The Town Energy Balance (TEB) model has been refined and improved in order to
explicitly represent street trees and their impacts on radiative transfer: a
new vegetated stratum on the vertical plane, which can shade the road, the
walls, and the low vegetation has been added. This modification led to more
complex radiative calculations, but has been done with a concern to preserve
a certain level of simplicity and to limit the number of new input parameters
for TEB to the cover fraction of trees, the mean height of trunks and trees,
their specific leaf area index, and albedo. Indeed, the model is designed to
be run over whole cities, for which it can simulate the local climatic
variability related to urban landscape heterogeneity at the neighborhood
scale. This means that computing times must be acceptable, and that input
urban data must be available or easy to define. This simplified
characterization of high vegetation necessarily induces some uncertainties in
terms of the solar radiative exchanges, as quantified by comparison of TEB
with a high-spatial-resolution solar enlightenment model (SOLENE).
On the basis of an idealized geometry of an urban canyon with various vegetation
layouts, TEB is evaluated regarding the total shortwave radiation flux
absorbed by the elements that compose the canyon. TEB simulations in summer
gathered best scores for all configurations and surfaces considered, which is
precisely the most relevant season to assess the cooling effect of deciduous
trees under temperate climate. Mean absolute differences and biases of 6.03
and

For counteracting the adverse environmental effects that can result from
continuous process of urban expansion, numerous projects of local urban
planning or design support and favor the preservation and
reintroduction of vegetation in the city. From an environmental point of
view, the natural soils and vegetation play a important role and bring
significant benefits in different sectors

In order to investigate some of the physical processes related to the presence of vegetation in an urban environment, e.g., for microclimate, hydrology, or building energy consumption issues, the modeling is definitely a necessary tool. It is also pretty relevant and powerful to assess greening strategies by quantifying the potential impacts, and it consequently enables to answer to some important expectations of public stakeholders and urban planners.

The Town Energy Balance (TEB) urban canopy model

For such modeling exercises, TEB had been previously improved in order to
explicitly represent urban vegetation within the canyon and to parameterize
at small scale the radiative and energetic interactions between the built-up
covers and the vegetation

Until recently, very few urban climate models were able to take into account
natural soils and vegetation. This fact constitutes a significant limitation
in modeling the radiative and energetic exchanges in urban environments,
according to the results of the intercomparison exercise of urban models
performed by

Many different approaches are currently applied for implementing high
vegetation and its implication in calculation of radiative and energetic
exchanges. Among single-layer models with integrated vegetation schemes,

The building effect parameterization with trees (BEP-Tree) model is the first multilayer model of urban energy exchange and flow at
the neighborhood scale that includes trees and both their radiative

For large eddy simulations (LESs) in an urban environment, a vegetated urban
canopy model (VUC) has been integrated by

Comparison of the spatial arrangement of elements composing the urban canyon and of associated geometric parameters applied in the TEB model in the reference case (top) and in the case with explicit high vegetation (bottom).

Main descriptive parameters of the urban canyon, including vegetation, in the TEB model. The parameters followed by an asterisk are the input data prescribed by user, the other ones are computed in the model using the input parameters.

At each mesoscale model grid point, TEB describes the average characteristics
of the local environment by a single urban canyon composed of a ground-based
surface bordered by two flat-roof buildings of same height. The urban
environment is thus described in TEB based on four distinct elements that
compose the urban canyons: “roof”, “wall”, and for the ground-based
surfaces, a combination of impervious and natural covers referred to as
“road” and “garden”, respectively (Fig.

A set of geometric parameters are defined to describe the canyon
(Table

For natural soils and vegetation, the radiative and energetic exchanges with
atmosphere, as well as the hydrological and thermal processes in the ground,
are parameterized with the interaction soil–biosphere–atmosphere model (ISBA)
model

This reference version of TEB is based on two important simplifications. First, there is no explicit spatial arrangement of the garden within the canyon. They are only represented as land cover fractions. In addition, the vegetation stratum, even if it can be composed of trees (through the definition of specific physiological properties), is always placed on the ground without vertical extent. This means that shadow effects on the ground and buildings related to the presence of high vegetation are not taken into account, and that there is no vertical distribution of turbulent energy exchanges between vegetation and atmosphere.

