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Geosci. Model Dev., 13, 1335–1372, 2020 https://doi.org/10.5194/gmd-13-1335-2020 © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. Overview of the PALM model system 6.0 Björn Maronga1,2 , Sabine Banzhaf3 , Cornelia Burmeister4 , Thomas Esch5 , Renate Forkel6 , Dominik Fröhlich7 , Vladimir Fuka8 , Katrin Frieda Gehrke1 , Jan Geletič9 , Sebastian Giersch1 , Tobias Gronemeier1 , Günter Groß1 , Wieke Heldens5 , Antti Hellsten10 , Fabian Hoffmann1,a,b , Atsushi Inagaki11 , Eckhard Kadasch12 , Farah Kanani-Sühring1 , Klaus Ketelsen13 , Basit Ali Khan6 , Christoph Knigge1,12 , Helge Knoop1 , Pavel Krč9 , Mona Kurppa14 , Halim Maamari15 , Andreas Matzarakis7 , Matthias Mauder6 , Matthias Pallasch15 , Dirk Pavlik4 , Jens Pfafferott16 , Jaroslav Resler9 , Sascha Rissmann17 , Emmanuele Russo3,c,d , Mohamed Salim17,18 , Michael Schrempf1 , Johannes Schwenkel1 , Gunther Seckmeyer1 , Sebastian Schubert17 , Matthias Sühring1 , Robert von Tils1,4 , Lukas Vollmer19,e , Simon Ward1 , Björn Witha19,f , Hauke Wurps19 , Julian Zeidler5 , and Siegfried Raasch1 1 Institute of Meteorology and Climatology, Leibniz University Hannover, Hannover, Germany 2 Geophysical Institute, University of Bergen, Bergen, Norway 3 Institut für Meteorologie, Freie Universität Berlin, Berlin, Germany 4 GEO-NET Environmental Services GmbH, Hannover, Germany 5 German Aerospace Center (DLR), German Remote Sensing Data Center (DFD), Oberpfaffenhofen, Germany 6 Karlsruhe Institute of Technology, IMK-IFU, Garmisch-Partenkirchen, Germany 7 Research Center Human Biometeorology, Deutscher Wetterdienst, Freiburg, Germany 8 Department of Atmospheric Physics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic 9 Institute of Computer Science, The Czech Academy of Sciences, Prague, Czech Republic 10 Finnish Meteorological Institute, Helsinki, Finland 11 School of Environment and Society, Tokyo Institute of Technology, Tokyo, Japan 12 Deutscher Wetterdienst, Offenbach, Germany 13 Software Consultant, Berlin, Germany 14 Institute for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, Helsinki, Finland 15 Ingenieurgesellschaft Prof. Dr. Sieker mbH, Hoppegarten, Germany 16 Hochschule Offenburg, Offenburg, Germany 17 Geography Department, Humboldt-Universität zu Berlin, Berlin, Germany 18 Faculty of Energy Engineering, Aswan University, Aswan, Egypt 19 Carl von Ossietzky Universität Oldenburg, ForWind – Research Center of Wind Energy, Oldenburg, Germany a currently at: Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, CO, USA b currently at: NOAA Earth Systems Research Laboratory, Chemical Sciences Division, Boulder, CO, USA c currently at: Oeschger Centre for Climate Change Research, University of Bern, Bern, Switzerland d currently at: Climate and Environmental Physics, Physics Institute, University of Bern, Bern, Switzerland e currently at: Fraunhofer Institute for Wind Energy Systems, Oldenburg, Germany f currently at: energy & meteo systems GmbH, Oldenburg, Germany Correspondence: Björn Maronga (maronga@muk.uni-hannover.de) Received: 13 April 2019 – Discussion started: 7 June 2019 Revised: 12 November 2019 – Accepted: 19 January 2020 – Published: 20 March 2020 Published by Copernicus Publications on behalf of the European Geosciences Union.
1336 B. Maronga et al.: The PALM model system 6.0
Abstract. In this paper, we describe the PALM model system method along the x and y directions on a Cartesian grid with
6.0. PALM (formerly an abbreviation for Parallelized Large- (usually) equally sized subdomains. Ghost layers are added
eddy Simulation Model and now an independent name) is a at the side boundaries of the subdomains in order to account
Fortran-based code and has been applied for studying a va- for the local data dependencies, which are caused by the need
riety of atmospheric and oceanic boundary layers for about to compute finite differences at these positions. A Cartesian
20 years. The model is optimized for use on massively par- topography (complex terrain and buildings) is available in
allel computer architectures. This is a follow-up paper to the PALM, which is based on the mask method (Briscolini and
PALM 4.0 model description in Maronga et al. (2015). Dur- Santangelo, 1989) and allows for explicitly resolving solid
ing the last years, PALM has been significantly improved obstacles such as buildings and orography. PALM also has
and now offers a variety of new components. In particular, an ocean option, allowing for studying the ocean mixed layer
much effort was made to enhance the model with compo- where the sea surface is defined at the top of the model, and
nents needed for applications in urban environments, like which includes a prognostic equation for salinity.
fully interactive land surface and radiation schemes, chem- Furthermore, PALM has offered several embedded mod-
istry, and an indoor model. This paper serves as an overview els which were described in the precursor paper, namely bulk
paper of the PALM 6.0 model system and we describe its cur- cloud microphysics parameterizations, a Lagrangian particle
rent model core. The individual components for urban appli- model (LPM) which can be used for studying dispersion pro-
cations, case studies, validation runs, and issues with suitable cesses in turbulent flows, or as a Lagrangian cloud model
input data are presented and discussed in a series of compan- (LCM) employing the superdroplet approach. Moreover, a
ion papers in this special issue. plant canopy model can be used to study effects of plants
as obstacles on the flow. A 1-D version of PALM can be
switched on in order to generate steady-state wind profiles
for 3-D model initialization.
1 Introduction Due to the enormous amount of data that come along with
computationally expensive LES (in terms of the number of
Since the early 1970s, the turbulence-resolving so-called grid points and short time steps), the data handling plays a
large-eddy simulation (LES) technique has been increas- key role for the performance of LES models and for data
ingly employed for studying the atmospheric boundary layer analysis during post-processing. PALM is optimized to pur-
(ABL) at large Reynolds numbers. While the earliest stud- sue the strategy of performing data operations like time or
ies were performed at coarse grid spacings on the order of domain averaging to a great extent online instead of post-
100 m (Deardorff, 1970, 1973), today’s supercomputers al- pone such operations to a post-processing step. In this way,
low for large domain runs at fine grid spacings of 1–10 m the data output (e.g., of huge 4-D data or temporal averages)
(e.g., Kanda et al., 2004; Raasch and Franke, 2011; Sul- can be significantly reduced. In order to allow the user to per-
livan and Patton, 2011, among many others) or even less form their own calculations during runtime, a user interface
(Sullivan et al., 2016; Maronga and Reuder, 2017; Maronga offers a wide range of possibilities, e.g., for defining user-
and Bosveld, 2017). LES models solve the three-dimensional defined output quantities. PALM allows data output for dif-
prognostic equations for momentum, temperature, humid- ferent quantities as time series, (horizontally averaged) verti-
ity, and other scalar quantities (such a chemical species). cal profiles, 2-D cross sections, 3-D volume data, and masked
The principle of LES dictates a separation of scales. Turbu- data. All data output files are in netCDF format, which can
lence scales larger than a chosen filter width are being di- be processed by a variety of public domain and commercial
rectly resolved by LES models, while the effect of smaller software. The only exception is data output from the LPM,
turbulence scales on the resolved scales is fully parameter- which is output in Fortran binary format for a better perfor-
ized within a so-called subgrid-scale (SGS) model. The filter mance. For details about PALM’s specifics, application sce-
width strongly depends on the phenomenon to be studied and narios, and validation runs, see Maronga et al. (2015) and
must be chosen in such a way that at least 90 % of the turbu- references therein.
