As detailed in section 2a, following a 3-yr spinup with climatological winds, two parallel runs of the OGCM were made: a control run that continued the climatological annual cycle forcing, and a run in which idealized MJO wind stress anomalies were added on top of the climatology in the western equatorial Pacific. The MJO anomalies had equal-amplitude easterly and westerly phases so the low-frequency wind stress forcing of the two runs was the same. The effects of MJOs are evaluated by comparing the two runs during year four. Difference fields between these two runs are taken to be the effect of the MJO on the model ocean.
a. Model temperature and current differences due to MJO winds
Figure 3 shows the difference in SST and surface zonal current along the equator during year four between the run with idealized MJO winds imposed on top of climatology and the run with climatology alone. The top panels show the unsmoothed differences, while the bottom panels are a 60-day running mean to remove the intraseasonal fluctuations. The smoothed difference fields can be interpreted as the rectified signature of the MJO wind anomalies in the OGCM.
Figure 3. SST and surface zonal current differences along the equator due to oscillating MJO winds. In each case the fields plotted are the difference, during model year 4, between the run with added MJO winds and the control run with climatological winds. (left) SST; (right) zonal current. (top) unsmoothed; (bottom) 60-day running means. The scale for all fields is at right (°C for SST; m s 1 for zonal current). The overlaid slant lines in the top panels show the 1st baroclinic mode Kelvin wave speed for the model stratification (3 m s-1).
Consider first the zonal current effects (right, Fig. 3). The OGCM response to the initial MJO episode in the early months of year four appears roughly as would be expected from linear dynamics: easterly winds spin up a westward current, then westerly winds spin up an eastward current (Fig. 3, top right). These signals propagate east of the forcing region at close to the model first baroclinic mode Kelvin wave speed (about 3 m s-1; see section 3.3 of Moore et al. 1998). However, by the second MJO cycle, the oscillation is overshadowed by a lower-frequency eastward surface current anomaly, and this eastward trend continues through subsequent cycles (note the trend to red shading in Fig. 3, top right). Figure 4 shows the surface current difference averaged over year four in plan view. Under the oscillating winds in the western equatorial Pacific, a mean eastward surface jet has been generated, and the eastward tendency extends all the way to the eastern boundary, within about ±2° latitude. On both sides of the equator, but especially in the northern hemisphere, surface current differences are generally westward. The magnitude of these rectified currents is about 15-20 cm s-1 under the strong winds and up to 5 cm s-1 outside the anomalous wind region, not a small fraction of the climatological flows, particularly on the equator where the South Equatorial Current is weak.
Figure 4. Mean surface current difference due to MJOs: the difference between the MJO and the climatological control runs, averaged over four MJO cycles.
SST differences (Fig. 3, left panels) also demonstrate low-frequency changes in addition to the intraseasonal oscillation. Under the strongest MJO winds (west of about 170°E), SST cools during each easterly wind period and warms under the westerlies, as might be expected due to equatorial upwelling, with an amplitude of about ±0.5°C. However, the cooling is larger, resulting in a net rectified SST drop of about 0.4°C compared to the climatological run, within a couple of MJO cycles (Fig. 3, bottom left). East of the strong wind region, SST also oscillates intraseasonally, and these signals are seen to progress eastward at a slightly slower speed than the Kelvin wave (Fig. 3, top left). The low frequency SST change in this eastern region is, in contrast to the cooling in the west, a net rise of a tenth of a degree or so compared to the climatological run.
b. Rectifying processes in the OGCM
In this section, the mechanisms producing the changes in zonal currents and SST noted in section 3a are diagnosed. Three main processes were noted, all of which act in the sense to cool the far western Pacific and warm the central Pacific.
1) EVAPORATIVE COOLING
Latent heat flux is evaluated in the OGCM according to standard bulk formulas, assuming that humidity is a fixed proportion (0.78) of the saturation humidity at the model SST (Seager et al. 1988). Latent heat flux is thus taken to be a function of wind speed and SST. This choice is reasonable since humidity varies over a relatively small range in the west Pacific warm pool (in the more than 6 yr of humidity record at the TAO mooring at 0°, 165°E the rms of daily-average relative humidity was 4.4% about a mean of 78%) and its fluctuations are apparently a second-order influence on evaporation in this region. Variations of wind speed are far more important (Shinoda et al. 1998; Hendon and Liebmann 1990).
