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Augmenting empirical stand projection equations with edaphic and climatic variables
P0res~~;olog-j Management Forest Ecology
and Management
98 (1997)
267-275
Augmenting empirical stand projection equations with edaphic and climatic variables R.C. Woollons a3*, P. Snowdon b, N.D. Mitchell ’ a School of Forestry. University of Canterbuy, Primzte Bag, Christchurch. New Zealand b CSIRO Forestr?; and Forest Products. PO Box E4008. Kingston ACT 2604, Canberra, Austmlia ’ Deportment of Botany, Univer.~i@ of Auckland, Auckland, New Zealand Accepted
26 March
1997
Abstract Builders of management growth and yield models have shown ingenuity in supplying projection equations with additional variables (for example, site index, time and amount of thinning) to enhance the quality of predictions. Other variables, edaphic or mechanistic in origin, have not been utilised because of difficulties in obtaining precise area1estimates at an affordable cost. Environmental (for example, rainfall, solar radiation) data have become available through response surface splining algorithms using data from weather station networks; long-term climate averages are available at any chosen location. This paper describes the building of mean-top-height and basal area ha-’ projection equations, utiiising climate variables in conjunction with traditional plot measures. The data were secured from the Nelson region of New Zealand, where stands of Pinus rudiatu are established on four contrasting soil groupings. No improvement in precision was found for the prediction of mean-top-height, by including temperature, solar radiation, or rainfall data, nor by recognising the diverse soils. Conversely, an improvement of 10% was obtained in modelling basal area ha-‘. Radiation and rainfall (but not temperature) significantly improved precision and accuracy, varying in functional form by soil type. The individual effects of soil-type and climate are heavily confounded. It is argued that forest process and empirical-based modelling has been independently researched for too long. There is evidence enough to suggest that hybrid modelling, encompassing both approaches, could improve the predictive ability of current growth prediction systems. 0 1997 Elsevier Science B.V. Keywords:
Growth
and yield modelling:
Difference
equations;
Weather
1. Introduction It is over 30 years since Clutter, 1963 produced his landmark paper on the principles of empirical stand growth modelling and the desirability of producing consistent, path-invariant growth equations which also possess a logical compatibility between growth and yield. From these considerations, a * Corresponding
author.
0378-I 127/97/$17.00 0 1997 Ekevier PII SO378-1 127(97)00090-X
Science
B.V. All rights reserved.
and soil variables
plethora of contributions to the growth modelling literature have emerged, many of which are the genesis of numerous growth and yield prediction systems. Many studies have been specifically concerned with improving the predictive power and precision of growth model equations. These have included (a) alternative estimation procedures to ordinary least squares, recognising the autocorrelative nature of permanent sample plot data (see, for example, Sullivan and Clutter, 1972; Ferguson and Leech.
1978; West et al.. 1984; Borders, 19891; (b) alternative sigmoidal functions (the original model of Clutter, 1963 was founded on the log-reciprocal Schumacher, 1939 model, but other formulations have been suggested (for example, the Chapman-Richards, Pienaar and Turnbull, 1973; the Weibull, Yang et al.. 1978, or the Hossfeld, Woollons et al., 1990)); and (cl variants of historical models; (see. for example, Clutter and Jones, 1980, who added a power term to the age variable of the basic Schumacher yield equation. or Murphy, 1983, where an inverse age term was included in the Chapman-Richard’s growth equation). In most of these models, the response variable. perhaps basal area ha-’ or mean-top-height, are formulated in projection or difference form (Clutter et al.. 1983). where the inputs are normally limited to an initial response variable value at a given (initial) age. That is: Y =.f’( T.T, .Y, )
(1)
where in Eq. (1) Y, Y, = response variable yields at ages T, T,, respectively. Increasingly, however, modellers have incorporated additional inputs in their difference equations. For example, the original Clutter, 1963 basal area equation contained a site index term, as did Sullivan and Clutter, 1972, Garcia, 1984, and Bailey and Ware, 1983. Candy, 1989 utilised all of site index. a stand density index (Lawrence, 1976). and a stand pruning ratio in a Pinus radiata basal area model. Woollons and Hayward, 1985 added an altitude term to a mean top height equation, while several authors have incorporated time and amount of thinnings as adjunct variables (see, for example, Pienaar and Shiver, 1986, Bailey and Ware, 1983, or Murphy and Farrar. 19881. In the cases above, modellers were keen to in crease the precision and predictive power of their models by utilising adjunct variables in addition to initial state inputs. It is well recognised, of course. that many other factors, edaphic, climatic, physical or physiological in origin, also contribute to stand growth. While some of these factors have been included in models of site index or productivity (Czamowski et al., 1976; Jacksonand Gifford, 1974: Hunter and Gibson, 1984; Turvey et al., 19901,they have been generally excluded from empirical sys-
terns of growth and yield. While there are some exceptions (for example, Turvey, 1983, who derived yield curves for different soil types). it was, and in some cases still is, almost impossible to measure many of these factors in a forest with an intensity sufficient for them to be included with permanent sampleplot data used to construct growth and yield models. There i$ considerable temporal and spatial variation to overcome, as well as cost constraints. These considerations, however. certainly have not prevented the building of many growth modelsbased on physiological and soil processes,and driveri by the input of environmental variables (see. for example, McMurtrie et al.. 1990, Makela and Hari, 1986. or Grace, 1990). Although originally intended as researchtools to help understandthe mechanismsOI‘ tree and stand growth. this has not deterred some scientists from considering them as managementdecision-making tools (for example. Kaut‘mann and Landsberg, I99 I 1. In practical terms. landscapescale process-based models of plantation productivity tend to have insul‘ficient spatial resolution for the 5- 100 ha stand units used by plantation managers,while detailed tree or stand based models tend to be too site-specific for generaluse. While theseproblemswith process-based models may be addressedin the future. there arc good prospectsfor utilisation of hybrid models.These aim to improve traditional forestry growth models basedon age, stand conditions and simple measures of site quality by including additional explanatory variables, such as growth indices derived from pro cess-basedmodels (for example. photosynthesis! or simple climatic indices such as annual rainfall. This approach has proved useful for describing annual differences in plantation growth due to year-to--yea1 differences in climatic factors (Nautiyal and C‘OLlt(J. 1984. Wickramsinghe. 1988. Snowdon and Waring, 19911 hut there have been no attempts to include such variables into projection models of type t I !. which form the heart of most empirical growth and yield systems(see, for example, Wooltons and Hayward. 1985; Candy, 1989). In New Zealand (and elsewhere). it has become possible to consider using climatic data as adjunct input variables in growth model equations. through the availability of excellent long-term a\ erapc weather statistics. obtained from an intensive grid of
R.C. Woollons
et al. / Forest Ecology
weather stations. The details are expanded below, but in essence, mean annual temperature, mean annual solar radiation and total annual rainfall (among other statistics) can be estimated for any permanent sample or inventory plot location, and so can be utilised together with stand and tree data. In this contribution, we report the building of mean-topheight and basal area ha-’ projection equations from one database. The results and ramifications of constructing these equations are discussed, and the potential of using these models for forest predictions is reviewed.
