PALM Create Static Driver (palm_csd)

In order to create comprehensive drivers for PALM runs in urban environments, PALM comes shipped with the tool palm_csd. This python3-based script was developed in the course of ​the MOSAIK project and thus is, in principal, only working for the democities Berlin, Hamburg, and Stuttgart. However, with some effort it is possible to adapt the script for other cities as well. Note that in the mid-term, palm_csd will be replaced by a more generic and universal tool based with a graphical user interface as front end.

Usage

Execution

In order to create a static driver, go to the working directory (usually ~/palm/current_version), prepare a palm_csd configuration file (see below, an exemplary file can be found here​). After set-up of the configuration file, execute palm_csd as follows:

palm_csd .csd.config.default

The static driver will be written to the directory specified in the configuration file. During compilation of the driver, palm_csd will print some more or less useful information to screen.

Configuration file

This section describes how to set-up a configuration file for creating a static driver for PALM based on pre-processed NetCDF data. In the following we will use data for Berlin, which is available via Open Access. The configuration file uses the well-known format of INI files, which are processed by the ConfigParser? package in python. It consists of the following sections:

[global]

A set of global attributes can be defined that will be passed to the static driver file. In details, the following attributes can be set (see also static driver description:

Attribute	Data type	Description
author	string	Author of the static driver. Use the format: name, email
contact	string	Contact person, format as for author
acronym	string	Institional acronym (formating rules applies to static drivers used in the ​MOSAIK project)
comment	string	Arbitrary text
data_content	string	Arbitrary text
dependencies	string	Arbitrary text
keywords	string	Arbitrary keywords
source	string	List of data sources used to generate the driver
campaign	string	Information on measurement capaign (if applicable)
location	string	Geo-location of the static driver content (if applicable)
site	string	Site description od the static driver content (if applicable)
institution	string	Institution of the driver creator
palm_version	float	PALM version for which the driver was generated (for comptatibility checks)
rotation_angle	float	Clockwise angle of rotation in degrees between North positive y axis and the y axis in the data, e.g. 0.0. This value overwrites the namelist parameter rotation_angle
references	string	Arbitrary text

Example:

author = Bjoern Maronga, maronga@muk.uni-hannover.de
contact_person = Bjoern Maronga, maronga@muk.uni-hannover.de
acronym = LUHimuk
comment = created with palm_csd
data_content
dependencies
keywords
source
campaign
location = Berlin
site = Berlin Mitte
institution = Institute of Meteorology and Climatology, Leibniz University Hannover
palm_version = 6.0
rotation_angle = 0.0
references

Note that most of the global attributes have no effect on the PALM simulations, except rotation_angle and palm_version.

[settings]

This section describes global parameters used to create the static driver. All following parameters are mandatory!

Variable	Data type	Description
bridge_width	float	In case that the simulation domain contains bridges, this parameter (in m) defines the vertical thickness of all bridge elements in the domain. Note that bridges require LOD2 building information (i.e. buildings_3d)
debug_mode	logical	Can be set to True or False. Used for debugging by model developers only, currently this parameter has no effect
lai_roof_extensive	float	Leaf are index for green roofs with extensive vegetation, defined by setting the appropriate building_pars field. The value is assigned to all extensive green roofs in the model domain
lai_roof_intensive	float	Leaf are index for green roofs with intensive vegetation, defined by setting the appropriate building_pars field. The value is assigned to all intensive green roofs in the model domain
lai_high_vegetation_default	float	Default leaf area index for (high) vegetation used to generate the 3D leaf area density field. This value is used for all pixels for which no other leaf area density is available (i.e. to fill missing data)
lai_low_vegetation_default	float	Default leaf area index for (low) vegetation used to fill data gaps in the leaf area index distribution. This parameter only will a LOD2 leaf area index for parameterized vegetation via vegetation_type, i.e., through the vegetation_pars field
lai_alpha	float	Parameter for reconstruction of vertical LAD profiles based on tree shape parameters (alpha, beta) and the integral leaf area index after Markkanen et al. (2003). This scheme is used for vegetation patches (parks, forests), where the canopy can be considered to be pseudo-1D and for which usually no information on individual trees is available.
lai_beta	float	Parameter for reconstruction of vertical LAD profiles based on tree shape parameters (alpha, beta) and the integral leaf area index after Markkanen et al. (2003). This scheme is used for vegetation patches (parks, forests), where the canopy can be considered to be pseudo-1D and for which usually no information on individual trees is available.
patch_height_default	float	Default patch height (in m), which is used in the canopy generator to process canopy patches (parks, forests) for which data for individual trees is usually lacking. This parameter comes into affect for data gaps where no other vegetation height is available
season	string	As palm_csd can work with different sets of input data regarding leaf area index, this switch parameter can be set to either "summer" or "winter" to select the most suitable leaf area index input file to account for differences in leaf amount. Data for summer is usually from August (fully leaved), while data for winter is usually from April.

