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Development of models to predict Pinus radiata productivity throughout New Zealand Michael S. Watt, David J. Palmer, Mark O. Kimberley, Barbara K. Ho¨ck, Tim W. Payn, and David J. Lowe

Abstract: Development of spatial surfaces describing variation in productivity across broad landscapes at a fine resolution would be of considerable use to forest managers as decision support tools to optimize productivity. In New Zealand, the two most widely used indices to quantify productivity of Pinus radiata D. Don are Site Index and 300 Index. Using an extensive national data set comprising a comprehensive set of national extent maps, multiple regression models and spatial surfaces of these indices for P. radiata were constructed. The final models accounted for 64% and 53%, respectively, of the variance in Site Index and 300 Index. For Site Index, variables included in the final model in order of importance were mean annual air temperature, fractional mean annual available root-zone water storage, mean annual windspeed, length and slope factor, categories describing Land Environments of New Zealand (LENZ), and major soil parent material. The variables included in the final model of 300 Index in order of importance included the degree of ground frost during autumn, fractional mean annual available root-zone water storage, categories describing LENZ, vegetation classification, foliar nitrogen, taxonomic soil order, and major soil parent material. These results highlight the utility of thematic spatial layers as driving variables in the development of productivity models. Re´sume´ : La mise au point de couches spatiales de´crivant la variation de la productivite´ de grands territoires a` une re´solution fine serait d’une grande utilite´ pour les ame´nagistes forestiers comme outil de support a` la de´cision pour optimiser la productivite´. En Nouvelle-Ze´lande, les deux indices les plus utilise´s pour quantifier la productivite´ de Pinus radiata D. ` l’aide d’un important fichier de Don sont l’indice de qualite´ de station (« Site Index ») et l’indice 300 (« 300 Index »). A donne´es a` l’e´chelle nationale comprenant un ensemble complet de cartes nationales d’e´tendue, nous avons construit des mode`les de re´gression multiple et des couches spatiales de ces indices pour P. radiata. Les mode`les finaux expliquaient respectivement 64 % et 53 % de la variance du Site Index et du 300 Index. Pour le Site Index, les variables incluses dans le mode`le final e´taient, par ordre d’importance, la tempe´rature annuelle moyenne de l’air, la moyenne annuelle de la fraction disponible de l’eau dans la rhizosphe`re, la vitesse annuelle moyenne du vent, la longueur et le facteur de pente, des variables cate´goriques de´crivant les environnements topographiques de la Nouvelle-Ze´lande (ETNZ) et le principal mate´riau d’origine du sol. Dans le cas du 300 Index, les variables incluses dans mode`le final e´taient, par ordre d’importance, l’intensite´ du gel au sol pendant l’automne, la moyenne annuelle de la fraction disponible de l’eau dans la rhizosphe`re, les cate´gories de´crivant de l’ETNZ, la classification de ve´ge´tation, l’azote foliaire, l’ordre taxonomique du sol et le principal mate´riau d’origine du sol. Ces re´sultats mettent en e´vidence l’utilite´ des couches spatiales the´matiques comme variables explicatives importantes dans la mise au point de mode`les de productivite´. [Traduit par la Re´daction]

Introduction The influence of climatic variables on tree growth and development has been well documented throughout both the growth modelling and the physiological literature (Landsberg and Waring 1997; Whitehead et al. 2001). Over recent decades, many process-based models have been developed to provide a framework for these relationships. Such models range in complexity from the simple light use efficiency approach (Monteith and Moss 1977) through to more complex growth models that link carbon, water, and nitrogen flows in the trees and soil (Kirschbaum 1999; Battaglia et al. 2004).

However, these models are seldom used as practical tools in forest management because they include too many uncertainties and often require values for a large number of parameters that are difficult to obtain (Ma¨kela¨ et al. 2000). One means of reducing this level of parameterization, while still retaining the link with physiological processes, is to use process-based components such as water balance in empirical models. Rapid increases in the capability of geographic information systems (GIS) over recent years have seen the development of spatial surfaces covering a diverse range of environmental variables (e.g., Leathwick et al.

Received 28 May 2009. Accepted 21 December 2009. Published on the NRC Research Press Web site at cjfr.nrc.ca on 2 March 2010. M.S. Watt.1 Scion, P.O. Box 29237, Christchurch 8540, New Zealand. D.J. Palmer, M.O. Kimberley, B.K. Ho¨ck, and T.W. Payn. Scion, Private Bag 3020, Rotorua 3046, New Zealand. D.J. Lowe. Department of Earth and Ocean Sciences, University of Waikato, Private Bag 3105, Hamilton 3240, New Zealand. 1Corresponding

author (e-mail: [email protected]).

Can. J. For. Res. 40: 488–499 (2010)

doi:10.1139/X09-207

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Watt et al.

