I have a problem related to the combination of 2 relations. I know the relation between the diffusion coefficient and the temperature (say D(T)) and I know the relation between the diffusion coefficient and the humidity (say D(H)). Now, I would like to write a function for the relation between the diffusion coefficient and both temperature and humidity (say D(T,H)).
$D(T)=\frac{e^{-4.054-\frac{3151.5}{T}}}{3600}$
$D(H)=5.128*10^{-13}*e^{13.5*H}$
Can I combine D(T) and D(H) to make a function D(T,H) and if so, than how can I do this?
Thanks for the advice!
You can't do that. $f(x)$ is known for a single $y_0$, and similarly $g(y)$ is known for a single $x_0$. $f(x,y_0)$ and $f(x_0,y)$ do not allow you to extrapolate reliably to arbitrary $f(x,y)$.
E.g.
assume we have $f(x,1)=x$ and $f(1,y)=y$.
This is compatible with
$$f(x,y)=x+y-1$$
but also
$$f(x,y)=xy,$$ two pretty different functions.
Update:
There are physical situations where you have enough insight in the modelled phenomenon to know that the effects of the variables are independent. For example, if you have multiplicative coefficients, you may adopt a separable model, such as
$$f(x,y)=g(x)h(y).$$