lence energy can be resolved (Heus et al., 2010). In the present paper, we describe the PALM model sys-
In a precursor paper (Maronga et al., 2015), we gave an tem version 6.0. Since version 4.0, the code has undergone
overview of the Parallelized Large-eddy Simulation Model massive changes and improvements. Above all, new com-
(PALM) version 4.0. PALM is a Fortran-based code and has ponents for applications of PALM in urban environments,
been applied for a variety of atmospheric and oceanic bound- so-called PALM-4U (PALM for urban applications) compo-
ary layers for about 20 years. The model is optimized for use nents, have been added in the scope of the Urban Climate Un-
on massively parallel computer architectures but can be used der Change [UC]2 framework funded by the German Federal
in principle also on small workstations and notebooks. The Ministry of Education and Research (Scherer et al., 2019b;
model domain is discretized in space using finite differences Maronga et al., 2019). Besides, a turbulence closure based
and equidistant horizontal grid spacings. The parallelization on the Reynolds-averaged Navier–Stokes (RANS) equations
of the code is achieved by a 2-D domain decomposition was added, enabling PALM to not only run in turbulence-
Geosci. Model Dev., 13, 1335–1372, 2020 www.geosci-model-dev.net/13/1335/2020/
B. Maronga et al.: The PALM model system 6.0 1337
resolving (i.e., LES) but also in RANS mode where the full approximated form, filtered based on a spatial scale separa-
turbulence spectrum is parameterized. Originally, the name tion approach after Schumann (1975) (described in Maronga
PALM referred to its parallelization as a special feature of the et al., 2015), or in an anelastic approximation, in which
model. Nowadays, however, most of the existing LES models the flow is treated as incompressible but allowing for den-
are parallelized. sity variations with height, while variations in time are not
Moreover, with the RANS mode implemented, PALM is permitted. This enables the application of PALM to simu-
more than an LES model, rendering the full name of the late atmospheric phenomena that extend throughout the en-
model inappropriate. As the name PALM has been estab- tire troposphere (e.g., deep convection). Both anelastic and
lished in the research community, we thus decided to drop Boussinesq-approximated forms are described by a single set
the full name and use the abbreviation PALM as a proper of equations that only differ in the treatment of the density ρ.
name from now on. The model is now referred to as the For the Boussinesq form, ρ is set to a constant value (and
PALM model system, consisting of the PALM model core then drops out of most terms), while the anelastic form re-
and the PALM-4U components. For the motivation for devel- sults from varying ρ with height during initialization.
oping the PALM-4U components and a description of model In the following set of equations, angular brackets denote
developments done within [UC]2 , the reader is referred to a horizontal domain average. A subscript 0 indicates a sur-
Maronga et al. (2019). As the model core in version 4.0 was face value. Note that the variables in the equations are implic-
described in detail in the precursor paper, we will focus here itly filtered by the discretization (see above), but that the con-
on the changes in the model core and give an overview of all tinuous form of the equations is used here for convenience.
the new components that have been added to the model. The A double prime indicates SGS variables. The overbar indi-
individual new PALM-4U components, case studies, valida- cates filtered quantities. The equations for the conservation
tion studies, and issues with suitable input data are presented of mass, momentum, thermal internal energy, moisture, and
and discussed in a series of companion papers in this spe- another arbitrary passive scalar quantity, filtered over a grid
cial issue. volume on a Cartesian grid, then read as
The paper is organized as follows: Sect. 2 deals with the
description of the model core, while Sect. 3 and Sect. 4 give ∂uj ρ
details about the embedded modules in the PALM core and =0 (1)
∂xj
the PALM-4U components, respectively. Sect. 5 provides ∗
technical details, including recent developments in model ∂ui 1 ∂ρui uj ∂ π
=− − εij k fj uk + εi3j f3 ug,j −
operation, data structure of surface elements, I/O data han- ∂t ρ ∂xj ∂xi ρ
dling, and optimization. The paper closes with conclusions θ v − θv,ref 1 ∂
2
+g δi3 − 00 00
ρ ui uj − eδij ,
in Sect. 6. Note that all symbols that will be introduced in θv,ref ρ ∂xj 3
the following are also listed in Tables 1–8. (2)
∂θ 1 ∂ρuj θ 1 ∂ lv
=− − ρu00j θ 00 − χq (3)
2 PALM model core ∂t ρ ∂xj ρ ∂xj cp 5 v
∂q v 1 ∂ρuj q v 1 ∂ 00 00
In this section, we give a detailed description of the changes =− − ρuj qv + χqv (4)
∂t ρ ∂xj ρ ∂xj
of the PALM model core starting from version 4.0. Here, we ∂s 1 ∂ρuj s 1 ∂ 00 00
confine ourselves to the atmospheric version. Details about =− − ρuj s + χs . (5)
∂t ρ ∂xj ρ ∂xj
the ocean version are given by Maronga et al. (2015) and in
Sect. 2.4. By default, PALM solves equations for up to seven
prognostic variables: the velocity components u, v, and w on Here, i, j, k ∈ {1, 2, 3}. ui is the velocity components (u1 =
a staggered Cartesian grid (staggered Arakawa C grid Har- u, u2 = v, u3 = w) with location xi (x1 = x, x2 = y, x3 = z),
low and Welch, 1965; Arakawa and Lamb, 1977), potential t is time, fi = (0, 2 cos(φ), 2 sin(φ)) is the Coriolis pa-
temperature θ , SGS turbulence kinetic energy (SGS-TKE) e rameter with = 0.729 × 10−4 rad s−1 being the Earth’s an-
(in LES mode), water vapor mixing ratio qv , and possibly a gular velocity and φ being the geographical latitude. ug,j is
passive scalar s. Note that, in PALM 4.0, it was only possible the geostrophic wind speed components, ρ is the basic state
to use either water vapor or the passive scalar as both used density of dry air, π ∗ = p∗ + 23 ρe is the modified perturba-
the same prognostic equation in the model code, while both tion pressure with p ∗ being the perturbation pressure and
are now fully separated and can be used simultaneously. e = 21 u00i u00i , g = 9.81 m s−2 is the gravitational acceleration,
δ is the Kronecker delta, and lv = 2.5 × 106 J kg−1 is the spe-
2.1 Governing equations of the PALM core cific latent heat of vaporization. The reference state θv,ref in
Eq. (2) can be set to be the horizontal average hθv i, the ini-
By default, PALM solves incompressible approximations tial state, or a fixed reference value. Furthermore, χqv and χs
of the Navier–Stokes equations, either in Boussinesq- are source/sink terms of qv and s, respectively. The potential
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1338 B. Maronga et al.: The PALM model system 6.0
Table 1. List of general model parameters.
