Growth and yield modelling

Growth and yield research and modelling have been long-term provincial stewardship responsibilities since establishment of the B.C. Forest Branch in the early 1900s, which evolved into the current ministry. Research into these tools enables comparison of the economic alternatives of various forest management regimes.

The information provided improves competitiveness and ensures management investments are cost effective.  The research supports management of forest values such as habitat, biodiversity, resilience, and visual quality.

A Transfer Function for Survival and Its Use in Developing Climate-sensitive Projections of Volume for Lodgepole Pine - TR151

Transfer functions relate attributes such as tree height and survival to climate transfer distance and are developed using data from provenance trials. Originally designed to inform seed deployment strategies, transfer functions have become useful in forecasting population responses to climate change. Recent studies have demonstrated that climate-sensitive growth and yield models may be developed by using transfer functions to adjust projections of growth and survival. For the current study, a transfer function for survival was developed for lodgepole pine using time-series measurements collected from a range-wide provenance trial with test sites situated throughout British Columbia. The transfer function that was developed predicts annual percent survival as a function of changes in mean coldest monthly temperature, mean annual precipitation, and site height. The function also included two statistically significant interaction terms, which signify that climate change will elicit a population-specific response for survival. A method was then developed that used the transfer function for survival to modify a difference equation that predicts the number of live stems ha–1 over time. Projections for the number of live stems ha–1 were then used in a metamodel together with projections of site height, the latter of which were generated using an updated version of a published transfer function for height and a site index equation for lodgepole pine. The meta-model was used to estimate stand level volume at three hypothetical planting sites for a future climate scenario. When compared to volume projections in a static climate, the results suggest that most populations of lodgepole pine in British Columbia will likely be negatively affected by climate change, with southern populations predicted to be the most severely affected. The negative effects on volume occurred despite an increase in survival that was predicted at the three planting sites. The study concludes by providing some discussion about the use of transfer functions when developing climate-sensitive growth and yield models

Leader Damage in White Spruce Site Trees in Northeastern British Columbia - TR113

Anecdotal information suggests that damage in leaders of white spruce (Picea glauca (Moench) Voss) is less in the Boreal White and Black Spruce (BWBS) biogeoclimatic zone than was found in a previous study in the Interior CedarHemlock (ICH) and Sub-Boreal Spruce (SBS) zones. The purpose of this project was to confirm or refute this assertion. Forty-six 0.01-ha stem analysis plots were established in managed stands in the BWBS zone and data from those plots were combined with data collected previously from the ICH and SBS zones. The stem of one sample tree per plot was split, and the heights of the nodes demarcating the ends of the annual height growth were measured. Leader damage was noted. 

Total and Merchantable Volume Equations for Common Tree Species in British Columbia - TR106

The British Columbia Ministry of Forests, Lands and Natural Resource Operations maintains tree taper equations that can be used to estimate individual tree volume; however, the calculations involved in making these estimates are non-trivial. A simple tree stem volume equation overcomes this issue and is easily programmed, for example, in a spreadsheet. Volume equations were developed in 1976. These equations show some bias when tested against the available stem analysis data. Therefore, four new sets of volume equations were developed: total volume by species and region (coast or interior); total volume by species and biogeoclimatic zone; merchantable volume by species and region (coast or interior); and merchantable volume by species and biogeoclimatic zone. Merchantable tree volume is total tree volume minus the volume of the stump and top. These equations provide more accurate volume estimates than the 1976 volume equations and the taper equations.

Revised Site Index Models for Western Redcedar for Coastal British Columbia - TR105

The British Columbia Ministry of Forests, Lands and Natural Resource Operations is implementing a program to update site index models by refitting the models with newer fitting techniques. The existing site index model for coastal western redcedar (Thuja plicata) was developed by MacMillan Bloedel Limited in 1978. This model was in particular need of updating because it gave unreasonable height and site index predictions for old trees and because some abnormalities in the height predictions were fixed with ad hoc adjustments. Data for the refit were obtained from four sources: pseudo-data from the existing model, stem analysis data from a wood quality study, a foliar nutrient–growth study, and a project done by MacMillan Bloedel. The grounded-Generalized Algebraic Difference Approach was applied to a Chapman-Richards function to derive a base-age invariant site index model for coastal western redcedar. 

