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1. F Units are kg ms 3 Write an equation that relates the wind stress curl to the vertical Ekman mass transport Be clear about units and direction je oo dz I Ppa dz pow d F ey Fa oe Units are kg m s 4 What is the rate at which salt is carried into a grid cell of volume V by the fluxes above given uniform salinity S What are the units of the divergence of the salt flux integrated over the grid cell The fluxes through the cell faces are ST Lys S Ly 27 z SL Ly All of these have units of kg s The integral of the divergence over the cell is the same as the sum of the fluxes through the faces so it also has units of kg s 5 What is the rate at which heat is carried into a grid cell of volume V by the fluxes above given uni form potential temperature T What are the units of the divergence of the heat flux integrated over the grid cell Here you will need to use the density and specific heat to convert from potential tem perature to energy The fluxes through the cell faces are T F Ly Cp TH Ly 2 z Cpl Laly All of these have units of J s W 6 Suppose salty water is brought upward at a rate so that a freshwater flux of 1m yr is balanced by horizontal flow If the upwelling rate is 0 lm day how much saltier is the upwelled water than the water flowing out horizontally This balance is the essence of the hconv zconv 0 balance in the baylor_budget on budgSa code The fresh water budget
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3. have you designed the most important metrics for your problem MOST IMPORTANT If possible include draft versions of the figures you plan to use in your paper based on the real data and the real metrics you plan to calculate Normally if you can get to this stage completing the paper on time is no problem If you are unable to get to the preceding step give your fallback plans if all else fails Because of the reviewing process and timeframe you will not be able to get an extension on the paper deadline if things don t go smoothly You can include more figures in the revised version of the paper if you figure it out after you turn in the first version of the paper 6 Paper 2 As you plan your paper go through my paper primer document available on the webpage 6 1 Topic I Get Around The goal here is to choose a region timeframe and straightforward diagnostic of the Ekman transport in that region You will relate the Ekman transport of some other property salt heat potential temperature nutrients etc to observations in that region e Find a region of interest based on the Ekman transport and its consequences For example download a wind stress dataset from ECCO COADS etc There are some wind files that I have pre processed These already have wind stress curl calculated too Can you find a region of particularly strong offshore or onshore wind stress An area where wind stress is variable throughout the year Alternativel
4. the dominant balance in the mass and heat or salt budgets for this subregion 1 Use the files in the nctiles_ budg directory to examine the mass flowing into and out of your region Which is largest the horizontal flux in the x direction trU the y direction trV or the vertical trW Note that these are not exactly zonal amp meridional fluxes especially in the Arctic At midlatitudes they are zonal amp meridional but which is which you need to sort out Does the largest flux balance itself e g zonal in E zonal out W If not which flux supplies the difference At the end of this exercise you should know which direction supplies the most water and which direction loses the most NOTE It is not required for you to examine the budget of every gridpoint in the domain just into and out of your interesting subregion which is the sum of over certain gridcells faces Pay particular attention to the most near surface egridcell It will have a lot of the Ekman transport 2 Now examine the wind field in your domain If you saw an important zonal mass transport is there a meridional wind If you saw a meridional transport is there a zonal wind If there is a vertical transport is there a wind curl You might check against the velocities UVELMASS VVELMASS to confirm your assessment How much of the mass transport can be explained by the winds see homework problem 3 Now repeat step 1 using either the salt budget So Si or th
5. Assignment 2 for GEOL 1520 Ocean Circulation and Climate or Notions for the Motions of the Oceans Baylor Fox Kemper March 29 2015 1 Contacts The professor for this class is Baylor Fox Kemper 401 863 3979 Office GeoChem room 133 http fox kemper com teaching http fox kemper com 1520 2 Getting Help I am usually available by email You can make an appointment other times Just check my calendar at http fox kemper com contact and suggest a time that works for you The most important commands in matlab are help and lookfor The first one allows to to get a description of any matlab function for example gt gt help plot tells you about the function named plot The second one allows to to search for keywords within a function description in case you don t know or can t remember the name of the function 3 Introduction As you know our assignments are structured to resemble a scientific journal s peer review process So when in doubt about procedures try to understand the assignments in that context I am listing together all of the pieces for the first paper at the same time here so that you can see the full flow all at once even though there are different due dates on each piece 4 Homework 2 Each of the subsections here is a homework problem that you should complete make a pdf of the results and turn in through canvas brown edu Please include screenshots as pdf or script file
