R.C. Woollons

Even-aged stand mortality estimation through a two-step regression process

It is argued that a conflict between data and models is inherent in many mortality functions. Equations are utilised which have the property that however short a chosen growth period, then some loss of stems/ha must occur. But permanent sample plot records frequently contains data which exhibit no mortality over several years. If these data are discarded then mortality must be overpredicted. If they are retained, difficulties can occur in residual plot analyses and fitting of models, through the creation of bimodal residual distributions and failure to produce average residual values near zero. To resolve this, a two-step modelling strategy is suggested. A logistic regression predicting the probability of stems/ha death is first constructed. A mortality equation is then built, but only utilising data where death has occurred over a period. Estimates from this second model are then reduced by a factor, equivalent to the probability of death occurring, acquired from the logistic equation. An example involving Pinus radiata data in New Zealand is given. It is argued that better behaved prediction emerges through adoption of the system and clearer information on stand death dynamics is obtained. The system can be utilised stochastically, if desired.

Augmenting empirical stand projection equations with edaphic and climatic variables

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 areal estimates 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−1 projection equations, utilising climate variables in conjunction with traditional plot measures. The data were secured from the Nelson region of New Zealand, where stands of Pinus radiata 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−1. 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.

Incorporation of climatic indices into models of growth of Pinus radiata in a spacing experiment

Schumacher models incorporating climatic indices are used to describe stand height, basal area and volume growth in an initial spacing trial with Pinus radiata. Annual photosynthetic carbon fixation estimated with a process based model, BIOMASS, was a better climatic index than annual rainfall. Incorporation of the growth index derived from BIOMASS into the time function in the Schumacher equation led to path invariant models which improved the fit compared to the basic equation by 13, 22 and 31% for mean tree height, stand basal area and stand volume respectively. Inclusion of the growth index into the asymptote function improved the fit for basal area and volume to 33 and 35% respectively but these models can only be fitted when annual growth data are available and growth estimates are restricted to annual time steps. The new models improve the descriptive power of the Schumacher model and open the avenues for wider interpretation of experimental results. The models should also prove useful for updating forest inventories.

Stand table modelling through the Weibull distribution and usage of skewness information

Abstract A very common practice in forest modelling is to summarise diameter distribution data through use of probability density functions. By far the most popular model is the Weibull which, as well as being versatile, has the distinct advantage that its parameters are readily estimable. In practice, the location parameter a is usually equated to a minimum (sample) value. The scale and shape parameters are estimated iteratively or (approximately) explicitly, through use of moments or percentiles. Here, we expand and develop the use of moments to estimate all three parameters; the essential enhancement is that information concerning the distribution asymmetry is utilised, via the sample skewness statistic. Normally, this information is ignored. Applying the methodology to a Pinus radiata dataset showed that the goodness of fit was improved on average by 15%. On modem computers the method is easily and quickly assayed, so its usage is recommended. There are grounds for suggesting that the method could be embedded in diameter distribution growth-and-yield systems to good effect.

Accuracy of the line intersect method of post-logging sampling under orientation bias

Abstract The Line Intersect Method of Post-Logging Residue Sampling is used extensively as a means of estimating waste volume on a clearfelled stand. Whilst the performance of the method under non-random spatial log arrangement conditions has been examined in the literature, similar examinations of method performance when the logs have a non-random orientation distribution have not been rigorously attempted. Thus, a corrected analytic approach to the calculation of expected sampling error under conditions of log orientation angle bias is presented, along with a correction to the Line Intersect Method literature. A simulation model is also used to calculate the standard deviation of the sampling error under orientation bias conditions. The two models are then used to examine the Line Intersect Method in the context of a typical New Zealand stand of Pinus radiata , comparing and evaluating the performance of the method under four patterns of line arrangements and varying line lengths. Our principal conclusion is that the fan and L arrangement provide considerable protection against the effects of orientation bias, although the presence of an orientation bias can considerably increase the size of the likely measurement error.

A model of the growth of juvenile radiata pine in the Central North Island of New Zealand: links with older models and rotation-length analyses of the effects of site preparation

Abstract Data from 27 site preparation experiments were used to construct a model that predicts growth, survival and size class distributions of radiata pine with respect to altitude, weed control, cultivation, fertilisation, and initial stocking during the first five years after planting. Only stand values, however, are used in this paper. The question of linking the model with existing growth and yield models for older crops is discussed, and a theoretical structure is proposed that clarifies assumptions required if the models are jointly used to evaluate the worth of establishment practices throughout complete crop rotations. It was found that the initial growth model generally predicted similar basal area growth rates to those of the Pumice Plateau Model (PPM88), a growth model for older crops, in age ranges where the two models overlapped, but some of the assumptions required for rotation-length analyses need further testing. Measurements over 8 years in a designed experiment examining alternative site preparation strategies showed that PPM88 was insensitive to the effects of site preparation in predicting growth that occurred after the establishment phase.

