FH, I have made some changes, and added a new slide#5. FH, Your results of the 2011 July and December shedding should provide a good opportunity to examine closely as to how and why the Loop Current sheds eddies. There are 3 things you need to understand about Loop Current and eddy-shedding – as I try to summarize in the next 3 slides. Pls. study them. I think they will then help you to think and plan what to analyze, and what to watch out for in the results etc., using methods (plots etc) some of which we discussed today. I will try to suggest some analyses in slides#5 etc, but I am very sleepy right now… Leo

First there is the following fundamental process that depends on basic mass conservation and Rossby wave dynamics: The Loop grows due to Yucatan influx Q i, and once it grows to a large enough size 200~300km, it becomes big and deep enough for beta to have effects, so the westward Rossby wave velocity = C i = - βR o 2, where R o = (g’h(t)) 1/2 /f, can then “peel” a portion of the Loop’s mass – i.e. a warm eddy – westward. Note that the upper-layer depth “h(t)” is a function of time to emphasize the time-dependency of the problem. This growing and peeling can be purely “upper-layer” (i.e. does not require a lower layer) and they account for ~50% of the total variance based on EOF. Second: there is coupling with the deep layer; the coupling can be inferred from basic mass conservation as indicated also in the above sketch. CiCi QiQi QiQi

Third: there is baroclinic instability (BCI) which as shown above occurs most dominantly over the North Campeche Bank (red region) from surface to deep layers z~-1000m. EOF analysis suggests that the coupled and baroclinic instability modes account roughly another 25~30%. The important point is: neither coupling nor BCI are necessary for eddy-shedding to occur.

EOF 1+2 EOF Mean time- lag EOF1+2 Mean time-lag EOF1+2+3 Shedding time of full model full model EOF1+2 full model EOF1+2+3 Both BCI & coupling can however, accelerate the shedding time. In other words, if BCI & coupling are absent, then eddy-shedding caused by Rossby wave alone (constant Q i ) can take a long time – as long as 2~3 months from start to finish as shown by the filled triangles in the plot above. BCI (~EOF3) accelerates by a mean of about 16days, and the remaining mean ~34 days are due to coupling and other processes.

Focus on the 2 cases of eddy shedding in Goal: were these shedding events forced by winds  transport+vorticity  InstabilityModification  shedding? Existing studies have shown that wind- forced mechanism should be relevant – and your goal is to (hopefully) provide case studies proof. A.Shedding Event 1: 2011/ Jul/30. 1.Conduct Jul/01, Jun/15 & Jun/01 experiments – done. 2.Plot time-transect contours of SSH & ζ/f, where ζ = ∂v/∂x-∂u/∂y, (u,v) = near-surface say at z=-50m, or you can directly do this on the curvilinear + sigma(k=1) grid, and f may be taken as a constant = 7x10 -5 s -1 for lat=26N – pls. check!! Time of 60days should be good, from (say) May/15-Aug/15. See example below. Using MATLAB, XH was able to extract “b” (4.i below) from similar contour plots. 3.Find the 18 o C and 12 o C isotherm depths h 18 & h 12, then plot their time-transect contours as in “2.” 4.Do similar time-transect contours of AVISO SSH & ζ/f (using geostrophic vel); and compare w/model 5.The goal in “2-4” is to see (i) where the LoopEdge = b(t) is, (ii) what C i (t) is, and (iii) how they vary with Yucatan inflow vorticity ζ i /f and Q i = transport/A Yuc, where A Yuc is the Cross Sectional Area Of Yucatan Channel, and ζ i is to be computed at the western (50km) side of the channel. 6.Now you can relate Q i and wind stress and wind stress curl over the Caribbean Sea; 7.Find out (research!) what the connection is – think logically and try different things – discuss w/me. 8.Compute BCI growth rates using my code; 9.Compute EOF of SSHA to check Q i & C i for modes1+2 and mode3 for BCI; 10.Determine upper-lower coupling by computing mass transports. Eda has codes for 9 & 10 (and others also); EOF is easy for you but may be convenient to have “10” from her. Goals & Methods: Analysis transect Here (right) is an example of time-transect contours of SSH from Yucatan to northern Gulf. Note edge of the Loop where red turns to yellow than blue…

Additional Background Material 1 – particularly panels “C, D & E” Seasonal cycles ( ) of (A) zonal wind stresses averaged over Gulf of Mexico and NW Caribbean Sea (negative westward), and (B) Yucatan transport anomaly from Exp.Basic with mean = 25.6 Sv shown. (C) Regression of Loop's northern boundary vs. ζ/f from Exp.Basic. Maps: correlations (wind leading 1 month; above the 95% significance, otherwise white) between Yucatan transport and (D) zonal wind stress and (E) wind stress curl; contours are 0.2 and 0.4, black positive and white negative. Panel C is from numerical model, note the linear connection between “b” & “ζ/f” -- see next slide for analytical formula that connects “b” and & “ζ/f”.

“b” becomes larger when:  o is large (we used symbol ζ slide#5 etc) v is large θ o increases (=90 o for a Loop entering the Gulf in pure northward direction) Changes in “b” may affect eddy shedding  Additional Background Material 2 – “b” vs. “ζ” (Reid’s formula)

Additional Background Material 3 – how wind may affect shedding A schematic plot of seasonal eddy shedding according to the dynamics explained in text. Upper panels from left to right: extended Loop when Caribbean wind and Yucatan transport are strongest (Jul and Jan), wind and transport weaken (Sep and Mar; squiggly arrow represents Rossby wave), and wind in the Gulf is strongest (Oct and May; blue arrows indicate wind-forced upper-layer circulation).