Larch is an important species in the boreal forest. Most larch forests are found in the Northern hemisphere, and they are most widely distributed in Siberia and Canada [1]. Of the 16 larch species that exist, European larch (Larix decidua Miller) and Siberian larch (Larix siberica Ledeb) are the main species in Sweden, although Siberian larch is the only indigenous larch species in the country. European larch was introduced in the 18th century [2]. Larch plantations cover only small areas, representing <0.1% of the growing stock [3]. However, in the past 20–30 years, planting hybrid larch on former farmland has become more common.

At the beginning of the 1900s the first larch hybrid (Larix × eurolepis Henry) was found on the Dunkfeld estate in Scotland [4,5]. “Dunkfeld larch” is a hybrid between European larch and Japanese larch (Larix kœmpferi (Lamb.) Carr). This hybrid grows best on soils containing 70%–80% silt and with a pH of 5.0–6.0 [6]. Larch grows more rapidly than Scots pine (Pinus sylvestris L.) and on the same soil types and under the same site conditions [7]. Hybrid larch is a fast growing tree species. It has been shown to grow rapidly during the initial 20–30 years of a rotation. However, studies have shown that hybrid larch stands planted on sites previously occupied by Norway spruce (Picea abies (L.) Karst) infested by root rot (Heterobasidion annosum L.) are severely damaged by the root rot [8]. According to Vollbrecht and Stenlid [8], the main reason is the fast growth of young larch. Timber from larch is expected to be durable when used as an external construction material. At present, timber prices are high, leading to a high timber expectation value for hybrid larch compared with other larch and spruce species in Sweden [7].

Site index curves are widely used by foresters for site quality characterization and to estimate potential productivity [9]. The use of site index curves is based on the fact that there is a correlation between stand height and total volume production [10] and that, on high quality sites, height growth is good [11,12]. Site index has historically been defined as the top height of a stand at a specified age [12]. The top height is the arithmetic mean height of the 100 trees ha⁻¹ with the greatest diameters [9]. Heights of individual trees can be measured easily and the average height growth of the dominant trees is less affected by thinning operations [11,12] and also less affected by stand density [13].

Traditionally, the site index base age selected is lower than the rotation age. However, modern dynamic equations allow for the use of any age as a base or reference age, linking ages directly to heights without converting the actual measurement to a fixed-base-age site index. Dynamic equations must fulfill specific requirements, as described by [14]: (1) they must pass through the origin; (2) the height must equal the site index (SI) at the base age; (3) they must be base age invariant curves; and (4) they must have a separate upper height asymptote. Cieszewski and Bailey [15] presented the Generalized Algebraic Difference Approach method (GADA), which is widely used when constructing index curves: [16,17,18,19,20,21,22,23,24,25].

Reports of site index curves for hybrid larch under Nordic conditions and especially for farmland sites are sparse. Various studies of the growth and yield of larch have been undertaken during the past century. Schober [26] constructed yield tables for European larch. In a study on Siberian larch, Wiksten [27] presented height development curves and yield production for southern and northern Sweden. Siberian larch (50–60 years old) grew at the same rate as Scots pine in southern Sweden but much more rapidly than Scots pine in northern Sweden. Tree volume functions and tables for European and Siberian larch in Finland were developed by Vuokila [28]. Ekö et al. [29] studied the growth pattern of hybrid larch grown in plantations in southern Sweden and produced a yield table. Site index curves for European and Japanese larch in Norway have been reported by Wielgolaski [30] and the growth and yield of hybrid larch have been studied by Ekö et al. [29] who presented a yield table representing the age range 15–45 years. The peak mean annual increment, 13 m³ ha⁻¹ year⁻¹, occurred at the age of 35 years.

As interest in planting and managing hybrid larch on former farmland is increasing in Sweden and there are now plantations older than 20 years, there is a need for site index curves for planning future management and forecasting stand production. Currently, no site index curves for hybrid larch growing under Swedish conditions are available. In the present study, models for the construction of SI curves are tested. The model chosen may be a first step towards prediction of stand volume production.

The objective of this paper is to present SI curves for young hybrid larch growing on former farmland in Sweden. The data originate from 26 localities, ranging in latitude from 55° to 60° N. Soils in the study were grouped into three main physical types and SI is reported in relation to these.

Parameter estimates for models 1–3 were determined on the basis of the data set (Table 2). The coefficient of determination (R²) for all models indicated a good correlation, 98%–99%, between the fitted curves and the estimated values. Further information about the parameter estimations is given in Table 2. The height predictions using Model (3) had the lowest RMSE (0.90 m). The fitted curves for different site indices overlaid onto the observed values (age and height) were examined visually (Figure 2).

