Forest GALES model

user_name Barry Gardiner
user_organisation Forestry Commission
Northern Research Station
Roslin
Midlothian EH25 9SY
Scotland, UK
date 12 June 1996
model_name Treesnap.pas
description A model to calculate the critical wind speed for breakage and overturning based on tree characteristics
software Turbo Pascal 7
operating_system PC in DOS or Windows
isumm Tree Characteristics a. Tree Height
b. Tree Diameter at 1.3m above base
c. Spacing between trees
d. Tree species
e. Soil type
ispecfile Tree species and soil selected from menus
Tree height, diameter and spacing input from keyboard

See below:
Please select Tree Species - (then Enter)
  Scots Pine
  Corsican Pine
  Lodgepole Pine
  Ponderosa Pine
  European Larch
  Japanese Larch
  Hybrid Larch
  Douglas Fir
  Norway Spruce
  Sitka Spruce
  White Fir
  Grand Fir
  Noble Fir
  Balsom Fir
  Western Hemlock
  Western Red Cedar
  Lawson Cypress
  Red Alder
Please select Soil Type - (then Enter)
  Brown Earth
  Intergrade (Brown Earth-Ironpan)
  Podzol
  Iron Pan
  Intergrade (Brown Earth-Gley)
  Peaty Gley
  Gley
  Flushed Basin Peat
  Flushed Blanket Peat
  Unflushed Sphagnum Bog
  Unflushed Blanket Bog
  Calcareous Soil
  Skeletal Soil
  Eroded Bog
  Littoral Soil

TREE CHARACTERISTICS
Enter Tree Height in metres 15
  
Enter Tree dbh in centimetres20
  
Are all the values correct (Y/N)?

iexpspecfile This model is an interactive version of a model designed
to read IDRISI .img files and output critical wind speeds
in the same format. It is designed to calculate the critical
wind speed for an individual tree.
ivar1 Tree Species
ifile1  
idescr1 Descriptor selected from menu

Please select Tree Species - (then Enter)
  Scots Pine
  Corsican Pine
  Lodgepole Pine
  Ponderosa Pine
  European Larch
  Japanese Larch
  Hybrid Larch
  Douglas Fir
  Norway Spruce
  Sitka Spruce
  White Fir
  Grand Fir
  Noble Fir
  Balsom Fir
  Western Hemlock
  Western Red Cedar
  Lawson Cypress
  Red Alder

isensitiv1 Very Sensitive
isensdescr1 Limited comparisons between Sitka spruce and Radiata pine
ivar2 Soil Type
ifile2  
idescr2 Descriptor selected from menu
isensitiv2 Very Sensitive
isensdescr2 Limited comparison between freely draining and poorly
draining soils in Britain
ivar3 Tree Height
ifile3  
idescr3 metres
isensitiv3 Not Very Sensitive
isensdescr3 Comparison of change in critical wind speed with change in height from 5 - 25 metres
ivar4 Tree diameter
ifile4  
idescr4 centimetres
isensitiv4 Sensitive
isensdescr4 Comparison of change in critical wind speed with change in
diameter from 10 -30 centimetres
ivar5 Tree spacing
ifile5  
idescr5 metres between trees
isensitiv5 Sensitive
isensdescr5 Tested model against measurements of change in wind loading
with spacings between 1.8 - 4.9 metres
csumm Various constants are used to calculate wind loading, tree
resistance to breakage and tree resistance to overturning

These constants are currently fixed but will be changed as
new analysis is completed

cspecfile Constants

Aerodynamic constants
  c=0.25; {constant}
  Cr=0.3; {Element drag coefficient}
  Cd=0.3; {Constant}
  Cs=0.003; {Surface drag coefficient}
  Cw=4; {Constant}
  ro=1.25; {Air density}
  k=0.4; {Von Karman's constant}
  Calc_Ht=10; {Height above d at which we require wind speed}

