Following the formulations of de Munck et al. (2013), as summarized by Zonato et al. (2021), the offline WRF-MLGR configuration contains 10 thermal layers in total. Six layers represent the green-roof substrate and have a combined depth of 0.15 m, consistent with the observed substrate depth of the experimental modules, while the remaining four layers represent approximately 0.15 m of underlying roof construction. Thus, the complete modeled thermal column is approximately 0.30 m deep, but only the upper 0.15 m represents the green-roof substrate. Temperature is calculated in all thermal layers, while volumetric water content is calculated only for the six soil layers. Layer-resolved soil temperature and moisture diagnostics are provided in Figs. S2 and S3.

During the offline evaluation, the indoor temperature is not simulated. Instead, the model uses a fixed temperature of 23 °C at the bottom of the green-roof system. representing a typical indoor/building temperature and providing the lower thermal boundary condition for the offline simulations. This temperature affects the amount of heat transferred between the green roof and the underlying roof. This model computes the roof's heat and water balances by accounting for net radiation, water added by rainfall and irrigation, evapotranspiration from the vegetation, convective heat exchange with the atmosphere, and the vertical diffusion of heat and moisture within the soil layers. In the original scheme, the model makes an important simplification: it does not distinguish a separate vegetation canopy in terms of radiation exchange, or a distinct canopy air layer for heat and moisture exchange. Instead, the green roof has a single surface and associated temperature which is effectively a soil surface with the ability to transpire (and with substantive thermal admittance, unlike a vegetation canopy). Therefore, the reported surface temperature Ts in the current WRF-MLGR formulation should be interpreted as a bulk or aggregated green-roof skin temperature, rather than as a separately resolved soil-surface temperature, vegetation-canopy temperature, or canopy-air temperature. It is this surface that exchanges heat and moisture with the atmosphere and conducts heat downward into the roof/substrate column. Heat transfer within the layers is then calculated based on Fourier diffusion, and for the soil-based roof layers the model uses a moisture-dependent thermal diffusivity (Zonato et al., 2021): 1λ=e-(log⁡10|Ψ|+2.7)Cs⋅4.186×107,if log⁡10|Ψ|≤5.1,4.1×10-5Cs⋅4.186×107,if log⁡10|Ψ|>5.1, where Ψ is the moisture potential (matric suction; negative under unsaturated conditions), and Cs=(1-θ)Cd+θCw is the volumetric heat capacity of wet soil (Jm-3K-1). It is computed as a weighted average of the volumetric heat capacity of dry soil (Cd) and water (Cw), with θ the volumetric water content Zonato et al. (2021).

For hydrology, rainfall (and optional irrigation) is added at the green roof (i.e., soil) surface, and water moves only vertically through the substrate in a one-dimensional column; therefore, lateral subsurface flow is not represented. Any excess water that reaches the drainage layer is removed as drainage. In the baseline scheme, moisture loss to the atmosphere is represented through plant transpiration (controlled by canopy and atmospheric resistances), and the model does not include a separate explicit term for direct soil-surface evaporation. The scheme also does not explicitly track a separate canopy-interception water store.

As discussed by Martinez Mendoza et al. (2026), the original green roof scheme in the WRF multi-layer urban canopy model exhibits important limitations, particularly in its representation of soil heat flux (Qg). The model does not correctly reproduce the timing and magnitude of Qg, and these errors propagate through the surface energy balance, leading to inaccuracies in both the strength and timing of latent (Qe) and sensible (Qh) heat fluxes. This issue is traced to the fact that there is no radiative canopy, and the soil layer (which has high thermal admittance relative to vegetation) is the radiatively active surface in the model instead of the vegetation. In the next section we detail several updates to this original model version that correct this problem as well as other model issues, and also add additional functionality and realism. To clarify the structural and process-level differences between the original and modified WRF multi-layer green-roof schemes, Fig. 1 provides a schematic comparison of the two model formulations. The figure highlights the main layer structure, the key heat and water flux pathways, and the locations of the five process-based modifications introduced in Sect. 2.3.

