Including radiative transfer processes within the urban canopy layer into microscale urban climate models (UCMs) is essential to obtain realistic model results. These processes include the interaction of buildings and vegetation with shortwave and longwave radiation, thermal emission, and radiation reflections. They contribute differently to the radiation budget of urban surfaces. Each process requires different computational resources and physical data for the urban elements. This study investigates how much detail modellers should include to parameterize radiative transfer in microscale building-resolving UCMs. To that end, we introduce a stepwise parameterization method to the Parallelized Large-eddy Simulation Model (PALM) system 6.0 to quantify individually the effects of the main radiative transfer processes on the radiation budget and on the flow field. We quantify numerical simulations of both simple and realistic urban configurations to identify the major and the minor effects of radiative transfer processes on the radiation budget. The study shows that processes such as surface and vegetation interaction with shortwave and longwave radiation will have major effects, while a process such as multiple reflections will have minor effects. The study also shows that radiative transfer processes within the canopy layer implicitly affect the incoming radiation since the radiative transfer model is coupled to the radiation model. The flow field changes considerably in response to the radiative transfer processes included in the model. The study identified those processes which are essentially needed to assure acceptable quality of the flow field. These processes are receiving radiation from atmosphere based on the sky-view factors, interaction of urban vegetation with radiation, radiative transfer among urban surfaces, and considering at least single reflection of radiation. Omitting any of these processes may lead to high uncertainties in the model results.
Urban climate models (UCMs) are useful tools to study the interaction between the urban environment and the atmosphere. They are broadly classified into two categories: the urban canopy-layer models and the urban boundary-layer models. The first category focuses on the microscale variations occurring below the canopy height
Modelling the radiative transfer processes (RTPs) within the urban domain is a key component in any UCM. It provides the surface radiation budget that is required for solving the surface energy balance. Indeed, an accurate prediction of surface radiation budget is fundamental to realistically model boundary-layer processes as it strongly affects turbulent surface heat fluxes (sensible and latent)
For these reasons, it is excessively difficult to consider all the RTPs in UCM. Therefore, there exists a range of radiative transfer models (RTMs) of varying sophistication in the UCMs ranging from neglecting altogether the RTPs to parameterize most of the important RTPs in the canopy-height. However, there is little knowledge on how these models compare across a range of urban geometries and material properties encountered in an urban area. This knowledge is needed to estimate when these models are valid and how large the errors resulting from neglecting some of the RTPs in such models.
Many studies focused on the general effect of including solar radiation on the simulation of the flow field and pollutant dispersion in urban areas
The main aim of this study is to investigate how much detail we should include to reasonably parameterize the radiative transfer in microscale building-resolving UCMs within the available computational resources. We introduce a generic method to individually evaluate the processes involved in the radiative transfer by isolating its effect on the surface radiative budget as well as the flow patterns. The comparison of the individual effects of each process allows an assessment of the applicability of the approximations applied in the UCMs. We focus on the major RTPs, such as the solid surface interaction with the incoming shortwave and longwave radiation, vegetation interaction with shortwave and longwave radiation, thermal emission of solid surfaces and vegetation, radiation reflection, and the interaction of vegetation with the reflected radiation. Those major RTPs exist in the commonly used UCMs. It is worth here mentioning that this study does not engage with validating the RTM of the Parallelized Large-eddy Simulation Model (PALM) against observations, which is the scope of other studies
The paper is organized as follows: in Sect.
The urban climate model adopted to this study is the PALM 6.0 model system. This model system is developed to be a modern and highly efficient model allowing for simulations over large domains (neighbourhood and city scale) with building-resolving spatial resolution
The PALM model system solves the three-dimensional, non-hydrostatic, filtered, incompressible Navier–Stokes equations of wind (
The PALM model system includes all the modules required for simulating most of the atmospheric processes in complex urban areas
The model exhibits excellent scalability on massively parallel computer architectures
The RTM within PALM 6.0 system models the major shortwave (SW) and longwave (LW) radiative processes inside the UCL
Another important process modelled by the RTM is the exchange of SW and LW irradiance by reflections, in the presence of vegetation. To enable this, RTM calculates mutual surface view factors (VFs). For computational reasons, however, the model uses a finite number of reflections
In all these processes, the absorption, scattering, and thermal emission by air mass are neglected. Consequently, the model application in some weather situations such as fog, heavy precipitation, or dense smog is limited at the moment.
