A conceptual model for a generalized canopy parametrization for atmospheric models

The forest canopy and the urban canopy are the two vertically most extended canopies and have a great influence on boundary‐layer processes. Many studies in the past have analyzed and discussed forest canopy effects (FCEs) and urban canopy effects (UCEs) on aerodynamics, thermodynamics, hydrology, and air quality individually. Few studies have compared them. To better understand to what extent FCEs differ from UCEs, this study carries out a qualitative assessment of FCEs and UCEs in comparison with grass‐covered surfaces. In addition, as canopy effects are represented in atmospheric models by employing canopy parametrizations, this study assesses the existing parametrizations with respect to their ability to consider the relevant canopy processes. For parametrizations being globally applicable and for multiple types of forest, urban, and forested urban canopies, it is desirable to treat both forest and urban canopies in models in a unified way. In this context, a conceptual model for a generalized canopy parametrization (GeCap) has been developed based on the assessments of this article. It focuses on the interactions between canopy characteristics, processes, and fluxes as they relate to canopy effects. GeCap can serve as a methodological framework for an integrated analysis of properties and dynamics of canopy systems and for the design of forested urban canopy parametrizations.

However, their effects on atmospheric processes in the lower planetary boundary layer should be included in the models (WMO, 2022).
Some UCPs include the effects of street trees (Lee and Park, 2008;Krayenhoff et al., 2014;Wang, 2014;Lee et al., 2016;Ryu et al., 2016;Redon et al., 2020); this type of parametrization is named forested UCP (FUCP). Compared with UCPs, FUCPs more realistically represent the effects of cities with vegetation on the atmosphere, as FUCPs include energetic and hydrological interactive processes between urban vegetation and built-up surfaces (Lee and Park, 2008), thermal and hydrological heterogeneities at the vegetation surfaces, roof, wall, and canyon surfaces (Wang, 2014), and short-wave and long-wave radiation exchange between buildings and trees (Krayenhoff et al., 2014). Grimmond et al. (2009) stated that FUCPs better simulate outgoing short-wave radiation, net radiation, and the turbulent fluxes than UCPs do. However, each existing FUCP has its limits and often neglects some important physical processes. For example, heat and water fluxes of vegetation are not addressed in BEP-Tree by Krayenhoff et al. (2014), and exchange of long-wave radiation between street trees and urban fabrics is not considered in the FUCP by Wang (2014).
Despite well-documented research on analyzing the effects of forest canopies and urban canopies, the similarities and differences between them are not fully clear. This article aims to fill this gap. We also explore in this study the possibility of developing a conceptual model for a canopy parametrization that sufficiently represents the important processes of forest, urban, and forested urban canopies in any combination and is usable in global-scale models. By conceptual model we mean a qualitative model representing the various components, complexities, and interactions of canopy effects with variables relevant for weather and climate (e.g., temperature, humidity). It provides an easily understood system interpretation for the canopy and can be used for the construction of a quantitative model. For developing the conceptual model, the following key questions are addressed: Q1: To what extent are parameters and processes in forest and urban canopies different from each other and from those above grass? Q2: Which processes are relevant for a forest, urban, and forested urban canopy and need to be considered in a parametrization? Q3: Is it possible to develop a generalized parametrization applicable to forest, urban, and forested urban canopies? The paper is structured as follows: Section 2 describes the definition of canopies, canopy-relevant processes, and canopy effects on aerodynamics, thermodynamics, hydrology, and air pollution. Section 3 reviews and assesses the existing canopy parametrizations used in previous studies. Section 4 introduces the conceptual model for a generalized canopy parametrization (GeCap) and discusses the possibilities of a GeCap. Section 5 provides conclusions of the study.
hydrosphere, and pedosphere. It extends from the ground level to the top of obstacles, which refer to vertically extended structures, such as buildings and trees ( Figure 1). Theoretically, also for example, grass forms a (grass) canopy with a vertical extension of a few centimeters to several tens of centimeters (Aylor et al., 1993;Phillips et al., 2012); effects of these canopies might be sufficiently well described in atmospheric models using a slab approach.
This article focuses on vertically more extended canopies created by buildings and trees with heights larger than the lowest model level that might be at ∼ 10 m for a high-resolution atmospheric model. Heights of forest, urban or forested urban canopies are 10 m up to a few 100 m (Figure 1). A forest canopy is generally defined as the assemblage of all foliage, twigs, fine branches, their attending flora and fauna, the air, and their environment (Nadkarni et al., 2004). An urban canopy is traditionally defined as the combination of buildings and the air volume between them. A forested urban canopy is defined as an urban canopy with vegetation and trees (Lee and Park, 2008). Oke et al. (2017) and WMO (2022) named the forested urban canopy as the urban canopy; however, the traditional definition of the urban canopy (without vegetation or trees) is used in this study. Even though the three types of canopy layers differentiate themselves by their definitions and characteristics, they have some similarities, especially in terms of their effects on the atmosphere (Sections 2.2 and 2.3). This, then, provides a baseline for developing a generalized parametrization for the forest, urban, and forested urban canopies (Section 4).

