. 6
( 11)


using PCA, results from the latter being given in Bateman and Lovett (1998) and
Bateman (1996).
While our approach to modelling is similar, in other key respects the methods of
Worrell and Macmillan were not appropriate to the speci¬c types of question asked
in our research. Our central aim was to identify areas over the entire surface of
Wales which might be suitable for conversion out of agriculture and into forestry.
This necessitated the development of a methodology which was capable of produc-
ing estimates for both upland and lowland areas and which had the capability of
extrapolating such ¬ndings across the entire surface area of the country. To this end

4 Although not speci¬ed in this or the Macmillan paper, this appears to be an unadjusted R2 statistic.
5 Earlier discussions of the potential for applying GIS to forestry research and management are given in Aspinall
(1991), Davidson (1991) and Blakeway-Smith et al. (1993).
Modelling and mapping timber yield and its value 161

we adopted a GIS-based approach to modelling.6 This takes our base YC data from
the Forestry Commission (FC) Sub-Compartment Database (SCDB) which holds
information on each discrete stand (sub-compartment) in the FC™s estate (described
in detail subsequently).7 As this covers both upland and lowland sites, results from
such a model are more generalisable than those described previously. Use of the
SCDB has the added bonus of massively increasing our sample size relative to
previous studies. However, rather than relate YC to the environmental variables
reported in the SCDB, for reasons discussed below we extract these from a sepa-
rate source, the Soil Survey and Land Research Centre™s Land Information System
(LandIS) database (described subsequently).8

Data and data manipulation
This research relies upon a range of data sources. Aside from the SCDB and LandIS,
further environmental and topographic data were obtained from a variety of sources.
In this section we describe all these data and how they were manipulated prior to
consideration within the subsequent statistical investigation of tree growth. It is im-
portant to remember that, while the SCDB holds detailed data regarding individual
plantation sites, it does not extend to the large part of Wales which is unplanted.
Therefore the environmental variables given in the SCDB are, for our purposes,
unsuitable predictors of YC as complete land surface coverages for these variables
are not available and therefore cannot be used for extrapolation of estimates to
presently unplanted areas. The complete land area coverages of variables held in
LandIS and the other data described subsequently are therefore needed to allow for
this extrapolation of regression results.

The FC Sub-Compartment Database (SCDB)
The SCDB is the Forestry Commission™s central forest inventory containing details
for all stands in the estate. As such it provides an invaluable source of high-quality
data, listing many thousands of sub-compartments for a variety of species across
both upland and lowland Wales. The FC kindly provided SCDB data collected in the
period 1972 to 1993 for a wide range of species among which were just over 6,000
Sitka spruce and over 700 beech records (the disparity re¬‚ecting the dominance

6 For other examples of GIS applied to agricultural or forest planning, see Gemmell (1995), Moxey (1996),
Corbett and Carter (1997), Hill and Aspinall (2000) and the ESRI website (e.g. at www.esri.com/industries/
7 We are greatly obliged to Adrian Whiteman, Chris Quine and the Forestry Commission for use of the SCDB.
8 We are greatly obliged to Arthur Thomasson, Ian Bradley and the Soil Survey and Land Research Centre
(Cran¬eld) for use of LandIS.
162 Applied Environmental Economics

of conifers over broadleaves in our Welsh study area).9 Some of the information
given in the SCDB concerned internal FC administration and was not of interest
to our investigation and so the ¬nal list of variables extracted for this study was as
shown in Table 6.1. This also indicates how certain of these data were manipulated
to produce further (often binary dummy) variables. In doing this, one-way analyses
of variance on the dependent variable (YC) were used to identify likely signi¬cant
divisions in the data.
The SCDB also contains a variety of environmental variables speci¬c to sub-
compartments such as soil type, altitude, terrain type and windblow hazard class.
Normally these would be ideal for modelling purposes. However, as the SCDB only
holds such data for plantation sites rather than as uninterrupted national coverages,
¬ndings based upon such data would not form a suitable basis for extrapolation to
other, currently unforested areas. This is somewhat unfortunate as these site-speci¬c
data are almost certainly more accurate than those obtainable from more general
databases such as LandIS. This means that the regression models produced using
LandIS are unlikely to ¬t the YC data as well as those using the site factor informa-
tion given in the SCDB. However, for the purposes of this research, the advantage
of being able to extrapolate out across the entire surface of Wales and consider cur-
rently unplanted areas easily outweighs such costs (which we subsequently argue,
on the basis of our results, are likely to be small).

The SSLRC Land Information System (LandIS)
The ¬rst systematic attempt to analyse and record British soil information was the
˜County Series™ of maps initiated by the Board of Agriculture in the late eigh-
teenth and early nineteenth centuries. Until comparatively recently this remained
the standard and unsurpassed source of soil data. During the 1940s the Soil Sur-
vey of England and Wales (SSEW) began a detailed mapping initiative. How-
ever, by the late 1970s, only one-¬fth of the country had been covered. In 1979
the SSEW, which in the late 1980s became the Soil Survey and Land Research
Centre (SSLRC), commenced a ¬ve-year project to produce a soil map of the whole
of England and Wales and to describe soil distribution and related land quality in
appropriate detail.
The data collected in this exercise were digitised, spatially referenced, and subse-
quently expanded to include climate and other environmental information (Bradley
and Knox, 1995). The resulting Land Information System (LandIS) database was
initially commissioned by the Ministry of Agriculture, Fisheries and Food, with the

9 The FC was, as always, most willing to allow access to its data, for which we are most grateful.
Modelling and mapping timber yield and its value 163

stated aim of ˜providing a systematic inventory capable of being used or interpreted
for a wide range of purposes including agricultural advisory work, but also for the
many facets of land use planning and national resource use™ (Rudeforth et al.,
1984, emphasis added). However, while the system has been used in a variety of
ways, particularly in relation to modelling agricultural pollution (see examples in
Hallett et al., 1996 and the SSLRC website10 ), the present research represents one
of the ¬rst attempts to use LandIS for its originally intended purpose: national land
use planning.

The data
De¬nitions, derivations and accuracy of the data extracted from LandIS are pre-
sented in Bateman (1996) and are summarised in Table 6.2. Further details of
LandIS and the data therein are given in Jones and Thomasson (1985) and Hallett
et al. (1996), with discussion of Welsh conditions given by Rudeforth et al. (1984).
LandIS data are supplied at a 5 km resolution.
An immediate problem with applying the LandIS data to modelling yield classes
arose from the plethora of differing soil codes contained in the database. These
are taken from the Soil Survey of England and Wales (1983) which lists many
hundreds of separate soil types, a large number of which were present in our Welsh
dataset. This level of detail far exceeds that used in previous yield class studies such
as Worrell (1987b) who uses seven soil type dummies derived from information
given in the SCDB, which in turn relies on the standard FC classi¬cation of soils.
The large number of soil codes given in LandIS was a problem both because of its
implication for degrees of freedom in our intended regression analysis and because
any such results would be of little practical use to the forester familiar with an
alternative and simpler system. Furthermore, consultations with an expert in the
¬eld of soil science and forestry suggested that, for our purposes, many of the
SSLRC soil codes could be merged with no effective loss of information and a
substantial increase in clarity.11 Details of the ¬nal categorisation are given in the
bottom row of Table 6.2.

Other data
Topex and wind hazard
Data referenced to a 1 km grid on both the topographical shelter of a site (topex)
and wind hazard were supplied by the Forestry Commission.12 Topex is usually
10 See www.silsoe.cran¬eld.ac.uk/sslrc/services/dataproducts/landis.htm.
11 Dr Bill Corbett of the School of Environmental Sciences, University of East Anglia, and formerly of the Soil
Survey of England and Wales, kindly advised on the merging of soil codes to produce a simple eight-category
system which groups together similar soils.
12 Our thanks go to Chris Quine at Roslin, the Forestry Commission™s northern research station.
164 Applied Environmental Economics

Table 6.1. Variables obtained from the SCDB1

Variable name2 Values Notes and recodings (in italics)
Grid reference Easting, Northing 100 m resolution O.S. grid
PHF = plantation high
Land use/crop type
PWB = uncleared Uncleared = 1 if PWB; = 0
windblown area otherwise
PRP = research plantation Research = 1 if PRP; = 0
1 = single storey Single = 1 if single storey; = 0
2 = lower storey
3 = upper storey
SS = Sitka spruce
Species Used to identify target species
BE = beech
Planting year Discrete variable Plantyr: year in which stand was
Survey year Discrete variable Survyr: year in which stand was
Yield class Even number YC: tree growth rate: average
m3 /ha/year over an optimal
rotation (the dependent variable)
Productive Hectares Area: stocked area of the
forest area sub-compartment
Unproductive Hectares Unprod: the area within the
forest area sub-compartment which has a
permanent effect upon the crop,
e.g. rocky outcrops, etc.
1 = 1st rotation on 1stRot = 1 for 1st rotation; = 0
formerly non-forest otherwise
2, 3 etc. = 2nd, 3rd 2ndRot = 1 for 2nd or subsequent
rotation; = 0 otherwise
rotation, etc.
9 = historical woodland Historic = 1 if historic site; = 0
sites otherwise
S = ancient, semi-natural Semi-nat = 1 if
woodland ancient/semi-natural
woodland; = 0 otherwise
P = single species crop MixCrop = 1 if mixed species
crop; = 0 otherwise
M = mixed species crop
P = purchased by FC Purchased = 1 if purchased; = 0
Legal status
L = leased Leased = 1 if leased; = 0
E = extra land, managed Extra = 1 if extra; = 0 otherwise
by FC outside its legal
Modelling and mapping timber yield and its value 165

Table 6.1. (cont.)

