Evaluation of a rooftop photovoltaics parameterization in the PALM model system using eddy-covariance observations

1 Introduction

The recent trend in photovoltaic (PV) deployment worldwide signifies a substantial move towards sustainable energy, supported by both technological progress and policy-driven initiatives. Global solar PV capacity reached about 2.2 TW by the end of 2024, following record annual additions of 449 GW in 2023 and 597 GW in 2024 (SolarPower Europe, 2025). In Germany, around 4.8 million grid-connected PV systems were installed and total cumulative PV capacity amounted to roughly 100 GWp by the end of 2024, illustrating the rapid expansion of PV systems in a mature market. Rooftop PV is also widely deployed: by the end of 2023, more than 1.2 million residential rooftop PV systems with battery storage were installed in Germany (Fraunhofer Institute for Solar Energy Systems ISE, 2025). On urban roofs, PV modules convert solar radiation into electricity while also changing the physical properties of the roof. They shade the roof surface and modify radiative exchange, heat storage, and heat transfer between the roof and the atmosphere. Rooftop PV can therefore influence the local thermal environment and should be considered in urban-microclimate modelling and climate-sensitive urban design (Sailor et al., 2021).

Utility-scale PV studies show that PV arrays can alter local thermal and radiative conditions in surrounding environments. Measurements at utility-scale PV plants have reported daytime warming above PV arrays and stronger sensible heat flux than over nearby reference surfaces (Barron-Gafford et al., 2016; Broadbent et al., 2019). Utility-scale PV modelling has also examined related microclimate and radiation-transfer processes. A photovoltaic-canopy representation based on UCRC-Solar was used to describe utility-scale PV arrays, with wind-speed and sensible-heat-flux parameterizations included for sunny, dry conditions; the simulations showed daytime heat-island effects, weakened local wind, increased net radiation, and reduced ground temperature (Li et al., 2024). An efficient radiation-transfer parameterization, PVRT (PV Plant Radiation Transfer), was also developed for large-scale PV plants and improved the calculation of radiation absorption by PV modules and the underlying ground surface (Zhang et al., 2025). These studies show that utility-scale PV arrays can modify local microclimate and radiation exchange, but their focus is large PV plants rather than rooftop PV systems within urban settings.

Urban rooftop observations and city-scale modelling studies have examined related PV effects in urban settings. Rooftop observations at Hong Kong indicate that air temperature above a PV roof can exceed that above a bare roof during daytime (Chen et al., 2025), while Fassbender et al. (2023) reported a maximum daytime warming of 1.35 K and nighttime cooling of −1.19 K over an urban rooftop PV system. City-scale modelling has been used to examine how widespread rooftop PV deployment may affect the urban thermal climate. A simulation for Los Angeles used an effective-albedo approach to represent the radiative and energy-conversion effects of large-scale PV deployment, predicting a small urban cooling effect of up to 0.2 °C (Taha, 2013). PV electricity production and panel-roof energy exchange were incorporated into the Town Energy Balance urban canopy model (TEB), allowing the effects of rooftop panels on the roof and the urban atmosphere to be represented. Under the tested deployment scenario, the Paris simulations indicated a reduction in summer urban air temperature during a summer heat-wave period (Masson et al., 2014). A related rooftop PV representation was subsequently embedded in WRF-BEP-BEM (the Weather Research and Forecasting model coupled with the Building Effect Parameterization and Building Energy Model), allowing city-scale responses of urban temperature and building cooling demand to be assessed. Simulations for Phoenix and Tucson suggested that rooftop PV could reduce urban temperature or cooling energy demand under the tested deployment scenarios (Salamanca et al., 2016). In WRF-BEP-BEM simulations of idealized urban configurations, rooftop PV increased daytime air temperature by up to about 1.5 °C and induced nighttime cooling of up to about 0.5 °C in the low-building configurations (Zonato et al., 2021). Similar diurnal responses, together with increasing sensible heat flux at higher PV coverage, were subsequently reported for Kolkata by Khan et al. (2024). Together, these studies show how widespread rooftop PV deployment can modify the urban energy balance and atmospheric conditions at the city scale.

Most previous urban rooftop PV modelling has been conducted with urban-canopy or mesoscale frameworks, where buildings and PV-covered roof areas are represented through grid-cell or canopy-averaged properties rather than as individual buildings with local airflow. These models are well suited to estimating city-scale responses, but they are not designed to evaluate roof-atmosphere exchange around a real building. Investigating rooftop PV impacts on the urban microclimate requires a roof-level energy-balance model and an atmospheric model that can couple roof-scale energy exchange to building geometry, local flow, and turbulent vertical heat transport. The UCRC-Solar model was introduced as a stand-alone PV surface-energy-balance model for utility-scale PV applications and was evaluated against observations of module temperature, electrical output, and sensible heat flux from a PV power plant (Heusinger et al., 2020). It was later adapted for rooftop PV applications by refining the parameterization of convective heat exchange around tilted modules, including the restricted airflow in the gap between the module and the roof (Heusinger et al., 2021). This adaptation provides a surface-energy-balance basis for representing rooftop PV systems in urban settings. PALM provides a building-resolving LES framework for urban microscale applications, resolving individual buildings, local flow adjustment, and turbulent transport while including coupled radiation and surface-energy-balance treatment (Maronga et al., 2020a). The value of this framework is that it allows roof energy exchange to interact with resolved building geometry, local flow, turbulence, radiation, and boundary-layer development. Building on the rooftop energy-balance approach of Heusinger et al. (2021), Anders et al. (2026) implemented a building-applied PV parameterization in PALM that represents the PV-roof air gap, thermal and radiative exchange, gap ventilation, PV material properties, and temperature-dependent power production.

Building-resolving LES also makes the spatial representation of rooftop PV relevant. At metre-scale resolution, a real roof is represented by multiple roof grid cells, while PV modules usually cover only part of the roof. At the same roof-average PV coverage, a model can either represent PV-covered and uncovered areas as spatially separated Mosaic surfaces or assign each grid cell a uniform fractional PV coverage using a Tile representation. Because radiative, thermal, and turbulent exchanges are nonlinear, these two approaches can produce different effective fluxes and near-surface states even when their mean surface fractions are identical (Koster and Suarez, 1992; Essery et al., 2003). Explicit representation of surface heterogeneity has been shown to affect simulated surface energy balance and near-surface conditions in land-surface models (Li et al., 2013), as well as turbulent heat fluxes in urban simulations (Hertwig et al., 2020). For PV arrays, idealized LES simulations have shown that module arrangement can modify convective cooling (Stanislawski et al., 2020). This modelling issue motivates testing how rooftop PV layout representation affects simulated roof-mean quantities.

