This paper describes the developing theory and underlying processes of the microscale obstacle-resolving model MITRAS version 2. MITRAS calculates wind, temperature, humidity, and precipitation fields, as well as transport within the obstacle layer using Reynolds averaging. It explicitly resolves obstacles, including buildings and overhanging obstacles, to consider their aerodynamic and thermodynamic effects. Buildings are represented by impermeable grid cells at the building positions so that the wind speed vanishes in these grid cells. Wall functions are used to calculate appropriate turbulent fluxes. Most exchange processes at the obstacle surfaces are considered in MITRAS, including turbulent and radiative processes, in order to obtain an accurate surface temperature. MITRAS is also able to simulate the effect of wind turbines. They are parameterized using the actuator-disk concept to account for the reduction in wind speed. The turbulence generation in the wake of a wind turbine is parameterized by adding an additional part to the turbulence mechanical production term in the turbulent kinetic energy equation. Effects of trees are considered explicitly, including the wind speed reduction, turbulence production, and dissipation due to drag forces from plant foliage elements, as well as the radiation absorption and shading. The paper provides not only documentation of the model dynamics and numerical framework but also a solid foundation for future microscale model extensions.

The urban boundary layer is considerably influenced by its surface characteristics. Within the canopy layer, atmospheric flow is disturbed by buildings and other obstacles located at the surface and hence all related atmospheric processes (Meng, 2015). This creates a complex three-dimensional, time-dependent flow, temperature, and humidity field. Studying the atmospheric boundary layer flow and its interactions with complex terrain in, e.g., urban areas is a complex problem for both the meteorological and engineering communities. Field experiments are one approach (e.g., Schafer et al., 2005); however, field measurements have a low spatial representativeness and largely depend on the turbulence structure within the urban area and the wind direction fluctuations. This implies that long averaging times are needed in order to obtain reasonable time-averaged values; on the other hand, long averaging times are not feasible because the atmospheric situation changes due to, e.g., the diurnal cycle or synoptic changes. Also, investigating future scenarios is not possible from field measurements. Subsequently, laboratory experiments in controlled conditions (wind tunnel) are used to overcome these problems after matching the major similarity parameters with the full-scale model. These physical models can be very detailed (Harms et al., 2011) and can provide comparison data for numerical models and field experiments (VDI, 2015). However, wind tunnel modeling is mostly limited to neutral atmospheric stratification due to the requirement of similarity to nature. Furthermore, it is sometimes difficult to satisfy the atmospheric boundary conditions and to resemble important features of the Earth system such as the Coriolis force effect. Alternatively, high-resolution numerical computer models are frequently used to simulate urban areas.

Numerical modeling of wind flow and pollutant dispersion in urban areas is a challenging task due to the geometrical variety of buildings. It inevitably involves impingement and separation regions, a multiple vortex system with building wakes, and jet effects in street canyons (Murakami et al., 1999). Furthermore, the neighbor buildings add their own impacts on the urban meteorology, resulting in interacting flow and dispersion patterns. Due to this complexity, explicit resolving of the buildings is necessary instead of only implicitly considering building effects by using surface roughness parameterizations. This gave rise to the development of obstacle-resolving microscale meteorological models such as PALM (Maronga et al., 2015), ASMUS (Gross, 2012), ENVI-met (Bruse and Fleer, 1998; Müller et al., 2014), MISKAM (Eichhorn, 1989; Eichhorn and Kniffka, 2010), MUKLIMO (Früh et al., 2011), MITRAS (Schlünzen et al., 2003; Salim et al., 2011), and OpenFOAM (Franke et al., 2012). These models are now widely used for environmental and engineering studies.

The microscale obstacle-resolving transport and stream model MITRAS is part of the M-SYS model system (Trukenmuller et al., 2004; Schatzmann et al., 2006). This model system is designed to investigate pollution transport, chemical reactions, and atmospheric phenomena in the atmospheric boundary layer. The obstacle-resolving MITRAS model calculates wind, temperature, humidity fields, cloud, and rainwater, as well as tracer transport within the obstacle layer. The model has been applied for more than 10 years; however, an overall description of the model theory has not been published in a refereed journal. This is timely because computers now allow for time-dependent long-term integration of the temperature and humidity equations in high resolution. In addition, MITRAS in its version 2 was extended and optimized for more realistic applications in urban areas (Salim et al., 2011; Röber et al., 2013). Specifically, more surface cover classes were added to better describe surface characteristics: fine tuning the code structure for maximum parallelization to make it faster and able to simulate larger domains and parameterizing the additional radiation, turbulence production and dissipation due to wind turbines, and urban vegetation.

