid-1986 and mid-1988, westward transport is large, and during 1987, westward transport is small. Delcroix et al. [1992] estimated the variation of the SEC transport at 165øE using current meter data. The period of the large westward transport as estimated from the

1

observations roughly agrees with the 17 layer model output • (Figure 3b).

Figure 4 shows the 1-year trajectories of the upper water column calculated backward every 1/2 ø latitude between 4øS

and 7øS along 165øE using the output of the 17 layer model. Each trajectory computation was started in the middle of each month during 1987-1988; 168 trajectories were calculated. Because of the variation of the SEC, the water column comes from various locations. During periods of strong SEC, the water column comes from the central Pacific and crosses the international date line. In other periods, the water column stays in the western Pacific. Since zonal velocity is dominant in this region, most of the trajectories do not cross the equator, where the vertical shear is very strong.

Figure 5 shows the upper layer thickness variation along

5øS from the output of the 17 layer model during 1986-1988. Pronounced upwelling during 1987 is seen, with the upper layer relatively thin in the western Pacific in mid-1987. The westward propagation of upper layer thickness variation is clearly seen in this area during the entire period. During 1988, downwelling occurs throughout entire region, and the upper layer becomes much thicker than it was in mid-1987. The phase speed of this propagation is approximately 0.7 m/s, which agrees with the phase speed of the equatorial Rossby wave of the first meridional mode (see the dashed line in Figure 5). Thus it is considered that these variations are caused partly by Rossby waves. Upwelling Rossby waves have also been observed by satellite altimetry data during this period [Delcroix et al., 1991].

The integration of the mixed layer model along all trajectories shown in Figure 4 was carried out, and the average temperature and salinity profiles along 165øE, 4øS-7øS were calculated for each month. Figure 6 shows the monthly variations of temperature and salinity along 165øE between 4øS and 7øS during 1987-1988. The dashed line shows the mixed layer depth predicted by the mixed layer model. Because of salinity stratification, the mixed layer was shallow except in mid-1988. The top of the thermocline was deep in early 1987, and it became shallow during 1987 because of upwelling Rossby waves. It became deep again in early 1988 because of downwelling Rossby waves. As a result, the barrier layer is seen during the beginning of 1987 and the first half of 1988. The mixed layer became deep during August- September 1988 due to the strong wind and relatively light precipitation in the western Pacific. The variation of the major features of the thermohaline structure predicted by the model is at least roughly consistent with the CTD data (Figure 1).

However, there are various quantitative differences. For instance, the mixed layer depth of the model in mid-1987 differs from the observation by more than a factor of 2. The mixed layer temperature of the model is higher than the

15N[ Trajectory

15S 140E 160E 180 160W 140W

Longitude

Figure 4. One-year trajectories of the water column derived from the l• layer model output. The locations of the end of the traject6ries are (165øE, 4øS) (165øE, 4.5øS), (165øE, 5øS), (165øE, 5.5øS), (165øE, 6øS), (165øE, 6.5øS), and (165øE, 7øS). Each trajectory reaches 165øE in the middle of each month during 1987-1988. Dots indicate grid points of land.

SHINODA AND LUKAS' LAGRANGIAN MIXED LAYER MODELING 2529

1988

Upper Layer Thickness (m) SS

• •-• -> _

1987

'* • I 16•_%0• 17•_.5 . 17

1986 • 17 .... ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ?iiiiilili::i::::::::i!•::•::•:• .......

160'E 170'E 180'E 170øW 160øW 150øW 140øW

Longitude

1 o Figure 5. Upper layer thickness of the 1= layer model along 5 S. Values smaller than 150 m are shaded. 2

Dashed line shows the characteristic of tlSe equatorial Rossby wave of the first meridional mode for the 1

17 layer model.

observation most of the time. The mixed layer salinity predicted by the model during April-May 1988 is too low.

Typical examples from the experiments will be shown in the following to discuss the important processes.

Figure 7a shows one of the trajectories. The location of the end of the trajectory is at 165øE, 5øS in July 1988. Since the SEC was strong from early 1988 to mid-1988 (Figure 3), the water column came from the central Pacific.

Figure 7b shows the temperature and salinity distribution along the trajectory. The wind stress and the evaporation minus precipitation along the trajectory are shown in Figure 7c, and net surface heat flux is shown in Figure 7d. Note that the time axis goes from right to left in these figures. The wind is strong and evaporation exceeds precipitation most of the time in the beginning because the water column started from the central Pacific; the wind becomes weak and the precipitation exceeds the evaporation as the water column moves to the western Pacific.