2002, 2003; Tait et al. 2006), including root-zone water storage estimated from a spatial water balance model (Palmer et al. 2009b). However, to date, little research has fully utilized the diverse array of GIS-derived environmental variables as independent variables in models of tree productivity. There are numerous advantages to using these GIS surfaces in growth models. Their use largely eliminates the need for costly data collection and provides a more comprehensive range of predictive environmental variables than would typically be collected from meteorological stations. As surfaces usually completely cover the landscape, the resulting model can be used to develop spatial representations of productivity across broad landscape scales at a reasonably high spatial resolution. A common limitation in the development of growth models is the representation of site fertility. Although there is a good understanding of the nutrients that play a key role in tree growth (Watt et al. 2005, 2008), development of input data that can be used operationally to predict site fertility remains a major challenge (Schoenholtz et al. 2000). One possible method of simplifying this process is the use of categorical variables in models that stratify areas based on similarity in edaphic properties. Within New Zealand, there are GIS surfaces describing potentially useful variables including major soil parent material and soil order. However, perhaps the most valuable of these layers for modelling is Land Environments of New Zealand (LENZ), which at the highest level (LENZ level 1) subdivides New Zealand into 20 categories on the basis of similarity between 15 key climatic, edaphic, and landform properties (Leathwick et al. 2003). Although these categorical variables could be used as surrogates for climate and soil fertility, little research has investigated the utility of these variables in growth models. In New Zealand, Pinus radiata D. Don is the most widely planted commercial forestry crop covering an estimated 1.6 million hectares comprising 91% of the entire national plantation estate (New Zealand Forest Owners Association 2005). There are two indices commonly used to quantify productivity of P. radiata within New Zealand. These are the 300 Index, defined as the stem volume mean annual increment (MAI) at age 30 years with a reference regime of 300 stems
ha–1 (Kimberley et al. 2005), and Site Index, defined as the mean top height (average height of the 100 largest diameter stems within a hectare) at age 20 years (Goulding 2005). An extensive set of Site Index and 300 Index measurements (1764 independent records), covering the complete climatic and edaphic range over which plantations are grown within New Zealand, were used in this study. From location information, these records were matched with a comprehensive set of variables derived from GIS surfaces. Using these data sets, the primary objective of this study was to develop models that describe the influence of climate, landform, and edaphic properties on 300 Index and Site Index for P. radiata. Additional objectives that were addressed in this study included (i) quantifying the importance of root-zone water storage as a determinant of productivity and (ii) determining the utility of categorical variables that subdivide the country based on similarity in climatic, landform, and edaphic variables as predictors of productivity.

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Methods Permanent sampling plot data and preliminary screening Stand-level data were extracted from the New Zealand Forest Research Institute Ltd. permanent sample plot (PSP) system (Pilaar and Dunlop 1990). These data were examined for sites that could adversely influence the integrity of the data set. Exclusions included Nelder (spacing), oversowing, disturbance (forest floor removal), and fertilizer (phosphorus, nitrogen, and potassium) trials. For these exclusions, trial control plots were identified and retained. Other exclusions included data from stands planted prior to 1975 and stands less than 7 years in age. These latter two groups were excluded, as data from young trees are inherently unreliable and a preliminary screening of the PSP data found that stands established after 1975 have 300 Index values ~25% higher than stands established during the 1930s. This interesting result was also noted by Kimberley et al. (2005) who attributed the increase in the 300 Index in more recently planted stands to improvements in genetics and management. Following Kimberley et al. (2005), 300 Index and Site Index values were calculated from these data using the procedure briefly summarized below. To calculate Site Index, a national height–age model (an equation for predicting height for any age and Site Index) was used. This model uses a Chapman–Richards (Richards 1959) model form using Site Index as a local parameter and with both slope and shape parameters expressed as functions of this local parameter. By inverting the equation, it is possible to obtain Site Index as a function of age and mean top height. In our study, the mean top height measurement closest to age 20 years was used for each PSP. This means that for plots with measurements made at precisely 20 years of age, the Site Index is simply the measured mean top height, while for plots not measured at precisely 20 years of age, the height–age model extrapolates backwards or forwards in time to 20 years from the nearest height measurement. Estimation of the 300 Index, which is a measure of stem volume productivity, is more complex because, unlike height, stem volume is strongly influenced by stocking and, to a lesser extent, thinning and pruning history. To calculate the 300 Index, a plot measurement consisting of the basal area, mean top height, and stocking at a known age along with stand history information (initial stocking, timing and extent of thinnings, and timing and height of prunings) is required. The 300 Index estimation procedure utilizes the 300 Index model, an empirical stand-level basal area growth model that expresses basal area as a function of age, stocking, Site Index, and the 300 Index, effectively a local site productivity parameter (Kimberley et al. 2005). The model accounts for the effects of pruning and thinning using ageshift adjustments. For example, field trials have demonstrated that the effect of a typical pruning regime is to lose about 1.4 years of basal area growth compared with a similar unpruned regime, and this effect is incorporated into the 300 Index growth model. The model is structured so that for stands using the standard 300 Index regime (pruned to 6 m height and thinned at the time of final pruning so that stocking density at age 30 years is 300 stems
ha–1), the stem volume MAI equals the 300 Index parameter. Therefore, the Published by NRC Research Press