Anders et al. (2026) implemented and evaluated the PALM rooftop PV parameterization in offline energy-balance mode, with the atmospheric prognostic equations switched off and meteorological observations prescribed as forcing. That setup allowed the PV and roof surface-energy-balance formulation to be tested directly, but it did not evaluate the parameterization within a full atmospheric LES or against turbulent flux observations. The present study therefore evaluates the parameterization in full PALM urban microscale simulations for a real rooftop PV system on an industrial roof near Dresden, Germany. In this setup, radiation, local atmospheric conditions, turbulence, and roof-atmosphere exchange evolve within the coupled LES. The model is evaluated against rooftop observations of incoming radiation, near-roof wind conditions, PV surface temperature, footprint-weighted sensible heat flux from eddy-covariance measurements, and PV power output. We further examine the sensitivity of simulated rooftop quantities to grid resolution and to the representation of rooftop PV layout. This combination extends previous work from either city-scale averaged PV impacts or offline rooftop energy-balance evaluation toward a building-resolving assessment of rooftop PV within a coupled urban atmosphere.

2 Data and methods

2.1 Rooftop PV model implemented in PALM

We use the PALM model system, an LES-based modelling framework for investigating the atmospheric boundary layer that is optimized for massively parallel computing (Maronga et al., 2020a). PALM includes specific modules for urban environments and land surfaces, including interactive land-surface and radiation schemes (Maronga et al., 2020a). PALM solves the non-hydrostatic, filtered Navier–Stokes equations under the Boussinesq approximation on a Cartesian grid. PALM has been widely applied in complex urban environments to study urban microclimates, assess heat stress (e.g., Geletič et al., 2021; Anders et al., 2025), and evaluate adaptation measures such as retrofitting (Maronga et al., 2022) or urban development projects (Anders et al., 2023).

The PV implementation in PALM is based on the surface energy balance that represents the main radiative and thermal exchange processes acting on a rooftop PV module (Anders et al., 2026). A schematic overview of the energy flows is shown in Figure 1. The model accounts for shortwave and longwave radiation interaction, convective heat exchange with both the air gap and the surrounding air, and electrical power generation. The PV module is represented as a layer with thermal properties derived from a simplified three-layer panel description (glass–cell–backing). The surface temperature of the PV module (T PV) is obtained from a prognostic energy-balance equation:

C PV d T PV dt = ( 1 − α PV ) S W ↓ + ε PV L W ↓ − ε PV L W ↑ − L W PV ↔ roof − H PV → gap − H ↑ − P out (1)

The terms in Equation 1, together with the additional energy-exchange pathways illustrated in Figure 1, are defined as follows. C PV is the total heat capacity of the PV module, α PV and ε PV denote albedo and longwave emissivity of the PV module; S W ↓ and L W ↓ are the incoming shortwave and longwave radiation; L W ↑ is the outgoing longwave radiation and L W PV ↔ roof is the net longwave exchange between the backside of the PV module and the roof; H ↑ is the upward sensible heat flux; H PV → gap and H roof → gap represent turbulent heat transfer toward the air gap from PV and roof surfaces; and P out denotes the electrical power output. H waste is the sensible heat flux transferred by ventilation from PV air gap to the ambient air (Anders et al., 2026).

Radiative fluxes were computed with PALM’s embedded radiative transfer model (RTM), which is coupled to the Rapid Radiative Transfer Model for Global Models (RRTMG; e.g., Clough et al., 2005). RTM represents three-dimensional radiative exchange between resolved urban surfaces, such as roofs, walls, ground, and building obstacles. It uses precomputed view factors and ray-tracing-based visibility between these surfaces, while direct solar radiation is treated by ray tracing along discretized solar directions and diffuse reflections between resolved surfaces are included (Krč et al., 2021).

PV conversion efficiency depends on module temperature. As a result, electrical power output varies with PV surface temperature. In the PV model implemented in PALM, efficiency is parameterized as a function of the simulated PV surface temperature (Equation 2), capturing the decrease in efficiency with increasing module temperature. The PV conversion efficiency (η) in the model is calculated as

η = η ref . max ( 0 , 1 − β ( T PV − T ref ) ) (2)

Where T PV is the modelled PV surface temperature, assumed uniform over the PV module; T ref = 25 °C is the reference temperature at standard test conditions; and η ref = 20.65% and β = 0.37% K⁻¹ are the reference conversion efficiency and temperature coefficient, respectively, taken from the manufacturer datasheet of the installed SOLARWATT Classic H1.1 module. For comparison, Heusinger et al. (2021) and Anders et al. (2026) used β = 0.5% K⁻¹. The current electrical power output is then obtained from the product of efficiency, incoming shortwave radiation, and module area.

2.2 Field campaign and evaluation-case selection

We conducted the field campaign on the roof of a large industrial facility operated by SICK AG in Ottendorf-Okrilla, approximately 15 km north of Dresden, Germany (51.18° N, 13.83° E). The roof provides an extensive, nearly unobstructed measurement area (≈ 120 m × 45 m), with PV modules covering approximately 37% of the roof surface (Figure 2). SICK AG provided electrical power production data for the PV system, enabling direct evaluation of simulated PV output.

Figure 2 summarizes the measurement setup and instrument locations. An eddy-covariance (EC) station was installed near the roof centre. Turbulent wind components, sonic temperature, CO₂, and H₂O were measured by an IRGASON instrument (Campbell Scientific Inc., Logan, UT), and all four components of net radiation were measured by an NR01 radiometer (Hukseflux Thermal Sensors BV, Delft, the Netherlands). These measurements were used to derive sensible heat flux, air temperature, humidity, three-dimensional wind components, and incoming and outgoing shortwave and longwave radiation. A scanning Doppler lidar (Halo Photonics Streamline XR; Lumibird Group, Lannion, France) was deployed adjacent to the building to provide vertical wind profiles throughout the atmospheric boundary layer during the observation period. PV surface temperatures were monitored using thermocouples attached to PV modules. The EC station and Doppler lidar were installed and started on 21 August 2024. The thermocouple used for PV surface temperature monitoring was installed during station maintenance on 10 September 2024; therefore, valid PV surface temperature observations were not available for 29 August 2024.