Symbol Value Description
c0 , c1 , c2 , c3 0.55, 1.44, 1.92, 1.44 Model constants in RANS turbulence parameterization
cp 1005 J kg−1 K−1 Specific heat capacity of dry air at constant pressure
g 9.81 m s−2 Gravitational acceleration
lv 2.5 × 106 J kg−1 Specific latent heat of vaporization
Pr 1 Prandtl number in RANS turbulence parameterization
p0 1000 hPa Reference air pressure
Rd 287 J kg−1 K−1 Specific gas constant for dry air
Rv 461.51 J kg−1 K−1 Specific gas constant for water vapor
S0 1368 W m−2 Solar constant
αCh 0.018 Charnock constant
atm 0.8 Atmospheric emissivity
κ 0.4 Von Kármán constant
ν 1.461 × 10−5 m2 s−1 Kinematic viscosity of air
π 3.14159 . . . Pi
σe 1.0 Model constant in RANS turbulence parameterization
σ 1.3 Model constant in RANS turbulence parameterization
σSB 5.67 × 10−8 W m−2 K−4 Stefan–Boltzmann constant
0.729 × 10−4 rad s−1 Angular velocity of the Earth
Table 2. List of general symbols.
Symbol Dimension Description
F N Random forcing term in parameterization of wave breaking
Nchem Number of chemical species
s kg m−3 Passive scalar
T K Absolute air temperature
Us m s−1 Wave amplitude in Stokes drift parameterization
ui m s−1 Velocity components (u1 = u, u2 = v, u3 = w)
ug,i m s−1 Geostrophic wind components (ug,1 = ug , ug,2 = vg )
us m s−1 Stokes drift velocity
utr m s−1 Transport velocity used for radiation boundary conditions at the model outflow
xd m Distance in x direction used for radiation boundary conditions at the model outflow
xi m Coordinate on the Cartesian grid (x1 = x, x2 = y, x3 = z)
zw m Wave height in Stokes drift parameterization
1 m Grid spacing
1x, 1y, 1z m Grid spacings in x, y, and z directions
1t s Time step of the LES model
δ Kronecker delta
θ K Potential temperature
θv K Virtual potential temperature
θv,ref K Reference state of virtual potential temperature
λw m Wavelength in Stokes drift parameterization
5 Exner function
π∗ hPa Perturbation pressure
ρ kg m−3 Density of dry air (basic state)
ρθ kg m−3 Potential density
ω s−1 Rotation of velocity
Geosci. Model Dev., 13, 1335–1372, 2020 www.geosci-model-dev.net/13/1335/2020/
B. Maronga et al.: The PALM model system 6.0 1339
temperature is defined as different filter operations, the overbar is used to denote vari-
ables that are filtered with the horizontal grid spacing 1 in
θ = T /5, (6) this subsection. While Kh is calculated as in the Deardorff
scheme, a dynamic approach is applied to calculate Km , viz.
with the absolute temperature T and the Exner function: √
Km = c∗ 1max e, (13)
Rd /cp
p
5= , (7) where 1max = max(1x , 1y , 1z ). Unlike in the Deardorff
p0 scheme, c∗ is not a fixed value but is calculated at each time
with p being the hydrostatic air pressure, p0 = 1000 hPa step for each grid cell. As for the Deardorff scheme, e is cal-
a reference pressure, Rd = 287 J kg−1 K−1 the specific gas culated using a prognostic equation:
constant for dry air, and cp = 1005 J kg−1 K−1 the specific ∂e ∂e ∂u
i g 00 00
heat of dry air at constant pressure. The virtual potential tem- = − uj − u00i u00j + u θ
∂t ∂xj ∂xj θv,ref 3
perature is defined as " #
∂ 00 p 00 e3/2
− uj e + − (0.19 + 0.74l/1) ,
Rv
θv = θ 1 + − 1 qv − ql , (8) ∂xj ρ l
Rd
(14)
with the specific gas constant for water vapor Rv =
with l being a mixing length. Note that, in the SGS closures,
461.51 J kg−1 K−1 , and the liquid water mixing ratio ql . For
θv,ref refers to either a given reference value or the local value
the computation of ql , see the descriptions of the embedded
of θ . The pressure term in Eq. (14) is parameterized as
cloud microphysical models in Sect. 3.1 and 3.4. " #
00 p 00 ∂e
2.2 Turbulence closures uj e + = −2Km . (15)
ρ ∂xj
By default, PALM employs a 1.5-order closure (LES mode) The left-hand side of Eq. (9) is called deviatoric subgrid
after Deardorff (1980) in the formulation by Moeng and
∂ui ∂u
stress. Using the rate of strain tensor Sij = 0.5 ∂xj + ∂xji ,
Wyngaard (1988) and Saiki et al. (2000) (hereafter referred
to as the Deardorff scheme). Details are given in Maronga it can be written as follows:
et al. (2015). Since version 6.0, an alternative dynamic SGS τnn
τijd = τij − δij = −2Km S ij , (16)
closure can be used, which will be described in the following. 3
Moreover, two turbulence closures are available in RANS where we used the summation convention. The subgrid stress
mode (i.e., the full spectrum of turbulence is parameterized): can also be expressed as τij = ui uj − ui uj . This expression
a so-called TKE-l and a TKE- closure, where l is a mixing makes clear why the subgrid stress has to be modeled, since
length and is the SGS-TKE dissipation rate. only the second term of the right-hand side is known. Follow-
ing Germano et al. (1991), a test filter is introduced, which
2.2.1 Dynamic SGS closure is 1T = 21 in our case. The subgrid stress on the test filter
scale then is Tij = ud i uj − ui uj , where also the first term on
bb
The dynamic SGS closure follows Heinz (2008) and
the right-hand side is unknown (the hat denotes a filter opera-
Mokhtarpoor and Heinz (2017). In general, the dynamic SGS
tion with the width of the test filter). The difference between
closure employs the same equations for calculating the SGS
subgrid stress on the test filter level and the test-filtered sub-
fluxes as the Deardorff scheme, assuming that the energy
grid stress is the resolved stress Lij = Tij −bτij = udi uj −ui uj .
bb
transport by SGS eddies is proportional to the local gradients
Both terms on the right-hand side are known, and Lij can
of the mean resolved quantities and reads
thus be calculated directly by application of the test filter
2
∂ui ∂uj
to the resolved velocities on the grid cells. As described in
00 00
ui uj − eδij = −Km + (9) Heinz (2008), c∗ can be calculated via
3 ∂xj ∂xi
∂θ Ldij b
Sj i
u00i θ 00 = −Kh (10) c∗ = − , (17)
∂xi 2ν Tb
S b S
∗ mn nm
∂q v
u00i qv00 = −Kh (11) where ν∗T = 1T (Lii /2)2 is the subtest-scale viscosity. The
∂xi
∂s stability of the simulation is ensured by using dynamic
u00i s 00 = −Kh , (12) bounds that keep the values of c∗ in the range
∂xi √
23 e
where Km and Kh are the local SGS diffusivities of momen- |c∗ | ≤ √ q , (18)
tum and heat, respectively. In order to distinguish between 24 3 1 S S
ij j i
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Table 3. List of SGS model symbols.