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300 Index is an index of stem volume productivity, defined as the volume MAI at age 30 years for this standard regime. Because the model is sensitive to departures from this standard regime (e.g., different stocking levels and different intensities and timing of thinning and pruning regimes) and can also adjust for the stand age, it can be used to predict the index for any plot measurement. To do this, an iterative procedure is used to determine the 300 Index parameter value compatible with the plot measurement and management history associated with the plot. Data extraction and preprocessing A 100 m grid was overlaid on the plot locations, and where more than one plot estimate of Site Index and 300 Index occurred within any one grid cell, the estimates were averaged so that they aligned with the independent variables used in the modelling of forest productivity. Following exclusions, and this averaging, there were 1764 independent measurements of Site Index and 300 Index available for modelling. From the coordinates of each of these measurements, data were extracted from biophysical GIS surfaces that included primary and secondary terrain attributes (Palmer et al. 2009a), monthly and annual climate variables (Mitchell 1991; Leathwick et al. 2002), fundamental soil layers and land resource information (Newsome et al. 2000), vegetative cover (Newsome 1987), nitrogen and phosphorus foliar nutrition (Hunter et al. 1991), and biophysical surfaces (Leathwick et al. 2003) for New Zealand. A spatial soil water balance model (Palmer et al. 2009b) was used to determine mean annual and seasonal root-zone water storage (W) for all PSP locations. Fractional available root-zone water storage, Wf, was then determined from these data and the maximum available root-zone water storage, Wmax, as W/Wmax. The data set was randomly split into fitting (n = 1176) and validation (n = 588) data sets (Fig. 1). The validation data set was used to validate the models of 300 Index and Site Index developed using the fitting data set. Site variation Variation in tree productivity and climate was very similar between the fitting and validation data sets. Tree productivity substantially varied across sites, ranging threefold and 10-fold, respectively, for Site Index and 300 Index (Table 1). Climatic variation between sites was also considerable. Air temperature ranged twofold and fourfold for mean (Ta) and minimum (Tm) annual air temperature, respectively (Table 1). Mean annual windspeed exhibited a sixfold range (Table 1) that was right skewed (skewness = 0.94) with the 50th, 75th, and 100th percentiles equalling 10.6, 13.0, and 26.6 km
h–1, respectively. Similarly, mean annual rainfall ranged sixfold and was right skewed (skewness = 1.20) with respective mean and maximum values of 1283 and 3372 mm. In contrast, the threefold and fourfold respective range (Table 1) in mean annual Wf was left skewed when averaged during the year (skewness = –0.84) and summer (skewness = –0.48). These left skewnesses reflected the relatively low number of forested areas in dryland regions within New Zealand where rainfall is less than 1000 mm
year–1.

Can. J. For. Res. Vol. 40, 2010

Data analysis All analyses were undertaken using the SAS (SAS Institute Inc. 2000) general linear model procedure. Bivariate correlations between the response and independent variables were examined within the fitting data set to identify the strongest determinants of both Site Index and 300 Index. Comparisons of relationship strength between independent variables were undertaken using the coefficient of determination (R2). Multiple regression models for 300 Index and Site Index were constructed using the fitting data set. Variables were introduced sequentially into each model starting with the variable that exhibited the strongest correlation until further additions were not significant or did not improve the overall model R2 by at least 2%. Variable significance was determined manually using an F test, with the significance tested for each variable addition against the residual sum of squares from the previous model. Variable selection was undertaken manually one variable at a time to ensure that nonlinear relationships and relationships with categorical variables were identified from residual plots and correctly incorporated into the model. Models were initially developed using climatic variables. Once these were finalized, the utility of categorical variables in accounting for additional variance in site fertility were compared by determining the gain in precision that single additions of each of these variables made to the model. These variables were singly added one at a time to the base models of the 300 Index and Site Index that included all significant climatic variables. For all of the independent categorical variables included in the Site Index and 300 Index models, values of productivity between classes within the variable were assessed through examination of least square means. This procedure effectively levels the effect of climate, throughout the data set, so that the real effect of other vegetative, landform, or edaphic properties can be discerned. Multiple range testing was undertaken on these least square means using Tukey’s test. Final multiple regression models were constructed by adding significant categorical variables to the model with climatic variables. For the final models, residuals were plotted against predicted values and independent variables to determine model bias and to ascertain that independent variables were included in the model using an unbiased functional form. Model precision was assessed through examination of the R2 and root mean square error (RMSE). An independent validation was undertaken to check bias and precision of both final models by comparing model predictions with observed values from the validation data set. Model precision and bias were ascertained for the validation using the previously described tests.

Results Bivariate relationships between environment and productivity The LENZ categories were the strongest determinant of both Site Index and 300 Index, accounting, respectively, for 36% and 30% of the variance in these variables (Table 2). The major soil parent material and Ta were important determinants of Site Index (R2 = 0.31 for both). For 300 Index, Published by NRC Research Press

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Fig. 1. Distribution of the permanent sample plot data in relation to 14 of the 20 most general classes (level 1) of Land Environments of New Zealand (LENZ) (Leathwick et al. 2003) used to delineate and group biophysical and environmental variables. These were the classes used in the modelling of the 300 Index and Site Index. Land areas shown in grey include the six other level 1 classifications on which permanent sample plots were not located.

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Can. J. For. Res. Vol. 40, 2010 Table 1. Site-level variation in stand structural and climatic variables for the fitting and validation data sets. Variable

Fitting data set

Structural (mean (range)) Site Index (m) 300 Index (m3
ha–1
year–1) Climatic (mean (range)) Mean annual Ta (8C) Mean annual Tm (8C) Mean annual daily radiation (MJ
m–2
day–1) Total mean annual rainfall (mm
year–1) Mean annual windspeed (km
h–1) Mean annual W (mm) Mean annual Wf (%) Mean summer Wf (%) Table 2. Strength of bivariate correlations between productivity indices and continuous and categorical independent variables. Variable

Site Index R2

300 Index R2

Continuous Mean annual Ta Mean annual daily radiation Mean total annual rainfall Mean annual windspeed Mean annual Wf Fa

0.31 0.20 0.25 0.19 0.21 0.08

0.11 0.02 0.12 0.01 0.15 0.14

Categorical LENZ 21 Major soil parent material Soil order Foliar nitrogen Foliar phosphorus