The study region in eastern Germany has a temperate climate influenced by both maritime air masses from western Europe and more continental conditions from eastern Europe, with warm summers and cold winters. Based on data from the nearby DWD station Dresden-Klotzsche (station 01048), approximately 8.5 km southwest of the rooftop site, monthly mean air temperature was 21.5 °C in August 2024, 16.9 °C in September 2024, and 1.1 °C in February 2025. Mean daily global shortwave radiation was 5.25, 3.36, and 1.83 kWh m⁻² day⁻¹ in August, September, and February, respectively. Monthly mean wind speed was 3.17, 4.23, and 3.88 m s⁻¹ in the three months. For the selected days, daily mean air temperature from DWD station Dresden-Klotzsche was 26.4 °C, 17.0 °C, and −0.6 °C on 29 August, 22 September, and 03 February, respectively. At the rooftop site, total daily incoming shortwave radiation was 5.94, 4.61, and 2.25 kWh m⁻², with corresponding peak irradiance reaching 761.5, 647.0, and 386.3 W m⁻². Daytime mean roof-level wind speeds were 1.04, 1.56, and 0.75 m s⁻¹, and daytime maxima remained below 3 m s⁻¹ on all three days. Thus, the August case was warm with strong solar input, the September case was cooler with reduced solar input, and the February case was cold with low incoming shortwave radiation. Supplementary Figure 1 shows that on 29 August and 03 February the study region was under broad high-pressure influence over central/eastern Europe, while on 22 September nearby frontal systems were present over western and southern Europe but did not directly affect eastern Germany. This large-scale background is consistent with the observed clear-sky, weak-wind conditions at the rooftop site.

Evaluation cases were selected to provide a constrained clear-sky, weak-wind setting for assessing the rooftop PV parameterization in PALM. Clear-sky conditions were chosen to minimize cloud-related variability in incoming radiation. Cloud formation and dissipation, together with moving cloud shadows, can produce strong local fluctuations in shortwave radiation, making it difficult to distinguish whether model-observation differences arise from the radiation input, the rooftop PV parameterization, or the representation of clouds. Weak-wind conditions are well suited for detecting the local thermal signal of rooftop PV because advection and mixing driven by the background flow are limited. Under stronger winds, enhanced turbulent mixing and advection increasingly control the near-roof energy balance, reducing the sensitivity of local microclimate conditions to PV-related energy exchange. Thus, under clear-sky, weak-wind conditions, we expect a strong contrast between the PV roof and the bare-roof reference, providing a clear signal for evaluating the rooftop PV parameterization. Fully clear-sky days were limited during the field campaign; after additionally requiring weak background winds and complete key observations for model evaluation, three case days were identified. In summary, the selected cases provide clear-sky, weak-wind evaluation conditions across late-summer and winter radiative and thermal backgrounds. Cloud variability, precipitation, and strong wind-enhanced convective cooling would introduce additional processes that require a broader evaluation that is beyond the scope of this first coupled evaluation.

2.3 Simulation setup

We performed simulations over a 2.5 × 2.5 km² domain centred on the measurement site with a horizontal grid spacing of 5 m. The vertical grid spacing was 5 m near the surface, with a vertical stretching factor of 1.08 applied from 100 m up to the model top at 2.5 km. Lateral boundary conditions were cyclic, meaning that flow leaving one lateral boundary re-enters through the opposite boundary. Each simulation started at 2100 UTC + 1 on the day preceding the case day to allow turbulence to develop, and the subsequent 24 h were used for analysis.

Simulations were initialized from observed atmospheric profiles. Wind profiles were derived from Doppler lidar measurements, while potential temperature and humidity profiles were taken from radiosonde observations at Lindenberg (52.21° N, 14.12° E), located approximately 114 km from the study site. A geostrophic wind derived from radiosonde data was prescribed for each case day as a constant background forcing; the corresponding geostrophic wind components U_g and V_g are listed in Table 1. Incoming shortwave and longwave radiation were computed by RTM and RRTMG.

Table 1. Geostrophic wind values used in the simulations for the three selected days.

To assess sensitivity to PV representation, two layout configurations were applied (Figure 3). In the Mosaic layout, PV modules follow the observed spatial distribution on the target roof (total PV coverage 37.6%), with each roof grid cell assigned a PV fraction of either 100% or 0%. In contrast, in the Tile layout, each roof grid cell is assigned a uniform PV fraction of 37%, consistent with the roof-mean observed coverage. To assess sensitivity to grid resolution, the Mosaic layout was repeated at 2 m grid spacing (with 2 m vertical spacing near the surface and stretching starting at 100 m). Unless stated otherwise, the 5 m Mosaic simulation is used as the reference configuration for model–observation evaluation, while layout and resolution sensitivities are evaluated using simulation–simulation comparisons. The coupled PALM simulations were computationally demanding. Core-hours are defined as wall-clock time multiplied by the number of CPU cores used. In the present setup, one 5 m run required approximately 28,000 core-hours, while the corresponding 2 m resolution sensitivity run required approximately 120,000 core-hours. Together with the clear-sky, weak-wind selection criteria described in Section 2.2, this computational demand led to the case-based evaluation design used here rather than an annual or all-weather simulation ensemble.

PV electrical parameters were taken from the manufacturer’s datasheet for the SOLARWATT Classic H1.1 module (375 Wp, SOLARWATT GmbH, Dresden, Germany), including reference efficiency and the temperature coefficient. The PV system is connected to a SUN2000-100KTL-M1 inverter (400 Vac; Huawei Technologies, Shenzhen, China). Module tilt was measured on site, while azimuth orientation and roof PV coverage were derived from satellite imagery. Thermal and radiative properties were prescribed based on literature values for crystalline-silicon modules (e.g., Pfreundt et al., 2019). All PV-related parameters are summarized in Table 2.

Table 2. Physical and electrical parameters of PV modules used for the simulation.

