Hi Caro,
Hopefully I can provide some guidance on your questions. In regards to your first post on the comparability of reference air temperature and surface temperature, you are correct in thinking that the two describe different phenomena and there may be issues in using them together. However, InVEST is designed with an eye to broad applicability, especially to data-poor regions. As you have no doubt discovered, good data on local urban heat island effects (and even reference rural air temperatures) are often unavailable and so although it predicts surface UHI, the UHI Global Explorer data is sometimes the best and only available datapoint for a given city’s UHI. If you do have better local data, that is indeed preferable. You can also use local temperature station measurements to calibrate the model, if available, using the UHI Global Explorer data as an initial parameter value that you can adjust accordingly.
For your second question about Eq 111: “UHImax” is the same thing as the “UHI Effect” parameter!
I hope this helps, good luck with your project.
Chris