Writeup of Kessler work. 12 Feb - 3 May 2002

Writeup of Kessler work

Done at CSIRO, Hobart during a Frohlich Fellowship
12 Feb - 4 May, 2002

Under construction!

Lacking word processing capability, I wrote this in html. I suggest you bring up this page on your web browser, then print it out to read while looking at the web pages with the figures on the computer. That will be a lot simpler than me linking to all the figures from this page directly.

The figures pages are reached from my home page (www.marine.csiro.au/~kessler), under the heading "Links to CSIRO work", and are numbered 1-6:

     1a. TAO/model comparisons
     1b. Model exploration 1 (E Pacific mixing)
     2.   Model Exploration 2 (Other things)
     3.   Model Exploration 3 (Circulation east of Australia)
     4.   Two-delta-x wave?
     5.   Throughflow XBT lines

     6.   Write-up (this page)

     This page is written (roughly) chronologically, however, the main work (which is continuing) is in the third section ("Circulation east of Australia"). There are an astonishing number of dead ends, false leads, misconceived approaches, things that cannot be computed correctly from the model, etc, all documented here in great detail.

     Instead of piles of paper on my desk, I keep plots electronically. In addition to saving paper, they are easier to organize and share with other people. However, like the piles of paper that we have on our desks, not all of them are useful, to say the least. Many of them were made in the course of checking more important calculations. Since these are extremely easy to skip through, I don't throw any of them out. There is no reason to look at all of them. It would be approximately like rummaging through folders of papers on someone's desk. My hope is that between this writeup pointing to the ones I think are important, and the brief descriptions on the figures pages themselves, that some of them will be of interest.

     All the figures pages number each plot or related set of plots, and they will be referred to here by that numbering system. Thus I may refer to, for example, figure 2.1.b on page 4.
     Not every figure is described here! Some of them are garbage! Some of them are merely boring. However, I can document each figure; please ask if there are questions.
     Much of this work is uncompleted (in fact it all is). Some of this description is rather vague because no conclusion has been arrived at. Some of it is vague because I haven't yet understood what is going on.
     In the course of writing this summary many new thoughts and issues came up. This is on-going work, and these questions and ideas are mentioned here as a roadmap for further work.

§ 1. Subthermocline mixed layers in the eastern equatorial Pacific (Figures pages 1a and b):
      This work was done in response to Stuart's questions about subthermocline mixed layers developed in the ACOM2 model. These questions arose because the coupled model produced small-scale SST anomaly patches in the east Pacific, and the BOM blokes thought that might be screwing up the coupled forecasts. That has not been resolved, but in search of a mechanism by which the ocean model might produce such anomalies, the occurrence of subthermocline mixed layers was noted and explored for a couple of weeks. This work reached no conclusion, partly because of my lack of comprehension about the nature of subthermocline mixed layers, and partly because it remains unclear to what extent the model vertical profiles represent anything real. This work was eventually dropped as not likely to lead to a conclusion in 12 weeks (as well as my lack of understanding of how to approach it).
      The mixed layers are seen in several of Stuart's plots (http://www.marine.csiro.au/~godfrey -> Further Links -> Eastern Pacific convection work), which show (x,z) sections of density, vertical velocity and Richardson number. Profiles comparing ACOM2 to TAO are on my page 1a, Figures 1.7 (see, e.g., the development from late July into August). The model develops an extremely sharp thermocline (the entire thermocline within 1 gridpoint), with a nearly vertical T(z) profile below it. This sharp a thermocline is highly unrealistic, but there are examples of subthermocline almost-mixed T(z) in daily-average TAO data (Fig 1.7, August, 5th TAO profile). A few plots documenting the occurrence of these layers in ACOM2 are on page 2. Maps were made by finding the difference delta-T between level k=7 (97.5m) and k=13 (194.25m) (Figs 1.1-6 on p1b, where delta-T <2°C is shaded gray). At least sometimes, the occurrence of these layers developed and then decayed in an equatorial wave-like pattern, starting closely trapped to the Eq, advancing east, then broadening after reaching the eastern boundary (e.g., the sequence in Figures 1.6 on p1b). Some suggestion was noted that low Ri was correlated with downwelling (Fig 2.2 on p1b), but this was not pursued further.
     One idea is that the eastern equatorial Pacific just below the thermocline is near critical Ri much of the time. Central/western Pacific winds can generate 2nd baroclinic mode Kelvin waves that would lower Ri by stretching the stratification and increasing the velocity. This would connect interannual winds to occurrences of low Ri and the development of subthermocline mixed layers. TO investigate this, a linear baroclinic mode Kelvin wave model was developed, forced with ACOM2 winds, to describe this effect. Figures showing results from this model are on p1, section 4. The point of this exercise would be to see if the occurrence of these KW can be related to low Ri in ACOM2. This was not done as the work was dropped.
§ 2. A jumble of plots while learning about the model and the throughflow (Figures page 2):
     This is really a mishmash. I was learning about the model and about the ITF. The aim was to look at the density structure of the ITF in ACOM2/3, but in the process a lot of dead ends came up. Many of these plots are those dead ends. Perhaps this section can be skipped.