2.4 Eddy-covariance data processing

The EC system measures turbulent fluxes over an area, rather than at a single point. As the EC footprint spreads across the model domain, a direct comparison between a single point value in the simulation and the EC measurement is not appropriate. A footprint-weighted aggregation of model fluxes is therefore required.

Flux processing and footprint estimation were performed using the TK3 software package (Mauder and Foken, 2015) together with the footprint model of Kormann and Meixner (2001). TK3 applies standard eddy-covariance processing steps. Sensible heat fluxes were computed after conversion from sonic temperature to actual air temperature according to Schotanus et al. (1983), and a correction for spectral losses was applied according to Moore (1986). TK3 then estimates the source area of the measured fluxes using the analytical footprint model of Kormann and Meixner (2001). The model provides a set of contribution weights w i that describe the relative influence of each grid cell within the footprint on the observed flux. The PALM-simulated surface fluxes were aggregated using the TK3 footprint weights to obtain a footprint-weighted model flux for comparison with the EC measurements. The footprint-weighted model flux (F model) was computed using Equation 3:

F model = ∑ i = 1 N w i F i (3)

Where F i denotes the modelled surface flux in grid cell i and w i is the corresponding footprint weight derived from TK3. This procedure helps align the modelled fluxes with the effective source area of the EC observations. TK3 also provides uncertainty estimates, including random errors associated with the stochastic nature of turbulence. Sensible heat flux data were averaged over 30 min intervals.

3 Results and discussion

This section evaluates the performance of PALM simulations with the rooftop PV parameterization and examines sensitivity to resolution and PV layout configurations. Section 3.1 characterizes the simulated thermal and wind background for the three selected cases. Section 3.2 evaluates incoming radiation, Section 3.3 examines roof-level wind-speed distributions, and Section 3.4 compares PV surface temperature, power output, and footprint-weighted sensible heat flux against observations. Unless stated otherwise, results in Sections 3.1–3.4 are based on the 5 m Mosaic configuration, which is used as the reference simulation and is labelled Sim. Model performance is assessed using the coefficient of determination (R²), regression slope, mean bias (MB), and root mean square error (RMSE). Sensitivity to grid resolution is assessed in Section 3.5.1 by comparing 2 m Mosaic against the 5 m Mosaic reference. Sensitivity to PV layout is assessed in Section 3.5.2 by comparing the 5 m Tile configuration against the 5 m Mosaic reference.

3.1 Meteorological background

The three evaluation days were selected as clear-sky, weak-wind cases with contrasting radiative and thermal backgrounds (Section 2.2). Figure 4 shows vertical profiles of potential temperature (θ), wind speed (U), and wind direction over the diurnal cycle for the three simulated days. These profiles characterize the simulated thermal stratification and wind background for the rooftop PV parameterization evaluation.

The potential-temperature profiles reflect the thermal contrast between the three cases. On 29 August and 22 September, the daytime θ profiles indicate mixed-layer development, with a deeper mixed structure on 29 August and a shallower one on 22 September. This difference is consistent with the stronger solar input and warmer background on 29 August, and the reduced solar input and cooler background on 22 September. In contrast, 03 February has the lowest θ values, and the profiles change only weakly over the day, reflecting the low winter solar input and weak daytime boundary-layer development.

Wind speed profiles show clear case-to-case differences. On 29 August, the 0600 profile shows stronger variation in wind speed below 1,500 m, whereas the later profiles remain more vertically uniform. On 22 September, wind speeds vary less with height than on 29 August. The winter case (03 February) exhibits the weakest winds, with small vertical gradients and only modest differences between the selected times. Wind direction rotates with height in the lower part of the domain and tends to be more uniform aloft. In the upper part of the domain, the simulated wind direction is mainly from southerly to westerly sectors across the three cases. These upper-level wind directions are broadly consistent with the synoptic context described in Section 2.2 and Supplementary Figure 1, where the selected days were characterized by high-pressure influence over central/eastern Europe or by nearby frontal systems that did not directly affect eastern Germany. Near the surface, wind speed is lower and wind direction changes more strongly with height, indicating modification by building geometry and local roughness. These profiles describe the weak-wind, clear-sky meteorological background used to evaluate the rooftop PV parameterization.

3.2 Incoming radiation

Figure 5 presents 10-min averaged time series of incoming shortwave (SW↓) and longwave (LW↓) radiation for the 3 days, together with a regression analysis. Shortwave radiation in the model was updated every 60 s. Across all three cases, simulated and observed radiation follow the same diurnal cycle, with closely matched timing and magnitude.

For SW↓, the regression slope is 0.96 with a high coefficient of determination (R² = 0.99), indicating very strong correspondence between simulated and observed values. The overall MB and RMSE are −3.3 and 26.3 W m⁻², respectively. On 29 August, peak SW↓ reaches approximately 780 W m⁻², and the simulation shows small morning-afternoon differences, tending to be slightly higher before noon and lower after noon at comparable radiation levels, as reflected by the elongated scatter pattern in the linear regression panel of Figure 5. This asymmetry may be related to small differences between the atmospheric transmissivity represented in RRTMG/RTM and the actual atmospheric transmissivity at the site. On 22 September, peak values are lower (around 650 W m⁻²) and the simulated and observed time series overlap closely throughout the day. The February case shows lower peak radiation (around 400 W m⁻²), and the diurnal cycle is well captured despite minor deviations in late morning and afternoon.

For LW↓, the linear regression also shows strong agreement (slope 1.06, R² = 0.99). The overall MB and RMSE are −1.1 and 7.2 W m⁻², respectively. LW↓ varies within a narrower range compared to SW↓, and the temporal evolution is smooth across all days. On 29 August, the simulated LW↓ is slightly higher than the observations after sunrise. On 22 September, the simulated LW↓ is marginally lower until 1900. On 03 February, LW↓ remains near 220–240 W m⁻², with only small deviations during midday.

Together with the vertical profiles in Section 3.1, the radiation comparison indicates that the simulations provide a coherent meteorological background and realistically represent the observed diurnal evolution of incoming radiation for the three selected days.

3.3 Roof-level wind speed distribution

Figure 6 presents the vertical distribution of simulated wind speed above the roof at selected times. Boxplots represent the spatial variability across the roof, and crosses denote the EC measurement at the observation location.