Symbol Dimension Description
c∗ Dynamic subgrid-scale coefficient
e m2 s−2 Subgrid-scale turbulence kinetic energy (total turbulent kinetic energy in RANS mode)
l m Mixing length
lB m Mixing length after Blackadar (1962)
lwall m Minimum mixing length
Kh m2 s−1 SGS eddy diffusivity of heat
Km m2 s−1 SGS eddy diffusivity of momentum
Lij m2 s−2 Resolved stress tensor
Sij s−1 Strain tensor
Tij m2 s−2 Subtest-scale stress tensor
m2 s−3 SGS-TKE dissipation rate
ν∗T m2 s Subtest-scale viscosity parameter
τij m2 s−2 SGS stress tensor
τd,ij m2 s−2 Deviatoric SGS stress tensor
as derived by Mokhtarpoor and Heinz (2017). This model
does not need artificial limitation of the range of c∗ for stable ∂e ∂e
∂ui ∂uj ∂ui
runs and allows the occurrence of energy backscatter (i.e., = − uj + Km +
∂t ∂xj ∂xj ∂xi ∂xj
negative values of Km ). Unlike other dynamic models, this
formulation of c∗ is not derived using model assumptions for g ∂θ v ∂ 2e
− Kh + Ke 2 − . (21)
the subgrid stress and the stress on the test filter level but is θv,ref ∂z ∂xj
derived as consequence of stochastic analysis (Heinz, 2008;
Heinz and Gopalan, 2012). Here, Ke = Kσem is the diffusivity of e, with the model con-
stant σe = 1 as default value, and is calculated as
2.2.2 RANS turbulence closures √
3 e
= c0 e . (22)
For RANS mode, PALM offers two different turbulence clo- l
sures – a TKE-l and the standard TKE- closure (Mellor and
The mixing length l is calculated using the mixing length
Yamada, 1974, 1982) – to calculate the eddy diffusivities,
after Blackadar (1962) lB and the similarity function of
which then describe diffusion by the complete turbulence
momentum 8m for stable conditions in the formulation of
spectrum. While the TKE-l closure uses a single prognostic
Businger–Dyer (see, e.g., Panofsky and Dutton, 1984):
equation to calculate the TKE, the standard TKE- closure
(
applies an additional prognostic equation for in addition to min 8lBm , lwall for Lz ≥ 0 ,
the equation for e. l= (23)
In the TKE-l closure (e.g., Holt and Raman, 1988), the min (lB , lwall ) for Lz < 0 ,
eddy diffusivities are calculated via e and l as with
√ κz
Km = c0 l e, (19) lB = κz , and (24)
1+ 0.5
Km 0.00027 u2g,1 +u2g,2 f
Kh = , (20)
Pr z
8m = 1 + 5 , (25)
where Pr = 1 denotes the Prandtl number and c0 = 0.55 de- L
notes a model constant. The Prandtl number can be changed where κ = 0.4 denotes the von Kármán constant, L the
to a user-specific value for different stability regimes. Note Obukhov length, and z the height above the surface. The mix-
that, in the case of RANS mode, e denotes the total turbu- ing length is limited by lwall , which is the distance to the near-
lent kinetic energy as the full turbulence spectrum is param- est solid surface.
eterized. To calculate e, Eq. (14) is modified by introducing Aside from the TKE-l closure, also a standard TKE-
gradient approaches for the turbulent transport terms: model is available as a turbulence closure. When choosing
the standard TKE- model, Km is calculated via
e2
Km = c04 . (26)
Geosci. Model Dev., 13, 1335–1372, 2020 www.geosci-model-dev.net/13/1335/2020/B. Maronga et al.: The PALM model system 6.0 1341
The modeled TKE is calculated using Eq. (21) and an addi- In PALM, u∗ is calculated from uh at zmo by vertical integra-
tional prognostic equation is used to calculate : tion of Eq. (28) over z from z0 to zmo .
From Eqs. (28), (31), and a geometric decomposition of
∂ ∂ ∂ui ∂uj ∂ui
= − uj + c1 Km + both the wind vector and u∗ , it is possible to derive a formu-
∂t ∂xj e ∂xj ∂xi ∂xj lation for the horizontal wind components, viz.
g ∂θ v ∂ 2 2
− c3 Kh + K 2 − c2 , (27)
e θv,ref ∂z ∂xj e ∂u −u00 w00 0 z ∂v −v 00 w00 0 z
= 8m and = 8m .
∂z u∗ κz L ∂z u∗ κz L
where K = Kσm with σ = 1.3 and c1 = 1.44, c2 = 1.92, and (32)
c3 = 1.44 being model constants (e.g., Launder and Spald-
ing, 1974; Oliveira and Younis, 2000). As the constants Vertical integration of Eq. (32) over z from z0 to zmo then
c0 − c3 as well as σe and σ depend on the situation studied, yields the surface momentum fluxes u00 w 00 0 and v 00 w00 0 .
they might need to be adjusted by the user. The formulations above all require knowledge of the scal-
ing parameters θ∗ and q∗ . These are deduced from vertical
2.3 Boundary conditions integration of
2.3.1 Constant flux layer ∂θ θ∗ z ∂q v q∗ z
= 8h and = 8h (33)
Following Monin–Obukhov similarity theory (MOST), a ∂z κz L ∂z κz L
constant flux layer assumption is used between the surface over z from z0,h to zmo . The similarity function 8h is given
and the first computational grid level (k = 1, zmo = 0.5 · 1z). by
Using roughness lengths for heat, humidity, and momentum
(z0,h , z0,q , and z0 , respectively), MOST then provides sur- 1 + 5 Lz z
for L ≥ 0,
face fluxes of momentum (shear stress) and scalar quantities 8h = −1/2 (34)
1 − 16 Lz for z
L < 0.