It has been noted that the active-convection phase of the MJO is associated with strong wind events on a variety of time- and space scales, including local storms and squall lines as well as the intraseasonal westerlies, while the anticonvection phase can be characterized by moderate, but relatively steadier, trade winds. The question of accounting for the effect of high-frequency, small spatial-scale winds on evaporation and mixing has not been satisfactorily answered, either for models or low-resolution observations, and we follow the common practice in ocean modeling of specifying a gust factor, in which the wind speed is assumed never to go below 4 m s-1. This choice has a large effect in the warm pool region where climatological monthly winds are typically 1-2 m s-1 (each component). In the present study, the climatological wind speed used to force the control run never goes above 4 m s-1 in the warm pool region, so the control run latent heat fluxes are always based on the gust factor minimum (Fig. 5, middle). The imposed MJO wind stresses produce speeds usually larger than the climatological winds during peaks of both signs. This results in a 30-day periodicity for the wind speed and a mean latent heat flux cooling tendency about 5-10 W m-2 larger than that in the climatological run (Fig. 6, top). Another measure of the magnitude of this intraseasonal evaporation effect on model SST can be estimated by comparing the MJO run with the stress-only run in which the idealized MJO anomalies were not allowed to modify the wind speed, but forced the model only through the dynamics (see section 2.a). In the stress-only run, the roughly 0.4°C low-frequency cooling compared to the climatological run seen in Fig. 3 (bottom left) was reduced by about half.
Figure 5. Zonal wind stress, wind speed, and latent heat flux at the equator, 150°-170°E, comparing the climatological control run (solid line) and the MJO run (dashed line). (top) zonal wind stress (10-2 N m-2); (middle) wind speed (m s-1) [the dotted line at 4 m s-1 shows the value of the model's gust factor, see section 3b(1)]; (bottom) Latent heat flux (W m-2, with negative values indicating heat loss by the ocean).
Figure 6. Mean heat flux difference terms (the difference between the MJO and the climatological control runs) averaged over four MJO cycles (W m-2). (top) Latent heat flux; (middle) zonal advection heat flux; (bottom) vertical advection heat flux. Negative values (cooling the ocean) are shaded; positive values are hatched.
2) NONLINEAR ZONAL CURRENT FORCED BY OSCILLATING ZONAL WINDS
Figures 3 and 4 document that the purely oscillating zonal wind stress anomalies of the MJO run produced a net eastward current on the equator, and westward current off the equator, most strongly at the longitudes of the imposed winds, but also extending well eastward. Robinson (1966; also see Gill 1975) showed that the first-order nonlinear effect on equatorial zonal currents is eastward, whatever the sign of the wind. This effect is due to the Ekman divergence associated with equatorial zonal winds. Easterly winds directly force a westward surface current, but also cause Ekman divergence that advects the westward momentum away from the equator, resulting in an eastward advective contribution at the equator, and corresponding westward term off the equator. Westerly winds, on the other hand, directly force a surface eastward current, but also produce Ekman convergence, concentrating the eastward momentum on the equator. Thus both signs of zonal winds produce an eastward nonlinear modification at the equator, a westward modification off the equator, and the result is the pattern of current differences seen in Fig. 4. These nonlinear eastward equatorial currents produce the rectified warming seen to the east of the strong wind region (near 170°W) in Fig. 3 (left panels), through zonal advection of the background SST gradient. Note that the intraseasonal SST oscillations east of the strong wind region propagate eastward at a speed less than that of the Kelvin wave (Fig. 3, top left), consistent with an advective rather than a wave process.
In addition to the SST advection due to the rectified current itself, there
is a further rectification due to the intraseasonal correlation between u
and dT/dx. For the intraseasonal variation, the eastward current phase
occurs under westerly MJO winds and hence warmest SST in the west. Therefore
the zonal SST gradient at this time is more strongly negative than climatology
and zonal advection is an anomalous warming term. Conversely, in the easterly
phase, SST under the imposed MJO winds is cooler, therefore the zonal SST gradient
is weaker than average, and the westward currents that would be expected to
be cooling have reduced effect. Thus the term udT/dx anomalously warms
the region at the east edge of the MJO winds through both the oscillating and
low-frequency elements. That is, if u
is the oscillating (intraseasonal) and u
the nonlinear (low-frequency) zonal current, and T
the intraseasonal and the background temperature, both the terms u
dT/dx and u d
/dx are negative (since d/dx is negative). Therefore zonal advection warms
SST under and to the east of the MJO wind region due to both processes. The
magnitude of the rectified warming, averaged over four MJO cycles is about 10
W m-2 (Fig. 6, middle).
