Forestry Advance Access originally published online on June 19, 2008
Forestry 2008 81(3):447-463; doi:10.1093/forestry/cpn022
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This article appears in the following Forestry issue: Wind and Trees Special Issue [View the issue table of contents]
A review of mechanistic modelling of wind damage risk to forests
1 Forest Research, Northern Research Station, Roslin, Midlothian EH25 9SY, Scotland
2 Department of Forest Sciences, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4
3 Laboratory of Forest Management, Graduate School of Agricultural and Life Sciences, University of Tokyo, Tokyo 113-8657, Japan
4 Present address: Forestry and Forest Products Research Institute, 1 Matsunosato, Tsukuba, Ibaraki 7 305-8687, Japan
5 Faculty of Forest Sciences, University of Joensuu, FI-80101 Joensuu, Finland
6 Département des sciences du bois et de la forêt Faculté de Foresterie et de Géomatique, Pavillon Abitibi-Price 2405, rue de la Terrasse, Local 1212, Université Laval, Québec, Canada G1V 0A6
* Corresponding author. E-mail: barry.gardiner{at}forestry.gsi.gov.uk
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Summary |
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 Top Summary IntroductionMechanistic wind damage risk...Current limitations of...DiscussionConclusionsFundingAcknowledgementsReferences |
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This paper reviews the current status of mechanistic models for wind damage risk assessment, describing model structure, applicability, validation and current limitations. We focus particularly on the hybrid mechanistic/empirical models GALES and HWIND, which have been designed for calculating wind damage risk at the stand level within uniform forests and which are the most widely adopted models within the research community. These models have been integrated with different methods for predicting the local wind climate in order to calculate the probability of wind damage in a number of different countries. We also discuss ongoing modelling work and proposals for future development in order to deal with complex forest structures and to predict the wind damage risk of individual trees within stands through the integration of mechanistic risk models with forest growth and yield models within a geographical information system framework. This kind of model integration will enable spatial representation of tree lists and damage propagation and allow managers to evaluate the effect of different harvesting and thinning scenarios on the risk of windthrow of both stands and individual trees within a stand.
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Introduction |
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TopSummaryIntroductionMechanistic wind damage risk...Current limitations of...DiscussionConclusionsFundingAcknowledgementsReferences |
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Wind-induced failure of roots or stems is a common natural disturbance in forests that produces ecological impacts and imposes economic costs (e.g. Mitchell, 1995
). In this paper, we refer to any wind-induced damage such as uprooting or stem breakage as ‘windthrow'. Windthrow resulting from an infrequent occurrence associated with exceptionally strong winds generated locally by thunderstorm downbursts or by extensive intense low pressure systems is often termed catastrophic. Damage caused by frequently recurring peak winds that is concentrated in areas of low stand stability and/or high wind exposure where recent harvesting or thinning has increased wind loading on retained trees is described as endemic (Miller et al., 1987). Newly created windward-facing boundaries and excessively thinned stands are particularly prone to endemic damage (Gardiner et al., 2005; Lanquaye and Mitchell, 2005; Scott and Mitchell, 2005). Therefore, forest managers need tools for predicting windthrow risk and the consequent management efforts in order to reduce the risk of this type of damage. In engineering, ‘risk' integrates the likelihood of an event with the consequences of the damage caused by that event. The consequences of windthrow include ecological changes, timber loss, damage to infrastructure and loss of life. Given this broad range of possible consequences, it has been customary in the windthrow literature to limit the concept of ‘wind damage risk' to the likelihood of a particular level of tree uprooting or breakage. A more appropriate term might be ‘wind damage probability modelling'.
A range of observational tools and empirical and mechanical models have been developed over the last 20 years to help managers predict the risk of windthrow. Qualitative assessments are commonly used by decision makers to assess windfirmness (e.g. Miller et al., 1987; Mitchell, 1998). While these are useful field assessment tools and enable practitioners to incorporate local experience, they do not quantify the link between tree and stand attributes and wind damage. Empirical models have also been developed to assess the probability and expected proportion of stand damage based on tree and stand attributes (e.g. Valinger and Fridman, 1997; Lanquaye and Mitchell, 2005; Scott and Mitchell, 2005). These statistical models may be quite accurate for specific locations and may be portable to other locations (Lanquaye and Mitchell, 2005). However, they provide only general insights into the mechanisms of windthrow.
Mechanistic models attempt to characterize the physical processes involved in tree uprooting or failure. They are useful for developing hypotheses and investigating component processes, organizing experimental results and making predictions for new management scenarios. Specific information is, however, required to customize and validate these models in different forest types and regions. This paper reviews the current status of mechanistic models for wind damage risk assessment, describing model structure and applicability, validation and current limitations. We also describe the ongoing work and proposals for their future development. We focus particularly on the hybrid mechanistic/empirical models HWIND (Peltola et al., 1999) and GALES (Gardiner et al., 2000) because these are the models that have been most widely adopted within the research community. Although these models have so far been able to represent only simple harvesting and thinning scenarios, significant progress has been made in linking these mechanistic models to geographical information systems (GISs) in order to develop spatial interfaces that allow representation of more complex harvesting scenarios and stands.
