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After quite a lot of searching, I cannot seem to find an answer to my query, so I thought I would ask.

I am creating a contour plot of some function of two variables, $f(x,y)$, that is small ($|f(x,y)| \ll 1$) for positive values, and large ($|f(x,y)| \gg 1$) for negative values. Given that I am interested in properly resolving the behaviour of the function for positive values, I have currently been plotting the maximum of my function and zero, as follows:

xmin = 0.006; 
xmax = 10;
ymin = 0.01;
ymax = 3

ContourPlot[
 Max[f[x,y], 0],
 {x, xmin, xmax},
 {y, ymin, ymax},
 ScalingFunctions -> {"Log", "Log"},
 Contours -> {Automatic, 50},
 ContourStyle -> None,
 Exclusions -> None,
 FrameLabel -> {{Style[
     "\!\(\*SubscriptBox[\(k\), \(||\)]\)\!\(\*SubscriptBox[\(L\), \
\(T\)]\)/\!\(\*SqrtBox[SubscriptBox[\(\[Beta]\), \(e\)]]\)", 18], 
    None}, {Style[
     "\!\(\*SubscriptBox[\(k\), \(y\)]\)\!\(\*SubscriptBox[\(d\), \(e\
\)]\)\[Chi]", 18], ""}},
 LabelStyle -> 
  Directive[Black, FontSize -> 12, FontFamily -> "Times New Roman"],
 ColorFunction -> ColorData[{"ThermometerColors", {0, 1}}], 
 PlotLegends -> 
  BarLegend[Automatic, Ticks -> Table[i, {i, 0, 0.09, 0.01}]],
 PlotRange -> All,
 PlotRangePadding -> Automatic,
 PerformanceGoal -> {"Speed", "Quality"},
 WorkingPrecision -> MachinePrecision,
 GridLinesStyle -> {Dashed, Dashed}
 ]

with output

enter image description here

Note that I have not included the specific form of the function in the example code, as the code used to solve for $f(x,y)$ is too long for a post such as this.

Though the above plot shows most of the information that I would like it to, it is not always obvious as to where the surface $f(x,y) = 0$ actually occurs due to the choice of ColourFunction, and the fact that the function is continuous through zero, such there is no sharp --- and thus noticeable --- discontinuity in the colour.

Question: Is there a way to colour everything satisfying $f(x,y) \leqslant a$, for some constant $a$, (which, in the example above, would just be the values where $f(x,y)=0$) a particular colour, while preserving the ColourFunction everywhere else? Essentially, I would love to be able to append another colour to the bottom of the BarLegend that is the "zero-and-below" colour, and label it as such.

Any help would be greatly appreciated. Let me know if you need more information/code, as I'll be happy to provide it :)

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You can define a custom ColorFunction:

ClearAll[CF]
CF[cliprange_:{0, 1}, clipcolor_: Automatic, range_: Automatic, cf_: "TemperatureMap"] :=
  Module[{rng = range /. Automatic -> {0, 1}, 
     clipcols = ColorData[cf] /@ {0, 1}, 
     cc = clipcolor /. Automatic -> {White, White}}, 
    ColorData[{cf, rng}][Clip[#, cliprange, rng]] /. Thread[clipcols -> cc]] &;

Examples:

f[x_, y_] := Cos[x] + Cos[y];

{min, max} = Through[
   {MinValue, MaxValue}[{f[x, y], 0 <= x <= 4 Pi, 0 <= y <= 4 Pi}, {x, y}]];

Row[ContourPlot[f[x, y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
    Contours -> {Automatic, 50}, 
    ColorFunction -> CF[#, Blue, {min, max}], 
    ColorFunctionScaling -> False, ContourStyle -> None, 
    PlotLegends -> Automatic, ImageSize -> 300, 
    PlotLabel -> Style["clipped range: " <> ToString[#], 16, Black]] & /@ 
  {{-.5, max}, {min, 1}, {-1, 1.5}}, Spacer[10]]

enter image description here

Replace Blue with {Blue, Red} to get

enter image description here

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  • $\begingroup$ Hey @kglr, thanks for the great answer! This looks like a good solution to the problem, but I am having trouble applying it to my particular case. The second argument of CF[] is evidently the colour of the range not clipped, but I am not completely sure what the first and third arguments of CF[] correspond to? When I try to apply this to my problem, rather than your excellent MWE, these two arguments do not behave how I would expect. $\endgroup$
    – PhysyCola
    Nov 17 '21 at 10:36
  • $\begingroup$ @PhysyCola, the third argument is a list of minimum and maximum values of the function (f) over the range of x and y values specified in ContourPlot. $\endgroup$
    – kglr
    Nov 17 '21 at 18:46
  • $\begingroup$ Right, and the first argument is the clipping range? In any case, this is an excellent answer, so will be marking is as answered! $\endgroup$
    – PhysyCola
    Nov 18 '21 at 14:20

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