Canopy effects
It is important to consider canopy effects in high-resolution atmospheric models, since the canopy affects exchange processes within and above it and then influences weather and climate. To better understand how the atmosphere is modified due to the presence of canopies, we compare the forest canopy effects (FCEs) and urban canopy effects (UCEs) with the grassland effects from the perspective of aerodynamics, thermodynamics, hydrology, and air pollution. The differences and similarities are discussed at three vertical levels; namely, at ground level, within canopies, and at the top of canopies. Please note that for the comparison with grassland, we assume the same atmospheric stability and use the same heights above ground and thus compare values within the forest and urban canopies with above grass. Effects at different levels might be considered in single-layer canopy parametrizations (SLs) and multilayer canopy parametrizations (MLs). The main difference between these two types of parametrizations lies in the representation of the vertical structure of canopies (Masson, 2006). Whereas SLs treat an urban canopy as a single layer, MLs divide an urban canopy into multiple layers (Ryu et al., 2011). In contrast, SBs in general aim at representing an integral effect and are often using the information at the top of canopies above the displacement height. If the parameter/process is not applicable there, the surface values are used.
Canopies have multiple surfaces, such as leaves, stems, and branches in forest canopies, and walls, roofs, windows, and roads in urban canopies. Each surface has a separate effect on exchange processes with the atmosphere and thereby separately influences the aerodynamics, thermodynamics, hydrological, and pollutant-related processes. In this section, these processes are not discussed per obstacle, but the overall canopy processes are presented as we aim at parametrizing them in global-scale models that have the typical resolutions of ∼ 1 km and do not resolve obstacles explicitly.
As morphology and phenology play important roles in forest effects on the atmosphere, we only consider continuous forest canopies during the growing season here. For the current study, the forested UCEs are not discussed individually, because they are considered as a combination of the FCEs and UCEs.
The results of the comparison are summarized in Note: FCEs and UCEs are compared with grassland effects at ground level, within the canopy, and at the top of the canopy. Increase (+), decrease (−), little change (./.), or increases and decreases (±) can occur for a parameter/variable/process. Note that the assessment is done with values at the same heights; that is, a value for a parameter/variable/process above ground but within the canopy is compared with a value at the same height above grassland and thus, in fact, in the air. NA denotes not applicable. # refers to the number of the input parameters (PA-PC) and the variables/processes (P1-P16) to be considered in a canopy parametrization (Section 2.3). Yellow cells denote a forest canopy and an urban canopy share the same effect at the same vertical level. Abbreviations: AVOCs, anthropogenic volatile organic compounds; BVOCs, biogenic volatile organic compounds; CO, carbon monoxide; FC, forest canopy; GL, grassland; NO x , nitrogen oxides; PM, particulate matter; SO 2 , sulfur dioxide; UC, urban canopy.

Canopy effects on wind and turbulence
The aerodynamic effects of forest canopies and urban canopies have been of interest to forest climate and urban climate science for a long time. It is commonly accepted that there are similarities between forest canopies and urban canopies in terms of their effects on the mean and turbulent airflows. When air flows through forests or cities, a certain proportion of momentum is absorbed, leading to a reduction of wind speeds within and above canopies (Yamada, 1982;Oke, 1988b;P1 in Table 1).
For neutral stratification, mean wind-speed profiles above both types of canopies are expressed in the integral approach as follows (Oke, 1987): where U(z) is the horizontal wind velocity at height z, u * is the friction velocity, k is the von Karman constant (∼ 0.4), z is the height above the ground, z 0 is the aerodynamic roughness length, and d is the zero-plane displacement height (including z 0 ) at which the wind speed is 0 m ⋅ s −1 . z 0 depends on roughness geometry, and forests and cities have similar values (∼ 0.7 m) that are much greater than for the open ground with small obstacles such as grass (∼ 0.1 m) (Stull 1988; PA in Table 1). According to Cleugh and Grimmond (2012), the obstacle influences can extend to about two to three times above the heights of the buildings, varying with the building dimensions and spacing. Assuming the same stability, the turbulence intensity within the forest and urban canopies is lower than the turbulence above grassland due to the lower wind speed within canopies (P2 in Table 1). For instance, wind-tunnel experiments by Kastner-Klein and Rotach (2004) showed that turbulent kinetic energy (TKE) below the roof level in the modeled urban areas is lower than in non-urban areas. If the differences in stability are considered, for example, the higher vertical mixing at height due to urban heat island effects (Bohnenstengel et al., 2014), the turbulence might be larger in the urban canopy than at the same height above ground over grass. However, in our comparison, we assume the stability is the same. Above canopies, the turbulence intensity depends on the surface roughness: The larger the value of roughness length z 0 the greater is the turbulence intensity (Roth, 2000). As both forest and urban canopies have larger values of z 0 , turbulence above canopies is enhanced. Surface measurements by Bowne and Ball (1970) showed that turbulence intensity above the city of Fort Wayne, Indiana, was 30-50% higher at a height of 60 m than that at a similar level over the surrounding rural area. Cleugh and Grimmond (2012) pointed out that, under neutral stratification, TKE for forest canopies and urban canopies reaches its maximum value at similar heights just above the top of canopies and the flow forms a highly turbulent shear layer (P2 in Table 1). It should be noted that for both forest and urban canopies the wind profiles and turbulence characteristics within and above canopies are strongly influenced by atmospheric stability and canopy morphology, such as building and vegetation structure, foliage density, and the density and shapes of buildings (Roth, 2000;Zeng and Takahashi, 2000;Coceal and Belcher, 2005;Cleugh and Grimmond, 2012;Moon et al., 2019).