3) CHANGES IN VERTICAL PROFILES OF TEMPERATURE AND ZONAL CURRENT
A third nonlinear process due to the idealized MJO wind forcing contributes
to cooling the west Pacific through covariation of the vertical temperature
gradient and upwelling, and depends on the relation between the 60-day period
of forcing and the spinup time of the equatorial currents. In a linear model
in which upwelling fluctuations due to oscillating zonal winds acted on a constant
background vertical temperature gradient, vertical advection of temperature
due to oscillating upwelling would cancel over one cycle, but in the OGCM other
processes combine to make vertical velocity w
positively correlated with dT /dz and there is a net cooling.
When a zonal wind anomaly is imposed on the equator, a surface downwind current
is forced, and in addition an opposing pressure gradient is also generated.
This pressure gradient accelerates an undercurrent that is directed opposite
to the surface current. In the model the spinup time for the surface current
is about 8-10 days behind the wind, while for the undercurrent the lag is about
10-15 days, in agreement with observations (See Appendix B). Since the zonal
temperature gradients are in the same sense at both the surface and subsurface,
this pattern of current alternately strengthens the vertical temperature gradient
(following the westerly phase in which zonal advection anomalously warms the
surface and cools the subsurface) and weakens it (following the easterly phase).
The maximum temperature anomalies induced by these advective heating and cooling
signals further lag the currents by about one-quarter period (15 days). The
result of these lags is that the vertical temperature gradient is largest about
25-30 days following the maximum westerly winds, that is, almost at the time
of maximum easterly winds, and correspondingly weakest at the time of maximum
westerly winds. Since upwelling w
is directly forced by Ekman pumping it is nearly in phase with the winds, therefore
maximum upwelling occurs at the time of maximum vertical temperature gradient
and cools the surface more than would be expected based on the background gradient.
The vertical advection mean difference was tightly confined to the equator
with a magnitude of about 15 W m-2 (Fig.
6, bottom). The effect on SST was estimated by comparison with the parallel
stress-only model run in which the MJO wind stresses were allowed to force the
model ocean only through the dynamics, which removed the effect of evaporation
so most of the cooling was due to the interaction of w and dT /dz described here. The comparison suggested that
on the equator the magnitude of this influence on SST was about as large as
that due to evaporation. However, since equatorial upwelling has a narrow meridional
scale (about 1° latitude in this model), the vertical-advection-induced
SST effect was more equatorially trapped than that due to evaporation, which
does not depend on equatorial dynamics and had a scale more like that of the
strong MJO winds themselves (3°- 4° latitude). Therefore
the overall impact of the evaporative changes was more important.
c. Model tests of the sensitivity to parameter choices and the form of the wind
Observed intraseasonal variability is relatively broad-band and contains both coherent eastward-propagating components like those modeled by (2), and smaller spatial-scale features that may propagate in any direction. Therefore it is important to determine whether the OGCM results shown in Figs. 3-6 are sensitive to the values chosen for wind stress amplitude, eastward propagation speed and period, or to the large spatial scale of the idealized forcing functions. The purpose of these experiments was to evaluate whether the model results are likely to be a robust representation of the effects of actual broadband intraseasonal variability on the ocean or are due to peculiarities of the idealized and therefore unrealistic choices made here. We investigated these sensitivities through a series of model runs with varying forcing properties.
1) MJO-FORCING PARAMETERS
The first series of tests varied the parameters A, cm, and T (wind stress amplitude, MJO eastward propagation speed and period, respectively) that describe the idealized forcing functions in Eqs. (1) and (2). The model setup was otherwise exactly as described in section 2a. As a simple measure for the effect of the parameter variations, we use SST difference from climatology averaged over the equatorial warm pool region (1°S-1°N, 150°-170°E), and over three MJO cycles, denoted SSTav (inspection of the complete fields suggested that this was a reasonable metric for the overall rectified SST signature).