Variable name2 Values Notes and recodings (in italics)
1 = National Park NatPark = 1 if National Park; = 0
2 = AONB/National AONB/NSA = 1 if AONB/National
Scenic Area; = 0 otherwise
Scenic Area
3 = ESA (where not OthESA = 1 if ESA area not
included in above; = 0
included in 1 or 2
above) otherwise
1 = Forest Park FPark = 1 if forest park; = 0
Forest Park
1 = SSSI (Site of Special SSSI = 1 if SSSI; = 0 otherwise
Scienti¬c Interest)
2 = NNR (National NNR = 1 if NNR; = 0 otherwise
Nature Reserve)
3 = Non-FC Nature NonFCNR = 1 if non-FC nature
reserve; = 0 otherwise
1 = Forest Nature Reserve FCNR = 1 if Forest Nature
FC conservation
Reserve; = 0 otherwise
2 = Other FC FCcons = 1 if other FC; = 0
conservation otherwise
S = scheduled ancient Ancient = 1 if S, U or W; = 0
monument/Woodland monument otherwise
Monument = 1 if S or U; = 0
U = unscheduled ancient
W = ancient woodland
Further recodes from above:
NpAonbSa = 1 if any of NatPark or
AONB/NSA; = 0 otherwise
Cons = 1 if any of NNR,
NonFCNR, FCNR, FCcons; = 0
Reserve = 1 if any of Cons,
Park = 1 if any of NatPark, FPark,
SSSI; = 0 otherwise

Notes: 1 Except where shown otherwise.
Variables are listed in the order in which they appear in the database.

determined as the sum of the angle of inclination for the eight major compass
points of a site (Hart, 1991). Thus, a low angle sum (low topex value) represents a
high degree of exposure. The resultant GIS data coverage was labelled Topex1km.
Table 6.2. Variables obtained from LandIS

Variable name Label De¬nition
Average annual accumulated temperature (in o C)
Accumulated temperature Acctemp
above 0o C
Accumulated rainfall Rainfall Average annual accumulated rainfall (in mm)
Available water Avwatgra Amount of soil water available for a grass crop
after allowing for gravity-induced drainage
Avwatcer As for Avwatgra but adjusted for a cereal crop
Avwatpot As for Avwatgra but adjusted for potatoes
Avwatsb As for Avwatgra but adjusted for sugar beet
Moisture de¬cit Mdefgra The difference between rainfall and the potential
evapotranspiration of a grass crop
Mdefcer As for Mdefgra but adjusted for a cereal crop
Mdefsbpt As for Mdefgra but adjusted for a sugar
beet/potatoes crop
Field capacity Fcapdays Average annual number of days where the soil
experiences a zero moisture de¬cit
Return to ¬eld capacity Retmed Median measure from a distribution of the
number of days between the date on which a
soil returns to ¬eld capacity and
31 December of that year
Retwet The upper quartile of the above distribution
(measure of return to ¬eld capacity in wet
Retdry The lower quartile of the above distribution
(measure of return to ¬eld capacity in dry
End of ¬eld capacity Endmed Median measure from a distribution of the
number of days between the 31 December
and the subsequent date on which ¬eld
capacity ends
Endwet The upper quartile of the above distribution
(measure of the end of ¬eld capacity in wet
Enddry The lower quartile of the above distribution
(measure of the end of ¬eld capacity in dry
Workability Workabil A categorical scale indicating the suitability of
the land for heavy machinery work in spring
and autumn
Spring machinery SprMWD The average number of days between 1 January
working days and 30 April where land can be worked by
machinery without soil damage
Autumn machinery AutMWD The average number of days between 1
working days September and 31 December when land can
be worked by machinery without soil damage
SSLRC soil type classi¬cation code: Soil1 =
Soil type SoilX
lowland lithomorphic; Soil2 = brown earths;
Soil3 = podzols; Soil4 = surface water gley;
Soil5 = stagnogley (perched watertable);
Soil6 = ground water gley; Soil7 = peats;
Soil8 = upland lithomorphic; Soil23 =
areas with Soil2 or Soil3
Modelling and mapping timber yield and its value 167

Blakeway-Smith et al. (1994) de¬ne wind hazard on the basis of four factors: wind
zone, elevation, topex and soil type.13 The resultant continuous variable (Wind1km2 )
is inversely linked with tree productivity and growth rates.

Elevation and associated variables
The work of Worrell and Malcolm (1990a) shows that elevation and its associated
characteristics are key predictors of yield class. However, such a variable is not
included in the LandIS database and the SCDB only gives heights for existing
plantation sites. Clearly for extrapolation purposes this is inadequate and so an
alternative source of data was required. At the time the research was undertaken
access to the Ordnance Survey digital elevation models (DEMs) was impractically
expensive for UK university researchers (although a more recent access agreement
has altered this situation). Therefore a DEM was created from three other sources:
the Bartholomew 1:250,000 digital contour database for the UK, summit points from
Bartholomew™s paper maps and the spot heights of plantations from the SCDB. The
accuracy of the derived DEM was tested by omitting various data points from the
calculation, using the DEM to estimate heights from those points and comparing
actual with predicted values. These tests (detailed in Bateman, 1996) showed that
the DEM performed well and so was re-estimated using all available data and
incorporated into our yield class estimation model. The elevation data were also
used to generate two further GIS surface variables: slope angle (Dsl2) and aspect
angle (Wsaspgr2). Data on all these variables were produced at a 500 m — 500 m
cell resolution.

Creating GIS surfaces for explanatory variables
Prior to the regression analysis two fundamental issues had to be addressed re-
garding the de¬nition of a common extent and resolution for the environmental
variables as these parameters differed across the various data sources used. Data
were supplied at a wide array of resolutions ranging from the (nominal) 100 m
accuracy of the SCDB to the 5 km tiles of the LandIS variables. While the technical
operation of interpolating from a coarse to a ¬ner resolution is relatively straight-
forward within a GIS (Berry, 1993), it needs to be recognised that the precision
achieved may be rather higher than the underlying accuracy of the data (Goodchild,
1993), so deciding upon a common unit size was a matter for some deliberation.
Standardisation upon the smallest unit (100 m) did not seem a sensible choice.
For instance, the 100 m reference used in the SCDB is, the FC admit, spuriously
13 Blakeway-Smith et al. (1994) also discuss a funnelling variable which tends to have higher values in valley
bottoms. Zobeck et al. (2000) show how GIS techniques can also be adapted to the prediction of wind erosion
of soils, which may in turn impinge upon yields.
168 Applied Environmental Economics

precise. On the other hand, aggregation up to the 5 km scale of the coarsest data
was thought likely to result in a loss of much relevant detail (e.g. for topographic
features). As a compromise, a 1 km grid was settled upon and all the data were
converted to this resolution.
The spatial extent of Wales was de¬ned by converting a vector outline of the
Welsh coast and border with England (from the Bartholomew 1:250,000 scale
database) to a raster grid representation consisting of 1 km2 cells. This resulted in a
layer within the GIS containing 20,563 land cells and values of the variables in the
LandIS and non-SCDB datasets described above were then estimated for each grid
cell.14 For characteristics such as topex or elevation this was done by aggregation
and averaging, whereas with the LandIS variables each 1 km grid square was given
the value of the 5 km cell it fell within. With all data now at a common resolution and
extent we now had the necessary complete surfaces of potential predictor variables
for use in our regression model and from which extrapolation across all areas,
whether currently planted or not, would be possible.
A ¬nal task concerned the extraction of values for all environmental variables
for each yield class observation in the SCDB. This was achieved by using point-in-
polygon operations within the GIS to identify the 1 km grid cell corresponding to
each sub-compartment grid reference.