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Mechanistic wind damage risk modelling |
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TopSummaryIntroductionMechanistic wind damage risk...Current limitations of...DiscussionConclusionsFundingAcknowledgementsReferences |
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Outline of mechanistic modelling
The mechanistic wind damage models developed so far calculate windthrow probability in two separate stages. The initial stage is to calculate the above-canopy ‘critical wind speed' (CWS) required to break or overturn trees within a forest. The second stage is to use some assessment of the local wind climatology to calculate the probability of such a wind speed occurring at the geographic location of the trees. It is this probability of damage that is termed the ‘risk of damage'. The approaches taken to calculate the CWS and the local wind climate vary between models but all the models discussed adopt this approach. We will first review the basic background to the models used to calculate the CWS and then discuss the methods used to calculate the local wind climate.
Prediction of CWS
At the most basic level, mechanistic models calculate the CWS based on the applied forces on individual trees due to the wind and the resistive forces of the roots and stem. Applied forces depend on factors such as local wind speed, upwind conditions, tree position in the canopy, crown characteristics (e.g. mass, size and streamlining) and stem characteristics (e.g. shape, length and mass). The tree-resistive forces depend on factors such as stem characteristics (e.g. diameter and wood strength), root plate morphology, soil type and soil moisture. These factors can vary widely depending on vertical and horizontal location of the tree crown within the canopy, stand geographic location, wind exposure and tree species. As a result, the ideal mechanistic model needs to accurately integrate these factors and account for their variability spatially, temporally and between species (see Quine and Gardiner, 2007).
Models predicting the CWS can be regarded as hybrid models because the component calculations include both empirical relationships and physical relationships. For example, stem mass is an excellent empirical predictor of critical resistive bending moment and is also used in a simple physical equation to predict tree self-loading due to deflection. The streamlining of tree crowns under wind loading has been determined using wind tunnel experiments (e.g. Mayhead, 1973; Rudnicki et al., 2004), whereas the interaction between the wind and tree canopies has been quantified using field measurements (e.g. Gardiner, 1995; Hassinen et al., 1998; Rudnicki et al., 2000), wind tunnel measurements (e.g. Stacey et al., 1994; Gardiner et al., 2005) and numerical modelling (e.g. Yang et al., 2006).
The resistance of the trees to overturning and breakage is based on empirical relationships developed from tree pulling and timber strength tests (see e.g. Moore, 2000; Nicoll et al., 2006; Peltola, 2006). The resistance to overturning in all the models is based on correlations between the bending moment required to overturn trees and stem weight or root–soil plate weight (stem and root weight are highly correlated for individual tree species, e.g. Levy et al., 2004). The resistance to breakage is always calculated as the bending moment required to exceed the critical stress at the surface of the stem at which the wood breaks (modulus of rupture or MOR) and is related to the diameter of the stem and the tree species. These relations can be simplified to state that stem volume (e.g. height x (d.b.h.)2) best predicts the resistance to uprooting, whereas (d.b.h.)3 best predicts resistance to stem breakage (Quine and Gardiner, 2007).
The basic structures of the different mechanistic models developed so far (HWIND, Peltola et al., 1999; GALES, Gardiner et al., 2000; FOREOLE, Ancelin et al., 2004) are very similar (Peltola, 2006). The differences lie in the exact method for calculating the values at each stage of the model. In HWIND and FOREOLE, the wind loading is calculated from the predicted wind profile within or in front of the forest and the canopy frontal area, whereas in GALES, the wind loading on the trees is usually calculated using the ‘roughness method' which calculates the wind-induced stress distribution on the trees within a forest. However, if required, it is also possible to use the profile method in GALES.
Prediction of wind climate
The second stage needed in mechanistic modelling is to predict the probability of the CWS being exceeded. This relies on some sort of estimation of the local wind climate. In relatively flat terrain, peak wind return periods can be estimated using Weibull parameters for the wind speed distribution by direction calculated from time series data of local wind climate (Quine, 2000). The predominant option to predict the local wind climate is to use the airflow model WAsP (Mortensen et al., 2005). With this approach, airflow between climate stations in hilly terrain is estimated using a linearized airflow model, originally formulated for low hills by Jackson and Hunt (1975). Another option is to link the mechanistic model with an empirically derived windiness scoring system such as the Detailed Aspect Method of Scoring (DAMS; Quine and White, 1993), which has been shown to accurately predict local Weibull parameters. In more complex terrain and wind climates, it may be appropriate to use Weibull parameters derived by using weather forecast data from high-resolution numerical simulation (Mitchell et al., 2007). Finally, if accurate data from local climate stations are available, these can be used directly. The combined information of CWS and wind climate is needed in order to build risk management tools for assessing the impact of silviculture, landscape, forest growth and stand location on the wind damage risk. In the following sections, we will discuss in more detail the current status and applications of the GALES and HWIND mechanistic models, which have been used as the basis for the recent development of a range of wind risk management (WRM) tools (see Table 1 and Figure 1).
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Current status and applications of mechanistic models GALES and HWIND
GALES model
Current status.