The present study describes the improvements of the radiation budget
calculations in TEB by the implementation of explicit high vegetation.
Consequently, this section is focused on the description of the radiative
exchanges in the initial version of TEB. The parameterization of turbulent
heat fluxes and of heat conduction processes, as well as the calculations of
microclimate parameters within the canyon, are not presented here but they
are detailed by

The TEB urban canyons are assumed to be of infinite length so that there is no street intersection. The radiative calculations are consequently done on a two-dimensional plane which crosses the canyon according to an axis perpendicular to the street direction. Two main options are available for radiative calculations: (1) a street orientation can be prescribed, so that the two walls of the canyon (referred to as “wall A” and “wall B”) are managed separately; or (2) the hypothesis of isotropic orientation of streets is applied, and in this case, walls are managed together (implying that they will have identical temperature evolutions).

The shortwave and longwave radiation budgets are resolved in TEB for each element composing the urban canyon (roofs, walls, road, ground-based vegetation, and now tree canopy) with the aim of determining the energy absorbed by each element that is used afterward to compute the surface energy budget.

More specifically for the shortwave radiation budget, three contributions are
considered for a given element:

The direct solar radiation received before any reflections depends on zenith angle since the incident direct radiation is unidirectional, street orientation, and canyon aspect ratio.

The diffuse solar radiation received before any reflections depends on the sky view factor of the considered element since the diffuse radiation is assumed to be isotropic.

Finally, the total shortwave radiation received after multiple reflections within the canyon is computed. After a first reflection on one of the elements of the canyon, initial contributions of direct and diffuse radiation are isotropic and are treated the same way. The part of radiation received by a given element then depends on the view factors of all the other elements and on their albedo to determine the reflected radiation part.

Although this paper focuses on resolution and evaluation of the shortwave radiation budget, it is worth to note that the validation of our shortwave radiation scheme contributes to verifying our future longwave radiation scheme. Indeed, the same view factors used for the multiple reflections will be applied to the longwave radiation interactions within the canyon. The longwave exchanges are computed following a linear approximation of the Stefan–Boltzmann law. For numerical stability purposes, an implicit formulation is applied for longwave radiation budgets; it includes the surface temperatures at the previous numerical time step and at the current time step.

To take into account the tree canopy in TEB, it is required to add a new
vegetated stratum on the vertical plane, which can shade the road, the walls,
and the low vegetation. This modification led to more complex radiative
calculations, but is done with a concern to preserve a certain level of
simplicity and to limit the number of new input parameters for TEB. This is
motivated by the type of applications which are conducted with the TEB model,
and more generally with the SURFEX land surface modeling platform

The arrangement of tree canopy is described here using three parameters only
(Fig.

For now, the shape of the foliage and the vertical distribution of leaves are
not defined. The crowns of trees are considered as rectangular
parallelepipeds (namely computed as a rectangular cross-section in a two-dimensional
plane perpendicular to the street axis) with homogeneous foliage
which is described by a leaf area index (LAI

In this part, equations related to the implementation of a tree layer into the TEB model are presented. In order to calculate these terms in TEB, Sect. 4.1 and 4.2 describe how direct and diffuse solar radiation fluxes reach canyon surfaces. Then, absorption is obtained by separately resolving the first absorption of total shortwave radiation on each surface and the sum of absorbed shortwave radiation after infinite reflections within the canyon.