To improve the representation of heat and water exchange in the WRF multi-layer green-roof scheme, we implemented five physically based modifications. The two thermal modifications mainly change how heat moves through the green roof substrate and how much energy is stored as QG. The revised soil thermal conductivity provides a more realistic representation of heat transfer as soil moisture changes, while the vegetation-dependent surface conductivity reduces excessive heat storage at the soil surface to represent the effect of vegetation shading on heat storage.

The three hydrological modifications mainly affect evapotranspiration and soil water. Soil evaporation allows water to evaporate directly from the substrate surface. Multilayer root uptake allows plants to take up water from several soil layers rather than only from the top layer. Canopy interception allows rainfall to be temporarily stored on the vegetation, evaporated back to the atmosphere, and also allows dew formation. Together, these modifications change QG and QE and therefore also affect how the remaining available energy is partitioned into QH.

Performance of the original and modified WRF multi-layer green-roof models was assessed against measurements of latent (QE) and ground (QG) heat fluxes at the surface, surface temperature (Ts), and soil water content (θ), along with a residual estimate of sensible heat flux (QH).

Time series show small warm biases for both modelled surface temperatures (Fig. 2a and b). For latent heat flux (QE), the original and modified models show similar overall performance in summer, with identical RMSE and R2 values (61.8 Wm-2 and R2=0.40, respectively). However, the original model has a slightly lower MAE and higher refined index of agreement (d) than the modified model (40.4 vs. 43.9 Wm-2; d=0.67 vs. 0.64). In fall, the modified model shows a lower RMSE and higher R2 than the original model (59.7 vs. 64.7 Wm-2; R2=0.29 vs. 0.17), while the original model has a slightly lower MAE and slightly higher d (39.6 vs. 41.0 Wm-2; d=0.60 vs. 0.59) (Table 1; Fig. 2e and f). For ground heat flux (QG), the largest model observation discrepancy occurs at night, when the observed QG signal becomes nearly flat and approaches zero, whereas both model versions simulate a stronger nighttime heat release. The experimental configuration can influence measured QG throughout the full diurnal cycle because the elevated modules leave an air space beneath the green roof system and the individual modules introduce exposed lateral boundaries. These effects appear to be strongest at night due to smaller energy balance forcing (i.e., Q∗) at this time, but may also influence daytime measurements. We therefore additionally report daytime-only QG metrics (QG_daytime) in Table 1. Nevertheless, the air gap may also impact the daytime measurements (further discussed later in this section based on measurements in 2025).

Overall, for QG the modified model delivers a clear, season-independent improvement, with significant reductions in total error. The removal of bias evident in the original model simulations (lower RMSE and higher index of agreement; Table 1) is visible in both seasons (Fig. 2c and d). This indicates a substantive correction to substrate heat storage, which impacts modelled QE and critically, QH.

In terms of soil water content (θ), the original model shows slightly better statistical agreement with the observations during summer, with a lower RMSE and higher refined index of agreement (d) than the modified model (Table 1). In fall, however, the modified model shows slightly better agreement, with a lower RMSE and a less negative d. Overall, the two model configurations produce similar seasonal evolution of soil water content, particularly during summer (Figs. 3d and 4d). The relatively good summer performance of the original model does not necessarily indicate that its simpler hydrological representation is more physically realistic, because compensating differences in atmospheric water loss and drainage reduce overall errors. This behaviour is examined further in Sect. 3.2 based on the seasonal water-balance analysis presented in Sect. S3 and Table S1 in the Supplement.

