plus2k.brian

1. "Control" & "Flat"

In our attempt to keep close to the Aqua Planet Experiment framework, we have tried to come up with a warmer SST distribution that would be close to the original analytical ones, keeping polar regions at 0 C while warming the tropics and midlatitudes by about 2 C.

We retain the APE functional forms, but adjust the maximum temperature and the latitude where the temperature reaches 0 C. In doing this, we choose a latitude where the meridional SST gradient will remain unchanged between the APE SST and the warmer SST. That latitude is chosen to minimize the RMS difference between the two curves.

For the "Control" and "Flat" SST, the prescribed latitudes are chosen as 30 and 37 degrees respectively. The RMS error for "Control" is 0.53 and for "Flat" it is 0.58. The curves are shown in the figure [png][eps], with "Control" in blue and "Flat" in green. The differences are shown as dashed lines of the same colors.

Once we apply this method, the resulting expressions are given by:
T_control = 29.*(1. - sin²(1.40369*lat))
T_flat = 29.*(1. - sin⁴(1.43883*lat))
In the control case, the cutoff latitude, where Tcontrol = 0. C, is at 64.12 degrees. For the flat case, it is at 62.55 degrees.

2. "QOBS"

APE defines the "QOBS" SST distribution as the average of "Control" and "Flat," so we did the same thing. This figure [png][eps] shows the APE "QOBS" and the +2K version obtained by taking the average of the curves in the previous figure. For reference those curves are left as grey, dotted lines. The RMS difference between the APE "QOBS" and this new curve is 0.50.

The expression is simply:
T_qobs = 0.5 * (T_control + T_flat)
or equivalently, T_qobs = 29.*(2 - sin²(1.40369*lat) - sin⁴(1.43883*lat))
There is not a precise cutoff latitude for this function, since it never reaches 0 C, but when the full form of the "control" and "flat" distributions are applied (i.e, when we actually impose T=0 poleward of the minimum) the cutoff latitude is equal to that of "control." To see this slight difference, a figure zooms in on the region around the minima. The dashed lines show the results for the trigonometric functions alone, while the solid curves show the trigonometric functions up the cutoff latitude with T=0 poleward [eps][png], in the figure blue is "control," green is "flat," and red is "qobs," obtained by averaging the other two.

3. Preliminary results

Some early plots from "qobs" and "flat" have been drafted to get an idea of the climate and sensitivity of the APE-style aqua planet. The plots give a sense of the temporal evolution of the runs, the TOA budgets, and the surface budgets. A table also summarizes some of these findings [TABLE]; the table includes all our configurations, including the T85 versions where available (in red).
UPDATE: Although not as pretty yet, I made a new set of tables for the tropics only, where the tropics are defined using an objective algorithm instead of the arbitrary 30S-30N we have used until now; the results are not very sensitive to this change [new tables] (7 March 2006).

In these timeseries, there are four curves. The darker ones are the monthly means from "QOBS" while the lighter ones are from "FLAT." The solid lines are the APE runs (unperturbed SST), and the dashed lines are the "+2K" runs.

4. more results

The TOA radiative flux plots have 3 panels each, with latitude on the horizontal axis and flux (W/m2) on the vertical. The APE runs (original APE SST profile) are shown as solid, color curves in the upper two panels, with solar fluxes in red shades and longwave fluxes in green. The clear-sky fluxes are shown as lighter hues than the full-sky fluxes. The "+2K" fluxes are shown by grey, dashed lines.

The top panel shows the zonal mean fluxes from the 3-year climatology.

The middle panel shows the difference between the clear-sky and full-sky flux for both solar and longwave in both experiments.

The bottom panel shows the difference between the +2K and the original APE runs for all the fluxes, using the same colors as the top panel.

The table summarizing the TOA balances and cloud forcing is below, or click here. The table was also made using just the tropics (30S-30N) [link], and results from GFDL's AM2 were also included [link].

Another figure showing a comparison between QOBS and FLAT of (a) surface air temperature, (b) precipitation rate, (c) latent heat flux, and (d) net surface radiation. [png][pdf]

A further figure expands this view by showing zonal mean TOA fluxes and cloud forcing. [png][pdf]

Using the 3-year climatology, the "Bony-gram" was constructed for the total, LW, and SW cloud forcing. [png][pdf]

4.1 more more results

For each of the aqua planet configurations I have plotted temperature, specific humidity, relative humidity, and omega for the "control" and "+2K" runs, along with the difference. The results are simple panel plots. These are rough, so be careful of the color scales being different for different figures. I'll try to include the Cess runs soon.
UPDATE: I added the zonal-meridional streamfunction, which gives us a sense of the size and strength of the mean meridional circulation and how it changes.
UPDATE2: I added the time mean zonal mean precipitation. Each precipitation figure has two panels: in the upper panel is the total (grey), convective (red), and large-scale (blue) precipitation rates for the APE SST runs (solid) and the +2K runs (dashed). The lower panel just shows the differences. Note that the CAM also has a "shallow convection" precipitation rate that is not plotted, so it would be a residual term here.

5. the history files

The history files for these runs are available on the NCAR MSS. In each experiment, the naming convention follows the CAM defaults, case.cam2.hN.YYYY-MM.nc for monthly files for example. The case names and paths are:

CONTROL + 2K: /BRIANPM/csm/atm/hist/ape_control_p2kc.*

FLAT + 2K: /BRIANPM/csm/atm/hist/ape_flat_p2kc.*

QOBS + 2K: /BRIANPM/csm/atm/hist/ape_qobs_p2kc.*

The 'h0' history files are monthly means, the 'h1' files are 6-hourly averages, and the 'h2' files are daily averages. There are around 3.5 years for each experiment, but there might be a few extra months too. The CONTROL+2K run was extended to over 6 years in order to investigate the convergence of the solutions.

The APE runs were obtained courtesy of Jerry Olson at NCAR. Copies of those runs are stored on the MSS, and are temporarily stored on the machine 'tempest' at NCAR in /ptmp/brianpm/aque*30a/, where the * is for the particular configuration (control= 'a,' flat='b,' qobs='c'). The CAM control and +2K runs were those posted on the CPT page.

6. Bony-decomposition

Some bony-analysis -- decomposing the data into dynamical regimes -- has also been started. This figure [png][pdf] shows the liquid water as a function of height and dynamical regime. Note the horizontal axis is stretched so that the distance along the horizontal direction is proportional to the fraction of total area (between 30S and 30N) covered. The data, in fact, are binned by equal fractional area, with each bin covering 1% of the total area. This is why there are so many divisions along the horizontal. The figure shows 8 panels, with the default CAM at the top and the aqua planets below, and the +2K versions in the right column.

The same bony-analysis was done with the AM2, and can be seen in this figure [png][pdf]. Note that this figure is very preliminary, as evidenced by the fact that the vertical coordinate has not been interpolated from the model levels, which is why there is so much data at low altitudes.

We have wondered whether using vertical velocity at 500 hPa is really the most useful way to make these bony-style figures. At least sometimes there seems to be some ambiguity in discerning shallow cumulus convection and stratocumulus in the subsidence regimes. To start investigating this a little, I've made a few plot of w500 versus surface divergence. There seems to be a pretty strong correlation between the two. The figures show results from the GFDL AM2 for aqua, qobs, and flat along with the +2K versions of each. The colors represent the PDF of the data, so red means there is a high density of points around those coordinates. To make the colored field, I constructed a series of histograms and made a 2-D field of the results. The regression line (and equation) give the best fit linear regression between the two variables. Note that these are for the tropics (30-30) only, and white is part of the color table, so even places that are white may have a significant number of points, just not enough to get colored.

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