The RTM processes are briefly described in Sect.
In order to perform this study, the PALM 6.0 model is edited to implement the stepwise parameterization method described in Sect.
The Rapid Radiative Transfer Model for Global models (RRTMG;
The RRTMG–RTM coupling is an important feature of PALM. In Sect.
A bottom-up approach is used to put together the compositional sub-RTPs to give rise to the more complex RTM. In other words, a specific RTP is selected and integrated into the previous RTM to form the next RTM. Thus, the effect of adding this particular process to the RTM can be isolated and quantified. In this way, a series of RTMs with different sophistication emerged in a stepwise manner, starting from a simple RTM to the full RTM (Table
Composition of radiative transfer processes (RTPs) for each radiative transfer model (RTM) used in the stepwise parameterization method (SPM).
Radiation is ignored altogether in this parameterization step so that there are no RTPs within the urban domain. This resembles the simulation of the neutral atmospheric boundary layer. Although radiation is ignored in this parameterization step, it is used here as a baseline for comparing the different RTPs.
All surfaces receive equal incoming radiation (SW and LW) from the radiation model without any interference with obstacles (buildings or trees). The value of the received radiation,
This means that both SVFs and VFs are not needed here. Although this simplification reduces the memory and the CPU time requirements considerably (see Sect.
In this parameterization step, the RTM calculates the SVF of each grid-box face, to account for diffuse radiation, as well as shape factors to determine if, for a specific point in time, a face is exposed to direct sunlight. This will have a major influence on the surface-received SW and LW fluxes for two reasons. First the model can predict the shadow due to buildings, and second the model can prescribe proper SW flux from the Sun and LW flux from the atmosphere to the vertical surfaces. The incoming SW and LW fluxes are improved, compared to the simple RTM; however, they result in an increase in the runtime as well as the memory requirements to calculate SVFs. This RTM does not include the effect of trees on the radiative transfer.
Resolved vegetation (urban trees) is represented in the model as a porous media by its leaf area density (LAD). In this RTM, each grid box with a non-vanishing LAD, i.e. urban vegetation canopy box, absorbs part of the SW radiant flux passing through it, according to its transmittance (the factor that defines how much incoming radiation is passing through). The transmittance,
In this step, RTM allows all surfaces to receive LW radiation not only from the atmosphere but also from the outgoing LW radiation emitted from other building surfaces. According to the Stefan–Boltzmann law, a surface of a skin temperature
The interaction of vegetation with LW irradiance includes mainly two processes: thermal radiative emission from vegetation towards the urban surfaces and the sky and the absorption of LW radiation within the vegetation. Minor processes such as mutual LW radiative transfer and reflections within vegetation itself are neglected to save computations. Such an approximation is reasonable since vegetation in urban area usually has low reflectivity (high emissivity) in the longwave spectrum and similar surface temperature. The received irradiance of a surface
The extra geometrical factors required for this parameterization step, i.e. VF and CSF, are derived from the geometrical factors calculated for the previous parameterization steps. Detailed derivations for vegetation view and sink factors are given in
Urban surfaces in this parameterization step may receive reflected LW and SW irradiance in addition to the received irradiance from the main sources described above. Here, we enable only one iteration of reflection of LW and SW irradiance. This process is particularly important for the surfaces located in shadows because it is their source of SW irradiance along with the incoming diffuse SW radiation from sky. Also it enhances receiving LW irradiance along with receiving LW radiation from thermal emissions of other surfaces. The view factors needed for this step are already calculated (Sect.
In this parameterization step, vegetation partially absorbs the reflected SW and LW radiation from all the surfaces where vegetation boxes exist between the target and the source surfaces. The absorbed radiation is directly released to the atmosphere since vegetation is assumed to have zero heat capacity. The irradiance absorbed by vegetation is calculated using CSF, similar to Sect.
