A new method of calculating crown projection area and its comparative accuracy with conventional calculations for asymmetric tree crowns

This paper introduces a new method of calculating crown projection area(CPA),the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and integration.This novel method and other four existing methods of calculating CPA were compared using detailed crown radius measurements from 30 tall trees of Eucalyptus pilularis variable in crown size,shape,and asymmetry.The four existing methods included the polygonal approach and three ways of calculating CPA as the area of a circle using the arithmetic,geometric and quadratic mean radius.Comparisons were made across a sequence of eight non-consecutive numbers(from 2 to 16)of measured crown radii for each tree over the range of crown asymmetry of the 30 trees through generalized linear models and multiple comparisons of means.The sequence covered the range of the number of crown radii measured for calculating the CPA of a tree in the literature.A crown asymmetry index within the unit interval was calculated for each tree to serve as a normative measure.With a slight overestimation of 2.2%on average and an overall mean error size of 7.9%across the numbers of crown radii that were compared,our new method was the least biased and most accurate.Calculating CPA as a circle using the quadratic mean crown radius was the second best,which had an average overestimation of 4.5%and overall mean error size of 8.8%.These two methods remained by and large unbiased as crown asymmetry increased,while the other three methods showed larger bias of underestimation.For the conventional method of using the arithmetic mean crown radius to calculate CPA as a circle,bias correction factors were developed as a function of crown asymmetry index to delineate the increasing magnitude of bias associated with greater degrees of crown asymmetry.This study reveals and demonstrates such relationships between the accuracy of CPA calculations and crown asymmetry and will help increase awareness among researchers and practitioners on the existence of bias in their CPA calculations and for the need to use an unbiased method in the future.Our new method is recommended for calculating CPA where at least four crown radius measurements per tree are available because that is the minimum number required for its use.

An Assessment of the Within-Year Seasonality in the Loan Loss Provisioning Behavior of European Banks

This study aims at assessing whether a significant within-year seasonality exists in the loan loss provisioning behavior of European listed banks observed in the period from 2004 to 2013. Since the accuracy of auditing processes and the level of disclosure requirements in financial reports differ among quarters, during the year, banks may have a leeway to underestimate and postpone the complete provisioning of loan losses in the less regulated and less audited quarters. We hypothesize that those differences are relevant factors which determine non-lower or significantly higher average levels of loan loss provisions in the half-yearly and especially in the annual financial reports than in the interim management statements disclosed in the first and the third quarters of the year. We also investigate the impact of the recent financial crisis and develop a special analysis for the ltalian banks＇ case. The empirical results support our hypotheses, suggesting that, in some cases, a convergence among quarterly levels of auditing processes and disclosure requirements may be needed. Our work contributes to the existing literature by providing additional evidences and considerations on the within-year seasonality in the loan loss provisioning behavior of European listed banks observed in the last decade.