The foliage of trees plays a role of obstruction and attenuation of incident
direct solar radiation (

The direct solar radiation potentially reaching the top of trees by
geometrically taking into account the shading of buildings depends on
building height (

As previously explained, this radiation flux is partially transmitted through
the foliage (

The proportion of direct solar radiation transmitted through the foliage is
estimated by the Beer–Lambert law

The reflected radiation part simply depends on the part of incident solar
radiation untransmitted through the foliage and on the albedo of trees
(

Finally, the incident direct solar radiation part absorbed by trees is
neither transmitted nor reflected and calculated as the residual term from
Eq. (

The direct solar radiation received by the ground (indiscriminately road or
garden fraction) is deduced by correcting the incident solar radiation above
the canyon from the interception of radiation by high-vegetation canopy (i.e.,
reflected and absorbed radiation weighted by high-vegetation cover fraction,
referred to as

In this way, tree foliage is assumed to be uniformly distributed across the
canyon at the height of the trees (

The direct solar radiation which is not received by high vegetation, road or garden is assigned to the sunlit wall, whereas the opposite wall is in the shadow. By convention in TEB in the case of an oriented canyon, we define wall A as the most sunlit wall and wall B as the shaded one.

Note that shading effects of high vegetation on roofs are not represented, since urban trees are less tall than buildings by definition in the current version of TEB (SURFEX v8.0).

The incoming diffuse solar radiation (

We admit that the residual flux of diffuse solar radiation which is not
intercepted in the canyon by previous surfaces reaches the tree canopy:

This method presents two major advantages: (1) the diffuse solar radiation budget is always closed, and (2) the computed diffuse solar radiation flux for the high vegetation is already corrected from the transmitted part, reaching the other surfaces.

The fluxes of each surface are expressed here according to the total
ground-based surface of the canyon, with

The first absorption of total shortwave radiation

For the tree canopy, the part of absorbed direct solar radiation is corrected
by the transmitted flux:

Our goal is to compute the total shortwave radiation absorption for each
element

The view factors related to the high-vegetation stratum are expressed in Appendix A. Specific coefficients are applied, in the shortwave scheme only, to constrain the reflections from the high vegetation toward the sky and the top part of walls. In nature, the solar radiation is mainly redirected upwards by the receiving face of sunlit leaves in the top of crown during the first reflection. We suggest here to neglect the small amount of shortwave radiation which the tree stratum is supposed to reflect to the low part of the canyon during multiple reflections in favor of realistically representing the upward isotropic first reflection of solar radiation, which is by far the most energetic reflection. Solar reflection calculations are fully explained in Appendix C. As previously mentioned, view factors used for the multiple reflections in the shortwave radiation scheme will be applied to the longwave radiation interactions within the canyon in future works.

An objective and exhaustive assessment of the new solar radiation
calculations in TEB related to the inclusion of tree layer effects is not an
easy exercise, essentially due to the lack of experimental data. Indeed, very
few measurements for documenting radiative effects of trees in an urban
environment are available

The SOLENE model

In this research work, we consider the shortwave radiation scheme only. The
incoming direct solar radiation is calculated by considering the sun as a
point source, related to solar height (following the formula in

The trees have been implemented from the evolution of SOLENE into
the microclimate model named SOLENE-microclimat

Description of simple geometries of an urban canyon selected for the comparison between TEB and SOLENE simulations. For each of them, the potential location of tree canopy is illustrated by dotted rectangles.

Description
of the SOLENE mockup and presentation of the ensemble of vegetation layouts
selected for the comparison between TEB and SOLENE simulations. The cases are
presented here for the example of the urban canyon with

List of input parameters for the ensemble of simulations performed with TEB.

The urban canyon geometry chosen for building SOLENE's mockups is as
simple as possible to reflect the hypotheses of TEB: an infinite street
(150 m in length in the mockups) bordered by two identical buildings with flat
roofs. As shown in Fig.

For each of these urban canyons, 13 different vegetation layouts are
prescribed (Fig.

To treat the ensemble of configurations, 55 digital mockups (52 canyons with vegetation and 3 canyons without vegetation) have been built with the computer-aided design (CAD) software Salome V7_4_0. All mockups have been meshed by the GMSH software which is a finite element mesh generator. We have applied a non-uniform meshing here, with a characteristic length of only 1 m in order to refine the spatial discretization of vegetation blocks, whose smallest ones for some of the vegetation layouts do not exceed 2.4 m width and 2.5 m height.

