2d interpolation

I understand your problem.

Among the functions lspline, pspline, cspline,  there is no function by which the value of the first derivative of a function on the boundary could be specified.

To solve your problem it is necessary to add boundary conditions (imaginary conditions).

Look at the small example for a function of one variable.

Я понимаю вашу проблему.

Среди функций lspline, pspline, cspline нет функции, с помощью которой можно было бы задать значение первой производной функции на границе.

Для решения вашей задачи необходимо добавить граничные условия (мнимые условия).

Посмотрите маленький пример для функции одной переменной.

Splines tend to oscillate, so its no surprise you also get negative values in your interpolation - especially given the wide range of your "Properties" values.

Its interesting to see that Freds interesting tricky way works and gives positive values.

I would stick with a simple 2D linear interpolation.

As Mathcads 2D interpolations restricts me to a square data matrix I had written a few 2D (and 3D) interpolation routines which do not have that restriction. See attached file

Here is the 3D-plot using Freds function

Maybe his function is more appropriate for your purpose - you'll have to decide.