The Quasi Geostrophic Global Atmosphere and Related Gyres

Guest essay by Michael Wallace, Hydrologist and Graduate Student at UNM Dept of Nanoscience and Microsystems.

I am a hydroclimatologist who works and researches in the area of solar based climate forecasting. In advancing that, I’ve adapted data from various sources of my interest and have run that data through various graphical and stochastic exercises. This has sometimes led to improvements in my forecasting techniques, as well as interesting and apparently unique graphics. I am presenting some of this material next week at a conference focused on the Animas River in the Southern Rocky Mountains. I also post on much of this material at my non-interactive blog at www.abeqas.com.

An internet search on “geostrophic winds” can set the background for this post. In my examples and likely those of others, these winds are averaged across the “entire” atmosphere (100 km according to many sources) and then mapped across the globe. The patterns can be both useful and intriguing. While most other researchers (both orthodox and skeptic alike) appear to favor one or several particular layer(s) of the atmosphere, I favor the full atmosphere for much of my climate work. Accordingly this post is about some examples of those full atmosphere based patterns. Much of my work is still on a steep learning curve across a number of fronts so my apologies in advance as I stumble through topics where my knowledge is still sketchy. I hope readers will view this post as simply an informal report of some work in progress and of course comments are welcome.

It seems safe to suggest that averages of the full atmosphere contoured over any region including and up to the full globe, are an intrinsic adoption of quasi-geostrophic theory (QG). I am still combing through the rich details that the QG perspective affords, precisely because of its useful and often overlooked simplifications.   These limitations are somewhat similar to the ones I’ve long worked in as a hydrogeologic modeler of energy and mass transport in porous media within multiphase flow conditions.

QG approaches are quasi-three dimensional and they can violate many more fully 3D principles at sub synoptic scales (synoptic scale is 1,000 kilometer (km)). For example, QG can nominally fail at some scales in the presence of other larger scale baroclinic and/or vertically sheared domains which are well known. Yet the QG simplifications have proven useful, even in many of those very environments, especially for forecasting moisture frontal movements associated with high velocity parcels moving within the jet streams.

QG theory based forecasts of storms that form in response to bends and velocity changes within jet streams are already well established. Moreover, they are widely agreed to work very well. The QG methods employ a curious conceptualization of a limited segment of relatively high velocity flow within a jet stream. Vortices exist in each corner. The directions of convection and subsidence vary with each corner vortex in relation to the direction of flow within the jet stream segment. All is explained well, by many sources, via reference to so called geostrophic flows which are linked to the Coriolis effect and thermal gradients. There are indeed challenging and dynamic 3D components to the actual systems as well, and notably some aspects of the circulations are often described in terms of the “atmospheric conveyor belt”. Even so, the QG simplifications work at the synoptic scale. I may not be the first to speculate that the same principals can therefore be applied to the entire global atmosphere.

I accordingly decided a few years ago to begin to build an atlas of full atmosphere global maps because in part I was curious to see if QG-styled representations of features such as jet streams and vortexes would manifest. I also wondered how such a map would reflect other well known features as Hadley and Walker circulations, the Intertropical Convergence Zone (ITCZ), and the OLR along the equatorial west Pacific, as well as a few other intersections of global hydrological interest.

Figure 1 is a typical example of the types of data I graph in this light. This is a comparison of the full atmosphere geopotential height (Z) over the month of December at the end of 2005 and at the end of 2013. I downloaded the underlying data from an ERA Interim archive at a UCAR site over a year ago. The archive included the parameters of Temperature (T), Geopotential Height (Z), Divergence of Latent Energy (LEDIV), and Evaporation – Precipitation (EP), in addition to numerous other parameters, averaged or integrated across the full atmosphere.

Figure 1. Comparison of two months for coverage of QG winds and full atmosphere geopotential heights Z.

Figure 1 and many subsequent figures are based in part on my coarsening of the ERA Interim data. Each cell is 2.8125 degrees in latitude and longitude dimensions. The row and column axes reflect the cell counts accordingly. As mentioned, this figure compares the Z contours across the planet for the month of December at the end of 2005 and at the end of 2013. These years and months are not necessarily any more or less interesting than any other two months. I simply was initially motivated to compare Z for a month following a high Atlantic cyclone count season and for a month following a low count season. According to the HURDAT reference [1], the Accumulated Cyclonic Energy (ACE) record indicates that 2005 was a high energy season and 2013 was relatively low.

I have introduced streamline origin points at various locations across the map to help define flows and gyres more clearly than the underlying vector plots could do. These lines are calculated from the original ERA Interim full atmosphere zonal and meridional wind speed data. As these are excerpts from works in progress, the streamline origin and identification features and later parcel tracking features are not always consistent. For the most part, green streamlines originate along a meridian in the east Atlantic (yet west of the Greenwich Meridian). Cyan streamlines originate along a meridian in the west Atlantic. Black streamlines originate along the east Pacific, and blue lines originate along the central Pacific. Red lines originate along the Greenwich Meridian which also defines the left boundary of each of the maps.