Each canyon is projected following the four street orientations 0, 45, 90,
and 135

In the same way, TEB is run for equivalent configurations to SOLENE
configurations, respecting hypotheses, approaches, and spatial resolution
differences between the two models. For TEB simulations, the geometrical
parameters describing the urban canyon form, as well as the height of trees
and trunks, are comparable to those of SOLENE simulations. But the different
spatial arrangements of trees simulated by SOLENE are simply prescribed as
cover fractions in TEB. As a result, some configurations (e.g., B1 and B2 with
different horizontal locations or B3 and B4 with different numbers of tree
lines, shown in Fig.

Statistical scores for absorbed shortwave radiation flux by surfaces regarding the seasons.

Finally, 880 solar radiation simulations are performed with both TEB and
SOLENE models. For each of them, hourly outputs are stored. They include the
direct and diffuse solar radiation received by the separated elements (road,
walls, and tree) before multiple reflections, as well as the total shortwave
radiation absorbed by the separate elements after multiple reflections. The
main objective of the comparative exercise is to evaluate the cover fraction
approach of TEB against a model (SOLENE) resolving the urban radiation budget
at fine scale and with trees explicitly represented by geometrical elements.
For this purpose, gaps between the simulations of received direct or diffuse
solar radiation fluxes by canyon surfaces have been investigated. During
multiple reflections, the radiation is assumed to be isotropic in both TEB
and SOLENE models. Reflections from the high vegetation in TEB are also
omnidirectional but just constrained upwards (in other words, they are based
on

The indexes

Table

Comparison of
TEB and SOLENE simulations of hourly direct (top) and diffuse
(middle) solar radiation fluxes (W m

The radiative calculations in TEB are first evaluated for the cases without
vegetation. Several comparisons with observations of radiation fluxes at
neighborhood scale have been performed

Scatterplots
comparing TEB and SOLENE simulations of hourly direct (top) and
diffuse (middle) solar radiation fluxes (W m

Both direct and diffuse solar radiation received by the road and the separate
walls before any reflections, as well as the total shortwave radiation
absorbed by these surfaces, are studied. An example of daily cycle is
presented in Fig.

The comparison between SOLENE and TEB simulations for the direct solar
radiation received by road and walls before any reflections highlights very
good results. TEB is able to reproduce the geometrical effects of the canyon
on radiation penetration according to the time of the day, as well as the
street orientation. For northeast–southwest and northwest–southeast-oriented streets, TEB correctly simulates
the dissymmetry of fluxes between the two walls, as well as the
temporal shift in peak of radiation received by the road in comparison with
the north–south-oriented street. For the east–west street case, the direct radiation
received by the road is marked by a plateau effect between 08:00 and
19:00 LT. The two walls have different behaviors: the wall most exposed to
the sun receives the maximum direct radiation at solar noon, whereas the most
shaded wall receives direct radiation only early in the morning and late in
the afternoon. The scores confirm the good performances of TEB: MAD are 4.39
and 2.49 W m

In the calculation of diffuse solar radiation, TEB does not consider the two
walls separately. Therefore, the diffuse solar radiation flux is compared
between the composite wall of TEB and the average of the diffuse solar
radiation fluxes received by separate walls of the SOLENE simulations
(Fig.

Statistical scores for direct solar radiation received by surfaces before multiple reflections for summertime.

Statistical scores for diffuse solar radiation received by surfaces before multiple reflections for summertime.

Statistical scores for total shortwave radiation absorbed by surfaces after multiple reflections for summertime.

Comparison of TEB and SOLENE simulations of hourly direct
(top) and diffuse (middle) solar radiation fluxes (W m

Finally, the total shortwave radiation absorbed by road and walls is well
estimated by TEB despite the simplified hypotheses of the model and the use
of a unique sky view factor by the surface: MAD and biases are 6.03 and

The same evaluations are conducted for vegetated canyons. The statistical
scores are computed as previously (see Eqs.