6. budgdepth 100 The closest value to this will be used These values are not relevant for Mi Hi Si budgets Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh END EDIT DOMAIN Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh After you run the baylor budget script you can examine the mask and the areaMask variables To look at the mask on face 4 gt gt figure 10 pcolor mask f4 colorbar Experiment with looking at the different faces They all reveal that mask is 1 in N Hemisphere ocean and 0 in the S Hemisphere ocean and NaN in land Now let s look at areaMask gt gt figure 10 pcolor areaMask f4 colorbar Which reveals that the areaMask is similar to mask but instead of ones in the right places it is the area of the upper grid face in m The variable mygrid RAC carries this area information The script baylor_budget2 m selects a different domain the NINO3 region Run that script and then go to that file and note how this region is specified by limiting the latitude and longitude range 4 3 Ekman Exercise This portion of the homework is to get you used to calculating the Ekman transport 1 Write an equation that relates the zonal wind stress to the meridional Ekman mass transport Be clear about units and directions f pove dz ae i Units are kg ms 2 Write an equation that relates the meridional wind stress to the zonal Ekman mass transport Be Ta clear about units and directions ja pote dz
7. e heat budget Ho Hi depending on your topic at hand Where is the salt or freshwater arriving What about the heat In this case you will have to consider fluxes through the top surface from the sun or freshwater These are part of the TrWtop files 4 Now examine the ADV _SLT or ADV _TH files These represent only the advective fluxes of salt or theta The units are in cubic meters per second times the transported property psu gm kg for salt or C for potential temperature Use the results from the homework problem to convert these fluxes into units time of the conserved quantity i e Watts Joules s or kg of salt s Do these advective fluxes nearly equal the total fluxes in TrU TrV TrW What does that imply 5 Don t be afraid to piggyback off of other published work Use google scholar or Web of Science to locate articles by keyword and then see what they say Feel free to use the matlab references and refer to similar projects 7 Reviews 2 As you plan your reviews go through my review primer document available on the webpage You will read and review two of your colleagues work You can look at the peer reviewing primer for more details as to how to proceed Be sure that you are actually critical where you see room to improve Everything looks great Good work is not a useful review unless it is totally true but do not be heedless of feelings or unfriendly Make sure you comment on the science as well as the pre
8. ewer is reading more carefully than any other readers you are likely to get so if they don t understand what is going on easily no one else is likely to either e You don t have to go through small suggestions one at a time in the response document just say you took all suggestions 10 e Some reviewers will make complicated suggestions like additional computations rearranging sec tions deleting or adding figures etc Consider whether the outcome is guaranteed to be an im provement of the overall work If you are sure the reviewer is wrong just politely decline to make the change If you aren t sure give it a try but don t be afraid to compare to the original be fore accepting the change Whatever you do explain your process and thinking in the response to reviewers document e The reviewers are not perfect and they are equally or perhaps more likely to misunderstand what you ve done than to point out something you ve done incorrectly Be careful to figure out which before you make any changes Most often the changes you make will just be to clarify what you ve done rather than change what you ve done On the other hand good reviewers will catch inconsistencies in your work that are important to understand or fix as you finalize your revision References Adcroft A J M Campin S Dutkiewicz C Evangelinos D Ferreira G Forget B Fox Kemper P Heimbach C Hill E Hill et al The mitgcm user manual 2008
9. hanging to analyze a different region we will choose the NINO3 region but for your paper you will choose another region The NINO3 Region is bounded by 90 W 150 W and 5 S 5 N It is a good test example because it is limited in both zonal and meridional directions and it covers both hemispheres and the equator so we have to deal with changes to the Coriolis parameter f To begin do gt gt nameBudg budgMa For reasons I dont understand gt gt replace these quotes with single quotes for matlab if you cut and paste nameBudg budgMa gt gt baylor_budget This will look at the time averaged mass budget budgMa Each of the budgets has the horizontal flux in the x direction trU the y direction trV or the vertical trW Note that we are analyzing the mass flux here since we choose the budgMa directory rather than budgHa or budgSa Note that trU and trV are not zonal and meridional but oriented versus the local coordinate on the face in question Opening the baylor_budget m file you can see the crucial domain lines hhhhhhhhhhhhhhhhppryphhhhhhhhhhhhhttttettattetetetelelelolo1o10 101010 EDIT HERE TO CHANGE THE DOMAIN of INTEGRATION hhhhhhhhhhhhhhhhyppphphhhhhhhhhhhhhhttttatatttetelelelelo1o1o1o 1110 define northern hemisphere as domain of integration nameMask Northern Hemisphere mask mygrid mskC 1 mygrid YC gt 0 areaMask mygrid RAC mask define depth of budget for Mo Ho So or Ma Ha Sa