(heat and moisture flux) as bottom boundary conditions. In
PALM, it is assumed that MOST can be applied locally, even Previously, the implementation of the constant flux layer in-
though there is no theoretical foundation for this assumption. volved a diagnostic–prognostic equation for L, based on data
Hultmark et al. (2013), e.g., pointed out that this leads to a from the previous time step. Even though it was found that
systematical overprediction of the mean shear stress. How- this method introduces only negligible errors, we decided to
ever, this local method has the advantage that surface hetero- revise this procedure and calculate L based on using a New-
geneities can be prescribed at the surface, and therefore it has ton iteration method instead. By doing so, we can achieve a
become standard in most contemporary LES codes. correct value of L which can be important when the model
The surface layer vertical profile of the horizontal wind is coupled to a surface scheme. We also found that this does
1
velocity uh = (u2 + v 2 ) 2 is predicted by MOST through not increase the computational costs to a significant amount
(usually less than 1 %). Starting from PALM 6.0 (revision
∂uh u∗ z
= 8m , (28) 3668), Newton iteration is the only available method. The
∂z κz L Newton iteration method involves the calculation of a bulk
where 8m is the similarity function for momentum in the for- Richardson number Rib . Depending on whether fluxes are
mulation of Businger–Dyer (see, e.g., Panofsky and Dutton, prescribed or Dirichlet boundary conditions are used for tem-
1984): perature and humidity, Rib is related to L via
(
1 + 5 Lz for Lz ≥ 0,
( ϕh
zmo 2 for Dirichlet conditions,
8m = − 1 (29) Rib = · ϕ1m (35)
1 − 16 Lz 4 for Lz < 0.
L ϕ3
for prescribed fluxes,
m
The scaling parameters θ∗ and q∗ are defined by MOST as
where
w00 θ 00 0
θ∗ = − , zmo z
mo
z
0,h
u∗ ϕh = log − 9h + 9h (36)
z0,h L L
w 00 qv00 0
q∗ = − , (30) and
u∗
with the friction velocity u∗ (defined through the square root zmo z
mo
z
0,h
ϕm = log − 9m + 9m (37)
of the surface shear stress) as z0 L L
2 2 14 are the integrated universal profile stability functions of 9m
00 00
u∗ = u w 0 + v w 0 00 00 . (31) and 9h (see Paulson, 1970; Holtslag and De Bruin, 1988), so
www.geosci-model-dev.net/13/1335/2020/ Geosci. Model Dev., 13, 1335–1372, 20201342 B. Maronga et al.: The PALM model system 6.0
that a (bulk) Richardson number can be defined: Table 4. List of surface layer symbols.
gzmo θ v,mo −θv,0
2 for Dirichlet conditions, Symbol Dimension Description
uh θ v
Rib = (38) L m Obukhov length
00 00
− gzmo w3 θv 0 q∗ kg kg−1 MOST humidity scale
for prescribed fluxes.
2
κ uh θ v Rib Bulk Richardson number
uh m s−1 Absolute value of the horizontal
The above equations are solved for L by finding the root of
wind
the function fN : zmo m Height above the surface where
( [ϕ ]
h
MOST is applied
zmo 2 for Dirichlet conditions. z0 m Roughness length for momentum
fN = Rib − · [ϕ[ϕmh]] (39)
L for prescribed fluxes. z0,h m Roughness length for heat
[ϕ ]3 m
z0,q m Roughness length for moisture
The solution is then given by iteration of θ∗ K MOST temperature scale
8h Similarity function for heat
fN (Ln ) 8m Similarity function for
Ln+1 = Ln − , (40) momentum
fN0 (Ln )
9h Integrated similarity function for
with iteration step n, and heat
9m Integrated similarity function for
∂fN momentum
fN0 (L) = , (41) ϕh Integrated similarity function
∂L
term for heat
until L meets a convergence criterion. ϕm Integrated similarity function
The surface fluxes of sensible and latent heat, as well as term for momentum
the surface shear stress, are then calculated using Eqs. (30)
and (31). Note that for vertically oriented surfaces in com-
bination with an interactive surface model switched on (see aerodynamically smooth for low wind speeds. For ocean sur-
Sects. 3.5 and 4.5), the surface fluxes are calculated after faces, the roughness lengths are thus calculated for each sur-
Krayenhoff and Voogt (2007) as static stability considera- face grid point as
tions do not apply for such surface orientations (see also
Resler et al., 2017). Also note that the above formulation can 0.11ν u2
lead to violations of MOST for too-coarse grid spacings in z0 = + αCh ∗ , (45)
u∗ g
some cases, particularly for setups of stable boundary lay-
0.4ν
ers, as the first grid layer might be located in the roughness z0,h = , (46)
sublayer of the surface layer. For a discussion of this issue u∗
and an improved boundary condition, see Basu and Lacser 0.62ν
z0,q = , (47)
(2017) and Maronga et al. (2020). u∗
In the case of the TKE- RANS closure, the boundary con-
with αCh = 0.0018 being the Charnock constant, and ν =
dition for e, , and Km are
1.461 × 10−5 m2 s−1 being the kinematic viscosity. Note
u∗ that this parameterization is designed for large-scale mod-
e= , (42) els where waves are a subgrid-scale phenomenon. For fine
c0
grid spacings and/or large waves (in amplitude and wave-
u3∗ length), this parameterization can lead to erroneous rough-
= , (43)
κzmo ness lengths and should not be switched on without rigorous
z
mo testing.
Km = κu∗ zmo 8−1
m . (44)
L
2.3.3 Lateral boundary conditions
2.3.2 Wave-dependent surface roughness At lateral domain boundaries, various different conditions
can be applied, which are listed in Table 9.
As the ocean surface in PALM is assumed to be flat and By default, cyclic boundary conditions apply at all lateral
waves are not explicitly resolved, a Charnock parameteri- domain boundaries. Choosing an inflow boundary condition
zation can be switched on which relates the surface rough- at one of the four domain boundaries requires to set an out-
ness lengths to the friction velocity as described in Beljaars flow condition at the opposing boundary while keeping the
(1994). This accounts for the fact that water surfaces become boundaries in perpendicular direction cyclic. An exception
Geosci. Model Dev., 13, 1335–1372, 2020 www.geosci-model-dev.net/13/1335/2020/B. Maronga et al.: The PALM model system 6.0 1343
is made in the case of model nesting, where inflow/outflow the outflow boundary, the so-called turbulent outflow condi-
boundary conditions are set dynamically for each individual tion (Gronemeier et al., 2017). Instead of transporting the ve-
boundary grid point (see Sect. 4.8 and 4.9). locity components via the radiation condition, instantaneous
The simplest inflow condition is a purely laminar inflow values of u, v, w, θ , and e are taken from a vertical plane
using Dirichlet conditions at either domain boundary. A more situated at a distance xd from the outflow boundary which
sophisticated approach with fully developed turbulence al- are then mapped to the outflow boundary. By taking the in-
ready present at the inflow boundary can be achieved by us- formation of the flow field from within the domain, occurring
ing the turbulence-recycling method, which is implemented inflow regimes are disturbed and cannot intensify themselves
according to Lund et al. (1998) and Kataoka and Mizuno as long as a proper xd is chosen which needs to be a fair dis-
(2002). The turbulence-recycling method sets a fixed mean tance away from the outflow boundary. Note that the turbu-
inflow condition at one side of the simulation domain and lent outflow condition can be transformed into the radiation
adds a turbulent signal from within the model domain to condition, where utr = 1/1t if xd = 0. As for now, the tur-
these mean profiles. This then creates a turbulent inflow (see bulent outflow condition is only available at the right domain
Maronga et al., 2015). The turbulence-recycling method is boundary.