Both the top of the thermocline and the mixed layer are deep in the central Pacific due to the strong wind and downwelling Rossby waves. The shoaling of the mixed layer occurs due to weak wind and heavy precipitation as the water column moves westward. This causes the westward

advection of warm salty water below the fresh shallow mixed layer in the western Pacific, and the barrier layer is formed in the first half of 1988. The high salinity below the mixed layer is maintained. This mechanism is hypothesized by Lukas and Lindstrom [1991]. The same processes are frequently seen in the experiments.

The mechanism is seen in the experiments using the trajectories that reached 165øE, 4øS-7øS in March-May 1987, June-July 1988, and October 1988. In these cases the water came from the central Pacific due to the strong SEC, and the local wind in the western Pacific was not very strong. Also precipitation was heavy in the western Pacific. Thus the barrier layer was maintained due to the advection of warm and salty waters from the central Pacific.

The barrier layer was not seen in the model during

June-September 1987 and August-September 1988 in the western equatorial Pacific, although most of the water column came from the central Pacific during these periods. Different processes are seen in these periods, as will be shown in the following paragraphs.

Figure 8b shows the temperature and salinity distribution along the trajectory shown in Figure 8a. The end of the trajectory is at 165øE, 5øS in July 1987. Wind stress and evaporation minus precipitation along the trajectory are shown in Figure 8c, and net surface heat flux is shown in Figure 8d. Similar processes shown in Figure 7 are seen during the westward advection of the water column in the beginning, and both the mixed layer and the top of the thermocline are deep in the central Pacific. However, the upwelling Rossby waves reach the western Pacific in mid- 1987 (Figure 5) and cause the top of the thermocline to shoal. No barrier layer in the western Pacific is seen in this case because of the upwelling.

Figure 9 shows results for a trajectory ending at 165øE, 4.5øS in September 1988. The barrier layer is formed due to the same mechanism shown in Figure 7. However, the relatively strong wind and light precipitation in the western Pacific during this period cause a deep mixed layer, and the barrier layer is eroded.

The barrier layer is also seen in the beginning of 1988, but the salinity in this part of the water column is lower than in other periods (Figure 6). During this period, the water column stays in the western Pacific because of the weak SEC. The arrival of downwelling Rossby waves causes the deepening of the top of the thermocline in the western Pacific. In this case, the water below the mixed layer does not come directly from the central Pacific, and thus the salinity of the isothermal layer is lower. This is also seen in the observations (Figure lb).

Figure 10 shows the time series of the mixed layer temperature of the model and the observation along 165øE, 4øS-7øS during 1987-1988. The variation of the model roughly agrees with the observation. The correlation coeffi-


o

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150-

200

Temperature 165E 4S-7S a

1987 1988

5O

150

200

Salinity 165E 4S-7S

ß

1987

b

Time (year)

Figure 6. Monthly variations of (a) temperature and (b) salinity along 165øE between 4øS and 7øS predicted by the mixed layer model during 1987-1988. Dashed lines indicate the mixed layer depth.

cient of the mixed layer temperature between model and observation is 0.80. The model's mixed layer temperature is linearly interpolated to time of observations for the calculation. The prominent cooling that occurred in mid-1987 is seen in both model and observations, including the equatorial mooring data at 165øE during 1987 [McPhaden and Hayes, 1991]. The mixed layer warmed in late 1987 and cooled in mid-1988. The mixed layer temperature predicted by the model does not agree well with the observations in late 1988, which

could be due to the poor performance of the 17 layer'model. Figure 3 shows that the current of the model along 165øE, between 3øS and 7øS in this period was eastward. However, a strong SEC was measured by acoustic Doppler current profiler (ADCP) during this period [Bahr et al., 1990; Del- croix et al., 1992]. It is possible that horizontal advection of water from the central Pacific reduced the mixed layer temperature in the western Pacific during this period, since waters are colder in the central than in the western Pacific.

10N

5N

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10S ......................... .......................

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15S ...................... 130E 140E 150E 160E 17•E 1•0 17•)W 16•W 15•)W 140W Longitude

Figure 7a. One-year trajectory which ends at 165øE, 5øS in July 1988. Circle indicates the origin of the trajectory.


Temperature o

5o •

100 | ß • . :] :: .. ] • I. oOø '.oø •

88.5 88.0

Time (year)

Salinity o

• .

•35'

200 ••5'• 88.5 8•.0

Time (year)

Figure 7b. (Top) Temperature and (bottom) salinity distribution along the trajectory shown in Figure 7a. Dashed lines indicate the mixed layer depth.

The dominant process during mid-1987 is evaporative cooling. This is shown in Figure 8. Cooling occurs in the end of the experiment due to the strong wind (Figure 8c). Because of the penetrating solar radiation, warming below the bottom of the shallow mixed layer occurs before the cooling starts. The temperature inversion is maintained by the salinity stratification and rapid evaporative cooling. Entrainment cooling does not occur due to the temperature inversion in this case, even though deepening of the mixed layer occurs.