Canopy effects on energy balance
We discuss the thermodynamic effects of canopies using the integral canopy energy budget, which can be written as follows: where Q A is the anthropogenic heat flux, Q * is the net all-wave radiation, Q S is the sensible heat flux, Q L is the latent heat flux, and Q G is the net heat storage in canopies. Q * is the sum of the incoming and outgoing short-wave radiation (R S↓ and R S↑ respectively) and the incoming and outgoing long-wave radiation (R L↑ and R L↑ respectively), as given in Equation (2b). The incoming short-wave radiation R S↓ is the sum of the direct beam and diffuse radiation (P4 in Table 1). Forests have little impact on the R S↓ reaching the top of forest canopies (Baldocchi et al., 2004). As R S↓ penetrates through the forest canopies, a portion of the radiation is absorbed by canopy elements (tree crown, trunk, stem, etc.); the R S↓ within canopies and arriving at the forest floor is thus decreased (Ross, 1981;Baldocchi et al., 2000). The absorption and transmittance of R S↓ depend on the canopy structure, in terms of the size and location of the canopy gaps, as well as canopy density (Knyazikhin et al., 1998;Hardy et al., 2004). Higher canopy density results in a stronger reduction of R S↓ .
For urban canopies, the R S↓ reaching the canopy top can decrease if the urban atmosphere contains high levels of particles and radiation is scattered by air pollutants (Cleugh and Grimmond, 2012). In addition, cities have impacts on boundary-layer clouds through enhanced convergence due to increased surface roughness and the release of aerosols as cloud condensation nuclei resources (Shepherd, 2005). With increasing sky cloudiness, R S↓ declines (Liu and Jordan, 1960). The amount of R S↓ reaching the city ground is highly dependent on canopy architecture and structure, as the R S↓ within canopies is absorbed and intercepted by surfaces of canopy obstacles (Oke et al., 2017).
A portion of the incoming short-wave radiation is reflected by canopy elements (P4 in Table 1), and this loss depends on the albedo of canopy surfaces (PB in Table 1). Since only averaged canopy effects are considered in this section, a single albedo value for each canopy surface is not discussed. If canopies are treated as slab layers, the albedo of forest canopies (0.13-0.20) and urban canopies (0.14) is lower than that of grasslands (0.16-0.26) (Oke et al., 2017); thus, solar radiation reflected by forests and by cities is less than by grasslands (von Randow et al., 2004;Teuling et al., 2010;Cleugh and Grimmond, 2012). However, if we compare the reflection of short-wave radiation for both canopies with grassland at the same height above ground, it is higher within canopies and at the top of canopy layers than that for grassland, since at the same height above ground the air above grass is close to non-reflective, whereas forest and urban canopies have multiple reflecting surfaces. The multiple reflections and shades within the canopy result in three-dimensional radiative fluxes. Note that the reflection of short-wave radiation at obstacles' surfaces is not the same as the outgoing short-wave radiation R S↑ . The R S↑ within and over canopies is lower than for grasslands, because of the lower incoming short-wave radiation R S↓ and stronger absorption by obstacles.
The incoming long-wave radiation R L↓ above canopies is emitted from the atmosphere. Observation studies show that forests have little impact on the change of R L↓ over forest canopies ((Baldocchi et al., 2004;von Randow et al., 2004); P5 in Table 1). However, R L↓ above urban canopies can be enhanced due to high levels of greenhouse gas concentrations and aerosol emissions, elevated temperature and humidity levels (Cleugh and Grimmond, 2012;Wang et al., 2015), as well as higher cloudiness (Kotthaus and Grimmond, 2014). The R L↓ beneath canopies can be divided into two parts: the R L↓ emitted by canopy elements and the R L↓ passing through the canopies. Both of them are influenced by the canopy characteristics, such as building height heterogeneity, sky view factor, and leaf area index (LAI) or building coverage index (Blankenstein and Kuttler, 2004;Yang and Li, 2015). Compared with open areas, both forest and urban canopies increase the R L↓ reaching the underlying surface considering the radiation from obstacles (Blankenstein and Kuttler, 2004;Essery et al., 2008). Blankenstein and Kuttler (2004) measured R L↓ by car at a height of 3.3 m above ground level through the city of Krefeld, Germany, and demonstrated that R L↓ increases with a decreased sky view factor, suggesting that more R L↓ is emitted by horizon obstructions. For the R L↓ passing through the canopies, a numerical model study by Yang and Li et al. (2015) has shown that more radiation is absorbed as building heights become more heterogeneous.
The outgoing long-wave radiation R L↑ is generally enhanced for both forest and urban canopies relative to open areas due to the existence of the canopies (Hardy et al., 2004;Lawler and Link, 2011;P5 in Table 1). And as LAI or building coverage index increases, the portion of long-wave radiation from canopy elements increases. As R L↑ can be computed based on the Stefan-Boltzmann law, which depends on the emissivity of the canopy and the canopy temperature, the diurnal cycle of R L↑ should be calculated dependent on the respective temperatures of, for example, walls and roofs.
Sensible heat flux Q S refers to heat transfer from canopies to the surrounding atmosphere (P3 in Table 1); thus, Q S mainly depends on the temperature difference between canopy surfaces and air and on the wind speed. A comparison study of radiation over a Scots pine forest and an adjacent grassland in southwest Germany by Holst and Mayer (2006) showed that Q S over forests exhibited stronger diurnal patterns than over grassland throughout the whole year, and the peak difference occurred in July after midday. Another study measuring fluxes over forests and grasslands at all European FLUXNET sites revealed that, under high temperature and high incoming short-wave radiation (such as under heatwave conditions), forests emit more sensible heat than grasslands do (Teuling et al., 2010), which results from a different response of stomatal opening to radiation and atmospheric conditions (Teuling et al., 2010;van Heerwaarden and Teuling, 2014). The Q S over and within cities is generally higher than that for grasslands due to higher surface temperatures of obstacles than surroundings. Li et al. (2015) pointed out that Q S could far exceed that over non-urban areas, especially during heatwave days.
Latent heat flux Q L refers to the transfer of heat from canopies to the surrounding air by evaporation of water on the obstacle surfaces (P3 in Table 1); thus, Q L is related to the evaporation process and moisture transport. Water supply plays an important role in the variation of Q L for forests and grasslands. Studies indicate that Q L over forests can be lower than that over grasslands under sufficient soil moisture conditions (Wicke and Bernhofer, 1996;Holst and Mayer, 2006); the reverse might occur for low soil water supply (von Randow et al., 2004). In addition, atmospheric conditions, plant functional type, rooting depth of the vegetation, stomatal control, and topography also have impacts on the temporal evolution of Q L (Baldocchi et al., 2004;Holst and Mayer, 2006;Teuling et al., 2010;van Heerwaarden and Teuling, 2014). Q L in cities is generally low because there is less vegetation and more impervious surfaces, which results in low moisture availability and reduced evaporative cooling (Kotthaus and Grimmond, 2014).
Anthropogenic heat flux Q A is specific for urban canopies, as it results from human activities, including heat release of industrial plants, building heating, ventilation, and air conditioning systems, vehicle exhausts, and so forth. (P6 in Table 1). According to Sailor (2013), when including Q A as an additional source term in the urban canopy surface energy balance, the vertical distribution of Q A emission should be considered. At pedestrian level, heat emissions are from vehicles; within canopies, emissions from buildings occur throughout the vertical height of the building; at the tops of canopies, a substantial portion of Q A is from the mechanical heating, ventilation, and air conditioning equipment, which is usually located at roof levels (Sailor, 2013). The value of Q A depends on local climate and population density. In general, Q A in winter is greater than that in summer, and the greater population density at city scales results in substantially larger values for Q A (Sailor et al., 2015).
Heat storage flux Q G is a significant component of the surface energy balance for forests and urban areas (Roberts et al., 2006;Haverd et al., 2007). Compared with short grasslands, tall forests have higher heat storage, owing to larger volumes of air and biomass within the canopy (Holst and Mayer, 2006;Haverd et al., 2007;PC in Table 1). Cities can better store heat than grassland because, under urbanization, natural materials (e.g., soils and vegetation) are replaced with construction materials (e.g., concrete, asphalt, brick) (Oke et al., 2017), which offer higher heat capacity. In addition, more heat storage is created due to the three-dimensional building structures (Oke et al., 2017). As a result, more heat is retained in buildings during the daytime (Grimmond and Oke, 1999;Roberts et al., 2006). However, it should be noted that the Q G at the ground level in cities can be influenced by the shadow effects of tall buildings (P4 in Table 1), as buildings prevent solar radiation reaching the ground and thus reduce the heat storage underneath (Vuckovic et al., 2019).

