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Rectification of the Madden-Julian Oscillation into the ENSO cycle

W. S. Kessler1 and R. Kleeman2

1Pacific Marine Environmental Laboratory, National Oceanic and Atmospheric Administration, Seattle, Washington, 98115
2Bureau of Meteorology Research Center, Melbourne, Australia
Current affiliation: Courant Institute for Mathematical Sciences, New York University, New York, New York

Journal of Climate, 13(20), 3560–3575 (2000).
Copyright ©2000 by the American Meteorological Society. Further electronic distribution is not allowed.

2. Model formulations and data processing

a. Ocean general circulation model

The tropical upper ocean GCM used in this study consists of two physical components: a sigma-layer, tropical primitive equation general circulation model developed by Gent and Cane (1989), with the "hybrid" mixed layer formulation developed by Chen et al. (1994a,b) as its surface boundary layer. The entire model domain is the upper active layer (roughly 400-m thick) of a reduced-gravity ocean, assumed to overlie an infinitely deep, motionless abyss. There is thus no bottom topography. The model consists of eight sigma levels within the active upper layer, and the surface mixed layer. External forcing of the model is through specified wind stresses and clouds only, according to the heat flux formulation of Seager et al. (1988).

The hybrid mixing scheme of Chen et al. (1994b) defines a turbulent boundary layer that exchanges momentum and heat with the atmosphere at its surface and with the thermocline by entrainment at its base. The three major physical processes of upper ocean turbulent mixing are explicitly simulated. Mixed-layer entrainment and detrainment are related to wind stirring and surface buoyancy (heat) flux using a bulk mixed-layer (Kraus and Turner 1967) model, shear flow instability is accounted for by partial mixing controlled by the gradient Richardson number, and an instantaneous adjustment parameterizes free convection (Price et al. 1986). In essence this combines the most physically realistic features of a bulk mixed-layer model with those of an instability mixing model (Chen et al. 1994a).

The model domain is the equatorial Pacific with solid walls at 30°S and 30°N and no opening through the Indonesian Archipelago, but otherwise realistic east and west coasts. A stretched grid is used in which the zonal spacing is smallest at the east and west edges (x about 50 km) and largest in midbasin (x about 120 km) while the meridional spacing is smallest within 10°N and 10°S (y about 40 km) and largest at the poleward edges (y increases to about 220 km). The timestep is 1 h. The model is initialized with the Levitus (1982) mean temperatures (and zero currents). Relaxation to the Levitus climatological annual cycle temperatures becomes progressively stronger poleward of ±20° latitude to suppress coastal Kelvin waves that would otherwise contaminate the solution given these unrealistic poleward boundaries. In the present formulation the equation of state is a linear function of temperature, with no effect of salinity, although variations of salinity are likely to be an important contribution to density changes in the tropical Pacific (Murtugudde and Busalacchi 1998; Ji et al. 2000; Kessler 1999).

Average annual cycle forcing fields were used to spin up the model. The wind stress climatology was made from the Florida State University wind product (Stricherz et al. 1992) for the period 1961-91, with a constant drag coefficient c = 1.4 × 10-3. Clouds were based on the 1983-94 International Satellite Cloud Climatology Project C2 product (Rossow and Schiffler 1991), with solar radiation derived from solar harmonics and bulk formulae used for latent, longwave and sensible heat fluxes. A "gust factor," in which the wind speed was assumed to have a minimum of 4 m s-1 for the heat flux and vertical mixing computations, represented the unresolved high-frequency wind events (including during the imposed MJO anomalies described below).

The present experiment was conducted by comparing two parallel runs of the OGCM: one forced entirely with climatological annual cycle wind stress (denoted CLIM), and the other with climatological winds plus idealized intraseasonal anomalies meant to correspond to MJO winds. In each case the model was first spun up for 3 years with annual cycle winds. (Experiments with longer spinup times showed that initialization transients were not contaminating the solutions for the present purposes.) At the start of year 4 the two runs diverged: the "control run" simply continued the climatological forcing, while the "MJO run" added intraseasonally oscillating zonal wind stresses on top of the climatology in the western equatorial Pacific. The idealized MJO winds were defined to be purely sinusoidal with equal-amplitude easterly and westerly phases; therefore, they did not change the low-frequency wind stress climatology. It is not suggested that the real MJO winds always have this character; rather, the point of this idealized experiment is to isolate the possible rectification, aside from any simultaneous changes in the low-frequency winds that occur during El Niño events. This tricky issue is further discussed in section 5. The idealized MJO wind anomalies had the following characteristics: Gaussian about the equator; sinusoidal in x and t, with phase advancing eastward; at the eastern edge of the MJO region the anomalies ramped down to zero so winds remained climatological in the east. These wind stress anomalies xMJO were specified as the product of a function of (x,t) times a function of y:

Equation 1

where A is the wind stress magnitude (3.5 × 10-2 N m-2), and the functions f(x,t) and g(y) are

Equation 2

where cm is the eastward advancement speed of the oscillation (5 m s-1), T is the period of the oscillating winds (60 days), and Y is the meridional scale of the Gaussian (6° latitude). These values of speed and period imply a zonal wavelength for the MJO of about 230° longitude. The parameter values are based qualitatively on observations; relevant observations and experiments to test the sensitivity of the model solutions to these choices are discussed in section 3c. The linear ramp R(x) that defines the east edge of the MJO forcing winds is

Equation 3

The time-longitude structure of these idealized winds is shown in Fig. 2.