0.36 0.31 0.24 0.21 0.23

0.30 0.14 0.11 0.18 0.22

Note: Variables shown have an R2 that exceeds 0.14 for either of the dependant variables. All variables shown were significantly related to either Site Index or 300 Index at P < 0.001.

foliar phosphorus and nitrogen were key categorical drivers of productivity, while the most strongly related continuous variables were mean annual Wf and the degree of ground frost during autumn (Fa) (Table 2). Multiple regression model of Site Index When included in combination, the two main environmental determinants of Site Index were mean annual Ta and Wf, which accounted for a total of 49% of the variance in the data (Table 3). Both mean annual Ta and Wf were included in the model as downward-opening parabolas, with maxima reached at mean annual values of 13.2 8C and 88% (of Wmax), respectively (Figs. 2a and 2b). Addition of mean annual windspeed as a negative linear term (Fig. 2c) and length and slope factor as a downward opening parabola (Fig. 2d) with an asymptote at 17 accounted, respectively, for a further 4% and 2% of the variance in Site Index (Table 3). Inclusion of categorical variables one at a time into the Site Index model with only the climatic terms showed that LENZ accounted for most of the variance (partial R2 = 0.057, F = 6.4, P < 0.001) followed by major soil parent

Validation data set

29.9 (13.5–46.6) 26.4 (5.0–50.0)

30.1 (15.9–45.9) 26.5 (9.9–48.7)

11.7 (7.7–16.0) 6.8 (3.2–12.5) 14.5 (12.1–15.3) 1283.(600–3372) 11.0 (4.7–26.6) 114.(7–293) 81.(39–98) 68.(24–96)

11.7 (7.8–15.9) 6.8 (3.2–12.4) 14.5 (12.1–15.3) 1282.(600–2892) 10.9 (4.7–25.5) 113.(18–293) 82.(39–98) 68.(24–96)

material (partial R2 = 0.05, F = 5.2, P < 0.001) and then previous vegetation classification (partial R2 = 0.007, F = 2.8, P = 0.038). Soil order (highest taxonomic category for grouping soils) did not significantly (P > 0.05) improve the climatic model, with only continuous variables. As LENZ and major soil parent material were the strongest categorical variables, these were added to the Site Index multiple regression model (see Table 3 for final statistics). After addition of these two variables, no other categorical variables were significant at P = 0.05. Examination of least square means showed that southern lowlands and southeastern hill country/mountains had site indices that were significantly higher than many of the other classes including the least productive classes of northern recent soils and central well-drained recent soils (Table 4). For the major soil parent material classes, plots located on soils derived from loess, young sedimentary rock, and extremely weak to weak volcanic/pyroclastic materials were most productive for Site Index and had values of Site Index significantly higher than those of all other classes (Table 5). The plots with the lowest Site Index were those found on dune sands (Table 5). Addition of LENZ and major soil parent materials to the final model, as class-level terms, contributed an additional 5% and 4% to the final model, respectively (Table 3). The final model accounted for 64% of the variance in Site Index and the RMSE was 3.03 m. All terms were significant (Table 3), and the residual values exhibited little apparent bias against either predicted values or independent variables (data not shown). Parameter values are shown in Appendix A). Multiple regression model of 300 Index The Fa and average annual Wf were the two continuous variables most strongly correlated with the 300 Index and in combination accounted for 31% of the variance (Table 3). For Fa and average annual Wf, downward-opening parabolas, with respective maxima at 3.0 frosts
month–1 (Fig. 2e) and 89% (Fig. 2f), were used to characterize the relationship between these variables and the 300 Index. Inclusion of categorical variables one at a time into the climate adjusted model showed that LENZ accounted for most of the variance (partial R2 = 0.093, F = 12.4, P < 0.001) followed by major soil parent material (partial R2 = Published by NRC Research Press

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Fig. 2. Partial response curves showing the influence of (a) mean annual air temperature, (b) mean annual Wf, (c) mean annual windspeed, and (d) length and slope factor on Site Index. Also shown are the influence of (e) degree ground frost in autumn and (f) mean annual Wf on 300 Index. For each partial response curve, the response is shown as a black line and the lower and upper 95% confidence limits are shown as grey lines.

0.092, F = 17.7, P < 0.001), previous vegetation classification (partial R2 = 0.087, F = 50.4, P < 0.001), and finally soil order (partial R2 = 0.042, F = 8.4, P < 0.001). After levelling out the effect of climate, LENZ categories that had the highest values of 300 Index included southern lowlands and northern hill country, which significantly exceeded the lowest values found on the eastern South Island plains, western South Island foothills, and northern recent soils (Table 4). Climate-levelled predictions of 300 Index values were highest on the major soil parent materials of lo-

ess and very weak or weak volcanic or pyroclastic deposits and lowest on dune sands (Table 5). After adjustment had been made for climate, there was considerable variation in 300 Index between soil orders that ranged from 24.5 to 30.5 m3
ha–1
year–1. Climate-levelled predictions of 300 Index values showed that the highest productivity soil orders (Hewitt 1998) were Allophanic (30.5 m3
ha–1
year–1) followed by Melanic (27.8 m3
ha–1
year–1), Pumice (27.7 m3
ha–1
year–1), Gley (27.7 m3
ha–1
year–1), Pallic (27.6 m3
ha–1
year–1), Recent (26.9 m3
ha–1
year–1), Brown Published by NRC Research Press

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Can. J. For. Res. Vol. 40, 2010 Table 3. Model statistics for the two final models developed for Site Index and 300 Index. Dependant variable Site Index