In most cases, the observed wind speed lies near the lower half of the simulated distribution and is often below the simulated median. On 29 August at 0600, simulated wind speeds at the first level (2.5 m above the roof) range approximately from 0.4 to 1.4 m s⁻¹, and the observed value (about 0.9 m s⁻¹ at 1.96 m above the roof) falls within this range. The largest spatial variability on this day occurs at 1800. At that time, the observed value lies below the lower whisker of the simulated distribution, indicating higher simulated wind speeds at the observation height. On 22 September, the largest variability appears at 1200 rather than 1800. At 0600, both simulated and observed wind speeds are low (around 0.7–1.0 m s⁻¹) and closely aligned. At 1800, spatial variability is limited, and the observed value lies near the upper side of the simulated distribution. The 03 February case shows generally lower wind speeds and smaller spatial variability throughout the day. At 1200, wind speed varies little with height, remaining near 1.5 m s⁻¹ across all levels, and the observed value is close to the simulated distribution. Near the lowest model levels, PALM applies a Monin–Obukhov similarity theory (MOST) surface-layer treatment rather than resolving turbulence explicitly, and this approach can produce excessive near-surface wind shear in LES (Maronga et al., 2020b). This near-surface wind speed bias can affect the surface energy balance by modifying aerodynamic exchange and turbulent heat transfer.

Figure 7 further compares the standard deviation of vertical velocity (σ_w) at the measurement location. On 29 August, the simulated σ_w follows the observed daytime increase and reaches a similar midday magnitude, although the simulated increase begins slightly earlier and remains elevated longer in the afternoon. On 22 September, σ_w is clearly underestimated around midday, when observations reach about 0.4–0.5 m s⁻¹ but the simulation remains mostly below about 0.2 m s⁻¹. On 03 February, both observed and simulated σ_w are lower than in the late-summer cases, and the simulation captures the timing of the daytime increase but underestimates part of the midday variability. These differences indicate that the simulation reproduces the general diurnal development of roof-level turbulence, while underestimating vertical velocity fluctuations most clearly on 22 September. This turbulence bias is relevant for the SHF comparison in Section 3.4.1 because weaker vertical velocity fluctuations can reduce simulated turbulent heat exchange near the roof.

3.4 Energy balance

3.4.1 Thermal response

Figure 8 shows 30-min averaged time series of PV surface temperature and upward sensible heat flux (SHF) for the three simulated days. SHF is evaluated using the footprint-weighted model equivalent of the EC observations. Overall, PALM captures the diurnal evolution of both surface temperature and SHF, while systematic amplitude differences remain.

The linear regression of surface temperature shows a strong linear relationship with observations (R² = 0.98; Figure 8, bottom left). The regression slope of 0.79 indicates a reduced amplitude in the simulation, with clear overestimation at lower temperatures (below ~10 °C) and clear underestimation at temperatures higher than 30 °C. The MB and RMSE are 1.4 and 4.1 °C, respectively. Separating the data by time of day shows a slight daytime underestimation and a nighttime overestimation, with similar deviation magnitudes in both periods (Table 3). The timing of the daytime temperature increase is well reproduced, particularly during the morning transition (0600–0800 on 22 September and 0830–1,000 on 03 February). On 22 September, observed PV surface temperature rises rapidly and reaches a maximum of approximately 40 °C, whereas the simulation peaks near 35 °C, resulting in a notable negative bias at noon. In contrast, on 03 February, both timing and magnitude (peak around 18 °C) are reproduced more closely.

Table 3. Mean bias (MB; simulation minus observation) and root mean square error (RMSE) for PV surface temperature and sensible heat flux.

Daytime is defined as 0800–1800.

For SHF, the linear regression shows substantial agreement (R² = 0.86), with a slope of 0.79 (Figure 8, bottom right). The MB and RMSE are −22.0 and 36.5 W m⁻², respectively. Separating the data by time of day shows underestimation in both periods, with stronger daytime underestimation and larger deviations (Table 3). Observed midday maxima reach approximately 230 W m⁻² on 29 August, 210 W m⁻² on 22 September, and 100 W m⁻² on 03 February. The simulations reproduce the timing of the daytime rise and decline across all cases. On 29 August, the simulation approaches the observed midday peak, while the No-PV simulation remains substantially lower throughout the daytime period. On 22 September, the midday peak is clearly underestimated, although agreement is closer during the morning transition. On 03 February, the simulated peak remains below the observed maximum.

The No-PV simulation provides a model reference for assessing how rooftop PV modifies the simulated roof-atmosphere exchange. In the PV case, surface temperature refers to the PV module surface, whereas in the No-PV case it refers to the bare roof surface. Across all three cases, the PV surface warms more rapidly after sunrise and remains warmer than the bare roof through most of the daytime hours. The largest temperature difference between the PV and No-PV cases is about 17 °C on 29 August and 22 September, and about 20 °C on 03 February. This difference is largest from morning to around midday and then decreases during the afternoon as both surfaces cool.

A similar daytime contrast is found for footprint-weighted SHF. During the main heating period, the No-PV reference produces much weaker upward heat flux than observed. Its daytime SHF peaks reach only about 108, 41, and near 0 W m⁻² on 29 August, 22 September, and 03 February, respectively, whereas the observed peaks reach about 228, 204, and 103 W m⁻². When the rooftop PV representation is included, the simulated SHF moves much closer to the observed magnitude, with daytime peaks of about 230, 160, and 81 W m⁻² on the 3 days. This contrast shows that the PALM rooftop PV parameterization captures a substantial daytime enhancement of roof-atmosphere heat exchange that is absent in the bare-roof reference. The magnitude of this effect in our simulations indicates that PV-related enhancement of roof-atmosphere heat exchange can be substantial under clear-sky, weak-wind conditions, when local thermal contrasts are less strongly masked by cloud variability or advective mixing.