Four iterative reflections of LW and SW irradiance are applied in this RTM. The number of reflection iterations is chosen so that the absorbed radiation at the last reflection step is small enough so that any further reflections can be ignored
This RTM represents the RTM version 3.0, which is used in PALM 6.0 model system. Since it contains all the RTPs covered in this study, we use it as a comparison RTM.
Two study cases are employed in this study. The first case has a rather simple geometry, while the second one has a realistic urban configuration. The test cases are designed to this study so that the changes due to each SPM step are explained first on a simple configuration and then demonstrated on a realistic case.
Uniformly distributed buildings of cubic shapes are considered to represent a simple urban configuration with 16 buildings. However, imposing cyclic boundary conditions at the domain sides implicitly indicates unlimited domain. All buildings have the same size (building height
All trees in the domain (24 trees in total) are identical in size and foliage density. They are uniformly distributed in the domain so that a tree is centred between two buildings. The following empirical equation, suggested by
Illustration of the simple urban configuration showing the simulation and the focus domain. The trees (shown in green) are centred between buildings.
Tree height,
A domain extending
An aerial view of the realistic urban configuration showing the 3-D buildings (fitted to the grid) and the plant canopy boxes (trees, shown in green points). The configuration is centred around Ernst-Reuter-Platz in Charlottenburg in Berlin (52
In order to quantify the quality of each UCM, we introduce quantification measures that compare the model results of each step with the step before or with RTM_08, which contains all the RTPs considered in RTM version 3.0
The individual RTPs are quantified by calculating the change of a relevant radiation flux,
For each SPM step, the change in the flow properties is evaluated using a relative error measure of a flow property magnitude (wind speed and air potential temperature) between the model results of this step and those based on RTM_08. A vector of relative error values is determined for all grid points located in the focus domain. The normalized root-mean-square error,
The normalized volumetric flow rate,
These two measures, i.e.
The full 3-D simulations for all cases begin at 00:00 local solar time (LST) on 30 June and lasted for 2 d. No cloud formation is applied for all cases to ensure clear-sky conditions. Before the 3-D simulation, a precursor simulation for 1 d using the PALM spin-up mechanism was done for each case. This is done to properly initialize the surface temperature of all surfaces and to reduce the computational load. Further details on the spin-up mechanism in PALM is given in
Before proceeding to examine the effect of each RTP on the surface radiation budget, we discuss the incoming SW and LW radiation fluxes from the RRTMG radiation model at the top of the UCL (Fig.
The daily course of incoming
In the next sections, we compare the surface radiation fluxes within the focus domain of both the simple and the realistic urban domains when applying the SPM procedures. We focus mainly on the incident SW and LW irradiance because they explicitly show the behaviour of RTM associated to each SPM step.
Beside the violin plots, we occasionally show examples of the spatial distribution of the changes in some relevant radiation flux components for the surfaces. The walls, the roof, and the pavements of the simple urban configuration are folded in a 2-D plot, showing the radiation flux changes in all the surfaces. The surface fluxes shown on these plots are based on the surface fluxes at 14:00 LST (instantaneous flux for SW radiation and hourly averaged flux for LW radiation). At this time, the surfaces are exposed to direct solar radiation and all surfaces are heated.
The figures are based on the surfaces located only in the focus domain to eliminate boundary effects. The number of surfaces in the focus domain of the simple configuration is 3200 surfaces (1600 vertical and 1600 horizontal surfaces of 1 m
The incident SW and LW irradiance for the surfaces in the focus domain are compared to those of the no-radiation-interaction case (RTM_00) (Fig.
Changes in the received SW and LW irradiance within the focus domain of the simple urban configuration when applying the simple RTM (RTM_01) compared to the neutral case (RTM_00). Since all surfaces receive the same radiation in the simple RTM, the violin plots appear as concentrated points. The mean values are shown by a dashed black line and the median values are shown by black circles.
The calculated SVFs and Sun visibility enable the model to more realistically predict the incoming direct and diffuse SW radiation flux from the Sun on both horizontal and vertical surfaces, giving rise to building shadows. Also, the SVFs adjust the received LW flux for the horizontal surfaces and add the corrected value to the vertical surfaces. In Fig.