and Management
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Table 2 Correlations between each soil type
weather,
site index and location
Variable
R
T
SR
R
T
Altitude Latitude Longitude Site index
EHS 0.10 - 0.76 0.83 - 0.14
-0.98 - 0.40 0.35 0.26
-0.01 0.00 -0.12 0.23
HFG 0.40 -0.50 0.47 -0.21
-0.98 0.67 -0.04 -0.15
0.19 0.04 0.26 0.65
Altitude Latitude Longitude Site index
MC 0.3 1 - 0.71 - 0.95 -0.17
- 0.79 0.32 0.68 -0.07
- 0.35 0.11 0.44 -0.02
MG 0.58 - 0.25 -0.64 0.00
-0.92 - 0.33 0.36 -0.07
-0.09 0.14 -0.03 -0.02
T = mean annual
variables
for
SR
2. Method
R = mean annual (total) rainfall: SR = mean annual solar radiation.
temperature;
The climatic data used in this study were prepared as follows. For any sample plot measures at a given location, solar radiation (MJ me2 dd ‘), annual rainfall (mm) and mean temperature (“Cl values were estimated, after supplying latitude and longitude, altitude, aspect and slope of the plot. A full discussion is given by Mitchell, 1991. The basic climate data were acquired from the New Zealand network of recording stations. The modelling procedure makes use of algorithms developed by Hutchinson, 1984, in which Laplacian smoothing splines are used to derive mathematical surfaces (Wahba and Wendelberger, 1980). Four categories of climate data are utilised; solar radiation, rainfall, minimum and maximum temperature. For each, separate monthly surfaces were constructed. The surfaces are then interrogated by the program BIOCLIM, (Nix, 1986) to estimate monthly values of each variable at each location. These monthly figures are then summarised to give annual statistics. Estimated standard errors
for these calculations are given in the appendix of Mitchell, 199 1. The chosen study area is at Nelson, in the top northwest of the South Island of New Zealand, where CHH (Carter Holt Harvey) own or manage 3407 1 hectares of P. rudiatu plantations. The forest is tightly located on four contiguous but distinct soil types, colloquially referred to as the (1) Eastern hill soils (EHS), (2) High fertility granites (HFG), (3) Mapua clays (MC) and (4) Moutere gravels (MG), which represent 13 019, 3886, 4296, and 12 870 ha, respectively, of the total resource. Details of these soil types are given by Chittenden et al., 1966. A total of 205 permanent sample plots are available for analyses. Table 1 summarises climatic and other data, while Table 2 gives the correlation matrices between location and weather variables, for each soil type. From these, it is clear that the effects of soil and climate are quite strongly related and thus
Table 1 Weather data for each soil type Soil type
Average
EHS HFG MC MG
27.7 29.5 27.5 29.1
Figures
in brackets
site index
(19) (11) (19) (15) are coefficients
Average 345 348 83 264
altitude
(36) (34) (25) (27)
of variation
Average 10.9 10.8 12.4 11.3
(‘%)
(6) (6) (1) 4)
temperature
Total annual rainfall
Average
1458 (8) 1753 (6) 1154(8) 1286 (7)
11.5 11.1 12.6 12.1
(12) (11) (5) (11)
solar radiation
270
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cant ( 17< 0.0001). The discriminant functions correctly classified 66% of EHS, 97% of HFG. 95% of MC, and 73% of MG zones. in total 162 of the 205 data points. The first two mean canonical scores together with a 99.9% confidence region of each soil type are plotted in Fig. I; the independence of the four soil types is clearly portrayed. The first two standardised canonical variates are given by-: z, = 0.58
dba
6 First Canonical
Fig. I. 99.9% confidence regions the first two canonical variates.
in terms
Z’ = --0.66
of
X
X
X
S + 0.93
X
rain - 0.08
temp
ah -- 0.13 X S + 0.52 i’ rain + 0.21
.X solar-t 0.38 X temp. The first is obviously dominated by the effect of rainfall, while the secondvariate probably represents an interaction between altitude and rainfall. Table 3 summarisesthe extent of the mensuration data for each of the soil types. Several modelling principles were followed when building the projection equations. Basic sigmoid functions considered were those discussedby WoolIons and Wood, 1992. namely the Schumacher, Weibull, Gompertz, Chapman-Richards, and Wossfeld equations. In all cases,goodness-of-fit was assessedby lesser mean square values and rigorous inspection of residual plottings by soil type.
partially confounded. For example, the Mapua clays are characterised by low altitudes and corresponding high temperature and radiation but low rainfall; the HFG are conspicuous for high altitude and rainfall. but lower temperature and radiation. Conversely, Table 1 emphasises that the range of climatic data within soil zones is relatively low, especially so for the Mapua clays. In general, stands established on the latter soil have lesser wood production than those on the other three soil types, but overall the area is fertile, with site indices (mean-top-height at age 20, where mean-top-height is defined as the average of stem height of the top 100 stems ha-‘, by diameter breast height (dbh)) generally around 27-29 m. A preliminary discriminant analysis was assayed between the four soil types and the variables, annual total rainfall, average solar radiation, mean temperature, site index and plot altitude. The first two canonical variates accounted for 94.6% of the variation, but all three variates (available) were highly signifi-
Table 3 Basic mensuration
alt + 0.04
X solar + 0.41
Variate
of the four soil types
X
3. Results For mean-top-height, it became quickly apparent that a polymorphic form was appropriate, but three sigmoid formulations -the Hossfetil Schumacher, and Weibull (Woollons and Wood, 1992) - gave
data
Soil
Plot
Meas
Age
EHS HFG MC MG
57 34 38 74
336 206 230 397
13.3 10.7 12.5 12.5
(2-28) (3-26) (3-27) (3-27)
G ha-’
MTH
N
27.6 28.3 ‘2.4 3 I .2
18.2 (2-38) 16.4 (2-38) 18.5 C-40) 18.4(3-41)
544 749 562 760
(I -85) (I -84) (I-77) (2-94)
Plot = number of plots: Meas = number of measures: C ha- ’ = mean net basal area ha- ’ Cm’): stocking (stems ha-’ ). The figures in parentheses gives the minimum and maximum values.