300 Index

Independent variable Mean annual Ta Mean annual Wf Mean annual windspeed Length and slope factor LENZ (level 1) Major soil parent material Fa Mean annual Wf LENZ (level 1) Vegetation classification Foliar nitrogen Soil order Major soil parent material

F 259 213 99 23 12 11 90 137 13 34 25 5 5

R2 0.31 0.18 0.04 0.02 0.05 0.04 0.14 0.17 0.09 0.05 0.04 0.02 0.02

(0.31) (0.49) (0.53) (0.55) (0.60) (0.64) (0.14) (0.31) (0.40) (0.45) (0.49) (0.51) (0.53)

RMSE 4.11 3.56 3.42 3.36 3.16 3.03 5.44 4.87 4.56 4.36 4.21 4.14 4.07

Note: For each variable introduced into the model, the partial and cumulative (in parentheses) R2 and RMSE are shown following addition of the variable to the model, with all previous terms included. The RMSE has units of m for Site Index and m3
ha–1
year–1 for 300 Index. The F values from an F test are shown for each variable addition. All F values are significant at P < 0.001.

Fig. 3. Relationship between (a) predicted and residual Site Index and (b) predicted and residual 300 Index for the validation data set.

(26.3 m3
ha–1
year–1), and Ultic (24.6 m3
ha–1
year–1). The lowest productivity soil order was Podzol, which had a 300 Index significantly lower than that of all other soil orders (24.5 m3
ha–1
year–1).

Climate-adjusted predictions of 300 Index values increased relatively linearly across the four foliar nitrogen categories from the least (23.4 m3
ha–1
year–1) to most fertile (28.4 m3
ha–1
year–1) classes. Significant differences were noted between all four foliar nitrogen categories, apart from the two least fertile. Climate-adjusted 300 Index values for land classed as ex-pasture (29.5 m3
ha–1
year–1) were significantly higher than for the other two classes that included exotic forest (25.8 m3
ha–1
year–1) and scrubland/reverting native forest/native forest (25.9 m3
ha–1
year–1). Addition of LENZ categories and previous vegetation classification to the model accounted for an additional 9% and 5%, respectively, of the variance in 300 Index (Table 3). Inclusion of foliar nitrogen as a categorical variable with four categories, ranging from low to high foliar nitrogen, accounted for an additional 4% of the variance in 300 Index. Model coefficients show that the 300 Index increased with higher levels of foliar nitrogen. Both soil order and major soil parent material added 2% to the model. The final model accounted for 53% of the variance in 300 Index, all terms were highly significant, and the RMSE was 4.07 m3
ha–1
year–1. Residual values exhibited little apparent bias against either predicted values or independent variables (data not shown). Parameter values are shown in Appendix A. Model validation For Site Index, application of the developed model to the validation data set showed the model to be relatively precise (R2 = 0.61, RMSE = 3.05 m) and unbiased with little apparent trend visible in plots of residual values against either predicted values (Fig. 3a) or any of the independent variables (data not shown). The model developed for the 300 Index was found to be somewhat less precise when applied to the validation data set (R2 = 0.46, RMSE = 4.12 m3
ha–1
year–1). However, residuals for this model were relatively unbiased when plotted against predicted values (Fig. 3b) or any of the independent variables used in the model (data not shown).

Discussion In this study, two different P. radiata site productivity inPublished by NRC Research Press

Watt et al.

495 Table 4. Variation in least square means for 300 Index and Site Index between LENZ classes. LENZ category Southern lowlands Northern hill country Central sandy recent soils Western/southern North Island lowlands Southeast hill country/mountains Central hill country Central dry lowlands Northern lowlands Central dry foothills Central mountains Central well-drained recent soils Eastern South Island plains Western South Island foothills Northern recent soils

Site Index (m) 34.3a 31.0b 30.6bc 30.4bcd 32.0ab 30.3bc 28.2d 29.9bc 29.0cd 30.5bc 27.3d 28.8cd 28.3cd 27.3d

300 Index (m3
ha–1
year–1) 31.8a 30.0ab 28.8ab 28.0abc 26.1cd 27.3c 28.0c 26.0cd 26.0cd 24.5d 27.6bc 24.0de 21.5de 22.1de

Note: Categories have been sorted in descending order using values averaged across Site Index and 300 Index. Values followed by the same letter are not significantly different at P = 0.05.

Table 5. Variation in least square means for 300 Index and Site Index between the major soil parent material classes (after Leathwick et al. 2003). Major soil parent material Volcanic or pyroclastic rocks/deposits: extremely weak to weak Sedimentary rocks and deposits: Tertiary and younger Volcanic or pyroclastic rocks/deposits: loose basaltic/ultramafic materials Loess Other sedimentary rocks plus schist: pre-Tertiary sedimentary rocks and schist Sedimentary and metamorphic rocks (carbonates): limestone and marble Alluvium, till, colluvium, soft sediments Volcanic or pyroclastic rocks/deposits: weak to extremely strong Intrusive rocks, including gneiss Dune sands

Site Index (m) 28.3a 28.0a 26.4b 28.2a 24.8c 23.3c 24.1c 23.9bc 23.0cd 19.7d

300 Index (m3
ha–1
year–1) 30.8ab 30.8ab 31.9a 29.8abc 29.1c 29.5abc 28.4c 27.6bc 27.6bc 25.9cd

Note: Categories have been sorted in descending order using values averaged across Site Index and 300 Index. Values followed by the same letter are not significantly different at P = 0.05.