Yield models for Sitka spruce and beech
Sitka spruce
Our regression analyses followed the approach set out by Lewis-Beck (1980) and
Achen (1982). An initial objective concerned the identi¬cation of an appropriate
functional form for our models. Tests indicated that a linear model performed
marginally better than other standard forms and, given that such a form is both
easily interpretable and typical of other studies, this seemed a sensible choice.15
A variety of stepwise regression analyses were undertaken yielding models com-
posed of raw variables, PCA factors and a combination of these. Resultant models
are reported in full in Bateman (1996) and Bateman and Lovett (1997, 1998). For
reasons of brevity, here we only report the best-¬tting regression models for Sitka
spruce and beech. These models used raw variables rather than PCA factors as
predictors of YC. Furthermore, a number of observations are omitted from these
models, mainly those for which the measurement of YC was taken relatively soon

14 This exercise revealed some relatively minor missing observations in the LandIS database. Measurements for
these cells were proxied using interpolation and related techniques. For details see Bateman and Lovett (1997).
15 Semi-log (dependent and independent), double-log and quadratic forms were also tested and cross-product
terms investigated.
Modelling and mapping timber yield and its value 169

Model 6.1. Best-¬tting regression model predicting Sitka spruce YC

Predictor Coeff. S.d. t-ratio p
Constant 16.7097 0.3487 47.92
’0.00167 ’15.65 <0.001
Rainfall 0.00011
’0.00878 ’22.31 <0.001
Wselvgr2 0.00039
Topex1km 0.02426 0.00759 3.20 0.001
Soil23 0.80489 0.08046 10.00
’4.8827 ’5.05 <0.001
Soil1 0.9660
Area 0.00395 0.00038 10.43
Plantyr 0.04989 0.00484 10.31
’1.9280 ’17.64 <0.001
1stRot 0.1093
’0.30832 ’4.02 <0.001
MixCrop 0.07670
Park 0.94769 0.09385 10.10
Ancient 0.9266 0.3089 3.00 0.003
Uncleared 2.6411 0.2276 11.61
’0.08543 ’10.49 <0.001
Unprod 0.00814
’0.43395 ’4.59 <0.001
Reserve 0.09452
’5.1415 ’6.73 <0.001
Semi-nat 0.7644

n = 4,307 R2 = 43.0% R2 (adj.) = 42.8%

after planting (full details in Bateman and Lovett, 1998).16 Assessment of YC for
young trees is inherently more dif¬cult than for more mature stands and tests in-
dicated that omitting those stands measured at a particularly young age improved
model ¬t, suggesting that such a procedure reduced random measurement error and
yielded more reliable results (results for models without any observations omitted
are given in Bateman and Lovett, 1998, and are similar in coef¬cients to those re-
ported here). This procedure left a sample of 4,307 Sitka spruce sub-compartments,
for which our best-¬tting model is reported as Model 6.1.
The ¬rst point to note about Model 6.1 is that the use of the SCDB permitted
a very substantial increase in sample size, which, at over 4,300, compared very
favourably to the few hundred observations typically used in many YC studies. This
is in part responsible for the comparatively high degree of explanation provided
by the model, which exceeds all conventional studies and is comparable with the
GIS-based study of Elston et al. (1997) cited previously.
Inspection of the model revealed a number of highly signi¬cant predictors of
YC. With respect to the environmental characteristics of sites we can see that YC
fell with increasing rainfall (Rainfall)17 and elevation (Wselvgr2) and increased as

16 The idea of omitting plantations which were measured relatively soon after planting was suggested by Chris
Quine and Adrian Whiteman of the Forestry Commission and Douglas Macmillan of the Macauley Land Use
Research Institute, to whom we are grateful.
17 This result underscores the fact that Wales is a high rainfall area. Waterlogging rather than drought is the main
water-related problem in the area.
170 Applied Environmental Economics

topographical shelter improved (Topex1km). Because of its categorical nature, soil
type is considered as a series of dummy variables, two of which proved statistically
signi¬cant. YC was signi¬cantly elevated by planting on brown earth or podzol
soils (Soil23, which is a simple combination of Soil2 and Soil3) and signi¬cantly
depressed by planting on lowland lithomorphs (Soil1). Both results conformed to
prior expectations.
The model also highlighted the importance of silvicultural factors. The positive
relationship with the size of the plantation (Area) is interesting and, to our knowl-
edge, has not previously been formally identi¬ed. This would seem to indicate that
trees growing as part of a large plantation are more likely to thrive than those in
small areas. This might be because large stands provide advantages in terms of the
ease of adopting species-speci¬c management regimes, or because such stands tend
to condition their environment to their own advantage (for example, by reducing
competition from both ¬‚ora and fauna). Conversely, this latter factor may be one
of the pressures militating against smaller stands. A strong and positive in¬‚uence
of the time variable (Plantyr) is also identi¬ed. This is usually explained as re¬‚ect-
ing improvements in silvicultural methods such as the introduction of ploughing,
fertiliser applications or enhancement of the genetic stock.
Two further silvicultural factors were identi¬ed. Trees planted on ground which
has not been previously used for afforestation (1stRot) perform worse than those
planted in successive rotations. This may be because second rotation trees have,
on average, been planted more recently than those in the ¬rst rotation (although a
relatively low correlation with Plantyr indicated that this may not be all of the story)
or because second rotation trees inherit a nutrient-enriched and/or pH-modi¬ed soil
base from their forebears. Trees also seem to perform less well when grown in a
mixed species plantation (MixCrop) than in monoculture, a ¬nding which suggests
that there may be a timber productivity bene¬t associated with the amenity cost of
the latter.
Next, a number of site factors arising from the interaction of environmental char-
acteristics and management practice appear important. YC was signi¬cantly higher
in parkland areas (Park), a result which may re¬‚ect more careful silvicultural man-
agement. The higher YC associated with planting in areas which were previously
ancient woodland (Ancient) seems to be the corollary of the impact of 1stRot. A
further and rather interesting boost to growth is implied by the variable Uncleared
which identi¬es trees growing in areas that have been previously affected by wind-
blow but have not yet been cleared. It seems that the surviving trees actually pro¬t
from windblow in that their immediate neighbours (and competitors) are removed,
thus boosting their access to sunlight and nutrients. However, while growth rate
may bene¬t from such events, the ensuing lack of cover raises the probability that
the survivors will subsequently fall victim to windblow themselves.
Modelling and mapping timber yield and its value 171

Table 6.3. Comparing actual with predicted YC for Sitka spruce
(cell contents are counts)

Predicted YC
Actual YC 4 6 8 10 12 14 16 18 20 All
4 0 0 1 0 0 0 0 0 0 1
6 0 0 7 63 0 0 0 0 0 70
8 1 3 12 161 220 0 0 0 0 397
10 0 0 9 169 395 141 0 0 0 714
12 0 0 4 176 516 285 63 0 0 1,044
14 0 0 0 90 415 276 124 33 1 939
16 0 0 0 0 201 313 179 33 1 727
18 0 0 0 0 0 152 144 45 3 344
20 0 0 0 0 0 0 41 26 3 70
22 0 0 0 0 0 0 0 1 0 1
All 1 3 33 659 1,747 1,167 551 138 8 4,307
Predicted YC compared to actual YC Percentage of total sample
Prediction is two classes too high 12.8
Prediction is one class too high 23.4
Predicted YC equals actual YC 27.9
Prediction is one class too low 25.2
Prediction is two classes too low 11.4

Finally, three negative environmental/management factors were identi¬ed. Plan-
tations with higher amounts of unproductive land (Unprod) not surprisingly perform
worse than otherwise similar sites. Sub-compartments which fall within the bound-
aries of conservation areas (Reserve) also exhibit relatively lower YC, as do areas
which are allowed to remain as semi-natural habitat (Semi-nat). These results may
re¬‚ect the application of less intensive silvicultural techniques in such areas.
In order to examine its predictive capabilities, Model 6.1 was assessed by round-
ing the predictions to the nearest point on the YC scale and then comparing them
with actual YC for the 4,307 observations used in the model. Results of this analysis
are presented in Table 6.3 which shows that 76.5 per cent of YC predictions are
within one division of actual YC.