Model (3) fitted the data from the sampled trees well and the curves reflected the observed data throughout the entire age interval for which data were available. Height growth decreased with increasing age. The growth curves for models (1) and (2) did not follow the typical decrease in height growth with increasing age. The residuals for the tested models (age vs. residuals and predicted height vs. residuals) were examined visually. Model (3) exhibited the best fit (Figure 3).

Average differences (MRES) between the observed and predicted tree heights were calculated for five age classes: 1–10, 11–20, 21–30, 31–40 and >40 years. Models (1) and (2) underestimated the height for age classes 31–40 and >40 years. Model (3) produced reasonable predictions and its performance was similar for all the age classes examined (Table 3).

There were small differences in ME for the models, −0.03 to 0.07 m, with the lowest value (−0.03) for model (2) (Table 2). MAE ranged between 0.66 and 0.83 m, with model (3) exhibiting the best performance. The accuracy (MAPE) of the tested models ranged between 10.69% and 13.46% with the best value for model (3), see Table 2. In the “leave-one-out-cross-validation” analyses RMSE was the same as for the fitted models (Table 2).

The mean SI (H₂₀) for hybrid larch growing on specific soil types was calculated. The site index means for these soil types were: light clay 13.4 ± 3.0 m, medium clay 13.4 ± 3.3 m and till 13.1 ± 3.7 m. A t-test (LSD) indicated that there were no significant differences between the soil types. The different site locations had no impact on the results of the analysis.

Site index should be assessed in young stands, but it can be difficult to estimate site index with any reliability [49]. In fact, in young stands site index estimates are highly variable and most researchers recommend that site index should be estimated for trees >20 years old, thus avoiding large prediction errors [14,50,51]. Most of the hybrid larches used in this study were planted at the end of the 1980s and the mean age was 23 ± 10 (17–49) years. The height curves for the stands examined represent the site index and the growth of the sampled trees and are related to the site productivity.

When estimating SI, height growth, especially for the tallest trees, should not have been influenced by thinning operations or by extreme competition, which reduces the mean height [9]. However, some of the hybrid larch stands studied had not been thinned even though the stands were dense. In contrast, stem number in some stands was low as a result of damage caused by wildlife. The sampled stems from these stands were carefully examined: the stem should not have had any visible signs of older gnawing damage; the annual ring width should have exhibited a “normal” development without groups of narrow rings followed by broader rings.

The collected data were suitable for constructing curves representing ages up to 50–60 years. Most of the stands were >11 m tall when they were 20 years old. The results of the constructed functions showed that model 3 fitted the data well. But models (1) and (2) had high asymptotes and the approach to get an asymptote parallel to age axis failed. They did not indicate a decrease in height development by increasing age. In the present study RMSE for model (3) was 0.90 m and the “leave-one-out cross validation” value was 0.93 m. In a study on the RMSE level related to the choice of base age, [37] found that RMSE decreased with increasing base age e.g., 1.7 m at <20 years to 0.8 m at 35–40 years. The RMSE value of 0.90 m in the present study seems to be within the range mentioned above.

Available data were restricted with regard to both the number of stands and the variation in stand age. Furthermore there was variation among the unmanaged stands (≈20 years old) with respect to stem number and growth capacity. The main reasons might be a lack of fencing or variable quality fencing, especially during the first five years after planting, and poor or no soil preparation at the site before planting. The tree height within a stand growing on former farmland is more uniform than on forest land. However, the standard deviations (SD) for hybrid larch diameter and height found in the present study show that there are differences between trees within stands (164 ± 73 mm and 14.2 ± 5.5 m respectively) and between the top heights of trees (184 ± 41 mm and 14.3 ± 3.2 m respectively).

There are few reports presenting the results of site index studies of hybrid larch. The site index curves in the present study were compared with a calculated curve for the estimated top heights of hybrid larch growing on farmland in Sweden [7] corresponding to H₂₀ = 16–18 m for the age interval 15–45 years (Figure 4). There are some studies reporting site indexes for Japanese larch. In a Danish study the site “Bon. B” corresponds to H₂₀ = 12 m [52], indicating a faster growth in older stands than found in the present study. In a Norwegian study, with H₄₀ = 26 and 29 m, representing H₂₀ = 14 and 17 m respectively, the curve indicates faster growth than in the present study [30] of Figure 4.

This first Swedish site index, developed for hybrid larch growing on former farmland, can be recommended for practical use. However the proposed site index model should be revised and improved as soon as more data and information are available. When planted on former farmland, hybrid larch has the potential to achieve good early growth. In the present study most stands were growing on sediments (light-medium clay soils). However it is important to undertake appropriate soil treatment to facilitate the establishment of seedlings and to fence the plantation to avoid damage by wildlife.