Integrating data for the construction of forest growth and yield models:
An example based on even-aged stands of ash (Fraxinus excelsior L.)
M.E. Baldwin1and R.W. Matthews2
1
Empirical Modelling Unit, 2Forest Resources Evaluation Group,
Biometrics, Surveys and Statistics Division, Forest Research,
Alice Holt Research Station, Farnham, Surrey, GU10 4LH, United Kingdom
e-mail: miriam.baldwin@forestry.gsi.gov.uk
Introduction
Reliable growth and yield models are essential for the sustainable management of forests.
Standard growth and yield tables are available for all major tree species in the UK (Edwards
and Christie 1981). The construction of these tables for the key commercial species was
informed by long-sequence data from permanent mensuration sample plots (Hummel et al.,
1959; Edwards, 1976). Availability of such data sets has enabled the production of yield
tables covering a wide range of productivity classes and silvicultural regimes.
For a number of tree species previously regarded as minor in commercial terms, available
data were limited to a few long-term series, augmented by one-off assessments obtained
from temporary sample plots. Thus, the range of growth rates and management regimes
covered by yield tables for these species is often limited, with provisional yield estimates
presented for some species.
Forest Research has been developing a methodology aimed at addressing weaknesses in
the available suite of yield models. This includes the specification of data sets for formulation
and calibration of models, recognising the scoping, assessment and analysis of data as an
integral part of the modelling exercise. Recently this approach has been applied to the
development of an improved yield model for ash (Fraxinus excelsior L.) growing in Britain.
Project methodology
The main stages in the methodology involve:
• Scoping the requirements for the model being developed.
• Specifying data needed for model formulation and calibration.
• Reviewing existing data holdings against the ideal requirement.
• Establishing purpose-designed networks of sample plots addressing data gaps.
• Integrating data sets as an intrinsic element of model development.
Model scoping
The 'M-series' system for classifying growth and yield models (Matthews and Methley, 1998)
identifies five broad classes of model (M1 to M5), which represent increasing levels of
complexity and process description. Critically, these are aligned to key policy, commercial
and research applications for which each model class constitutes an optimal solution (Table
1). The main objective of the study on ash was to estimate the economic potential of newly
established stands across a range of ex-agricultural sites in England and Wales. A
secondary objective was to inform silvicultural practice in these stands to support sustainable
management and to achieve an acceptable return on investment. These applications
indicated that a growth and yield model of the M2 class was an appropriate solution.
Table 1. 'M-series' model classification system
Model
class
M1
Description
Simple stand-level regression
relationships.
M2
Stand-level, 'state-space'
models.
M3
Tree size-class based, 'statespace' models.
M4
Individual tree 'state-space'
models including positional
relationships.
M5
Full biophysical-based models.
Principal applications
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Estate forecasting
Investment appraisal
Demonstrating sustainable management.
Estate forecasting
Site-species matching
Investment appraisal
Demonstrating sustainable management
Evaluating stand management options
Planning of forest design and operations.
Demonstrating sustainable management
Evaluating stand management options
Forest design planning
Forecasting stem quality and stand structure
Optimising stand production
Demonstrating sustainable management
Evaluating stand management options
Forecasting stem quality and stand structure
Optimising stand production.
Demonstrating long-term impact of silviculture
Support to 'continuous cover' management.
Forest-environment interactions.
Data specification
Formulation and calibration of M2-class models require data on key stand variables across a
range of stand ages and, annual or periodic increments of these variables. The most
important variables are dominant height, basal area per hectare, numbers of trees per
hectare and quadratic mean diameter at breast height (DBH). Information is also needed on
stand volume per hectare to characterise relationships between volume and other variables.
Thus, robust model development requires data on stand variables and increments at
different points in time, representing a range of stand productivity and silvicultural regimes.
Reviewing existing data
Data holdings consisted largely of observations from two mensuration plot types: time series
obtained from permanent sample plots and one-off assessments in temporary sample plots.
Existing data from permanent sample plots were reviewed by examining the range of stand
ages and broad classes of productivity (yield class, see Edwards and Christie, 1981) and
silvicultural regime (no thinning, light thinning, and heavy thinning). For each of the three
broad silvicultural regimes, a matrix was created representing ten 15-year stand ageclasses, and three yield-class bands ('high'', 'medium' and 'low’). The age-class and yieldclass bands were based on prior knowledge of the typical life span and yield class range
covered by ash stands in Britain. Existing sample plot data were classified using these
matrices. The presence of data for conditions represented by each cell within the matrix was
marked. Empty cells indicated a gap in the existing data and therefore a potential target for
new plot assessments.