Model validations of MITRAS-01 have been performed in comparison to wind tunnel data (Schlünzen et al., 2003; Grawe et al., 2013). MITRAS 2 is evaluated using the VDI guideline for obstacle-resolving microscale models (Grawe et al., 2015). The results will be presented in a separate paper.

Equations and the solution method will be described in Sect. 2, including the turbulence parameterization (Sect. 2.2) and numerical treatment (Sect. 2.3). Further sub-grid-scale processes need to be parameterized, even in a very highly resolving atmospheric model like MITRAS. This concerns cloud microphysical processes and radiation. Both are calculated with the same parameterizations as its sister model METRAS (Schlünzen, 2003; Schlünzen et al., 2018b). The boundary conditions, including surface, lateral, and top boundaries, are given in Sect. 3. The treatment of obstacle-induced effects is described in Sect. 4, including wind, shading, and heat transfer effects. MITRAS parameterizes momentum and heat fluxes on obstacle surfaces dependent on the local roughness length (Sect. 4.1, 4.2) and explicitly resolves obstacles such as buildings, including overhanging obstacles (e.g., bridges or overpasses), trees, and wind turbines, to account for its aerodynamics and thermodynamic effects. The handling of wind turbines in the model and their effects is described in Sect. 4.3. Vegetation effects, especially their effect on radiation, are given in Sect. 4.4.

MITRAS is based on the physical conservation equations, specifically the Navier–Stokes equations, the continuity equation, and the conservation equation for scalar quantities such as potential temperature and humidity. This set of equations is written in flux form, transformed in a terrain-following coordinate system and filtered before it is used in MITRAS.

The equations of MITRAS in flux
form are transformed in a three-dimensional nonuniform terrain-following
coordinate system

Here

Vertical cross section to illustrate the MITRAS grid in the terrain-following coordinate system (not to scale). The blue blocks denote buildings. Not all grid cells are shown.

Reynolds averaging is used to filter the equations after the coordinate
transformation: the atmospheric state variables are divided into a value

To increase the numerical accuracy further, the pressure deviation,

The Boussinesq approximation is used, and thus density variations in the
Navier–Stokes equations are neglected except for the buoyancy term.

The solved prognostic equations in MITRAS are as follows.

Due to the filtering, sub-grid-scale (SGS) fluxes arise. The three SGS
turbulent fluxes in the momentum equations (

The SGS fluxes can be expressed in terms of the Reynolds stress tensor

At the lowest model layer, the validity of Monin–Obukhov surface layer
similarity theory (Monin and Obukhov, 1954; Foken, 2006) is assumed. The grid-box-averaged values of

Above the lowermost model layer the SGS turbulent fluxes are derived from a
first-order closure (Detering, 1985; Etling, 1987).

The turbulent fluxes for scalar quantities, e.g., potential temperature, are
expressed as

The exchange coefficients in MITRAS are either calculated using the
Prandtl–Kolmogorov closure (Sect. 2.2.3, first subsection) or the

Sketch showing the staggering of the variables of a domain
in

The exchange coefficients are calculated as follows.

This closure is based on the standard

It has been shown by Schlünzen et al. (2003) that using Kato and
Launder (1993) modifications for both the turbulent kinetic energy equation
and the dissipation equation in MITRAS leads to overestimation of the
momentum fluxes at the stagnation point. To overcome this drawback, they
suggested limiting the Kato and Launder reformulation to the energy equation
only. So, for the

The buoyancy term is calculated in the same way as in the
Prandtl–Kolmogorov closure. The values for the constants

The model equations are solved using finite-volume methods on a staggered
Arakawa C grid (Arakawa and Lamb, 1977). On this grid, scalar variables are
defined at the cell center, while the velocity components are defined on their
respective normal cell faces (Fig. 2). The obstacles faces are set where the
corresponding wall normal velocity components are defined. Since

The advection and diffusion terms in the momentum equations are solved in
MITRAS using the Adam–Bashforth scheme in time and centered differences in
space. The vertical diffusion terms are determined using the Crank–Nicholson
implicit scheme in order to increase the time step for vertical exchange
processes. All other terms in the momentum equations except dynamic pressure

The dynamic pressure

To avoid numerical artifacts that might appear due to nonlinear interactions and result in shortwave energy accumulation, artificial diffusivity is added.