2.2.3
Canopy effects on water balance Canopy effects on water balance are discussed using the canopy surface's water budget, which can be written as (Anderson et al., 1976;Grimmond and Oke, 1991) where W P is precipitation, W I is piped water supply, W A is water released due to anthropogenic activities, W E is evapotranspiration, W R is surface runoff, and ΔW S is the change in water storage in the soil and ground-water aquifers for the period of interest. Forests play important roles in regulating precipitation patterns over land (Ellison et al. 2017;P7 in Table 1). Modeling studies suggest that tropical forests increase precipitation compared with pastureland (Bonan, 2008). Meier et al. (2021), who used an observation-based continental-scale statistical model, found that converting agricultural land to forest can increase summer precipitation by 7.6% on average over Europe. Moreover, a study by Hoek van Dijke et al. (2022) found that increasing large-scale tree cover enhances precipitation indirectly, which combined with directly enhanced evaporation will shift regional water availability.
For cities, precipitation connections are complex. Comprehensive reviews on urban impacts on precipitation indicate that both increase and decrease in precipitation caused by urbanization are possible (Han et al., 2014;Liu and Niyogi, 2019). The urban rainfall modification can be related to urban heat island intensity, large surface roughness, and aerosols (Han et al., 2014;Liu and Niyogi, 2019). For instance, precipitation downwind as well as over cities can be enhanced due to updrafts induced by the urban heat island (Han et al., 2014;Liu and Niyogi, 2019). Aerosols influence the development of clouds and precipitation as they serve as condensation nuclei for the formation of cloud droplets and atmospheric ice particles (Han et al., 2014). By using a cloud-resolving mesoscale model, van den Heever and Cotton (2007) found that, under low background aerosol concentrations, increased urban aerosols can enhance convective storms and associated precipitation. However, according to Ntelekos et al. (2009), whether the increasing aerosol concentration can enhance the precipitation in intense convective storms depends on relative humidity, convective available potential energy, and wind shear. In addition, convective systems connected to precipitation can be disrupted by the larger urban surface roughness (Han et al., 2014).
Canopy interception of precipitation is an important component of the water balance (Xiao and McPherson, 2002;Miralles et al., 2010). Precipitation within forest canopies is partitioned into three fractions: interception (precipitation remains on trees), stemflow (precipitation flows to the ground via trunks or stems), and throughfall (precipitation that may or may not contact the canopy and falls to the ground between the various components of the trees) (Anderson et al., 1976). Adane et al. (2018) pointed out that rainfall interception rate in dense pine forests was 70% greater than in grassland. Therefore, precipitation reaching the forest floor is strongly reduced relative to grasslands (P7 in Table 1). Similarly, rainfall within urban canopies can be intercepted by canopy surfaces, such as roofs and walls of buildings, awnings, balconies, and so forth. This effect on precipitation patterns at the ground might be less relevant than influences of urban structures on the boundary-layer clouds, as found by Ferner et al. (2022). Nonetheless, the rainfall interception by high-rise buildings should be additionally considered in urban hydrological studies for megacities, as mentioned by Yoo et al. (2021). Cho et al. (2020) proposed an empirical equation for estimating the amount of rainfall intercepted by a building, which depends on the rainfall intensity observed at the ground, the width and the height of the building wall, and the wind speed.
The evapotranspiration process W E consists of evaporation from soil and plant surfaces and transpiration of water by trees (P8 in Table 1). Forests typically have increased evapotranspiration rates compared with grassland (Bonan, 2008) due to deeper roots (Schenk and Jackson, 2003) and higher LAI (Henderson- Sellers, 1993). However, Breil et al. (2021) demonstrated that whether forests have higher evapotranspiration rates than grasslands actually depends on the canopy resistance and the saturation deficit between the plant and the atmosphere, which relates to the surface temperature and the input of net radiation. Hence, both an increase and a decrease in W E of forests relative to grasslands are possible. Evapotranspiration in cities is lower than in grassland, as natural surfaces are replaced by plenty of artificial surfaces (roads, pavements, and buildings) (Sterling et al., 2013;Oke et al., 2017). Sterling et al. (2013) analyzed the impact of the global land cover change on the terrestrial water cycle using the geographical information system method and found that the conversion from grassland to urban landscape leads to a decrease in evapotranspiration by 14% globally.
Surface runoff W R refers to water that moves overland and occurs when there is more water than can be absorbed by the surfaces (P9 in Table 1). Runoff in forests usually occurs at ground level. It is well agreed that forests reduce surface runoff rates (Anderson et al., 1976;Alaoui et al., 2011). Cities enhance runoff and reduce infiltration, due to the replacement of natural land cover with impervious cover like roads, bridges, and parking lots (Boyd et al., 1994;Armson et al., 2013). Apart from these runoff processes occurring on the ground, runoff on building facades and rooftops also occurs in cities.
Forest soils have higher values of water storage capacity than grassland does (Alaoui et al. 2011;P10 in Table 1). Forest soil structure is characterized by higher values of hydraulic conductivity and the structural porosity, as well as larger water uptake by tree roots, and these characteristics enhance infiltration processes (Alaoui et al., 2011). For urban canopies, horizontal exchange of soil water is impeded by urban infrastructure (e.g., basements, pipes, and tunnels), whereas vertically the infiltration processes for water to enter the soil decline due to the increased impervious cover (Oke et al., 2017).
Piped water supply W I and water released due to anthropogenic activities W A are very important for the urban canopy surface water balance (Grimmond and Oke, 1991). Watering of plants or irrigation is used in agricultural areas; as mentioned by Siebert et al. (2007), approximately 40% of the total area used for agricultural production worldwide is irrigated, though not much over grasslands and forests. Therefore, "not applicable (NA)" is added for P11 in Table 1.