dices, namely Site Index and 300 Index, were shown to be linked to site factors. However, the link between site productivity and site factors relies on the fact that these indices are themselves good indicators of site productivity. Logically, the most direct measure of productivity would be the quantity of wood grown within a given period or, as a close surrogate, stem volume growth. However, because this is strongly influenced by stocking, thinning history, mortality, and stand age, direct measurement of volume MAI does not necessarily provide a reliable indicator of site quality. A commonly used approach to overcome the effect of stocking is to use the mean height of dominant trees because height growth is little affected by stocking or thinning. As discussed by Assman (1970), this concept originated with F. von Bauer in 19th century Germany and has since become widely used internationally. Site Index, defined for P. radiata in New Zealand as the mean top height at age 20 years, provides such an index and has been used in a number of previous studies relating P. radiata productivity to site factors (Truman et al. 1983; Hunter and Gibson 1984; Grey 1989; Louw 1991). The recent standardization of volume in the form of the 300 Index (Kimberley et al. 2005) provides a superior and more accurate means of ascertaining site productivity for P.

radiata than Site Index (Kimberley et al. 2005). Importantly, recent research has clearly shown that accurate and unbiased values for 300 Index can be obtained using measurements taken from stands differing in age or stocking from those of the 300 Index standard regime (30 years and 300 stems
ha–1 stocking; Kimberley et al. 2005). Air temperature and Wf were found to be key determinants of productivity for both Site Index and 300 Index. Results show that the use of categorical variables that aggregated regions were able to substantially improve these models. Of the categorical variables considered, LENZ provided the largest increase in predictive power, both as a sole predictor and when added to the models with climatic variables. For Site Index and 300 Index, major soil parent material was found to provide similar gains to LENZ that were substantially greater than increases attributable to addition of soil order. The inclusion of variables related to air temperature in both models is sound from a physiological point of view. Although the quantity of radiation intercepted controls the maximum growth attainable, temperature is a primary determinant of the amount of intercepted radiation that can be utilized by the plant (Monteith and Moss 1977). The positive relationship often found between tree growth and Ta Published by NRC Research Press

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(Watt et al. 2005, 2008) is thought to be principally driven by the lengthening of the growing season (Lieth 1973). The importance of such lengthening of the growing season was demonstrated recently by Kerkhoff et al. (2005) who showed that net primary production expressed as net primary production per month of growing season was virtually invariant with temperature. The decline in the 300 Index with increasing frost frequency found in this study is consistent with this theory. As the growth pattern of P. radiata is strongly temperature regulated over the year (Whitehead et al. 1994; Kimberley and Richardson 2004; Watt et al. 2004), Fa is likely to control the duration over which trees can grow during autumn and therefore the length of the growing season. The relationship between Site Index and Ta is also likely to be partially mediated through the relationship between Ta and growing season length. However, the decline in Site Index with increases in Ta above the optimum temperature suggests that air temperature also has a more direct effect on the height growth rate during the growing season. Soil water balance has long been recognized as a major determinant of P. radiata growth at specific locations exhibiting seasonal water deficits (McMurtrie et al. 1990; Richardson et al. 2002; Watt et al. 2003). Consequently rootzone water storage, expressed as a fraction of the maximum available, has often been utilized as a growth modifier in both process-based (Landsberg and Waring 1997) and hybrid growth models (Watt et al. 2009a). Despite this, very few national or regional management models use this variable in a predictive capacity in operational settings. Our research clearly demonstrates the utility of average annual Wf as a key determinant of productivity. The finding also endorses the use of national scale water balance models, such as SWatBal (Palmer et al. 2009b), in providing estimates of Wf at a fine scale that can be used as input into management models, such as those developed in this paper. Results described in this study provide an insight into how P. radiata responds to water balance and air temperature. Optimum Site Index was found to occur at a mean annual Ta of 13.2 8C. This temperature – Site Index relationship is broadly consistent with findings from previous research (Hunter and Gibson 1984) that indicate that maximum Site Index occurs within the Ta range of 7.7–16.0 8C found within New Zealand. For both Site Index and 300 Index, productivity increased rapidly from a mean annual Wf of 39% to a maximum at ~88% (Fig. 2). Gains over this range were substantial, ranging from 65% (19.7–32.6 m) for Site Index to 148% (11.9–29.5 m3
ha–1
year–1) for 300 Index. After this optimum value, there was a slight reduction in productivity as mean annual Wf further increased from 88% to 98%. These reductions were very low for both Site Index (2% or 0.60 m) and 300 Index (2% or 0.54 m3
ha–1
year–1) and were relatively similar to the difference between the mean and lower 95% confidence limit for both productivity measures at Wf = 98% (Fig. 2). It is likely that the decline in productivity over this range is attributable to the reduced aeration that occurs in soils that are saturated for prolonged periods (Schoenholtz et al. 2000). The fitted functional form for mean annual Wf found in this study is very similar to that described in the widely used process-based model 3-PG (Landsberg and Waring