Examinations of the resulting flow patterns appear to confirm the expected Hadley and Walker circulation related middle latitude westerlies, equatorial easterlies, polar vortices, jet streams, and gyres at the very least. One interesting artifact of the QG approach that I looked forward to observing was the inevitable singularities of both “sink” and “source” vortex features created automatically from this mapping of a 3D circulation to an essentially 2D surface.

Figure 1 documents a small number of QG transformed sources and sinks, some of which might be persistent across the years. Each source and sink vortex identified through the streamline coverages are largely understood to be QG artifacts and they are positioned at well known locations. “Sink” gyres appear in the polar regions and two types of “Source” gyres appear in sub equatorial regions. In my view, these more or less stationary gyre features and their arrangement with respect to the ITCZ are reminiscent of the previously mentioned and most curious QG representation of a jet stream and storm generation. But this is just an idle thought and perhaps it has already been more deeply explored by others.

From a conventional perspective, the gyres are simply giant rotating masses of air that are caused by horizontal shear between the mid latitude westerlies and the equatorial easterlies. A purely QG artifact of interest to me which is animated shortly, is that air parcels actually disappear into the sinks and reappear from the sources. That wouldn’t happen of course in the real world. Or would it? 😀

In addition to these fantastic artifacts, actual known weather events can easily be visualized fully automatically using this system. For example, the “Great Polar Vortex” of early 2014 can be seen in Figure 2. This is a good time to note that manually developed artworks are customarily used in depictions of items such as polar vortices and jet streams[2]. Such renderings typically are motivated because the raw data depictions are not often clear. I think however that many would agree that these new automatic QG based maps appear to express more accurate fidelity to observations and appear to naturally highlight the very features most desired to illustrate.

Having said that, it is clear that I’ve somewhat arbitrarily chosen colors, resolutions etc., which give the streamlined maps a ropey texture. That may have risen from personal preference, but my guess is that many would agree that at the very least, these jet streams and vortices are captured in an intuitive way. For my part, I have generated several thousand such images now, which cover about 25 years of satellite data for the three main parameters T, Z and EP.

Our understanding of global atmospheric flow through QG streamlines and isocontours might be augmented further by selected particle (air parcel) tracking. Figure 3 introduces my preliminary application of parcel tracking as a .gif animation of the North Atlantic Gyre for a sampled month. As for all QG styled representations, the featured animation expresses various trajectories and relative velocities of hypothetical full atmosphere-averaged air parcels (symbolized by the red dots).  Note that the velocity field is held constant for this simple comparative trajectory demonstration. Therefore the animations are only suitable for selective relative comparisons between profiled full atmosphere parcel particle tracking (red dot motions).

Figure 2. QG Representation of the Great Polar Vortex of 2014

Hurricanes are not depicted, although the eyes of many hurricanes are roughly the same size as the red dots.  If hurricanes in the west NH Atlantic were rendered over time, they would be confirmed to rotate counter clockwise even as their trajectory takes them in a clockwise path over their lifetimes.

A second animation follows in Figure 4 for a month (July, 2014) in which numerous hurricanes were reported. This image is rougher and only captures three particle tracked frames.  However the equatorial easterlies, middle latitude westerlies, and some aspects of gyre circulation can be seen.    Notably the tracks of the NH Atlantic gyre for this month are in apparent alignment with trajectories of hurricanes in that lobe at that time.  This can be explored and approximately verified via this Wikipedia page[3]. Again please note that the animation is only suitable for relative comparisons of particle trajectories. In other words the time series does not necessarily represent one month. I am working on this for soon to be released updates so that particle trajectories can be properly updated at the end of each month of the “simulation”.

insert animation file into post: NthAtlanGyr1979thru2014ParticleTracking.gif

Figure 3. Animation of the North Atlantic Gyre for a Specified Month.

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Figure 4. Animation of the North Atlantic Gyre for July, 2014.

Readers might also find it interesting to compare this animation to Figure 5 in which the counterpart and much larger North Pacific Gyre is shown. In that animation, I’ve averaged about 25 years of monthly data (432 months from 1979 through 2014) to produce the parcel tracks. In this quarter century average and in the other animations, the QG air parcels exit the NH Atlantic Gyre to the north and proceed east.   Meanwhile the parcels in the NH Pacific gyre exit to the south and proceed west.  This arrangement is roughly mirrored in the southern hemisphere (SH).  Mass balance is thereby preserved quasigeostrophically.

insert file into post: GyreFlowExMWAfromERAIUV1979through2014.gif

Figure 5. Animation of Selected Parcel Tracks Based on Average QG Winds from 1979 through 2014.