Compared to the situation for Sitka spruce, the SCDB contains only a small number
of beech compartments within our study area. These observations were analysed in
a similar manner to before (for full details see Bateman and Lovett, 1997, 2000a),
and this analysis identi¬ed a much higher proportion of stands being assessed
172 Applied Environmental Economics

Model 6.2. Optimal model for beech

Predictor Coeff. S.d. t-ratio p
’4.428 ’2.30
Constant 1.923 0.022
’0.00386 ’4.22 <0.001
Wselvgr2 0.00091
Plantyr 0.07995 0.01279 6.25
AONB/NSA 0.4751 0.2710 1.75 0.081
’1.4812 ’2.98
OthESA 0.4969 0.003

n = 205 R2 = 35.7% R2 (adj.) = 34.4%

at relatively young ages. Details of models using all observations are given in
Bateman (1996) and Bateman and Lovett (1997), with related analysis being given
in Bateman and Lovett (2000a). However, here we report results for only the subset
of 205 sites unaffected by the early measurement problem. The best-¬tting model
for these sites is reported as Model 6.2.
Examining Model 6.2 we can see that, as for our Sitka spruce results, the yield
class of beech declines with increasing elevation (Wselvgr2) and rises as we consider
more recently planted sub-compartments (Plantyr). However, the smaller sample
size of just over 200 observations fails to reveal many of the previously noted
relationships, with just two management regime variables proving signi¬cant (and
one of these only at ± = 10 per cent). Nevertheless, the overall degree of explanation
is reasonably satisfactory as is the predictive power of the model, as indicated in
the actual versus predicted test summarised in Table 6.4.
As a side analysis, regression models for both species under investigation were
re-estimated after inclusion of variables representing the aspect of each sub-
compartment. In both cases, aspect variables proved to have only a weak impact
on yield class;18 however, the nature of this effect is interesting and is illustrated in
Figure 6.1 which compares the results with those of Worrell and Malcom (1990b)
in their study of Sitka spruce in the uplands of northern Britain.
Inspection of Figure 6.1 tells a clear and coherent story. In the upland areas of
northern Britain the intensity of the prevailing westerly wind causes aspect to be
a major factor determining tree growth such that trees in relatively sheltered, east-
facing (θ = 90o ) sites perform signi¬cantly better than those facing west (θ =
270o ). The radiative energy advantage of south-facing slopes is completely negated
by the impact of the prevailing wind. In our Welsh study of Sitka spruce we consider
both upland and lowland sites. Here both the magnitude and statistical signi¬cance
of the impact of aspect is reduced. Furthermore, the reduction in the power of the
prevailing wind (occurring because we are considering sites at lower altitude as
well as the less arduous conditions of Wales relative to northern Britain) means that
At best only signi¬cant at ± = 10 per cent. Full details are reported in Bateman and Lovett (1997, 1998).
Modelling and mapping timber yield and its value 173

Table 6.4. Comparing actual with predicted YC for beech
(cell contents are counts)

Predicted YC
Actual YC 4 6 8 All
2 0 1 0 1
4 9 29 2 40
6 7 66 20 93
8 0 29 37 66
10 0 0 5 5
All 16 125 64 205
Predicted YC compared to actual YC Percentage of total sample
Prediction is two classes too high 1.5
Prediction is one class too high 23.9
Predicted YC equals actual YC 54.6
Prediction is one class too low 20.0
Prediction is two classes too low 0.0

Figure 6.1. Aspect effects for Sitka spruce and beech in differing locations.

the solar energy advantage of southerly sites can now be detected, as our aspect
effect is now maximised at south-east (rather than east) facing sites. This trend is
continued when we consider our beech sub-compartments. Here, most sites are at
lower elevations such that the absolute magnitude (and statistical signi¬cance) of
the aspect effect is markedly reduced. Furthermore, the reduction in the impact
of the prevailing westerly wind means that the solar energy advantage of being
south-facing is further boosted such that we ¬nd that the aspect curve for beech
sites now peaks for sites facing south-south-east.
174 Applied Environmental Economics

Mapping yield class
We have now estimated yield class (YC) models for both of the tree species con-
sidered. In this section these models are used to generate GIS-based maps of YC
which are presented and analysed below.

Producing predicted yield class maps within a GIS
To generate a YC map (or, more speci¬cally, a raster image) the GIS requires data
on predictor variables for all the grid cells in the area for which we wish to estimate
yield, in this case the 20,563 1 km squares representing the entire land area of Wales.
If we take our model (6.1) of Sitka spruce yield as an example, we can see that this
is predicted by a constant and a number of explanatory variables. The constant is in
essence a data layer in its own right which has identical values (here 16.709) for all
land grid cells. The ¬rst explanatory variable in this model is the predictor Rainfall
for which we have estimates from the LandIS database. We can therefore begin to
build up our predicted YC map by employing the GIS software to calculate a new
raster map which contains the values from multiplying the values in the Rainfall
grid by the relevant coef¬cient (“0.00167).
The above procedure was repeated for all predictor variables. However, some
variables were related to management (e.g. Area), policy (e.g. Reserve) or when the
site was planted (e.g. Plantyr). These are not speci¬cally spatial variables so they
were treated by holding them at certain ¬xed values (i.e. as for the constant) and
varying some of them in a sensitivity analysis. The variables MixCrop, Ancient,
Unprod, Reserve, Park, Uncleared and Semi-nat are all dummies for infrequently
occurring, unusual sites and were consequently held at zero (their modal value)
for all analyses. Similarly the variable Area was held at its median value of 33 ha.
Given the very low value of the coef¬cient on this variable and its relatively small
range (see the descriptive statistics given in Bateman, 1996), sensitivity analysis
did not seem justi¬ed here. However, this was not the case for the variables Plantyr
and 1stRot and full sensitivity analyses were conducted for these.
Once the data coverage for each predictor variable has been multiplied by its
estimated coef¬cient all the resulting maps can be overlaid and their values summed
to obtain the ¬nal prediction of YC in each area. The same methodology was then
employed to generate a YC map from our beech model.

Timber yield maps for Sitka spruce
In producing YC maps based on our Sitka spruce model we considered the impact
of changing the Plantyr variable from 0 (being the base year in which the Forestry
Commission started to plant Sitka spruce) to 75 (being the present day, i.e. Sitka
Modelling and mapping timber yield and its value 175

spruce planting commenced about 75 years ago) thereby arguably re¬‚ecting tech-
nological progress over that period. For both of these analyses we initially held
1stRot = 1, i.e. we examined ¬rst-rotation trees at both of these time periods.
However, many present-day Sitka spruce plantations are now in their second rota-
tion. Therefore, we also tested the effect of letting 1stRot = 0 (i.e. second rotation)
when Plantyr = 75.
Raster maps were produced using the procedure outlined in the previous section.
Plate 1a illustrates the predicted YC image created from our Sitka spruce model
with Plantyr = 75 (present day) and 1stRot = 0 (replanting on a previously planted
Inspection of Plate 1a clearly shows the very strong in¬‚uence which environmen-
tal characteristics have upon our predictions of YC. The in¬‚uences of lower altitude,
better soil and lower rainfall combine to produce high YC. The pattern of lower
YC produced by higher elevations is particularly noticeable, with the mountain
ranges of Snowdonia, the mid Cambrians and the Brecon Beacons clearly evident.
Less extreme upland areas such as the Preseli Mountains produce YC values which
lie between these extremes. Also rather noticeable are the adverse effects of the
rain-shadow lying to the east of the Cambrians which results in large areas of rela-
tively depressed YC values stretching in some cases up to the English border. The
negative impact of sandy and estuarine soils upon growth can also be seen in the
small but signi¬cantly depressed areas of low yield at places such as the tip of
the Gower Peninsula and nearby Pembrey, the southernmost part of Anglesey and
the Llandudno peninsula.19
Plate 1a assumes 1stRot = 0 (i.e. predictions for plantations which are not in their
¬rst rotation) and Plantyr = 75 (i.e. predictions for trees planted in the mid 1990s).
To provide a contrast with these assumptions, maps of predicted YC for Sitka spruce
with Plantyr = 0 (i.e. trees planted at the start of Forestry Commission operations in
1920) and 1stRot = 1 (i.e. sites with trees in their ¬rst rotation) were also produced.
Following the predictions of Model 6.1 both of these latter scenarios give lower YC
predictions than those illustrated in Plate 1a, although the pattern of YC variation
remains similar. These differences are quanti¬ed in Table 6.5 which presents the
frequency distributions of predictions from these three scenarios. As can be seen,
differences are substantial, with these two alternatives producing appreciably lower
YC predictions in each case.
While our YC maps seem highly plausible (and we would defend them as such
for the majority of Wales), Table 6.5 and Plate 1a do indicate a weakness in our
models in their ability to estimate YC for extreme environmental conditions such
as, for example, mountain tops. Our best-¬tting model for Sitka spruce fails to
19 Interestingly both Pembrey and Newborough (Anglesey) are the sites of large forests, underlining the point
that forests are often con¬ned to the most marginal land.
176 Applied Environmental Economics

Table 6.5. Predicted Sitka spruce YC under three scenarios

Plantyr = 75; Plantyr = 75; Plantyr = 0;
1stRot = 0 1stRot = 1 1stRot = 1
YC Freq. % Freq. % Freq. %
2 ” ” ” ” 10 0.049
4 ” ” 1 0.005 46 0.224
6 1 0.005 15 0.073 367 1.785
8 16 0.079 54 0.263 2,255 10.966
10 56 0.272 504 2.451 4,691 22.813
12 554 2.694 2,524 12.274 8,747 42.538
14 2,609 12.688 5,106 24.831 4,447 21.626
16 5,209 25.332 9,287 45.164 ” ”
18 9,416 45.791 3,072 14.939 ” ”
20 2,702 13.140 ” ” ” ”
Mean 17.05 15.12 11.38

