Belowground biomass functions and expansion factors in high elevation Norway spruce

Biomass allocation to above- and belowground compartments in trees is thought to be affected by growth conditions. To assess the strength of such influences, we sampled six Norway spruce forest stands growing at higher altitudes. Within these stands, we randomly selected a total of 77 Norway spruce trees and measured volume and biomass of stem, above- and belowground stump and all roots over 0.5 cm diameter. A comparison of our observations with models parameterised for lower altitudes shows that models developed for specific conditions may be applicable to other locations. Using our observations, we developed biomass functions (BF) and biomass conversion and expansion factors (BCEF) linking belowground biomass to stem parameters. While both BF and BCEF are accurate in belowground biomass predictions, using BCEF appears more promising as such factors can be readily used with existing forest inventory data to obtain estimates of belowground biomass stock. As an example, we show how BF and BCEF developed for individual trees can be used to estimate belowground biomass at the stand level. In combination with existing aboveground models, our observations can be used to quantify total standing biomass of high altitude Norway spruce stands.

Self-tuning property of state-space self tuners

The basic assumption from implicit self-tuning theory is that, for self tuning to occur, the control input obtained from the estimated system model converges to the value whic would be obtained if the system parameters were known. As as direct result of this, only certain control strategies are acceptable. Here a general rule for the self-tuning property of pole-placement self tuners is obtained, and previous strategies are shown to be special cases of this.

Wiener System identification using B-spline functions with De Boor recursion

A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.