currently only available at the left domain boundary, i.e.,
at x = 0. 2.4 Ocean option
The downside of the turbulence-recycling method is the
requirement of an additional recycling area within the model PALM’s ocean option has been extended to include wave ef-
domain which is purely needed to generate turbulence and fects to account for the Langmuir circulation, which can be
cannot be used for data evaluation of the studied phe- optionally switched on. For this, the momentum equation is
nomenon. To avoid the necessity of including an additional modified by including a vortex force and an additional ad-
recycling area within the simulation domain, a synthetic tur- vection by the Stokes drift following the theory by Craik and
bulence generator can be used instead of the turbulence- Leibovich (1976), similarly to McWilliams et al. (1997) and
recycling method at the inflow boundary (Gronemeier et al., Skyllingstad and Denbo (1995). Furthermore, a simple pa-
2015). This turbulence generator is based on the method pub- rameterization of wave-breaking effects has been included.
lished by Xie and Castro (2008) with the modification of The modified momentum equations for the ocean then reads
Kim et al. (2013) for divergence-free inflow. The turbulence- ∂ui ∂ui
generation method calculates stochastic fluctuations from an = − (uj + us,j ) − εij k fj (uk + us,k )
∂t ∂xj
arrayed random number. This is realized via given length
∂π ∗
scales that are added to the mean inflow profiles using a Lund + εi3j f3 ug,j − + εij k us,j ωk
rotation (Lund et al., 1998) and a given Reynolds stress ten- ∂xi
sor. In order to apply the synthetic turbulence generator, in- ρ θ − hρθ i ∂ 00 00 2
−g δi3 − ui uj − eδij + Fi , (48)
formation on the turbulent length scales for the three wind hρθ i ∂xj 3
components in the x, y, and z directions, as well as the
where us is the Stokes drift velocity, ρθ the potential den-
Reynolds stress tensor, is required. These information can be
sity, and ωi = εij k ∂u k
∂xj the rotation of the velocity field. F
either obtained from idealized precursor simulations or from
observations (Xie and Castro, 2008). In combination with the is a random forcing term that represents the generation of
offline nesting (see Sect. 4.9), PALM also offers the possibil- small-scale turbulence by wave breaking. It should be kept
ity to compute turbulent length scales and Reynolds stress in mind that the incompressibility assumption is used in the
following the parameterizations described by Rotach et al. ocean option. It is assumed that wind stress and wave fields
(1996). are in the same direction, and that the wave field is steady and
At the outflow boundary, radiation conditions are used by monochromatic. The magnitude of the Stokes velocity along
default for the velocity components as proposed by Orlan- the wind stress direction is then given by
ski (1976). Velocity components are advected by a trans-
4π z
port velocity utr which is calculated from the gradients of us = Us exp , (49)
λw
the transported velocity components normal to the bound-
ary at the grid points next to the outflow boundary (see also with Us = (π zw /λ)2 (gλw /2π )1/2 , where zw is the wave
Maronga et al., 2015). The transport velocity is restricted to height and λw is the wavelength. The current implementation
0 ≤ utr ≤ 1/1t, where 1t denotes the time step. of wave effects strictly follows Noh et al. (2004), in partic-
In cases with weak background wind in a convective ular the parameterization of wave breaking. Note that Noh
boundary layer, it was found that using the radiation con- et al. (2004) used an earlier version of PALM, where the pro-
dition can lead to instabilities and strong self-intensifying gramming of the wave effects was completely realized via
inflow regimes at the outflow boundary (Gronemeier et al., PALM’s user interface.
2017). In order to prevent such artificial inflow situations at As part of the general code modularization effort, all
the outflow boundary, an empirical approach can be used at ocean-related code has been put into one Fortran module, and
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a separate namelist has been created containing all ocean- (2019) for studying nocturnal radiation fog. Besides this
related steering parameters. physical improvement, the bulk microphysics is now fully
modularized in PALM 6.0.
3 Embedded models 3.1.1 Activation of cloud droplets
In this section, we first describe major revisions of the em- As activation is the major source term for nc , this process is
bedded models in the PALM core, namely in the bulk cloud represented by so-called Twomey-type parameterizations in
microphysics parameterization (Sect. 3.1) and in the La- PALM 6.0, which are available in two modes. Per default,
grangian particle model (Sect. 3.3–3.4). Subsequently, we in- the number of activated cloud condensation nuclei (CCN) is
troduce three new embedded models in PALM 6.0: a fully given by a simple power-law expression:
interactive land surface model (LSM, Sect. 3.5), which can
be coupled to two different radiation models (Sect. 3.6), and NCCN = Na slkact , (56)
a parameterization scheme for taking into account the effect
of wind turbines (Sect. 3.7). where NCCN is the number of activated CCN, Na is the num-
ber concentration of the dry aerosol and the exponent kact
3.1 Bulk cloud microphysics improvements depending on the type of analyzed aerosol (Twomey, 1959).
The supersaturation over a liquid-phase surface is given by
In PALM 4.0, the bulk liquid-phase (i.e., no ice) two-moment sl = q v /qv,sat −1, where qv,sat stands for the water vapor satu-
microphysics scheme of Seifert and Beheng (2001, 2006) ration mixing ratio. Moreover, a more advanced method con-
was implemented, which only predicts the rain droplet num- sidering physiochemical properties of the dry aerosol can be
ber concentration (nr ) and rainwater mixing ratio (q r ). This used after Khvorostyanov and Curry (2006). Therein, it is
was extended by additional prognostic equations for the assumed that the dry aerosol spectrum follows a log-normal
cloud droplet number concentration (nc ) and the cloud wa- distribution which is given by
ter mixing ratio (q c ) instead of using a fixed value for nc and " #
only diagnostically calculated values for q c . The additional Na ln2 (rd /rd,av )
prognostic equations are thus given by fd = √ exp − , (57)
2π ln σd rd 2ln2 σd
∂nc ∂nc ∂ 00 00
= −uj − u n + χnc , (50) where rd and rd,av are the radius and the mean radius of the
∂t ∂xj ∂xj j c
dry aerosol, respectively. The dispersion of the dry aerosol
∂q c ∂q ∂ 00 00
= −uj c − u q + χqc , (51) spectrum is displayed by σd . Hence, the number of activated
∂t ∂xj ∂xj j c aerosol is calculated by
with the sink/source terms for χnc and χqc and the SGS
Na
fluxes: NCCN (sl ) = [1 − erf(u)];
2
∂nc ln(s0 /sl )
u00j n00c = −Kh , (52) u= √ , (58)
∂xi
2 ln σs,l
∂q
u00j qc00 = −Kh c . (53)
∂xi where “erf” is the Gaussian error function, and
The sink and source terms for nc and q c include the same 1/2
4A3
microphysical processes as described by Maronga et al. −(1+β)
s0 = rd,av ,
(2015), namely autoconversion, accretion, and sedimenta- 27b
tion of cloud droplets, as well as activation and diffu- 1+β
σs = σd . (59)
sional growth, which has been newly added. Accordingly, the
source and sink terms are given by A is the Kelvin parameter, and b and β depend on the chemi-
∂nc ∂nc ∂nc ∂nc ∂nc
cal composition and physical properties of the soluble part of
χnc = + + + + , the dry aerosol. Both schemes have in common that Na must
∂t act ∂t evap ∂t auto ∂t accr ∂t sed,c be prescribed and nc is calculated as a function of the aerosol
(54) concentration and the supersaturation. However, for the latter
∂q c ∂q c ∂q c ∂q c ∂q c scheme, the physiochemical properties, such as the mean dry
χqc = + + + + .
