ATM S 509/OCEAN 512     SLN: 1548 (ATM), 6180 (OCN)

MWF 10:30-11:20, and 2.30pm on Thursdays for labs and problem solving sessions.
Lectures in ATG 310c (Atmospheric Sciences), labs in Ocean Sciences 107, the GFD lab . Note, we may shift lectures to JHN 022 if construction noise is too extreme in ATG310c.

Geophysical Fluid Dynamics - I - Winter 2011

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While 1-layer models seem unlike either ocean or atmosphere, their horizontal space-time structure is nearly identical to the fully stratified model, for each vertical (~cos mz-) mode. Thus one can understand a wide range of atmosphere/ocean geostrophic adjustment from these beginnings. Following this UW GFD-1 course, the various GFD-2 courses introduce the evolution of geostrophically balanced flows in Rossby waves, baroclinic instability, geostrophic turbulence => general circulation.
(4th image above): contours of 250HPa jet-stream level dynamic height (colors, blue = low, red = high), and 30HPa stratospheric dyanamic height showing the much more symmetrical polar cyclonic vortex in wintertime. Using m_map projection 'satellite' with Matlab. Such images are easily animated.

NEWS NOTES

• Lecture notes to the end of term are posted below (internal waves, flow over mountains, Ekman layers and spin-up). Note that the Ekman layer material has come at the end of the term, so only its basic ideas may be on the exam (not the detailed derivations).

• Problem set 5 is attached below with extensive comments on how to proceed with the boundary condition in problem 2.
• Solutions to problem set 3 are posted below, also with extensive comments and plots.
• Lab 8 this week will look at jet streams, boundary currents, synoptic-scale (mesoscale for oceanographers) eddies.
• Reading about Ekman layers and Ekman pumping is posted below.
• We continue to update the lecture notes which are an ongoing project (essentially a compact GFD textbook). Lecs 9-14 have some added material this week, and there may be some Matlab plots still to come, for stratified geostrophic adjustment.

• We reset the due date for Problem Set 4 to Friday 25 Feb.
• Solutions to the mid-term quiz are posted below (under homework).
• reading in Gill: sections on stationary waves on a mean flow are posted below under Reading
• Notes on Prob set 4:
  • If you want to superimpose the mountain topography on a meridional section of the atmosphere (say of u-velocity and theta), you need to convert height in m. of the topography to pressure (the NCEP data is stored at 17 pressure levels). The dynamic height variable z(lon,lat,level,time) is in meters, and is in fact the altitude in m. of that constant=pressure surface. So the idea is to use this: z changes every day, so the topography/pressure relationship does too, but use an approximate conversion. Simply plot z against p at a (lon,lat) point of interest: load hgt_2011.mat or whatever the height file you are using and plot(20,119,plevel,1) for example. This gives a curve, height in m versus pressure in HPa (millibars) for the first time record, here in the Rocky Mountain region. In the lower troposphere (levels 1-5 roughly) z(p) is not too far from a straight line: make a rough calculation of the slope of that line and use it to plot the topographic height as hh*A in Hpa on your meridional section. You can look at the exact height field by contouring z on your meridional section and you'll see that the heights change with (lat,lon) much less than other variables like theta or u. My estimate is dp/dz ~ 0.11 Hpa/m for the lower troposphere (levels 1-5, pressures 1000-500 HPa). The top of Greenland at 3 km is about 650 HPa (delta p/delta z = 350/3000). Notice that this slope is simply -gρ, so you could calculate density from temp and pressure, but that will not make a big improvement...the density of air near the ground is roughly 1.2 kg m^-3.
  • The amount of writing is not rigidly specified (we suggested 5 pages total for the 2 problems). Just write what you have found out, trying to be quantitative and to use GFD ideas where possible. Include figures in addition to this text, preferrably on your Google Doc. Note Google Docs have size limitations on text (512K characters of text, uploaded files (like a .pdf of your results) can be up to 1 Mb each..you can have several or many; 'presentations' like a powerpoint can be up to 10 Mb. Individual figures seem to have no size limit.
  • Notes on the ocean dataset 'SODA' are posted below, with the datasets. Oceanographers can either use this data or work with NCEP data.
  • An updated NCEP dataset is posted below. It extends from 1 Jan 2011 to 16 Feb 2011, 4 times daily. The scale factor and offset corrections have been made already and theta (potential temperature) is included in the temperature file. THe data is already stored as double-precision so all the plot commands work with it. The numbers seem to check out well, but let us know of any inconsistencies.
  • Testing thermal wind balance takes some work (to get all the numbers together; at a single (lat,lon) point you can form f du/dz and - g/T dT/dy fairly easily (T is temperature). Even here the differentiation by taking differences between u at adjacent pressure levels will leave you with one fewer point in the vertical so it's easiest to plot against the first 16 (instead of 17) pressure levels. The Matlab command "diff" does the finite differencing for you. For dT/dy simply take the difference between two adjacent latitude values and divide by the distance (111km x 2.5 degrees latitude). For du/dz you can use the stored dynamic height variable z( ) to get dz (using diff(u....) ./ diff(z...)).
    Matlab is annoying in requiring that we 'squeeze' frequently (often the cure for an error message about array dimensions not matching).