MTH
(156-1720) (150-1733) (150-1604) ~450-1916)
= mean top height (m);
N = mean
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very good and virtually equivalent results. Finally, the Weibull-type projection equation:
form (1) for each soil type were then formed. It soon becameapparent that the Schumacherformulation:
H=~-~((~-w/~)”
G= w[lodG,W’,/T)P
+ ~(1 - (WY’)]
and
(4)
o= (T/T,y
Eq. (4), where G,, G = initial and future basal area ha-’ at ages T,, T, was easily the best equation for all four soil types, but the Mapua clays and HFG were not especially well modelled, partially due to relative lack of data. Accordingly, a pooled model was constructed that produced a plausible model, but it contained evidence of predictive bias (see Table 4). Further modelling with empirical variables gave two more equations:
(2)
where, in Eq. (2), H, H, = meantop height at agesT, T, was adopted, giving an excellent fit, unbiasedover all four soil types. Attempts were made to include stocking in the formulation; in New Zealand, evidence has emergedthat thinning to low densitiescan induce sharp reductions in P. radiata height growth (Woollons et al., 1994; Maclaren et al., 1995); but for these data, there were only weak signsof significance. This is logical enough, since heavily thinned plots are not strongly representedin the data. Disappointingly, no climate variable significantly (practically or statistically) improved the model residual error of Eq. (2). To examine this result more critically, a heightage equation was constructed. A model, of the form:
G=exp(log(G,)(T,/T)P+(a+
13s)
x (1 - wT)P))
(5)
and G = exp(log(G,)(T,/T)(P’V’og(N”o))
+ ( CY+ 6s)
~(1 _ (T,,T)(B+?l”g(H/lo))))
(6)
H=exp(cu+$.mg+v.ehs+0.hfg+P/fi) (3) Eq. (3), where mg = 1, if associatedwith Moutere gravels, else= 0; ehs= 1, if associatedwith Eastern hill soils, else= 0; hfg = 1, if associatedwith HFG, else= 0; fitted the data well, but adding environmental variables to model (3) did not improve precision at all. The modelling of net basal area ha-’ began with the construction of a yield-age model, the residuals of which showed strong correlations with both climatic and soil type variables. Projection equationsof
Table 4 Behaviour
of residuals
Soil
Average
where, in Eq. (5) and Eq. (6), S = stand site index (m) and N = initial stems ha-‘. Models (5) and especially (6) clearly improved the goodness-of-fit and decreasedbias in prediction, without fully resolving the problem for some soil types. Altitude was examined as another adjunct variable, but with no success. Climatic variables were introduced into analyses by augmenting them to model (6), but initially using separateequations for each soil type. From these it was clear that temperaturewas an ineffective covariate in associationwith any soil type, but rainfall and
with model and soil type residual
Standard
deviation
of residuals
Skewness
of residuals
(4)
(6)
(7)
(4)
(6)
(7)
(4)
(6)
(7)
EHS HFG MC MG
0.40 -0.20 -0.64 0.08
0.23 - 0.09 0.56 0.07
0 0 -0.11 0.07
1.59 1.33 0.99 1.27
1.51 1.25 0.9 1 1.23
1.46 1.22 0.92 1.21
0.48 0.94 -0.76 0
0.59 - 0.90 - 0.63 0.21
0.24 -0.87 -0.21 0.13
The numbers
in parenthesis
refer to the models
defined
above.
213-
R.C. Woollons
et al. / Forest Bcologv
solar radiation did contribute significantly to better precision, although differing in formulation, depending on soil type. The exception was Mapua clays. which failed to show any evidence of growth and climatic relations. After much modelling, a pooled model was derived: G = exp(log(G,)(T,/T)‘B”ll”“‘N”“” + a”(,
_ (T,,T)‘B+?lop(N/Il)))
and LY* =(cu+6.mg.log(rain)+e.ehs.log(rain) + 4 . hfg . solar)
(7)
where in Eq. (7) rain = annual total rainfall Cm); solar = average solar radiation (MJ m-l dd ‘) ‘. The estimated parameter values were: (~==4.6405@=0.61396=0.4714~=0.6904 q=O.1421
qb=O.O069
Model (7) includes three dummy variables representing three distinct edaphic types. which in turn are coupled with rainfall and solar radiation variables. Set simultaneously to zero, the model collapsesto a predictor of basal area ha-’ for the Mapua clays. The site index term in model (6) became redundant with the introduction of the soil and climate variables, and so was discarded. Latitude and longitude (of each plot) were tested as possiblerefinements of the dummy variables, but no gain was achieved. To utilise model (7) annually, it is necessary to have a prediction of live stems ha ’ Mortality is very light in the region, with thinned standsexhibiting virtually zero death. A predictor of stemsha-’ survival is available through a model of form. N = 529 + (N, - 529)exp( p(T2 - rf))
where ( N, > 529)
(8)
else N = N, where (N, < 5291 where in Eq. (8) N, , N = live stemsha ’ at agesT, and T. The data for model (8) were obtained from the permanent sampleplots summarisedin Table 3.
--i---NB:
rainfall
values were resealed
to metres
rind Management
98 f 1997) 267-275
The residual sum-of-squares for the respective models are: (4) (5) (6)
(7)
Basic Schumachermodel (Eq. (4)) Addition of site index Addition of site index/stand stocking Addition of soil and climate variables
1828 1718 1614
1484
Thus, from the basic model (4) the successive introduction of site index. stocking, edaphic and weather variables has increased precision by almost 19R, but a fairer evaluation of model (7) is the difference between models(6) and (7). namely 9.6%. since model (6) represents the best model found basedon empirical variables alone. Table 4 gives the mean, standard deviation and skewnessof residualsresultant from models (4). (6) and (7), for each soil type. Table 4 shows that while the best empirical model (6) reduces overall variation by somt: 10%. it remains a somewhat biased predictor for the Eastern hill soils and Mapua clays. Model (7). with the inclusion of the soil and climate variables, is considerably less biased for all four soil types. and has better precision.
4. Discussion and conclusions The discriminant analysis is notable for the extent by which the data are successfully separated into their correct groupings, and serves to emphasisethat the soil zones are very different. Examination of the derived coefficients for model (7) show several logical or expected outcomes. All the values-are positive (note. however, that this will only occur if the NLapua Clays is chosenasthe intercept soil zone); in the caseof the coefficient with the logarithmic stocking variable, the effect is to give lesser(disproportionate) growth with very low densities.This is in agreement with Whyte and Woollons, 1990 and Woollons et al.. 1994, who both reported lesser basal area ha ~’ growth in heavily thinned P. rudiata stands. In general, the model reasonabIy predicts greater basal area production with higher rainfall, but both terms are upper-boundedby logarithmic terms. It is conjectured that the preference for solar radiation with HFG might reflect a fully adequate rainfall in this area. Growth on the Mapua clays is nor modelled by
R.C. Woollons
et al. / Forest Eco1og.v and Management
climatic variables very probably because they are virtual constants for this soil type; in any event, production here is limited by predominantly nutritional factors (Balneaves et al., 1991). The limitations of the climatic variables (in particular, temperature) to substantially contribute to growth prediction in this study should be interpreted very carefully. Projection equations of form (1) or specifically, Eq. (7) are not likely to show much association because of their structure. These models always include an input yield term, Y, in Eq. (1) or G, in Eq. (7) as an explanatory variable that must account for considerable climatic and local variation. Essentially forms (I) or (7) are yield prediction equations, but assuming the a priori existence of initial yield estimates at known (early) ages. In a sense, they are inefficient models to demonstrate basic relationships between climate and growth; conversely, they are utterly essential equations in empirical growth systems. Our overriding objective in this study was to ascertain whether projection equations can be improved in their predictive power by inclusion of climatic variables. In no way, however, do our results infer, for example, that temperature does not influence stand growth. In nationwide surveys, annual rainfall has been found to contribute to the prediction of site index in New Zealand (Jackson and Gifford, 1974; Hunter and Gibson, 1984, and elsewhere (Czamowski et al., 1967; Czamowski et al., 1976). Environmental variables from the Nelson region fail to contribute to the height projection equation or not even to a height yield model. This would suggest that height development within the Nelson region is governed by soil type (perhaps nutritional in origin), recognised implicitly in model (2) by the initial height term. There is a growing recognition in New Zealand of the usefulness of soil information for guiding plantation management and research. Several forestry agencies are developing site-specific management regimes for plantation establishment, fertiliser application and harvesting based on soil, physical and chemical characteristics (Turvey and Lieshout, 1983; Knott and Ryan, 1990). Our results are in accord with this practice and parallel the results obtained by Turvey. 1983. Usage of the model in a growth and yield system poses no special problems, although users need to be