Both models slightly overestimate daytime surface temperature maxima; at night, the modified model shows a stronger cold bias, while the original exhibits a smaller bias (Figs. 3a and 4a). The original model underestimates daytime latent heat flux and largely misses the immediate post-rainfall increase, whereas the modified model better matches both the timing and magnitude of the peaks. For direct visual comparison of the timing and magnitude of the original and modified model responses, the corresponding time series are overlaid in Fig. S4. In particular, the sharp increase in QE after rainfall is clearly seen in the observations but is missed by the original model. By adding evaporation from intercepted water on the foliage, the modified model can now reproduce this post-rainfall boost in latent heat flux. This addition allows the model to respond quickly to wet conditions and better match the observed evapotranspiration peaks (Figs. 3b and 4b). To illustrate the post-rainfall latent-heat-flux response more clearly, Fig. 5 shows an event spanning 15–17 July 2014 (DOY 196–198). Following precipitation on DOY 196, the leaf wetness sensor signal increases sharply, indicating rapid wetting of the sedum canopy surface. At the same time, the modified model produces a strong, short-lived increase in modeled latent heat flux (QE), consistent with enhanced evaporation immediately after rainfall (including evaporation of intercepted water on the canopy). As the leaf surfaces dry, both the leaf wetness signal and modelled QE decrease. The lysimeter-derived observed QE also increases rapidly following rainfall and shows close temporal agreement with the modeled response, with only a small difference in the timing of the peak. In fact, observed QE is derived from changes in lysimeter mass over each measurement interval, which can contribute to small differences in the apparent timing of the responses. In contrast, the original model shows a much more muted response and largely fails to capture the rapid post-rainfall peak.

The most pronounced differences between the model versions appear in the ground heat flux: the modified model damps the exaggerated daytime spikes seen in the original model and exhibits a more realistic nocturnal recovery, consistent with improved substrate thermal conductivity and heat storage – and hence better phase and amplitude (Figs. 3c and 4c). In addition to the long-period evaluation, Fig. 6 shows an event-scale comparison of observed and modeled ground heat flux (QG) for 11–18 October 2025 (DOY 284–291), a week with clear observations. During this period, the experimental green-roof module was placed directly on the roof deck (i.e., without an airspace beneath), providing lower-boundary conditions for vertical heat-flux measurements that are both more typical of actual green roofs and which match the model assumptions. Under these conditions, the observed QG exhibits a physically consistent diurnal cycle, and the modified model reproduces the main phase and amplitude of QG variability, including the daytime peaks and nighttime recovery (R2=0.642).

The original model exaggerates the diurnal cycle of QG, diverting energy from the turbulent fluxes and depressing morning values as well as midday peaks in QE and QH (Fig. 7a). Figure 7b demonstrates that the modified model captures both the magnitude and timing of peak latent heat flux QE, yielding a realistic daytime partitioning of available energy. The modified model tempers the large positive morning QG bias in the original model and as a result better reproduces the timing and amplitude of the daytime peaks of QH and QE. Differences in Q∗ are small between the models.

Figures 8 and 9 present a one-at-a-time sensitivity analysis, where each of the five modifications summarized in Table 2 and described in detail in Sect. 2.3 is switched off individually while the other updates remain active. These experiments are used to isolate the role of each added process and to show how the different modifications shape the modelled surface energy partitioning relative to the observations.

In Fig. 8, the six panels focus on moisture related processes and how they affect the total latent heat flux (QE) in both summer and fall (focus on daytime-only). When multi-layer root uptake is removed (–root uptake; Fig. 8a and b), plants rely primarily on moisture from the uppermost soil layer. As this layer dries during dry-down periods, transpiration becomes increasingly water-limited, leading to a modest reduction in mean daytime QE, with a small decrease in the median, particularly in summer, bringing median modeled values below both the observations and the fully modified configuration, and a narrowing of the upper distribution. Removing canopy interception storage and its subsequent evaporation (–intercepted water; Fig. 8c and d) suppresses short-lived evaporation pulses following rainfall events, lowering the summer maximum and the fall upper quartile of the daytime QE distribution and shifting the median to lower values in both summer and fall relative to the observations and the fully modified model. Eliminating explicit soil-surface evaporation (–soil evap; Fig. 8e and f) further decreases daytime QE by removing direct evaporation from the exposed soil. In the present simulations, vegetation cover is high (86 %), limiting the exposed soil fraction and therefore the magnitude of this effect. Under lower vegetation coverage, however, soil-surface evaporation would contribute more substantially to daytime QE, and the sensitivity to this process would be expected to increase.