Because of heavy precipitation during this period (Figure 8c), the temperature inversion is maintained for a relatively long time even though the wind is strong. Entrainment cooling starts only after the temperature inversion layer is eroded by the mixing due to the strong wind. The entrainment cooling does not significantly affect the mixed layer temperature variation compared with the evaporative cooling in all experiments during July-September 1987 when the

upwelling Rossby waves reach the western equatorial Pa- cific. Thus the observed cold mixed layer temperature can be explained by the evaporative cooling due to the strong wind during this period. This result is consistent with the conclusion of McPhaden and Hayes [1991] that evaporative cooling is the most important process for the variation of sea surface temperature (SST). However, it is possible that shorter timescale, strong wind events cause much larger entrainment cooling. This will be discussed in section 5.

In summary, the subduction mechanism shown in Figure 7 is seen during periods of strong SEC except when the upwelling Rossby waves reached the western equatorial Pacific or when a prominent deepening of the mixed layer occurred. During periods when the subduction mechanism is seen, high salinity below the mixed layer is maintained because the water below the mixed layer is advected from the central Pacific. The cooling of the mixed layer in mid-1987 is mainly caused by evaporative cooling due to the strong wind.


0.12

0.1

E 0.08

• 0.06 .c_

0.04

Wind Stress Net Surface Heat FlUx , , i , i , I i , ,

0.5

E 0

'•o -0.5

.o_ -1

o

•.-2.5

-3.5

Time (year) Time (year)

Evaporation-Precipitation

I

Time (year)

Figure 7c. (Top) Wind stress and (bottom) evaporation minus precipitation along the trajectory shown in Figure 7a.

Figure 7d. Net surface heat flux along the trajectory (pos- itive downward).

4. Locally Forced Eulerian Mixed Layer Model In this section, we discuss the results when the mixed

layer model is run in a Eulerian framework that uses local forcing in the warm pool. The effect of horizontal advection is examined by comparison with the results of the Lagran- gian mixed layer modeling. Vertical motions caused by remote and local forcing are included in the mixed layer model, and horizontal advection is neglected. The model was run during 1986-1988 at locations every 1/2 ø latitude between 4øS and 7øS along 165øE. The surface forcing of the model is computed in the same way as in the Lagrangian mixed layer model.

The vertical velocity is calculated using the following equation:

Ohr W_h(t ) =

ot

1

where h r is the upper layer thickness of the 1• layer model. Figures 11a and l lb show the temperature and salinity

time series of the model results averaged over 4øS-7øS along

165øE. The results are compared with the temperature and salinity of the water parcels that arrive at this area at different time periods. Since the temperature and the salinity profiles in the Lagrangian model in January 1987 shown in Figure 6 are the results of 1-year integration from January 1986, the Eulerian model was integrated also from January 1986 for comparison. The variation of the thermal structure is similar to that of the Lagrangian mixed layer model. Because of the vertical motion and variation of wind, the barrier layer is evident during the same period as in the Lagrangian mixed layer model (Figure 6a). The mixed layer depth is also similar, as in the Lagrangian model results.

The upper.layer salinity is significantly different from the results of the Lagrangian mixed layer model. The initial surface salinity was about 34.8 psu at the beginning of 1986, and it decreased because of heavy local precipitation. The salinity became less than 34 psu in early 1986 and increased because of the enhancement of entrainment due to the

upwelling in mid-1986. The mixed layer salinity decreased again, down to about 33.0 psu by early 1987. Then the mixed layer salinity increased in mid-1987 because of the enhance-

10N

5N

10S ........................ .......................

.......................

.......................

....................

....................

....................

....................

.....................

15S ...................... 130E 140E 150E 160E 170E 180 170W 160W 150W 14•

Longitude

Figure 8a. One-year trajectory which ends at 165øE, 5øS in July 1987.


Temperature

2

87.$ 87.0

Time (year)

Salinity

150

87.5 87.0

Time (year)


ment of entrainment due to the upwelling. In 1988 the mixed layer salinity became very low due to heavy precipitation, down to approximately 32.8 psu by mid-1988. During this period, a much higher mixed layer salinity occurred in the Lagrangian mixed layer model. For instance, in July 1988 the mixed layer salinity was about 34.8 psu because the high- salinity water below the mixed layer is mixed with the waters of the mixed layer (Figure 7b). Near the end of 1988 the salinity of the upper 100 m was less than 33 psu, which is much less than the observed upper ocean salinity in this region. Since stratification of salinity was weak in late 1988, the mixed layer was deeper than in the results of the Lagrangian model.

