Calibrating predicted tree diameter distributions in Catalonia, Spain

Several probability density functions have been used in describing the diameter distributions of forest stands. In a case where both the stand basal area and number of stems per hectare are assessed, the fitted or predicted distribution is scaled using only one of these variables, with the result that the distribution often gives incorrect values for the other variable. Using a distribution that provides incorrect values for known characteristics means wasting information. Calibrating the distribution so that it is compatible with the additional information on stand characteristics is a way to avoid such wasting. This study examined the effect of calibration on the accuracy of the predicted diameter distributions of the main tree species of Catalonia. The distributions were calibrated with and without considering the prediction errors of the frequencies of diameter classes. When prediction errors were assumed, the calibration was done with and without making allowance for estimation errors in the stand level calibration variables. Calibrated distributions were more accurate than non-calibrated in terms of sums of different powers of diameters. The set of calibration variables that gave the most accurate results included six stand variables: number of trees per hectare, stand basal area, basal-area-weighted mean diameter, non-weighted mean diameter, median diameter, and basal area median diameter. Of the tested three-variable combinations the best was: number of trees per hectare, stand basal area, and basal-area-weighted mean diameter. Means were more useful calibration variables than medians.

[1]  M. Tomé,et al.  Growth and yield model for Pinus halepensis Mill. in Catalonia, north-east Spain , 2004 .

[2]  Timo Pukkala,et al.  Optimising the Management of a Heterogeneous Stand , 2005 .

[3]  C. Särndal,et al.  Calibration Estimators in Survey Sampling , 1992 .

[4]  Matti Maltamo,et al.  Comparing basal area diameter distributions estimated by tree species and for the entire growing stock in a mixed stand. , 1997 .

[5]  T. R. Dell,et al.  Quantifying Diameter Distributions with the Weibull Function , 1973 .

[6]  Timo Pukkala,et al.  Comparison of beta, Johnson’s SB, Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain) , 2007, European Journal of Forest Research.

[7]  M. Maltamo,et al.  Calibrating predicted diameter distribution with additional information in growth and yield predictions , 2003 .

[8]  Timo Pukkala,et al.  Using past growth to improve individual-tree diameter growth models for uneven-aged mixtures of Pinus sylvestris L. and Pinus nigra Arn. in Catalonia, north-east Spain , 2004 .

[9]  Annika Kangas,et al.  Calibrating Predicted Diameter Distribution with Additional Information , 2000, Forest Science.

[10]  Werner Cajanus.  Ueber die Entwicklung gleichaltriger Waldbestände , 1914 .

[11]  M. Maltamo,et al.  Comparison of percentile based prediction methods and the Weibull distribution in describing the diameter distribution of heterogeneous Scots pine stands , 2000 .

[12]  M. Maltamo,et al.  Comparison of beta and weibull functions for modelling basal area diameter distribution in stands of pinus sylvestris and picea abies , 1995 .

[13]  Arto Haara.  Kasvuennusteiden luotettavuuden selvittäminen knn-menetelmällä ja monitavoiteoptimoinnilla , 1970 .

[14]  T. Pukkala,et al.  Modelling the diameter distribution of Pinus sylvestris, Pinus nigra and Pinus halepensis forest stands in Catalonia using the truncated Weibull function , 2006 .

[15]  Paul A. Murphy,et al.  Characterizing diameter distributions with modified data types and forms of the Weibull distribution , 1986 .

[16]  T. Pukkala,et al.  Individual-tree growth and mortality models for Scots pine (Pinus sylvestris L.) in north-east Spain , 2003 .

[17]  Growth and yield model for uneven-aged mixtures of Pinus sylvestris L. and Pinus nigra Arn. in Catalonia, north-east Spain , 2004 .

[18]  J. Grau,et al.  Elaboración de un modelo preliminar de calidad de sitio y modelos preliminares de mortalidad y crecimiento de árbol individual para Pinus nigra Arn. en Cataluña , 2003 .

[19]  M. Palahí,et al.  Preliminary site index model and individual-tree growth and mortality models for black pine ( Pinus nigra Arn . ) in Catalonia ( Spain ) , 2003 .