2.2.4
Canopy effects on air pollution Air pollution can have influences on human health and well-being, ecosystem health, and climate. We discuss the emissions of eight air pollutants due to the presence of forest and urban canopies: particulate matter (PM), ozone (O 3 ), nitrogen oxides (NO x ), sulfur dioxide (SO 2 ), carbon monoxide (CO), anthropogenic volatile organic compounds (AVOCs), biogenic volatile organic compounds (BVOCs), and pollen. These air pollutants are selected because they are the most common pollutants investigated in previous air-quality measuring and modeling studies and are most relevant to human and ecosystem health (Seinfeld, 1989;Fenger, 1999;Mayer, 1999;He et al., 2002;D'Amato et al., 2010;Nowak et al., 2014;Eisenman et al., 2019). Trees in forests can have positive and negative effects on air quality. On the one hand, trees remove gaseous air pollutants (e.g., O 3 , SO 2 , and NO x ) through uptake via leaf stomata, and capture PM from the atmosphere through interception and resuspension processes on plant surfaces (Nowak et al., 2006;Nowak et al., 2014;P17 in Table 1). On the other hand, trees emit pollen and BVOCs (P13 in Table 1), which contribute to PM2.5 and O 3 formation and reduce air quality (Chameides et al., 1988;Nowak et al., 2014). O 3 is not directly emitted from trees but is formed in the atmosphere when NO x and BVOCs react in the presence of sunlight. A feedback loop of O 3 production in forests works as follows. BVOCs released by trees result in high O 3 levels, which inhibits tree growth and survival, and further prompts the release of BVOCs and enables more O 3 production (Eisenman et al., 2019). Thus, the influence of trees on O 3 concentrations depends on whether direct O 3 uptake outweighs indirect O 3 production by trees through the emission of BVOCs (Eisenman et al., 2019;Fitzky et al., 2019;P14 in Table 1).
Air quality is one of the major concerns in cities. Many cities across the world suffer from serious air pollution caused by anthropogenic activities, including industry, trade, power plants, vehicle traffic, and so forth. (Mayer, 1999). Urban air pollutants mainly include PM, O 3 , NO x , SO 2 , CO, and AVOCs. Five of these pollutants (PM, NO x , SO 2 , CO, AVOCs) are emitted from a variety of direct sources (P12 and P15 in Table 1), whereas O 3 is not directly emitted. O 3 in cities is formed when NO x reacts with AVOCs in the presence of sunlight; but at the same time, O 3 can be degraded by NO. Observational studies show that O 3 concentrations are higher at suburban or rural sites than at urban sites, as heavy traffic in cities causes higher NO concentrations, which help destroy photochemically produced O 3 and further results in lower O 3 concentrations compared with suburban areas (Klumpp et al. 2006; P14 in Table 1). As AVOC concentrations are higher in cities than in grasslands, a similar photochemical reaction can take place as for BVOCs from forests; thus, an increase of O 3 formation in cities is also possible. Moreover, similar to forests, air pollutant uptakes can also occur in cities (P17 in Table 1), such as dry deposition of NO x and SO 2 gaseous pollutants on building surfaces (Haneef et al., 1992;Grøntoft and Raychaudhuri, 2004).
Vertical and horizontal distribution of air pollutants within and above canopies are highly dependent on meteorological factors, including atmospheric stability, wind speed and direction, surface friction, and so forth (Baumbach and Vogt, 2003;Velasco et al., 2008). For instance, Baumbach and Vogt (2003) reported that a surface-based temperature inversion limited the vertical dispersion of O 3 and that emitted pollutants were kept beneath this inversion. Cichowicz et al. (2017) found that dispersion of atmospheric air pollution in summer and wintertime, which have different meteorological patterns, were different. Air pollution was reduced during the summer season with high temperature and low wind speed and humidity; the opposite situation occurred in wintertime (Cichowicz et al., 2017). Moreover, canopy structures such as canyon configurations, roof shapes, and distribution of trees also play important roles in the dispersion of air pollutants (Oke, 1988a;Yazid et al., 2014). In addition, all chemical reactions that include reactions with gas phase, gas to particle, particle reactions, and photochemical reactions are relevant and need to be considered in forest and urban canopies (P16 in Table 1).

Relevant canopy processes for a forested urban canopy
The parameters and processes that are relevant for a forest canopy and an urban canopy are also relevant for a forested urban canopy. As shown in Table 1, there are three important parameters; namely, roughness length (PA), albedo (PB), and heat storage (PC). The relevant processes are P1, P2 (aerodynamic processes), P3-P6 (thermodynamic processes, as illustrated in Figure 2), P7-P11 (hydrological processes, as illustrated in Figure 3), and P12-P17 (processes related to air quality). Note that P1-P11 are usually considered in a parametrization for forested urban canopies, whereas P12-P17 are usually represented in emission models (Section 3.2).
We found that there are similarities and differences between FCEs and UCEs (Table 1). On the one hand, forest canopies and urban canopies have the same following effects on the atmosphere: • P1, wind speed reductions at the three vertical levels (at the ground, within canopies, and at the top of canopies); • P2, reduced turbulence intensity within canopies and enhanced turbulence intensity at the top of canopies, if the same stability is assumed; • P3, enhanced sensible heat flux at the three vertical levels; • P4, enhanced absorption, and thus reduced incoming short-wave radiation, by the ground and obstacles within canopies, also resulting in reduced outgoing short-wave radiation; • P4, enhanced reflection of short-wave radiation by the ground and obstacles' surfaces within and at the top of canopies; • P4, shadowing induced by obstacles; • P5 enhanced absorption and emission of the long-wave radiation by obstacles within canopies; • P7, enhanced precipitation interception induced by obstacles within canopies leading to reduced precipitation at the ground; • P17, enhanced pollutant uptakes within canopies and at the top of canopies; • PA, increased roughness length; • PB, reduced albedo.
On the other hand, the following effects induced by forest and urban canopies go in opposite directions, and they require a more detailed consideration if represented for a forested urban canopy: • P9, surface runoff -reduced in forest canopies but increased in urban canopies; • P10, infiltration and soil water storage -increased in forest canopies but reduced in urban canopies.
In addition, anthropogenic heat (P6) and anthropogenic water (P11) as well as AVOC emissions (P15) only occur in urban canopies, whereas photosynthesis (P8) and BVOC emissions (P13) are typical forest-related processes, but all should be included in a FUCP.