The advection of scalar quantities is solved forward in time and using the
upstream scheme for advection. Even though the upstream method is known for being
diffusive with its implicit diffusivity

Since Eq. (13) implies that dissipation rate and sub-grid-scale turbulent
kinetic energy are directly coupled, the dissipation cannot be calculated
with very large time steps. Equation (13) is solved by determining an
analytic solution (Appendix A) as suggested by Fock (2015). This avoids
unphysical values of

In MITRAS, several types of boundary conditions can be used in physically consistent combinations to allow for different kinds of simulations. At the ground surface (lower boundary) and obstacle faces (Sect. 4) material interfaces are given, while the lateral boundaries and the upper boundary are artificial due to the use of a limited area model.

For the horizontal wind velocity components, a no-slip boundary condition
(

The boundary condition for the pressure

Due to the terrain-following coordinate system (Eq. 1) the vertical gradient
of the dynamic pressure

The calculated temperature values of all physical boundaries (ground and
obstacles surfaces, i.e., wall and roof) are used at the lower boundary and
at the obstacle surfaces. The necessary additions for buildings are provided
in Sect. 4.2. These temperature values are calculated using the force-restore
method for the ground soil heat flux. Following Tiedtke and Geleyn (1975) and
Deardorff (1978), the temperature at the surface,

Both

For obstacles, the calculated surface temperature (Sect. 4.2) of the obstacle surfaces is used at the corresponding grid cells.

The following budget equation, introduced by Deardorff (1978), is used to
calculate the humidity at the lower boundary (

At the ground surface and at the obstacle surface

The empirical constant

Dirichlet boundary conditions are used in two different formulations. They can be used in MITRAS in arbitrary combinations to describe the lateral boundaries of the domain: open boundary (radiative) and fixed boundaries. The appropriate combination of boundary value calculations depends on the application. For instance, a realistic application with comparison to field data in mind needs open boundaries. In these the boundary normal wind components are calculated as far as possible from the prognostic equations. The boundary normal advection is treated with the use of the Orlanski condition at inflow boundaries and by the upstream scheme at outflow boundaries. For the boundary parallel velocity components a zero-flux condition is assumed (Schlünzen, 1990).

When comparison with wind tunnel measurements (e.g., Grawe et al., 2013b) is performed, fixed boundaries are advantageous. In these the wind profiles are to be imposed at the inlet boundary and kept fixed at the initial values, while at the outflow the wind velocity is treated as an open boundary.

The normal gradients of pressure

For the vertical wind, which is defined at the model top, the Dirichlet condition
is used, prescribing it to initial values (mostly vertical wind zero). For
all other variables a Neumann boundary condition is employed for which the
gradients normal to the boundary are zero. In order to avoid reflections of
vertically propagating waves at the upper model boundary, Rayleigh damping
layers (absorbing layers) are used in MITRAS. The Rayleigh damping terms,
which are added to the flow equations (Eqs. 3–6), are written here.

The normal pressure gradient, temperature gradient, turbulent momentum fluxes, and their gradients are all set to zero at the upper boundary. This assumption results in zero vertical heat and moisture fluxes as well as zero momentum fluxes at the upper model boundary.

The concept of the mask method (Briscolini and Santangelo, 1989) is employed
in MITRAS to explicitly resolve the buildings within the 3-D model domain.
This method is based on the immersed boundary method (Mittal and Iaccarino,
2005), which allows for flow simulation in the vicinity of complex geometries that
do not conform on Cartesian grids. Impermeable grid cells at the building
positions are defined using 3-D fields of weighting factors, vol(

A building mask containing these data is prepared by the preprocessor GRIMASK (Sect. 5.3). In the model, e.g., the wind velocity components vanish at the building boundaries by multiplying the fluxes with the face markers (impermeable walls). Additional wall functions are included to address friction effects properly.

Masking concept in MITRAS.

Building surfaces influence the ambient air temperature. Their effect is
taken into account by simulating the sensible heat flux. In grid cells that
are adjacent to building surfaces, the term

This concept allows for a consideration of not only surface-mounted buildings but also overhanging obstacles such as bridges and overpasses or pathways to courtyards. They can all be considered in complex urban geometries.

In order to obtain an accurate surface temperature of the buildings (obstacles), most exchange processes at the building surfaces are considered in MITRAS, including turbulent and radiative processes (Gierisch, 2011). Thus, the physical properties of the façade and wall materials are to be introduced as model inputs. These properties include reflectivity, emissivity, heat transfer coefficient, and specific heat capacity.