Example:

bridge_width = 3.0
debug_mode = False
lai_roof_extensive = 3.0
lai_roof_intensive = 1.5
lai_high_vegetation_default = 5.0
lai_low_vegetation_default = 1.0
lai_alpha = 5.0
lai_beta = 3.0
patch_height_default = 10.0
season = "summer"

[output]

This section describes the location for the static driver output.

Variable	Data type	Description
path	string	Directory where the output file shall be stored. Note that the static driver can - depending on model domain size - be quite large (in the order of several GB).
file_out	string	Output file name. The final output will be stored under path/file_out_domain, where domain will be "root" for the parent (root) domain, and "N01", "N02", etc., for child domains N01, N02, etc., respectively
version	integer	User-specific setting to track updates of a static driver. This value will be added as global attribute to the static driver

Example:

path = /ldata2/MOSAIK/
file_out = winter_iop1_test
version = 1

[input_01] - [input_XX]

The configuration file can include several sets of input data for different grid spacing. For each set of input data, an individual section must be provided and numbered accordingly (i.e., [input_01], [input_02], etc.).

Variable	Data type	Description
path	string	Directory where the NetCDF input files reside
pixel_size	float	Horizontal grid spacing (m) of a surface pixel of size dx*dy where dx = dy in the input data
file_x	string	UTM x-coordinates for the simulation domain (m)
file_y	string	UTM y-coordinates for the simulation domain (m)
file_lat	string	Latitude (degrees N) for the simulation domain
file_lon	string	Longitude (degrees E) for the simulation domain
file_zt	string	Terrain height (m)
file_buildings_2d	string	2D Building height (m)
file_building_id	string	Building ids
file_building_type	string	Building type distribution
file_bridges_2d	string	2D Map of bridge height (m)
file_bridges_id	string	Bridge ids
file_lai	string	Leaf area index
file_vegetation_type	string	Vegetation type distribution
file_vegetation_height	string	Vegetation height (m)
file_pavement_type	string	Pavement type distribution
file_water_type	string	Water type distribution
file_soil_type	string	Soil type distribution
file_street_type	string	Street type distribution (used for parameterized chemistry emissions and multi-agent model)
file_street_crossings	string	Street crossings (used for multi-agent model)
file_tree_height	string	Tree height (m) for street trees. For each tree only one value can be given at the center of the tree location
file_tree_crown_diameter	string	Tree crown diameter (m). For each tree only one value can be given at the center of the tree location
file_tree_trunk_diameter	string	Trunk diameter at breast height (m). For each tree only one value can be given at the center of the tree location
file_tree_type	string	Tree type according to the canopy generator tree inventory. For each tree only one value can be given at the center of the tree location
file_patch_height	string	2D distribution of the vegetation canopy height
file_vegetation_on_roofs	string	2D distribution of green roofs. Values can be 0.0-1.0. Intensive vegetation is considered for values >= 0.5, while extensive vegetation is assumed for values > 0.5

Example:

path = /ldata2/MOSAIK/Berlin_static_driver_data
pixel_size = 15.0
file_x = Berlin_CoordinatesUTM_y_15m_DLR.nc
file_y = Berlin_CoordinatesUTM_x_15m_DLR.nc
file_lat = Berlin_CoordinatesLatLon_y_15m_DLR.nc
file_lon = Berlin_CoordinatesLatLon_x_15m_DLR.nc
file_zt = Berlin_terrain_height_15m_DLR.nc
file_buildings_2d = Berlin_building_height_15m_DLR.nc
file_building_id = Berlin_building_id_15m_DLR.nc
file_building_type = Berlin_building_type_15m_DLR.nc
file_bridges_2d = Berlin_bridges_height_15m_DLR.nc
file_bridges_id = Berlin_bridges_id_15m_DLR.nc
file_lai =  Berlin_leaf_area_index_15m_DLR_WANG_summer.nc
file_vegetation_type = Berlin_vegetation_type_15m_DLR.nc
file_vegetation_height = Berlin_vegetation_patch_height_15m_DLR.nc
file_pavement_type = Berlin_pavement_type_15m_DLR.nc
file_water_type = Berlin_water_type_15m_DLR.nc
file_soil_type = Berlin_soil_type_15m_DLR.nc
file_street_type =  Berlin_street_type_15m_DLR.nc
file_street_crossings =  Berlin_street_crossings_15m_DLR.nc
file_tree_height =  Berlin_trees_height_clean_15m.nc
file_tree_crown_diameter =  Berlin_tree_crown_15m_DLR.nc
file_tree_trunk_diameter =  Berlin_trees_trunk_clean_15m.nc
file_tree_type =  Berlin_trees_type_15m_DLR.nc
file_patch_height =  Berlin_vegetation_patch_height_15m_DLR.nc
file_vegetation_on_roofs =  Berlin_vegetation_on_roofs_15m_DLR.nc

[domain_root] - [domain_XXX]

This section contains settings for each model domain for the PALM run. The section for the root domain domain must be named [domain_root]. In case of non-nested runs, this is the default model domain. In case of a nested run, the sections for the non-root domains must be named [domain_N01], [domain_N02], etc. as it is done in the PALM parameter file.

Variable	Data type	Description
pixel_size	float	Grid spacing in x and y / pixel size (m)
origin_x	float	x-origin of the model domain (m) with respect to the input data UTM coordinates
origin_y	float	y-origin of the model domain (m) with respect to the input data UTM coordinates
nx	float	Number of grid points in x-direction (equals the nx setting in the PALM parameter file
ny	float	Number of grid points in y-direction (equals the ny setting in the PALM parameter file
buildings_3d	logical	Use 3D buildings via the buildings_3d array to buildings instead of buildings_2d. This parameter must be true if bridges are present in the simulation domain. Note that the processing of 3D buildings by palm_csd is slower than 2D buildings
dz	float	Vertical grid spacing in PALM (m). This parameter is needed when buildings_3d}, {{{street_trees, canopy_patches, interpolate_terrain, or use_palm_z_axis is used
allow_high_vegetation	logical	If set to True, it is allowed to have high vegetation classes according in the vegetation_type distribution. Note that this can involve very large roughness lengths > 0.5 m. If the vertical grid spacings is close or smaller than this threshold the PALM run will crash and/or does not provide meaningful results. It is generally recommended to set this parameter to False whenever the grid spacing in small enough to resolve canopy patches be 2 or more vertical grid levels. If set to False pixels where a high vegetation type was prescribed will be converted into a 3D leaf area density canopy using the canopy generator
generate_vegetation_patches	logical	If set to True the embedded canopy generator will convert all surface pixels that contain high vegetation into a 3D leaf area density distribution. This applies to pixels where vegetation_type is set to a high vegetation type, or where the vegetation height field suggests high vegetation. Note that only pixels with heights > 2*dz are converted, while all other pixels will be parameterized via the vegetation_type field
use_palm_z_axis	logical	If set to True, the static driver will raster the input data on the z-grid of PALM for output. Note that PALM will convert continuous static driver data itself on its grid and apply additional filtering procedures. It is thus recommended to set this parameter to False unless interpolate_terrain = True in nested set-ups.
interpolate_terrain	logical	If set to True, the terrain height is interpolated and blended over between parent and child domains in order to avoid severe steps in terrain height due to different grid spacings between parent and child
domain_parent	string	Name of the parent domain of the current domain. If the current domain is the root domain, leave this parameter empty.
vegetation_on_roofs	logical	If set to True, allow green roofs
street_trees	logical	If set to true, information on individual street trees will be used to generate a 3D leaf area density and basal area density distribution for each tree. In contrast to vegetation patches, where a closed canopy is assumed and information is only distributed vertically for each pixel, street trees have a 3D shape that is mapped on the simulation domain

Example:

pixel_size = 15.0
origin_x = 19605
origin_y = 20895
nx = 199
ny = 199
buildings_3d = False
dz = 15.0
allow_high_vegetation = True
generate_vegetation_patches = True
use_palm_z_axis = False
interpolate_terrain = False
domain_parent
vegetation_on_roofs = True
street_trees = True

Required input data

At the moment it is required to provide all input files as listed under [input_XX]. For a given pixel size (i.e. horizontal grid spacing), only one set of input files can be provided. All input data must be two-dimensions (y,x). Currently, palm_csd expects all variables in the respective input files to be named 'Band1'. It is planned to implement a more flexible interface in the near future.