GALES calculates the threshold wind speeds required for overturning and breakage as a function of tree height, diameter, current spacing, soil type, cultivation, drainage and choice of species. The average wind loading on each tree is calculated from the stress imposed on the canopy by the wind by assuming that this stress is evenly distributed between the trees. The resistance to stem breakage is calculated from the bending moment required to cause the stress in the outer fibres of the stem to exceed the MOR of the wood. As a result, the CWS at canopy top for stem breakage can be calculated as follows (Gardiner et al., 2000):
 | (1) |
where k= 0.4 is Von Karman's constant, d (m) is the zero-plane displacement, z0 (m) is the aerodynamic roughness, D (m) is the average spacing between trees, G is an empirically derived gust factor, d.b.h. (m) is diameter at breast height (1.3 m above ground), h (m) is mean tree height and 
(kg m–3) is the air density. The factors fknot, fedge and fCW account for the reduction in wood strength due to knots, the position of the tree relative to the edge and the additional load due to the overhanging weight of the crown, respectively. In the most recent versions of the model, the need for fCW has been removed by the direct calculation of the bending of the stem following the methodology outlined by Neild and Wood (1999).
Similarly, the resistance to overturning can be calculated based on tree pulling experiments (e.g. Nicoll et al., 2006) and it is found to be strongly related to stem weight. The CWS at canopy top for overturning can be calculated as follows (Gardiner et al., 2000):
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where Creg is a regression constant that is dependent on soil and rooting depth and SW (kg) is the stem weight of the tree. For more details of the theoretical background to these calculations, see Quine and Gardiner (2007).
One of the most critical parameters in calculating the CWS is the empirical gust factor, G. This is an attempt to capture in a single term the complex influence of the turbulent wind structure in a forest canopy and the dynamic response of trees to this fluctuating wind. The turbulent wind structure in forests is dominated by coherent tree height scale eddies formed above the forest that penetrate into the canopy at intermittent intervals (Finnigan, 2007). The trees respond to this gusting wind similar to a damped harmonic oscillator but with complex interactions between branches and stem and between neighbouring trees (see Gardiner, 1995; Rudnicki et al., 2000; Moore and Maguire, 2008).
GALES was designed for the calculation of the CWS at 10 m above the zero plane displacement height (d) in even-aged conifer monocultures. The model is best parameterized for Sitka spruce (Picea sitchensis (Bong.) Carr.), Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and lodgepole pine (Pinus contorta Dougl. ex Loud.) and for trees up to a maximum d.b.h. of 
45 cm. For other species, it is assumed that the rooting (depth and width) is equivalent to Sitka spruce unless better information is available in which case the model is parameterized for that species, soil and rooting combination. Mixed species stands can be considered only by running a simulation for each species in turn and assuming all trees in the stand are of that species. The model can be used to calculate the risk at any distance from a newly created edge and for any size of upwind gap. For existing edges, the risk is considered constant from the edge because of adaptation by the trees (Telewski, 1995). The gap edge is assumed to be facing the dominant storm wind direction.
Applications.
Although originally developed for use in the UK, GALES has so far been adapted for use in New Zealand, Canada (Quebec and British Columbia), France, Denmark and Japan (e.g. Moore and Somerville, 1998; Ruel et al., 2000; Byrne, 2005; Cucchi et al., 2005; Mikklesen, 2007; Kamimura et al., 2008). The main requirements to use GALES in different circumstances are tree pulling data and MOR for the green timber of the tree species of interest and details of the crown characteristics (width, depth and drag coefficient) as functions of tree size in these species. For example, in Canada, extensive tree pulling tests have been carried out recently to build the critical resistive bending moment equations for black spruce (Picea mariana (Mill.) BSP), white spruce (Picea glauca (Moench) Voss), jack pine (Pinus banksiana Lamb.) and balsam fir (Abies balsamia (L.) Mill.) in the Quebec region (Meunier et al., 2002; Achim et al., 2005; Élie and Ruel, 2005; Bergeron, 2007) and for western hemlock (Tsuga heterophylla (Raf.) Sarg.), western red cedar (Thuja plicata Donn ex D.Don), interior spruce (Picea engelmannii Parry ex Engelm. X Picea glauca (Moench) Voss) and lodgepole pine (Pinus contorta Dougl. Ex Loud. var. latifolia Engelm.) in British Columbia (Byrne, 2005) in order to adapt GALES for Canadian species (Ruel et al., 2000).
Data from wind tunnel experiments have also been used to calculate drag coefficients for four British Columbia conifers, which enable adjustments to the wind loading equations in GALES (Rudnicki et al., 2004). Tree pulling on Hinoki (Chamaecyparis obtuse Siebold & Zucc. ex Endl.), Sugi (Cryptomeria japonica (L.f.) D.Don) and Japanese larch (Larix kaempferi (Lam.) Carr.) have also been recently completed to incorporate overturning factors in GALES for trees growing under Japanese conditions (Kamimura, 2007) and similar work has been carried out for maritime pine (Pinus pinaster Ait.) in France (Cucchi et al., 2005).
GALES has been linked with the DAMS windiness scoring system in Britain to produce the WRM tool called ForestGALES (Gardiner et al., 2004), which has further been integrated with the GIS package ArcView® to create a spatial version (Gardiner et al., 2003).
HWIND model
Current status.