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careful to use input predictors strictly within observed ranges for any soil type. In practice, it is efficient if latitude, longitude, average altitude, aspect and slope of stands are a priori translated into rainfall and solar estimates, then these can be summarised in a file, so that any number of simulations can be run at will. There are several limitations of the proposed methodology. In this study, we deliberately chose a forest area with a big altitude range, and known to have appreciable differences in rainfall and temperature. Clearly, these characteristics are atypical of many other forests. Moreover, the success of methods described here must depend to a degree on the existence of frequent, long-running and reliable weather stations in forest regions; unfortunately, not many afforested areas have these. Although the climatic surfaces are logically and sensibly constructed, additional errors are introduced by the fitting process, particularly when they are interrogated to within very short distances, for example, sometimes to less than 1 km. Notwithstanding these reservations, we believe we have achieved enough results in this study to encourage others to conduct similar investigations. A sensitivity analysis of model (7) suggests that the model can predict at age 30, around + 1-2 m’ ha- ’ in basal area than otherwise would be the case, which loosely equates to f 15-25 m3 ha-’ in volume production. For clear-fell scheduling purposes, this represents a useful increase in precision. Clearly, we have not considered many other possibilities. Climatic variables including evaporation in conjunction with rainfall may give better definition, especially in drier regions. Alternatively, more refined expressions of the environment (for example, total rainfall during the summer months, or maximum/minimum temperatures) may prove to be superior adjunct explanatory variables. There also exist many alternative ways of modelling process and climate variables in growth and yield systems, especially with diameter distribution and individual tree models (Munro, 1974). Over the last 15 years, mechanistic and management growth modellers around the world have tended to work independently of each other. Results presented here suggest that there is much to gain with collaborative research. with a view to create ‘hybrid’
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growth models, containing elements of both approaches. Historically, there seems to be some confusion as to the role and objectives of the two approaches. Landsberg, 1986 saw conventional forestry models as ‘scarcely qualify(ing) as models; they are not hypotheses but descriptions of observations’. This is unfortunate, because it infers process modelling alone is worth pursuing, and overlooks that mechanistic growth models have never remotely achieved the predictive ability (in volume or tonnes ha-’ of wood) of empirical models as conceded by Landsberg, 1986 and upheld by all of Vanclay, 1994, Goulding, 1994, and Shvets and Zeide, 1996. A very balanced review of the respective strengths of process and empirical modelling is given by Mohren and Burkhart, 1994.
References Bailey, R.L., Ware, K.D., 1983. Compatible basal area growth and yield model for thinned and unthinned stands. Can. J. For. Res. 13, 563-571. Balneaves, J.M., Skinner, M.F., Lowe, A.T.. 199t. Improving the reestablishment of radiata pine on impoverished soils in Nelson. New Zealand. In: Dyck, W.J., Mees. C.A. (Eds.), Longterm field trials to assess environmental impacts of harvesting. Proc. IEA/BE T6/A6 Workshop, FL, USA. IEA/BE T6/Ah No. 5. Forest Res. Inst., Rotorua. New Zealand, FRI Bull. No. 161, pp. 137-150. Borders, B.E., 1989. Systems of equations in forest stand modelling. For. Sci. 35, 548-556. Candy, S.G., 1989. Growth and yield models for Pinus radiuta in Tasmania. N.Z.J. For. Sci. 19, 112-133. Chittenden, E.T., Hodgson, L., Dodson, K.J., 1966. Soils and agriculture of Waimea county of New Zealand. Soil Bur. Bull. No. 30, N.Z. Dept. of Sci. and Ind. Res. Clutter, J,L., 1963. Compatible growth and yield models for loblolly pine. For. Sci. 9, 354-37 1. Clutter, J.L., Jones, E.P.. 1980. Prediction of growth after thinning in old-field slash pine plantations. USDA For. Serv. Res. Paper SE-2 17. Clutter, J.L., Fortson, J.C., Pienaar, L.V., Brister, G.H., Bailey, R.L., 1983. Timber Management: a quantitative approach. Wiley, USA. Czamowski, M.S., Humpherys, F.R., Gentle, S.W.. 1967. Site-index as a function of soil and climatic characteristics. A preliminary note based on man-made stands of Pinus radiutu in New South Wales, Australia. FAO World Symp. on Manmade Forests and their Industrial Importance, Canberra, April 1967. Vol. 2, 965-979. Czamowski, M.S., Humpherys, F.R., Gentle, S.W.; 1976. Quantitative expressions of productivity in Monterey pine plantations
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in Australia and New Zealand in terms of lome soil and climate characteristics. IUFRO, Section 21 Research on site factors. XV IUFRO Congress. Gainsville, Florida. March I971. 190-199. Ferguson. 1,s.. Leech. J.W.. 1978. Generalised least squares e& mation of yield functions. For. Sci. 24, 27.-47. Garcia, 0.. 1984. New class of growth models for even-aged stands: Pbzus rcrdiatu in Golden Downs forest. N.Z.J. For. Sci. 14. 65-86. Goulding, C.J., 1994. Development of growth models for &IC.\ radiuta in New Zealand-experience with management and process models. For. Ecol. and Manage. 69, 33 l-343. Grace. J.C.. 1990. Process models for investigating alternative spacing patterns. In: James, R.N., Tarlton. G.L. (Eds.), Prw. IUFRO Symp. New approaches to spacing and thinning in plantation forestry. April 1989. Rotorua. N.Z. Ministry oi Forestry, FRI, Bull. 15 1, 267-27 1. Hunter, I.R.. Gibson. A.R.. 1984. Predicting Pinup radiutu site index from environmental variables. N.Z.J. For Sci. 14, .53--64. Hutchinson, M.F.. 1984. A summary of some surface fitting and contouring programs for noisy data. Consulting Repour No. ACT 84/6 Div. Math. and Stats. and Div. of Water and Land Rea. CSIRO, Canberra, Australia. Jackson, D.S.. Gifford, H.H., 1974. Environmenrdl variables ml’luencing the increment of radiata pine (1) periodic volume increment. N.Z.J. For. Sci. 4, 3-26. Kaufmann, M.R., Landsberg, J.J. (Eds.). 1991. Advancing towards closed models of forest ecosystems. Tree Physiol.. 9, l-324. Knott. J.. Ryan, P.J.. 1990. Development and practical applicahon of a soils database for the Pinus plantation of the Bathurbt Region. For. Comm. NSW Res. Pap. 1 I. Landsberg, J.J., 1986. Physiological Ecology of Forest production. Academic Press. London. Lawrence, P.R., 1976. Stand density index tables for Ph.r KU/~utu. Tasmanian Forestry Commission. Maclaren, J.P.. Grace. J.C., Kimberley. M.O., Knowles, R.L., West. G.G.. 199.5. Height growth of Pinus wdktu as affected by stocking. N.Z.J. For. Sci. 25, 73-90. Makela, A., Hari. P., 1986. Stand growth model based on carbon uptake and allocation in individual trees. Ecnl. Model. ;3. 204-229. McMurtrie, R.E.. Rook, D.A., Kelliher. FM., 1990. Modelling the yield of Pinus radioto on a site limited by water and nitrogen. For. Ecol. and Manage. 30, 381.-413. Mitchell, N.D., 1991. The derivation of climate burtaces for New Zealand, and their application to the bioclimatic analysis of the distribution of kauri (Agathis uustrah). J. Royal Sot. N.Z. 31. 13-24. Mohren, G.M.J., Burkhart. HE. 1994. Contrasts between blologitally based and management-oriented growth and yield models. For. Ecol. and Manage. 69, l-5. Munro, D.D., 1974. Forest growth models- a prognosis. ln: Fries, J. (Ed.). Growth models for tree and stand simulation. Royal College of Forestry Stockholm. Sweden, 7-71. Murphy, P.A., 1983. A nonlinear timber yield equation system for loblolly pine. For. Sci. 29, 582-591.