ANALYSES OF CANOPY PARAMETRIZATIONS
The canopy processes mentioned in Section 2.3 cannot be resolved explicitly in the atmospheric models with a typical horizontal resolution of ∼ 1 km, and thus they need to be parametrized. In the past five decades, a wide range of canopy parametrizations has been developed. We analyzed 28 canopy parametrizations, including eight FCPs, 16 UCPs, and four FUCPs (Table 2). For each, an acronym of the parametrization name is given that is used hereafter to describe it.
As mentioned in Section 1, canopy parametrizations can be categorized into three types in terms of their representation of the surface: SB, SL, and ML.
SB is the most traditional and simple method among the three approaches. It treats forest or urban areas as a flat surface and does not consider canopy geometry. Surface physical properties, such as roughness length, albedo, and thermal conductivity, represent the characteristics of the whole forests or urban areas.
Single-layer urban canopy parametrizations (e.g., Mills, 1997;Masson, 2000;Kusaka et al., 2001) were first developed based on single-layer forest canopy parametrizations (Deardorff, 1978;Dickinson et al., 1986;Sellers et al., 1986;Walko et al., 2000). SL has one atmospheric layer in the canopy and calculates meteorological variables and fluxes on several surfaces of canopy obstacles differently. Compared with SB, geometry is more realistic in an SL, especially in terms of energy and momentum transfer between different surfaces and the atmosphere (Kusaka et al., 2001). Thus, SL simulates successfully some features of urban canopies, such as urban heat island, radiative trapping, and turbulent exchange (Masson, 2000;Kusaka et al., 2001). MLs (e.g., Brown, 2000;Martilli et al., 2002;Otte et al., 2004;Kanda et al., 2005;Bonan et al., 2018) calculate variables and fluxes at several vertical layers within the canopy. Even though an SL can already parametrize shadowing, reflections, and trapping of the radiation (e.g., Kusaka et al., 2001), these radiation interactions are simplified (Masson, 2006). ML better represents the aerodynamic and thermodynamic processes occurring within the urban canyon (Garuma, 2018). However, because the ML has higher resolution than the SB and SL approaches, ML is computationally more demanding. For both urban and forest canopies, MLs need as input the vertical distribution of obstacle structures.

Parametrizing aerodynamic effects
As explained in Section 2.2.1, both forest and urban canopies have similar aerodynamic effects on flows: reduced mean wind speeds within canopies and enhanced turbulence intensity at the top of canopies. Therefore, it is reasonable to use the same approach to represent these effects for forest and urban canopies. In previous studies, two approaches are commonly used: the roughness-length approach and the drag-force approach. The roughness-length approach uses a roughness length z0 and a displacement height d to calculate wind velocity and turbulent fluxes at the ground surface; see Equation (1). This approach is principally based on the Monin-Obukhov similarity theory, assuming stationary conditions and horizontal homogeneity. The main advantage of the roughness-length approach is that it is easy to implement, and thus commonly applied in models. However, this approach cannot capture the flow dynamics within the canopy (Brown, 2000).
The drag-force approach was first used for the forest canopy (Yamada, 1982) and then extended to the urban canopy (Brown, 2000;Martilli et al., 2002;Otte et al., 2004;Santiago and Martilli, 2010;Nazarian et al., 2020). In this approach, a pressure force and viscous drag force are added in the momentum equation to represent the momentum loss, and a source term is added in the TKE equation to represent the production of TKE of canopies. The drag term considers the height dependence of the obstacles' density, and thus the blocking effect. Otte et al. (2004) mentioned that the drag approach is better than the roughness-length approach in terms of simulating wind and temperature fields within and above canopies. However, there are two disadvantages to both approaches. First, there is difficulty in determining the values of roughness length and drag coefficient (Brown, 2000;Masson, 2000). Second, canopy morphology diversity is not well represented. For example, wind flows in west-east and south-north directions behave differently due to the asymmetrical shapes and structures of street canyons. However, these effects are not calculated in either the drag-force approach or the roughness-length approach since the values of building area density (or leaf area density) and roughness length for one specific grid cell in both approaches do not change according to the wind directions.

Parametrizing thermodynamic and hydrodynamic effects and air pollutant effects
Both FCP and UCP represent thermodynamic and hydrological effects by modifying the surface energy and water balance equations. Depending on the complexity of representing canopy obstacles, equation modifications can be implemented at a slab surface or a single layer or multiple layers.
The main difference between FCP and UCP lies in the representation of specific canopy processes, such as photosynthesis processes for forests and anthropogenic heat and water emissions for cities. FCPs generally (e.g., Ronda et al., 2001;Bonan et al., 2018) consider photosynthesis processes (water, carbon dioxide uptake and release) and consider time-varying properties related to forest phenology, which are excluded in UCPs. For urban canopies, anthropogenic heat fluxes are parametrized by heat released directly into air (Brown, 2000;Masson, 2000) or being added into the surface energy budget (Arnfield, 2003). In addition, some FCPs (e.g., Deardorff, 1978;Noilhan and Planton, 1989) consider foliage interception reservoirs, whereas UCPs (e.g., Oke, 1988b;Masson, 2000) consider liquid or solid precipitation intercepted by urban surfaces and urban dew. Some FCPs (e.g., Walko et al., 2000;Gustafsson et al., 2003) consider canopy properties and processes influenced by snow. The change of surface snow-cover properties, freezing and thawing of soil, and local runoff of heavy precipitation and snowmelt are parametrized (Walko et al., 2000). Several UCPs (e.g., Kusaka et al., 2001;Ryu et al., 2011;Wouters et al., 2016) take the change of solar azimuth angle into account for calculating radiation reflection and shading effects within canyons; however, this factor is often neglected in FCPs.
The impact of canopies on air quality mainly depends on the flow field (advection and diffusion of pollutants), which is considered in the parametrizations for the canopy effects on aerodynamics. A second influence of canopies is on chemical reactions as a result of changes in radiation and humidity; these are considered in parametrizations for the canopy effects on thermodynamics and hydrodynamics. A remaining influence of canopies on air quality is that canopies as pollutant sources influence chemical reactions. These are accounted for in the emissions models. The sources are frequently attributed to their actual height. Last but not least, a very important influence of forest canopies and vegetation in general is photosynthesis, and thereby carbon dioxide uptake and evapotranspiration. In summary, the canopy effects are considered without additional parametrizations by using the correct emission heights and parametrization types and approaches for dynamic, thermodynamic, and hydrodynamic effects.