The current version of the HWIND model was developed by Peltola et al. (1999) to describe the mechanistic behaviour of Scots pine, Norway spruce and birch (Betula pendula Roth; Betula pubescens Ehrh.) trees grown in pure stands on podzolic soils under wind (and snow) loading. HWIND was originally designed for calculations of the CWS of trees at the newly created edge of stands, but it can also be used for calculations at different distances from the upwind gap edge and for different sizes of upwind gap. It predicts the mean CWS lasting 10 min at 10 m above ground level (at the downwind stand edge) at which trees will be uprooted and/or broken. The forces acting upon a tree are divided into the horizontal force due to the wind and the vertical force due to gravity, including the stem and crown weights and, if required, the weight of snow. Trees are assumed to deflect to a point of no return when acted upon by a wind of constant mean velocity and direction. The mean wind loading and gravity-based forces are calculated at each height in the canopy using a predicted wind profile at the stand edge and the vertical distribution of stem and crown weights. The total mean wind-induced force is the sum of the wind forces acting at each point on the stem and crown (F1), which is given (Jones, 1983; Peltola and Kellomäki, 1993; Peltola et al., 1999) at height z by:
 | (3) |
where u is the mean wind speed (ms–1), A (m2) is the streamlined projected area of the stem and crown against which the wind acts, Cd is the drag coefficient and (kg m–3) is the density of the air. The wind profile in equation (3) is assumed to be logarithmic.
In the model, a tree is assumed to be uprooted if the maximum bending moment exceeds the resistance of the root–soil plate and the stem is assumed to be broken if the breaking stress exceeds the critical value of MOR. The inputs needed for the model are tree species, tree height, d.b.h., stand density, distance from the stand edge and gap size. Usually, only mean stand characteristics are used as inputs in HWIND simulations. However, multi-species even-aged stands or different tree cohorts could also in principle be considered by running a simulation for each species or tree cohort separately, assuming that the stand density (and the wind profile at the stand edge) remains the same in all simulations regardless of the proportion of each tree species or tree cohorts. Similar to GALES, any inaccuracies in the input d.b.h. especially, but also in other variables, which control the magnitude of the wind loading (e.g. tree height, crown depth and width, gust factor, drag coefficient and crown streamlining), can have a significant influence on the predicted CWS (Peltola et al., 1999; Gardiner et al., 2000; Zeng et al., 2006).
Applications.
The HWIND model has previously been applied with stand growth and yield and airflow models (GEO–SIMA–HWIND) to investigate the impacts of forest management on short- and long-term wind damage risk in Finland (Talkkari et al., 2000; Zeng et al., 2004, 2006, 2007a, b). It has also been applied in Sweden where the whole system is named WINDA (Blennow and Sallnas, 2004). In these studies, the model outputs have also been displayed within a GIS framework in a similar manner to ForestGALES. One of the most interesting and potentially valuable applications has been the use of HWIND within a heuristic optimization scheme for balancing forest stability against timber production in forest planning (Zeng et al., 2007b). Schelhaas et al. (2007) have also recently adapted the HWIND model approach when they built a wind damage module (or GEM-W) within the individual tree growth model ForGEM in order to assess, in the Netherlands, the risk of wind damage to individual trees grown in Douglas-fir stands (Pseudotsuga menziesii Franco).
Validation of mechanistic modelling approach
The GALES and HWIND models have been compared against each other for a limited set of tree species and soil types and show good agreement (see Gardiner et al., 2000). In addition, reasonable agreement was also found when these models were compared with predictions by the FOREOLE model (Ancelin et al., 2004), which was a first attempt to deal with complex stand structure by assuming an empirical wind profile within the canopy and calculating the horizontal wind loading on individual trees. However, parameters related to the wind profile, crown streamlining and tree attributes in FOREOLE were the same as those found in GALES and HWIND.
HWIND has also been validated previously in a qualitative way by visually comparing stands predicted to be damaged against those actually damaged during storms in southern Sweden (Blennow and Sallnas, 2004) and Eastern Finland (Talkkari et al., 2000). Testing of these models against an independent set of data is much more difficult because measurements of the wind speeds within forests occurring during wind damage events are very uncommon. However, the predicted CWS has been found to be in line with the speeds required to cause damage to trees from the limited number of observational datasets that do exist (e.g. Oliver and Mayhead, 1974; Talkkari et al., 2000; Pellikka and Järvenpää, 2003).
Furthermore, HWIND did predict wind damage in individual Scots pine, Norway spruce and birch trees relatively well in a small forest unit, which was located in south-western Finland. In two individual storms with mean wind speeds of 15–19 ms–1 and 10–15 ms–1 (gusts of 30–50 ms–1 and 25 ms–1, respectively) in southern and central Finland in 2001, the range of correctly predicted damage varied between 36 and 60 per cent of all damaged trees (Peltola, H., unpublished data). Unfortunately, only the characteristics of damaged trees were available for the simulations and it was not possible to analyze how well the model predicted an absence of damage.