Figure 7 shows that differences in σ_w between observations and simulations are much smaller at night, when vertical velocity fluctuations remain weak, than during daytime convective periods. Since SHF is directly linked to turbulent vertical exchange, this pattern is consistent with the stronger daytime SHF underestimation and larger daytime deviations shown in Table 3. The clearest SHF discrepancy occurs on 22 September, when σ_w is underestimated around midday (Figure 7), indicating weaker vertical velocity fluctuations at the measurement location. This reduced turbulent activity can directly limit the simulated upward heat flux. On 22 September, the simulated PV surface is also cooler than observed around midday, which further reduces the roof-air temperature contrast that drives sensible heat exchange. Together, these factors suggest that the SHF underestimation on 22 September reflects a combination of insufficient vertical turbulent transport and reduced simulated surface heating. Other contributing factors may include differences in near-roof stability, local representativeness, and uncertainties in surface forcing and roughness relevant for rooftop turbulence. Model-structure limitations may also contribute; for example, the rooftop adaptation of UCRC-Solar by Heusinger et al. (2021) assumes boundary-layer development from the roof edge and uses a distance to the roof edge to modulate convective heat exchange, which is not explicitly represented in the present setup.

The daytime PV surface temperature statistics indicate a slight underestimation, with the clearest case occurring around midday on 22 September. Around this time, the simulated roof-level wind speed is higher than the observed value (Section 3.3), which may strengthen aerodynamic cooling of the PV surface and contribute to the underestimated surface temperature. In contrast, simulated and observed wind speeds are closer on 03 February, and surface temperature agreement is correspondingly improved. Similar sensitivity of PV surface temperature to meteorological forcing has also been reported in mesoscale rooftop PV simulations (Yin et al., 2025).

The nighttime statistics indicate an overestimation of PV surface temperature. This nighttime bias is most evident during the winter case. On 03 February, observed PV surface temperature remains below 0 °C until about 1,000, while nearby DWD Dresden-Klotzsche weather observations also showed freezing and humid morning conditions, with air temperature ranging from −4.7 to −0.7 °C and relative humidity reaching 93%. These conditions suggest that frost was likely present on the modules during the morning, which is not explicitly represented in the model. Such conditions may contribute to the overestimation of surface temperatures during nighttime, but they cannot be verified directly because no site photographs or module surface-condition records are available.

3.4.2 PV power production

Figure 9 shows 30-min averaged time series of PV power output for the three case days and a linear regression between simulated and observed values. Overall, the simulation follows the observed diurnal evolution well, capturing the onset and the timing of the daytime peak.

On 29 August 2024, the simulation closely tracks the observed evolution throughout the day. As shown in Table 4, the observed peak power is 277.7 kW, compared with 304.1 kW in the simulation, and the daily integrated energy is 2112.6 kWh versus 2413.8 kWh. On 22 September 2024, power production is lower than in late August, but the diurnal pattern remains similar. The observed peak is 243.7 kW, while the simulation reaches 279.6 kW; daily integrated energy is correspondingly lower than on 29 August. On 03 February 2025, the simulation still captures the onset and peak timing, but the magnitude bias is largest: the observed peak is 150.0 kW, whereas the simulation reaches 205.1 kW. Overall, the simulated PV power output exceeds the recorded production across all three days, with the largest discrepancy in winter. The linear regression indicates high correspondence (R² = 0.98), while the regression slope of 1.15 indicates that the amplitude of simulated power output is overestimated. The MB and RMSE are 14.0 and 23.7 kW, respectively.

Table 4. Summary metrics for observed and simulated PV power output for the three evaluation days.

Peak time refers to the time of maximum power output.

All three cases show a positive power bias, whereas incoming shortwave radiation is generally well reproduced (Section 3.2). This indicates that the positive bias is linked to the conversion from incoming radiation to electrical power, rather than to the incoming radiation itself. The simulated power production is simplified: electrical output is estimated from incoming shortwave radiation, module area, and temperature-dependent conversion efficiency. In contrast, the observed PV power represents recorded AC system output and therefore includes system-level and operational losses that are simplified or not explicitly represented in PALM. These include inverter DC/AC conversion losses, partial shading, operational constraints, and other system-level effects. For example, inverter DC/AC conversion losses occur when direct-current power generated by the modules is converted to alternating-current power recorded by the system. For the SICK rooftop system, the PV*SOL yield prediction identifies annual losses of 1.9% from inverter conversion (Supplementary Table 1). These simplified or omitted system-level effects are the most likely explanation for the persistent positive power bias, especially during periods when incoming radiation and PV surface temperature are well reproduced.

Additional losses are more dependent on solar angle and irradiance level. Incidence-angle losses occur when solar radiation reaches the module at an oblique angle and a larger fraction is reflected at the module surface instead of entering the cells. Low-irradiance performance losses refer to reduced module or system efficiency under low-light conditions, especially during early or late daylight periods. These mechanisms are commonly reported in PV performance studies and yield simulations (Mavromatakis et al., 2017; Ríos-Ledesma et al., 2026). For the SICK rooftop system, the PV*SOL yield prediction identifies annual losses of 3.75% from module-surface reflection and 2.35% from low-light performance (Supplementary Table 1). These loss terms can explain part of the positive bias, especially during early or late daylight periods.

The remaining bias differs among the three cases. For 29 August, PV surface temperature observations are unavailable, which limits attribution of the power bias. For 22 September, the underestimated daytime PV surface temperature (Section 3.4.1) may increase simulated conversion efficiency and contribute to the overestimated power output; this effect is most relevant around midday, when the temperature difference between simulation and observation is largest.

For 03 February, the power bias is largest despite good agreement in both incoming radiation and PV surface temperature, suggesting that additional system-level or winter surface-condition effects may be involved. Winter surface conditions may provide an additional morning contribution: as discussed in Section 3.4.1, freezing and humid conditions suggest that frost was likely present on the modules during the morning. Frost could block or reflect part of the incoming radiation and reduce measured winter power production during early daylight hours. However, because the positive power bias persists into noon and afternoon, frost cannot fully explain the 03 February overestimation. This explanation cannot be verified directly because no site photographs or module surface-condition records are available for 03 February. Other surface-condition effects, such as partial soiling, meaning spatially uneven dust or dirt deposits on the module surface, could also reduce measured power by lowering transmitted radiation.

3.5 Sensitivity analysis

3.5.1 Resolution sensitivity

Figure 10 compares the 2 m and 5 m simulations to assess the sensitivity of roof surface results to grid resolution. Differences are evaluated for PV surface temperature, SHF, and PV power output using daytime samples (0800–1800), excluding nighttime and near-sunrise/sunset periods. Across all three case days, the 2 m simulation shows a similar thermal response and energy production as the 5 m simulation, with only small differences relative to the overall diurnal variability.