Notes: The column headings de¬ne the values of the variables Plantyr and
1stRot used in each map, where: Plantyr = year in which stand was planted
(0 = 1920; 75 = 1995); 1stRot = 1 if stand is the ¬rst planted in that
sub-compartment, = 0 otherwise (i.e. sub-compartment is in second or
subsequent rotation).
The frequency columns refer to the number of 1 km grid squares. Each
map consists of 20,563 such squares.

predict any sites of less than YC6. However, clearly if trees were planted at or near
mountain peaks they might well not survive or would at best produce only very low
YC. Similarly our model does not predict any cells to have YC in excess of 20, yet
our dataset indicated a few cases of YC being as high as 24. We therefore appear to
be overestimating YC at the lower extreme and under estimating at the upper end
of the range.
Two factors seem pertinent in explaining this. First, we are predicting average
YC over 1 km grid squares. This will tend to remove extremes and therefore gives
some support to our ¬ndings. Second, as there is relatively little planting at the
extremes of altitude, low YC observations are under-represented in the FC™s sub-
compartment database resulting in a lesser ability of statistical models based on such
data to estimate accurately for such locations.20 However, while these are problems,
the actual versus predicted YC comparison reported in Table 6.3 suggests that the
degree of over- and underestimation at the tails is not too serious.

20 A third possibility, discussed in Bateman (1996), is a resolution issue. Our DEM estimates elevations based upon
surrounding points and therefore may not fully capture the upper extremes of altitude. Any underestimation of
elevation at the tops of mountains may result in overestimation of YC at those points.
Modelling and mapping timber yield and its value 177

Table 6.6. Predicted beech YC under two scenarios

Plantyr = 162; 1stRot = 1 Plantyr = 144; 1stRot = 1
YC Freq. % Freq. %
3 ” ” 1 0.005
4 ” ” 84 0.409
5 17 0.083 1,970 9.580
6 421 2.047 10,437 50.756
7 7,003 34.056 8,071 39.250
8 12,925 62.856 ” ”
9 197 0.958 ” ”
Mean 7.69 6.25

Note: The frequency columns refer to the number of 1 km grid squares.
Each map consists of 20,563 such squares.

Timber yield maps for beech
As with Sitka spruce, we attempted to produce maps of predicted beech YC con-
sidering the impact of changing the Plantyr and 1stRot variables. In the case of the
Plantyr variable, unlike our Sitka spruce analysis there was no distinct year in which
beech planting commenced. Thus, although we have a date at which Plantyr =
0, this corresponds simply to the oldest record in the dataset (some 162 years ago)
rather than to some actual initial planting date. Accordingly it was decided to adopt
a somewhat different strategy here and our sensitivity analysis examined two val-
ues: Plantyr = 144 (which equalled both the mean and median planting date of
the early 1970s); and Plantyr = 162 (mid 1990s). The dataset showed that most
beech sub-compartments were in their ¬rst rotation and so this sensitivity analysis
was not performed, 1stRot being held at a value of 1 for all beech images.
We therefore produced two YC maps for beech and Plate 1b illustrates the version
holding Plantyr = 162 (and 1stRot = 1). Both maps show a similar pattern of
YC distribution to that of Sitka spruce; however, the range of these distributions is
far narrower than for the latter as is shown in Table 6.6. As before, ceteris paribus,
increasing Plantyr leads to a rise in predicted YC.

Producing timber yield value maps
In Chapter 5 we developed models for estimating timber values which were sensitive
to a variety of factors including the following:
(i) species: Sitka spruce or beech
(ii) a full range of yield class levels
(iii) a full range of subsidy and grant schemes
178 Applied Environmental Economics

(iv) single, optimal-length rotation or perpetual replanting
(v) a range of discount rates
(vi) private or social values
NPV and annuity sums.21

Note that, at this point in our analysis, we have not included the woodland recreation
values discussed previously or the carbon storage values estimated in the following
chapter. Therefore, the ˜social™ values referred to above and in the remainder of this
chapter are only those directly associated with the production of timber. Essentially
these take the private values received by farmers or other forest operators and
remove grant and subsidy transfer payments and add in the timber-related shadow
values (such as the value of ensuring supply continuity) discussed in Chapter 5.
These models produce timber value/YC curves for each combination or ˜scenario™
of the above factors such as those illustrated for a variety of subsidy schemes in
Figures 5.5 and 5.6. As those diagrams showed, for any given subsidy scheme,
timber value is approximately linearly related to YC. This result provides a ready
method for converting our maps of timber YC to maps of timber value.
For each species and all combinations of factors (iii) to (vi) above, a linear
equation linking predicted timber value to YC was estimated (details for all com-
binations are given in Bateman, 1996). In all cases a simple straight-line model
provided an excellent ¬t.22 As an example, the function predicting farmers™ private
annuity value, calculated at a 3 per cent discount rate, for perpetually replanted
Sitka spruce receiving grants at non-disadvantaged area rates is:23
ANNSS = ’136.32 + 21.32 YC
(’17.88) (44.90)
ANNSS = farmers™ private annuity value per hectare of perpetually replanted
Sitka spruce timber production, calculated using a 3 per cent
discount rate
YC = yield class
R2 (adj.) = 99.6%. Figures in brackets are t-statistics.
With the resultant suite of regression equations having been estimated, the GIS was
used to convert our YC maps to their timber value equivalents. For each scenario
this was achieved by selecting the appropriate YC map and conversion regression
equation. The GIS was then used ¬rst to multiply predicted YC across the timber

21 The relation of NPV and annuity sums was discussed in Chapter 5. Annuity values are likely to be of more
interest to the farmer than NPVs.
Lowest R2 (adj.) = 97.2 per cent.

So, for this example, predicted ANNSS for YC20 Sitka spruce = £290/ha (see the lower curve in Figure 5.4).
Modelling and mapping timber yield and its value 179

yield map by its coef¬cient in the conversion equation, and second to subtract the
constant given in the same equation. The resultant map contains predicted timber
values for the desired scenario.
Using this procedure NPV and annuity value maps were created for a variety of
scenarios. Figure 6.2 illustrates the social (i.e. removing grants and subsidies) NPV
map for perpetually replanted Sitka spruce timber production calculated using a 3
per cent discount rate (remembering that non-timber values such as recreation and
carbon sequestration have yet to be added to this value). The distribution of values
re¬‚ects that of the YC image (Plate 1a) upon which it is based and so comments
remain as before.
The number of permutations of the factors considered in this analysis precludes
full reporting here (details are given in Bateman, 1996). However, Tables 6.7 and
6.8 report social NPV and annuity equivalents for Sitka spruce timber values across
three discount rates, while Tables 6.9 and 6.10 repeat this analysis for beech. For
any given discount rate, the distribution of values is given in terms of (i) the number
of 1 km grid squares in our study area falling in each value category and (ii) that
frequency count expressed as a percentage of the 20,563 1 km squares which
constitute Wales.
Considering Tables 6.7 to 6.10 we can see that, for both species, the choice of
discount rate has a substantial impact upon values, with higher rates yielding lower
NPV and annuity sums. This effect is somewhat more pronounced in the case of
Sitka spruce, a result which re¬‚ects its short rotation length relative to beech. With
a long rotation length (such as that for beech) discount factors are already relatively
low at felling irrespective of the chosen discount rate. In such cases, variation
in that rate has less impact upon NPV and annuity values than for short rotation
species where, with low discount rates, discount factors are still reasonably high at
felling. This effect also explains why discounted Sitka spruce values are higher than
those for beech despite the latter attracting higher nominal values at felling. In the
absence of other monetised bene¬ts, these results clearly illustrate why market-led
assessments of forestry projects argue in favour of planting conifers rather than

We have estimated yield class models for Sitka spruce and beech based in part upon
variables drawn from GIS databases covering the whole of Wales. This has allowed
us to use those models to produce predicted yield maps for both species for the
entire Principality. We have then used these maps in conjunction with the timber
value model derived in Chapter 5 to produce NPV and annuity equivalent maps. In
general we are reasonably happy with this analysis. However, we should mention at
180 Applied Environmental Economics

£/ha, 1990
< 3,999
5,000’5,999 Motorway
6,000’6,999 Dual carriageway
7,000’7,999 Single carriageway
5 0 km
0 10 20 30 40
8,000’8,999 Urban
Figure 6.2. Predicted timber social NPV sums for perpetually replanted Sitka spruce: 3%
discount rate.
Modelling and mapping timber yield and its value 181

Table 6.7. NPV sums for perpetually replanted Sitka spruce timber across various
discount rates