Compared with HWIND, GALES has been validated in a more comprehensive manner for UK forests. In this work, the observed damage was compared with the predicted damage using ForestGALES (GALES + DAMS) for plots set out on a 100 x 100 m grid in two forests in Britain (Cwm Berwyn and Carradale) over a 10-year period (1988–1998). These forests formed part of a wind monitoring network (Quine and Bell, 1998) and had a repeat survey done 10 years after the initial survey and after they had experienced wind damage in a reasonable number of plots (16 per cent of plots in Cwm Berwyn and 26 per cent of plots in Carradale). The plots were 0.01–0.05 ha in size in order to contain between 7 and 20 trees as recommended by Edwards (1983). Damage was said to have occurred if at least one of the trees in the plot was damaged by wind during the year. The wind climate was obtained from 10-m masts situated in open ground within the forest and the wind climate over the forest was adjusted using the DAMS score for each plot location. Each year, the CWS was calculated for each plot (based on the mean plot characteristics) and if the measured wind speed exceeded this value during the year, damage was predicted to have occurred. ForestGALES correctly predicted whether damage had occurred or not in 71 and 59 per cent of the time in Cwm Berwyn and Carradale, respectively (Table 2). The model was found, however, to be pessimistic and tended to overpredict the occurrence of damage. Increasing the CWS for each prediction by 1 ms–1 improved the accuracy of the model to 76 and 63 per cent, respectively.
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When validation of GALES was conducted for the ForestTYPHOON system in Japan (Kamimura, 2007
), reasonable agreement was obtained for forests in Himi, Toyama prefecture, but less good agreement was observed in Yotei, Hokkaido Island, and particularly on the north side of the very steep volcano where the test forest was located. Again, an increase of the predicted CWS by the addition of a fixed value of 1 ms–1 improved the accuracy of the model predictions in Himi to greater than 70 per cent. This suggests that GALES tends to be generally pessimistic and underpredict the CWS slightly. The reasons for this are not totally clear but it may be due primarily to exaggerated values for the gust factor (G), which are based on limited field and wind tunnel experimental data (Stacey et al., 1994; Gardiner et al., 1997). So far, no detailed validation for GALES has taken place in other countries and agreement has been mainly qualitative. In some countries such as Canada, it may be difficult to locate stands with a simple structure that would match the conditions the model is presently able to simulate. |
Current limitations of mechanistic modelling of wind damage risk |
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Assumptions and empiricisms
In all modelling systems, there is a requirement at some point to make use of empirical relationships. Ideally, the use of empirical relationships should be minimized and they should function at a smaller scale than the scale of interest. This allows the model to be extended to conditions outside the parameter space over which the empirical relationships were developed. In wind damage modelling, the empirical functions are typically regression equations that relate stand and tree physical properties to mechanical properties and behaviour under wind loading. Where the smallest scale of interest is likely to be the tree, then ideally empirical relationships will be at the sub-tree scale and apply to scales of centimetres rather than metres. However, it is always important to bear in mind that empirical relationships provide a simplification of the real world and allow models to be developed with limited inputs. On the other hand, extending the mechanistic aspects of the models will inevitably lead to increased data input requirements.
Functions that relate wind loading to wind speed and tree properties are currently parameterized using wind tunnel experiments in which drag force and crown streamlining are measured at various wind speeds (e.g. Mayhead, 1973; Rudnicki et al., 2004). In addition, crown characteristics such as width and depth and leaf area are generally based on further empirical relationships. Thus, models which rely on estimating wind loading can be very sensitive to any inaccuracies in estimation of crown characteristics. However, it is unlikely that a completely mechanistic model of canopy drag could be developed in the short term or in a manner that will allow simple incorporation into models for calculating the CWS.
Functions that relate tree resistance to tree properties are also parameterized using tree pulling tests to obtain the maximum bending moment at tree failure. Simple linear relationships between critical bending moment and stem mass or stem dimensions obtained using tree pulling have been reported for many species (e.g. Fraser and Gardiner, 1967; Smith et al., 1987; Moore, 2000; Peltola et al., 2000; Achim et al., 2005; Nicoll et al., 2006; Byrne and Mitchell, 2007). Of the properties examined, stem mass is generally found to be the best predictor (Nicoll et al., 2006). Ideally, it should be possible to come up with more directly applicable relationships between resistance to uprooting and root dimensions (Achim et al., 2003). It has been universally observed that the regressions relating critical bending moment to stem dimensions and crown drag to branch mass are very tight, with coefficients of determination in the 0.80–0.95 range. These tight relationships give greater confidence in CWS predictions, and more importantly they suggest that trees within a given population follow some consistent principle of biomechanical design.
The current, most critical empiricism is the estimation of gust factor in the models, which as was discussed above represents the complex dynamical interaction between trees and the turbulent wind. All the models are extremely sensitive to variations in gust factor (Gardiner et al., 2000; Ancelin et al., 2004), the value of which we know to be uncertain. Therefore, fully understanding the dynamics of trees in strong wind must be an important goal for research over the next few years in order to construct a complete mechanistic model of their behaviour. The work of Sellier et al. (2006) and Moore and Maguire (2008) are steps in that direction.
Validity of risk predictions in structured stands
The most serious limitation in the current CWS models such as HWIND and GALES is that they were originally built to represent the risk to a ‘mean tree' within a stand and not to consider the risk to individual trees. Therefore, they can predict only the occurrence of damage, not the actual volume of damage. Thus, in this sense, realistic results are not produced as presently configured in the complex structured stands commonly found in semi-natural or partially harvested forests. FOREOLE (Ancelin et al., 2004) was a first attempt to deal with complex stand structure but it has not yet been validated against data from complex stand structures because such data do not exist and only simulations of probable damage distributions can currently be made.