Figure 9 highlights the thermal-related modifications, which produce the clearest and most systematic sensitivity in the soil heat flux QG. Turning off the revised soil thermal-conductivity formulation (–ksoil) causes the QG distribution to widen substantially and more extreme values occur, showing that the updated substrate thermal treatment is one of the key controls on soil heat exchange. Removing the vegetation-modulated effective surface thermal conductivity term (–heat storage) also increases the spread and magnitude of QG. This modification primarily affects the mean behavior of QG by regulating how efficiently incoming radiation is conducted into the substrate. Without vegetation modulation, the roof surface behaves more like bare soil, absorbing and storing a larger fraction of solar energy, which systematically enhances heat storage and leads to stronger daytime QG peaks. Together, these results indicate that while the revised substrate thermal conductivity governs the range and extremes of QG, the vegetation-dependent surface thermal conductivity plays a dominant role in controlling the mean partitioning of energy into heat storage, thereby reducing persistent biases in QG.

Figure 10 compares the seasonal cumulative drainage over the full observation periods in summer (DOY 182–243) and fall (DOY 244–304) 2014, together with the total observed rainfall during each season. In summer, both model configurations produce lower drainage than observed (45.90 mm), with the original model giving 43.31 mm and the modified model giving 32.54 mm. In fall, both models produce more drainage than observed (104.90 mm), reaching 131.21 mm in the original model and 125.10 mm in the modified model. Overall, the seasonal totals indicate an underestimation of drainage in summer and an overestimation in fall, while the modified configuration consistently reduces drainage relative to the original model. As an additional conservation diagnostic, the seasonal water-balance closure errors were 1.95 % and 1.31 % for the original model in summer and fall, respectively, compared with only 0.13 % and 0.16 % for the modified model, after accounting for precipitation, net atmospheric water loss, drainage, and changes in water storage (Sect. S3 and Table S1). These results also help explain why the original model can reproduce soil water content reasonably well despite its simpler hydrological representation. In summer, the original model produces lower atmospheric water loss but higher drainage than the modified model, so these differences partly compensate and result in a similar seasonal change in soil water storage. Therefore, the slightly better summer soil water content statistics of the original model do not necessarily indicate a more physically realistic representation of the water balance.

The performance of the modified WRF multi-layer green roof scheme can be evaluated relative to other physically based green roof models. Simulations of extensive green roofs, such as those presented by Heusinger et al. (2018) with a modified version of the EnergyPlus green roof model “EcoRoof”, explicitly represent vegetation processes including canopy transpiration, soil evaporation, and evaporation of intercepted water, supported by a detailed canopy microclimate sub-model that resolves radiative and turbulent exchanges between the atmosphere, the canopy, and the surface. Simulations with this modified EcoRoof (ER-modified) model for London indicate that the enhanced canopy microclimate formulation improves surface temperature predictions relative to the original WRF multi-layer green-roof scheme, but with a tendency to overestimate latent and ground heat fluxes (Martinez Mendoza et al., 2026). Because ER-modified and WRF-MLGR v2.0 are evaluated against the same observational dataset, a direct quantitative comparison can be made. ER-modified demonstrates stronger agreement for surface temperature and ground heat flux, with a index of agreement (d) of 0.77 for Ts and 0.74 for QG, when evaluated over the full July–October 2014 period (i.e., combined summer and fall). In comparison, WRF-MLGR v2.0 yields seasonal values of 0.56 (summer) and 0.62 (fall) for Ts and 0.35 (summer) and 0.37 (fall) for QG in WRF-MLGR v2.0. In contrast, WRF-MLGR v2.0 exhibits improved skill in simulating latent heat flux, with d values of 0.64 (summer) and 0.59 (fall), exceeding the long-period performance of ER-modified (d=0.55).

It is relevant to additionally compare other green-roof models. A separate WRF green-roof scheme has also been developed for the single-layer urban canopy model (Yang et al., 2015). This scheme is different from the multi-layer WRF-BEP+BEM green-roof scheme of Zonato et al. (2021) evaluated and modified in the present study. The single-layer scheme does not document a dedicated interception storage and evaporation process; however, it was shown to reproduce surface temperature and turbulent energy fluxes within a reasonable range when evaluated against observations over a 6 d period. Another approach is that the TEB-GREENROOF model directly couples the vegetated substrate to the roof layers without a canopy air space. When evaluated, it showed underestimated substrate moisture, overestimated drainage, and larger than observed temperature amplitudes, reflecting a warm bias and discrepancies in moisture dynamics (de Munck et al., 2013). In the following, we assess the behavior of the modified WRF multi-layer green roof scheme and its strengths, weaknesses, and the impacts of the applied updates.