Assessment of canopy parametrizations
We assess in Table 3 the 28 parametrizations listed in Table 2 to investigate how detailed existing canopy parametrizations represent canopy-relevant processes, which are given as P1-P11 in Section 2.2.3. TA B L E 3 Canopy parametrizations with canopy-relevant processes (P1-P11; see Section 2.3)

Aerodynamic
Thermodynamic Hydrological Note: Parametrization types include slab model parametrization (SB), single-layer parametrization (SL), and multilayer parametrization (ML). Aerodynamic parametrization approaches include roughness-length approach (RA) and drag-force approach (DA). For acronyms, see Table 2. Y means the process is represented; P means the process is partially represented. The table is divided into three blocks: forest canopy parametrizations, urban canopy parametrizations, and forested urban canopy parametrizations (see Table 2). Note that each block is sorted by parametrization type.
Aerodynamic processes are considered in most FCPs (six of eight) and UCPs (14 of 16), and in all four FUCPs. It can also be noticed that all multilayer parametrizations (type ML) employ the drag-force approach (DA) for representing the aerodynamic processes. The roughness-length approach (RA) is used in SB and SL.
All the 28 parametrizations partially or totally take account of thermodynamic processes, including radiation transfer and heat transport. Although all FCPs consider the effects of long-and short-wave radiation attenuation, trapping, and emissions due to trees, only some of them (BATS, FCM, and CLM-ml) account for the shadowing effects (P4). Compared with the FCPs, the majority of UCPs consider the shadowing effects except for SUEWS, SURY, and UP. Most UCPs and FUCPs take account of anthropogenic heat emissions (P6). All FUCPs consider all relevant aerodynamic and thermodynamic processes (P1-P6). They differ in the complexity of hydrological processes; for example, infiltration and soil water storage (P10) is only considered by ASLUM v3.1, which treats evapotranspiration (P8) somewhat less complexly. Regarding the evapotranspiration, TEB-Tree is more complete, but it currently neglects infiltration. Hydrological processes are partially considered in all FCPs, but only half of the UCPs. Table 3 also shows that the parametrization type (SB, SL, ML) does not play a role in the number and the complexity of the represented processes. For example, CLMU, ASLUM v2, and v3.1, which are SLs, consider almost all the relevant processes except photosynthesis. However, MLs, such as UP, BEP, and UCLM, only consider aerodynamic and thermodynamic processes.

CONCEEPTUAL MODEL FOR A GENERALIZED CANOPY PARAMETRIZATION (GECAP)
Based on that (a) the concepts of the forest canopy and the urban canopy are similar (Section 2.1), (b) there are similarities between FCEs and UCEs, and similarities between relevant processes within both types of canopies (Section 2.3), (c) existing FCPs and UCPs use identical approaches to represent, for example, aerodynamic processes occurring in forest and urban canopies (Section 3), we conclude that it is possible to develop a generalized canopy parametrization (GeCap) for forest, urban, and forested urban canopies. This section introduces the conceptual model of GeCap and discusses its possibilities.

Basic architecture of the conceptual model
The basic architecture of the GeCap consists of three parts; namely, atmosphere, canopy, and soil ( Figure 4). The three parts are connected with each other, and the canopy layer is acting as an interface between the atmosphere and the soil system. By introducing this concept, the canopy layer includes not only large obstacles, like trees and buildings, but also uncovered soils. In practice, canopy parametrizations are usually coupled with atmospheric models and soil models, and these models provide, for example, meteorological information to the parametrizations (e.g., background wind, temperature, humidity, etc.) and force the F I G U R E 4 The basic architecture of the conceptual model for generalized canopy parametrization. Arrows indicate relations between the canopy system and the external atmosphere and soil system [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 5 As Figure 4, but with details within the canopy system. The thin arrows indicate relationship between the main four factors. The thick arrows indicate relationship between the canopy system and the external atmosphere and soil system [Colour figure can be viewed at wileyonlinelibrary.com] parametrizations, which in turn influence the atmospheric and soil variables. Therefore, atmosphere and soil as the external systems play important roles in affecting the whole canopy system.
As GeCap aims to represent FCEs and UCEs in atmospheric models, the conceptual end-point is the canopy effects on the meteorological fields. Canopy effects are related to three main factors, namely canopy characteristics, processes occurring within canopies, and fluxes ( Figure 5). Each factor has its function in the GeCap parametrization. Canopy characteristics serve as input data for GeCap, while fluxes serve as output. Processes represented in GeCap can be considered in atmospheric models by modifying the fluxes in the basic governing equations (e.g., conservation equation of momentum, surface energy balance, surface water balance, etc.), which is the main focus of GeCap. The thin arrows in Figure 5 indicate relations between factors. Canopy characteristics directly influence the processes. The processes taking place within canopies result in the changes of meteorological fluxes, which indicate canopy effects and are considered in the equations of the atmospheric or the soil model.

Elements and relations in the conceptual model
Each factor in Figure 5 consists of a set of parameters or variables that are detailed in Figure 6.
To represent the diversity and heterogeneity of forests, forest canopy characteristics' parameters are categorized into four groups: forest structure, forest type, forest phenology, and forest function. The parameters in each category commonly used in FCPs are summarized in Table 4. Different to the invariant parameters for urban canopies, many forest canopy characteristics' parameters are time-varying parameters (e.g., LAI, albedo, canopy greenness fraction) due to forest phenology. For forest functions, GeCap mainly considers air pollutant emissions (BVOCs and pollen) and the carbon storage-sink function, which are associated with photosynthesis and stomatal parameters.
The heterogeneity of urban canopy structures demands a large number of input parameters for the canopy parametrizations (Grimmond et al., 2009;Schlünzen et al., 2011). By reviewing previous studies, the parameters that describe urban canopy characteristics can be categorized into four groups: urban geometry, surface cover, materials, and urban functions (Table 4). Urban morphology parameters consist of basic canyon or building information parameters (e.g., height, width, and canyon orientation) and the derived parameters (e.g., canyon aspect ratio and plan area index). Surface cover and materials of canopy elements are related to thermal parameters (e.g., thermal conductivity) and radiative parameters (e.g., albedo, emissivity), which contribute to modifying the surface energy balance at ground and building walls. Urban function parameters, like anthropogenic heat emission, can directly be used as direct input or be captured by specifying fixed internal temperatures and traffic counts (Grimmond et al., 2009).
For the FUCP the forest/urban canopy characteristics should all be considered. It needs to be ensured that they are georeferenced so that the trees and buildings are placed correctly within the urban areas and with respect to each other. This is important for the simulation of all the relevant processes. In addition, canopy characteristics serving as input should be combined and consistently given to the parametrization. It is challenging to use multiple data sources (e.g., with different types, resolutions, years). GeCap should include the P1-P11 processes discussed in Section 2.3. After representing the relevant processes by modifying the fluxes in the governing equations, GeCap should predict several types of canopy-layer-influenced fluxes (e.g., momentum flux, radiative flux, heat flux). Note that using fluxes in models can better ensure mass and energy conservation than using just variables.