Validating the Site Productivity Layer for British Columbia with Equivalence Testing - TR85

The site productivity layer is a database of site indexes for commercial species, which can be linked to a particular area (a site) in the province. It was created in response to a need for improved accessibility to site index information. The site index estimates in the layer were obtained from either the Site Index − Biogeoclimatic Ecosystem Classification (SIBEC) model coupled with an ecological map, or from a biophysical model. This document reports on the validation of the site productivity layer. The validation data consist of site indexes for various species from inventory plots (e.g., monitoring plots, Growth Natural Permanent Sample Plots, Vegetation Resources Inventory plots) and research and silviculture plots. These site indexes were paired with site index estimates from the site productivity layer for the same location and species. Equivalence testing, which tests for overall bias and 1:1 correspondence between the predicted and observed site indexes, was used to perform the validation. The equivalence test was applied to the complete layer and to strata created from the layer.

Years-to-Breast-Height Model for Engelmann Spruce in the Engelmann Spruce – Subalpine Fir Biogeoclimatic Zone - EN115

A years-to-breast-height model for Engelmann spruce (Picea engelmannii) has been lacking; the years-to-breast height model for natural stand white spruce (P. glauca) has been used to fill this void. Recently, stem analysis data for Engelmann spruce were collected to develop site index models. These data were used in this project to develop a years-to-breast-height model specifically for Engelmann spruce. A linear function with the inverse of site index as the independent variable was deemed to be the best fitting years-to-breast-height model. This model is similar to the previously used model.

An Errors-in-Variable Model with Correlated Errors: Engelmann Spruce Growth Intercept Models - TR84

Engelmann spruce (Picea engelmannii Parry ex Engelm.) is a high-elevation species found in northwestern North America. Its importance is increasing as the interest in these high-elevation sites grows. Consequently, growth intercept models that predict site index for this species need to be developed. Previous growth intercept models were fit with nonlinear least squares regression. With this technique, the assumption that the “x” variable (i.e., height) in the fitting is known without error is violated, resulting in a bias. The aim of this study was to remove this source of bias with the errors-invariable method of moments fitting technique. This involved developing errors-in-variable method of moments estimators for growth intercept models and fitting these models to stem analysis data.

Estimating Inventory Attributes for the Lakes Timber Supply Area from Remeasured Vegetation Resources Inventory Ground Data - TR78

Ninety-three Vegetation Resources Inventory plots were remeasured and analyzed to assist in making decisions regarding future timber supply and lumber manufacturing in the Lakes Timber Supply Area, British Columbia. The live and dead volumes were analyzed at various utilization levels in two sets of domains: Immature, pine leading (Pl) <80, Pl 80+, and Mature; and South, Central, and North. Histograms of the diameter distributions, small tree densities, log grades, and damage and loss factors were used to assess the quality of the timber.  At the 12.5+ utilization level, the estimated live (dead) volumes for the Immature, Pl <80, Pl 80+, and Mature domains were 3.2 (0.4), 11.8 (19.2), 12.0 (25.4), and 43.8 (18.1) million m3 , respectively. The estimated live (dead) volumes at the 12.5+ utilization level were 10.3 (17.9), 25.8 (24.0), and 34.7 (21.1) million m3 for the South, Central, and North areas, which included the Burns Lake and Cheslatta Community Forests.

A Biophysical Model for Estimating Site Index for the Major Commercial Tree Species in British Columbia - TR73

A site index geographic information system (GIS) layer is being developed for British Columbia so that estimated site indices are available for the major commercial tree species across their ranges. The Site Index – Biogeoclimatic Ecosystem Classification (SIBEC)/predictive ecosystem map (PEM)/terrestrial ecosystem map (TEM) method will be used to populate the layer with site index by species. However, there will be gaps in the layer where there are no PEM/TEM or SIBEC data. The biophysical models resulting from this project will be used to fill these gaps. They predict, by species, site index from biogeoclimatic zone, slope, aspect, elevation, and climate variables. Data for these models come from the SIBEC project and various Site Index Adjustment projects. The climate variables are predicted from the Climate WNA model.

The Growth of Bigleaf Maple 20+ Years after Harvesting - EN108

Bigleaf maple (Acer macrophyllum Pursh) (Figure 1) is a component of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco) and red alder (Alnus rubra Bong.) stands and occasionally occurs in pure stands in southern portions of the Coastal Western Hemlock biogeoclimatic zone (Meidinger and Pojar 1991) of British Columbia. Its best growth is on the moist and rich soils of river terraces, floodplains, and seepage sites at relatively low elevations (below 300m) (Haeussler et al. 1990; Minore and Zasada 1990).