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Technical documentation

Under construction.

Overview

Processing of nested domains

Canopy generator

Single trees

# #1 Tree shapes were manually lookep up. # #2 Crown h/w ratio - missing # #3 Crown diameter based on Berlin tree statistics # #4 Tree height based on Berlin tree statistics # #5 Tree LAI summer - missing # #6 Tree LAI winter - missing # #7 Height of lad maximum - missing # #8 Ratio LAD/BAD - missing # #9 Trunk diameter at breast height from Berlin

Index	|=Species	Shape	Crown height/width	Height of maximum LAD (m)	ratio	Crown diameter (m)	Height (m)	LAI summer	LAI winter	LAD/BAD ratio	DBH (m)
0	Default	1.0	1.0	4.0	12.0	3.0	0.8	0.6	0.025	0.35
1	Abies	3.0	1.0	4.0	12.0	3.0	0.8	0.6	0.025	0.80
2	Acer	1.0	1.0	7.0	12.0	3.0	0.8	0.6	0.025	0.80
3	Aesculus	1.0	1.0	7.0	12.0	3.0	0.8	0.6	0.025	1.00
4	Ailanthus	1.0	1.0	8.5	13.5	3.0	0.8	0.6	0.025	1.30
5	Alnus	3.0	1.0	6.0	16.0	3.0	0.8	0.6	0.025	1.20
6	Amelanchier	1.0	1.0	3.0	4.0	3.0	0.8	0.6	0.025	1.20
7	Betula	1.0	1.0	6.0	14.0	3.0	0.8	0.6	0.025	0.30
8	Buxus	1.0	1.0	4.0	4.0	3.0	0.8	0.6	0.025	0.90
9	Calocedrus	3.0	1.0	5.0	10.0	3.0	0.8	0.6	0.025	0.50
10	Caragana	1.0	1.0	3.5	6.0	3.0	0.8	0.6	0.025	0.90
11	Carpinus	1.0	1.0	6.0	10.0	3.0	0.8	0.6	0.025	0.70
12	Carya	1.0	1.0	5.0	17.0	3.0	0.8	0.6	0.025	0.80
13	Castanea	1.0	1.0	4.5	7.0	3.0	0.8	0.6	0.025	0.80
14	Catalpa	1.0	1.0	5.5	6.5	3.0	0.8	0.6	0.025	0.70
15	Cedrus	1.0	1.0	8.0	13.0	3.0	0.8	0.6	0.025	0.80
16	Celtis	1.0	1.0	6.0	9.0	3.0	0.8	0.6	0.025	0.80
17	Cercidiphyllum	1.0	1.0	3.0	6.5	3.0	0.8	0.6	0.025	0.80
18	Cercis	1.0	1.0	2.5	7.5	3.0	0.8	0.6	0.025	0.90
19	Chamaecyparis	5.0	1.0	3.5	9.0	3.0	0.8	0.6	0.025	0.70
20	Cladrastis	1.0	1.0	5.0	10.0	3.0	0.8	0.6	0.025	0.80
21	Cornus	1.0	1.0	4.5	6.5	3.0	0.8	0.6	0.025	1.20
22	Corylus	1.0	1.0	5.0	9.0	3.0	0.8	0.6	0.025	0.40
23	Cotinus	1.0	1.0	4.0	4.0	3.0	0.8	0.6	0.025	0.70
24	Crataegus	3.0	1.0	3.5	6.0	3.0	0.8	0.6	0.025	1.40
25	Cryptomeria	3.0	1.0	5.0	10.0	3.0	0.8	0.6	0.025	0.50
26	Cupressocyparis	3.0	1.0	3.0	8.0	3.0	0.8	0.6	0.025	0.40
27	Cupressus	3.0	1.0	5.0	7.0	3.0	0.8	0.6	0.025	0.40
28	Cydonia	1.0	1.0	2.0	3.0	3.0	0.8	0.6	0.025	0.90
29	Davidia	1.0	1.0	10.0	14.0	3.0	0.8	0.6	0.025	0.40
30	Elaeagnus	1.0	1.0	6.5	6.0	3.0	0.8	0.6	0.025	1.20
31	Euodia	1.0	1.0	4.5	6.0	3.0	0.8	0.6	0.025	0.90
32	Euonymus	1.0	1.0	4.5	6.0	3.0	0.8	0.6	0.025	0.60
33	Fagus	1.0	1.0	10.0	12.5	3.0	0.8	0.6	0.025	0.50
34	Fraxinus	1.0	1.0	5.5	10.5	3.0	0.8	0.6	0.025	1.60
35	Ginkgo	3.0	1.0	4.0	8.5	3.0	0.8	0.6	0.025	0.80
36	Gleditsia	1.0	1.0	6.5	10.5	3.0	0.8	0.6	0.025	0.60
