Dealing with changing lat/lon values within equation with multiple gradients.

Hello,

I am a meteorologist trying to apply this Thermal Front Parameter Equation (pg 3089 in the paper http://journals.ametsoc.org/doi/pdf/10.1175/JCLI3386.1) but the problem is the y-derivative values from gradient would need to be divided by the fixed # meters per spacing (e.g., 111000*2.5 for 2.5 degree spacing), the longitude values need to be divided by the longitudinal spacing which changes with latitude. I am having trouble attempting to code this so if anyone could give advice that would be helpful. I initially had something that looked like this:

tfp = dot(1*gradient(gradient(abs(temp))),gradient(temp)/abs(gradient(temp))));

but my advisor said I was missing what I stated above.

Any help would be great thanks!

Answer 1

[Andrew Newell]

I'm not sure how the coordinates in the gradient relate to longitude, but let's just say that the scaling parameters are xs,ys,zs and you define scalingParams = [xs ys zs]. Then you could create a function

function grad = gradScaled(f,scalingParams)
  [gx,gy,gz] = gradient(f);
  grad = [gx gy gz]./scalingParams;

Next, for particular values of scalingParams, e.g., s0, define an anonymous function

g = @(f) gradScaled(f,s0);

and define

h = @(f) abs(g(f));

Then

tfp = dot(g(h(temp)),g(temp)/h(temp));

(note, by the way, that your first abs is in the wrong place).