Can. J. For. Res. Vol. 40, 2010

1997). In 3-PG, the soil moisture modifier and growth are not reduced until Wf declines below a threshold. The threshold and the rate of decline in the modifier are dependent on soil type (a taxonomic category below soil series, typically expressed using a soil texture class), with the Wf threshold ranging from ~60% for sand to 100% for clay. Because we do not currently have a spatial layer describing soil type, variation in this functional form by soil type could not be assessed. However, further research should be undertaken into this aspect of the growth model, as it may provide a useful means of more accurately modelling the effects of Wf on growth at broad scales. Despite the relatively coarse nature of categorical variables, these provided a reasonable improvement in model explanatory power for both Site Index and 300 Index. The significance of LENZ categories, after adjustment had been made for climate, highlights the sensitivity of this classification to landform and edaphic properties and also provided an insight into fertility between the categories. Results clearly show major soil parent material to provide a greater gain than soil order when variables were introduced one at a time into the climatic models. This outcome may reflect a closer linkage between major soil parent material and soil fertility than soil order. The patterns of 300 Index and Site Index values essentially mimic each other with regard to the major soil parent material classes depicted as least square means (Table 5) as follows: the highest values for both indices are associated with loess, two of the volcanic/ pyroclastic parent material classes, and the Tertiary and younger sedimentary deposits; intermediate values are related to a third, more indurated volcanic/pyroclastic parent material class, a range of alluvial, glacial and colluvial sediments, limestones and marbles, pre-Tertiary sedimentary rocks and schist, and intrusive rocks; and the lowest values are associated with dune sands. These relationships are broadly in keeping with the general fertility of soils associated with these amalgamated parent material groups (e.g., see Cornforth 1998; Leathwick et al. 2003) but it is emphasized that fertility relates to a wide range of attributes including soil physical, chemical, and biological properties as well as lithological composition and texture. Soil orders on which plantation forests are grown within New Zealand have been shown to be predominantly differentiated on the basis of soil phosphorus retention, carbon content, and air capacity (Ross et al. 2009). These three soil properties have been found to have little effect on growth of P. radiata compared with other edaphic properties such as total phosphorus and carbon to nitrogen ratio (Watt et al. 2005, 2008). For 300 Index, addition of soil order made a relatively modest improvement to the model, through highlighting the high productivity of the Allophanic, Melanic, and Pumice soils and the low productivity of the strongly leached and infertile Ultic and Podzol soil orders. These rankings accord well with expert knowledge and previous research (Ross et al. 2009). For example, Allophanic soils are typically deep with low bulk densities, large rooting volumes, and very high water storage, Melanic soils are fertile and with stable structure, and Pumice Soils, although weakly weathered and deficient in many elements, are typically deep rooting, have high water storage because of fine pumice vesicularity, and have a special ‘‘phosphorus-releasing’’ capacity (Hewitt Published by NRC Research Press

Watt et al.

1998; Lowe and Palmer 2005; Palmer et al. 2005). Findings presented here also show a substantial increase in productivity for stands established on ex-pasture sites that are more likely to have had a history of fertilization than ex-forest/ mixed scrubland sites. This relationship between land-use history and productivity is consistent with results from previous research for both P. radiata (Maclaren and West 2005) and Cupressus lusitanica Mill. (Watt et al. 2009b). Gains in predictive power through inclusion of categorical variables that predominantly represented edaphic variables were greater for 300 Index than for Site Index (R2 gain = 0.17 versus 0.09). This disparity is likely to reflect the fact that diameter and volume are commonly found to be more sensitive to site fertility than tree height. Previous research has shown that P. radiata volume productivity within New Zealand is most strongly related to soil total phosphorus, nitrogen, and carbon to nitrogen ratio (Watt et al. 2008). Development of surfaces describing soil-based variables such as these that represent the extensive range in site fertility throughout New Zealand (Watt et al. 2008) are likely to further improve the models described in this paper. Although the technique used to determine 300 Index and Site Index could introduce errors, these are unlikely to be of major consequence, as the projection intervals used are relatively short. For plots measured at age 20 years, the Site Index is simply the mean top height and no model is required for its estimation, while for plots measured at close to age 20 years (most of our plots), the height–age model is only used to extrapolate a little from the measurement age to age 20. The 300 Index estimates are more model dependent, although for plots close to 300 stems
ha–1, the model is effectively only adjusting the measurement to a standardized age (30 years). As the productivity estimates are generated using a single measurement for each plot, they may sometimes be slightly biased. Similarly, the indices are just as likely to have extreme values as the measurements they are estimated from. It is also worth noting that although both productivity indices use models to adjust for the effects primarily of age (Site Index) or age and stocking (300 Index), these adjustment models are not themselves influenced by the independent variables used for developing the 300 Index and Site Index productivity models. In conclusion, these results highlight the utility of thematic spatial layers as driving variables in the development of productivity models. The consistency of key driving variables with those previously reported, for P. radiata, strongly supports the use of spatial layers to develop productivity models. Models developed from these layers are likely to improve in the future as more variables, such as soil chemical properties, become available. This approach greatly reduces model development cost. The development of detailed maps of 300 Index and Site Index from these models will provide invaluable decision support for determining optimal sites for species such as P. radiata.

Acknowledgements We gratefully thank Carolyn Andersen and Mark Dean for their assistance in obtaining permission to use and extract PSP data. We are also indebted to the numerous forestry companies and private owners for supporting this research. David Palmer acknowledges the Foundation for

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Research Science and Technology and the University of Waikato (Doctoral Scholarship) for funding. Barbara Ho¨ck acknowledges Foundation for Research Science and Technology funding (protecting and enhancing the environment through forestry CO4X0304). We are also grateful for useful comments made by two anonymous referees.

