To evaluate model performance, two analysis periods of 62 d were selected, each encompassing multiple precipitation events interspersed with drying intervals. Period selection was guided by a monthly stratification of the dataset, for which summary statistics (mean, standard deviation, and 25th, 50th, and 75th percentiles) were computed for net radiation, air temperature, vapor pressure deficit (VPD), and wind speed. Based on similarities in these environmental characteristics, July–August was grouped as “summer” and September–October as “fall”. These labels are used only for descriptive convenience and do not correspond to full meteorological seasons.

Two additional subsets were defined to isolate model performance under contrasting environmental conditions: dry versus rainy days and low versus high net radiation (Q*). For the moisture-based classification, a daily rainfall threshold of >5 mm was used to identify rainy days, while dry days were defined as having <0.2 mm of rainfall on the target day and during the preceding 2 d. This classification yielded 15 rainy days in summer and 11 in fall, and 13 dry days in summer and 14 in fall.

For the radiation-based classification, high- and low-net radiation days were identified using percentile thresholds: days below the 25th percentile of daytime mean net radiation were classified as low-net radiation conditions, and days above the 75th percentile were classified as high-net radiation conditions. This procedure resulted in 31 low-net radiation days and 31 high-net radiation days across the analysis periods.

Although the model simulates energy balance continuously, the focus of the evaluation is not on the accuracy of fluxes during precipitation itself, but rather on how well the model responds to rainfall inputs over time. To isolate this response, time steps with active precipitation (rainfall > 0.2 mm) were excluded at the analysis stage. This approach is consistent with the study objectives, as Qe cannot be reliably estimated from lysimeters measurements during rainfall and moreover, evapotranspiration is minimal under these conditions due to high humidity and reduced vapor pressure gradients.

The evaluation was restricted to daytime conditions (Q*>0), when surface energy exchanges are dominated by radiative forcing and turbulent fluxes are most pronounced. In addition, time steps affected by instrument malfunction, calibration activities, or missing data were removed. All exclusions were applied only to the observed and modeled outputs used for evaluation; the simulations themselves were performed using the complete forcing datasets.

The models to be compared are stand-alone versions of ER – an original version of the model, as found withing EnergyPlus v8.6.0 (Sailor, 2008), and a modified configuration following Heusinger et al. (2018) – and a stand-alone version of the green roof parametrization embedded in WRF v.4.3.1 (Zonato et al., 2021). Table 1 provides an overview of each model.

In addition to input parameters, which need to be specified in the program, the models require an input file with atmospheric forcing data, which is common to both models. It consists of time series measurements of eight variables: incoming solar radiation, incoming longwave radiation, wind speed, air temperature, humidity, precipitation, air pressure and irrigation. Most variables were directly measured on site, except air pressure, which was retrieved from London A weather station (WMO ID: 71623), located at London International Airport.

Both models also require prescribed vegetation and substrate parameters, as well as initialization variables specific to each model. Key model input parameters and prescribed values are summarized in Table 2. Additional details are provided in Sect. S5 of the Supplement. Some parameters such as LAI, and vegetation height, may vary seasonally; however, continuous time series measurements were not available. Therefore, representative values appropriate for each study period were selected based on available measurements and previous studies conducted on the green roof. Although albedo was measured continuously, period-specific values were used to provide a single representative parameter value for each simulation period.

The models are initialized (forcing file starts) at 03:00 LT on the first day of the period and end at 23:00 LT on the last day of the period. The timesteps are 5 min long and the values used for the initialization correspond to the value at the 03:00 time step for all variables except albedo, which is an average.

The hourly composites (Fig. 7) show the two ER configurations (ER_o and ER_m) exhibiting early-morning underestimations and an afternoon positive bias, peaking around ∼50 W m⁻². In contrast, WRF-MLGR consistently underestimates Qe during the morning, and most of the afternoon, with biases reaching 100 W m⁻², later in the afternoon the model switches to overestimations. The shaded envelopes show larger variability for ER than for WRF-MLGR. In the summer period (Fig. 7a), ER_o shows stronger early-morning underestimations but smaller midday overestimation that ER_m, while WRF-MLGR maintains its predominantly negative bias, particularly in the morning. In the fall period (Fig. 7b) all models show reduced amplitudes, but the same general patterns persist: ER transitions from morning underestimation to afternoon overestimation and WRF-MLGR remains negatively biased.

