Hydrologic Modeling for Green Roofs

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What do we mean by "modeling"?

A model, in the sense we are using it, is a mathematical representation of predicted outcomes. You have probably heard the term used in weather and climate forecasts. When a hurricane forms in the ocean, models are used to predict its path.

Models are very simple, yet very complex. Models are simple in that they have inputs and outputs. A hurricane model, for example, has inputs that may include water temperatures, existing and forecasted weather patterns, hurricane strength, topography, and air temperatures.

Also, simple conceptually, is that models have an output. In a hurricane model that output is generally a path, with strength levels and wind speeds along the path.

Though inputs and outputs are conceptually simple, models are most beneficial due to their ability to process many complexities. Think about all the variables just listed as inputs; even though oversimplified, that is still a lot of variables to consider, particularly when considering that most models include multiple timesteps.

By multiple timesteps, we mean that the model will produce a prediction, or forecast, for every minute, or several minutes, or hour, or day. A hurricane model wouldn't be very useful if it only showed the one point in the future; instead, the model shows multiple points in time, which can be viewed sequentially like frames in a movie.

Climate forecast models follow very similar principles.

A green roof hydrologic model is parallel to weather and climate models in many ways. There are inputs (green roof profile, weather, roof slope, etc.) and an output (retention, runoff, plant health, etc.) at multiple timesteps. Hurricane forecasts produce some pretty terrific maps, which is not something we get with green roof models... but we can produce some pretty cool graphs!

Why model?

Let's consider the alternatives to modeling. In fact, green roof modeling is not very common (yet), so if you have ever designed or permitted a green roof, you probably have used one of the alternatives.

Just about every alternative can be described as a static analysis, meaning that it is a calculation that examines only one scenario at one point in time. Sometimes a handful of static analyses are used together, but even though a small collection of scenarios are considered, that is still far more simplistic than modeling.

A good example of a static analysis is the ASTM E-2396 through E-2399 tests. ASTM E-2399 is often used to estimate the retention of a green roof but in a very incorrect way. Using ASTM E-2399 to estimate retention is basically saying "if my green roof is completely bone dry, and I flood it with water such that the surface is completely underwater, then unclog the drain, when the drain catches up, my green roof would hold this much water".

Seriously, that's what the test estimates. Rainfall doesn’t flood a green roof because the water is being pulled down by gravity before it fully fills the soil capacity. But the ASTM test was never intended to estimate the hydrologic performance of a green roof; it was intended to estimate the maximum weight to estimate the load the building would be exposed to via determining maximum potential retention capacity, and it does a great job at that. But maximum potential retention capacity is not the same as predictive retention capacity; in reality, the maximum is rarely reached. Another interesting observation that became evident through testing is that the wilting point of a soil needs to be considered. In a nutshell, the water that is at or below wilting point is not retrievable through the ET process, so it never leaves. This could easily be 15% of the predicted ASTM values.

Contrast that with modeling. In modeling, we might say, "assume my green roof starts off mostly dry, then it rains, so let's see how much water it absorbs. Then my green roof is wet, so over a few days of sunshine, it will dry out, but not completely. Hence, let's estimate the evapotranspiration during those days, and see how wet it is at the end.

After that, it will rain again on my partially wet green roof, so let's estimate how much is absorbed and how much runs off in that condition, which is different from when it was mostly dry." And so on. And so on.

Conceptually simple. Mathematically quite complex. BUT far more accurate.

Curve numbers are not any better than an ASTM test. Curve numbers are still a type of static analysis, and application of curve numbers to green roofs is misguided, which we explain in this post (coming soon).

In short, the curve number method is not able to produce an accurate prediction of green roof performance over time.

So why do we model? Because modeling is superior.

Modeling is the best way to accurately predict hydrologic performance of any project. When done properly, modeling factors in a wide range of climatic, geometric, and biologic variables that are generally not addressed by other currently available, but more common, methods.

Still not convinced? Let's look at ASTM E-2399 again.

For a generic 10cm (4-inch) green roof, that test might indicate that the green roof will retain approximately 35% of its volume in water (35% volumetric water content, or VWC), which is 3.6cm (1.4 inches) of water. If taken at face value, one might assume that the green roof would absorb 100% of rainfall up to 3.6cm (1.4 inches). But when not submerged in water, most laboratory tests done by GRD of full assemblies show that the green roof only retains approximately 2.8cm (1.1 inches) of water. And that after it appeared to be completely dry at the starting point.

So let's assume that it never gets completely dry (which would be very bad for plants anyway). Also, before our hypothetical rainfall, it is holding 0.8cm (0.3 inches) of water. So now, of that 2.8cm (1.1inches) total absorbed only 2.0cm (0.8 inches) is water from that rain event. But this is still mostly a static analysis.

To make this dynamic, let's assume rainfall patterns, say over the course of one month. Temperatures range from 16-27°C (60 to 80 degrees F), there are 10 hours of sun per day, humidity ranges from 40% to 70%, and a total of 12.7cm (5 inches) of rain occur in a variety of storm sizes, with two storms over 3.8cm (1.5 inches) each.

Now, how much water does the green roof retain, i.e., how much is runoff reduced versus a non-green roof? That requires a lot more math! But that's just what a model does.

Now assume that the exact same green roof (which ASTM says retains 3.6cm (1.4 inches) of water) is placed in a climate where half as much rain occurs. Now how much does the green roof retain? Likely more. Or imagine that the green roof is located in a climate where the same amount of rain occurs, but in very small rainfalls almost daily. How does that change the hydrologic performance? It changes the performance outcome completely.

The answers can be found, with a fairly high degree of accuracy, via modeling. If green roofs are used for specific performance, shouldn't that performance matter? Shouldn't that performance be valuable enough to actually try to calculate accurately?

OK, I'm convinced! But isn't modeling hard?

Modeling green roof performance is far easier than the GPS app you probably used to navigate within the past week. Modeling does not have to be hard. As with anything, more inputs from the user (a little more work by the user) will result in a more precise model, but absolutely minimal input (location and profile only) can yield some ballpark results.

We are so certain that you will enjoy and benefit from modeling, that we are going out on a limb and developing this tool and making it accessible because we think that will improve the industry.

But we don't know exactly what you want, or how you want to use modeling. So send us feedback. Want a demo at your office or a video call? Drop us a line. Got a specific project that you think could benefit, but not exactly sure how to start? Give a shout, as we love those challenges. Let us know how we can grow and adapt the modeler to help you. We think it's a much better approach than static analyses, but you (engineers, regulators, architects, etc.) are better judges of that, so let us hear from you!

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