Overturning Resistance Constants
  c=0.25; {constant}
  case species of
  1:case soil of
  1:overturn:=194;
  2:overturn:=154;
  3:overturn:=148;
  4:overturn:=161;
  5,6,7:overturn:=160;{using data from CP}
  8,9,10,11:overturn:=174;{using data from LP}
  12,13,14,15:overturn:=172;
  end;
  2:case soil of
  1,2,3:overturn:=148; {no data for brown earth or podzol}
  4:overturn:=120;
  5,6:overturn:=143;
  7:overturn:=160;
  8,9,10,11:overturn:=174;{using LP data}
  12,13,14,15:overturn:=172;
  end;
  3:case soil of
  1,2,3:overturn:=149;{no data for brown earth or brown earth-Ironpan}
  4:overturn:=157;
  5,6,7:overturn:=135;
  8,9,10,11:overturn:=174;
  12,13,14,15:overturn:=172;{using SP data}
  end;
  5,6,7:case soil of
  1,2,3:overturn:=149;{using data from LP}
  4:overturn:=176;
  5,6,7:overturn:=135;{using data from LP}
  8,9,10,11:overturn:=174;{using data from LP}
  12,13,14,15:overturn:=172;{using data from SP}
  end;
  8:case soil of
  1,2:overturn:=155;
  3:overturn:=174;
  4:overturn:=156;{using data from LP}
  5,6,7:overturn:=168;
  8,9,10,11:overturn:=174;{using data from LP}
  12,13,14,15:overturn:=172;{using data from SP}
  end;
  9:case soil of
  1,2:overturn:=161;
  3:overturn:=166;
  4:overturn:=171;{using data from SS}
  5,6:overturn:=136;{using data from SS}
  7:overturn:=124;
  8,9,10,11:overturn:=146;{using data from SS}
  12,13,14,15:overturn:=172;{using data from SP}
  end;
  10,11,15,16,17:case soil of
  1:overturn:=168;
  2:overturn:=161;
  3:overturn:=165;{using data from NS}
  4:overturn:=171;
  5,6:overturn:=136;
  7:overturn:=161;
  8,9,10,11:overturn:=146;
  12,13,14,15:overturn:=172;{using data from SP}
  end;
  12,13:case soil of
  1,2:overturn:=206;
  3:overturn:=174;{using data from DF}
  4:overturn:=156;{using data from LP}
  5,6,7:overturn:=168;
  8,9,10,11:overturn:=174;{using data from LP}
  12,13,14,15:overturn:=172;{using data from SP}
  end;
  end;

Tree Breakage Constants

   case species of
  1:MOR:=4.6E7;{+-8.1}
  2:MOR:=4.1E7;{+-7.2}
  3:MOR:=4.1E7;{+-8.3}
  4:MOR:=3.8E7;{+-5.8}
  5:MOR:=5.3E7;{+-8.5}
  6:MOR:=4.8E7;{+-10.5}
  7:MOR:=4.3E7;{+-4.6}
  8:MOR:=5.3E7;{+-9.1}
  9:MOR:=3.6E7;{+-6.0}
  10:MOR:=3.4E7;{+-7.0}
  11:MOR:=3.5E7;{+-6.9}{Using Grand fir}
  12:MOR:=3.5E7;{+-6.9}
  13:MOR:=3.4E7;{+-5.4}
  14:MOR:=4.3E7;{+-7.8}
  15:MOR:=4.1E7;{+-7.3}
  16:MOR:=3.8E7;{+-6.5}
  17:MOR:=4.8E7;{+-6.4}
  18:MOR:=4.9E7;{+-6.1}
  end;
 end;

cexpspecfile Constants

Aerodynamic constants
  c=0.25; {constant}
  Cr=0.3; {Element drag coefficient}
  Cd=0.3; {Constant}
  Cs=0.003; {Surface drag coefficient}
  Cw=4; {Constant}
  ro=1.25; {Air density}
  k=0.4; {Von Karman's constant}
  Calc_Ht=10; {Height above d at which we require wind speed}