For PV surface temperature, the 2 m and 5 m results are nearly identical (Figure 10, bottom left), with a regression slope close to 1 and R² close to 1. Consistent with this, the PV surface temperature difference distributions (Figure 10, top left) are tightly clustered around zero for all days (Table 5), indicating only a slight tendency for lower surface temperatures at 2 m.

Table 5. Daytime (0800–1800) median values of resolution-induced differences (2 m − 5 m) for surface temperature, sensible heat flux (SHF), and PV power output.

For SHF, the regression between 2 m and 5 m remains strong (R² = 0.93; Figure 10, bottom middle). The SHF difference distributions show the largest day-to-day variability among the three variables. On 29 August, SHF difference spans the widest range (approximately −35 to 28 W m⁻²), with a slightly negative median (−8.5 W m⁻²; Table 5). On 22 September, differences are smaller (roughly −5 to 15 W m⁻²) and the median is positive. On 03 February, SHF difference is narrowly distributed (about −10 to 5 W m⁻²) with a relatively small negative median (−2.0 W m⁻²). Overall, SHF differences are modest but less uniform than for surface temperature.

For PV power output, the 2 m and 5 m simulations are closely linearly related (R² = 0.99; Figure 10, bottom right). The PV power output difference distributions indicate small differences, with the largest spread on 29 August and smaller spreads on the other 2 days. Median differences are on the order of a few kilowatts, indicating that grid refinement from 5 m to 2 m has only a minor impact on daytime power production in these cases.

Overall, this resolution sensitivity test suggests that reducing grid spacing from 5 m to 2 m does not materially change the simulated daytime surface temperature and PV power output, and mostly affects SHF. For the metrics examined here, the 5 m resolution provides results comparable to the 2 m simulation while reducing computational cost.

3.5.2 Layout sensitivity

The layout sensitivity analysis examines how the representation of rooftop PV coverage affects thermal response, sensible heat exchange, and PV power production of the whole roof. For this purpose, Mosaic and Tile are compared using roof-mean quantities, so that both layouts are evaluated over the same roof area and with nearly identical roof-average PV coverage. Mosaic is used as the site-specific reference layout because it preserves the observed spatial arrangement of PV-covered and uncovered roof areas. Tile represents a simplified configuration in which the same roof-average PV coverage is applied uniformly to all roof grid cells. Figure 11 presents the Mosaic and Tile layout results for roof-mean surface temperature, SHF and PV power output.

To focus on periods when layout differences are most relevant for fluxes and production, the analysis is restricted to daytime hours (0800–1800), excluding nighttime and near-sunrise/sunset periods.

Roof-mean surface temperature shows close correspondence between the two layouts (Figure 11, left column). The Tile–Mosaic regression is close to the 1:1 line (slope 0.97, intercept 0.14 °C, R² = 0.99), indicating that both layouts capture similar temporal evolution. The daytime Tile-Mosaic differences remain relatively narrow, with the largest absolute difference below 2 °C on 22 September compared with a daytime roof-mean surface-temperature range above 30 °C (Table 6). This suggests that Tile can provide a useful approximation when the analysis focuses on roof-mean surface temperature and detailed PV layout information is unavailable.

Table 6. Daytime (0800–1800) median, minimum and maximum values of layout differences (Tile − Mosaic) for roof-mean surface temperature, sensible heat flux (SHF), and PV power output.

Sensible heat flux is more sensitive to layout representation than roof-mean surface temperature. Median SHF differences are modest compared with the full daytime SHF range, but the 30-min Tile-Mosaic differences vary much more strongly than the surface-temperature differences. For example, on 29 August, the largest absolute Tile-Mosaic SHF difference reaches about 77 W m⁻², corresponding to roughly one third of the daytime SHF range. The Tile-Mosaic regression (Figure 11, bottom middle) has a slope of 0.90 and a small negative intercept (−5.4 W m⁻²). These results indicate that Tile may still be informative for median SHF, but it is less reliable when the analysis depends on 30-min SHF variability.

For PV power output, Tile yields systematically higher values than Mosaic. The regression remains close to linear (slope 1.04, intercept 3.96 kW, R² = 0.99), but the daytime Tile-Mosaic differences are mostly positive across the three cases (Table 6). Median Tile-Mosaic power differences range from about 9 to 15 kW, indicating that the homogenized Tile representation introduces a positive offset in the simulated electrical conversion term of the rooftop energy balance, even though the two layouts have nearly identical roof-mean PV coverage.

The Mosaic layout also preserves explicit contrasts between PV-covered and uncovered roof cells. During 0800–1800, PV-covered cells in Mosaic are on average 3.1–8.1 °C warmer than uncovered roof cells and produce 32–53 W m⁻² higher SHF. In the Tile layout, these contrasts are nearly removed, with temperature differences close to 0 °C and SHF differences mostly within about 0–2 W m⁻², because the same roof-mean PV fraction is assigned to all roof grid cells. This confirms that Mosaic retains local contrasts that are smoothed by Tile.

Overall, the layout comparison helps identify where the Tile configuration is useful and where the Mosaic representation is preferable. Tile can be useful when only roof-mean PV coverage is available and the analysis focuses on roof-mean surface temperature. For SHF, Tile may still be informative for median values, but Mosaic is preferable when realistic layout data are available and the analysis focuses on 30-min SHF variability. For PV power output, Tile should be used with caution because it produces a systematic positive offset relative to Mosaic. The stronger sensitivity of SHF is physically plausible because Mosaic preserves spatial contrasts between PV-covered and uncovered roof fractions, whereas Tile distributes the same roof-mean PV fraction uniformly across roof grid cells. By smoothing these local surface contrasts, Tile can change the near-surface gradients that control turbulent heat exchange. Dedicated spatial diagnostics of the surface energy budget and near-roof turbulence would be useful for further isolating the mechanisms behind these differences.

4 Limitations and future work

Several limitations should be considered when interpreting the results of this evaluation. The selected cases define a clear-sky, weak-wind evaluation regime rather than an all-weather sample. These conditions were chosen to reduce cloud-related radiative variability and strong advective mixing, allowing the rooftop PV parameterization to be evaluated in PALM under relatively constrained conditions relevant to rooftop PV thermal effects. The results therefore support the behavior of the parameterization within this selected regime. Future evaluations should extend this assessment to cloudy, rainy, windy, and highly unstable conditions.

