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What if the models ... just don't work?

Urban hydrology relies a lot on modeling to predict the effect of changing conditions on the water management needs of the future. For example, designing stormwater infrastructure that will be suitable for an area as it progressively undergoes development and experiences climate change might be a "typical" problem for which a hydrological model could be used. But what if the models we use are just ... unable to do this?

We - Anneliese Sytsma, Chelsea Panos, Matt Kondolf and I - explored this issue for the semi-distributed component of the urban hydrology model SWMM, and you can check the paper out in Water Resources Research. We wanted to understand if model parameters describing a particular urban landscape and which would usually be treated as "constants" for that landscape would change if the model were parameterized over a variety of impervious fractions and climatic conditions.

To dig a bit deeper, SWMM doesn't catch all the spatial variations that are present in an urban catchment (like in panel "a" below). A distributed model (like that shown in panel "b" below) can capture a lot of this variation, but SWMM simplifies all of that into one permeable area (in green in panels "c" and "d" below) and one or two impervious areas (grey areas in panels "c" and "d"). Our suspicion was that the best division of the catchment into effective geometry parameters W and L, and the permeable/impervious areas might change depending on how intense rainfall was, and what the "real" pattern of these areas was in the city.

One way to check this stuff out is to use synthetic or model experiments where we generate "data" with one model (in this case a distributed model) and then try to replicate it with the other model - SWMM. What's great about this is that we know the "true" behaviour of the city block over lots of different storms and situations in a way we almost never can for real places. So, we used a distributed model to make a bunch of data for the same urban areas as storm/soil properties changed and impervious surface area increased or decreased. We calibrated SWMM to this data and looked at how the best performing SWMM parameters were distributed for each case.

If the model was suitable for use under all conditions, you'd expect to see the "good" model parameters being about the same for all conditions. Instead, we saw these "good" parameters migrating around as impervious area and rainfall/soil changed - look at how different the grey areas are in the plots below. What this means is that a model calibrated under one set of conditions probably can't make good predictions under another set of conditions. And that... well, it sucks a bit if that's what we're hoping to use models for!

For specific cases, the errors in the model if used outside the conditions it was calibrated for can be as high as 60%. For a situation where you modeled how the city might behave with climate change and urbanisation, the average error was 21%. Thats what the plots below show in red.

So this paper was a bit of a head-scratcher, because while we concluded that there's a need of real caution in applying calibrated models like SWMM in conditions they were not calibrated to, the alternatives aren't super clear - don't we need these models to help us work out how to manage future scenarios and build suitable infrastructure?

Possibly we can borrow from other fields - using a broader range of calibration conditions, using ensembles of models, or potentially moving more towards real time observations and true adaptive management. None of these is an easy solution.

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