Changes in the received SW and LW irradiance within the focus domain of the simple urban configuration when considering the surface sky-view factors (RTM_02) compared to the RTM_01. The roof, the wall, and the ground surfaces are shown in the violin plots in orange, blue, and green, respectively. Similar to Fig.
Large changes in the SW radiation flux (
Changes in the received LW radiation flux within the focus domain of the simple urban configuration when considering the surface sky-view factors (RTM_02) compared to the RTM_01. Walls (left plot), pavements (in the centre of the right plot), and roofs (rectangles on all four sides in the right plot) are folded. See the details of the focus domain of the simple urban configuration in Fig.
The increased LW radiation flux (up to
The changes in the received SW and LW irradiance due to considering the vegetation interaction with the incoming SW radiation flux are shown in Fig.
Changes in the received SW irradiance within the focus domain of the simple urban configuration when considering vegetation interaction with SW solar radiation (RTM_03) compared to the RTM_02. Violin, mean, and median colours are used in the same way as those in Fig.
Changes in the received diffuse SW radiation flux within the focus domain of the simple urban configuration when considering vegetation interaction with SW solar radiation (RTM_03) compared to the RTM_02. Walls, roofs, and pavements are folded the same way as those in Fig.
Although this parameterization does not allow direct interaction of vegetation with LW radiation, slight changes in the incoming LW irradiance, compared to the previous step, are noticed. This is attributed to the changes in the incoming LW radiation from the radiation model (RRTMG) due to the RRTMG–RTM coupling, Fig.
The changes in the received LW irradiance shown in Fig.
Changes in the received LW irradiance within the focus domain of the simple urban configuration when considering surface thermal emissions (RTM_04) compared to the RTM_03. Violin, mean, and median colours are used in the same way as those in Fig.
Changes in the received diffuse LW radiation flux within the focus domain of the simple urban configuration when considering surface thermal emissions (RTM_04) compared to the RTM_03. Walls, roofs, and pavements are folded the same way as those in Fig.
The SW radiation parameterization is not changed; hence, negligible changes less than
The considered process in RTM_04 has also an implicit implication on the radiation budget. For instance, when a surface receives extra LW irradiance from thermal emission of other surfaces, its surface temperature increases. Accordingly, the thermal emission from this particular surface increases with increasing the surface temperature to the power of 4 according to the Stefan–Boltzmann law. Thus, in turn, the other surfaces will receive higher LW irradiance as well.
Including this process decreases the incoming LW radiation from the atmosphere by about
So far, the entire vegetation interaction with LW transfer has been ignored. The justification is that the absorbed LW radiation by vegetation may be compensated by the emitted LW radiation from vegetation. This simplification is acceptable provided that the surface temperature of the plant canopy is similar to the temperature of the surrounding surfaces. However, this is not always the case. Therefore, both the absorption and the emission of LW radiation by vegetation are included in this step.
Changes in the received LW irradiance within the focus domain of the simple urban configuration when considering tree thermal emissions (RTM_05) compared to the RTM_04. Violin, mean, and median colours are used in the same way as those in Fig.
Changes in the received LW radiation flux within the focus domain of the simple urban configuration when including vegetation interaction with LW radiation (RTM_05) compared to RTM_04. Walls, roofs, and pavements are folded the same way as those in Fig.
Here, surfaces receive more LW emissions compared to the previous case by up to
Allowing vegetation interaction with LW radiative transfer modifies the radiation balance in urban areas. Particularly, it increases the outgoing LW radiation due to increasing the LW radiation absorption within vegetation, reflection from surfaces, and emission from surfaces due to its higher temperature compared to RTM_04. This in turn modifies the effective urban parameters which control the RRTMG–RTM coupling.
Figure
Changes in the received SW and LW irradiance within the focus domain of the simple urban configuration when considering one reflection (RTM_06) compared to RTM_05. Violin, mean, and median colours are used in the same way as those in Fig.
Changes in the received SW radiation flux within the focus domain of the simple urban configuration when considering one reflection (RTM_06) compared to RTM_05. Walls, roofs, and pavements are folded the same way as those in Fig.