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et al./Forest
Ecology
Murphy, P.A., Farrar, R.M. Jr.. 1988. Basal area projection equations for thinned natural even-aged forest stands. Can. J. For. Res. 18, 827-832. Nautiyal, J.C., Couto, L.. 1984. The nature and uses of the timber production function: Eucalyptus grandis in Brazil. For. Sci. 30, 761-773. Nix, H.A., 1986. A biogeographic analysis of Australian Elapid snakes. In: Longmore, R. (Ed.), Atlas of Elapid snakes of Australia. Amt. Govt. Publishing Serv., Canberra. Australia. Pienaar, L.V., Turnbull, K.J., 1973. The Chapman-Richards generalisation of Von Bertalanffy’s growth model for basal area growth and yield in even aged stands. For. Sci. 19, 2-20. Pienaar, L.V., Shiver, B.D.. 1986. Basal area prediction and projection equations for pine plantations. For. Sci. 32. 626633. Schumacher. F.X., 1939. A new growth curve and its application to timber yield studies. J. For. 37, 819-820. Shvets, V., Zeide, B., 1996. Investigating parameters of growth equations. Can. J. for Res. 26, 1980-1990. Snowdon, P., Waring, H.D., 1991. Effects of irrigation and artificial drought on the growth and health of Pinus radiata near Canberra. A.C.T. Aust. For. 54, 174-186. Sullivan, A.D., Clutter, J.L.. 1972. A simultaneous growth and yield model for loblolly pine. For. Sci. 18, 76-86. Turvey, N.D., 1983. Soil-type yield curves for Pinus radiata in Gippsland. Victoria. Aust. For. 46, 118-125. Turvey, N.D., Lieshout, H., 1983. Some uses of soil survey information for improved management of planted forests in southeastern Australia, USDA For. Serv., Tech. Rep. PNW163,46-52. Turvey. N.D., Booth, T.H., Ryan, P.J., 1990. A soil technical classification system for Pinus radiata (D. Don) plantations. II. A basis for estimation of crop yield. Aust. J. Soil Res. 6. 8 13-824.
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Vanclay, J.K., 1994. Modelling forest growth and yield: applications to mixed tropical forests. CAB International, UK. 312 PP. Wahba, Cl., Wendelberger, J.. 1980. Some new mathematical methods for variational objective analysis using splines and cross validation. Monthly Weather Rev. 108, 1122- 1143. West, P.W., Ratkowsky. D.A., Davis, A.W., 1984. Problems of hypothesis testing of regressions with multiple measurements from individual sampling units. For. Ecol. Manage. 7, 207224. Whyte, A.G.D., Woollons, R.C., 1990. Modelling stand growth of radiata pine thinned to varying densities. Can. J. For. Res. 20, 1069-1976. Wickramsinghe, A., 1988. Modelling tree growth potential based on effective evapotranspiration. For. Sci. 34, 864-881. Woollons. R.C.. Whyte, A.G.D., Xu, L., 1990. The Hossfeld function: an alternative model for depicting growth and yield. Jap. J. For. 15, 25-35. Woollons, R.C., Hayward, W.J., 1985. Revision of a growth and yield model for Radiata pine in New Zealand. For. Ecol. and Manage. 11, 19 l-202. Woollons, R.C., Wood, G.R., 1992. Utility and performance of five sigmoid yield-age functions, fitted to stand growth data. In: Wood, G.B.. Turner, B.J. (Ed%). Integrating forest information over space and time. IUFRO Conf. 13-17 Jan. ANU., Canberra, Australia. Woollons, R.C.. Smale, P.J., Du Burgess, F.F., 1994. Analytical methods to aid interpretation of thinning experiments, N.Z.J. For. Sci. 24, 18-24. Yang, R.L., Kosak. A., Smith. H.J.G., 1978. The potential of Weibull-type functions as flexible growth functions. Can. J. For. Res. 8. 424-431.
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Augmenting empirical stand projection equations with edaphic and climatic variables R.C. Woollons a3*, P. Snowdon b, N.D. Mitchell ’ a School of Forestry. University of Canterbuy, Primzte Bag, Christchurch. New Zealand b CSIRO Forestr?; and Forest Products. PO Box E4008. Kingston ACT 2604, Canberra, Austmlia ’ Deportment of Botany, Univer.~i@ of Auckland, Auckland, New Zealand Accepted
26 March
1997
Abstract Builders of management growth and yield models have shown ingenuity in supplying projection equations with additional variables (for example, site index, time and amount of thinning) to enhance the quality of predictions. Other variables, edaphic or mechanistic in origin, have not been utilised because of difficulties in obtaining precise area1estimates at an affordable cost. Environmental (for example, rainfall, solar radiation) data have become available through response surface splining algorithms using data from weather station networks; long-term climate averages are available at any chosen location. This paper describes the building of mean-top-height and basal area ha-’ projection equations, utiiising climate variables in conjunction with traditional plot measures. The data were secured from the Nelson region of New Zealand, where stands of Pinus rudiatu are established on four contrasting soil groupings. No improvement in precision was found for the prediction of mean-top-height, by including temperature, solar radiation, or rainfall data, nor by recognising the diverse soils. Conversely, an improvement of 10% was obtained in modelling basal area ha-‘. Radiation and rainfall (but not temperature) significantly improved precision and accuracy, varying in functional form by soil type. The individual effects of soil-type and climate are heavily confounded. It is argued that forest process and empirical-based modelling has been independently researched for too long. There is evidence enough to suggest that hybrid modelling, encompassing both approaches, could improve the predictive ability of current growth prediction systems. 0 1997 Elsevier Science B.V. Keywords:
Growth
and yield modelling:
Difference
equations;
Weather
1. Introduction It is over 30 years since Clutter, 1963 produced his landmark paper on the principles of empirical stand growth modelling and the desirability of producing consistent, path-invariant growth equations which also possess a logical compatibility between growth and yield. From these considerations, a * Corresponding
author.
0378-I 127/97/$17.00 0 1997 Ekevier PII SO378-1 127(97)00090-X
Science
B.V. All rights reserved.
and soil variables
plethora of contributions to the growth modelling literature have emerged, many of which are the genesis of numerous growth and yield prediction systems. Many studies have been specifically concerned with improving the predictive power and precision of growth model equations. These have included (a) alternative estimation procedures to ordinary least squares, recognising the autocorrelative nature of permanent sample plot data (see, for example, Sullivan and Clutter, 1972; Ferguson and Leech.