This study develops a modified version of the WRF multi-layer green-roof scheme and evaluates it against observations in summer and fall of 2014 in London, Canada. The goal of the updates is to address specific process-based limitations identified in the original scheme. In brief, the modified configuration adds (i) a revised non-linear moisture-dependent substrate thermal conductivity formulation (replacing the original linear relationship), (ii) a vegetation-modulated effective surface thermal conductivity term, (iii) explicit soil-surface evaporation, (iv) multi-layer root water uptake, and (v) a canopy interception module that represents interception storage, evaporation of intercepted water, and dew formation on the canopy. Below, we summarize which aspects improve model results most clearly, where key biases remain, and what these results suggest for future development and applications within WRF.

Across both seasons, the largest improvement is in ground heat flux (QG). In summer, QG mean absolute error decreases from 87.4 to 17.6 Wm-2 and RMSE decreases from 105.9 to 24.0 Wm-2 (Table 1). In fall, QG RMSE decreases from 94.2 to 24.0 Wm-2 (Table 1). The time series and diurnal plots explain this improvement: the original scheme produces QG that swings too strongly, with peaks that are too large during the day and also exaggerated at night, especially an unrealistically sharp morning spike. The modified scheme reduces these exaggerated peaks, so the daily cycle has a more realistic timing and magnitude (Figs. 2–4 and 7).

It is also important to interpret QG in the context of the measurement setup. During the 2014 deployment the design of the experimental green roof array provides an elevated platform to allow installation of lysimeters and drainage units below the modules, which also results in an air layer beneath the green roof array. This configuration allows heat to exchange through the bottom (and potentially sides) of the module, which can make the plate-based QG measurement harder to interpret – particularly at night, when signals are smaller and boundary effects can be more influential. For this reason, we emphasize a separate one-week period (11–18 October 2025), when the modules were placed directly on the roof deck and the physical setup more closely matched the model's lower-boundary assumption of direct contact between the green roof soil and the roof deck underneath. During this week, the observed QG shows a clearer diurnal cycle, and the modified model aligns closely with the measurements in both timing and magnitude (Fig. 6), providing strong evidence that the revised physics substantially improves the simulation of ground heat flux (QG) under conditions that best match the model configuration (and the configuration of most actual green roofs).

Reducing the unrealistic daytime QG peak changes how the available energy is divided between the different heat fluxes. Net radiation (Q∗) is very similar in the original and modified simulations. Therefore, when QG becomes smaller in the modified model, more energy is available for QE and QH.

The main reason for the large change in QG is the improved soil thermal conductivity. Ground heat flux depends on both the temperature difference within the soil and the soil thermal conductivity. Therefore, QG can change a lot even if the modeled surface temperature does not change very much. In the original model, the soil thermal conductivity became unrealistically high in the morning, which caused too much heat to move into the soil. In the modified model, the revised soil thermal conductivity and especially the vegetation-dependent surface conductivity reduce this excessive heat transfer. As a result, more of the available energy is directed to QE and QH, particularly earlier in the day, shifting the timing of the diurnal cycle of these fluxes.

The hydrological modifications further influence this coupled energy balance. Soil evaporation provides an additional pathway for water loss from the green roof, canopy interception allows stored rainfall to evaporate rapidly after rain, and multilayer root uptake allows plants to access water from deeper soil layers as the upper soil becomes dry. These processes generally enhance QE when water is available. The resulting changes in QE, QG, surface temperature, and moisture conditions also affect QH. Therefore, the modified model produces a more realistic overall partitioning and diurnal evolution of the surface energy fluxes, even though changes in surface temperature remain relatively small.