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Can. J. For. Res. Vol. 40, 2010 SAS Institute Inc. 2000. SAS/STAT user’s guide: version 8. Vols. 1, 2, and 3. SAS Institute Inc., Cary, N.C. Schoenholtz, S.H., Van Miegroet, H., and Burger, J.A. 2000. A review of chemical and physical properties as indicators of forest soil quality: challenges and opportunities. For. Ecol. Manag. 138(1–3): 335–356. doi:10.1016/S0378-1127(00)00423-0. Tait, A., Henderson, R., Turner, R., and Zheng, X. 2006. Thin plate smoothing spline interpolation of daily rainfall for New Zealand using a climatological rainfall surface. Int. J. Climatol. 26(14): 2097–2115. doi:10.1002/joc.1350. Truman, R., Humphreys, F.R., and Lambert, M.J. 1983. Prediction of site index for Pinus radiata at Mullions Range State Forest, New South Wales. Aust. For. Res. 13: 207–215. Watt, M.S., Whitehead, D., Richardson, B., Mason, E.G., and Leckie, A.L. 2003. Modelling the influence of weed competition on the growth of young Pinus radiata at a dryland site. For. Ecol. Manag. 178: 271–286. Watt, M.S., Kimberley, M.O., Richardson, B., Whitehead, D., and Mason, E.G. 2004. Testing a juvenile tree growth model sensitive to competition from weeds using Pinus radiata at two contrasting sites in New Zealand. Can. J. For. Res. 34(10): 1985– 1992. doi:10.1139/X04-072. Watt, M.S., Coker, G., Clinton, P.W., Davis, M., Parfitt, R., Simcock, R., Garrett, L., Payn, T., Richardson, B., and Dunningham, A. 2005. Defining sustainability of plantation forests through identification of site quality indicators influencing productivity — a national view for New Zealand. For. Ecol. Manag. 216(1–3): 51–63. doi:10.1016/j.foreco.2005.05.064. Watt, M.S., Davis, M.R., Clinton, P.W., Coker, G., Ross, C., Dando, J., Parfitt, R.L., and Simcock, R. 2008. Identification of key soil indicators influencing plantation productivity and sustainability across a national trial series in New Zealand. For. Ecol. Manag. 256(1–2): 180–190. doi:10.1016/j.foreco.2008.04.024. Watt, M.S., Kimberley, M.O., Richardson, B., Schou, W., and Gous, S.F. 2009a. Vegetation manager-a decision support system developed to optimise forest vegetation management across an environmental gradient. Proceedings of the IUFRO International Forest Biosecurity Conference, 16–20 March 2009, Rotorua, New Zealand. New Zealand Forest Research Institute Limited, Rotorua, New Zealand. pp. 110–113. Watt, M.S., Palmer, D.J., Dungey, H., and Kimberley, M.O. 2009b. Predicting the spatial distribution of Cupressus lusitanica productivity in New Zealand. For. Ecol. Manag. 258(3): 217–223. doi:10.1016/j.foreco.2009.04.003. Whitehead, D., Kelliher, F.M., Frampton, C.M., and Godfrey, M.J.S. 1994. Seasonal development of leaf area in a young, widely spaced Pinus radiata D. Don stand. Tree Physiol. 14(7– 9): 1019–1038. PMID:14967667. Whitehead, D., Leathwick, J.R., and Walcroft, A.S. 2001. Modeling annual carbon uptake for the indigenous forests of New Zealand. For. Sci. 47(1): 9–19.

Appendix A Appendix continued on following page.

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Table A1. Parameter values used for the described 300 Index and Site Index models. Term Intercept Degree of ground frost in autumn (Degree of ground frost in autumn)2 Mean annual air temperature (Mean annual air temperature)2 Mean annual fractional available root-zone water storage (Mean annual fractional available root-zone water storage)2 Mean annual windspeed Length and slope factor (Length and slope factor)2 LENZ (level 1)

Major soil parent material

Vegetation classification

Foliar nitrogen

Soil order

Category (for categorical variables only)

300 Index –29.74 0.1478 –0.1026

1.350 –0.0079

Central hill country Western and southern North Island lowlands Western South Island foothills and Stewart Island Central mountains Central sandy recent soils Central well-drained recent soils Central dry lowlands Central dry foothills Eastern South Island plains Southeastern hill country and mountains Southern lowlands Northern lowlands Northern hill country Northern recent soils Dune sand Loess Volcanic rocks: loose basaltic/ultramafic rocks Volcanic rocks: extremely weak to weak Volcanic rocks: weak to extremely strong Alluvium, till, colluvium, soft sediments Sedimentary rocks: limestone and marble Older sedimentary rocks: pre-Tertiary and schist Sedimentary rocks: Tertiary and younger Intrusive rocks, including gneiss Pasture Exotic forest Scrubland Other Very low Low Medium High Brown Melanic Gley Allophanic Pumice Organic Pallic

0.2737 1.587 2.727 1.300 1.915 5.012 3.788 1.734 3.353 3.560 7.144 1.481 1.894 0 –5.109 –0.9933 –0.9598 0.6848 –1.850 –2.342 –2.833 –2.357 –2.274 0 4.016 0.4701 0.5596 0 –2.424 –3.570 –0.3334 0 0.6324 0.5378 0.9660 3.760 1.479 0.0276 0.6035

Site Index –94.08

13.41 –0.4978 0.9913 –0.00587 –0.2854 0.2153 –0.00513 –1.358 0.8731 –1.178 0.0160 –0.922 –0.0392 –2.482 –1.338 –0.5937 2.595 4.673 –1.144 –0.5211 0 –5.896 –2.241 0.7809 0.2069 –3.855 –2.427 –2.573 –2.345 –3.308 0

.

Note: Shown are values used for both continuous and categorical variables.

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