Help with equation 108 urban cooling

equation 108 computes the area of green spaces within a search distance d around each pixel

It is discussing cooling effect of large green spaces >2 ha, but I cannot understand where in this notation is it defined that the green area has to be contiguous? I expect it is my misunderstanding of the notation. please help!

I have many pixels that have a total of >2ha green space with the search distance but I have always assumed this effect does not kick in because they are many and small, not one large area.

any help much appreciated

Hi @southplainfield ,

Thanks for the question.

You are correct that when the model and User Guide refer to large green spaces, they mean CONTIGUOUS. Perhaps it’s not written super clearly, but to me this is what is meant by “large”, as in, if there are many pixels that add up to this area, they are not large spaces, but rather many small ones.

This is confirmed in the referenced sources:

Please also see Sugawara et al. 2016 which is referenced in McDonald et al. 2016. Note that these sources refer to the sizes of individual parks within cities, not to the total area of many parks.


thanks for the answer.

can you clearup something related? Does Invest look outside of the AOI shape file when doing its urban cooling processing? I have been supplying ‘oversized’ layers for LU and ETO assuming everything is just clipped to my AOI? however I’ve seen an urban cooling effect being reported on an AOI with no forest and all I can think is that its air blending on woodland features just outside the extent. If this is how it works i need to delete all nearby features because i am only interested in the effect of new woodland in my AOI,

Hi @southplainfield,

The model does clip the LULC and ETO to the AOI. Could you speak more towards:

however I’ve seen an urban cooling effect being reported on an AOI with no forest and all I can think is that its air blending on woodland features just outside the extent.



i guess the simplest way is to look at some of my results.

In feb_flood_merged.png (results of runoff retention model) you can see 206201 and 206302 have the same result for baseline and fitted. This is because the LU layer for ‘fitted’ was actually identical to baseline - the algorithm I wrote to ‘fit’ forests into impervious areas did not find any suitable locations. (I obviously expect zero influence from outside my AOI in terms of runoff retention)
However when you look at aug_uhi_merged.png (results of the urban cooling model) you can see that 206201 and 206302 values for baseline and fitted are different. But the LU for fitted and baseline are still identical.

The model probably clips the rasters to the bounding box of the AOI, not the AOI polygon itself.


Looking at the source code, it seems to me that the model does not determine if the green spaces are contiguous. It sums the area of green space within the radius d of each pixel. Is this something that should be corrected? Or is it a reasonable simplification?

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Hey @dave ,

This sounds like a possible mistake. My understanding has definitely been that we’re meaning to differentiate the effects of contiguous green spaces from disconnected ones. But, now this thread has me questioning all of that. Perhaps @elonsdorf or @chris could provide their perspective on this.


Would it be possible to get an update on this? Is it a mistake? It will have an impact on my work so some guidance would be much appreciated.

Hi @southplainfield ,

Sorry for the delay. Reviewing this item with the model’s developers, @Perrine and @royremme, is on the agenda for the next meeting of our Urban Team (which I’m NOT a part of). These meetings are not super frequent because the model’s developers and maintainers are spread across 3 continents.

Until then, I’m the only NatCapper that’s speculated that the large green areas are meant to be contiguous, but we’ve certainly raised some doubt. Perhaps Perrine or Roy can chime in here with their view(s) before that meeting. I’ve also pinged some others again internally to prioritize this question.

Please remain patient as we seek the correct solution. Again, I apologize for the ambiguity about this point in the model and for the slow response, but we want to be sure we’re providing the most accurate information possible, especially considering that my May 15th post was overly confident! I understand that this is holding up progress on your work and I’ll continue to pursue a resolution as quickly as possible.


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no need to apologise, and thank you for the update.

Hi @southplainfield ,

I believe I do owe an apology now as I have misguided you and any others who read my post. According to the model’s creators, “currently any green pixel within the search radius counts towards the 2 ha, so contiguity is NOT part of the model.”, despite my claim in that previous response. Thanks @dave for checking the source code and correcting me.

The science on the effect of park size and shape is still developing (and as you can guess, effect is context-specific). A great review can be found here (p.4 “Size and shape of park”:” Also, see Figure 4f on page 6.

So, “two 1.1-ha parks separated by one pixel would essentially behave like a ‘large park’ (2-ha).

There is discussion of if contiguity should be required by the model for the greater cooling effect of large green spaces to kick-in, but that’s NOT implemented at this time.

Sorry for any confusion or delay in your work that I’ve contributed to,


thanks for the clarification.

It seems that 101 parks of 200m2 would also act like a single >2ha large green space? Maybe they would but, as you say, the science is still developing, and its not a helpful feature with this uncertainty. Perhaps a quick fix for the model is to allow users to enable this effect when they are specifically investigating large spaces? And disable it at other times. It’s also misleading that the user guide refers to ‘large green spaces’. It does not say contiguous but there is definately an implication.

I am too far down the line with my work (lots of small green spaces) to go back and unpick the consequence of this but it will certainly have a place in my discussion (its only a masters dissertation, not a phd!)


Thank you for your suggestion! We have noted it in our issue tracker for InVEST and have also clarified in the User’s Guide that the model does not distinguish between contiguous and noncontiguous green spaces within the search distance.


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