The surface temperature of a building surface,

The rate of temperature change of the slab is governed by the imbalance
between the forcing term

The surface energy balance for the inside wall surface can be written as

From Eq. (34), the relation between

Substituting for

Wind turbines are represented in MITRAS by impermeable grid cells at the position of the tower and the nacelle, similar to other buildings (i.e., vanishing wind speed and zero turbulent kinetic energy are assumed at grid points within the tower and nacelle). The orientation of the nacelle changes in relation to the wind direction during the model simulation. The wind turbine rotor is parameterized by using the actuator-disk concept (Molly, 1978; Mikkelsen, 2003; El Kasmi and Masson, 2008). In this concept the rotor is replaced by an imaginary permeable disk subjected to a distribution of forces that acts upon the incoming flow at a rate defined by the period-averaged kinetic energy that the rotor extracts from the atmosphere.

According to the actuator-disk model, the reduction of the wind speed is
caused by the rotor thrust,

This wind turbine rotor blades create wake vortices of the wind turbines,
which are associated with increased turbulence intensity. The turbulence
generation in the wake is parameterized in MITRAS by adding an additional
term,

In MITRAS, the tangential velocity

There are two modes of vegetation treatment in MITRAS: the implicit mode and the explicit mode. In the implicit mode, the effect of the vegetation (grass, bushes, trees, etc.) is implicitly considered in the surface parameterization using the roughness length. This is done by allocating the vegetation surface cover class for the corresponding surface grid cells and using the corresponding input parameters (e.g., roughness length, soil water, content, etc.; Sect. 5.2).

Principal elements of the MITRAS model inputs.

In explicit mode, vegetation effects are explicitly resolved. These effects include wind speed reduction (Schlüter, 2006), turbulence dissipation due to drag forces from plant foliage–atmosphere interaction (Salim et al., 2015), and radiation absorption and shading.

The wind speed reduction is parameterized by introducing a local
three-dimensional sink term,

Here

The reduction of the shortwave radiation flux is considered by including
local reduction coefficients (ranging from 1 to 0) according to the vegetation
characteristics. The reduction coefficients are described in terms of the
vertical leaf area index, LAI, of the plant (see Sect. 5.4).

Several model inputs are required to run MITRAS to accurately simulate a domain for, e.g., an urban area (Fig. 4). These include, for instance, the orography heights of the domain, the surface cover types, the building data (dimensions, shape, and position), and the vegetation data for such a domain. Integrating these inputs to the computational domain of MITRAS is done in a separate preprocessor called GRIMASK (Salim, 2014). A complete description of this preprocessor is outside the scope of this paper, but the required input data and how they are in general achieved is outlined here (Sect. 5.1–5.4). Moreover, the representative meteorological conditions for the domain are required as inputs to run MITRAS; they are provided in consistency with the model physics and numeric using a preprocessor.

The physical parameters for some surface cover classes as used in
MITRAS: albedo (

Urban domains might include elevated terrain. To better describe the domain
terrain, the orographic effects of the domain are considered in MITRAS by
virtue of the terrain-following coordinate system (Sect. 2.1). Both the
aerodynamic and the radiative (shading) effects of the slopes are
considered in MITRAS. For realistic applications, the orography data (terrain
height above sea level) of the domain are introduced to GRIMASK in the standard
ASCII grid format of a geographic information system (GIS). Usually these
data are in much finer resolution (less than 0.25 m) compared to the
computational domain horizontal resolution (

For idealized studies and test cases, GRIMASK can generate artificial orography heights according to the objective of the test case, e.g., a bell mouth hill or a Gaussian hill.

It is essential to define the surface cover characteristics of the urban
domain because they govern the surface energy budget (Eq. 19) and all surface-dependent fluxes. In realistic cases, the urban domain usually contains
several surface cover types (water, sealed surfaces, vegetation, sand, ice,
etc.) and it becomes imperative to define an appropriate data structure to
encode information on surface cover characteristics. To this purpose, the
surface cover data are first introduced to GRIMASK in the GIS standard ASCII
grid format. GRIMASK then integrates these data into the computational grid
cells at the surface. Each grid cell is composed of at least one surface
cover class, but more SGS surface covers are allowed. The preprocessor
calculates how many surface cover classes exist in the domain and the
portion of each surface cover class in each grid cell. This is done following
the approach used to calculate the orography heights. Each grid cell at the
surface is divided into sub-grids and the surface cover class of each
sub-grid is defined. The data structure of the surface cover consists of two
datasets: (a) the portion of each surface cover class in each grid cell and
(b) a list of surface cover classes existing in the domain. Several classes
are also prepared in the surface cover class database for the different
vegetation types (coniferous trees, deciduous trees, bushes, etc.). A
database of several surface cover classes with attributed physical
parameters is available in the 1-D MITRAS model. The physical parameters
given per surface cover class include albedo (