The daily evolution of direct solar radiation received by the different
elements of the canyon can be compared to the case without vegetation
(Fig.

As expressed in Eqs. (

For the same configuration, when comparing TEB results to the SOLENE simulations
as reference, the total shortwave radiation absorbed by the different
elements of the canyon is simulated with correct daily dynamics
(Fig.

Further works (not shown) have investigated the sensitivity of TEB results and performances according to the characteristics of the different vegetation layouts. They do not demonstrate clear and systematic patterns when studying the impact of (1) tree horizontal coverage (or the tree fraction), (2) tree canopy height compared to the building height, and (3) tree location – centered or on the side – in the canyon on the MAD and difference percentages recorded. It could be explained by the interaction between opposite effects regarding the vegetation layout characteristics.

In this section, simulations provided by the initial version of TEB and by the implemented version are compared. For this
purpose, we use equations in the new version related to the transmission of
radiation fluxes from the high vegetation following the expression presented
in Eq. (

Scatterplots
comparing TEB and SOLENE simulations of hourly direct (top) and
diffuse (middle) solar radiation fluxes (W m

Comparison of
the total shortwave radiation flux (W m

The shortwave radiation received and absorbed by the walls and the road can
be strongly affected by the presence of tree vegetation. The comparison
between the initial version of TEB which deals with vegetation at ground
level, and the new version which explicitly includes an additional tree
stratum shows differences illustrated in Fig.

Comparing the fluxes before and after their weighting based on their canyon
fraction, the road absorption by squared meters of canyon can extremely vary
following the garden fraction at the ground in the initial version. Indeed,
in the reference cases, the high vegetation is treated as a ground-based
vegetation fraction which is included in the garden fraction
(

The albedo of the canyon (

Comparison of
the canyon albedo at solar noon between the reference TEB simulations without
distinction between low and high vegetation, and the new version including a
tree canopy by aspect ratios for all vegetation layouts combined within
north–south-oriented canyons during a summer day. See Sect. 5.2.1 and
Fig.

For each simulation, these fluxes are used at the solar noon in order to
compute an instantaneous canyon albedo. The results in summertime are
presented as box plots (Fig.

The aspect ratio has a significant impact on the canyon albedo: the canyon
albedo decreases with an increasing aspect ratio. Since the geometry and
radiative properties of the vegetationless canyons and ground-based
vegetation canyons in the reference version of TEB are comparable, they
provide similar canyon albedos. It is explained by the absence of foliage in
the vertical plane and identical albedos of road and garden (

In order to investigate some of the physical processes related to the presence of vegetation in an urban environment, e.g., for microclimate, hydrology, or building energy consumption issues, the modeling is definitely a necessary tool.

The TEB model has been refined and improved in order to explicitly represent street trees and their impacts on radiative transfer. The new parameterization is based on the simple hypotheses of TEB: (1) a little-detailed geometry without specific spatial arrangement of ground-based surfaces and (2) a single view factor for each emitting and receiving surface applied for radiative calculations.

To take into account the tree canopy in TEB, it was however required to add a new vegetated stratum on the vertical plane, which can shade the road, the walls, and the low vegetation. This modification led to more complex radiative calculations, but has been done with a concern to preserve a certain level of simplicity and to limit the number of new input parameters for TEB. It is important to emphasize that the model is designed to be run over whole cities, for which it can simulate the local climatic variability related to urban landscape heterogeneities at the neighborhood scale. This means that computing times must be acceptable, and that input urban data must be available or easy to define. Consequently, the high vegetation is described here using only five input parameters: cover fraction of trees, height of trees, height of trunks, leaf area index, and albedo.