Plot establishment and assessment
Having established the extent of data gaps, complementary data were gathered by
establishing a network of 'single-period' sample plots. The primary aim of single-period plots
is to rapidly obtain a large body of stand increment assessments across a wide range of
stands.
Single-period plots were established in a similar manner to permanent plots, but intensive
monitoring continued for only five years. DBH was recorded annually, with other
mensurational variables collected only in the first and final year. All measurements were
taken as prescribed by standard Forest Research protocols (Hummel et al., 1959; Edwards,
1976), with modifications appropriate to the single-period plot approach (Proudfoot and
Craig, 1999). This was the first application of single-period plots by Forest Research.
A total of 400 potential sites were identified by reference to the Forestry Commissions
database of publicly owned woodlands, and information from private landowners. The criteria
for assessing suitability for plot establishment was:
• Presence of ash as either a pure or mixed stand.
• The distribution of age classes represented by the stands by reference to matrices.
• Stand area greater than 0.1 hectare.
• The UK map reference, to ensure good geographical representation.
• Representation of as wide a range of different soil types as possible.
The final data set represented over 48 major soil types and climatic variation was accounted
for by reference to a reduced version of Pyatt’s 8 climatic regions (Pyatt and Suarez, 1997),
consisting of the classes 'cold and wet', 'cold and dry', 'warm and wet', and, 'warm and dry'. A
total of 101 sites were identified as suitable for establishment of single-period plots.
Figure 1
Integration of data from different sample plot types to inform model
development illustrated for stand quadratic mean DBH with respect to age.
Data Integration
Mean dbh (cm)
Data from different sources
were integrated in the following
way.
Permanent, Temporary
and Single-period
Age (years)
•
Increment data from
single-period plots were
used
for
model
calibration.
•
One-off
assessments
from temporary plots
were used to verify that
data from single-period
plots
covered
an
adequate range of age
and productivity classes.
•
Long-term
trajectories
from permanent plots
were used to inform
model formulation (e.g.
broad assumptions about growth patterns) and for validation of models.
Advantages and disadvantages of single-period plot approach
Building models by relying heavily on data from single-period plots has a number of
advantages:
• Data for many growth variables can be collected over a relatively short period.
• Data protocols can be directed towards current requirements for model development
based on current technologies.
• The consistency of measurements is improved by the involvement of the same field
teams and equipment in data collection.
• A larger number of sites and growth conditions can be observed.
• More intensive monitoring of the single-period plots allows more complex analysis
compared to one-off assessments from temporary plots.
However, there are also disadvantages:
• Validation from long-term trajectories is impossible if single-period plots are used without
a complementary long-term monitoring in permanent plots.
• Previous site and stand management history will not always be well documented.
• Historical observations on the effects of management on growth are lost.
• Analysis of growth trends and model development has to assume that current stand
development is not strongly affected by previous management, stand conditions and
growth dynamics. Alternatively these influences must be accounted for implicitly within
the growth model.
Conclusions
The strategy of filling data gaps by establishing single-period plots for the purposes of rapid
data collection to support and supplement data holdings has been successful. As a result,
the single-period plot approach is being integrated into the permanent sample plot network
throughout Britain. It must be noted that data from the single-period plots is best used in
complement to data collected from temporary and, permanent sample plots. The singleperiod plots have also provided data for additional short-term research programmes.
Acknowledgments
This work was undertaken with the financial support of DEFRA and the Forestry Commission
under the project, Development of Improved Site Yield Models for Ash in Britain (WD0209,
1999-2004) and the Forestry Commission’s Yield Modelling and Forecasting research
programme.
Reference
Edwards, P.N. (1976) Sample Plot Code, Forest Research internal report.
Edwards, P.N. and Christie, J.M. (1981) Yield Models for Forest Management. Forestry
Commission Booklet 48, Forestry Commission: Edinburgh.
Hummel, F.C.; Locke, G.M.; Jeffers, J.N.R.; Christie, J.M. (1959) Code of Sample plot
Procedure, Forestry Commission, London: Her Majesty’s Stationary Office.
Matthews, R. and Methley, J. (1998) Development of Interactive Yield Models for UK
Conditions, Forest Research Annual Report 1997-1998, The Stationary Office, London.
Proudfoot, J. and Craig, I. (1999) Temporary Sample Plot Code. Project - "Development of
improved site yield models for ash in Britain", Forest Research internal report.
Pyatt, D.G. and Suarez, J.C. (1997) An Ecological Site Classification for Forestry in Great
Britain: with special reference to Grampian Scotland, Technical Paper 20, Forestry
Commission, Edinburgh.