In the future, other adjustments may also be needed before using CWS models for structured stands. Differences in light environment can lead to different biomass allocation or natural pruning patterns (Ruel et al., 2004). This in turn can lead to differences in stem shape and crown size even for a similar stem diameter. In addition, winching experiments have shown that the relationship between critical bending moment and stem mass can be influenced by stand composition and structure (Élie and Ruel, 2005; Bergeron, 2007).
Damage propagation and tree-to-tree variability
Mechanistic models, in their current form, do not capture the process of windthrow in real stands, where failure of one stem alters the wind regime for its surviving neighbours. Thus, methods of accounting for spatial variability and propagation of windthrow need to be developed to predict windthrow at the tree level in stands with horizontal and vertical heterogeneity or with multiple species. Schelhaas et al. (2007) present one of the first attempts to incorporate tree–tree interactions into CWS model development. Furthermore, functions that more accurately reflect the variability in tree properties are also required to explain why even with trees of similar general appearance some trees fail and others do not. The variation and uncertainty in the empirical components of mechanistic models are not currently represented and measures of variability in the predictions are required to improve the veracity of the model.
Impacts of semi-spatial and non-directional wind climate on risk predictions
A major limitation of WRM tools using a wind exposure scoring system such as DAMS is that in their present form they cannot incorporate variations in wind climate for different directions. In contrast, WRM tools such as WINDA (Blennow and Sallnas, 2004), ForestTYPHOON (Kamimura, 2007) and the coupled models of Zeng et al. (2004, 2006) that use WAsP to predict the wind climate are able to calculate the probability of damage as a function of variations in wind climate with direction. However, often these models are used in a non-directional manner and only provide an average risk for all wind directions (or only selected directions). In addition, WAsP is limited to gentle terrain (slopes <10°), which is acceptable in regions like southern Sweden and Finland (see e.g. Venäläinen et al., 2004), but does not always work well in other parts of the world (Suárez-Minguez et al., 1999; Kamimura, 2007).
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Discussion |
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TopSummaryIntroductionMechanistic wind damage risk...Current limitations of...DiscussionConclusionsFundingAcknowledgementsReferences |
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New developments required of mechanistic modelling of wind damage risk
Accuracy of risk predictions for complex stand structure, terrain and wind climate.
Even though current mechanistic models are simplifications, they promote investigation of the functional components of windthrow and are useful for simulating the effect of management actions in locations beyond their development locations. However, to better match real-world conditions, there is a need for mechanistic models that can reflect windthrow risk in more spatially complex terrain, wind regimes, forest types and forest management scenarios.
FOREOLE was the first attempt to include some measure of variability within mechanistic models by assuming a constant wind profile within a stand and calculating the wind loading on individual trees as a function of their leaf area distribution. However, recent measurements by Wellpott and Gardiner (2006) suggest that this approach does not represent the wind loading on individual trees well enough. A possible alternative approach is to make use of the competition indices developed for predicting the growth conditions of individual trees within stands. For example, Achim et al. (2007) have shown that competition indices are extremely well correlated to the wind loading of individual trees in a mature Sitka spruce plantation.
The problem of the profile method applied by Ancelin et al. (2004) for calculating wind loading is that it is very sensitive to the exact shape of the wind profile. Previous wind tunnel and modelling studies (Gardiner et al., 2005, Dupont and Brunet, 2008a) have shown that the structure of the stand changes the shape of the profile enough to give measurable and significant changes to the wind loading of individual trees. Therefore, empirical fits to wind profiles will need to be replaced by computational one-dimensional or two-dimensional airflow models such as those developed by Lee et al. (1994) or Dupont and Brunet (2008b).
When the canopy is located on a hill, the computation becomes even more complex. However, recently new models for predicting the flow in forested complex terrain have become available that use the same physics as WAsP, but with an additional layer occupied by the canopy close to the ground (Finnigan and Belcher, 2004). These models will deal much more accurately with the flow within canopies on hills, but will still be confined in their use to shallow sloping terrain.
These recent airflow modelling studies could be used to replace the current equations derived from wind tunnel studies for gust and gap factors in future CWS models and to modify the wind profile parameters at the downwind edge of newly created gap or where stands of different structure are located upwind. However, further validation of these possible approaches is required before they can be incorporated into improved mechanistic models such as HWIND or GALES3. This is particularly true for GALES3, which is being designed to evaluate the wind loading on individual trees within multi-structured, multi-species stands.
The main purpose of further model development and validation of the HWIND model will be to predict the risk of wind damage of individual trees growing at newly created forest edges, which could be either even-aged or multi-structured or consist of single- or multi-species stands. At the same time, it is hoped that HWIND can be developed to evaluate the risk of wind damage at the downwind stand edge of clear-cut areas over time, together with the growth of upwind neighbouring seedlings established in the clear-cut areas. This further model development work is expected to increase its applicability in the risk assessment of wind damage as part of forest planning.