Douglas-fir Provenance Survival and Growth in the British Columbia South Submaritime Seed Planning Zone - EN105

In southwestern British Columbia, the South Submaritime (ssm) seed planning zone is a geographically and ecologically complex transition zone between the Pacific coast and the interior plateaus. The ssm follows a long, narrow band along the Coast Range (Figure 1), and is characterized by steep, incised valleys. The highly variable climate is strongly influenced by prevailing warm, moist maritime air masses, and towards the east it is characterized by a cool, dry continental climate. Throughout the ssm, survival rates of the 1.3 million annually planted Douglas-fir seedlings are far below those that are typical or expected for post-harvest plantations: below 80% by age 3, declining to under 70% by age 5 (Ministry seedling survival database; Hunt 2002), compared to typically over 95% at comparable ages for most operational areas. Douglas-fir is approximately 40% of the harvested volume (biogeoclimatic subzone averages within the ssm range from 36 to 65%) and is the preferred species on most sites. Most of the seedlings currently planted in the ssm originate from seed orchard #181 that produces Class A seed bred to increase yields and maintain adaptability to the planting site throughout the ssm (Forest Genetics Council 2010).

Amabilis Fir Height–Age and Growth Intercept Models for British Columbia - EN94

Amabilis fir is a common species on the coast of British Columbia. It is found mainly in the Coastal Western Hemlock (CWH) biogeoclimatic zone, from the southern-most parts of the CWH to as far north as Stewart, as well as in the Mountain Hemlock zone and, to a lesser extent, the northern wetter submaritime Interior Cedar-Hemlock zone (Meidinger and Pojar 1991; Klinka et al. 2000).

Modelling Boreal Mixedwoods with the Tree and Stand Simulator - EN80

Boreal mixedwood forests are a complex mixture of conifer and broadleaf species (Figure 1). These forests vary in structural, spatial, and temporal composition (Green 2004). The management of boreal mixedwoods continues to evolve as our understanding of mixedwood ecology, regeneration, and stand dynamics grows. Gap analysis of present boreal mixedwood management has suggested that several key issues need addressing, including: lack of fundamental ecological data, inadequate forest inventory, and limited development of site productivity and growth and yield modelling tools tailored for boreal mixedwood forests (unbc 2002). Modelling the growth and yield of boreal mixedwood forests is one of the main concerns of northern forest managers. The key to improving boreal mixedwood management is accurate modelling, which forecasts mixedwood responses to silviculture practices, natural disturbance, succession, and stand dynamics (Chen and Popadiouk 2002; Greene et al. 2002; unbc 2002; Hawkins and Maundrell 2003). 

Using TIPSY to Evaluate Windthrow Effects on Regeneration in Variable Retention Harvests - EN77

The Table Interpolation Program for Stand Yields (tipsy) enables forest managers and timber supply analysts to explore the impacts of variable retention. tipsy variable retention adjustment factors (vrafs) are calculated based on the level and pattern of both group and dispersed tree retention using four primary variables from the retained stand: percent crown cover, average group or crown size, initial edge length (perimeter), and top height. Windthrow losses in the years shortly after harvest can now be estimated using two methods; empirical regression equations that predict windthrow effects, or specifying expected windthrow losses for a given location. vrafs reduce post-harvest regenerated yields on a per-hectare basis over the entire cutblock as a function of the area occupied by retained trees. Windthrow losses will reduce the crown cover retained and therefore increase the growing space and future yields for the regeneration.

Variable Retention Yield Adjustment Factors for TIPSY - EN69

Variable retention adjustment factors (VRAFs) incorporated in the Table Interpolation Program for Stand Yields (TIPSY version 3.2) enable forest managers and timber supply analysts to explore the impacts of the variable retention approach to harvesting on future harvest yields. VRAFs are based on the level and pattern of both group and dispersed retention. The VRAF model uses three primary variables from the retained stand: percent crown cover, edge length (perimeter), and top height. The system also includes subordinate models to predict edge length and retained crown cover from other retention measures such as basal area.

Growth Intercept and Site Series–Based Estimates of Site Index for White Spruce in the Boreal White and Black Spruce Biogeoclimatic Zone - TR13

Foresters were concerned that site index estimates from the growth intercept models for white spruce were too high in the Boreal White and Black Spruce (bwbs) biogeoclimatic zone. The purpose of this research was to validate the growth intercept models for spruce in the bwbs zone and re-fit the models. At the same time, additional Site Index–Biogeoclimatic Ecosystem Classification (sibec) data were collected to bolster the spruce data in the bwbs zone. Two types of data were collected: stem analysis data for growth intercept model validation and sibec data. The stem analysis data followed the stem analysis standards for site index research. Natural stands were targeted for sampling, and the stem splitting and node measuring technique was used to collect the data.