In summary, the upper layer salinity gradually decreases due to the heavy local precipitation in this region except during periods of upwelling. On the interannual timescale the occasional upwelling cannot maintain the observed upper layer salinity, and it decreases gradually. Thus these results

indicate that the horizontal advection of salty water from the central Pacific significantly affects the upper layer salinity variation and that it is necessary to maintain the upper ocean thermohaline structure of the warm pool.

5. Discussion

Despite the simplicity of the model, the results of the Lagrangian mixed layer model roughly agree with observations, and important processes are identified. In this section, major assumptions and uncertainties of the model are discussed.

One of the major uncertainties of this study is the velocity

field of the 15 layer model. Although the period of the strong zonal current of the model roughly agrees with the observation, the magnitude of the velocity does not agree well. In

general, the observed SEC is stronger than the 15 layer model output. For instance, during May 1988 the average

2534 SHINODA AND LUKAS' LAGRANGIAN MIXED LAYER MODELING

0.12

0.1

E 0.08 z

03 0.06

.c_

0.04

0.02

Wind Stress

08715 8714 Time (year)

Evaporation- Precipitation , , , i

-3.5r

-4

-4.5

Time (year)

Figure 8c. (Top) Wind stress and (bottom) evaporation minus precipitation along the trajectory shown in Figure 8a.

velocity of the upper 200 m near 165øE, 5øS measured by ADCP is approximately 0.5 m/s [Bahr et al., 1990; Delcroix et al., 1992]. On the other hand, the model output shows that the velocity in this region is about 0.2 m/s.

If the SEC in the 15 layer model is stronger, the subduction mechanism discussed in the previous section is seen more frequently in the model results, since more trajectories originate in the central Pacific. Also, strong westward current may affect the mixed layer salinity of the model. For instance, the mixed layer salinity during May 1988 predicted by the Lagrangian model is approximately 32.8 psu, which is much lower than the observation. Since the water column

stays in the western Pacific during 1 year in this case, the precipitation is always heavy along the trajectory. Thus low mixed layer salinity is predicted. If the SEC is stronger, the water column comes from the central Pacific, where the evaporation exceeds the precipitation, and higher mixed layer salinity may be predicted. This is demonstrated by experiments that use the velocity field multiplied by 2 [Shinoda, 1993]. Thus it is considered that the results will be improved if more accurate velocity data are used.

One of the major assumptions of the model is that there is

Net Surface Heat Flux , , , • , , ,

Time (year)

Figure 8d. Net surface heat flux along the trajectory.

no vertical shear throughout the water column in the upper 200 m. Thus the subduction mechanism is not seen in the

model during periods when the upper layer velocity is eastward. However, it is possible that, in reality, the subsurface westward current causes the horizontal advection of

the water from the central Pacific below the mixed layer during this period. Westward flow below a surface eastward current is often observed in this region. For instance, during January-February 1990, ADCP data along the equator show this westward flow below the eastward flow in the upper 80 m in the western Pacific, and a strong convergence of zonal current near the date line was found [Kuroda and McPhaden, 1993]. If this zonal convergence of mass is not compensated by meridional divergence, subduction occurs due to the subsurface westward current and the downwelling near the date line. Thus it is considered that subduction

occurs more frequently in the real ocean because of the vertical shear neglected in the model.

The vertical shear observed above the top of the thermocline may in fact be related to the strong horizontal salinity

gradient. Roemmich et al. [1994] used a 15 layer model that includes horizontal salinity gradients to show that the zonal

10N

5N

'..

...

10S ........................ .......................

.......................

.......................

....................

....................

::::::::::::::::::::::

z5•S3o•. z4o•. zs•)•. zo•)•. z?o•. z8o z?ow zoow z•ow z4ow Longitude

Figure 9a. Trajectory which ends at 165øE, 4.5øS in Sep- tember 1988.


Temperature o

- :.

100 ' ø' •

200 '• •.5 •.0

50

• 100

150-

200

Salinity Time (year)

.

88.5 88.0

Time (year)


salinity gradient created by the difference of freshwater flux between the western and the central Pacific drives the

vertically sheared eastward jet. They also suggest that this vertically sheared eastward jet produces the salinity barrier layers at the onset of E1 Nifio. However, their study only addressed short timescale processes. The timescale of accel- eration of the jet is about 20 days, and longer timescale processes due to the zonal salinity gradient are far more complicated [Roemmich et al., 1994].

The comparison of the results of the present study with a three-dimensional model that includes the surface mixed

layer is necessary to examine the effect of vertical shear in further detail. Recently, Gent and Cane [1989] developed a reduced gravity, primitive equation model of the upper equatorial ocean. Since the model is able to include an arbitrary number of numerical layers below the mixed layer by means of a sigma-coordinate system, it can be modified for the present problem. Modification of the model by

including an explicit salinity budget and turbulent mixing was already proposed, and it is expected that the results will be reported soon (L. Rothstein, personal communication, 1993). Thus comparison with the three-dimensional model will be possible in the near future. However, because of the complexity of the three-dimensional model, it may be diffi- cult to identify the various important processes from the results. Since the model in this study is fairly simple, it is very useful to understand the essential processes in the complex model.