∂t cond ∂t evap ∂t auto ∂t accr ∂t sed,c radius, chemical composition, and dispersion of the aerosol
evap
(55) spectrum of the aerosol, must be prescribed by the user. The
activation rate is then given by
In the following, the source/sink terms for activation, con-
densation, and evaporation are described. This improved mi- ∂nc NCCN − nc
crophysics was recently applied by Schwenkel and Maronga = max ,0 , (60)
∂t act 1t
Geosci. Model Dev., 13, 1335–1372, 2020 www.geosci-model-dev.net/13/1335/2020/B. Maronga et al.: The PALM model system 6.0 1345
where nc is the number of previously activated aerosols child domains are automatically transferred from the parent
that are assumed to be equal to the number of pre-existing to the respective child model. Vice versa, particles leaving a
droplets and 1t is the length of the model time step. How- child domain are automatically transferred back to its parent
ever, it must be mentioned that in regions with significant model. A technical description of this approach as well as
autoconversion and accretion growth, the subsequent deple- implications concerning the treatment of SGS particle veloc-
tion of nc might lead to an overprediction of activation with ities when particles are transferred between parent and child
this method. will be discussed in a follow-up study.
3.2 Improved representation of diffusional growth 3.4 Lagrangian cloud model improvements
Additionally, for treating condensational growth, a sec- PALM’s Lagrangian cloud model (LCM) is based on its
ond method (diagnostic approach) apart from the well- LPM, using Lagrangian particles as so-called superdroplets
established saturation adjustment scheme was implemented (e.g., Shima et al., 2009), each representing an ensemble of
(see Maronga et al., 2015). This method diagnoses the cur- identical droplets that change their properties (e.g., water
rent supersaturation from the fields of T and q v . Subse- mass, aerosol mass, number of represented real droplets – the
quently, the diagnosed supersaturation is used for calculat- so-called weighting factor) by undergoing cloud microphysi-
ing the condensation and evaporation rates for cloud droplets, cal processes. PALM’s approach has been applied in various
which is given by (Khairoutdinov and Kogan, 2000) studies to further process-level understanding of warm-phase
cloud microphysics, covering deliquescent aerosols, their en-
∂q c 4π 0(T , p)ρw nc
= sl rc . (61) trainment and mixing with the cloud, as well as droplet acti-
∂t cond ρa vation, growth by diffusion, and collision and coalescence
evap
(Riechelmann et al., 2012; Hoffmann et al., 2015, 2017;
Here, rc is the volume mean radius of cloud droplets and 0 is Hoffmann, 2017; Noh et al., 2018).
a function of temperature and pressure including the thermal
conduction and diffusion of water vapor in air. Ventilation ef- 3.4.1 Collision and coalescence
fects which can affect the effective evaporation rates are con-
sidered for rain droplets separately, as described in Maronga While the modeling of aerosol activation and diffusional
et al. (2015). Note that this diagnostic scheme is an appropri- growth of cloud droplets is based on first principles and is
ate alternative, particularly if the assumptions made for sat- very similar in all available LCMs (Andrejczuk et al., 2008;
uration adjustment (assuming equilibrium) are violated, i.e., Shima et al., 2009; Riechelmann et al., 2012), the represen-
for time steps shorter than a few seconds. tation of collision and coalescence (i.e., collection) depends
heavily on model formulation. In a recent review paper, Un-
3.3 Lagrangian particle model improvements terstrasser et al. (2016) compared all available representa-
tions of collection in LCMs to analytical and other bench-
In the last years, the embedded LPM has been successfully
mark solutions. They showed that PALM’s previous repre-
used to study scalar dispersion in urban environments (e.g.,
sentation of collection is very stable but significantly un-
Auvinen et al., 2017; Lo and Ngan, 2017; Gronemeier and
derestimates the growth of the largest droplets, with com-
Sühring, 2019). The LPM is based on Weil et al. (2004) to
mensurate effects on the initiation of rain. Therefore, our
separate the particle speed into a deterministic and a stochas-
previous default collection algorithm by Riechelmann et al.
tic contribution, which corresponds to dividing the turbulent
(2012) was replaced by the so-called “all-or-nothing” algo-
flow field into a resolved-scale and a SGS portion, respec-
rithm that is based on the ideas of Shima et al. (2009) and
tively. The resolved-scale velocity is provided by the LES at
Sölch and Kärcher (2010), and performed best in the com-
each time step, while the SGS velocity is predicted by inte-
parison by Unterstrasser et al. (2016). The basic ideas of the
grating a stochastic differential equation according to Weil
all-or-nothing algorithm will be summarized below, but the
et al. (2004). For details on the model and its implementa-
interested reader is referred to Hoffmann et al. (2017) for
tion, we refer to Steinfeld et al. (2008) and Maronga et al.
more details on its implementation in PALM.
(2015).
In the all-or-nothing approach, each real droplet of the su-
As particle boundary conditions at solid walls, PALM 6.0
perdroplet with the smaller weighting factor collects one real
offers absorption and reflection boundary conditions. The
droplet of the superdroplet with the larger weighting factor.
particle reflection boundary conditions were revised and ad-
The probability P of this interaction is given by
justed to the revised topography implementation where also
overhanging structures may appear. Now, within a time step, 1t
particles can be reflected multiple times at different solid Pmn = KKmn · Aw,n , (62)
1V
walls, which is especially important near building corners.
Furthermore, the LPM was adjusted to the self-nesting where m and n are the indices of the superdroplets with the
(see Sect. 4.8). Particles that enter the region of one of the smaller and larger weighting factor, respectively, KK is the
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collection kernel depending on the properties of both su- subgrid-scale velocities and collisional growth rates due to
perdroplets, 1V is a prescribed volume in which the su- the stochastic nature of these routines. Note that the splitting
perdroplets are allowed the collide (which equals the size procedure is only applied in grid boxes where a threshold
of an LES grid box in PALM), and Aw is the superdroplet for the number of superdroplets per grid box is not exceeded
weighting factor. If Pmn exceeds a random number chosen to ensure computational feasibility. The merging algorithm
uniformly from the interval [0, 1], the collection takes place. is designed to save computational costs by merging super-
First, the mass of each real droplet of superdroplet m in- droplets in regions where an increased superdroplet resolu-
creases, while the mass of each real droplet of superdroplet tion is not required, e.g., outside of clouds. If a superdroplet
n remains unchanged: grows smaller than a prescribed radius and exhibits a large
enough (larger than a prescribed value) weighting factor, the
bm = mm + mn and m
m bn = mn , (63) superdroplet will be merged with another superdroplet in the
same grid box that also fulfills these requirements. By doing
where the (.d. .) marks the variable after collection. Second,
so, the first superdroplet is deleted and the weighting factor
the aerosol mass of each real droplet changes:
of the other superdroplet is adapted to obey mass conserva-
bs,m = ms,m + ms,n and m
m bs,n = ms,n . (64) tion. The splitting/merging algorithm is described in detail in
Schwenkel et al. (2018). Their results show that the merging
Finally, the change in the weighting factor diverges from this algorithm improves the representation of the collection pro-
pattern: cess significantly, while decreasing computational time by up
to 18 % compared to a simulation with a globally increased
bm = Am and A
A bn = An − Am . (65) superdroplet number.