10. ifications of the budgets of mass salt and heat in the directory nctiles_budget There are three versions of the mass budget Mo full 240 months all depths Ma time average of Ho Hi depth integrated version of Mo The time average budget files are to be used for the homework here and they are 240 times smaller than the total budget files The terms in the budget supply in the inflow and outflow through each face of a gridcell The trW files give the flow through the upper and lower surfaces and the trU and trV files give the fluxes through the horizontal faces The surface value of trW gives the evaporation minus precipitation and runoff The units of all variables in the mass budget are kg s indicating the delivery of mass through each face per unit time Likewise there are three versions of the heat budget Ho Ha Hi units of W J s and salt budget So Sa Si units of salt kg s I have created copies of the most crucial files for your analyses The files needed to do only the homework problems here Ma Ha Sa wind stresses nctiles_avg and the base code of gcmfaces can be downloaded from http fox kemper com data ECCOv4base_v3 zip The remaining budget files Ho Hi So Si Mo Mi can be downloaded here and added to your nctiles_budget subdirectory fox kemper com data ECCOv4budg zip The rest of the nctiles_climatology files can be downloaded from and added to your nctiles_climatology subdirectory The correct directory structu
11. is Fy Fu Fh 0 the salt budget is Sy Fy Sp Fp 0 Thus Su Sh 1 027 So the upwelled water is 2 7 saltier 7 Suppose cold water is brought upward at a rate so that a warming solar surface flux of 200W m is balanced If the upwelling velocity is steady at 1m day how much colder must the deeper water be than the horizontal outflow water to bring about this balance This balance is the essence of the hconv zconv 0 balance in the baylor_budget on budgHa code The water budget is Fy Fp 0 the heat budget is Qs cpTuFu cpThFh 0 Thus Qs cp Tu 7 Pa which when solved is Ty Tp 4K 4 4 Budget Exercise For this part you ll examine the mass transports produced by Ekman transport and the consequences for heat and salt budgets in a region 1 Run the baylor budget code on budgMa budgSa budgHa and examine the code comments Explain the figures that are produced using your equations from Ekman Exercise Are the horizontal and vertical convergences exactly balanced or just close Run the baylor budget2 code on budgMa budgSa budgHa and examine the code comments Explain the figures that are produced using your equations from Ekman Exercise Explain how the change to the crucial domain lines works Run the baylor_ekman code and examine it Explain why the rotated coordinates are needed to make UVEL and VVEL into surfzonal and surfmerid Compare the average wind plots to the Ekman t
12. nary longitude and latitude With the help of Gael Forget I have assembled what I hope is an easy introduction to how to open the model files and use them Here is a brief tutorial on using these variables assuming that you have downloaded the ECCOv4base zip unzipped it and changed into the base directory iap idma gt gt test_gcmfaces_and_mitprof This makes sure that you have everything expanded appropriately Next let s fire things up quickly so you can work with the gcmfaces software just type gt gt gcmfaces_init In both cases a few example figures are generated which show what you can do easily with the gemfaces program It is a good idea to make figures by cutting and pasting from the gcmfaces_init m file it is in the iap idma gcmfaces directory The first figure generated shows the ETAN variable which is the sea surface height anomaly from the climatology Note that I have altered the gcemfaces gcmfaces IO read_nctiles m function to always tell you the path and field name that are begin opened so you can learn the directory structure better The path that is reported as this data is opened from the climatology directory Also note the gridsize as it varies over the globe This is the horizontal resolution of the model data we are working with This figure is made by the function gcemfaces sample_analysis plot_std_field m The second figure generated shows the five faces of the globe labeled by the indices of each face Note h