Figure 8 presents the composite differences between modeled and observed Qe – during daytime hours without active precipitation –, separated into dry days (<0.2 mm of rainfall on the target day and during the preceding 2 d; Fig. 8a) and rainy days (daily rainfall > 5 mm; Fig. 8b). On dry days, model behavior closely resembles that of the full-period composites and shows relatively small variability. In contrast, rainy days exhibit substantially larger variability across all models. The ER configurations retain the morning-to-afternoon bias reversal but with less consistent timing and a wider spread, whereas WRF-MLGR shows strong and persistent underestimation accompanied by a pronounced spread. Figure 8 summarizes the hourly mean bias for each moisture regime, whereas the supplementary scatter plots (Fig. S6, panels a and b) show all hourly model–observation pairs and reveal tighter clustering around the 1:1 line under dry conditions and greater dispersion during rainy periods.

Days with high net radiation (Fig. 9a) reproduce the full-period diurnal pattern, with both ER configurations showing slightly larger mean differences, and all models exhibiting a relatively narrow spread. In contrast, low net radiation days (Fig. 9b) display a markedly different behavior, characterized by substantially increased variability and much smaller mean biases across all models.

The statistical metrics (Table 3) are consistent with these patterns. ER shows slightly superior performance during the summer period: both ER versions retain positive MBE yet achieve marginally lower MAE than WRF-MLGR and higher dr values (both ER_o and ERm≈0.60 vs. 0.50). For the fall season MAE and dr are very similar between ER_o and WRF-MLGR, while ER_m shows slightly lower MAE and higher dr. RMSE decomposition shows that ER errors are dominated by unsystematic errors. WRF-MLGR shows the opposite behavior, with systematic underestimation dominating.

Both ER configurations show a persistent warm bias throughout the day, with the largest differences occurring in the afternoon. In contrast, WRF-MLGR shows a different pattern, characterized by morning underestimation followed by substantial afternoon overestimation. During the summer period both ER configurations maintain this warm bias and exhibit greater day-to-day variability than WRF-MLGR, particularly during the warmest hours. In the fall period, bias magnitudes are reduced for all models and variability decreases for ER, reflecting the overall weaker radiative forcing and more moderate surface temperatures (see Fig. S2 of the Supplement).

Mean surface temperature biases are generally amplified under dry conditions and reduced on rainy days. This contrast is modest for the ER configurations, which maintain a similar warm bias across both moisture regimes, but is much more pronounced for WRF-MLGR. Under wetter conditions, bias magnitudes and diurnal range are dampened, and variability decreases (see Fig. S3 of the Supplement). The supplementary scatter plots reinforce this pattern at the point scale, showing a narrower spread under rainy conditions and a somewhat broader dispersion under dry conditions, together with slightly larger bias magnitudes (Fig. S6, panels c and d of the Supplement).

High net radiation conditions (Fig. 10a) accentuate both diurnal temperature biases and variability. Under these conditions, ER exhibits increased daytime variability, while WRF-MLGR shows a comparatively narrower spread. Mean bias magnitudes remain comparable to those of the full evaluation periods, although morning underestimation in WRF-MLGR is slightly enhanced under strong radiative forcing. In contrast, low net-radiation conditions (Fig. 10b) are characterized by substantially reduced mean temperature differences for all models, most notably for WRF-MLGR. While variability in WRF-MLGR increases slightly under low net radiation conditions, the ER configurations show more stable behavior.

Table 4 summarizes the statistical metrics for Tsurf and reinforces the patterns seen in the diurnal composites. All models exhibit positive MBE, confirming Tsurf warm biases. ER shows lower MAE values and higher dr than WRF-MLGR in both periods, indicating smaller overall deviations from observations. The RMSE decomposition shows that ER's errors are dominated by their systematic component, consistent with the stable warm bias seen in the diurnal plots. WRF-MLGR, in contrast, exhibits a greater contribution from the unsystematic component. However, this statistical partitioning should not be interpreted as random variability. Rather, it reflects the consistent shift from morning underestimation to afternoon overestimation within the daytime period. These opposing biases partly offset each other in the MBE but remain large in magnitude, leading to elevated RMSE. Therefore, the large error components in WRF-MLGR indicate a structural timing and magnitude error in surface heating rather than random variability.

