Green Roof Model Overhaul Slashes Heat Flux Errors by More Than 75 Percent

Green roofs are among the most visible weapons cities wield against urban heat, but the computer models used to predict their cooling power have long been quietly miscalculating one of the most fundamental processes involved: how heat moves through the thin layer of soil on which the plants depend. Now, a team of Canadian and European researchers has rebuilt the green-roof physics inside a widely used weather model, and the results are striking. The conductive heat flux through the roof substrate, the quantity that determines how much solar energy is stored in the growing medium rather than released to warm the city air, once simulated with errors exceeding 100 watts per square meter, is now reproduced with errors of just 24 watts per square meter in both summer and fall.

The work, published in the journal Geoscientific Model Development, comes from Alireza Saeedi, Eric Scott Krayenhoff and colleagues at the University of Guelph, the University of Western Ontario, the CIMA Research Foundation and Environment and Climate Change Canada. Their target was the multi-layer green-roof scheme embedded in the Weather Research and Forecasting model’s urban canopy framework, known as BEP-BEM. That scheme allows researchers to test, at the scale of entire neighborhoods and cities, what would happen if rooftops across a metropolis were covered in vegetation. But an earlier process-level evaluation had exposed structural flaws: the model lacked soil evaporation, had no radiative buffering from the plant canopy, and produced systematic warm biases in surface temperature alongside badly distorted daily cycles of latent and ground heat flux.

The diagnosis traced many of these problems to a single simplification. The original scheme treats the green roof as one bulk surface, essentially a soil surface that can transpire, rather than distinguishing a vegetation canopy, a canopy air layer, and a substrate surface. Because soil has a much higher thermal admittance than leaves, the model’s radiatively active surface absorbed and stored far more energy than a real sedum canopy would. The consequence was an exaggerated ground heat flux that swallowed energy that should have gone into turbulent sensible and latent heat exchange, depressing the morning and midday peaks of the very fluxes that deliver urban cooling.

The team’s remedy consisted of five targeted, physically based upgrades. First, they replaced a linear relationship between soil thermal conductivity and moisture with a Johansen-type formulation that interpolates between dry and saturated conductivities using a Kersten number. The original linear approach had driven simulated conductivity to peaks exceeding 49 watts per meter per kelvin under wet conditions, far beyond what is reasonable for engineered growing media; the revised formulation kept values within 0.32 to 0.98 watts per meter per kelvin. Second, they added a vegetation-dependent effective surface thermal conductivity, in which the bare-soil value is scaled by an exponential function of fractional vegetation cover, mimicking the shading that plants provide. Third, they introduced explicit evaporation directly from the substrate surface using a bulk-transfer approach with a soil-wetness factor. Fourth, they allowed plant roots to draw water from all substrate layers in proportion to layer thickness, rather than only from the thin top layer, which had dried out prematurely and throttled transpiration. Fifth, they implemented a canopy interception module, adapted from earlier green-roof work, that stores rainfall on leaves in proportion to leaf area index, evaporates it, and even permits dew formation on foliage at night.

To test the new physics, the researchers turned to an extensive green roof planted with Sedum spurium on the rooftop of Talbot College at Western University in London, Ontario. The modules carry a substrate depth of 0.15 meters, matching the six soil layers represented in the model, which together with four layers of underlying roof construction form a thermal column about 0.30 meters deep. Running the green-roof scheme in offline mode, driven directly by observed radiation, air temperature, humidity, wind, precipitation and pressure rather than by the full atmospheric model, they evaluated two continuous periods in 2014: a summer window from 1 July to 31 August and a fall window from 1 September to 31 October.

The headline result concerned the ground heat flux. In summer, the root-mean-square error fell from 105.9 to 24.0 watts per square meter after the upgrades; in fall, it dropped from 94.2 to 24.0 watts per square meter. The mean absolute error in summer decreased from 87.4 to 17.6 watts per square meter. The original scheme had produced an unrealistically sharp morning spike in ground heat flux and exaggerated nocturnal heat release, artifacts that the revised thermal treatment damped substantially. Because net radiation was nearly identical in both model versions, correcting the ground flux automatically redirected energy toward the turbulent fluxes, improving the timing and magnitude of daytime peaks in both latent and sensible heat.