The RTM in PALM is designed in such a way that surfaces absorb all the received reflected radiation after the last reflection step which in the case of RTM_06 is one reflection. In other words, surfaces do not reflect part of the received radiation from reflection. For this reason, the consideration of only a single reflection is not enough to account for realistic simulations especially for surfaces with low emissivity or high albedo.
Since the change in the incoming SW radiation from the RRTMG radiation model is negligible in this step (Fig.
The received SW and LW radiation gained by increasing the reflection steps from a single reflection to four reflections is depicted in Fig.
Changes in the received SW and LW irradiance within the focus domain of the simple urban configuration when considering multiple reflections (RTM_08) compared to RTM_07. Violin, mean, and median colours are used in the same way as those in Fig.
It is important when performing multiple reflections to monitor the residuals after each reflection step. That is to assure that the absorbed radiation at the last reflection step is small enough so that any further reflections can be ignored. As a matter of fact, reflected radiation flux density has an order of
Generally speaking, the changes in the surface radiation flux of the realistic urban configuration when applying SPM show similar behaviour to the simple urban configuration. However, due to the complexity of the building configurations and the heterogeneity of the surface characteristics of the realistic case, these changes are more complex. As a matter of fact, the buildings of the simple configuration have the same height; therefore, the differences of the radiation incident on the roofs result mainly from the RRTMG–RTM coupling. Also, the trees are chosen so that they are shorter than buildings, which may underestimate the their effect.
In this section, we show examples of the changes in the radiation fluxes for the realistic case and we highlight the differences compared to the simple case.
The daily course of
First, the incoming SW and LW radiation fluxes from the RRTMG radiation model, shown in Fig.
Changes in the received SW and LW irradiance for the surfaces of the realistic urban configuration when considering vegetation interaction with SW solar radiation (RTM_03). Violin, mean, and median colours are used in the same way as those in Fig.
Secondly, the magnitude of the changes in the radiation fluxes due to considering a specific RTP is higher than the changes in the simple urban configuration. This can be attributed to the complexity of the urban configurations and its surface characteristics. Also, the variability in the incoming radiation from the RRTMG radiation model to the urban domain contributes to these changes. For instance, including the vegetation interaction with SW radiative transfer (RTM_03) decreases the received SW radiation of the surfaces located in the view of the vegetation (Fig.
Changes in the received SW radiation flux for the realistic urban configuration at 10:00 LST due to including the vegetation interaction with the SW radiative transfer (RTM_03). The copyright for the underlying satellite image is held by © GeoBasis-DE/BKG 2009, Google 2009.
Changes in the received LW irradiance for the surfaces of the realistic urban configuration when considering
Thirdly, the effect of the RTPs related to the vegetation interaction with LW radiation transfer is more pronounced and even more complex compared to the simple case. As described in Sect.
Changes in the received LW radiation flux for the realistic urban configuration at 12:00 LST due to including multiple reflections (RTM_08). The copyright for the underlying satellite image is held by © GeoBasis-DE/BKG 2009, Google 2009.
The general effect of the thermally driven flow within the UCL has been discussed in many previous studies
Each parameterization step of SPM yields RTM, and hence UCM, with varying combinations of radiative interaction processes (Sect.
Since the flow in each simulation responds to different combinations of RTPs, results are presented in a normalized form. The average building height,
During the simulations, instantaneous flow properties such as wind velocity components (
Horizontal- and time-averaged (1 h) vertical profiles of the simple urban configuration at 10:00 LST of
Horizontal- and time-averaged (1 h) vertical profiles of the realistic urban configuration at 10:00 LST of
Comparing the profile shapes and the vertical gradients reveal that the effect of radiation parameterization on the flow is considerable below and above the street canyons. This is even visible in the simple urban geometry, compared to the realistic case where the horizontal surfaces are distributed at many vertical levels. Three groups of profiles can be identified. The first group is related to the results based on RTM_00 to RTM_03. Basing the PALM only on these RTMs produces high discrepancies in both the wind and the turbulence characteristics compared to RTM_08. The second group includes the profiles based on RTM_04 to RTM_06 which allow surfaces to receive LW irradiance from surfaces and vegetation as well as reflected SW radiation from surfaces. These parameterizations enhance both the wind and the scalar profiles and remarkably adjust the vertical profiles and hence represent the minimum parameterization of radiation interaction in order to produce reasonable vertical profiles of flow properties. The third group includes the profiles based on the last RTMs, i.e. RTM_07 and RTM_08. These parameterizations have subtle effect on the profiles shape and merely serve to fine tune the flow profiles. This finding is not surprising since the change in surface radiation budget due to the additional radiation interaction processes in these RTMs is low, compared to those in the previous RTMs.