     Some documentation of the ITF in different versions of ACOM. Much of this will only be of interest as a part of understanding details of the different versions of ACOM. I needed to make these plots as part of learning how the model worked. Of possible interest are Figs 2.4 and 2.6, which show the vertical structure of the ITF (sections along 2°S) in both models. Fig 2.6 also shows the density structure of the three passages in ACOM3. Most of the ACOM3 throughflow enters the Indian Ocean via Lombok Strait (Fig 2.9c). Some may appreciate the meridional sections of u across the Pacific equator on both depth and density (Figs 2.10).

     Deep currents in ACOM3.   In the course of finding cross-equatorial transport, I noticed that the structures of deep currents in the equatorial Pacific looked distinctly Rossby wave-like (e.g. the sections in Fig 4.2, and the time series in Fig 4.5). Signatures of annual and interannual variability appear to propagate downward as well. Since subthermocline Rossby waves have been a long-time interest of mine (e.g. Kessler and McCreary 1993), I wasted a few days looking into this. I was hoping to see the evolution of equatorial deep jets in the model, since these things are very difficult to describe from observations. In the end I decided that deep jets and deep waves are not relevant to increasing the reliability of predictions of Australian climate, and went on to other things.

     Nonlinear terms compared to G/C:    One of our early ideas was to repeat the estimates of advection and friction effects on the equatorial vorticity balance (I spoke about this in one of the Frohlich lectures) using the more-realistic ACOM model. In that talk, I viewed these nonlinear terms as analogues to forcing, which could then be compared to the wind forcing, and integrated westward as Rossby waves (or as a contribution to the Sverdrup-like balance in the mean). Since the ACOM models include topography and a realistic ITF, unlike the much simpler Gent/Cane model used originally, I thought that that would allow evaluating the earlier results and extending them to the Mindanao Current and possible effects of these equatorial terms into the throughflow and perhaps into the Indian Ocean (via an island rule-like argument). That turned out not to be possible because of the difficulty of estimating friction from the output of the ACOM models. In Gent/Cane, I found the friction by rerunning the model with the code modified to compare velocities before and after calling the friction subroutines each timestep. That is obviously not realistic with the long ACOM3 runs. There was some flailing around with trying to make an estimate from the model output before giving up ..... However, a few figures may be of interest. Fig 5.1 compares vertically-integrated transport in the equatorial Pacific between ACOM2 and Gent/Cane. They are reasonably similar in pattern, especially in crucial (and realistic) aspects: the east-central EUC maximum and the strong SEC east of the dateline and close to the Equator in the south. Figs 5.4 compare the curl and Sverdrup-like zonal transport due to the advective terms in both models. ACOM2 shows much larger effect of the nonlinear terms, which act to pump up both the EUC and SEC branches. Yet the fact that the zonal transport in ACOM2 is smaller than Gent/Cane suggests that the ACOM2 friction must be significantly larger.