The hydrological upgrades showed their value most vividly after rainfall. During a three-day event in mid-July 2014, a leaf wetness sensor recorded a sharp rise as the sedum canopy soaked up precipitation, and the modified model responded with a strong, short-lived spike in latent heat flux closely matching lysimeter-derived observations. The original model, lacking interception storage, produced only a muted response and largely missed the post-rainfall peak altogether. Sensitivity experiments in which each upgrade was switched off individually confirmed the mechanism: removing interception evaporation suppressed these brief evaporation pulses, while removing multi-layer root uptake reduced transpiration during dry-down periods, and removing soil evaporation lowered daytime latent heat flux further, an effect expected to grow at sites with sparser vegetation cover than the 86 percent observed at the London roof.

Water balance diagnostics reinforced the picture. Seasonal water-balance closure errors shrank from 1.95 percent to 0.13 percent in summer and from 1.31 percent to 0.16 percent in fall, indicating strict conservation of mass in the revised scheme. Drainage totals fell relative to the original model, though both configurations underestimated the observed summer drainage of 45.90 millimeters and overestimated the fall total of 104.90 millimeters. The authors attribute these residual biases to the seasonal contrast in rainfall character: a relatively dry summer in which soils rarely approached saturation, and a fall punctuated by intense thunderstorms delivering more than 73 millimeters in three hours. Notably, the original model’s seemingly better summer soil moisture statistics appear to stem from compensating errors in evaporation and drainage rather than more realistic hydrology.

The team also staged a decisive test of the model’s lower-boundary assumption. In 2014, the instrumented modules sat elevated above the roof surface to accommodate lysimeters, leaving an air gap that allowed unmodeled heat exchange through the base and sides, complicating interpretation of the ground heat flux measurements, especially at night when the observed signal flattened toward zero. So during 11 to 18 October 2025, the researchers moved the flux module directly onto the roof deck, matching the model’s assumption of direct contact between substrate and roof. Under these conditions the observed diurnal cycle was clear and physically consistent, and the modified model reproduced the phase and amplitude of the variability closely, with a coefficient of determination of 0.642.

Honest caveats remain. Surface temperature is still biased warm during the day and cool at night, and latent heat flux remains somewhat low and less variable than observed, with refined indices of agreement of 0.64 in summer and 0.59 in fall. The authors attribute these residuals primarily to the persistence of the single bulk surface temperature: without a separately resolved canopy, canopy air, and substrate surface, the model cannot distinguish whether temperature errors arise from the vegetation or the soil. The three-dimensional structure of a real sedum canopy, with sunlit and shaded elements and sheltered pockets at night, is also flattened into a uniform layer. Future development, the researchers argue, should therefore focus on a more realistic vegetation canopy submodule, and potentially on cold-season processes such as snow, freezing and thawing that matter for Canadian climates, along with trace gas exchange. Even so, the dramatic reduction in ground heat flux error means that city-scale simulations of green-roof scenarios in the WRF model now rest on substantially firmer physical ground, providing what the authors describe as a stronger basis for WRF-based urban climate applications.

Subject of Research: Process-based upgrades to the WRF multi-layer green-roof scheme evaluated against field observations of energy and water fluxes

Article Title: Process-based upgrades to the WRF multi-layer green-roof scheme (WRF-MLGR v2.0) and evaluation against field observations

Article References: Saeedi, A., Martinez Mendoza, M., Krayenhoff, E. S., Voogt, J., Yin, H., Zonato, A., Leroyer, S., & Wagner-Riddle, C. (2026). Process-based upgrades to the WRF multi-layer green-roof scheme (WRF-MLGR v2.0) and evaluation against field observations. Geoscientific Model Development, 19(20), 10103-10122. https://doi.org/10.5194/gmd-19-10103-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-10103-2026

Keywords: green roofs, WRF model, urban heat island, urban canopy model, soil thermal conductivity, latent heat flux, evapotranspiration, canopy interception, drainage, model evaluation, urban climate, Geoscientific Model Development