AAIR Project: Sub Task 3.1 Empirical model of breakage
Participant : The Forestry Authority,
Northern Research Station,
Roslin, Midlothian,
Scotland, EH25 9SY
Contact: C P Quine, B A Gardiner, P D Bell.
Description:
Development of an empirical model of breakage and overturning of a single tree by wind. Derivation of mathematical relationships which take individual tree and site characteristics and calculate the critical windspeed required to break or overturn the tree.
Inputs:
Species (wood strength - growth rate), tree height and diameter, spacing, soil type and site preparation. Information on ht/diam relationships may be obtained from
Umea in task 2.2, and details of strength properties from Aberdeen at task 2.1, and Umea at 2.2. Information will also be required from mensurational databases and any empirical relationships developed from them.
Outputs:
Critical windspeed for breakage and critical windspeed for overturning (for incorporation by MLURI at Task 6).
Method:
A mathematical model will be used to determine the mean force on a tree due to a particular wind speed above the canopy as a function of the tree and stand characteristics (tree height, canopy width, canopy depth, drag coefficient and stand spacing). This will then be converted to an extreme bending moment on the tree using an empirically derived gust factor and assuming the wind load acts at the height of the zero plane displacement (d). The empirical relationships derived by the Forestry Authority in Task 2.3 and values for the Modulus of Rupture of the species in question (link with Aberdeen in Task 2.1) will be used to derive the windspeeds at which the tree will fail by overturning or stem breakage.
Uses:
Single tree model to be combined into a stand model through developments in Task 4 (by Forestry Authority, MLURI and Joensuu in 4.1 and 4.2), to form part of the predictive model at Task 6 put together by MLURI. Output to be tested against that of the independently derived mechanistic model of Joensuu (Task 3.3).
References:
Gardiner, B. A. 1992. Mathematical modelling of the static and dynamic characteristics of plantation trees. In 'Mathematical Modelling of Forest Ecosystems' (eds. J. Franke and A. Roeder), Sauerländer's Verlag, Frankfurt am Main, pp 40-61.
Gardiner, B.A., Stacey, G. R., Belcher, R. E. and Wood C. J. 1995. Field and wind tunnel assessment of the implications of respacing and thinning on tree stability. In preparation.
Oliver, H. R. and Mayhead, G. J. 1974. Wind measurement in a pine forest during a destructive gale. Forestry, 47, 185-194.
Peltola, H. 1995. Studies on the mechanism of wind-induced damage of Scots pine. PhD, Faculty of Forestry, University Of Joensuu, Finland.
Raupach, M. R. 1992. Drag and drag partitioning on rough surfaces. Boundary Layer Meteorology, 60, 375-395.
Participant: The Forestry Authority
MODELS USED FOR DATA ANALYSIS
I. Model Name: ECBREAK.MCD, ECBREAK.PAS (in preperation)
II. Source of Model: Forestry Commission
III. Computer language: Mathcad 5.0+, Turbo Pascal 7.0.
IV. Hardware needed: 386/486/586 PC
V. Data Inputs needed: Tree species, height, diameter, stem volume, canopy width, canopy depth, stand spacing and soil type.
VI. Model Outputs
VII. Accuracy/Sources of Uncertainty/Method of Handling: Largest error will be the inaccuracy of the empirical relationships for calculating the overturning moment developed by the Forestry Authority in Task 2.3. Model output will be tested for its sensitivity to variation in input parameters. Model predictions of applied bending moment will be tested against existing field and wind tunnel measurements of bending moment. A more difficult test is whether the critical wind speed predictions are correct because there is very little reliable data of the wind speed above forests during damaging storms. Comparisons of the model output with those from the model being developed by Joensuu in Task 3.3 will be carried out to identify any differences that might indicate logical inconsistencies. One difficulty is that the model at present can only predict the critical wind speeds for the mean tree in the forest and cannot say anything about variation in vulnerability within a stand. This is to be addressed in Task 4. Furthermore, it calculates the mean loading on the trees which has to be converted to an extreme value using an empirically derived gust factor which may vary between species.
VIII. Existing linkages between data and software:
Initial tests of the effect of spacing in Sitka spruce on the predicted applied bending moment have given very good agreement against experimental data from field and wind tunnel experiments (Gardiner et al., 1995). Further model tests against measurements of applied bending moment made in the field are planned. Model predictions of aerodynamic roughness (z0) and zero plane displacement (d) (Raupach 1992) are being compared against field and wind tunnel measurements of these parameters for a variety of tree spacings. Predictions of critical wind speed will be tested against data from storms known to have caused damage (Oliver and Mayhead, 1974).
IX. GIS Software used:
X. Modelling Software used:
XI. Database Software used:
XII. Any other comments:
Prepared by C P Quine/B A Gardiner/ P D Bell
May 1995