Qg exhibits the largest model–observation discrepancies for WRF-MLGR in both evaluation periods. Bias magnitudes are substantially larger than for the ER configurations, with peak overestimations exceeding 200 W m⁻², followed by a reversal to substantial underestimation in the late afternoon. In contrast, both ER configurations remain close to observations, with small consistently positive biases and low variability. Seasonal differences are modest: WRF-MLGR errors are larger in summer, while ER shows similarly stable behavior across both seasons, with reduced variability during fall (see Fig. S4 of the Supplement).

Mean Qg differences are generally reduced during rainy days relative to dry conditions. Under rainy conditions, the ER configurations remain close to zero throughout the day, while WRF-MLGR shows a marked reduction in bias magnitude but a substantially wider spread, indicating increased variability and less consistent timing (see Fig. S5 of the Supplement). The supplementary scatter plots (Fig. S6, panels e and f) further illustrate these differences, with ER configurations clustered close to the 1:1 line and WRF-MLGR exhibiting a much larger vertical spread and weaker correspondence with observations.

High net-radiation conditions (Fig. 11a) strongly amplify Qg biases, particularly for WRF-MLGR, which exhibits large midday overestimations that peak near ∼250 W m⁻² and a relatively narrow spread. In contrast, the ER configurations remain close to observations with limited variability. Under low net radiation conditions (Fig. 11b) the magnitude of Qg biases decreases for all models. For WRF-MLGR, mean differences are substantially reduced, however, the spread widens substantially, reflecting increased day-to-day variability under weaker radiative forcing.

Table 5 reinforces these contrasts. ER performs well, with both configurations showing nearly the same performance during both seasons, in the fall they show modest MAE values (∼7 W m⁻²), relatively high RMSE (∼35 W m⁻²) and high index of agreement (dr=0.77 for ER_o and 0.78 for ER_m). The summer period shows a small MAE for both configurations (∼7 W m⁻²) and relatively low RMSE (∼9 W m⁻²), these errors were dominated by the systematic component during the fall period, and by the unsystematic component during the summer period.

In contrast, WRF-MLGR performs very poorly, showing very large MAE (83 W m⁻² for the fall and 103 W m⁻² for the summer), RMSE (110 and 128 W m⁻²), and strongly negative dr values (-0.64 and -0.75), indicating poor temporal agreement. As observed for Tsurf, the RMSE decomposition attributes a large portion of the error to the unsystematic component; however, the diurnal composites display a consistent phase pattern. The large error magnitudes in WRF-MLGR therefore reflect a systematic mismatch in the timing and magnitude of Qg rather than random variability.

Figure 12 shows the evolution of observed and modeled water content throughout summer (Fig. 12a) and fall (Fig. 12b). All models reproduce the timing of rainfall events, showing sharp increases in SWC after precipitation. However, the magnitude of these responses differs substantially across models.

During the summer period (Fig. 12a), ER_m shows the closest agreement with the observed peaks and subsequent dry-down trajectories. ER_o responds well to rainfall but generally produces larger peak values and drains more rapidly, leading to underestimation between events. WRF-MLGR consistently underpredicts SWC, with peak magnitudes consistently lower than observed and with faster post-rainfall declines.

In the fall period (Fig. 12b), the two ER configurations converge, producing very similar dynamics, with ER_o slightly closer to observations, particularly during the later part of the dry-downs. WRF-MLGR continues to reproduce the correct timing of wetting and drying but maintains well below observed magnitude.

Table 6 highlights the contrast in model performance for water content. All models show negative MBE, confirming overall underestimation. The MAE values for the ER configurations are relatively small (0.030 m³ m⁻³ in the summer and 0.022 m³ m⁻³ in the fall for ER_o; 0.021 m³ m⁻³ in the summer and 0.035 m³ m⁻³ in the fall for ER_m), when compared with WRF-MLGR, which shows larger errors, with MAE reaching 0.045 m³ m⁻³ in the summer and 0.070 in the fall. Model agreement follows the same trend: ER achieves moderate dr values, with the original configuration performing more consistently. In contrast, WRF-MLGR yields dr values near zero (or negative), indicating poor agreement in magnitude despite reproducing event timing; its strong systematic dry bias (relatively large negative MBE) and damped storage response dominate the agreement score. RMSE values also favor ER (0.038 m³ m⁻³ and 0.029 for ER_o; 0.025 m³ m⁻³ and 0.039 for ER_m) over WRF-MLGR (0.048 and 0.073 m³ m⁻³). For ER_o, RMSE reflects a balance of systematic and unsystematic components, while ER_m shows larger unsystematic errors during summer but larger systematic errors in the fall. WRF-MLGR errors are dominated by systematic underestimation, consistent with its low storage representation.

