### Calculate equivalent latitude

 The purpose of this document is to tell you how to calculate equivalent latitude from a potential vorticity (PV) field on a prescribed isentropic level. For a more general discussion on the uses of equivalent latitude and extending it to define the vortex edge, read Nash, E.R., P.A. Newman, J.E. Rosenfield, and M.R. Schoeberl, An objective determination of the polar vortex using Ertel's  potential vorticity, Journal of Geophysical Research, 101 (D5), 9471 to 9478, 1996. But for now, this document tells you exactly how to do it. All code in this document is pascal code (more specifically Borland Delphi). If you don't use Delphi, you should. If you want to stick with weird old languages like fortran, you should still be able to understand the code below. Step 1 The calculation of equivalent latitude is done separately for each hemisphere. The first step is to find the maximum and minimum PV value in the hemisphere of interest. I extract the PV data at 2.5o×2.5o resolution but this isn’t an absolute requirement. Here is my code that does that: `  if AHemis=south then StartInd:=1 else StartInd:=37;` `  if AHemis=south then EndInd:=37 else EndInd:=73;` `  MaxPV:=-1E25;` `  MinPV:=1E25;` `  for I:=1 to 144 do` `  begin` `    Long:=(I-1)*2.5;` `    for J:=StartInd to EndInd do` `    begin` `      Lat:=-90+(J-1)*2.5;` `      CurrentPV:=ExtractPVFromGrid(Long,Lat);` `      if ((CurrentPVMaxPV)) then MaxPV:=CurrentPV;` `      if ((CurrentPV0.0001 then` `      for I:=1 to 100 do AreaTotal[I]:=AreaTotal[I]*2*Pi/TotalArea;` So now we have our areas enclosed by 100 PV isolines. The next step is to calculate what true latitudes enclose the same areas as the areas for those 100 PV values (this is the equivalent latitude corresponding to each PV value). So:Step 3Here is the code I wrote to do this:`  for I:=1 to 100 do``  begin``    if AHemis=north then J:=I else J:=101-I;``    Eqlat[I]:=CalculateEquivLat(AreaTotal[J]);``  end;`where CalculateEquivLat is defined as follows:`function CalculateEquivLat(Area:double):double;``begin``  Result:=57.29577951*arcsin(1-(Area/6.283185307));``end;`Figure 1: examples of PV vs. equivalent latitude profiles for the northern hemisphere and southern hemisphere.So now you should have 100 PV values in your hemisphere of interest, and an equivalent latitude associated with each one. Examples of two such profiles are shown in Figure 1. So now, if for example you have an ozone measurement at a certain latitude and longitude and want to know what equivalent latitude that corresponds to, you go and get the PV value at that latitude and longitude and at the potential temperature at which your equivalent latitude calculation was done (of course this choice is somewhat arbitrary but people tend to choose 450K, 475K, or 550K), and, using the PV vs. equivalent latitude profile, determine the equivalent latitude associated with that PV value. Of course the PV vs. equivalent latitude profile is date and time specific and you need to use the one for the date and time of your measurement.If anything I have written above is unclear, please email me at and ask.