CTD data analyses show that there is a barrier layer in the region of the eastward North Equatorial Counter Current (NECC), even though it is thinner than in some other regions [Shinoda, 1993]. Since strong vertical shears are usually seen in this region, the model is not adequate, and trajecto-

ries calculated from the 17 layer model may not be reliable. Using the current observations, possible explanations for the existence and maintenance of the barrier layer in the NECC


0.12

0.1

0.08

0.06

0.04

0.02

Oh 88.7

0.5

-3.5

Wind Stress i i i i i i i i ,

Time (year)

Evaporation-Precipitation i i i i i i i i i

-4.;

Time (year)

Figure 9c. (Top) Wind stress and (bottom) evaporation minus precipitation along the trajectory.

region are provided. During the U S-PRC 4 cruise, strong subsurface westward currents at depths shallower than 100 m were observed at 165øE between 3.5øN and 7øN [Bahr et al., 1989]. In this case, the high-salinity water below the mixed layer was possibly advected from the central Pacific to the NECC region. Subsurface westward currents at depth near 100 m were also evident at 141.5øE between 4øN and

6øN during the U.S.-PRC 3 cruise. Since the current usually flows eastward in this region, the barrier layer is much thinner. Because the position and the width of the NECC changes in time, this could be the explanation for the existence and maintenance of the barrier layer in this region. During the US-PRC 4 cruise, a northward meridional velocity of 0.2-0.4 m/s in the upper 100 m was observed at 165øE between the equator and 4øN. Thus it is possible that the warm and salty waters below the mixed layer in the SEC region are advected to the NECC region. A three- dimensional model is necessary to demonstrate these processes in further detail.

Uncertainty of the surface forcing is the major problem for mixed layer studies at present. In particular, in the western equatorial Pacific, where the freshwater flux plays such an

Net Surface Heat Flux

.

-20

10 887 886 885 884 883 882 881 88 879 8 8

Time (year)

Figure 9d. Net surface heat flux along the trajectory.

important role in the mixed layer thermodynamics, the accuracy of precipitation affects the results. However, the accuracy of the estimated rainfall accumulation of GPCP data cannot be quantified because the required high- resolution "ground truth" data sets are not yet available [Janowiak and Arkin, 1991]. However, preliminary results from the Tropical Ocean Global Atmosphere-Coupled Ocean Atmosphere Response Experiment (TOGA-COARE) suggest that the GPCP data are accurate to about 20% in the warm pool (P. A. Arkin, personal communication, 1994).

Short timescale wind variation may also affect the upper ocean structure, especially in the western equatorial Pacific, where wind forcing is fairly intermittent [Lukas, 1988; Lukas and Lindstrom, 1991]. For instance, in the case of strong SEC, the results in the central Pacific, where easterly trade winds are relatively steady, may not be strongly affected, but when the water column reaches the western Pacific, the results may be modified by energetic high-frequency variability of the wind. During mid-1987 the entrainment cooling

30.5 Mixed Layer Temperature 165E 4S-7S

30

29.5

28.5

-- Model ........ Observation

Time (year)

Figure 10. Time series of the mixed layer temperature along 165øE, between 4øS and 7øS as predicted by the model and observation.


50

lOO

150

200

Temperature 165E 4S-7S

1986

':; ' "' .;:...•v •

...........

1987 1988

Salinity 165E 4S-7S b 0 u

100

1501

200

1986 1987 1988

Time (year)

Figure 11. Results of the locally forced Eulerian mixed layer model for (a) temperature and (b) salinity averaged over 4øS-7øS along 165øE.

does not significantly affect the mixed layer temperature variation compared with the evaporative cooling due to the temperature inversion maintained by the salinity stratification and rapid evaporative cooling. However, since monthly wind data are used in this study, entrainment cooling in the western Pacific might be underestimated because energetic wind events can rapidly deepen the mixed layer. The evaporative cooling is proportional to the wind speed in the bulk formula. On the other hand, the entrainment cooling depends on the deepening rate of the mixed layer, which is a function of u, 3, where u, is the friction velocity defined by u, = (r/p)•/2. Thus the relative importance of entrainment cooling and evaporative cooling might strongly depend on the wind speed [Lukas, 1988]. Wind data from the equatorial mooring at 165øE show that short timescale strong westerly wind events frequently occurred during mid-1987 [McPhaden et al., 1990]. Thus it is possible that entrainment

cooling significantly affects the SST during the period when upwelling Rossby waves reach the western Pacific.