Overturning Resistance Constants

overturn:=194; {Slope of regression between stem weight and
resistance to overturning. Value is Nm/kg. Value is a
function of species and soil}

MOR:=4.6E7;{Modulus of rupture in Pa. Value is function
of tree species. From G.M. Lavers, The Strength Properties
of Timber, BRE Report}
osumm Model outputs critical wind speed for breakage and
overturning at 10 metres above the zero plane
displacement (approximately 80% tree height) and
at canopy top. It also outputs the value of base
bending moment to cause damage and the mean base
bending moment during an hour in which damage would occur.
ospecfile
 RESULTS
 Tree Species = Scots Pine
 Soil Type = Brown Earth
 Tree Height = 15.0 m
 Tree dbh = 20.0 cm
 Spacing between Trees = 2.0 m
  
 Wind Speed at 10m above d Required for Overturning = 47.6 m/s
 Wind Speed at Canopy Top Required for Overturning = 20.0 m/s
 Wind Speed at 10m above d Required for Breakage = 52.8 m/s
 Mean Bending Moment at Tree Base at Failure = 5254 Nm
 Max Bending Moment at Tree Base at Failure = 38302 Nm
  
 Hit any key to continue
oexpspecfile Wind speeds are in metres/sec
Bending Moments are in Nm
stat_meth The drag values used to calculate the wind loading are
based on wind tunnel measurements on full size trees by
Mayhead, G. J. (1973), Agricultural Meteorology, 12, 123
-130.

The canopy width is based on an empirical relationship
calculated by Rollinson,T. J. D. (1988), Forestry, 61, 1-22

The resistance to overturning is based on empirical relationships
between stem weight and overturning moment from tree pulling
experiments on over 1500 trees. See Fraser, A. I. and
Gardiner, J. B. H. (1967). Rooting and stability in
Sitka spruce. Forestry Commission Bulletin, 40, HMSO,
London, 28p.

The gust factor used in the calculations is based
on an empirical relationship between the ratio of
mean to maximum loading versus the ratio of spacing
to tree height derived by Gardiner, B. A. et al. (1997),
Field and Wind Tunnel Assessments of the Implications
of Respacing and Thinning for Tree Stability, Forestry, 70(2).

The effect of self weight in overturning the tree is an empirical
relationship based on analysis of the tree pulling database
mech_meth There are mechanistic relationships used to calculate
the wind loading on the tree based on tree height, tree
spacing,canopy depth and canopy width. This involves
calculating the zero plane displacementand aerodynamic
roughness using the method of Raupach, M. R. (1992),
Drag and drag partitioning on rough surfaces,
Boundary-Layer Meteorol., 60, 375-395.

The calculation of the critical loading to break the
tree is based on engineering principles, see for
example Morgan, J. and Cannell, M. G. R. (1994),
Shape of tree stems: a re-examination of the uniform
stress hypothesis, Tree Physiology, 5, 63-74. The
values of MOR used are based on test on samples in the
laboratory (G.M. Lavers (1983), The Strength Properties
of Timber, BRE Report)
b. Tree Diameter at 1.3m above base
c. Spacing between trees
d. Tree species
e. Soil type
log_meth  
scope The parameters currently in the model are based on data
for British trees. Trees growing in other countries
will have different empirical relationships between
resistance to overturning and stem weight and different
MOR values. The MOR values are a function of wood density
so this can probably be built into the model but the
resistance to overturning values will require analysis
of tree pulling experiments from other countries. In
Europe data are available from Finland, Ireland, Germany,
Denmark and Sweden that we know about.

The model assumes that the forest is completely uniform
and cannot deal with uneven height forests. Currently
no account is taken of the tree's position in the forest
but this will be remedied shortly.
other This is a preliminary description of the model. More
information will be added in the future. A joint
publication is currently being written by B. A. Gardiner
and H. Peltola describing and comparing their two models.
Submission should be by August/September 1997
copyright None
contact Barry Gardiner B.A.Gardiner@forestry.gov.uk