For buildings the explicit treatment is normally chosen. If the implicit
consideration of obstacles is chosen, i.e., they are not explicitly resolved
in the model grid, a much larger roughness length would be required, which
conflicts with a high vertical grid resolution. This is similarly true for
trees. The roughness length for water is modified during the model
calculations with dependence on wind speed (Fischereit et al., 2016). The
roughness length of scalar quantities over water,

To distinguish surface cover classes, water, buildings, and sea ice, identifiers are incorporated for each surface cover class. These act as the Kronecker delta function to mark the particular class.

In order to generate the building mask used to provide the building data to the model, detailed information about the buildings in the domain is required. For instance, the building dimensions, shape, and location are needed for each building located in the domain to calculate the 3-D array volume and the building wall-based markers discussed in Sect. 4.1. This process is done in the preprocessor, GRIMASK, which allocates the buildings to the computational grid.

Since in the current version of MITRAS the 3-D field volume can be either 0 (building cell) or 1 (atmosphere cell), buildings are approximated to fit into the grid. For grid cells that are partially filled with buildings, the determination of whether these cells are building or atmosphere cells depends on how much volume of the cell is filled with building. A grid cell is considered a building cell if at least 50 % of its volume contains building. Otherwise it is counted as an atmosphere cell. This approximation is computationally efficient to consider the effect of buildings since the model equations only need to be multiplied by the 3-D field volume.

For realistic applications, complex urban building geometry can be
provided to GRIMASK in either the raster digital elevation model (DEM)
format, which is commonly used due to the advances in remote sensing
technologies, or in the ASCII 3-D computer-aided design (CAD) format. GRIMASK
integrates the high-resolution DEM data, which is a grid of squares
representing the elevation of each small grid, to the computational grid and
calculates how much volume of the building is contained in each grid cell.
When the building data are provided in the ASCII CAD format, GRIMASK uses an
approach similar to

The vegetation input to MITRAS depends on the selected vegetation treatment
in the model. In the implicit mode, the vegetation is defined as a surface
cover class (Sect. 5.2). In explicit mode, however, vegetation inputs
are the 3-D arrays LAD and LAI prepared by GRIMASK. Two approaches are
available in GRIMASK in order to calculate these arrays based on the
available plant data: the measurement approach and the analytic approach. In
the first approach, the following data for each plant in the model area are
processed in GRIMASK: the measured 1-D vertical leaf area index profile
LAI(

In the analytical approach, GRIMASK uses the following empirical relation
proposed by Lalic and Mihailovic (2004) to describe LAD profile from plant
parameters.

The plant parameters used in these equations can be obtained from the forest phenology calendar.

A large-scale surface-friction-free meteorological situation is required as input to MITRAS to calculate the microclimate of a certain domain. This input is prepared by a one-dimensional model without explicit consideration of buildings but with inclusion of all relevant turbulence processes (including surface friction and Coriolis force) to provide the required meteorology data needed for the initialization of all the variables in the three-dimensional model. Among the inputs for the one-dimensional model are the large-scale speed wind components, which are taken to be the geostrophic wind and should not include any frictional effects or wind rotation with height that will both be imposed by the 1-D model, the large-scale potential temperature gradient or temperature profile, the large-scale relative humidity profile, the deep soil temperature, and the number of days without precipitation (dry days) prior to the simulation. The one-dimensional model calculates the initial values, the wind inflow profile if fixed boundary values are used, and the values at the top boundary. Since the one-dimensional model calculates the average mesoscale conditions, large-scale phenomena can be integrated into the model by controlling the inlet boundary condition using the time-slice approach for nesting (Schlünzen et al., 1990). For some applications (e.g., comparisons with wind tunnel data) it is essential to fix the inflow profiles as described in Sect. 3.2.

This section provides examples of some simulations recently performed using MITRAS. The intent is not to provide model validations or verifications, as these will be done in a separate paper with a focus on this aspect, but rather to give the readers some impression about the model capacities and potential.