Further quantitative discussion is not possible at present, considering the uncertainty of the surface forcing. It is necessary to examine short timescale variability of the upper ocean using the short timescale surface forcing data. This would be possible in the near future, since a substantial amount of atmospheric and oceanic data were taken during the recent TOGA-COARE [Webster and Lukas, 1992]. It is expected that the effects of various short timescale processes of the upper ocean on the interannual variation will be identified.

6. Conclusions

A Lagrangian mixed layer model was utilized to examine how various atmospheric and oceanic processes control the


upper ocean structure in the western Pacific. A one- dimensional mixed layer model was integrated along the

trajectories derived from the 15 layer reduced gravity model. Although the model is fairly simple, it is able to simulate the barrier layer and its variation. The subduction mechanism was demonstrated by this simple model. Model results indicated that when the SEC is strong, the deepening of the mixed layer and thermocline in the central Pacific due to the strong wind causes the westward advection of warm salty water below the fresh shallow mixed layer in the western Pacific. This shallow mixed layer is due to the weak wind and heavy precipitation prevailing in this region.

The comparison of the results of the Lagrangian mixed layer model with the locally forced Eulerian version of the mixed layer model indicated that horizontal advection of salty waters from the central pacific strongly affects the upper layer salinity variation in the western Pacific and that this advection is necessary to maintain the upper ocean thermohaline structure in the warm pool.

The results suggest that the variation of surface forcing in the central Pacific affects the upper ocean structure in the western equatorial Pacific, since formation of a barrier layer in the western Pacific is associated with a deepening of the warm and salty mixed layer in the central Pacific.

The processes in the model are examined in more detail. During mid-1987, the barrier layer was not found, even though the water came from the central Pacific east of the dateline. During this period, upwelling Rossby waves reached the western Pacific and caused a relatively shallow thermocline. Although the mixed layer in the western Pacific during this period was shallow due to heavy precipitation, the barrier layer was not found in the model results because of the shallow thermocline.

During August-September 1988, a barrier layer was absent in the model results. The SEC was strong during this period, and water also came from the central Pacific. Warm and salty water in the central Pacific was advected to the western Pacific, but strong wind and light precipitation in the western Pacific during this period eroded the barrier layer.

The results of various model cases indicate that local

mixing processes, remotely forced Rossby waves, and advection in the SEC are all important for determining the variation of the upper ocean structure of the western equatorial Pacific, and the dominant processes are different in each period.

The mixed layer temperature of the model is roughly consistent with observations during 1987-1988. A prominent cooling in mid-1987 was seen both in the model and the observations. The dominant process during this period is evaporative cooling due to the strong wind. However, short timescale strong wind events possibly caused a significant amount of entrainment cooling. Since monthly wind data are used in this study, entrainment cooling is underestimated. Further studies focused on the short timescale response of the upper ocean are necessary to understand the processes that control the variation of mixed layer temperature. After the short timescale response is thoroughly examined by observation and modeling, the importance of the thermohaline structure variation for the heat budget in this region can be fully established.

Appendix A' Trajectory Simulation

The trajectory simulation during 1982-1983 was carried

out by Balena [1992] using a diagnostic 15 layer reduced gravity model. His method is used for the trajectory simulation in this study.

The integration of the velocity is carried out using a fourth-order Runge-Kutta stepping scheme and a 16-point Lagrangian spatial interpolation scheme. A stepping size of 7

days is used, since weekly outputs of the 15 layer reduced gravity model are available. The trajectory is calculated backward. The daily successive positions are calculated from the 7-day interval location. Each variable, longitude, and latitude is treated as an independent sequence of values in time, and these variables are interpolated at uniform 1-day intervals using cubic spline interpolation.

Water parcels in the western Pacific usually come from the east because of the westward flowing SEC in the area of this study. Water parcels that come within a grid cell of the western boundary were simply cut to avoid complex and inaccurate spatial interpolation [Balena, 1992]. Also, calculation near the western boundary is not very reliable because of the noisy velocity field probably due to instabilities in the western boundary current and the complex land topography

1

of the 15 layer reduced gravity model. Furthermore, since strong vertical shears in the upper layer due to the complex current structure exist in this area [e.g., Lindstrom et al.,

1987], the trajectory simulation using the 15 layer model is inappropriate. Thus the integration of the mixed layer model was started at the western boundary in this case.

Balena [1992] examined the error of the trajectory simulation using the artificial velocity field. He discussed the cases with time steps of 1 day, 5 days, and 1 month. The results show that the error of the displacement of the water column does not exceed 2.5 ø in all experiments of 1-year integration using the various artificial velocity fields. Since the time interval of 7 days is used in this study, the error of the trajectory simulation appears insignificant. Thus it seems that results of the mixed layer model are not influenced by the error caused by trajectory simulation, considering the resolution of surface forcing data.