The hydrological modifications also help explain the changes in latent heat flux (QE). Figures 3b and 4b show the diurnal cycles with a noticeable increase in QE right after rainfall. The original model often represents this response too weakly or misses it, which contributes to an overall underestimation of QE during wet periods. In contrast, the modified model captures these short-lived post-rain increases more consistently and provides a better overall prediction of QE variability and magnitude. This behavior is especially clear during 15–17 July 2014 (DOY 196–198). Following rainfall, the leaf wetness sensor signal rises sharply, indicating rapid wetting of the sedum canopy surface, and the modified model simultaneously produces a strong, short-lived spike in modeled QE. As the leaf surfaces dry, both the sensor signal and modeled QE decrease. The original model, however, produces a much weaker response and largely fails to capture this rapid post-rainfall peak (Fig. 5). Overall, this suggests that the modified scheme better represents fast evaporation pathways immediately after wetting, consistent with the inclusion of evaporation from intercepted water on the canopy. The most direct explanation is the added canopy interception module, which allows intercepted water stored on the canopy to evaporate quickly after rainfall (and also represents dew formation), rather than relying only on slower changes in substrate moisture and evaporation. This is consistent with the broader land-surface modeling literature, where interception loss is recognized as an efficient, rapid pathway for returning precipitation to the atmosphere and is often needed to reproduce these short post-rain evaporation responses (e.g., Cammalleri et al., 2010; Heusinger et al., 2018).

Another important improvement comes from the updated root water uptake. In the original scheme, transpiration draws water mainly from the thin top layer, so QE drops when that layer dries and more water ends up draining from the bottom of the soil layer. In the modified model, uptake can access moisture from multiple soil layers, which supports more realistic QE during dry-down and reduces excess drainage. We also added explicit evaporation from the soil surface. Together, these changes improve the overall energy partitioning. The drainage comparison is consistent with this behavior: the modified model produces less drainage than the original model (Fig. 10). However, drainage remains underestimated in summer and overestimated in fall in both model configurations.

Even with these improvements, some biases remain. First, daytime surface temperature (Ts) is still too warm in both model configurations (Figs. 3a and 4a). A key reason for this remaining Ts bias is that the current WRF-MLGR formulation calculates only a single bulk surface skin temperature for the green-roof system. Separate computation of the soil/substrate surface temperature, vegetation/canopy surface temperature, and canopy-air temperature is not available in the present formulation. As a result, Ts cannot be directly interpreted as either a soil-surface temperature or a vegetation-canopy temperature, but instead represents an aggregated surface temperature produced by the simplified bulk representation of the green roof. This limits the ability to diagnose whether the remaining Ts bias arises primarily from the substrate thermal state, vegetation thermal response, or both. Second, QE is still low and shows less variability than the observations (Fig. 8). The sensitivity tests help explain this: when canopy interception storage and its evaporation (–intercepted water) or multi-layer root uptake is removed (–root uptake), QE decreases further and more energy can shift into QH and QG (Fig. 8). This shows that the added moisture pathways are working as intended. However, the remaining underestimation of QE variability suggests that the model still misses some real-world controls, such as microclimatic gradients within the canopy air space and plant physiological responses (for example, a more detailed canopy microclimate). For example, the EnergyPlus green roof (EcoRoof) model represents vegetation as an explicit canopy, including within-canopy radiative exchange (e.g., shading effects) and canopy air exchange processes that regulate evapotranspiration, which may help capture some of the canopy-microclimate controls that are still simplified in the present WRF configuration (Sailor, 2008). Future development should therefore separate the vegetation canopy, canopy air, and soil/substrate surface in the model, instead of representing them with one bulk surface temperature. This would allow the model to calculate their heat exchange processes separately, including radiation, turbulent heat exchange, and heat conduction into the substrate. It would also make it possible to identify whether any remaining errors in Ts come mainly from the vegetation or the soil surface, and to improve the inaccurate model component.