13. ow the Arctic cap is 90 x 90 while the other faces are different sizes To illustrate examine the matlab structure mygrid A structure is a collection of many different related variables They are used extensively in gcmfaces Mygrid is an important structure which contains basic information about the model grid such as longitude of the gridcell centers XC latitude of the gridcell centers YC distance below the surface of the cell center RC the area of the top face of each cell RAC and the angle of the model grid versus the coordinate directions cosine AngleCS sine AngleSN gt gt mygrid mygrid dirGrid Users baylor Documents Research matlab iap idma GRID nFaces 5 fileFormat compact gcm2facesFast 1 memoryLimit 1 ioSize 90 1170 facesSize 6x2 double facesExpand missVal 0 XC 1x1 gcmfaces XG 1x1 gcmfaces YC 1x1 gcmfaces YG 1x1 gcmfaces RAC 1x1 gcmfaces RAZ 1x1 gcmfaces DXC 1x1 gcmfaces DXG 1x1 gcmfaces DYC 1x1 gcmfaces DYG 1x1 gcmfaces hFacC 1x1 gcmfaces Depth 1x1 gcmfaces RC 50x1 double RF 51x1 double DRC 50x1 double DRF 50x1 double AngleCS 1x1 gcmfaces AngleSN 1x1 gcmfaces RAZfull 1x1 gcmfaces gcem2faces 1x1 gcmfaces faces2gcmSize 90 1170 faces2gcm 1x1 gcmfaces gt gt mygrid XC nFaces 5 fi 90x270 double 2 90x270 double 3 90x90 double 4 270x90 double 5 270x90 double gt gt ma
14. ransport plots are the directions what you expect The magnitudes What is happening at the equator Compare the zonal and meridional surface velocities to the Ekman transport figures Can you find regions where the surface flow is consistent with the Ekman transport Regions where they are not consistent 5 Plans 2 You now have some experience with making a plans document Again you will produce one However this time there are some specific constraints on what you will calculate see below so take that into account as you prepare your plans For the plans document you will outline what plans you have for the project including as many details as you have collected by this time Here are some critical points to make in the plans document which will help me to better advise you in moving to the paper stage Describe your region and timeframe of interest Give a working title Make a list of 1 3 hypotheses you plan to address Identify specific journal articles papers or subsections of the book that are relevant Briefly sum marize what they say that is relevant to your planned paper and what missing hypotheses to test that you will try to test Identify datasets that you have located that are relevant Indicate whether you have been successful in opening them i e have you mastered the file format locating the relevant dates locations have you mastered the data subselection data layout and which figures you intend to create
15. re should be that you have the base directory iap idma which is provided in ECCOv4base zip and which has example m files in it and subdirectories The gcmfaces subdirectory is important where the analysis code and sample examples of how to use analysis input and processing files exist Another subdirectory of the base directory is releasel which is where the model simulation data will live In the releasel directory you should have subdirectories MIT prof nctiles_budget and nctiles_climatology These include Argo and other profiles in MITprof the heat salt and mass budgets in nctiles_budget and the climatology i e the normal year in nctiles_climatology If you need to get any other files e g to assess climate trends over the 20 years then you ll have to download the files yourself from http mit ecco group org opendap ecco_for_las version_4 releasei contents html 4 1 2 Earlier Versions In previous versions of this course I have used versions of this model that did not include the Arctic v2 199 and v3 73 However the newest version v4releasel is significantly better in many respects So we will use that one this year 4 2 Opening Files The ECCOv4 simulations are global and use 5 faces of a cube divided amongst 13 different nc files to cover the globe s oceans in a nearly uniform way The data is output in nc files but some care is needed to convert between the measures used in the data files and ordi
16. s as m if that is needed 4 1 MITgcm ECCO v4 Release 1 This homework and paper we will begin working with one particular simulation of the MIT General Circulation Model MITgem Adcroft et al 2008 This particular simulation is the Estimating the Circulation and Climate of the Ocean ECCO v4 release 1 simulation This kind of simulation has been built by a consortium of scientists worldwide http www ecco group org I have chosen this particular model for us to analyze because 1 It is a state of the art modeling framework 2 Not just the vague variables such as salinity and temperature are saved Also available are the advective amp diffusive fluxes winds surface forcing etc Thus unlike observations in the real world we will have everything we need to understand the behavior of the model 3 This model is data assimilating It is constrained to closely resemble a suite of satellite and in situ data which you can access directly here http mit ecco group org opendap ecco_for_las version_4 release1 MITprof contents html Thus as closely as possible it resembles the real world except without data gaps 4 The model s numerical basis is finite volume discretization This framework is identical to that we have been discussing in class with fluxes into and out of the faces of gridded volumes and each volume contains tracers and momentum Gael Forget from MIT recently taught a short course using