Appendix B: Garwood [1977] Model

The Gatwood model is a bulk mixed layer model based on an integrated form of the turbulent kinetic energy budget. The model calculates the turbulent kinetic energy explicitly and distinguishes between the horizontal and vertical component of turbulent kinetic energy. The entrainment rate depends on the relative distribution of the horizontal and vertical components of turbulent kinetic energy. There are two dissipation processes. One is an isotropic dissipation which depends on the total turbulent kinetic energy, and the other is a background dissipation which depends on the Earth's rotation and the mixed layer depth.

The rate of entrainment at the base of the mixed layer is

Abhmwe = m4(q2)(w,2)1/2 (3) where

1 f_0 = q z) dz


1 f_ ,2( = w z) dz (Wt2> •mm hm where q2 = u' 2 q_ V' 2 q_ W' 2. , V' ' , u , , and w are the turbulent deviations from the average velocities; w e is the entrainment velocity, m 4 is the model constant, h m is the mixed layer depth, and Ab is the difference of the buoyancy across the base of the mixed layer.

Separate equations for the horizontal and vertical components of turbulent kinetic energy are used:

m3tt, 3- m2((q 2) - 3(w' 2))(q2)1/2

2 (m (q2 3/2 -- • 1 ) + msfhm( q ) = 0 (4)

1 1

--hmAbw - Bh +m2((q 2)- 3(w'2))(q2) 2 e • rn

ml( 2)3/2 m5 2)) • (q + • fhm( q = 0 (5) ml

B is the sum of surface buoyancy flux and the vertical integral of buoyancy flux by the absorption of heat due to the penetrating component of solar radiation, f is the Coriolis parameter, u. is the friction velocity defined by u. = (r/p) 1/2 where r is the surface wind stress and m I m2 m 3 and m5 are the model constants.

There are three unknowns (q2), (W--W'Z), and w e in (3)-(5). For given B, u., and the current he, (3)-(5) are solved

algebraically. In the case of w e < 0, (W' '•) is taken to be zero, and (4) and (5) are solved.

The prognostic equation for the mixed layer depth is given by

dhm •= -w(z = -he) + W e (6)

dt

where w is the vertical velocity. The prognostic equations for the mixed layer temperature

and salinity are

pocph -•-+ PocpATwe = Qo + Q(z) dz h

(7)

OSm h + ASw e = (E- P)S m (8)

Ot

where Q0 is surface heat flux, Q(z) is the absorption of heat due to the penetrating component of solar radiation, E is evaporation, P is precipitation, T m and S m are the mixed layer temperature and salinity, respectively, cp is specific heat, P0 is water density, AT and AS are changes of temperature and of salinity at the base of the mixed layer, respectively.

The prognostic equations for the temperature and salinity below the mixed layer are

OT OT m+ w m=0 (9) ot oz

as as •+ w•=0 (10) ot oz

where T and S are the temperature and salinity below the mixed layer, respectively.

In this study, the valuesm3 = 4.5, ml = m2 = m4 = 1, and m5 = 4.6 are used. These constants are determined by comparing with the observation at ocean weather station Papa and November, where horizontal advection is very small [Martin, 1985]. Since the model includes one of the important characteristic scales of the turbulent boundary layer u,/f [Rossby and Montgomery, 1935], it is likely that the model is applicable to a wide range of latitudes using the same constants in comparison with other bulk mixed layer models based on the turbulent energy budget. The tuning of these constants in the equatorial region is not trivial because of the effect of horizontal advection due to strong equatorial currents and the vertical advection due to equatorial waves. Since the present study provides only the qualitative agree- ment of the model results with the observations, it is believed that the use of these constants in the equatorial region is appropriate for this particular study.

The resolution of the grid for storing the profiles below the mixed layer is 1 m, and a time step of 1 hour is used. The absorption of solar radiation is approximated by an expo- nential depth dependence, assuming only part of the radia2 tion passes through the uppermost layer. The e-folding length scale of 20 m is used for the fairly clear water (type 1A [Jerlov, 1968]) in the western equatorial Pacific, and 62% of incoming solar radiation is absorbed at the surface [Paulson and Simpson, 1977]. Mixing below the mixed layer is not included.

