I am investigating the changes in heat fluxes from a given body of water where the measurements are shown in units of W/m2. There are alternative methods for determining the heat fluxes from a given body of water by calculating the change in internal (thermal) energy of the system. This second method provides a change in internal energy in units of J/m2. How can I compare both results i.e. how can I see if the result obtained by method 1 which is given in W/m2 is the same as the result given by method 2 (J/m2). Given the description I have provided, is it possible to convert W/m2 to J/m2?
First off, I think this kind of question might be better off on perhaps Physics.
Either way, it's important to remember that $1 W = 1 J/s$, so you can't directly convert between these units. Actually, $J/s^2$ seems more like an energy density unit while $W/s^2$ seems more like a typical unit of heat flux.
Assuming that concepts really aren't getting confused here, then you should be able to divide the $J/m^2$ measure by some appropriate length of time in seconds to find the relevant power flux.
For example, say that you have two compatible measurements:
$A = 3600 J/m^2$ for the course of 1 hour $B = 2 W/m^2$
$A/1 h = A/3600s = 1 (J/m^2)/s = 1 (J/s)/m^2 = 1 W/m^2$
Perhaps something like this could be done, but you should probably consult with someone on the details to make sure that these two measurements aren't simply referring to different things altogether.