Possibilities of GeCap parametrization
The conceptual model of GeCap systematizes canopy characteristics, relevant canopy processes, and canopy effects and gives an overview of those factors and parameters that are relevant for developing the parametrization. In this subsection, we discuss the possibilities of GeCap.
First, GeCap can serve as criteria for the parametrization assessment. GeCap helps to define which canopy processes and effects are required to be represented by a parametrization and helps to analyze if the fluxes are simulated consistently (e.g., evapotranspiration flux and latent heat flux). For instance, all four FUCPs mentioned in Section 3 (VUCM, TEB-Tree, ASLUM v3.1, and BEP-Tree) consider aerodynamic, thermodynamic, and hydrological processes, as well as the related effects. Theoretically, evapotranspiration can be calculated from latent heat by dividing by latent heat of vaporization; thus, the values of these two fluxes should be consistent. GeCap should be able to check if the modified latent heat flux is consistent with the modified evapotranspiration flux due to the presence of canopies.
Second, GeCap can serve as a guideline for the design of canopy parametrizations. As its name indicates, GeCap is designated to be suitable for forest, urban, and forested urban canopies. In practice, forest-and urban-specific surfaces (e.g., roofs, walls, windows, roads, leaves, branches, and soil) should be first defined. The values for the relevant surface parameters (e.g., fractions, albedo, roughness length, thermal diffusivity, heat capacity) should be determined. Then one could modify and solve the surface energy budget equation and water balance on different surface types. To represent radiation attenuation, multiple reflections, and trapping effects, GeCap should use a multilayer short-wave and long-wave radiation exchange scheme (P4 and P5 in Table 1). To represent aerodynamic effects induced by trees and buildings, and to capture vertical wind and TKE profiles within canopies (P1 and P2 in Table 1), the drag-force approach can be used in GeCap. The three-dimensional values for drag coefficient, leaf (building) area density, and frontal area index can be supplied as input.
GeCap should be able to represent the common effects of forest and urban canopies described in Section 2.3 for atmospheric models. Once realized and implemented, GeCap should help to answer concrete questions. For example, how much cooler cities will be in the summertime if more trees and vegetation are planted, or how much the power output of a wind turbine in urban or suburban areas will be reduced due to the modification of the urban area, or how urban forms implemented for future' sustainable cities affect local meteorology.
The utility of GeCap will depend on the model and the model physics used, so some of the parametrization approaches will not be applicable. For example, using the drag-force approach to parametrize TKE production is not suitable for a prognostic mesoscale model that uses empirical equations for the eddy diffusivity (Brown, 2000). As GeCap aims to incorporate FCEs and UCEs into one parametrization scheme, representation of the effects induced by urban and forest canopies that go in opposite directions should be considered as discussed in Section 2.3. Moreover, one of the main differences between GeCap and existing FUCPs is that GeCap is suitable to be used in global-scale models, as GeCap considers forests, cities, and forested cities at the same time. On local to global scales, forests and cities strongly affect the land-atmosphere interaction by modifying fluxes of water, energy, momentum, and greenhouse gases (Jackson et al., 2010;Boysen et al., 2020). For better understanding potential effects of deforestation and urbanization on climates of varying scales, deforestation and urbanization should be included in global-scale models (Jackson et al., 2010;Boysen et al., 2020). However, existing canopy parametrizations are generally only coupled with regional-scale models, such as WRF (Lee et al., 2016) and COSMO (Wouters et al., 2016). In this context, GeCap provides the framework for developing an advanced version of the current parametrizations that aims at including forest, urban, and forested urban effects in global-scale models at the same time. Practically, there are global-scale forest and urban datasets available that can serve as input for GeCap, such as a global Local Climate Zone map (Demuzere et al., 2022), a global LAI map (Liu et al., 2012), and a global anthropogenic heat flux map (Dong et al., 2017).

CONCLUSIONS
Forest canopies and urban canopies play critical roles in affecting boundary-layer processes. This study investigates the most important effects of these two types of canopies on the atmosphere and highlights the importance of including canopies in the atmospheric models with a typical resolution of ∼ 1 km. It was found that forest canopies and urban canopies, although they differ in terms of morphology, structure, and function, share many of the same effects on aerodynamics and thermodynamics. Shadowing and radiation-trapping effects should be considered for both types of canopies. In addition, wind speeds are reduced within canopies, and turbulent intensity is enhanced above canopies. The different and opposing effects of forest canopies and urban canopies are related to hydrological processes and air quality relevant processes. It is recommended that the similarities and differences between FCEs and UCEs should be taken more into account when including tree processes in urban canopies or developing FUCPs for atmospheric models.
By reviewing previous canopy parametrization studies, we find that few parametrizations have incorporated all important processes in canopies. Thermodynamic processes are considered in most parametrizations, but hydrological processes are usually neglected or only partially parametrized, especially in UCPs and FUCPs.
With increased model resolution, global-scale atmospheric models should be able to represent the averaged overall canopy effects by employing canopy parametrizations (WMO, 2022). In this context, a GeCap applicable to the forest, urban, and forested urban canopies is useful. The conceptual model for GeCap helps to better understand the relationship between canopy characteristics, processes, fluxes, and effects. In addition, GeCap can serve as a design outline for a parametrization to be used in atmospheric models of the forested urban canopy and enables a more general and abstract consideration of modeling future forested cities. It was beyond the scope of this paper to apply GeCap to mathematical quantitative models, providing instead a simple overview. Future work must be devoted to realizing the conceptual model numerically.