The missing 29 August surface temperature record highlights the need for more robust rooftop thermal measurements. Because the thermocouple used for PV temperature monitoring was installed after that case day, the warmest and highest-radiation case lacks direct surface-temperature evaluation. Future rooftop PV campaigns should include redundant module-temperature sensors, early sensor deployment before the first evaluation period, and routine data-quality checks to ensure continuous thermal records under high-radiation conditions.

Model-observation comparability is affected by meteorological forcing and footprint uncertainty. The simulations were initialized from observed atmospheric profiles but were not continuously constrained by mesoscale forcing during the day. As a result, simulated temperature and wind profiles may drift from the observed evolution, and part of the model-observation mismatch may reflect background meteorological forcing rather than the rooftop PV parameterization itself. Although footprint weighting provides a practical model equivalent to the EC observations, the effective source area can vary with wind direction, stability, roughness, and measurement height. Future work should combine stronger mesoscale forcing constraints with more detailed wind-direction- and stability-dependent footprint evaluation.

Model simplifications affect the interpretation of the power-output results. Several optical and thermal PV-module parameters, including albedo, emissivity, and heat capacity, were taken from literature values rather than measured directly. System-level loss processes are also simplified or not explicitly represented in the PALM power calculation. Inverter conversion losses, partial shading, operational constraints, and other system-level effects may contribute to the positive power bias in all three cases. Incidence-angle and low-irradiance losses may also contribute, especially in winter, but they are most pronounced under oblique or low-light conditions and are unlikely to fully explain the large midday discrepancy on 03 February by themselves. Surface-condition effects may also contribute to the power-output bias. Partial soiling could reduce transmitted radiation under any of the selected cases. For the winter case, frost formation is meteorologically plausible because both the PV surface-temperature observations and the nearby DWD weather data indicate freezing, humid morning conditions. However, no direct module surface-condition records, site photographs, or maintenance records are available to verify whether frost or soiling affected the modules on 03 February. Future winter campaigns should include PV-module surface-condition checks, site photographs, maintenance records, and, where possible, module- or inverter-level diagnostics to separate meteorological, surface-condition, and system-operation effects.

The Tile-Mosaic comparison provides application-oriented guidance for layout representation, but the processes behind the differences require further analysis. The stronger SHF sensitivity is physically plausible because Mosaic preserves local contrasts between PV-covered and uncovered roof fractions, whereas Tile smooths these contrasts across roof grid cells. A fuller explanation would require spatial diagnostics of surface-energy-budget components, PV-covered and uncovered roof patches, local roof-air gradients, and near-roof turbulence statistics. Such diagnostics would be valuable in future studies focused on rooftop PV layout effects.

5 Conclusion

This study evaluated a recently implemented rooftop PV parameterization in PALM for building-resolving urban microclimate applications using rooftop observations from a PV system near Dresden, Germany. Simulations were conducted for three clear-sky, weak-wind cases from late summer to winter and were evaluated against incoming radiation, available PV surface temperature observations, footprint-weighted sensible heat flux, and recorded PV power output.

Within the selected clear-sky, weak-wind cases, the simulations reproduced the observed incoming shortwave and longwave radiation well. The simulations captured the diurnal timing of PV surface warming and cooling and the daytime evolution of sensible heat flux and PV power output. PV surface temperature shows a strong linear relationship (R² = 0.98), although the simulated amplitude is reduced (slope = 0.79), with daytime underestimation and nighttime overestimation. The corresponding MB and RMSE are 1.4 and 4.1 °C, respectively. The simulated sensible heat flux shows substantial agreement with observations (R² = 0.86), but the simulated flux amplitude is reduced (slope = 0.79), and the MB of −22.0 W m⁻² indicates an overall underestimation, with an RMSE of 36.5 W m⁻². The simulated PV power output reproduces the observed diurnal shape and peak timing (R² = 0.98). However, the amplitude of simulated power output is overestimated (slope = 1.15), and the MB of 14.0 kW shows an overall positive bias, with an RMSE of 23.7 kW. The No-PV comparison further shows that, under the selected conditions, rooftop PV produces stronger daytime surface heating and roof-atmosphere heat exchange compared with the No-PV case.

The sensitivity experiments clarify how resolution and PV layout representation affect the simulated rooftop quantities. Refining grid spacing from 5 m to 2 m produced nearly identical daytime surface temperature and PV power output and only modest changes in sensible heat flux. However, the comparison between Mosaic and Tile showed stronger dependence on layout representation. Tile can be useful when only roof-mean PV coverage is available and the analysis focuses on roof-mean surface temperature. For sensible heat flux, Tile may still be informative for median values, but Mosaic is preferable when realistic layout data are available and the analysis focuses on the SHF time series. For PV power output, Tile should be used with caution because it produces a systematic positive offset compared with Mosaic.

Overall, the results of this evaluation suggest that the PALM rooftop PV parameterization can reproduce the main diurnal behavior of rooftop PV thermal response and roof-atmosphere exchange under clear-sky and weak-wind conditions, while remaining biases in sensible heat flux and PV power output require further evaluation. A key value of the parameterization is that it links rooftop PV energy exchange with resolved building geometry, local flow, turbulence, radiation, and urban-boundary-layer development within building-resolving urban microclimate simulations. To our knowledge, this is the first evaluation of the PALM rooftop PV parameterization for a rooftop PV system using rooftop observations of radiation, PV surface temperature, eddy-covariance fluxes, and power output. In this evaluation, the parameterization is embedded in PALM, so that radiation, local atmospheric conditions, roof-atmosphere exchange, and PV response are calculated interactively rather than prescribed separately. The combined evaluation provides an observation-constrained basis for future applications of the PALM rooftop PV parameterization across broader meteorological conditions and more complex urban settings.

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Supplementary material

The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/frsc.2026.1866648/full#supplementary-material

Large-scale weather maps over Europe for the three selected evaluation days. The charts show sea-level pressure patterns and frontal systems. Source: WetterKonto, www.wetterkontor.de. Supplementary material at the source

Supplementary material Supplementary material at the source

Footnotes

Edited by: Hamed H. Saber, Royal Commission for Jubail and Yanbu, Saudi Arabia

Reviewed by: Liwei Yang, Chinese Academy of Sciences (CAS), China

Chongxing Fan, Princeton University, United States