The heterogeneity of surfaces with different radiation budgets due to their orientation and surface characteristics creates local flow changes that are not visible in the flow profiles discussed above. Each process ultimately initiates different thermally induced forces which interact with both the shear forces of the flow above the surfaces and the driving forces induced by building corners, creating eddies yielding to the complex three-dimensional flow field. This spatial variability in the flow field arising from using different RTMs is quantified by calculating the root mean square of the relative error vector in the flow properties,
Box plots of the error measure,
Box plots of the normalized root mean square error,
For the relative error measures, the flow properties chosen are the normalized horizontal and vertical wind speed and the air potential temperature. According to these measures, successive incorporation of RTPs results in reduction in
The normalized volumetric flow rate for
For the normalized volumetric flow rate,
Based on the above discussion, the effect of using different RTMs on the flow properties may be summarized as follows:
In combination, our analysis confirms the hypothesis that using different combinations of RTPs considerably alters the flow properties (scalar and turbulence) within the urban canopy layer. Each RTP affects the flow field differently, based on its contribution to the surface radiation budget. Some processes have primary effects on the flow, while other processes have only secondary effects. Considering the SW interaction with buildings and vegetation (shadow casting) only in the RTM is not recommended, especially during the day, and may produce high discrepancies in the flow properties and all its related parameters. The processes of buildings and vegetation interaction with LW transfer, such as thermal emissions, are essential in RTM to assure acceptable quality of the model results. Including SW and LW radiation reflection process in RTM affects the flow properties. It is important to include both SW and LW reflection in the RTM to produce high-quality model results. The changes in the radiation budget of surfaces due to considering vegetation interaction to reflected irradiance and/or multiple reflections in the RTM are not strong enough to create a considerable effect on the flow properties. Generally, the effects of RTPs depend on the time of the simulation. For example, processes related to the interaction with SW radiation obviously are only important during the day. The change in the flow properties due to the sophistication of RTM is not limited to the flow between buildings, but its influence extends above street canyons.
As pointed out in Sect.
Table
The computational resources requirement of the RTMs used in the SPM for the realistic urban configuration. The CPU time is given relative to the CPU time of RTM_08 (3422
As Table
The generalizability of the results of this study is subject to certain limitations. For instance, all the simulations were performed on a typical urban scenario during a summer day with clear-sky conditions. Neither clouds nor rain were considered in this study. The effect of RTPs, especially those controlling SW radiation, will change for other than clear-sky conditions. However, clear-sky conditions are usually used for urban-specific applications. Since the study was based on the model system of PALM, it was not possible to consider the effect of absorption, emission, and scattering of radiation due to air constituents (fog, pollutants, etc.). Also, all surfaces are assumed to be Lambertian reflectors; therefore, directional reflection is not considered. Another limitation is the dependency of the results on the surface properties (albedo, emissivity, roughness, and skin layer thermal conductivity) and parameters of building and pavement materials (volumetric heat capacity and thermal conductivity). Although we made sure to use typical surface properties in the two urban configurations, simulations for domains with different surface properties may show different results.