17. sentation and writing For example it is more important to catch unfounded claims that to fix spelling errors Do you believe the metrics used Do you understand the fundamentals of the dataset and measurement technique Do you suspect that the data is cherry picked Etc 8 Revisions 2 Learning how to respond to reviews both positive and negative is a crucial part of any scientist s or just person s training There are a number of things to consider which I ll just itemize here e Your first paper was not a draft it was a complete version of a completed scientific work in your opinion Thus if the reviewers and editor a k a me don t point out anything you don t have to change anything e If you do have reviews to respond to you should make a short response to reviewers document which might just be a text set of comments a text file attached to the revised document or a cover email to go with the revised version of the paper e You may catch your own mistakes that were missed by the reviewers it is OK to change these too Please itemize them in the response to reviewers document e You should consider very carefully whether the reviewer is right before making changes Generally make all easy changes that are suggested by the reviewer Things like clarifying unclear sentences or phrases making notation more consistent labeling figures better etc are all in this category You should expect that the revi
18. this simulation and his lecture notes can be browsed here Click on the version numbers in the Rev column to see the slides Gael is responsible for the gcm faces code base which makes it possible to do what we want to even with the data distributed among the 13 peculiar files 4 1 1 This Version Details This version is ECCO v4 release 1 It simulates the Earth over the 240 month period from 1992 to 2011 Data and readme files may be found at http mit ecco group org opendap ecco_for_las version_4 release1 contents html1 The news release is at http www ecco group org There are three different collections of data that are useful for our purposes The nctiles directory contains many of the model output variables depending on time 240 months latitude longitude and depth 50 levels The files in this format are big e g the salinity field is 13 files which are 735 Megabytes each Two dimensional variables such as wind stress are 50 times smaller The directory nctiles_climatology contains the average over all years of all variables for each month that is the typical January the typical February etc For many projects this climatological version will be adequate and the data files are 20 times smaller Finally I have made you an average of the climatology so it no longer has any seasonal information This average of the whole model is in nctiles_avg and is 240 times smaller than the nctiles directory Gael has created simpl
19. x mygrid XC f1 ans 64 8192 gt gt max mygrid XC f2 ans 141 8379 gt gt max mygrid XC f3 ans 179 9739 gt gt max mygrid XC f4 ans 179 9869 gt gt max mygrid XC f5 ans 38 1621 So this tells us that my grid contains lots of substructures or variables The important ones for us are XC longitude in degrees and YC latitude in degrees Notice in the example above that XC varies between 180 and 180 i e 180 W and 180 E and that each face has different longitude limits obviously To access the data on a particular face you add the f1 or f2 at the end of the structure name Similarly gt gt max mygrid YC f5 ans 71 8329 gt gt min mygrid YC 5 ans 88 1027 Thus latitude varies from 90 to 90 i e 90 S and 90 N Actually some of the Earth is not covered where Antarctica and therefore no ocean is The third figure shows all five faces but this time has them connected in a pseudo lat lon arrangement Figure 4 shows you the whole globe in an ugly projection where latitudes and longitudes are equal in distance The final plot is a polar centered projection of the sphere If you want to do gcmfaces_init without all of these plots you can change the verbose variable in the myenv structure Now we want to begin to assess the budgets of mass heat and salt We will begin with a default analysis over the whole Northern Hemisphere and then work on c
20. y you might examine maps of sea surface temper ature or chlorophyll to look for upwelling presumably Ekman driven and choose that region you could make these maps yourself from satellite data or just find them online Alternatively you might choose a region based on interest or based on another paper that mentions Ekman or wind driven processes e Find your region using the ECCOv4 gcmfaces functions manual and download the needed files from hep mit ecco group org opendap ecco_for_las version_4 releasei contents btm Note that docx is useful for identifying what variables are what and http mit ecco group org opendap ecco_for_las version_4 releasei ancillary data standardAnalysis pdf isa very useful start ing point to see how the model compares to data Make plots of the annual mean and annual cycle of SST SSS windstress Ekman transports curl of the windstress and Ekman upwelling downwelling in this region using gcmfaces and the EkmanTools package I have provided e Choose a subregion of your domain based on the patterns of SST SSS and other data you might have chlorophyll etc Relate the changes you see in SST or SSS to the effect you are interesting in examining e g upwelling causes chlorophyll and causes colder SSTs e Use the total transport fluxes into this region to identify the primary balance of mass and either heat or salt depending on which you found to be anomalous in the previous step Determine

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