The circulation and vorticity mapping of the QG continuum may also be consistent with Hadley Walker circulation dynamics papers and maps by numerous authors.  It also seems possible within the narrow QG focus that momentum balances can be achieved in examinations of all or any subsets of this data. For example, the inner particles of the gyres in Figures 3 and 5 complete full revolutions much faster than outer particles. Often cyclones are described as if they do not express conservation of angular momentum but that appears to be more of a question of whether the momentum is perfectly balanced or slightly out of balance. The animations suggest gyre flow is not unlike flow down a drain (or out of a fountain) for example. To me this lends a robust and dynamic flavor to the QG simplifications, even though no global circulation models (GCMs) were used in the development of this post.

If I’m not mistaken, these QG maps and animations appear to offer additional prospects for improved understanding of our global circulation. For example, descriptions and models of global circulation often bypass clear quantification of flows into the ITCZ. Maybe I’ve missed it, but I’ve never seen a flow description such as Figure 5 and its annotated companion Figure 6. In that figure I have placed two open circles over the map to highlight the remarkably few “QG portals” where sub equatorial air parcels can directly reach the ITCZ without first getting hijacked by a gyre.

Figure 6. Identification of ITCZ Inflection Entry Points from Five Year Trailing Average QG Winds for 2004.

In this explicit QG conceptualization of the Hadley Walker circulation pattern, many air parcels passing through the middle latitudes ultimately enter the ITCZ via first entering the two Pacific gyres. QG parcels then exit the ITCZ largely through the two Atlantic gyres. Of course this is a QG simplification that doesn’t capture the realities of top of atmosphere divergence and the like. But as I’ve said, the QG simplification has impressive fidelity to many observed climate and weather features. For those mindful of the benefits and drawbacks of such simplifications, value can be added over the status quo.

Peer review papers on residence times of air parcels in gyres are not common, but the few I’ve seen, such as Wyrtki, 1989 [4] or Groth et al., 2017 [5], suggest that such parcels are trapped in these gyres for up to a decade. I’ll be working further on related characteristic times of gyres and the stable or unstable attractors that they may represent in my ongoing learning and research. For now, I think that given the amazing fidelity of the QG method to capture gyres, jet streams, equatorial easterlies, mid latitude westerlies, polar vortexes, and even hurricane tracks, that that these “portals” to the ITCZ are potentially important to know more about.

Much might be gained through hybridizing the information further with a more literal implementation of the concept of a global atmospheric conveyor belt. In many ways this is expected to be somewhat of a mirror to the well known ocean conveyor belt. One can find precedence for these thoughts at least in part from various sources including Webster, 2005 [6] where the Hadley circulation is evaluated for both the atmosphere and the oceans.

Gyres are also largely dry as well. Accordingly the heat that they tie up is sensible heat as opposed to latent heat for the most part. Anyone who views the QG gyre plots over the 25 years will not be able to miss these giant vortices routinely apparently spinning up and then winding down. What doesn’t seem to change much are the centers of each major subequatorial gyre. Perhaps others have already speculated that these roughly 4 semi stationary, sub equatorial gyres serve as energy capacitors for the entire planet. If one also attributes some confidence to the idea of a global atmospheric conveyor belt, then in principal, trajectories of “full atmospheric thickness heat parcels” may be estimated months and years in advance, perhaps even regardless of diabatic or adiabatic transport. If this sounds absurd, I recommend skeptical readers take a look at a recent post in which I forecast the AMO 8 years in advance.

I’ve only scratched the QG surface in this guest post. I think the full atmospheric simplifications cannot be seriously disregarded given the potential suggested here. Readers are invited to visit my non-interactive web site posts for the numerous QG lines of exploration and the resulting, often highly accurate multi year forecasts of streamflows and of temperature that I derive from that.

For those who see some of the potential of these maps for climate and planning applications, I’ve also created a stochastic atlas, covering QG maps of T, Z and EP for every month from 1979 through 2014 (and counting) which I call a stochATLAS at my site. It is available for a nominal subscription license under $60 per year to cover costs.

REFERENCES

[1] HURDAT reference: http://www.aoml.noaa.gov/hrd/hurdat/comparison_table.html

[2] 2014 Polar vortex reference: https://climate.nasa.gov/news/2262/the-2013-2014-polar-vortex-adds-data-points-to-the-books/

[3] Wikipedia page on July 2014 hurricane tracks

https://en.wikipedia.org/wiki/2014_Atlantic_hurricane_season#/media/File:2014_Atlantic_hurricane_season_summary_map.png

[4] Wyrtki, K. 1989 Some thoughts on the Pacific Warm Pool. in Western Pacific International Meeting and Workshop on TOGA COARE (May 24 – 30) 1989, New Caledonia Proceedings

[5] Groth, A., Y. Felix, D. Kondrashov, and M. Ghil, 2017. “Interannual Variability in the North Atlantlic Ocean’s Temperature Field and Its Association with the Wind Stress Forcing” Journal of Climate Vol. 30. pp. 2655-2678

[6] Webster, P.J. 2005. “The Elementary Hadley Circulation” Chapter 1. H.F. Diaz and R.S. Bradley (ed.), THE HADLEY CIRCULATION: PRESENT, PAST, AND FUTURE. 2005 Kluwer Academic Publishers, The Netherlands.