1978; West et al.. 1984; Borders, 19891; (b) alternative sigmoidal functions (the original model of Clutter, 1963 was founded on the log-reciprocal Schumacher, 1939 model, but other formulations have been suggested (for example, the Chapman-Richards, Pienaar and Turnbull, 1973; the Weibull, Yang et al.. 1978, or the Hossfeld, Woollons et al., 1990)); and (cl variants of historical models; (see. for example, Clutter and Jones, 1980, who added a power term to the age variable of the basic Schumacher yield equation. or Murphy, 1983, where an inverse age term was included in the Chapman-Richard’s growth equation). In most of these models, the response variable. perhaps basal area ha-’ or mean-top-height, are formulated in projection or difference form (Clutter et al.. 1983). where the inputs are normally limited to an initial response variable value at a given (initial) age. That is: Y =.f’( T.T, .Y, )
(1)
where in Eq. (1) Y, Y, = response variable yields at ages T, T,, respectively. Increasingly, however, modellers have incorporated additional inputs in their difference equations. For example, the original Clutter, 1963 basal area equation contained a site index term, as did Sullivan and Clutter, 1972, Garcia, 1984, and Bailey and Ware, 1983. Candy, 1989 utilised all of site index. a stand density index (Lawrence, 1976). and a stand pruning ratio in a Pinus radiata basal area model. Woollons and Hayward, 1985 added an altitude term to a mean top height equation, while several authors have incorporated time and amount of thinnings as adjunct variables (see, for example, Pienaar and Shiver, 1986, Bailey and Ware, 1983, or Murphy and Farrar. 19881. In the cases above, modellers were keen to in crease the precision and predictive power of their models by utilising adjunct variables in addition to initial state inputs. It is well recognised, of course. that many other factors, edaphic, climatic, physical or physiological in origin, also contribute to stand growth. While some of these factors have been included in models of site index or productivity (Czamowski et al., 1976; Jacksonand Gifford, 1974: Hunter and Gibson, 1984; Turvey et al., 19901,they have been generally excluded from empirical sys-
terns of growth and yield. While there are some exceptions (for example, Turvey, 1983, who derived yield curves for different soil types). it was, and in some cases still is, almost impossible to measure many of these factors in a forest with an intensity sufficient for them to be included with permanent sampleplot data used to construct growth and yield models. There i$ considerable temporal and spatial variation to overcome, as well as cost constraints. These considerations, however. certainly have not prevented the building of many growth modelsbased on physiological and soil processes,and driveri by the input of environmental variables (see. for example, McMurtrie et al.. 1990, Makela and Hari, 1986. or Grace, 1990). Although originally intended as researchtools to help understandthe mechanismsOI‘ tree and stand growth. this has not deterred some scientists from considering them as managementdecision-making tools (for example. Kaut‘mann and Landsberg, I99 I 1. In practical terms. landscapescale process-based models of plantation productivity tend to have insul‘ficient spatial resolution for the 5- 100 ha stand units used by plantation managers,while detailed tree or stand based models tend to be too site-specific for generaluse. While theseproblemswith process-based models may be addressedin the future. there arc good prospectsfor utilisation of hybrid models.These aim to improve traditional forestry growth models basedon age, stand conditions and simple measures of site quality by including additional explanatory variables, such as growth indices derived from pro cess-basedmodels (for example. photosynthesis! or simple climatic indices such as annual rainfall. This approach has proved useful for describing annual differences in plantation growth due to year-to--yea1 differences in climatic factors (Nautiyal and C‘OLlt(J. 1984. Wickramsinghe. 1988. Snowdon and Waring, 19911 hut there have been no attempts to include such variables into projection models of type t I !. which form the heart of most empirical growth and yield systems(see, for example, Wooltons and Hayward. 1985; Candy, 1989). In New Zealand (and elsewhere). it has become possible to consider using climatic data as adjunct input variables in growth model equations. through the availability of excellent long-term a\ erapc weather statistics. obtained from an intensive grid of
R.C. Woollons
et al. / Forest Ecology
weather stations. The details are expanded below, but in essence, mean annual temperature, mean annual solar radiation and total annual rainfall (among other statistics) can be estimated for any permanent sample or inventory plot location, and so can be utilised together with stand and tree data. In this contribution, we report the building of mean-topheight and basal area ha-’ projection equations from one database. The results and ramifications of constructing these equations are discussed, and the potential of using these models for forest predictions is reviewed.
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269
Table 2 Correlations between each soil type
weather,
site index and location
Variable
R
T
SR
R
T
Altitude Latitude Longitude Site index
EHS 0.10 - 0.76 0.83 - 0.14
-0.98 - 0.40 0.35 0.26
-0.01 0.00 -0.12 0.23
HFG 0.40 -0.50 0.47 -0.21
-0.98 0.67 -0.04 -0.15
0.19 0.04 0.26 0.65
Altitude Latitude Longitude Site index
MC 0.3 1 - 0.71 - 0.95 -0.17
- 0.79 0.32 0.68 -0.07
- 0.35 0.11 0.44 -0.02
MG 0.58 - 0.25 -0.64 0.00
-0.92 - 0.33 0.36 -0.07
-0.09 0.14 -0.03 -0.02
T = mean annual
variables
for
SR
2. Method
R = mean annual (total) rainfall: SR = mean annual solar radiation.
temperature;
The climatic data used in this study were prepared as follows. For any sample plot measures at a given location, solar radiation (MJ me2 dd ‘), annual rainfall (mm) and mean temperature (“Cl values were estimated, after supplying latitude and longitude, altitude, aspect and slope of the plot. A full discussion is given by Mitchell, 1991. The basic climate data were acquired from the New Zealand network of recording stations. The modelling procedure makes use of algorithms developed by Hutchinson, 1984, in which Laplacian smoothing splines are used to derive mathematical surfaces (Wahba and Wendelberger, 1980). Four categories of climate data are utilised; solar radiation, rainfall, minimum and maximum temperature. For each, separate monthly surfaces were constructed. The surfaces are then interrogated by the program BIOCLIM, (Nix, 1986) to estimate monthly values of each variable at each location. These monthly figures are then summarised to give annual statistics. Estimated standard errors
for these calculations are given in the appendix of Mitchell, 199 1. The chosen study area is at Nelson, in the top northwest of the South Island of New Zealand, where CHH (Carter Holt Harvey) own or manage 3407 1 hectares of P. rudiatu plantations. The forest is tightly located on four contiguous but distinct soil types, colloquially referred to as the (1) Eastern hill soils (EHS), (2) High fertility granites (HFG), (3) Mapua clays (MC) and (4) Moutere gravels (MG), which represent 13 019, 3886, 4296, and 12 870 ha, respectively, of the total resource. Details of these soil types are given by Chittenden et al., 1966. A total of 205 permanent sample plots are available for analyses. Table 1 summarises climatic and other data, while Table 2 gives the correlation matrices between location and weather variables, for each soil type. From these, it is clear that the effects of soil and climate are quite strongly related and thus
Table 1 Weather data for each soil type Soil type
Average
EHS HFG MC MG
27.7 29.5 27.5 29.1
Figures
in brackets
site index
(19) (11) (19) (15) are coefficients
Average 345 348 83 264
altitude
(36) (34) (25) (27)
of variation
Average 10.9 10.8 12.4 11.3
(‘%)
(6) (6) (1) 4)
temperature
Total annual rainfall
Average
1458 (8) 1753 (6) 1154(8) 1286 (7)
11.5 11.1 12.6 12.1
(12) (11) (5) (11)
solar radiation
270
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98 f 1997)
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cant ( 17< 0.0001). The discriminant functions correctly classified 66% of EHS, 97% of HFG. 95% of MC, and 73% of MG zones. in total 162 of the 205 data points. The first two mean canonical scores together with a 99.9% confidence region of each soil type are plotted in Fig. I; the independence of the four soil types is clearly portrayed. The first two standardised canonical variates are given by-: z, = 0.58
dba
6 First Canonical
Fig. I. 99.9% confidence regions the first two canonical variates.