Discount rate, r (%)
1 3 6
NPV (£/ha, 1990) Freq. % Freq. % Freq. %
’500“ ’1 ” ” ” ” 1 0.005
0“499 ” ” ” ” 31 0.151
500“999 ” ” 1 0.005 187 0.909
1,000“1,499 ” ” 2 0.010 2,232 10.854
1,500“1,999 ” ” 8 0.039 5,786 28.138
2,000“2,499 ” ” 20 0.097 11,208 54.506
2,500“2,999 ” ” 24 0.117 1,118 5.437
3,000“3,499 1 0.005 48 0.233 ” ”
3,500“3,999 ” ” 163 0.793 ” ”
4,000“4,499 4 0.019 514 2.500 ” ”
4,500“4,999 5 0.024 1,019 4.956 ” ”
5,000“5,499 10 0.048 1,307 6.356 ” ”
5,500“5,999 11 0.053 1,757 8.544 ” ”
6,000“6,499 8 0.039 2,556 12.430 ” ”
6,500“6,999 17 0.083 3,380 16.437 ” ”
7,000“7,499 23 0.112 4,055 19.720 ” ”
7,500“7,999 62 0.302 4,534 22.049 ” ”
8,000“8,499 80 0.389 1,173 5.704 ” ”
8,500“8,999 207 1.007 2 0.010 ” ”
9,000“9,499 352 1.712 ” ” ” ”
9,500“9,999 525 2.553 ” ” ” ”
10,000“10,499 649 3.156 ” ” ” ”
10,500“10,999 739 3.594 ” ” ” ”
11,000“11,499 826 4.017 ” ” ” ”
11,500“11,999 1,112 5.408 ” ” ” ”
12,000“12,499 1,194 5.807 ” ” ” ”
12,500“12,999 1,595 7.757 ” ” ” ”
13,000“13,499 1,820 8.851 ” ” ” ”
13,500“13,999 2,162 10.514 ” ” ” ”
14,000“14,499 2,225 10.820 ” ” ” ”
14,500“14,999 2,605 12.668 ” ” ” ”
15,000“15,499 2,600 12.644 ” ” ” ”
15,500“15,999 1,561 7.591 ” ” ” ”
16,000“16,499 168 0.817 ” ” ” ”
16,500“16,999 2 0.010 ” ” ” ”
mean (£) 13,362 6,707 2,023
s.d. 1,938 1,189 438
182 Applied Environmental Economics

Table 6.8. Annuity values for perpetually replanted Sitka spruce timber across
various discount rates

Discount rate, r (%)
1 3 6
Annuity(£/ha, 1990) Freq. % Freq. % Freq. %
’25“ ’1 ” ” ” ” 1 0.005
0“24 ” ” ” ” 21 0.102
25“49 ” ” 3 0.015 53 0.258
50“74 1 0.005 16 0.079 479 2.329
75“99 2 0.010 22 0.107 2,183 10.616
100“124 15 0.073 60 0.292 4,068 19.783
125“149 18 0.088 263 1.279 7,318 35.588
150“174 34 0.165 993 4.829 6,434 31.289
175“199 115 0.559 1,682 8.180 6 0.029
200“224 411 2.000 2,413 11.735 ” ”
225“249 1,044 5.077 3,962 19.268 ” ”
250“274 1,460 7.100 5,175 25.167 ” ”
275“299 1,994 9.697 5,626 27.360 ” ”
300“324 3,010 14.638 348 1.692 ” ”
325“349 4,172 20.289 ” ” ” ”
350“374 4,837 23.523 ” ” ” ”
375“399 3,380 16.437 ” ” ” ”
400“424 70 0.340 ” ” ” ”
mean (£) 329 246 133
s.d. 54 48 30

Table 6.9. NPV sums for perpetually replanted beech timber across various
discount rates

Discount rate, r (%)
1 3 6
NPV(£/ha, 1990) Freq. % Freq. % Freq. %
500“999 ” ” ” ” 20,563 100.000
1,000“1,499 ” ” 10 0.049 ” ”
1,500“1,999 ” ” 1,281 6.229 ” ”
2,000“2,499 10 0.049 14,524 70.626 ” ”
2,500“2,999 97 0.472 4,748 23.088 ” ”
3,000“3,999 5,410 26.307 ” ” ” ”
4,000“4,999 15,046 73.165 ” ” ” ”
mean (£) 4,251 2,327 942
s.d. 495 331 317
Modelling and mapping timber yield and its value 183

Table 6.10. Annuity values for perpetually replanted beech timber across various
discount rates

Discount rate, r (%)
1 3 6
Annuity(£/ha, 1990) Freq. % Freq. % Freq. %
40“49 20 0.097 20 0.097 37 0.180
50“59 179 0.870 327 1.590 16,203 78.797
60“69 1,798 8.744 4,756 23.129 4,323 21.023
70“79 6,253 30.409 10,841 52.721 ” ”
80“89 8,960 43.573 4,619 22.463 ” ”
90“99 3,353 16.306 ” ” ” ”
100“149 ” ” ” ” ” ”
150“199 ” ” ” ” ” ”
200“249 ” ” ” ” ” ”
250“310 ” ” ” ” ” ”
mean (£) 81 74 58
s.d. 13 12 12

least one point of caution regarding the methodology developed in this study. The
YC regressions ¬t the data quite well by the standards of models reported in the
literature. Furthermore, the equations linking YC to NPV and annuity equivalents
also ¬t well. If this were not the case the possibility exists that errors in the ¬rst of
these models might be further propagated by those in the second. This is a point to
be wary of in any wider application of such a methodology.
Accepting that such a possible problem does not seem to be present here, the
timber value maps produced permit a common unit comparison with the recreation
value maps produced previously. Given that woodland recreation frequently takes
place in productive woodlands it seems reasonable to assume that these values may
be additive.
We now turn our attention to the last forest value we shall consider in our analysis:
carbon sequestration.
Modelling and valuing carbon sequestration in trees,
timber products and forest soils

The global process of industrialisation which has grown so rapidly over the past two
centuries has, in more recent years, led to detectable increases in the concentration
of insulating greenhouse gases (GHGs). These have in turn resulted in increases
in global temperatures, and these are expected to continue rising with GHG emis-
sions for the foreseeable future (Houghton et al., 1992; Wigley and Raper, 1992;
IPCC, 1996a, 2001a, 2001b; Zecca and Brusa, 1997). The most recent report of
the Intergovernmental Panel on Climate Change (IPCC) summarises the ¬ndings
of contemporary research as showing:

that the globally averaged surface temperatures have increased by 0.6 ± 0.2 o C over the
20th Century; and that, for the range of scenarios developed in the IPCC Special Report on
Emission Scenarios (SRES), the globally averaged surface air temperature is projected by
models to warm 1.4 to 5.8 o C by 2100 relative to 1990, and globally averaged sea level is
projected by models to rise 0.09 to 0.88 m by 2100. (IPCC, 2001b: p. 3)

The consequences of such climatic change are uncertain but potentially highly
adverse (Warr and Smith, 1993; Parry, 1993, 2000). The IPCC concludes that:

Projected climate changes during the 21st Century have the potential to lead to future large-
scale and possibly irreversible changes in Earth systems resulting in impacts at continental
and global scales. . . . Depending on the rate of ice loss, the rate and magnitude of sea-
level rise could greatly exceed the capacity of human and natural systems to adapt without
substantial impacts. (IPCC, 2001b: p. 6)

Growing concern regarding climate change has raised interest in the potential for
using forestry as a way of reducing atmospheric concentrations of carbon diox-
ide (Sedjo, 1989; Myers, 1990; Nordhaus, 1991a; Galinski and Kuppers, 1994),

This chapter extends the analysis presented in Bateman and Lovett (2000b).