§ 3. Circulation east of Australia (Figures page 3):
     The aim of this research is to understand the relation between changes in the East Australia Current (EAC) and the Indonesian Throughflow (ITF). (In the following, "truth" is taken to be the ACOM3 model results; comparison with observations will have to be done.) Noting that the instantaneous island rule gives a plausible simulation of important features of the annual and interannual variability of the model ITF, and that a simple first baroclinic mode Rossby wave model appears to simulate annual changes of the bifurcation of the SEC into the EAC and New Guinea coastal current (NGCC), and that the 1997-98 depth-integrated steric height (DISH) difference between Tasmania and Chile in ACOM3 is well-simulated by the island rule, suggests that a linear approach will elucidate some of the essential physics. Discrepancies point to nonlinearities, especially with regard to
§ 4. A 2-delta-x wave? (Figures page 4):
     Much of this is explained in the text on p4. There is an apparent 2-delta-x standing oscillation in the v component, especially where strong currents from near topography. Remarkably, the oscillation is standing in x, though its magnitude varies somewhat with time. Thus it appears in plots of v at a single timestep, or of time-averaged v, or of mean v. An unfortunate effect of this is that the subsampled files, which are sampled every 4th gridpoint, hit all peaks of the same sign (Figs 1 on p4), and as a result transports cannot be calculated from the subsampled files (Fig 3 on p4).
     One way to examine the magnitude of the oscillation is to zonally high-pass the velocities by subtracting a 3-point triangle. Maps of the magnitude of these high-passed fields (Fig 4 on p4) show maxima near coastlines and topography. Although there is some high-passed signature in the zonal component, it is very much less than that in the v component, and it generally does not have the 2-delta-x character seen in v (Figs 6a and 5a on p4). Similarly, there is relatively little signature in high-passed temperature (near the coast of New Guinea there are oscillations that do not have a 2-delta-x scale); away from the coast a 2 dx signal is seen in temperature with alternating sign between each peak in v (Fig 5.c on p4). This could be due to w (I should have made a plot of w as well). It is worth noting that the relative vorticity associated with these oscillations is large, with values around 2x10^-5/s near the equator (Figs 6.c and d on p4). In some cases the oscillation reverses sign with depth (Fig 5.b on p4), which is unexplained.
     We can conclude that the 2-delta-x oscillation:
  1. is related to strong currents near topography (Fig 4)
  2. is very much stronger in the meridional component (Figs 4 and 6.a)
  3. does not propagate (Figs 2 and 6d)
  4. does not have any 2-delta-y amplitude (checked but not shown)
  5. extends over large vertical distances (Fig 5.a)
  6. can have phase reversal with depth (Fig 5.b)
  7. is only weakly related to temperature (Fig 5.c)
The cause remains unknown. An element which could be of importance in interpreting the model is that there is likely to be significant frictional dissipation of momentum between the gridpoint peaks, which would mean that the model effectively is producing more friction than would be thought based on the large-scale shear.
§ 5. Throughflow XBT lines (Figures page 5):
     A few plots were made based on the Wijffels constructed XBT sections across the ITF. The purpose of making these plots was for comparison with ACOM3, but this was never implemented. Of possible interest is Figs 2.4, which give a direct comparison with cross-track mean velocity between IX1 and ACOM3. First, it is useful to look at how the ACOM3 ITF enters the Indian Ocean, which is primarily through Lombok Strait (see Fig 2.4.c on p2). In ACOM3, the ITF leaves Lombok Strait and extends about 300km south before bending west. Along the IX1 line, the ACOM3 ITF has a surface maximum near 11°S, which reduces in magnitude with depth to about 800m (Fig 2.4 on p5). In the real ocean, there is a similar surface maximum at 11°S, but a secondary westward core is pressed against the Java coast below the surface at 75-200m (Fig 2.4 on p5). This feature is absent from ACOM3.