The value chosen for wind stress amplitude A in the main MJO run was 3.5 × 10-2 N m-2; we tested values ranging from 2 to 6 × 10-2 N m-2. Shinoda et al. (1998) used ECMWF winds to estimate a peak-to-peak composite MJO wind stress as 5 × 10-2 N m-2 (about 30% smaller than our choice), while individual events seen in the TAO moorings were up to twice as large (Cronin and McPhaden 1997; Ralph et al. 1997). In the model experiments varying the forcing amplitude, SSTav cooled roughly linearly with increasing wind stress, about 0.1°C for every 1 × 10-2 N m-2 increase in wind stress. In general, the nonlinear effects [especially the nonlinear eastward current discussed in section 3b(2)] became smaller as the wind forcing became smaller. Therefore the weak warming near the date line, due to eastward advection by this current, was more sensitive to the forcing amplitude than was SST cooling farther west (due substantially to evaporation, which depends on the square root of wind stress and therefore varies less than forcing amplitude). These sensitivities to forcing amplitude suggest that it takes a moderate or larger intraseasonal event (winds of 3 × 10-2 N m-2 or stronger) to produce a significant rectified interaction with the coupled system.
It is also worth noting that the magnitude of the SST cooling in the OGCM was comparable to those observed during strong MJO events. The peak-to-peak intraseasonal SST oscillations were 1°-1.5°C (the intraseasonal rms was about 0.5°C). This is larger than composite MJO SST (Shinoda et al. 1998 found composite SST oscillations of about 0.5°C) but similar to observed intraseasonal SST signals during the moderate MJO events of the Tropical Ocean and Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) intensive observation period in 1992-93 (Ralph et al. 1997; Cronin and McPhaden 1997).
The second parameter, MJO propagation speed cm, was chosen to be 5 m s-1; we tested speeds ranging from 2.75 to 10 m s-1,, which span the range of reported values (Shinoda et al. 1998; Rui and Wang 1990). MJO propagation speed could potentially affect the solution since eastward-moving wind forcing projects more strongly onto the Kelvin mode if its speed is near the oceanic first baroclinic mode Kelvin wave speed (about 3 m s-1; Weisberg and Tang 1983). However, the projection enhancement is significant only when the zonal fetch of the propagating forcing is long; in this case the zonal extent of the idealized MJO winds is only 40° longitude, which is too short to have much of an effect. For this reason we found little difference in the OGCM intraseasonal Kelvin waves due to this range of cm, and virtually no difference in the resulting rectified SST. In addition, most of the rectifying effects seen in these runs are essentially local processes, so the MJO propagation speed is not a critical factor in this situation.
The third parameter that defined the idealized MJO winds is the period T. Observed MJO periods range from about 30 to 70 days with a broad peak near 50-60 days (Hendon et al. 1999); we chose the value 60 days for the main MJO run, but tested periods ranging from 20 to 120 days. In general, there was a roughly linear increase in the rectified SST cooling signature SSTav as the period increased, from about 0.15°C at 30-day periods to 0.3° at 60-day periods to 0.5°C at 90-day periods. Changes in SSTav flattened out in runs with periods shorter than 30 days or longer than 90 days. It is not known what determines the model sensitivity to MJO period, but the effects were seen in all three advection terms, and apparently represented a complicated interaction between the spinup times for various aspects of the equatorial circulation and the temperature gradients resulting from advection. As the delicacy of the phase relations between vertical velocity and temperature gradient [section 3b(3)] illustrates, these interactions can become quite complex. However, the results do show that the rectification occurs throughout the intraseasonal band. Overall, the exercise of varying the MJO parameters A, cm, and T indicates that the SST changes shown in Figs. 3-6 and discussed in section 3b are a robust response in this OGCM to reasonable choices of parameters to describe the MJO.
2) SINUSOIDAL TEMPORAL STRUCTURE OF THE MJO FORCING
A second set of model runs was intended to examine the implications of our choice of a sinusoidal form for the MJO anomalies [Eq. (2); Fig. 2]. In reality, intraseasonal wind variations do not have equal and parallel positive and negative phases; often the westerly phase is characterized by higher wind speeds than the easterly (Cronin and McPhaden 1997). However, our choice was made in order to isolate the question of rectification without the complication of the general shift to low-frequency westerlies that is often observed during the onset of El Niño. Our assumption of stronger than normal easterlies as well as westerlies is particularly significant in regards to the importance of evaporation, which was a cooling term during both phases of the anomalous wind, since the background climatological winds over the west Pacific warm pool are very weak. Some observations [e.g., Cronin and McPhaden (1997), working with the 4-month TOGA COARE time series, and Hendon and Glick (1997), working with European Centre for Medium-Range Weather Forecasts atmospheric reanalysis fields] show that at least in some periods the anticonvection (easterly) phase of the MJO is instead associated with generally low wind speeds, which would imply weak evaporation and contradict that aspect of the rectification found in the present experiments. However, even if this alternate scenario is a more accurate description, these studies suggest that an active MJO period represents anomalously strong overall winds and evaporative cooling, relative to climatology, so net cooling during a full cycle should still occur. M.F. Cronin (1998, personal communication) points out that west of about 160°E the anticonvection phase usually has quiet winds with only occasional easterlies, while east of this longitude MJO westerlies occur as an episodic interruption of trade winds; therefore our assumption of strong winds in both phases may be most appropriate only to the region east of 160°E. This is a difficult question to evaluate from existing observations, because it is not straightforward to statistically extract the evaporation signal of the MJO, since its highest wind speeds occur at many time- and space scales, including local storms and squall lines that are associated with the convection phase of the MJO but have much smaller scales than it. Therefore bandpass filtering to intraseasonal frequencies can remove much of the evaporative signal. We examined many individual events in hourly time series of winds from TAO moorings in this region, and found examples of events with high wind speeds in both phases as assumed here, and also examples in which the anticonvection phase had quiet winds; overall it was not possible to make a compelling characterization either way from the existing sparse data.