Modelling and valuing carbon sequestration 185

the gas which in absolute terms provides the largest contribution to global insu-
lation. Two issues of scale should be emphasised here. First, given the scale of
global fossil fuel use, carbon sequestration in forests can only be a stopgap mea-
sure, providing temporary relief in advance of necessary reductions in emissions.1
Second, stocks of carbon and the potential for future sequestration in temperate
woodlands are relatively small compared to those of tropical forests, while both are
dwarfed by the storage and sequestration potential of the world™s oceans (IPCC,
2000; Matthews et al., 2000; UNDP et al., 2000).2 Accepting these caveats does not
diminish the value of carbon sequestration (irrespective of the biome concerned),
while issues of practicality and cost highlight the fact that forest ecosystems may
be considerably more amenable to initiatives to change policy than are the ocean
Carbon sequestration bene¬ts therefore constitute a separate category of forest
value (Dore et al., 2001). Such bene¬ts have been recognised both by economists
and policy-makers internationally (IPCC, 2001b). In our study area of Wales the
National Assembly™s recent Draft Document on the Future of Agriculture (National
Assembly for Wales, 2001b) explicitly recognises the need to commission research
concerning ways in which both forestry and farming can contribute to cutting
emissions and promoting carbon sequestration.
This chapter attempts to quantify the impact upon carbon storage of afforest-
ing an area of previously unplanted land.3 However, assessment of this bene¬t is
not straightforward. An initial and daunting problem concerns the valuation of se-
questered carbon. This has been a subject of heated debate within the economics
literature. A number of articles have been heavily criticised for failing to grasp the
complexity of the climatic processes which underlie global warming. We reviewed
the literature in some detail in Bateman (1996) and defend our use of the valuation
work of Sam Fankhauser as being both more sophisticated and based upon signif-
icantly more realistic climate change models than preceding work. A brief review
of the debate is presented at the start of the next section.
Our review of literature also considered the physical processes of carbon se-
questration in trees and forest soils, carbon storage within timber products, and
eventual liberation back to the atmosphere, for carbon storage within trees is only
a transitory process and total storage can only grow while the volume of timber
increases. Nevertheless, the potential for expanding forest areas (heightened in the
1 As Nowak (1993) emphasises, planting 10 million trees per annum for the next ¬fty years will sequester less
than 1 per cent of US emissions during that period.
2 Global carbon stocks in the vegetation and soils of tropical forests are estimated at 212 GtC (gigatonnes of
carbon) and 216 GtC respectively. By comparison those for temperate forests are 59 GtC and 100 GtC. These
compare to estimates for all biomes of 466 GtC in vegetation and 2,011 GtC in soils, the majority of this storage
being in seas and oceans (IPCC, 2000).
3 We do not appraise the current storage of carbon in the study area. For estimates of the latter, see Cannell and
Dewar (1995).
186 Applied Environmental Economics

EU by surpluses of agricultural land) means that forests do provide a vital breathing
space before policy and technological change can address the root cause of global
The following section presents a brief overview of our research methodology.
This is then applied to the modelling of carbon sequestration in both Sitka spruce and
beech trees, while the next section considers subsequent liberation of carbon from
the products and felling waste of both species. The impacts of afforestation upon
soil carbon levels are then considered. Results from these analyses are presented,
including the monetary value maps necessary to make results compatible with the
¬ndings of previous chapters.

Literature review4
This section opens by considering the ongoing debate concerning the valuation
of carbon emissions and their storage. It then moves to consider three aspects of
carbon sequestration by means of afforestation: the storage of carbon in trees; its
post-felling liberation; and the impact of afforestation upon soil carbon ¬‚ux.

The shadow price of carbon emissions
While a number of studies have examined the costs of ¬xing carbon via afforestation,
relatively few have attempted to quantify its bene¬ts. For our purposes the most
interesting of these are those adopting a damage-avoided approach to valuation.
If accurate, estimates produced by such methods are shadow prices which may be
directly incorporated within the cost-bene¬t framework which underpins our wider
The pioneering work on the shadow price of CO2 emissions is that of
Nordhaus (1991b,c). Using a very simple model and assuming a 3 per cent dis-
count rate he calculates social costs of $7.3/tonne of carbon (tC) emitted. This
estimate has provoked a number of critical responses (Ayres and Walter, 1991;5
Daily et al., 1991; Cline, 1992a; Grubb, 1992; Price, 1997b). Typical of these, Cline
(1992a) highlights the simple linear structure of the underlying model, implying
4 For a review of land use and climate change issues and policy, see the essays in Adger et al. (1997) and Sedjo
et al. (1997). Other economic and physical analyses from around the world of the impacts of forests upon
carbon storage are given in Maclaren and Wakelin (1991), Kauppi et al. (1992), Makundi et al. (1992), Kurz
et al. (1992, 1994), Kolchugina and Vinson (1993), Turner et al. (1993, 1995), Backlund et al. (1995), Maclaren
et al. (1995), Bureau of Transport and Communications Economics (1996a,b), Maclaren (1996a,b), Mauldin
and Platinga (1998), Motha and Heyhoe (1998) and IPCC (2001a,b).
5 It is somewhat ironic that Ayres and Walter criticise the Nordhaus (1991b,c) estimates as too low given that in
an earlier paper they assess emissions damage costs at $5“10/ton CO2 ($18“37/tC) (Walter and Ayres, 1990).
In their subsequent critique of Nordhaus they apply different assumptions to his model to produce a damage
estimate of $30“35/tC (Ayres and Walter, 1991). However, given the problems of the simple linear Nordhaus
model, such estimates must be treated with caution.
Modelling and valuing carbon sequestration 187

both a constant level of CO2 emissions6 and a constant shadow price through
In subsequent work Nordhaus (1992a,b) addresses many of these criticisms.
His Dynamic Integrated Climate Economy (DICE) model uses optimal economic
growth analysis in combination with a climate model which feeds climate changes
back into the economy as damages. The resulting carbon shadow prices are similar to
his earlier estimates ($5.3/tC in 1995 rising to $10/tC in 2025). However, Nordhaus™
results have again been criticised by Cline (1992b) who suggests that the parameter
values used result in an underestimation of true costs.
A similar model, utilising a more detailed economy component, is used by Peck
and Teisberg (1992a,b). Their Carbon Emission Trajectory Assessment (CETA)
model produces estimates of the shadow price of carbon ranging from $10/tC in
1990 to $22/tC in 2030. Given that the CETA model is structurally similar to DICE,
the main reason explaining differences in the shadow price estimates produced
appears to be discrepancies in assumptions regarding carbon damages.
Important contributions to the shadow pricing debate are provided by the papers
of Fankhauser (1993, 1994a,b, 1995). These introduce a fully stochastic, green-
house damages model, explicitly recognising the highly non-linear and uncertain
aspects of the climate process. Uncertainty is incorporated by modelling all key pa-
rameters as random variables.7 The model consists of modules examining: future
emissions; atmospheric concentration; radiative forcing; temperature rise; annual
damage; costs of sea-level rise protection; and discounting.
The issue of discounting is, arguably, the central problem in the appraisal of
global warming response, and this is a focal point for much research (Howarth,
1996; Azar, 1998; Hasselmann, 1999; Pollock, 1999; Revesz, 1999; Hammitt and
Harvey, 2000). Fankhauser (1994b) tackles the discounting problem in a direct,
although still debatable, manner. Considering the literature on the subject, he sets
the pure rate of time preference (ρ) as a random variable with upper and lower
bounds of 0 and 3 per cent respectively and with a best guess (modal) value of
0.5 per cent. Similarly, the income elasticity of utility (ω) is de¬ned as a random
variable with upper and lower bounds of 0.5 and 1.5 respectively and a best guess
(modal) value of 1. This random variable discounting captures the uncertainty
regarding these parameters. Furthermore, if we recall our discussion of discounting
in Chapter 5, the low discount rate resulting from such a choice of parameter
values seems defensible as a re¬‚ection of social preference regarding the assessment
of global warming impacts. However, to allow comparability with other studies
6 Annual CO2 emissions are predicted to rise from 7.4 GtC in 1990 to 9“14 GtC by 2025 (IPCC, 1992). Climate
processes are clearly not ¬rst-order linear.
7 Here triangular distributions (using upper/lower bounds and the best-guess estimate) are generally assumed
although where upper and lower bounds were unknown a modest range of ±10 per cent around the best guess
was used.
188 Applied Environmental Economics

Table 7.1. The social costs of CO2 emissions ($/tC): comparison across studies

Study Measure 1991“2000 2001“2010 2011“2020 2021“2030
←’ ’’
Nordhaus Best guess 7.3 (0.3“65.9)
(1991a,b)1 (mode)
←’ ’’
Ayres and Best guess 30“35
Walter (1991)1 (mode)
Nordhaus Best guess 5.3 6.8 10.0
(1992a)1 (mode)
10“122 12“142 14“182 18“222
Peck and Best guess
Teisberg (1992b)1 (mode) (3.4“57.6)
Fankhauser Expected 20.3 22.8 25.3 27.8
(1994b)3 (mean)
5th percentile 6.2 7.4 8.3 9.2
95th percentile 45.2 52.9 58.4 64.2
standard dev. 14.3 16.0 17.5 19.0
skewness 2.5 2.5 2.5 2.4

Notes: Figures in brackets denote con¬dence intervals.
Discount rate = 3 per cent for all studies except Fankhauser (1994b).
Figures measured from graph as reported in Fankhauser (1994a).
Random variable discounting: ρ = (0, 0.005, 0.03); ω = (0.5, 1, 1.5).

Fankhauser also conducts a conventional discounting sensitivity analysis using
values of ρ = 0 and 0.03 with ω = 1 throughout.
The Fankhauser (1994b) model differs therefore from its predecessors in at least
three important aspects:
(i) it models climate feedback mechanisms in a more detailed and realistic manner
(ii) it uses expected (means) rather than best guess (modal) values
(iii) it employs a discount rate sensitivity analysis.

