# Verification of the Scots Pine (_Pinus sylvestris_ L.) Crown Length Model
## 1 Introduction  
Modeling the structure and dynamics of tree stands is a fundamental element of ecological research and forest management, especially in terms of monitoring tree growth [1, 2], estimating forest resources [3, 4], and assessing forest health [5].  
Stand simulation models have been intensively developed since the beginning of the 1960s [6]. Forest modeling is constantly evolving through improving equations (models) and their adaptation to changing conditions on the local, regional, or continental scale [4, 7, 8]. The forestry sector actively encourages the creation and development of comprehensive forestry databases, such as national forest inventories [9]. After all, accurate forecasts are key to obtaining reliable results.  
At present, there is a wide range of mathematical models that allow for predictions of the growth or survival of trees and stands, taking into account numerous variables [10; 11; 12]. In recent decades, many studies in the field of modeling have focused on the determination of the crown size, i.e., its length [13; 14], width [15; 16; 17; 18; 19], or volume [20].  
The size of the crown significantly correlates with the growth and biomass of other tree parts [21], which is why crown dimensions are used as predictors in growth models [22; 23], biomass models [24; 25], taper and trunk volume models [26], and mortality models [27]. Crown size estimates are often used to infer the increase in the basal area [28], production efficiency [25; 29], as well as wood quality and its value [30; 31]. Detailed studies of the crown are also useful for assessing the density and stability of the stand [32]. Estimation of basic crown dimensions, i.e., its width and length at a tree or stand level, is of key importance in silviculture [33; 34].  
Parameters describing the crown size are significant indicators of its health and vitality [28; 35]. They also allow for predicting the tree's ability to carry out photosynthesis [36], allocate resources [21; 37], and resist environmental stress [38]. Crown length directly affects the tree's ability to absorb carbon dioxide, assimilate light energy, release oxygen, and transpire [37; 39]. It also affects competition for resources [40] and structural interactions with other trees in the forest ecosystem [41].  
Much attention is paid to the development of models that enable precise assessment of the parameters of pine stands growing in different climatic and edaphic conditions [42; 43]. Scots pine is an important forest-forming species in the Central Europe vegetation zone [44]. In Poland, it is the dominant species that currently makes up about 58% of the forest species composition [45]. It is characterized by a wide ecological amplitude and high adaptability, which is crucial in changing climatic conditions.  
The aim of the study was to verify the effectiveness of the allometric model of the Scots pine (_Pinus sylvestris_ L.) crown length using empirical material. The hypothesis is predicated on the assumption that the mean crown lengths in the pine stand, calculated with the model, are commensurate with the actual ones.