Growth Intercept, Years-to-Breast-Height, and Juvenile Height Growth Models for Ponderosa Pine - TR02

A suite of models consisting of height-age (site index), growth intercept, years-to-breast-height, juvenile height, and Site Index - Biogeoclimatic Ecosystem Classification (SIBEC) models are commonly used in British Columbia to estimate the height and site index of forest stands. Eighty plots of ponderosa pine stem analysis data were collected across the range of ponderosa pine in British Columbia. The years-to-breast-height, growth intercept, and juvenile height models were developed with these data. Height-age models were also developed, but are described elsewhere. The data were also used to further populate the SIBEC database. The growth intercept models were developed using standard techniques. The years-to-breast-height models used a slightly different functional form for the model. The juvenile height modelling technique was modified to more seamlessly splice the height curves into the height-age models.

Splicing Height Curves - EN60

Recent juvenile height models estimate height from germination up to total age15, 20, or 25, depending on the species. These models give better estimates of height at young ages and hence give better estimates of the number of years it takes to reach breast height or green-up height. In order to get continuous height estimates from germination up to maturity, the juvenile curves need to be spliced with the height-age models. The juvenile height models can be used stand-alone if height estimates only up to the maximum age of the models are desired; otherwise the spliced version should be used. In an earlier extension note, four ways of splicing juvenile height curves to height / breast height age curves were discussed, with one method giving better results for lodgepole pine (Pinus contorta var. latifolia Dougl.) This method uses the following procedure: • Estimate heights up to breast height age 0 with the juvenile height model; • Use the height / breast height age models to estimate heights above breast height age 2; • Obtain heights between breast height age 0 and 2 by linear interpolation of the height.

Growth Intercept Models for Black Spruce - EN57

Growth and yield information about black spruce in British Columbia is sparse. To help alleviate this situation, growth intercept models were developed using data from 91 stem analysis plots. These models, which are more precise than those for other species in British Columbia, provide a means of estimating site index (site productivity) in young black spruce stands.

Site Index Conversion Equations for Mixed Black Spruce–Lodgepole Pine Stands - EN39

Site index conversion equations allow the site index of one species to be estimated from the site index of another species when they are growing in mixed stands or for stand conversions. This study develops site index conversion equations for mixed black spruce (Picea mariana [Mill.] B.S.P.)– lodgepole pine (Pinus contorta var. latifolia Dougl.) stands. The data come from plots established in northern British Columbia by the University of British Columbia. Twenty-six plots with height and breast height age measurements for both black spruce and lodgepole pine were available. The site indexes for both species were estimated from these data and the geometric mean regression line was fit, resulting in a site index conversion equation.

Growth Intercept Models for Western Larch - EN38

Western larch (Larix occidentalis Nutt.) commonly grows in mixed stands, and is a relatively important tree species in the Nelson Forest Region. Researchers at the University of British Columbia undertook a larch productivity study, which included collecting data from 114 stem analysis plots. Of these, 99 plots were suitable for developing growth intercept models. The data were analyzed using a standard technique. The resulting set of 50 equations estimates site index for larch stands from breast height age 1 to 50. The models have accuracy comparable with those of interior spruce but are not as accurate as those for lodgepole pine.

Revised Growth Intercept Models for Coastal Western Hemlock, Sitka Spruce, and Interior Spruce - EN37

The original growth intercept models for Sitka spruce (Picea sitchensis [Bong.] Carr.), coastal western hemlock (Tsuga heterophylla [Raf.] Sarg.), and interior spruce-white spruce (Picea glauca [Moench] Voss), Engelmann spruce (P. engelmannii Parry), and their hybrids - are dated.

The original data, plus some additional data for interior spruce, were re-analyzed to incorporate new techniques into the models. The resulting models for Sitka spruce are more precise than the original models, although the revised models for western hemlock and interior spruce are slightly less precise. The advantages of the new techniques outweigh any loss of precision. The models for these species are upgraded to current standards and are consistent with models for other species.

Years to Breast Height and Green-up Age Models Based on a Juvenile Height Model for Lodgepole Pine - EN31

The iterative techniques that are currently used to obtain years to breast height and green-up ages (3 m green-up height) from the juvenile height model for lodgepole pine (Pinus contorta var. latifolia Dougl.) are cumbersome. Years to breast height and green-up age models were developed by generating age data from the juvenile height model and fitting a model to the data. These models result in years to breast height and green-up age estimates that are consistent with the juvenile height model.