Table 7.1 contrasts results from Fankhauser™s (1994b) random variable discounting
model of CO2 damage costs with those discussed previously. For the latter, only a
best guess (modal) value is reported. In contrast and to emphasise the importance of
damage distributions, Fankhauser reports expected (mean) values as well as 5th and
95th percentiles, standard deviation and skewness. Given factors (i) to (iii) above,
the discrepancy between Fankhauser™s results and those of other studies are to be
The Fankhauser model was adopted as a cornerstone of the report by the In-
tergovernmental Panel on Climate Change into the socio-economic impacts of the
greenhouse effect (IPCC, 1996b).8 Accordingly, we feel justi¬ed in adopting the

8 These ¬gures are slightly above the sum of $20/tonne used by the World Bank in a retrospective appraisal of
their previous funding decisions (World Bank, 1996).
Modelling and valuing carbon sequestration 189

above values for use in this study. However, as our analysis extends long beyond
the 2021 horizon considered by Fankhauser, we have to make some assumptions
regarding carbon sequestration values beyond that point. After reviewing the liter-
ature it became apparent that simply extending the trend of Fankhauser™s estimates
risks error if greenhouse abatement measures are implemented (although the de-
cision, in 2001, of President George W. Bush to withdraw the United States from
emission reduction obligations set under the 1997 Kyoto Climate Change Conven-
tion means that the future for global abatement policy is very uncertain). Given the
lack of any ¬rm evidence it was decided to treat the ¬nal (2021) carbon value as an
equilibrium level extending throughout the remainder of our analysis. While this is
clearly a key assumption we felt that no other course of action was justi¬ed given
the uncertainty that exists within the literature.9

Carbon storage in trees10
Much of the woody biomass of a tree is carbon; therefore, growing new trees ¬xes
carbon over the lifetime of those trees. However, the relation between timber yield
and carbon storage is not straightforward.
Timber yield models provide information on the merchantable volume (MV) of
trees throughout a rotation (Edwards and Christie, 1981). MV only concerns the
saleable volume of a tree but may be related to total woody volume (TWV) by
allowing for branchwood, roots, etc. (Matthews, 1991; Rasse et al., 2001). The
TWV/MV ratio is very high in the early life of a tree but falls rapidly as MV rises
with age.11 TWV is in turn related to the tree™s dry weight (DW) via its speci¬c
gravity (SG). SG varies substantially across species, being about 0.33 for Sitka
spruce and 0.56 for beech (Lavers, 1969; Thompson and Matthews, 1989a). How-
ever, the proportion of DW which is carbon is roughly similar for Sitka spruce and
beech at about 49 per cent (G. Matthews, 1993).
While timber yield and species affect carbon storage, forestry management also
has a major impact. The move from unmanaged woodland to managed plantation
results in a signi¬cant increase in MV (Bateman and Lovett, 1997). However,
pro¬t maximisation results in smaller stems being periodically removed (thinned)
so as to promote the growth of a reduced number of larger, high-value trees. This
alone causes a substantial reduction in potential carbon storage (Matthews, 1992).

9 It should be noted that the process of discounting very greatly diminishes the impact of this assumption. In effect
it is the initial period (for which we have published valuation estimates) which is of paramount importance.
10 This section draws upon Sedjo et al. (1995) and conversations during 1994 and 1995 with Robert Matthews,
mensuration of¬cer at the Forestry Commission™s Research Station, Alice Holt Lodge, Farnham.
11 This study uses the TWV/MV relationship given in Matthews (1991). As an example of how this changes with
tree age, Matthews reports a ratio value of 3.0 at age 20 for YC12 Sitka spruce, falling to a value of just below
2.0 at age 40 and declining more slowly thereafter to about 1.4 at age 75.
190 Applied Environmental Economics

Figure 7.1. Total carbon storage curves for unthinned and thinned Sitka spruce: 5% discount

Furthermore, the practice of discounting leads both to higher-yield stands being
felled on a shorter rotation than those in slower growing areas, and to all trees being
cut before they attain their maximum carbon carrying capacity.
Figure 7.1 illustrates the impact of these management decisions upon three stands
of Sitka spruce growing at yield classes (YC) 8, 16 and 24 (where YC8 denotes a
Modelling and valuing carbon sequestration 191

stand producing on average 8 m3 /year/ha over an optimal rotation). Here yield class
models (Edwards and Christie, 1981) are combined with data on carbon storage
in Sitka spruce (Cannell and Cape, 1991; R. Matthews, 1993) to plot out carbon
storage curves for both thinned and unthinned (denoted tYC and uYC respectively)
stands.12 Unthinned stands produce a characteristic S-shaped carbon storage curve.
Thinned stands follow this curve up to the date of ¬rst thinning (TD1), which arrives
sooner for faster-growing stands (as does the date of felling; F).13 After TD1 the
tYC curve becomes much more shallow than its uYC counterpart. Furthermore,
the relatively early F terminates the former curve considerably before that for
unmanaged crops. Therefore, while plantation forests may represent a new carbon
sequestration gain over previous land uses (see below), thinned stands sequester less
carbon than unthinned crops.14 Furthermore, as noted by numerous commentators
(Thompson et al., 1997; van Kooten and Bulte, 1999; Thornley and Cannell, 2000;
Healey et al., 2000), there is clearly a trade-off between managing forests for timber
yield and optimising carbon storage.

Carbon liberation from wood products
Once a tree is felled its ¬xed carbon store begins to be liberated back to the at-
mosphere as CO2 . This may occur quite quickly if the wood is used as fuel, left
to decompose (e.g. small trimmings) or used for short-term purposes. The carbon
liberation rates resulting from these various end uses can differ substantially. For
example, Thompson and Matthews (1989a) compare conventionally grown YC16
Corsican pine with short rotation coppice (SRC) poplar plantations, noting that the
latter ¬xes signi¬cantly more carbon per annum than the former. However, because
SRC is generally used as fuel, its long-term average sequestration rate is signi¬-
cantly lower than that of Corsican pine which is typically used for more durable

12 Note that a number of studies have considered a possible feedback loop between the greenhouse effect and
tree growth whereby higher atmospheric CO2 concentrations lead to enhanced timber yield (Waggoner, 1983;
D™Arrigo et al., 1987; Heath et al., 1995; Murray et al., 1995; Eamus and Jarvis, 1989; Cannell and Cape,
1991; Kellomaki et al., 1997; Bucher-Wallin et al., 2000). However, evidence also exists to indicate that some
trees may reduce rates of CO2 uptake within a CO2 -enriched atmosphere, an effect which may differ between
species (Egli, et al., 2001). These factors are still the subject of research and are not incorporated in our model.
13 Figure 7.1 and underlying calculations use a 5 per cent discount rate to determine TD1 and F. As the discount
rate is increased so TD1 and F decrease. For a full sensitivity analysis, see Bateman (1996).
14 R. Matthews (1993) also considers the carbon emissions associated with felling, etc. However, these are
found to be relatively minor, and substantial net carbon storage bene¬ts are found, particularly where wood is
subsequently used for biofuel as a substitute for existing high-carbon fuels such as oil or coal.
15 Marland and Marland (1992) and R. Matthews (1993) highlight an important consequence of such examples:
where timber is used as fuel and substitutes for existing high-carbon fossil fuels, a further net bene¬t will accrue.
We have not adopted such an assumption in our analysis because of uncertainties regarding likely substitution
rates. In effect we assume that capital commitments to non-timber fuelling systems mean that any conversion
rate will be very low.
192 Applied Environmental Economics

Figure 7.2. Longevity of Sitka spruce timber when put to different uses. (Source: Thompson
and Matthews, 1989b.)

A rigorous examination of the impact of end use upon carbon ¬xing is given in
Thompson and Matthews (1989a,b). Results are obtained for a variety of species,
those for Sitka spruce being graphically summarised in Figure 7.2.
Figure 7.2 makes it clear that end use has a major in¬‚uence upon plantation
average carbon storage levels. Indeed, Matthews (1995) cites this as the major
determinant of overall carbon storage, being signi¬cantly stronger than factors such
as silvicultural management regime.16 In order to incorporate this effect within a
general carbon ¬‚ux model we also require information regarding the proportion of
wood allocated to each end use. Statistics gathered from a variety of sources are
summarised in Table 7.2 which provides a breakdown of 1991/92 UK domestic
production data divided into softwood and hardwood species.

Carbon ¬‚ux in soils
Determinants of soil carbon levels
All soils contain a certain natural level of carbon. This generally consists of de-
caying soil organic matter (SOM) although a small amount (usually less than
16 A further issue, considered by Matthews (1992), is the level of manufacturing emissions associated with
differing end uses. These are relatively high for capital-intensive products such as paper and low for sawn
wood, etc.
Table 7.2. Softwood and hardwood end uses for UK domestic production 1991/92

Softwood Hardwood
Modal 95% carbon Modal 95% carbon
Production liberation year liberation Production liberation year liberation
3 3


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