The current study focuses on the flow changes within the urban domain. A further study could assess the performance of the RTMs using simulations with fixed meteorological conditions. In this way, the secondary effect of each RTM caused by the variation of meteorological conditions will be eliminated. This will keep the focus on the pure radiative transfer processes. Further research could also be conducted to determine the influence of using different radiation transfer processes on the atmospheric boundary-layer-scale structure and its impact on turbulent exchange at the canopy–atmosphere interface. Further studies need to be carried out in order to explore canopy exchange of scalars (e.g. pollutant dispersion). These suggested studies would make use of the output of the measurement campaign which was completed in the first phase of the [UC
The purpose of the current study is to determine how much detail should be included to parameterize the radiative transfer in UCMs. A generic parameterization method is used to quantify the effect of including the main RTPs into the RTM of an UCM in a stepwise manner. These processes include interaction of urban elements (buildings and trees) with both the incoming SW radiation (e.g. shadow casting) and LW radiation (e.g. thermal emission and absorption) as well as radiation reflections among urban elements. The results show that although these processes contribute differently to the surface radiation budget, they are necessary to accurately estimate the radiation budget of urban surfaces.
Although this study does not engage with validating the RTM, it highlights the main major RTPs which greatly affect the ultimate surface radiation budget. For instance, surface interaction with the incoming SW and LW radiation from the sky is greatly adjusted by calculating the proper SVFs, and hence the received radiation from sky to surfaces is correctly added to the radiation budget. Also, and as expected, the vegetation interaction with the incoming SW radiation from the sky has a great effect on the surfaces located in their view area. The radiation budget is greatly adjusted by estimating the vegetation shadows due to vegetation. Additionally, receiving LW irradiance from urban surfaces constitutes a major part of the received LW radiation budget. Similarly, the vegetation interaction with LW irradiance process affects the radiation budget of the surfaces located in their view by partially absorbing the LW irradiance from the sky and emitting LW irradiance from the biomass.
The study shows also that receiving irradiance from the reflected radiation (SW and LW) provides considerable radiation to the radiation budget of surfaces, especially to those located in the shadow. Most of the received radiation from reflections is received in the first reflection; however, multiple reflections are still needed to reduce the residuals. It is confirmed that using finite number of reflections is adequate to parameterize radiation reflections since radiation residuals decrease quickly with increasing the number of reflections. Nonetheless, the number of reflections should be chosen based on the surface properties (albedo and emissivity). Vegetation interaction with reflected irradiance has a minor effect on the radiation budget.
The flow field properties (scalar and turbulent) react to the type of the RTM used in the simulation. The flow field is shaped by the interaction between the inertia, mechanical shear, and buoyancy forces. The latter is mainly controlled by the RTPs considered in the RTM. The study identified three categories of RTMs, when compared to the full RTM 3.0, i.e. RTM_08. The first category (RTM_00 to RTM_03) produces low-quality model results. The second category (RTM_04 to RTM_06) gives acceptable model results, based on the quantification measures. Omission of any RTP in these RTMs may lead to considerable uncertainties in the model predictions. The third category (RTM_07) produces high-quality model results. Generally, RTPs modify the vertical distribution of turbulent momentum flux and control the exchange of momentum and scalars. As presented in Sect.
The study highlights the implicit effect of each RTP on the surface radiation budget and the flow field by altering the incoming radiation fluxes from sky, due to the coupling of the RTM with the radiation model.
The PALM model system is distributed under the GNU General Public License v3 (
The model output data that have been presented in this paper as well as the model driver data are available via
MHS participated in the design of the study, carried out the numerical experiments, analysed the data, and drafted the manuscript; SS participated in the design of the study and in the analysis of the results, and critically revised the manuscript; JR and PK designed the original RTM and revised the study. BM revised the manuscript and coordinated the development of the PALM 6.0 model system. FKS and MS supported the model implementations and the inputs for the test cases and revised the manuscript. CS coordinated the study and revised the manuscript. All authors have read and approved the manuscript for publication.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This study is funded by the German Federal Ministry of Education and Research (BMBF) under grant no. 01LP1601A within the framework of Research for Sustainable Development (FONA;
This research has been supported by the Federal Ministry of Education and Research (Germany) (grant no. 01LP1601A), the European structural and investment funds (grant no. CZ.07.1.02/0.0/0.0/16_040/0000383), Norway Grants, and the Technology Agency of the Czech Republic “Turbulent-resolving urban modelling of air quality and thermal comfort” project (TURBAN, project no. TO01000219).
This paper was edited by Gerd A. Folberth and reviewed by two anonymous referees.