in terms
Z’ = --0.66
of
X
X
X
S + 0.93
X
rain - 0.08
temp
ah -- 0.13 X S + 0.52 i’ rain + 0.21
.X solar-t 0.38 X temp. The first is obviously dominated by the effect of rainfall, while the secondvariate probably represents an interaction between altitude and rainfall. Table 3 summarisesthe extent of the mensuration data for each of the soil types. Several modelling principles were followed when building the projection equations. Basic sigmoid functions considered were those discussedby WoolIons and Wood, 1992. namely the Schumacher, Weibull, Gompertz, Chapman-Richards, and Wossfeld equations. In all cases,goodness-of-fit was assessedby lesser mean square values and rigorous inspection of residual plottings by soil type.
partially confounded. For example, the Mapua clays are characterised by low altitudes and corresponding high temperature and radiation but low rainfall; the HFG are conspicuous for high altitude and rainfall. but lower temperature and radiation. Conversely, Table 1 emphasises that the range of climatic data within soil zones is relatively low, especially so for the Mapua clays. In general, stands established on the latter soil have lesser wood production than those on the other three soil types, but overall the area is fertile, with site indices (mean-top-height at age 20, where mean-top-height is defined as the average of stem height of the top 100 stems ha-‘, by diameter breast height (dbh)) generally around 27-29 m. A preliminary discriminant analysis was assayed between the four soil types and the variables, annual total rainfall, average solar radiation, mean temperature, site index and plot altitude. The first two canonical variates accounted for 94.6% of the variation, but all three variates (available) were highly signifi-
Table 3 Basic mensuration
alt + 0.04
X solar + 0.41
Variate
of the four soil types
X
3. Results For mean-top-height, it became quickly apparent that a polymorphic form was appropriate, but three sigmoid formulations -the Hossfetil Schumacher, and Weibull (Woollons and Wood, 1992) - gave
data
Soil
Plot
Meas
Age
EHS HFG MC MG
57 34 38 74
336 206 230 397
13.3 10.7 12.5 12.5
(2-28) (3-26) (3-27) (3-27)
G ha-’
MTH
N
27.6 28.3 ‘2.4 3 I .2
18.2 (2-38) 16.4 (2-38) 18.5 C-40) 18.4(3-41)
544 749 562 760
(I -85) (I -84) (I-77) (2-94)
Plot = number of plots: Meas = number of measures: C ha- ’ = mean net basal area ha- ’ Cm’): stocking (stems ha-’ ). The figures in parentheses gives the minimum and maximum values.
MTH
(156-1720) (150-1733) (150-1604) ~450-1916)
= mean top height (m);
N = mean
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271
very good and virtually equivalent results. Finally, the Weibull-type projection equation:
form (1) for each soil type were then formed. It soon becameapparent that the Schumacherformulation:
H=~-~((~-w/~)”
G= w[lodG,W’,/T)P
+ ~(1 - (WY’)]
and
(4)
o= (T/T,y
Eq. (4), where G,, G = initial and future basal area ha-’ at ages T,, T, was easily the best equation for all four soil types, but the Mapua clays and HFG were not especially well modelled, partially due to relative lack of data. Accordingly, a pooled model was constructed that produced a plausible model, but it contained evidence of predictive bias (see Table 4). Further modelling with empirical variables gave two more equations:
(2)
where, in Eq. (2), H, H, = meantop height at agesT, T, was adopted, giving an excellent fit, unbiasedover all four soil types. Attempts were made to include stocking in the formulation; in New Zealand, evidence has emergedthat thinning to low densitiescan induce sharp reductions in P. radiata height growth (Woollons et al., 1994; Maclaren et al., 1995); but for these data, there were only weak signsof significance. This is logical enough, since heavily thinned plots are not strongly representedin the data. Disappointingly, no climate variable significantly (practically or statistically) improved the model residual error of Eq. (2). To examine this result more critically, a heightage equation was constructed. A model, of the form:
G=exp(log(G,)(T,/T)P+(a+
13s)
x (1 - wT)P))
(5)
and G = exp(log(G,)(T,/T)(P’V’og(N”o))
+ ( CY+ 6s)
~(1 _ (T,,T)(B+?l”g(H/lo))))
(6)
H=exp(cu+$.mg+v.ehs+0.hfg+P/fi) (3) Eq. (3), where mg = 1, if associatedwith Moutere gravels, else= 0; ehs= 1, if associatedwith Eastern hill soils, else= 0; hfg = 1, if associatedwith HFG, else= 0; fitted the data well, but adding environmental variables to model (3) did not improve precision at all. The modelling of net basal area ha-’ began with the construction of a yield-age model, the residuals of which showed strong correlations with both climatic and soil type variables. Projection equationsof
Table 4 Behaviour
of residuals
Soil
Average
where, in Eq. (5) and Eq. (6), S = stand site index (m) and N = initial stems ha-‘. Models (5) and especially (6) clearly improved the goodness-of-fit and decreasedbias in prediction, without fully resolving the problem for some soil types. Altitude was examined as another adjunct variable, but with no success. Climatic variables were introduced into analyses by augmenting them to model (6), but initially using separateequations for each soil type. From these it was clear that temperaturewas an ineffective covariate in associationwith any soil type, but rainfall and
with model and soil type residual
Standard
deviation
of residuals
Skewness
of residuals
(4)
(6)
(7)
(4)
(6)
(7)
(4)
(6)
(7)
EHS HFG MC MG
0.40 -0.20 -0.64 0.08
0.23 - 0.09 0.56 0.07
0 0 -0.11 0.07
1.59 1.33 0.99 1.27
1.51 1.25 0.9 1 1.23
1.46 1.22 0.92 1.21
0.48 0.94 -0.76 0
0.59 - 0.90 - 0.63 0.21
0.24 -0.87 -0.21 0.13
The numbers
in parenthesis
refer to the models
defined
above.