Better understanding of the interaction of rooting, soils and slopes (Nicoll et al., 2005; Nicoll et al., 2006; Achim et al., 2003, 2007) is also expected to provide improvements in the modelling of resistance to tree uprooting in GALES3. Rooting resistance can now be treated as a combination of physical and empirical modelling that uses rooting depth and soil type as the key characteristics and dispenses with the need to develop individual relationships for different cultivation systems and drainage. In addition, the new models will account for the directional variation in root architecture and resistance to uprooting on slopes.
Obtaining better dendrometric information using growth and yield models.
As discussed above, the specific representation of individual trees within a stand that accounts for differences in stem and crown attributes and species mix (dendrometrics) has not been fully incorporated in the current CWS models. However, growth and yield models such as Tree and Stand Simulator (TASS) use thousands of permanent sample plot data to estimate stem and crown form for trees of varying dominance in the canopy (Di Lucca, 1999) and are used by forest managers throughout British Columbia to estimate the forest yields. The simulated data represent individual trees with specific vertical and horizontal positions within the canopy as well as unique stem and crown attributes which are then output in text format. In the future, it will be important to incorporate both measured field mensurational data and tree lists generated by simulation software such as TASS or CAPSIS (Croissance d'Arbres en Peuplement avec Simulation d'Itinéraires Sylvicoles; de Coligny et al., 2002) and corresponding growth and yield models such as SIMA (see Kellomäki et al., 1992; Zeng et al., 2006, 2007a, b) in the improved models such as GALES3, HWIND and WINDFIRM (Di Lucca et al., 2007). These data may also be used in conjunction with technical advances in LiDAR to estimate spatial forest cover remotely (Suárez-Minguez et al., 2007). In particular, better representation of crown position and individual tree dendrometrics will provide for more accurate drag and bending calculations in CWS models.
Examples of recent and ongoing modelling
Modelling complex felling patterns/fetch and damage propagation within a stand.
In order to deal with wind risk in spatially complex forestry systems, it is necessary to use spatial modelling tools such as WINDFIRM (Figure 2), which uses ForestGALES_BC (Byrne, 2005) as the CWS model. WINDFIRM was originally developed as an ArcView extension to integrate scripts for building datasets for stand-level empirical windthrow risk modelling. It can be used to upload tree lists with x, y positional data for each tree, modify these tree lists to represent thinning or partial harvesting and upload locational variables such as local wind speed return intervals, soil properties and topex grids (Quine and White, 1993). These layers are assembled and overlayed to enable calculation of directional variables such as fetch and topographic exposure. WINDFIRM then passes these variables to ForestGALES_BC and the simulation is run for a single above-canopy input wind speed and direction that can be chosen to reflect the local 1-year, 5-year or longer return period wind speed. This is a departure from the original GALES model in the sense that a CWS is not calculated. Instead, the input wind speed, conditioned by the upwind stand conditions, is applied to each tree in the tree list, which either remains standing or fails. It is still possible to calculate the CWS for a whole stand by running WINDFIRM with a series of input wind speeds.
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WINDFIRM has been linked to the TASS growth and yield model to obtain spatial tree lists representing particular harvesting patterns. The tree lists are passed iteratively from WINDFIRM to ForestGALES_BC and back until all trees that are susceptible at the designated above-canopy wind speed have been deleted from the tree list. Iteration is necessary to represent the changes in the within-canopy wind environment of a given tree as upwind trees are damaged and removed from the list. This approach simulates the stand-level behaviour during a single storm event where the most susceptible trees fail first and permits the characterization of windthrow propagation through the stand. The iterations between WINDFIRM and ForestGALES_BC cease when no more trees are removed from the list. This propagation is characterized for a single wind event and not successive events over time. The final reduced tree list is then passed back to TASS for continued stand growth and seedling regeneration in any gaps created by windthrow.
Since WINDFIRM acts as an interface and passes data to ForestGALES_BC for wind loading and resistance computations, it could also be used as the spatial framework for the computational engines of other CWS models such as HWIND and FOREOLE.
Prediction of local wind regimes.
One of the most critical aspects of predicting wind damage risk is calculating the probability of a particular CWS occurring at a specific location. Although improved wind flow models are becoming available (as discussed above), it is extremely difficult to use such models to predict local wind climates because of the computational investment required. In British Columbia, 2 years of wind forecasts produced using numerical weather prediction models (MC2 and MM5) have been archived by the Faculty of Earth and Ocean Sciences at the University of British Columbia (Modzelewski, H. personal communication). These forecasts are at 1.3-km grid resolution covering south-western British Columbia and will enable estimation of Weibull or exponential distribution parameters for each grid cell when enough archived wind predictions are available. These parameters, which will be revised as the length of the archive extends, can be used to estimate local above-canopy wind speeds for user-specified return periods. The use of finer resolution predictions from local wind models should provide superior wind climate input into ForestGALES_BC than using, for example, UK-derived DAMS–Weibull relationships to predict return periods.
Validation of improved mechanistic models
For the new generation of mechanistic models, which are being developed from the innovations and improvements discussed above, there will be a critical need for detailed validation datasets. Such datasets are available in British Columbia where the ‘Silviculture Treatments for Ecosystem Management in the Sayward' (STEMS) is a large-scale experiment that compares seven silvicultural regimes replicated at three sites in the Sayward Forest, Vancouver Island (de Montigny, 2004). Consequently, there is a diversity of forest structure including a variety of canopy layers (vertical structure), spatial patchiness (horizontal structure) and a range of gap sizes. Windthrow is among the many studies being conducted and it is the intention to use recorded windthrow data from STEMS for validation of the next generation of WINDFIRM.