To test the OGCM response to this aspect of the variability, the original sinusoidal wind stresses were replaced by a time series of Gaussian humps composed of relatively short-lived but strong westerlies and longer-lasting but weaker easterly phases (the mean was still zero). For the same rms wind stress amplitude, the Gaussian hump winds produced weaker SST anomalies (by about 20%) than the sinusoidal winds, mostly because of reduced evaporation during the weak easterly phase. However, the qualitative response of cooling under the strong forcing and slight warming to the east remained similar to that of the sinusoidal winds.
It was noted in section 2a that in order to isolate the effects of intraseasonal
forcing without the complication of changing the low-frequency stress, we specified
wind stress anomalies 
xMJO rather than the wind itself.
The effect of adding oscillating zero mean wind component anomalies would have
been to increase the wind speed averaged over one cycle and thereby change the
low-frequency total stresses (both components). This change would be easterly
where xCLIM was easterly and westerly where
xCLIM was westerly. Since the real
MJO winds occur typically in October-March when the climatological background
over the western Pacific is westerly, the wind speed increase due to the oscillating
part alone of the MJO should preferentially favor increasing the westerly stress
forcing of the ocean. Our procedure of adding stresses should therefore be an
underestimate of the full effect of MJO winds on the western Pacific.
3) SPATIAL COHERENCE OF THE MJO FORCING
A final series of model runs tested the difference between the effects of the coherent MJO and those of the smaller spatial-scale intraseasonal variations, which make up about half the total intraseasonal variance in this region (Hendon et al. 1999). To model the incoherent intraseasonal signals, an SVD decomposition (Bretherton et al. 1992) of bandpassed OLR and the same field phase-shifted one-quarter period was done (e.g., Zhang and Hendon 1997); the first two eigenvectors of which were a quadrature pair that described a coherent, eastward-propagating MJO mode, similar to mode pairs extracted by various EOF-based techniques (e.g., Hendon et al. 1999). The third and fourth eigenvectors also stood out as a pair, but higher modes were apparently noisy with gradually decaying eigenvalues. Eigenvectors 5-14 were taken as representative of the spatial scales of incoherent intraseasonal variability and used to construct wind fields that had intraseasonal timescales but much shorter spatial scales (typically 1-2000 km in both the zonal and meridional directions). These ten fields were propagated both east and west in varying combinations and at varying speeds to produce five realizations of incoherent intraseasonal forcing with the same amplitude as the sinusoidal wind stresses of the main MJO run [still multiplied by the meridional Gaussian according to the second of Eqs. (2) and ramped on the eastern edge according to (3)]. Perhaps surprisingly, the rectified SST fields resulting from these experiments were not so different from the coherent wind run; in particular each of the incoherent-forcing runs had the same character of cooling under the strong winds and weaker warming to the east. In general, evaporative cooling in these model runs had a similar effect as in the main run, but both the zonal and vertical advection terms were less efficient, apparently because of the incoherence of the wind forcing [note that these terms oppose each other in the heat balance (Fig. 6) and therefore reduction of both tends to cancel the difference]. It was also found that meridional advection became relatively more important in the heat balance, since the empirical spatial patterns included meridional gradients at the equator, which the sinusoidal forcing described in (2) did not contain. Nevertheless, the fact that the rectified SST signal remained qualitatively the same as under the spatially coherent, MJO-like winds indicate that the results reported here do not depend heavily on the form of the forcing, but that strong intraseasonal winds over the warm pool will always produce this pattern of rectified SST.
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