1

Appendix C: The 1• Layer Reduced Gravity Model

1

Output from the NRL 1• layer reduced gravity global model is used in this study [e.g., Hurlbutt et al., 1992]. The model retains the free surface and uses a semi- implicit time scheme. The model equations are the nonlinear, shallow-water wave equations on a spherical grid over a latitudinal range from 71øN to 72øS. The vertically integrated equations of the model are

0V

• + (V. V + V. V)v + k x fV = -hr(GVh r + hrVG) Ot

g hr

Po 2 -• • Vpl + 'r/po + AHV2V- [max (0, -o.,)]v

Op• max (0, w) •+ ¾' •7pl = (P2-- Pl) Ot h r

mo

+ hr Crp(hl- Pl) + KHV2pl Ohr •+V.V=w

where

upper layer thickness; upper layer density; upper layer velocity;

V=hrv; layer thickness at rest;


Table 3. Model Parameters

Parameter Description Value

AH, m:/s Horizontal eddy diffusivity 2000 KH, m:/s Horizontal eddy diffusivity 5000

for density t/, m/s: Gravity 9.8 H, m Initial•lepth 250 h + m Layer thickness at which 75

entrainment starts

h-, m Layer thickness at which 650 detrainment starts

5•, m/s Interface reference vertical 0.003 mixing velocity

p:, kg/m 3 Lower layer density 1027.55

P0 constant reference density; P2 inactive layer density, constant in space and

time; G=g(P2 -- Pl)/Po; • wind stress; o•= o• + - o•- -

o• + =&[max (0, h + - h)/h +]2. o•- = •[max (0, h - h -)/h -] 2.

&- ff (•o + - w-)/ff a interface reference vertical mixingv•elocity;

h + layer thickness at which entrainment starts; h- layer thickness at which detrainment starts;

11(x, y) interface global mixing correction-scale factor; AH coefficient of horizontal eddy viscosity; Ka coefficient of horizontal density diffusivity; •r, reference coefficient of density climatology

relaxation; }l(x, y) layer density climatology;

H 0 constant reference layer thickness.

The vertical walls are rigid, and a no-slip condition is prescribed on the tangential flow. The grid resolution is 0.5 ø in latitude and 0.7 ø in longitude. The relaxation of upper layer density to climatology based on the data compiled by Levitus [1982] is included.

Artificial mixing is included in the model to avoid surfacing of the layer interface. When a layer becomes thin, fluid is entrained into it from the layer below. The entrainment does not occur in most of the cases in this study because the layer is thick enough in the area of the present study. It occurs only in one of trajectories computed for this study, and this particular trajectory is not used for integration of the mixed layer model because vertical velocity formulation in the model is inappropriate in this case. When the layer becomes too thick, detrainment occurs. Detrainment does not occur along any of the trajectories used in this study. Global mixing has been formulated to involve no net transfer of fluid between layers to allow long-term integrations. If there is local entrainment or detrainment, it will be balanced instan- taneously by regionwide mixing. The global mixing term is negligible in comparison with the divergence term in the area of the present study (J. Kindle, personal communication, 1994).

The model was spun up for 100 years in the following manner. For the first 40 years, climatological wind data [Hellerman and Rosenstein, 1983] and climatological density fields are used. Then, for the second 40 years, a density climatology based on the mean layer depths at each grid

point and the Levitus climatology were used, with the same wind data as were used for the first 40 years. For the final 20 years, annual mean wind data [Hellerman and Rosenstein, 1983] were used, superimposed with the monthly climatology of the ECMWF wind data from 1981-1987, from which the annual mean had been removed. This last step was taken because the amplitude of the seasonal variation of the ECMWF wind data is slightly greater than that of the wind data compiled by Hellerman and Rosenstein [1983].

The major model parameters are shown in Table 3. A detailed description of the numerical scheme in the model is given by Walcraft [1991].

Acknowledgments. We wish to thank John Kindle for kindly providing the NRL 1• layer reduced gravity model output. We also acknowledge Phillip •rkin and John Janowisk for generously providing the GPCP data. This research was sponsored by the National Science Foundation through grants OCE-8716510 and OCE- 9024452, and by the National Aeronautics and Space Administration through grants NAS5-31772 (EOS) and SAIC 19-920192-31 (TRMM).

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Arkin, P. A., The relationship between fractional coverage of high cloud and rainfall accumulations during GATE over the B-scale array, Mon. Weather Rev., 107, 1382-1387, 1979.

Arkin, P. A., and P. E. Ardanuy, Estimating climatic-scale precipitation from space: A review, J. Clim., 2, 1229-1238, !989.

Bahr, F., E. Firing, and J. Songnian, Acoustic Doppler current profiling in the western Pacific during the US-PRC TOGA cruises 2, 3 and 4, JIMAR Data Rep. 5, 199 pp., Joint Inst. for Mar. and Atmos. Res., Univ. of Hawaii, Honolulu, 1989.

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(Received April 8, 1994; revised August 8, 1994; accepted September 16, 1994.)

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Lagrangian mixed layer modeling of the western equatorial Pacific