Similarly, in Quebec a number of irregular black spruce–balsam fir stands were established in 2004 and 2005 as an experiment with four replicates and five treatments. There are 150 permanent plots where every individual tree has been mapped and windthrow is being monitored at the tree level. This dataset along with data from wind tunnel experiments (Gardiner et al., 2005) and field trials conducted in the UK (Achim et al., 2007) will provide key validation for GALES3.
Incorporating mechanistic models into forest management systems
In order to become more than research tools, the mechanistic models discussed in this paper need to be incorporated into forest management systems in ways that are useful and practical. GALES, HWIND and ForestGALES_BC have been linked with the GIS package ArcView to create the ForestGALES, WINDA and WINDFIRM WRM tools, respectively (Gardiner et al., 2003; Blennow and Sallnas, 2004; Di Lucca et al., 2007). However, these systems have not been widely adopted despite GIS being the management tool of choice for many forest managers. There are a number of reasons for this including difficulties in linking the WRM tools with stand-level data, high level of required user knowledge and involvement and interpretation of the model outputs.
To become true forest management tools, the complexities of operating the models needs to be removed and their operation and interpretation become routine and straightforward. One of the best ways for doing this is to make use of decision support tools (DSTs) as discussed by Kamimura et al. (2008). DSTs simplify the model operation to a decision tree involving a hierarchical set of questions on the characteristics of the crop and site (e.g. top height, d.b.h., slope, elevation, thin/no thin) and the outputs are different levels of risk (low to high). Such a system is not only extremely straightforward to implement within a forest management system such as a GIS but is also readily understandable by practitioners. A system of this sort can be constructed for different countries by running the most appropriate WRM tool for multiple cases covering relevant stand and site conditions and then modelling the results in the form of a decision tree or other statistical model.
At the same time, there is a need to ensure the correct interpretation of the model results from mechanistic models or ‘output' models such as decision trees. This requires formulating the results in a user-understandable format and having clear explanations of the limitations and uncertainties of the models. All the models discussed are sensitive to the input data, particularly tree size, so that inaccuracies in model inputs will lead to uncertainty in the results. Generally, the larger the uncertainty in input data, the larger the spatial or temporal scale at which the models are appropriate. Correct use and interpretation of wind risk models is a matter of careful explanation and training.
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Conclusions |
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TopSummaryIntroductionMechanistic wind damage risk...Current limitations of...DiscussionConclusionsFundingAcknowledgementsReferences |
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Mechanistic models provide useful predictions for relatively uniform stands of trees without decay or defects. They enable managers to evaluate tree and stand vulnerability to wind under various management scenarios. They have a logical structure grounded in the physical processes that lead to tree uprooting and failure. The model framework brings together and makes explicit the component processes and is useful for identifying knowledge gaps and integrating new theoretical or experimental results. However, the deterministic nature of mechanistic models is sometimes at odds with field observations of windthrow, particularly in more complex stands and landscapes. The refinements discussed in this paper we hope will address some of these factors in due course.
The more complex and potentially realistic a mechanistic model becomes, the more specific and extensive the data requirements are to successfully and reliably run the model. If the models are too complex, then only specialized and expert users may be able to operate them. This will lead to the models not being adopted by end-users and becoming only of value as research tools. It is, therefore, critical that the appropriate model, with the appropriate level of detail, is used for each particular application. This means that there will always continue to be a role for expert field diagnosis of individual trees and stands, statistical modelling and simplified decision support-based approaches (Kamimura et al., 2008). Ideally, insights gained through these empirical processes will then lead to further research and subsequent refinements in the mechanistic models.
Finally, the value of having different groups developing separate mechanistic models cannot be underestimated. It creates synergy and allows the best ideas from the different approaches to be incorporated into new models. It also provides a level of model validation if similar results are obtained when the models are compared for specific case studies (e.g. Gardiner et al., 2000; Ancelin et al., 2004). Therefore, this approach will be continued in the development of improved forest wind risk models such as GALES3, HWIND and WINDFIRM.
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Funding |
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TopSummaryIntroductionMechanistic wind damage risk...Current limitations of...DiscussionConclusionsFundingAcknowledgementsReferences |
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Interreg North Sea Region ‘STORMRISK' project to B.G. British Columbia Forest Science Program Grants Y062276, Y081107 and Y083169 to K.B. and S.M. 9th Academic Research Grant of the Japan Forest Technology Association (2005) to K.K. Two NSERC Canada grants to J-C. R. Academy of Finland Project Number 121623 to H.P.
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Acknowledgements |
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TopSummaryIntroductionMechanistic wind damage risk...Current limitations of...DiscussionConclusionsFundingAcknowledgementsReferences |
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The authors would like to thank Chris Quine, Bill Mason, Juan Suárez-Minguez, Axel Wellpott, John Moore, Mario Di Lucca, Alexis Achim, Veronique Cucchi, Celine Meredieu and all the other colleagues and friends who work on this fascinating subject.
Conflict of Interest Statement
None declared.
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References |
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