37	Gymnocladus	1.0	1.0	5.5	10.0	3.0	0.8	0.6	0.025	0.80
38	Hippophae	1.0	1.0	9.5	8.5	3.0	0.8	0.6	0.025	0.80
39	Ilex	1.0	1.0	4.0	7.5	3.0	0.8	0.6	0.025	0.80
40	Juglans	1.0	1.0	7.0	9.0	3.0	0.8	0.6	0.025	0.50
41	Juniperus	5.0	1.0	3.0	7.0	3.0	0.8	0.6	0.025	0.90
42	Koelreuteria	1.0	1.0	3.5	5.5	3.0	0.8	0.6	0.025	0.50
43	Laburnum	1.0	1.0	3.0	6.0	3.0	0.8	0.6	0.025	0.60
44	Larix	3.0	1.0	7.0	16.5	3.0	0.8	0.6	0.025	0.60
45	Ligustrum	1.0	1.0	3.0	6.0	3.0	0.8	0.6	0.025	1.10
46	Liquidambar	3.0	1.0	3.0	7.0	3.0	0.8	0.6	0.025	0.30
47	Liriodendron	3.0	1.0	4.5	9.5	3.0	0.8	0.6	0.025	0.50
48	Lonicera	1.0	1.0	7.0	9.0	3.0	0.8	0.6	0.025	0.70
49	Magnolia	1.0	1.0	3.0	5.0	3.0	0.8	0.6	0.025	0.60
50	Malus	1.0	1.0	4.5	5.0	3.0	0.8	0.6	0.025	0.30
51	Metasequoia	5.0	1.0	4.5	12.0	3.0	0.8	0.6	0.025	0.50
52	Morus	1.0	1.0	7.5	11.5	3.0	0.8	0.6	0.025	1.00
53	Ostrya	1.0	1.0	2.0	6.0	3.0	0.8	0.6	0.025	1.00
54	Parrotia	1.0	1.0	7.0	7.0	3.0	0.8	0.6	0.025	0.30
55	Paulownia	1.0	1.0	4.0	8.0	3.0	0.8	0.6	0.025	0.40
56	Phellodendron	1.0	1.0	13.5	13.5	3.0	0.8	0.6	0.025	0.50
57	Picea	3.0	1.0	3.0	13.0	3.0	0.8	0.6	0.025	0.90
58	Pinus	3.0	1.0	6.0	16.0	3.0	0.8	0.6	0.025	0.80
59	Platanus	1.0	1.0	10.0	14.5	3.0	0.8	0.6	0.025	1.10
60	Populus	1.0	1.0	9.0	20.0	3.0	0.8	0.6	0.025	1.40
61	Prunus	1.0	1.0	5.0	7.0	3.0	0.8	0.6	0.025	1.60
62	Pseudotsuga	3.0	1.0	6.0	17.5	3.0	0.8	0.6	0.025	0.70
63	Ptelea	1.0	1.0	5.0	4.0	3.0	0.8	0.6	0.025	1.10
64	Pterocaria	1.0	1.0	10.0	12.0	3.0	0.8	0.6	0.025	0.50
65	Pterocarya	1.0	1.0	11.5	14.5	3.0	0.8	0.6	0.025	1.60
66	Pyrus	3.0	1.0	3.0	6.0	3.0	0.8	0.6	0.025	1.80
67	Quercus	1.0	1.0	8.0	14.0	3.1	0.1	0.6	0.025	0.40#
68	Rhamnus	1.0	1.0	4.5	4.5	3.0	0.8	0.6	0.025	1.30
69	Rhus	1.0	1.0	7.0	5.5	3.0	0.8	0.6	0.025	0.50
70	Robinia	1.0	1.0	4.5	13.5	3.0	0.8	0.6	0.025	0.50
71	Salix	1.0	1.0	7.0	14.0	3.0	0.8	0.6	0.025	1.10
72	Sambucus	1.0	1.0	8.0	6.0	3.0	0.8	0.6	0.025	1.40
73	Sasa	1.0	1.0	10.0	25.0	3.0	0.8	0.6	0.025	0.60
74	Sequoiadendron	5.0	1.0	5.5	10.5	3.0	0.8	0.6	0.025	1.60
75	Sophora	1.0	1.0	7.5	10.0	3.0	0.8	0.6	0.025	1.40
76	Sorbus	1.0	1.0	4.0	7.0	3.0	0.8	0.6	0.025	1.10
77	Syringa	1.0	1.0	4.5	5.0	3.0	0.8	0.6	0.025	0.60
78	Tamarix	1.0	1.0	6.0	7.0	3.0	0.8	0.6	0.025	0.50
79	Taxodium	5.0	1.0	6.0	16.5	3.0	0.8	0.6	0.025	0.60
80	Taxus	2.0	1.0	5.0	7.5	3.0	0.8	0.6	0.025	1.50
81	Thuja	3.0	1.0	3.5	9.0	3.0	0.8	0.6	0.025	0.70
82	Tilia	3.0	1.0	7.0	12.5	3.0	0.8	0.6	0.025	0.70
83	Tsuga	3.0	1.0	6.0	10.5	3.0	0.8	0.6	0.025	1.10
84	Ulmus	1.0	1.0	7.5	14.0	3.0	0.8	0.6	0.025	0.80
85	Zelkova	1.0	1.0	4.0	5.5	3.0	0.8	0.6	0.025	1.20
86	Zenobia	1.0	1.0	5.0	5.0	3.0	0.8	0.6	0.025	0.40