Smoothing Top Height Estimates from Two Lodgepole Pine Height Models - EN30

The two models for estimating the top height of lodgepole pine (Pinus contorta var. latifolia Dougl.) are designed to function over different age ranges: a juvenile height model for total ages below 15 and a height-age model above breast height age ½. Four options are available to splice these models together to give a smooth height trajectory near the splice point. The option resulting in the smoothest trajectory uses the juvenile height model below breast height age 0 and the height-age model above breast height age 2, and linearly interpolates heights between breast height age 0 and 2.

Interim Validation of the Western Hemlock Growth Intercept Model - EN14

Growth intercept models estimate site index (a measure of site productivity) from average tree height growth measured immediately above breast height. These models have been developed for four species: coastal western hemlock (Tsuga heterophylla (Raf.) Sarg.) (Nigh) and Sitka spruce (Picea sitchensis (Bong.) Carr.) (Nigh); interior lodgepole pine (Pinus contorta Dougl.) (Nigh) and spruce (P. glauca (Moench) Voss, P. engelmannii Parry, and P. glauca x engelmannii) (Nigh). Growth intercept models are expected to be developed for all commercial species in British Columbia.

Interior Douglas-fir Growth Intercept Models - EN12

The objective of this study was to develop growth intercept models for interior Douglas-fir (Pseudotsuga menziesii var. glauca). These models relate site index to the early height growth of trees. They were developed using a well-established modelling technique and 72 sample plots established throughout the interior of British Columbia, and were tested with an independent data set. The test showed that the models were statistically biased below breast height age nine, but the practical significance of the bias may be such that the models can be used in young stands. The results of the model testing should be interpreted with caution.

Revised Growth Intercept Models for Lodgepole Pine: Comparing Northern and Southern Models - EN11

Growth intercept models relate site index to early tree height growth. To develop this model for lodgepole pine (Pinus contorta var. latifolia), 45 stem-analysis plots were sampled in northern British Columbia and another 45 plots were sampled in southern British Columbia. Tests were performed to detect differences in the site index–growth intercept relationship between the northern and southern plots. No practical differences were found, therefore one model suffices for both regions. This model should replace the existing model for lodgepole pine because it is more widely applicable in British Columbia.

Interim Validation of the Western Hemlock Growth Intercept Model - EN4

Growth intercept models estimate site index (a measure of site productivity) from average tree height growth measured immediately above breast height. These models have been developed for four species: coastal western hemlock (Tsuga heterophylla (Raf.) Sarg.) (Nigh 1996a) and Sitka spruce (Picea sitchensis (Bong.) Carr.) (Nigh 1996b); interior lodgepole pine (Pinus contorta Dougl.) (Nigh 1995a) and spruce (P. glauca (Moench) Voss, P. engelmannii Parry, and P. glauca x engelmannii) (Nigh 1995b). Growth intercept models are expected to be developed for all commercial species in British Columbia.

It is important that these models be validated (tested). Growth intercept models are empirical; hence they strongly reflect the behaviour of the model development data. Therefore, testing them with independent data (that is, data that were not used to develop the model) is important because the model development data may be atypical (Picard and Cook 1984). If a model validates well against an independent data set, it does not mean that it is correct; it simply provides more evidence that the model is adequate (Oreskes et al. 1994).

A Variable Growth Intercept Model for Sitka Spruce - EN3

Thirty-eight Sitka spruce stem analysis plots in the Queen Charlotte Islands were sampled and the height growth of the top height trees was reconstructed. A variable growth intercept model was developed for Sitka spruce from these data. This model (or a table) will be used to estimate site index for silviculture planning and other applications. Further research areas are identified that could improve the model. Introduction Growth intercept models allow site index to be accurately estimated in young stands. In British Columbia, site index is the top height of a stand at breast height (bh) age 50 (i.e., when the trees have 50 annual growth rings at breast height). Traditional growth intercept models estimate site index from the average annual height growth immediately above breast height. Typically, the height growth is identified from the annual branch whorls and is averaged over a 5-year period.

Site Index Conversion Equations for Mixed Sitka Spruce / Western Hemlock Stands - EN2

Site index conversion equations relate the site index of one species to the site index of a cohort growing in a mixed stand. These equations are useful for site quality evaluation, growth and yield modelling, projecting inventories, and, in some cases, obtaining a site index for a stand after converting the species. The geometric mean regression line (Ricker) is appropriate for modelling the relationship between the site indices of species growing in mixed stands (Nigh), and GMR site index conversion equations for some species mixes are available. This report describes new site index conversion equations for mixed Sitka spruce (Picea sitchensis (Bong.) Carr.) / western hemlock stands.