ER consistently overestimated Qe, whereas WRF-MLGR produced negative deviations. The ER bias can be traced to the model's simplified representation of vegetation controls on transpiration. Because ER computes latent heat flux as the sum of substrate evaporation, transpiration – and evaporation of intercepted water, in the case of ER_m – transpiration dominates under vegetated conditions and is strongly scaled by LAI. The relatively high LAI observed led ER to treat Sedum as fully active, despite the fact that CAM species typically maintain low transpiration rates through conservative stomatal regulation even under favorable environmental conditions (Gravatt and Martin, 1992; Huang et al., 2024).

The ER model's stomatal resistance formulation does not capture this conservative behavior. In ER, minimum stomatal resistance is adjusted only by radiation-, moisture-, and VPD-based stress functions, which allows stomata to remain relatively open until VPD becomes high. CAM plants, however, exhibit earlier stomatal closure, responding directly to atmospheric demand through a “feed-forward” mechanism that is not represented in the model (Males and Griffiths, 2017). As a result, ER overestimates transpiration during conditions under which Sedum would physiologically restrict water loss.

Overall, the results of this study suggest that vegetation physiological parameterization plays an important role in representing latent heat flux in Sedum-based green roofs within the ER model framework. In this model, calibration of MSR improved performance (see Sect. S5 of the Supplement), highlighting the sensitivity of Qe to transpiration-related parameters. Additional one-at-a-time sensitivity analyses further support this (see Sect. S6 of the Supplement), indicating a strong influence of vegetation parameters on ER performance. To our knowledge, CAM-specific parameterizations have not yet been implemented in green roof surface energy balance models. Given the distinctive physiological characteristics of CAM vegetation, incorporating CAM-specific formulations could potentially improve the representation of transpiration dynamics and surface energy partitioning, particularly in models where vegetation controls play a dominant role, such as ER.

WRF-MLGR represents latent heat flux solely through transpiration, as the current version does not include a substrate evaporation term. This structural limitation causes systematic underestimation of Qe. In addition, WRF-MLGR places greater emphasis on aerodynamic resistance and applies strong atmospheric controls on stomatal resistance, including air temperature. While this yields behavior more consistent with the conservative water-use strategy of CAM vegetation, it can also amplify the underestimations by suppressing transpiration prematurely under rising temperature and VPD, reinforcing the negative biases seen in the statistical evaluation. Thus, although WRF-MLGR represents Sedum's conservative stomatal behavior more realistically than ER, the absence of a substrate evaporation component and the strong atmospheric regulation of stomatal resistance contribute to underestimations over the diurnal cycle.

Both models overestimate daytime Tsurf and Qg, though for different reasons and with different magnitudes. ER shows a modest but systematic warm bias (≈1–3 °C), possibly because the model lacks vegetation heat capacity and therefore cannot buffer short-term fluctuations in net radiation. Combined with small energy misallocations among Qe, Qh, and Qg, this causes excess energy to accumulate at the surface, producing a consistent warm bias despite the model's tendency to overestimate latent heat flux. Correspondingly, ER produces small but systematic overestimations of Qg, which primarily stem from biases in the near-surface temperature gradient. Although the model includes a moisture-dependent conductivity formulation, this representation does not fully capture the observed variation in k for the studied substrate (Perelli, 2014). Nevertheless, retaining the original formulation results in realistic Qg magnitudes because the smaller conductivity partially offsets the warm bias in the simulated surface and shallow substrate temperatures. As a result, the residual errors in Qg remain modest and consistent throughout the day, as reflected in the small RMSE values and the relatively flat diurnal difference curves for both ER versions.