Vegetation canopies

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Best practices

The following example is a best practice setting for a high-resolution (1 m grid spacing) non-nested run in which most of the vegetation can be resolved via a 3D leaf area density distribution:

[domain_root]
domain_parent
pixel_size = 1.0
origin_x = ...
origin_y = ...
nx = ...
ny = ...
dz = ...
allow_high_vegetation = False
buildings_3d = True
generate_vegetation_patches = True
use_palm_z_axis= False
interpolate_terrain = False
vegetation_on_roofs = True
street_trees = True

For a nested run, the following settings should work nicely to avoid terrain height issues:

[domain_root]
domain_parent
pixel_size = 15.0
dz = 15.0
origin_x = ...
origin_y = ...
nx = ...
ny = ...
buildings_3d = False
allow_high_vegetation = True
generate_vegetation_patches = True
use_palm_z_axis= False
interpolate_terrain = False
vegetation_on_roofs = False
street_trees = True

[domain_N02]
domain_parent = root
pixel_size = 1.0
dz = 1.0
origin_x = ...
origin_y = ...
nx = ...
ny = ...
buildings_3d = True
allow_high_vegetation = False
generate_vegetation_patches = True
use_palm_z_axis= True
interpolate_terrain = True
vegetation_on_roofs = True
street_trees = True

---

Example static driver file

An example static driver file can be downloaded here​ (built for PALM r4311).

Snapshot of building heights in example static driver file (using ncview)

ncdump of the static driver file header

Literature

• Heldens, W., Burmeister, C., Kanani-Sühring, F., Maronga, B., Pavlik, D., Sühring, M., Zeidler, J., and Esch, T.: Geospatial input data for the PALM model system 6.0: model requirements, data sources and processing, Geosci. Model Dev., 13, 5833–5873, ​https://doi.org/10.5194/gmd-13-5833-2020, 2020.
• Lalic, B. and Mihailovic, D. T., An Empirical Relation Describing Leaf-Area Density inside the Forest for Environmental Modeling. Journal of Applied Meteorology, vol. 43, no. 4, pp. 641–645, 2004. doi:10.1175/1520-0450(2004)043<0641:AERDLD>2.0.CO;2.
• Markkanen, T., Rannik, Ü., Marcolla, B. et al. Footprints and Fetches for Fluxes over Forest Canopies with Varying Structure and Density. Boundary-Layer Meteorology 106, 437–459 (2003). ​https://doi.org/10.1023/A:1021261606719