    Note that thermal wind balance follows from horizontal geostrophic balance and vertical hydrostatic balance in the MOM conservation equations. Hydrostatic balance is very accurate at large scale (recall the (H/L)^2 parameter). So, testing geostrophic balance is close to testing thermal wind balance: one way to do this involves basic plots of dynamic height contours (in lat-lon maps) and superimposing horizontal velocity vectors on them using the "quiver" command in Matlab. Then line plots along specific longitudes could be made to quantitatively compare Coriolis force and dynamic height gradient, at different vertical levels. This strategy may be easier than the explicit comparision involved in thermal wind balance, but both approaches are valuable.

    Another way to test geostrophic balance is to calculate vertical vorticity ζ =dv/dx - du/dy and divide it by f. THis ratio is a Rossby number that will be <<1 for geostrophic flow. Maps of ζ/f are very rich (we mention this and PV maps in the original problem set). Note the connection between ζ and the horizontal Laplacian of the dynamic height or pressure:
    . Also think of Z or pressure as a streamfunction for the geostrophic velocity: constant Z contours or isobars are nearly streamlines of the horizontal flow, and their spacing is inversely proportional to fluid speed, with a scale factor 1/f that varies with latitude. The Matlab command zeta=curl(lon_m,lat_m,ua',va'); calculates vorticity from the stored velocity data, and this is the most direct way to create this Rossby number map (comparing this with the geostrophic approximation above would be interesting but some work). In "curl..." you need to adjust latitude and longitude in meters instead of degrees (that's what lon_m and lat_m mean). ua and va are the u and v velocities on a single pressure level).

  
  WEEK 7: Wednesday 16 Feb 2011
  • Matlab notes: our writeup on making Matlab plots doesn't always say to use "squeeze..." with arrays as in " pcolor(lon,lat,squeeze(z(:,:,3,100)')), shading interp " but it is often necessary when contracting the array index. Also, the problem with pcolor plots losing their colors when overplotted with a second "contour(...)" plot: you need to reset the colors with the caxis command before making the plot. So use " colorbar " to show you the numerical values (or enter " caxis " to see the numbers currently used) and define a vector with your choice of color limits (as in " tt = [300 950]; then call " caxis=tt; " each time you make the plot.
  • Below Problem Set 4 is posted, with remarks.
  • Lab 2.30 Thursday 17 Feb this week will be on waves...internal gravity waves, simple gravity waves in a single layer fluid, Kelvin waves, and maybe a Rossby wave or two.
  
  WEEK 6: Monday 9 Feb 2011.
  • A new NCEP data set, 4 times daily, for just 1 Jan - 4 Feb 2011 is posted below under Observational Data. It allows you to look at the series of snowstorms and cold air outbreaks that have occurred. This data every 6 hrs lets you make good animations and storm-tracking (the earlier NCEP 2010 data is daily averages, 1 per day). Note that the data is posted one variable at a time for those with computer memory limitations. And it is in integer format for example dynamic height is zint instead of z. So when using plot commands like pcolor that require double-precision data, write double(zint(..)) where previously you had just z(..)
  • Lectures from the past 2 weeks are posted as one compact document below, with added comments, figures and some sign corrections.
  • Solutions to problem set 2 are posted below.
  • Quiz Wednesday.
  • We had some good discussion of problem set 3 after class. A few notes have been added to the original handout and are posted below.
  • Posted below also or here, are slides showing some observations and some GFD lab demo experiments which may be useful in thinking about Quiz problems.
  
  WEEK 5: Wednesday 2 Feb 2011.
  • This week's lab (Thurs 3 Feb 2.30) will involve thermal wind balance: looking at actively forced flows (by heating and cooling), which develop a strong balance between horizontal temperature gradient and vertical gradient of horizontal velocity: like the jet streams or Gulf Stream. The specific flow of interest is the Hadley Cell which is the tropical meridional overturning cell driven by moist cumulus convection: hot sun evaporating warm ocean, with that latent heat released high in the troposphere.
  • This week's blizzards are producing near-record snowfall in Chicago, Oklahoma City, New York, Boston. In Oklahoma City it was sun-bathing at 80F last weekend and white-out snow at 10F, 60mph winds on Monday. See http://www.atmos.washington.edu/~ovens/loops/wxloop.cgi?npole_h500_slp+/-168// for weather loop. Can you spot the origin of the cold air outbreak that swept south from Canada in the US midwest, and seeded the next ridge that hit the US east coast?
    