Figure 2

Figure 2. The structure of the idealized MJO zonal wind stress anomalies along the equator during model year four. Line contours show eastward winds, dashed contours westward winds, with contours at ±1, 2 and 3 × 10-2 N m-2. The arrows are simply a visual aid to show the direction of each phase of the wind. The winds are described by Eqs. (1)-(3), and represent eastward-advancing oscillations. East of the anomaly region, the forcing remained climatological.

The wind stress anomalies xMJO were added directly to the climatological zonal stresses xCLIM (i.e., x = xCLIM + xMJO), although such addition is not strictly consistent, since a change in the zonal wind component affects the wind speed and therefore would also modify the background stresses CLIM. The correct way to perform this addition would be to add anomalies of zonal wind component to the climatological zonal wind, then recompute the total wind speed, then use that value to recompute both components of wind stress. We chose not to do this since we wish to compare two model runs with identical wind stresses averaged over one period of the intraseasonal anomalies; a correct wind component addition would change this low-frequency mean stress (the low-frequency change would be easterly in regions and times where xCLIM was easterly, and westerly where xCLIM was westerly). Such changes to the background stress would make it difficult to isolate and interpret the fairly subtle intraseasonal processes discussed here.

The imposed MJO forcing acted on the model both through the dynamics (wind stresses) and thermodynamics (wind speed). Wind speed affects the model through evaporation and through stirring and consequent changes of mixed-layer depth. For these purposes wind speed is calculated from the imposed total stresses by

Equation 4

To further decipher some aspects of the results, a third parallel model run was made in which MJO wind stress anomalies given by (1)-(3) were imposed, but the anomalies acted only on the dynamics, while the wind speed remained climatological [i.e., (4) was evaluated only with CLIM]. Thus in this run the evaporation and vertical mixing remained unaffected by the MJO winds. This experiment is referred to here as the "stress-only" run.

Although the convection-favorable phase of the MJO is associated with increased cloudiness, in the present paper, no effects of changes in solar radiation due to clouds are considered. Parallel model experiments with cloud anomalies similar in form to the winds showed that idealized MJO cloud variations did not produce a significant rectified signal. Of course the cloud fluctuations did induce an SST oscillation, but not a low-frequency SST change in these experiments. It may very well be, however, that coupled intraseasonal feedbacks could occur in reality associated with SST-convection interactions that are not simulated in the present uncoupled context (e.g. Flatau et al. 1997).

b. Intermediate coupled model

To evaluate the effects on the coupled system of rectified signals found in the OGCM, an intermediate anomaly model was used, comparable in complexity to the model of Zebiak and Cane (1987). It retains only those physical processes of the ocean and atmosphere thought responsible for the large-scale, low-frequency behavior of the tropical Pacific. The model is described in detail elsewhere (Kleeman 1993; Kleeman et al. 1992) and here we provide a relevant summary: The atmospheric component is steady-state and produces a unique (since the atmosphere has no internal variability) response to a given SST anomaly pattern. The dynamics are as described by Gill (1980) while a simplified convection scheme (Kleeman 1991) allows for the realistic depiction of midtropospheric latent heating. This model, unlike the Zebiak and Cane (1987) formulation, responds very nonlinearly to SST anomalies in that a high background SST field is required to obtain a significant dynamical response.

The ocean model dynamics consists of a prognostic shallow water equation set which is forced by wind stress anomalies. These equations assume the long wave approximation and for computational efficiency retain only the first six equatorial Rossby modes. The ocean model prognostic SST equation allows only for the influence of thermocline perturbations (that is, there is no horizontal SST advection) and has a Newtonian damping term.

Coupling is achieved by the exchange of SST anomaly (produced by the ocean) and wind stress anomaly (produced by the atmosphere). This model has been used operationally to predict ENSO at the Australian Bureau of Meteorology for the past four years. It has historical and real-time levels of skill which compare favorably with other routine ENSO prediction systems (Kleeman 1999), some of which are considerably more physically detailed. This suggests that it depicts the dominant modes of ENSO behavior realistically.

In the experiments described below, the model was initialized to 1 January 1997 using historical wind and subsurface data. These data were assimilated into the model ocean using a space-time variational method (Kleeman et al. 1995). As in the case of the OGCM, two parallel runs were made: a control run that ran freely following initialization, and a run designed to simulate the rectified SST effects seen in the OGCM, described in section 3b below.

c. Observational data used for comparison

In several sections, observations from the TAO array of temperature and surface meteorology moorings (Hayes et al. 1991; McPhaden 1993) are used to interpret model results. The TAO array consists of nearly 70 moorings arranged in pickets nominally 15° longitude apart across the equatorial Pacific. Each picket has moorings at the equator, ±2°, ±5°, and ±8° latitude, most of which are thermistor chain moorings that measure temperature at 1-m depth and 10 subsurface depths down to 500 m, as well as surface winds, relative humidity, and air temperature. At 0°, 165°E (and at three other longitudes) an enhanced mooring also measures zonal and meridional currents between the surface and 300 m; these are a combination of mechanical current meters and downward-looking acoustic doppler current profilers (ADCPs). Kessler et al. (1996) discuss statistical and sampling error characteristics of the TAO buoy network.


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