MITRAS results have been frequently compared to measurements of physical
models. For instance, Grawe et al. (2013) compared MITRAS results based on an
earlier model version to quality-ensured wind tunnel data for both idealized
(flow around quasi-two-dimensional beam, single cubic obstacle, and array of
cubic obstacles) and realistic (

Wind field at pedestrian height level in the city center of Hamburg
(Germany) showing the normalized wind speed

Snapshot of the wind speed in the city center of Hamburg (Germany)
from a simulation that includes the effect of trees. The simulated domain
(

MITRAS has been used to simulate the wind flow field in the city center of
Hamburg in Germany. The selected domain has a size of

Vertical cross section at the center of a high-rise building located
in Hamburg (Germany) on 1 February at 13:30 parallel to the wind direction.
Colors show the potential temperature of the air surrounding the building and
arrows depict the wind circulation for both the reference case (no thermal
energy exchange between building façades and environment,

MITRAS simulations with different parameterizations of urban vegetation (especially trees) were recently performed by Salim et al. (2015) to study the effect of the inclusion of trees when simulating the wind flow in different urban complexities. This study showed a significant effect of trees on the wind field and thus highlights the importance of the explicit representation of urban trees in microscale simulations. A snapshot of an animation created from the simulations performed in this study is shown in Fig. 6 and displays the wind field when the trees are considered in the simulation together with the tree sizes and locations. More details about this study can be found in Salim et al. (2015).

To show the thermal effect of a building on its surroundings, several
simulations have been done using MITRAS. The building surface temperature is
calculated as described in Sect. 4.2 to simulate a single high-rise building
located in an urban area in Hamburg on 1 February at 13:30 (GMT

Horizontal cross section of the domain at 38 m of height showing

The model MITRAS, with embedded wind turbine parameterizations (see Sect. 4.3), has been used to produce simulation data for model validations (Linde, 2011). The selected case in this study involved the Nibe wind turbines in Nibe, Denmark. This case is selected because there is a meteorological measurement dataset for these wind turbines (Taylor, 1990). Figure 8 gives one example of the model results from this study. Comparisons of model results with the measurements showed a good agreement.

The model theory of the obstacle-resolving microscale meteorological model
MITRAS version 2 has been described in this paper. Detailed descriptions of
the model equations and their formulations and approximations are presented.
The sub-grid-scale turbulence parameterization used in MITRAS is outlined
showing the Prandtl–Kolmogorov closure and the 1.5-order

Verification experiments of MITRAS version 2 with the simulation of urban areas with explicitly resolved obstacles (including buildings, wind turbines, and trees) will be presented in a separate paper. A recent application of MITRAS version 2 to vegetation effects in urban areas can be found in Salim et al. (2015).

Currently the MITRAS source code is distributed upon
request under the terms of a user agreement with the Mesoscale and Microscale
Modeling (MeMi) working group at the Meteorological Institute, University
of Hamburg (

Documentation for the M-SYS model system (Schlünzen et al., 2018a, b), in
which MITRAS is included, is available online at

The numerical method for calculating the dissipation term in the SGS TKE
equation is based on splitting the SGS TKE prognostic equation into two
parts. In the first part all processes except dissipation are integrated
within a time step

The dissipation is parameterized according to Eq. (13), which can be
simplified as

By integrating Eq. (A3), assuming

A similar solution for the dissipation term in the TKE equation of the SGS model suggested by Deardorff (1980), suitable for large eddy simulation, is presented in Fock (2015).

MS organized the paper and collected the contributions.
He also developed the preprocessor GRIMASK and is responsible for the ideas
behind it (Sect. 4). He included different vegetation treatments in MITRAS
(Sect. 4.4) and provided model results on this (Sect. 6.3) as well as a
realistic application (Sect. 6.2). HS coordinated the model development since
the beginning and is overall responsible for the model and its documentation.
She provided a number of comments on the paper, as did DG, who is
responsible for model evaluation (Sect. 6.1) and aspects concerning model quality
assurance and code provision. MB contributed the wind turbine development to
MITRAS (Sect. 4.3) and corresponding results (Sect. 6.5), and AG implemented the
calculation of building surface temperatures (Sect. 4.3) and provided results
on this (Sect. 6.4). BF derived the analytic solution for the

The authors declare that they have no conflict of interest.

This research is supported through the Cluster of Excellence “CliSAP” (EXC177) and the research project UrbMod funded by the state of Hamburg, Germany. The authors would like to thank the two anonymous reviewers and the topical editor David Ham for their helpful and constructive comments and support during the review process. Edited by: David Ham Reviewed by: two anonymous referees