This simplified characterization of high vegetation necessarily induces some
uncertainties on solar radiative exchanges. We estimated it by carrying out a
comparative exercise between TEB and a high-spatial-resolution solar and
lighting model (SOLENE). On the basis of an idealized geometry of an urban
canyon with various vegetation layouts, TEB is evaluated regarding the total
shortwave radiation flux absorbed by the elements that compose the canyon.
TEB simulations in summer gathered the best scores for all configurations and
surfaces considered, which is precisely the most relevant season to assess
the cooling effect of deciduous trees under temperate climate. Statistical
scores have demonstrated a good capacity of TEB to solve the radiative
balance of canyons without vegetation despite the use of a unique sky view
factor for each facet of the urban scene. Mean absolute differences and
biases of 6.03 and

The parameterization of shortwave radiation exchanges within the canyon is
now more realistic: shading effects of trees on vertical and ground-based
surfaces but also shading effects of buildings on trees are computed. This is
achieved by adding a new specific cover fraction describing the horizontal
extent of high vegetation. Infinite reflections within the canyon are also
conditioned to the transmissivity term calculated per pair of exchanging
surfaces. This study demonstrated the enhancement of new developments on the
computed absorbed shortwave radiation fluxes within the canyon between the
former reference version of TEB and the implemented version. In the current
version, trees can intercept and absorb the direct solar radiation at the
canopy level instead of from the ground. Consequently, the walls and ground
are more shaded. High and low vegetation fractions are now explicitly
dissociated. The grass and bare soil fractions only contribute to the garden
fraction. In this way, the road fraction, defined as

The future developments will focus on the separate calculation of turbulent energy fluxes for ground-based and high vegetation. The aerodynamic effect of trees on air flow within the canyon should also be parameterized. The adaptation of TEB to trees taller than buildings will broaden the range of potential neighborhoods to which its tree model could be applied. Based on this more sophisticated version of TEB, new impact studies could be conducted and greening adaptation strategies could be evaluated more precisely.

The TEB code is available in open source via the surface modeling platform
SURFEX, downloadable at

Sky view factors for road, garden, and wall (Eqs.

For the tree canopy, the sky view factor and view factors from road and walls
are computed in the middle of the canyon and at mid-height of the crown
(

The multiple reflections of solar radiation inside the canyon (as detailed in

Different transmissivity functions (referred to as

The limits of integrals involved in the calculation of the transmissivity
functions have been consistently defined with canyon sectors scanned by the
associated view factors. For example, Eq. (

Note that these expressions are in accordance with the one applied in
Eq. (

For solar radiation calculations, the TEB model takes into account an
infinite number of reflections between all elements composing the urban
canyon. At each reflection, the isotropic radiation intercepted by a given
element, (

The specific coefficients associated with the view factors related to the high
vegetation in shortwave reflections calculations are defined as

Only reflections from trees to sky or top part of walls are allowed. As explained in Sect. 4.4, this mode of reflection by the leaves during the first reflection, which is by far the most energetic one, is more likely to occur than in an isotropic way. This assumption could be easily bypassed by fixing the previous coefficients to 1.

For the first tree canopy reflection, the part of received direct solar
radiation is corrected by the transmitted flux (see Eq.

Some uncertainties remain about relevance of sky view or view factors which
could formulate to represent reflective contributions from other
surfaces at

During each inter-reflection, a part of

Finally, the solar flux which is intercepted by “tree” at

The solar energy which is reflected by tree at

The formulations can be simplified by gathering the equations for walls in a
single expression for a mean wall according to

As a result, after an infinite number of reflections, the equation system can
be written as

As a result, we resolve the linear system of four equations with four
unknowns:

The geometric and reflective factors are computed as the following:

The resolution of the equation system gives the following expressions for multiple reflections on tree, walls, road, and garden:

The denominator is expressed as the following:

The authors declare that they have no conflict of interest.

We acknowledge Laurent Malys for his technical support on the first SOLENE runs. We thank the anonymous reviewers for their helpful comments. Edited by: T. Poulet Reviewed by: two anonymous referees