Growth and yield of Douglas fir plantations in the central North Island of New Zealand

Abstract

Three growth and yield models have been developed for Douglas fir plantations in the Central North Island of New Zealand: DFCNIGM1, DFCNIGM2 and DFCNIGM3. DFCNIGM1 ___ Douglas Fir Central North Island Growth Model version 1, is a whole stand model for Central North Island plantations, that includes Kaingaroa, Pureora, Waimihia and Whirinaki. Data for Karioi and Whakarewarewa forests were also available but were excluded from the model, because their growth trends differed from the rest, they are separated geographically from the main block of forests and their plot data base was not big enough to allow adequate validation of their inclusion. The version 1 model, which was completed and put into routine operation in March 1989, consists of three parts: a growth and yield projector for (I) healthy, (II) diseased and thinned, and (III) diseased and unthinned stands. Each part consists of a basal area projection equation (Schumacher), a stand volume (combined variable) equation, and a merchantable volume equation (being a function of total volume). All three share the same site index equation (Chapman-Richards) and mortality equation (a simple decay function). Inputs to the model are initial age, initial stems/ha, initial basal area per hectare, site index (or mean top height) and values specified for proposed thinning operations. Outputs of future values generated by the model are basal area/ha, volume/ha, merchantable volume/ha to a 15 cm top diameter limit, stems/ha, mean top height and quadratic mean diameter of the stand. The version 1 model has been in use by New Zealand Forestry Corporation, Timberlands Ltd, since its completion and proved able to give good prediction for all stand statistics except regular mortality, which statistic appears to have been over-estimated. For this reason, the model was subsequently revised into DFCNIGM2 ____ Douglas Fir Central North Island Growth Model version 2, in October 1989, with the original mortality equation replaced by a new one. The new mortality equation was derived by establishing a rate of change in stems/ha over time as a function of stems/ha at beginning of the growth period, basal area/ha, dbh and site quality; mortality was obtained by integrating this rate function. This equation reduced the residual sums of squares by 37% in comparison with the original one. Although the basal area projection equations in DFCNIGM1 predict the future basal area/ha well, they were replaced with an even better-fitting Hossfeld equation. The Hossfeld equation has a more desirable property than the Schumacher: at age zero its yield is equal to zero, whereas it is not defined in Schumacher's equation. DFCNIGM3 ___ Douglas Fir Central North Island Growth Model version 3, is a diameter distribution model for the same plantations resources. This model consists of two parts, namely separate growth and yield projectors for healthy and diseased stands. Each part consists of a stand level and a diameter distribution model. The stand level model is basically the same as DFCNIGM2, and the diameter distribution is generated from stand variables. The reverse Weibull distribution was used as the probability density function distribution of diameters at for characterising the breast height over bark (dbhob) using maximum dbhob, arithmetic mean dbhob and standard deviation of dbhob as state variables. The maximum diameter and standard deviation projection equations were based on the Hossfeld function. Estimating the moments using difference equations makes use of initial values which are generally available in permanent sample plot (PSP) data and which can improve the fit substantially. The b and c parameters of the reverse Weibull distribution were estimated in the usual manner. The location parameter “a” was estimated through the type III Extreme Value Distribution and an extreme percentile calculated from the return period. Based on the stability postulate by Fisher and Tippett (1928) and comments from Gumbel (1958), it was shown that the type III Extreme Value Distribution should be used as the extreme value distribution when a reverse Weibull function is used as the initial distribution. Maximum diameters of each of the PSP plot measurements were extracted. Those maximum diameters were sorted by age, then the arithmetic mean, standard deviation and the maximum of the maximum diameters of each age class were calculated. Moments of the type III Extreme Value Distribution, i.e. the arithmetic mean, standard deviation of the extreme largest diameters, for generating the parameters of the type III Extreme Value Distribution were fitted to those calculated values just described using the Hossfeld function. The scale parameter bx and shape parameter cx of the type III Extreme Value Distribution are calculated using method of moments. The location of the type III Extreme Value Distribution is set equal to the projected maximum of the largest diameters. With parameters ax, bx and cx of the type III Extreme Value Distribution determined, the location of the reverse Weibull distribution was obtained by a = ax -bx [-log(p)] 1/cx Where the percentile p is calculated from the return period. Theoretically, p should be the 100th percentile on the extreme value distribution, which would ensure that the maximum diameter (or the location parameter of the initial distribution) chosen will not be exceeded at a specified age. In practice, the 100th percentile might not be able to produce a good fit and some lower percentile can be tried. But how much lower? Based on the return period, it is shown that it can be chosen between the 95 and 100 percentiles, and still ensure that the maximum diameter chosen will not be exceeded for a specified age, while producing a better fit. Thus by combining the extreme percentile with the extreme value distribution, a good fit can be obtained and bias can be safely avoided; this cannot be achieved if the percentile on the extreme value distribution is chosen arbitrarily. According to the symmetry principle, the Weibull itself should be used as the extreme value distribution when one works with the smallest diameter. Thus the proposed procedure can be applied to the conventional Weibull approach by using the Weibull distribution as the extreme value distribution, which is also called a type III Extreme Value Distribution (Gumbel, 1958). A modified linear equation was used to model the height corresponding to mid-point diameters. Existing volume and taper functions currently used to generate PSP results were employed for the purpose of this study. These functions could be the subject of further investigation to see if useful refinements to them could be made. In version 3 of DFCNIGM, thinned and unthinned data are pooled and the thinning effect on yield is treated by introducing a thinning index to relevant equations and fitting them to the pooled data. Inputs and outputs of DFCNIGM1 and DFCNIGM2 are the same as for most New Zealand growth and yield models and have been described elsewhere (Liu Xu, 1989). Inputs to DFCNIGM3 are age, area/ha, deviation site index or mean top height, initial basal initial stems/ha, maximum dbhob, standard of dbhob, initial extreme largest diameter/initial mean extreme largest diameter, standard deviation of the extreme largest diameter and values for specified thinning operations. Outputs are dbh class, number of trees/ha, mean height, volume and merchantable volume per hectare of each class plus basal area/ha calculated from a stand basal area equation that is compatible with that summed up from all the dbh classes. Preliminary verification and validation indicated that the proposed models give good predictions of both stand and diameter distributions statistics.