This procedure is repeated for all different (unordered) su-
3.5 Land surface model (LSM)
perdroplet pairs in the volume 1V .
LES models are often used with prescribed surface condi-
3.4.2 Splitting and merging of superdroplets
tions (either by prescribing surface fluxes or by explicitly
In recent studies with the LCM, it was observed that droplet setting surface temperature and humidity). However, in many
size distributions does not converge even for large num- cases, an LSM is required in which the surface fluxes have to
bers (approximately 200) of superdroplets per grid box (e.g., be calculated based on the state of the solid material (soil,
Riechelmann et al., 2012). Based on the original idea of water, pavement), the radiation budget of the surface, and at-
Unterstrasser and Sölch (2014), a splitting and merging al- mospheric conditions. This might be the case when respec-
gorithm for superdroplets has been adapted for our LCM. tive measurement data are absent, or when the interaction be-
The main goal of such algorithms is to improve statistics by tween atmosphere and surface becomes relevant, e.g., in the
splitting one superdroplet into several superdroplets with the case of cloud or fog formation (Maronga and Reuder, 2017).
commensurate reduction of the weighting factor, and to save Furthermore, LSMs are needed when the model is to be run
computational demand by merging several superdroplets into in a forecasting mode, where surface boundary conditions are
one superdroplet if appropriate. For a correct representation a priori unknown.
of the initiation of rain in warm clouds, a good statistical rep- The implemented LSM in PALM is similar to the Tiled
resentation of collecting droplets by a sufficiently high num- ECMWF Scheme for Surface Exchanges over Land (TES-
ber of superdroplets is indispensable. SEL/HTESSEL; Balsamo et al., 2009) and the derivative
The splitting algorithm is mainly steered by three param- (simplified) implementation in the LES model DALES (Heus
eters: (1) the minimum radius of superdroplets that will be et al., 2010). The scheme implemented in PALM 6.0 was
split potentially, (2) a threshold for the weighting factor of adapted for use with impervious surfaces (e.g., streets, pave-
that superdroplet (can either be prescribed or is approximated ments) as well as water surfaces, and was coupled to a radi-
by assuming a gamma distribution; see Schwenkel et al., ation model (see Sect. 3.6) and both bulk cloud physics and
2018), and (3) the splitting factor, which describes in how Lagrangian cloud model (see Sect. 3.1 and Maronga et al.,
many particles one superdroplet will be split (prescribed or 2015).
calculated by the LCM). However, the general splitting pro- The LSM consists of a solver for the energy balance of
cedure is simple. If one superdroplet fulfills all criteria, the the Earth’s surface using a resistance parameterization for the
superdroplet is ηspl − 1 times cloned and the weighting fac- surface fluxes and a multi-layer soil scheme. The energy bal-
tor of the original and all new superdroplets is reduced to ance of the Earth’s surface is calculated as
An,new = An /ηspl , while ηspl is the splitting factor, deter- dT0
mining how many new superdroplets will be created dur- C0 = Rn − H − LE − G, (66)
dt
ing one operation. All other properties of the affected super-
droplets remain unaffected. However, after a few time steps, where C0 and T0 are the heat capacity and radiative temper-
every cloned superdroplet will experience slightly different ature of the surface skin layer, respectively. Note that C0 is
Geosci. Model Dev., 13, 1335–1372, 2020 www.geosci-model-dev.net/13/1335/2020/B. Maronga et al.: The PALM model system 6.0 1347
Table 5. List of symbols related to clouds and precipitation.
Symbol Dimension Description
A m Kelvin curvature parameter
Aw Superdroplet weighting factor
b Parameter describing the physiochemical properties of dry aerosol
kact Exponent for aerosol activation with power-law expression
KK Collection kernel in LCM
NCCN m−3 Number of activated cloud condensation nuclei
Na m−3 Number concentration of dry aerosol
nc m−3 Cloud droplet number concentration
nr m−3 Rain droplet number concentration
P Collection probability in LCM
qc kg kg−1 Cloud water mixing ratio
qr kg kg−1 Rainwater mixing ratio
ql kg kg−1 Liquid water mixing ratio
qv kg kg−1 Water vapor mixing ratio
qv,sat kg kg−1 Water vapor mixing ratio at saturation
rc m Volume mean cloud droplet radius
rd m Droplet radius
rd,av m Mean droplet radius
s0 Supersaturation considering solute and curvature effects of the dry aerosol
sl Supersaturation over a flat water surface
β Parameter of the soluble fraction of the dry aerosol
0 Function used in cloud microphysics parameterization
ηspl Splitting factor in LCM
σd Standard deviation of the dry aerosol spectrum
σl,s Standard deviation of supersaturation considering solute and curvature effects of the dry aerosol spectrum
χnc kg kg−1 s−1 Source/sink term of nc
χqc kg kg−1 s−1 Source/sink term of qc
χqv kg kg−1 s−1 Source/sink term of qv
χs kg m−3 s−1 Source/sink term of s
usually zero as it is assumed that the skin layer does not have temperature (related to the radiative potential temperature via
a heat capacity (see below). Rn , H , LE, and G are the net ra- the Exner function) and Tsoil,1 is the temperature of the up-
diation, sensible heat flux, latent heat flux, and ground (soil) permost soil layer (calculated at the center of the layer). 3 is
heat flux at the surface, respectively. calculated via a resistance approach as a combination of the
H is calculated as conductivity between the canopy and the soil-top (constant
value) and the conductivity of the top half of the uppermost
1
H = −ρcp (θ mo − θ0 ), (67) soil layer:
ra
3skin 3soil
where ra is the aerodynamic resistance. θ0 and θ mo are the 3= . (70)
potential temperature at the surface and at a fixed height 3skin + 3soil
within the atmospheric surface layer (at height zmo ), respec-
When no skin layer is used (i.e., in the case of bare soil and
tively. ra is calculated via MOST as
pavements), 3 reduces to the heat conductivity of the upper-
θ mo − θ0 most soil layer (divided by the layer depth). In that case, it
ra = . (68) is assumed that the soil temperature is constant within the
u∗ θ∗
uppermost 25 % of the top soil layer and equals the radia-
G is parameterized as (Duynkerke, 1999) tive temperature at the surface. C0 is then set to a non-zero
value according to the material properties. The latent heat
G = 3(T0 − Tsoil,1 ), (69) flux (LE) is calculated as
with 3 being the total thermal conductivity between skin 1
layer and the uppermost soil layer. T0 is the radiative surface LE = −ρ lv q v,mo − qv,sat (T0 ) . (71)
ra + rs
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