In terms of substrate moisture, the original model better captured the observed temporal variability in volumetric water content (θ) during summer, whereas the modified model showed improved agreement in fall (Table 1). However, both model versions show a small bias in drainage, modestly underestimating summer totals and overestimating fall totals (Fig. 10). During the summer of 2014, conditions were relatively dry, with even the strongest convective rainfall events producing less than 14 mm. In contrast, fall 2014 saw powerful thunderstorms, with notable events exceeding 73 mm of rainfall in just 3 h and another event surpassing 45 mm in 2 h. This difference in seasonal rainfall intensity helps explain the models biases. During drier summer periods, the models may underestimate drainage since soils rarely reach near-saturation. Conversely, during fall's intense rain events, soil often approach saturation, prompting the models to produce excessive drainage. The modified model produces marginally lower drainage than the original, consistent with the added water-loss pathways through soil evaporation, transpiration via root uptake across all soil layers, and evaporation of intercepted water from the canopy.

Several limitations affect how these results should be interpreted and also highlight priorities for future work. The main observational limitation is ground heat flux (QG), which needs to be considered in the context of the experimental setup. During the 2014 deployment, the elevated green roof modules left an air space between the modules and the underlying roof, while the use of individual modules introduced exposed lateral boundaries. These conditions allow additional heat exchange through the bottom and side boundaries that is not represented in the model. The influence appears to be strongest at night, when observed QG becomes nearly flat and approaches zero, suggesting weak thermal coupling between the green roof modules and the underlying roof structure. However, the same boundary effects may also influence daytime QG. We therefore report daytime-only QG statistics (QG,day; Table 1) as an additional evaluation metric, while recognizing that daytime measurements are not completely unaffected by the experimental configuration. The October 2025 comparison, conducted under a configuration more representative of the modeled lower boundary, shows a clearer observed diurnal QG cycle, and the modified model reproduces the main timing and magnitude of the observed variability more closely (Fig. 6).

A related limitation is that the “observed” sensible heat flux (QH) is not measured directly. Instead, it is calculated as a residual: net radiation minus the sum of measured QE and measured QG. This means that any bias in QG, during the day and especially at night – will automatically appear as a bias in the residual QH, which makes nighttime QH comparisons harder to interpret. Importantly, this does not change one of the main conclusion of this study: the modified model dramatically reduces the large QG errors seen in the original scheme. Rather, the residual nature of QH mainly limits how confidently we can interpret the remaining nighttime QH differences as resulting from model physics.

From a model-development perspective, the upgrades in this study are focused on specific processes, but several simplifications remain. Even with the new interception module, the canopy representation is still basic. For example, the scheme does not fully represent a separate canopy microclimate (its own temperature and humidity near the leaves) or detailed radiation exchange within the canopy. It also simplifies how vegetation modifies near-surface aerodynamics, such as wind reduction, roughness, and the resistances that control heat and moisture transfer. Probably most important is separation of the soil surface and canopy radiation and energy balances together with addition of a clearer resistance/aerodynamic formulation. A likely contributor to the surface temperature bias is that the observed canopy surface (as seen by the infrared radiation thermometer) has substantial three-dimensional structure, with a mixture of sunlit and shaded elements during the day, and locally reduced sky-view factors at night that keep sheltered portions of the canopy warmer than exposed upper surfaces. However, the model represents the vegetation canopy as a flat, uniform layer, thus generating an apparent overheat during the day and too much nocturnal cooling relative to the measured values. These additions would likely help reduce the remaining surface-temperature biases (too warm during the day and too cool at night), improve the spread and magnitude of QE (Fig. 8), and further improve the daytime heat storage and nighttime release. Incorporating these processes consistent with field studies showing that green-roof energy partitioning depends strongly on soil moisture, vegetation state, and canopy wetness (e.g., Heusinger and Weber, 2017).

Also, this evaluation focuses on warm-season conditions (summer and fall 2014). For Canadian and broader climate applications, cold-season processes may also be important. Future development should include snow accumulation and melt, freezing and thawing of the substrate, and temperature-dependent hydraulic and thermal properties, because these processes can strongly modify wintertime heat exchange and spring moisture availability. In addition, the scheme could be extended to represent green roof uptake of trace gases – such as CO2 exchange through photosynthesis (e.g., Mirebeau et al., 2025) and a simple deposition/uptake pathway, so the model can also be used to explore potential green-roof impacts on urban air quality.

Finally, since the ground-level vegetation scheme in WRF-BEP+BEM is based on this green roof model, these upgrades can be applied in the future to further improve the accuracy of urban vegetation simulations within that framework.