    
  • The observational data section below now contains all the data and notes on analyzing it. Click on 'Observational Data' above.
  • The review problems/Prob Set 3 are posted below. Expect some additions and modifications over the next couple of days.
  • The Mid-term Quiz will be in class, Wednesday 9 Feb. Closed book/closed notes. We will provide any equations necessary to work out the problems, so memorizing them is not necessary. Facts like the long-wave propagation speed for gravity waves would be given if a problem required it.
  Tuesday 1 Feb 2011
  Here is a version 1.2 of a longer discussion of Google Doc project thoughts using NCEP atmospheric data (also posted below with Observational Data). It will be updated as we get more data sets in order. You can put a sparse number of plots on your Google Doc, and possibly save them as a group in a .pdf file which can be uploaded to the Doc (there is an upper limit to the size of your Google Doc which you might exceed otherwise...500Kb which is not much!)
  Sunday 23 Jan 2011.
  Solutions to problem set 1 are posted below.
  Figures from the numerical experiment video shown in class (geostrophic adjustment) are now appended to Lec7-8 posted below, and the discussion of the balanced flow (p.6) clarified.

  An atmospheric dataset for 2010 has been uploaded here. It is large..154 Mbytes. Try loading it and making some plots. If the size is a problem contact me. It is a Matlab file ncep-data-2010.mat The variables are dynamic height, u, v, temperature daily, at 17 pressure levels. It is also posted under Observational Data below. Here is some description.
  WEEK 4 Friday 21 Jan 2011.
  Because of AMS meeting next week due date for problem set 2 is now Friday 28 Jan.
  
  Images from lab 3 (geostrophic flow) with discussion are posted below or here.
  
  When 'typos' and other errors are found in lecture notes and problem sets they will be corrected in the .pdf's posted here, and listed. Today the following turned up: problem set 2: units of mass transport (prob 2) are kg/sec not kg m^-3 sec^-1 and cos(ikx -i sigma t) should read cos(kx -sigma t) in prob. 3. Also in lecture 5/6 notes the equation just following equation (7) should have a minus sign instead of plus sign; lecture 7/8 notes have been corrected for an error in the discussion of long waves with rotation. See reposted notes for more.

  In class today I described the goal of the Google Docs, which are to provide a site for you to describe work with observational data sets relating to gfd dynamics. Specific suggestions will be posted with each data set. While we want this to be relatively unstructured, it is an important part of the course and provides a mechanism for one-on-one interaction with you. Post your results (including figures or links to .pdf's or videos) on your Google Doc.

  The Google Doc is also a good place for you to give impressions about the course material: what in Fultz's movie Rotating flows made sense or was provocative or interesting? What in lectures or problems or labs was unclear and could be further explained? What in your own research area relates to GFD ideas presented? How do you find Gill as a text?
  Wednesday 19 Jan 2011.

  • GFD Lab: 2.30 pm Thursday 20 Jan will show geostrophic flows using optical altimetry...essentially using the rotating fluid as a Newtonian telescope.
  • Math review session will be Friday 21 Jan just following class, at 11.30 am in ATG 310c, the usual site.
  • Lectures newly posted to cover this week, below. Some typos corrected.
  • Problem set 2 is posted down below.
  • We are also working to get data sets for both ocean and atmosphere up on the website for you to analyze (for geostrophic balance, etc.). Have your Matlab ready to go.
  • Last week we suggested watching the MIT Fluid Film Rotating Flows by Prof. Dave Fultz of Univ. of Chicago. It is a great old film; Google 'MIT fluid films' to find it.
  • Reading is posted below, or see the lecture notes. The complete Bretherton lectures are posted under Reading.
  
  Monday 10 Jan 2011. See notes below under Week 2.
  WEEK 3: Friday 7 Jan 2011. Problem Set 1 (PS1) and lectures 1 and 2/3 and 4 (2 and 3 are a single .pdf) are posted below. An outline or syllabus is posted (click on Outline above. It turns out the handout version of PS1 was not quite the final version (several lines were added to the end of prob #4)..download it to see. It now has extra comments based on questions from the class. Alison has added a link to the GoPost bulletin board above. We will post reading assignments etc. shortly. Lecture notes are tweaked now and then in response to questions and typos.

  Thanksgiving 2010 snowstorm and GFD lab tornado illuminated with laser light-sheet cat-scan.
  
  
  

• Have a look at the web-cam time lapse videos of the atmosphere as seen from the top of the Atmos Sci building, looking west: http://www.atmos.washington.edu/images/webcam0/
  or go to Weather Discussions =>weather webcams=>Pacific Northwest live webcams on Univ of Washington Atm Sci Dept webpage. For example look at 19 December 2010, thinking dynamics.
  
  
• Neat link to some images of a pair of cyclonic systems..storms..in the Atlantic storm track near Iceland, some amazing gravity waves on the lower atmospheric inversion downwind of an island and other satellite images here.
  
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