In contrast, WRF-MLGR exhibits a much larger positive bias in Tsurf, particularly during the afternoon, along with very large Qg errors, and failure to reproduce the observed Qg diurnal cycle. The most likely reason for this bias is the lack of vegetation radiative representation, meaning all shortwave and longwave radiation is absorbed at the “combined substrate-vegetation” surface, with effectively no shading of the substrate surface, canopy heat storage, or radiative interactions to moderate surface warming. As a result, incoming radiation is applied directly to the substrate rather than to the vegetation that shades the substrate. Because the substrate has a much higher thermal admittance than foliage, a large fraction of the radiative forcing is initially stored as ground heat, leading to elevated morning values of Qg as the energy accumulates in the upper substrate layers. This stored energy governs the subsequent evolution of Tsurf and delays the development of Qh and Qe, causing Qg to dominate the diurnal partitioning of surface fluxes. This behavior contrasts with real vegetated surfaces, where the vegetation enables rapid adjustment of sensible and latent heat fluxes under increasing radiative forcing (Curtis, 1936; Tadeu et al., 2021). As part of the experimental green roof system tests, an unvegetated module was also instrumented and installed to monitor Qg. Figure 13 illustrates how, as a consequence of this substrate-dominated energy storage, the modeled Qg presents a diurnal pattern that is more consistent with that of a bare substrate than with observations from the vegetated module.

ER_o captures the timing of rainfall inputs but often produces larger post-rain increases in water content and a faster early decline than observed. This reflects the model structure in which precipitation is applied directly to the surface layer, producing an immediate increase in SWC in the upper layer. These peaks are followed by a rapid initial decline driven as internal redistribution transfers water from the surface layer to the subsurface layer, where it becomes available for gravitational drainage and transpiration. Redistribution also contributes directly to an early decrease in the depth-averaged water content by relaxing the unrealistically high surface-layer moisture. Although evapotranspiration is overestimated by the model, the early post-rain decrease is dominated by redistribution and drainage rather than an immediate enhancement of Qe. Once substrate moisture decreases, modeled and observed drying rates become more similar, however ER_o remains persistently drier because early post-rain redistribution and drainage reduce stored water more rapidly than in the observed system.

ER_m alters the water balance primarily through canopy interception and a moisture-dependent runoff formulation. A fraction of rainfall is temporarily stored on the foliage and evaporated directly, so only the remaining drip reaches the substrate. This dampens the sharp post-rain increases in substrate water content seen in ER_o and, for many events, brings the modeled peaks closer to observations. The new runoff parameterization also removes water from the surface layer as a function of saturation, providing an explicit drainage pathway when the substrate is wet. Together, these changes reduce the magnitude of storage peaks and promote faster loss of excess water, so ER_m tracks the observed dry-down more closely but often remains slightly drier than ER_o between rainfall events.

In WRF-MLGR, the substrate hydraulic parameters and free-drain bottom boundary allow water to percolate out of the substrate column very efficiently when the profile is wet. Hydraulic conductivity in the deeper substrate exhibits a strong nonlinear dependence on substrate moisture, and the multilayer diffusion scheme rapidly transfers infiltrated water downward toward this drainage sink. As a result, the deeper layers tend to dry quickly following precipitation. Because these lower layers represent a substantial fraction of the total substrate depth and the simulated bulk water content is computed as a depth-weighted average across all layers, their rapid drying strongly influences the overall column moisture. Consequently, the model exhibits a persistent dry bias relative to the lysimeter-derived bulk water content.

Model performance exhibits a clear sensitivity to moisture regime across all evaluated variables. Under dry conditions, model behavior is generally more stable, with limited variability in all variables and more consistent biases in Tsurf and Qg. These conditions correspond to a moisture-limited regime in which surface energy partitioning is more predictable. In contrast, during the dry daytime hours of rainy days, mean differences are reduced for some variables, but variability increases markedly, particularly for Qe and Qg; Tsurf shows a smaller but still evident change in spread and bias magnitude. The scatter plots (Fig. S6) further demonstrate this effect, showing broader model–observation dispersion under rainy conditions, especially for Qe, indicating less consistent model performance following rainfall events. This indicates that elevated substrate moisture and residual surface wetness likely increase the complexity of surface–atmosphere exchanges and introduce greater uncertainty in modeled fluxes and temperatures.

Separating days by net radiation shows that radiative forcing primarily scales existing model biases rather than altering their structure. Under high net radiation, biases in Qe, Tsurf and Qg are amplified, as greater available energy intensifies the expression of errors associated with each model's representation of vegetation and substrate processes, leading to more consistent error patterns. Under low net radiation, error magnitudes are reduced but become more variable, as limited energy availability constrains fluxes and increases sensitivity to day-to-day atmospheric variability. These results indicate that radiative forcing does not introduce new sources of error but instead governs how strongly underlying model assumptions are expressed.