Cork oak woodlands, or montados, represent 21% of the Portuguese forest area. Despite the importance of this tree species, the first growth model, SUBER, dates from 1997. The model combines forest inventory data gathered over the years, published results and empirical knowledge about montados with the aim of developing the most suitable methodology to simulate the growth of this species for management purposes. Along the way, several research gaps were identified. Due to the particular features of cork oaks the development of a growth model capable of predicting cork production and cork quality beside wood production adds complexity to the modelling process. The SUBER model was developed as an individual tree level empirical model because it coped better with the common uneven-aged structure and the heterogeneous distribution of trees within the stands. From 1997 until 2012, the Forest Research Centre (CEF), University of Lisbon, has been working towards the improvement of the SUBER model in cooperation with several forest owners associations. This research is based on the establishment and monitoring of permanent plots and trials that have allowed gathering a considerable amount of data on trees and cork. The data is stored in the SUBERDATA database, under the management of ForChange research group.

The present version of the model, SUBER 5.0, maintains the initial structure of the primordial versions described by Tomé et al. (1998, 1999, 2004, 2005) and integrates modules for data imputation, the  initialization of stands, stand regeneration, growth prediction, additional calculus and thinning simulation:

Prediction module (tree):

    • Site index curves (Sánchez-González et al. 2005)
    • Diameter growth (Tomé et al. 2006)
    • Cork growth (Almeida et al. 2010)
    • Evolution of cork growth index (Tomé et al. 1998)

Calculus module:

    • Height-diameter curves (Paulo et al. 2011)
    • Mature cork weight, for any cork age, (Paulo et al. 2010)
    • Virgin cork weight in virgin trees (Paulo et al. 2014)
    • Under-bark diameter in virgin trees (Paulo et al. 2014)
    • Crown diameter (Paulo et al. 2015a)
    • Stem volume up to a top diameter of 7.5 cm (Paulo e Tomé 2006)
    • Total biomass and biomass by tree components (Paulo e Tomé 2006).

Stand initialization module:

    • Site index prediction as a function of edafo-climatic factors (Paulo et al. 2015b)
    • The initialization of young stands takes the following unpublished procedure: 1) simulation of tree height distribution when dominant height reaches 3 m; 2) prediction of height growth before the tree reaches 3 m; 3) estimation of tree diameter based on tree height and stand density.

Regeneration module:

    • Stand regeneration can be achieved through planting or protection of natural regeneration by a process similar to the one for young stands through a user-defined density at planting.

Thinning module:

    • In SUBER 5.0 thinning is simulated using an equation developed by Paulo and Tomé (2005) which allows trees to be thinned depending on a combination of factors: the trees’ relative size, the thinning intensity and its cork quality. Thinning from below is considered.
    • The model includes two alternative thinning algorithms for even- and uneven-aged stands. In the even-aged one, the stand is considered as a whole with trees being thinned according to their thinning probability until the desired percent cover is met. In the uneven-aged thinning algorithm, trees are thinned by dimeter class to guarantee the same percent cover in all classes (inverted J shape diameter distribution). 

Data inputation module:

    • The main goal of this algorithm is to complete the missing inventory data. The compulsory information is the stand location (municipality), the plot size and the diameter of trees. The remaining variables can be simulates by the model. However, the more accurate the input the more reliable the simulation output will be. For example, for even-aged stands, if dominant height is measured then site index will be determined with better precision. In case it is not, site index will be estimated using the models developed by Paulo et al. (2015). Another example concerns cork quality, if no quality inventory has been carried out, the model will assign each tree the average cork growth index and the average quality observed for the corresponding municipality based on the data in the SUBERDATA database.


Almeida A, Tomé J, Tomé M, 2010. Development of a system to predict the evolution of individual tree mature cork caliber over time. Forest Ecology and Management 260(8): 1303-1314.

Paulo JA, Tomé M, 2005. Modelo probabilístico independente da distância para implementação de desbastes em povoamentos regulares de sobreiro In: Silva R, Páscoa F 2005 (Eds) Proceedings do 5º Congresso Florestal Nacional – A Floresta e as Gentes. Instituto Politécnico de Viseu de 16 a 19 de Maio de 2005 (

Paulo JA, Tomé M, 2006. Equações para estimação do volume e biomassa de duas espécies de carvalhos: Quercus suber e Quercus ilex. Publicações GIMREF - RC1/2006. Departamento de Engenharia Florestal, Instituto Superior de Agronomia, Lisboa.

Paulo JA, Tomé M, 2010. Predicting mature cork biomass with t years of growth based in one measurement taken at any other age. Forest Ecology and Management 259: 1993-2005. DOI:10.1016/j.foreco.2010.02.010.

Paulo JA, Tomé J, Tomé M, 2011 Nonlinear fixed and random generalized height-diameter models for Portuguese cork oak stands. Annals of Forest Science 68(2): 295-309. DOI: 10.1007/s13595-011-0041-y.

Paulo JA, 2011. Desenvolvimento de um sistema para apoio à gestão sustentável de montados de sobro. PhD thesis, Universidade Técnica de Lisboa, Instituto Superior de Agronomia, Lisboa, Portugal.

Paulo JA, Tomé M, 2014. Estimativa das produções de cortiça virgem resultantes das operações de desbastes e desboia em montados de sobro em fase juvenil. Silva Lusitana 22(1): 29-42.

Paulo JA, Faias SP, Ventura-Giroux C, Tomé M, 2015a. Estimation of stand crown cover using a generalized crown diameter model: application for the analysis of Portuguese cork oak stands stocking evolution. iForest.

Paulo JA, Palma JHN, Gomes A, Faias SP, Tomé J, Tomé M, 2015b. Predicting site index from climate and soil variables for cork oak (Quercus suber L.) stands in Portugal. New Forests:1-15 doi:10.1007/s11056-014-9462-4.

Sánchez-González M, Tomé M, Montero G, 2005. Modelling height and diameter growth of dominant cork oak trees in Spain. Annals of Forest Science 62 (7), pp.633-643. 633. doi:10.1051/forest:2005065

Tomé J, Tomé M, Barreiro S, Paulo JA, 2006. Age-independent difference equations for modelling tree and stand growth. Can J Forest Res 36:1621-1630. doi:10.1139/x06-065

Tomé M, Coelho MB, Lopes F, Pereira H, 1998. Modelo de produção para o montado de sobro em Portugal. In: H Pereira (Ed), Cork Oak and Cork, European conference on cork-oak and cork, Lisboa, Portugal, pp. 22-46.

Tomé M, Coelho MB, Pereira H, Lopes F, 1999. A management oriented growth and yield model for cork oak stands in Portugal. In: A Amaro, M Tomé (Eds), Empirical and Process-Based Models for Forest Tree and Stand Growth Simulation, Edições Salamandra, Novas Tecnologias, Lisboa, Portugal, pp. 271-289.

Tomé M, 2004. Modelo de crescimento e produção para a gestão do montado de sobro em Portugal. Projecto POCTI/AGR/35172/99. Relatório Final - Relatório de Execução Material (Volume I). Centro de Estudos Florestais, Instituto Superior de Agronomia, Universidade Técnica de Lisboa, Lisboa, Portugal

Tomé M, 2005. Demonstração da gestão do montado de sobro apoiada em inventário florestal e modelos de crescimento e produção. PROJECTO AGRO nº 81. Relatório Final – Relatório de Execução Material (Volume I). Publicações GIMREF RFP 1/2005. Universidade Técnica de Lisboa. Instituto Superior Agronomia. Centro de Estudos Florestais. Lisboa. 56 pp.

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