213-
R.C. Woollons
et al. / Forest Bcologv
solar radiation did contribute significantly to better precision, although differing in formulation, depending on soil type. The exception was Mapua clays. which failed to show any evidence of growth and climatic relations. After much modelling, a pooled model was derived: G = exp(log(G,)(T,/T)‘B”ll”“‘N”“” + a”(,
_ (T,,T)‘B+?lop(N/Il)))
and LY* =(cu+6.mg.log(rain)+e.ehs.log(rain) + 4 . hfg . solar)
(7)
where in Eq. (7) rain = annual total rainfall Cm); solar = average solar radiation (MJ m-l dd ‘) ‘. The estimated parameter values were: (~==4.6405@=0.61396=0.4714~=0.6904 q=O.1421
qb=O.O069
Model (7) includes three dummy variables representing three distinct edaphic types. which in turn are coupled with rainfall and solar radiation variables. Set simultaneously to zero, the model collapsesto a predictor of basal area ha-’ for the Mapua clays. The site index term in model (6) became redundant with the introduction of the soil and climate variables, and so was discarded. Latitude and longitude (of each plot) were tested as possiblerefinements of the dummy variables, but no gain was achieved. To utilise model (7) annually, it is necessary to have a prediction of live stems ha ’ Mortality is very light in the region, with thinned standsexhibiting virtually zero death. A predictor of stemsha-’ survival is available through a model of form. N = 529 + (N, - 529)exp( p(T2 - rf))
where ( N, > 529)
(8)
else N = N, where (N, < 5291 where in Eq. (8) N, , N = live stemsha ’ at agesT, and T. The data for model (8) were obtained from the permanent sampleplots summarisedin Table 3.
--i---NB:
rainfall
values were resealed
to metres
rind Management
98 f 1997) 267-275
The residual sum-of-squares for the respective models are: (4) (5) (6)
(7)
Basic Schumachermodel (Eq. (4)) Addition of site index Addition of site index/stand stocking Addition of soil and climate variables
1828 1718 1614
1484
Thus, from the basic model (4) the successive introduction of site index. stocking, edaphic and weather variables has increased precision by almost 19R, but a fairer evaluation of model (7) is the difference between models(6) and (7). namely 9.6%. since model (6) represents the best model found basedon empirical variables alone. Table 4 gives the mean, standard deviation and skewnessof residualsresultant from models (4). (6) and (7), for each soil type. Table 4 shows that while the best empirical model (6) reduces overall variation by somt: 10%. it remains a somewhat biased predictor for the Eastern hill soils and Mapua clays. Model (7). with the inclusion of the soil and climate variables, is considerably less biased for all four soil types. and has better precision.
4. Discussion and conclusions The discriminant analysis is notable for the extent by which the data are successfully separated into their correct groupings, and serves to emphasisethat the soil zones are very different. Examination of the derived coefficients for model (7) show several logical or expected outcomes. All the values-are positive (note. however, that this will only occur if the NLapua Clays is chosenasthe intercept soil zone); in the caseof the coefficient with the logarithmic stocking variable, the effect is to give lesser(disproportionate) growth with very low densities.This is in agreement with Whyte and Woollons, 1990 and Woollons et al.. 1994, who both reported lesser basal area ha ~’ growth in heavily thinned P. rudiata stands. In general, the model reasonabIy predicts greater basal area production with higher rainfall, but both terms are upper-boundedby logarithmic terms. It is conjectured that the preference for solar radiation with HFG might reflect a fully adequate rainfall in this area. Growth on the Mapua clays is nor modelled by
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climatic variables very probably because they are virtual constants for this soil type; in any event, production here is limited by predominantly nutritional factors (Balneaves et al., 1991). The limitations of the climatic variables (in particular, temperature) to substantially contribute to growth prediction in this study should be interpreted very carefully. Projection equations of form (1) or specifically, Eq. (7) are not likely to show much association because of their structure. These models always include an input yield term, Y, in Eq. (1) or G, in Eq. (7) as an explanatory variable that must account for considerable climatic and local variation. Essentially forms (I) or (7) are yield prediction equations, but assuming the a priori existence of initial yield estimates at known (early) ages. In a sense, they are inefficient models to demonstrate basic relationships between climate and growth; conversely, they are utterly essential equations in empirical growth systems. Our overriding objective in this study was to ascertain whether projection equations can be improved in their predictive power by inclusion of climatic variables. In no way, however, do our results infer, for example, that temperature does not influence stand growth. In nationwide surveys, annual rainfall has been found to contribute to the prediction of site index in New Zealand (Jackson and Gifford, 1974; Hunter and Gibson, 1984, and elsewhere (Czamowski et al., 1967; Czamowski et al., 1976). Environmental variables from the Nelson region fail to contribute to the height projection equation or not even to a height yield model. This would suggest that height development within the Nelson region is governed by soil type (perhaps nutritional in origin), recognised implicitly in model (2) by the initial height term. There is a growing recognition in New Zealand of the usefulness of soil information for guiding plantation management and research. Several forestry agencies are developing site-specific management regimes for plantation establishment, fertiliser application and harvesting based on soil, physical and chemical characteristics (Turvey and Lieshout, 1983; Knott and Ryan, 1990). Our results are in accord with this practice and parallel the results obtained by Turvey. 1983. Usage of the model in a growth and yield system poses no special problems, although users need to be
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careful to use input predictors strictly within observed ranges for any soil type. In practice, it is efficient if latitude, longitude, average altitude, aspect and slope of stands are a priori translated into rainfall and solar estimates, then these can be summarised in a file, so that any number of simulations can be run at will. There are several limitations of the proposed methodology. In this study, we deliberately chose a forest area with a big altitude range, and known to have appreciable differences in rainfall and temperature. Clearly, these characteristics are atypical of many other forests. Moreover, the success of methods described here must depend to a degree on the existence of frequent, long-running and reliable weather stations in forest regions; unfortunately, not many afforested areas have these. Although the climatic surfaces are logically and sensibly constructed, additional errors are introduced by the fitting process, particularly when they are interrogated to within very short distances, for example, sometimes to less than 1 km. Notwithstanding these reservations, we believe we have achieved enough results in this study to encourage others to conduct similar investigations. A sensitivity analysis of model (7) suggests that the model can predict at age 30, around + 1-2 m’ ha- ’ in basal area than otherwise would be the case, which loosely equates to f 15-25 m3 ha-’ in volume production. For clear-fell scheduling purposes, this represents a useful increase in precision. Clearly, we have not considered many other possibilities. Climatic variables including evaporation in conjunction with rainfall may give better definition, especially in drier regions. Alternatively, more refined expressions of the environment (for example, total rainfall during the summer months, or maximum/minimum temperatures) may prove to be superior adjunct explanatory variables. There also exist many alternative ways of modelling process and climate variables in growth and yield systems, especially with diameter distribution and individual tree models (Munro, 1974). Over the last 15 years, mechanistic and management growth modellers around the world have tended to work independently of each other. Results presented here suggest that there is much to gain with collaborative research. with a view to create ‘hybrid’
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growth models, containing elements of both approaches. Historically, there seems to be some confusion as to the role and objectives of the two approaches. Landsberg, 1986 saw conventional forestry models as ‘scarcely qualify(ing) as models; they are not hypotheses but descriptions of observations’. This is unfortunate, because it infers process modelling alone is worth pursuing, and overlooks that mechanistic growth models have never remotely achieved the predictive ability (in volume or tonnes ha-’ of wood) of empirical models as conceded by Landsberg, 1986 and upheld by all of Vanclay, 1994, Goulding, 1994, and Shvets and Zeide, 1996. A very balanced review of the respective strengths of process and empirical modelling is given by Mohren and Burkhart, 1994.
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