Modeling internode length and branch characteristics for Pinus radiata in New Zealand

Abstract It is recognized that estimation of internode length and maximum branch size is important for the prediction of clearwood in unpruned timber stands, as well as for evaluating the quality and value of logs in general. A review of existing branch models reveals a diversity of approaches as well as a tendency for results to be species specific. Here, a branch model is developed for Pinus radiata in New Zealand, capable of predicting successive internode lengths, the number of branches on each branch cluster, and the size of each branch up to the green crown (GC) at site index age 20. Inputs to the model include tree height and diameter at breast height (dbh) (both at age 20) and basal area per hectare of the top 100 stems. Further optional inputs are an ocular count of the number of branch clusters up to the green crown, and branch factor (BF)—the size of the biggest branch in the first cluster encountered above 6xa0m. The vertical distributions of internode length and maximum branch diameter are found to reach maxima around 0.3–0.4 of relative height. Internode length and the number of branches per whorl were found to be independent of tree size, site index and stand density. Stems per hectare is not required as an explicit predictor variable but it appears implicitly through tree dbh. Some model output is given and the results are discussed.

Utility of reverse Weibull and extreme value density functions to refine diameter distribution growth estimates

Abstract This article sets out theoretical and practical benefits of forming diameter distributions for growth and yield modelling purposes through use of the reverse Weibull and extreme value functions. Locating the start of a diameter distribution at its maximum rather than its minimum results in a more accurate representation of the more valuable crop component, namely, the larger trees. Maximum diameter, it is generally accepted, is more easily and reliably predicted in crops subject to a wide range of stocking levels than is minimum diameter: low precision in projecting minimum diameter is a feature of most of the examples found in the literature. A series of 48 permanent sample plots of radiata pine in New Zealand, remeasured annually for up to 18 years, is used in this study to demonstrate the efficacy of the approach. If the absolute or average maximum diameter is chosen as the location variable, however, the resultant distributions are somewhat biased. Such biases can be eliminated through choosing an upper percentile (between 90 and 95%) of the extreme value distribution to define the location parameter objectively.

Multiple covariance: its utility in analysing forest fertilizer experiments

Abstract Forest fertilizer trials are often impaired by high experimental variability. Multiple covariance analysis provides a means of removing not only the confounding effect of differences in initial growing stock between experimental plots but also the influence of other variables such as initial foliar and soil nutrient levels, and inter-tree competition. Unblocked fertility gradients can sometimes be partially controlled by using plot position or dummy variables as covariates. Considerable gains in precision and additional information from available data can be achieved by use of multiple covariance methodology. Three examples are presented to illustrate the efficacy of the technique and the specific benefits its application confers.

Utility of multivariate analyses in examining foliage composition and soil nutrition in a factorial fertilizer experiment

The data for this paper were derived from a previously reported field trial with Pinus radiata which was treated with fertilizer at planting and three subsequent occasions. The experiment tested factorial combinations of urea (n), dicalcium phosphate (p), gypsum (s) and potassium chloride plus trace elements (b).At 5 years-of-age bole development was substantially increased by p alone, but p and n in combination increased growth further still. Urea, applied alone, had no, or retardive effects. Foliage concentrations of N, P, K, Ca, Mg, Fe and Mn were raised by p or n and p in combination, but Zn concentrations were not changed. Urea alone caused significantly lower Fe, Mg, Ca, and K concentrations in foliage.The 16 fertilizer combinations created a series of diverse soil nutrient conditions. For the ameliorative treatments (p and np), soils were characterized by high levels of total P and N, and exchangeable NH4+and Ca 2+ whereas soils treated with n alone had low levels of the cations Mg2+, Ca2+, and Na+, but higher A13+. While not contributing to stem growth, the s and b treatments also formed unique soil nutrient concentrations; s induced appreciable increases in Ca2+ while b resulted in a 3.5-fold increase in K+.Multivariate statistical analyses aided examination of the experimental data, whereas univariate analyses became cumbersome or repetitive, or gave no insight into individual contributions to overall variation. Eigenvalues extracted from discriminant analyses did provide this information, and ranked effects in order of importance. The effects of urea fertilizer on concentration of a number of elements in the foliage and on soil nutrient status were small but had marked effects on growth. It is envisaged that multivariate techniques can be utilized with other trial data, provided such experiments are soundly designed and adequately replicated.