Plotting geographic data not oriented on a grid

Using griddata, you can mesh out your current dataset into a grid:

latmin = min(lat_piomas);
latmax = max(lat_piomas);
lonmin = min(lon_piomas);
lonmax = max(lon_piomas);
gridSize = [100 200];
latvec = linspace(latmin, latmax, gridSize(1));
lonvec = linspace(lonmin, lonmax, gridSize(2));
[LatQ LonQ] = ndgrid(latvec, lonvec);
ThickQ = griddata(lon_piomas, lat_piomas, thickness, LonQ, LatQ);

From there, it's a simple matter to show the data in whichever format you like:

figure
axesm('mercator', 'MapLonLimit', [0 360])
geoshow(LatQ, LonQ, ThickQ, 'DisplayType', 'surface')

And if you want to get real fancy, you can use topological data to show the elevation of the surface, while using the color to show the "thickness" data. Here's an example using built-in example topography data:

% Get example topography data
load topo topo topolatlim topolonlim
Rtopo = georefcells(topolatlim, topolonlim, size(topo));
ElevQ = geointerp(topo, Rtopo, LatQ, LonQ, 'cubic');

% Display the surface
figure
axesm('mercator', 'MapLonLimit', [0 360])
geoshow(LatQ, LonQ, ElevQ, 'DisplayType', 'surface', 'CData', ThickQ)
daspectm('m', 1000) % To exaggerate the height of the topography