Wet Canopy Evaporation Rate of Three Stands in Western Sichuan, China

The wet canopy evaporation rate (Er) was calculated by Penman-Monteith combination model based on three assumptions and with meteorological variables 2 m above the canopy in three stands, dominated by spruce (SF), fir (FF) and birch (BF) trees, respectively, in the subalpine forests in western Sichuan, China over a growing season. The total amount of the E was 44.5 mm for SF, 88.5 mm for FF and 57.8 mm for BF, accounting for 9.2%, 16.6% and 10.2% of the gross rainfall, respectively, in the measuring period. There was the highest average monthly Er and percentage of E to gross rainfall for FF compared with SF and BF.Mean Er was 0.097 mm h^-1 (ranging from 0.028 to0.487 mm h^-1), 0.242 mm h^-1 (from 0.068 to 0.711 mm h^-1) and 0.149 mm h^-1 (from 0.060 to 0.576 mm h^-1) for SF, FF and BF, respectively. The highest average monthly Er occurred in June was 0.120 mm h^-1 for SF, 0.317 mm h^-1for FF and 0.169 mm h^-1 for BF, and the lowest value in October was 0.083 mm h^-1 for SF, 0.187 mm h^-1 for FF and 0.101 mm h^-1 for BF, respectively. The averages of Er from 8:00 to16:00 were significantly higher than those from 0:00 to 8:00 and from 16:00 to 0:00 for the three stands. The marked daily and monthly differences of Er were contributable to the variations of solar radiation, air temperature and relative humidity above the canopy.     

A chain regularization method for the few-body problem

A regularization method for integrating the equations of motion of small N-body systems is discussed. We select a chain of interparticle vectors in such a way that the critical interactions requiring regularization are included in the chain. The equations of motion for the chain vectors are subsequently regularized using the KS-variables and a time transformation. The method has been formulated for any number of bodies, but the most important application appears to be in the four-body problem which is therefore discussed in detail.     

Evolution of the Archean crust in Finland

An Archean age for Finnish rocks in the range 2500–3000 Ma has been determined north of the NW-striking Ladoga—Raahe shear belt. The Archean may be divided into two main units: the granitoid association and the greenstone-belt association. The complex is characterized by stockwork tectonics. The granitoid association forms the basement infrastructure and the greenston-belt association forms the suprastructure which is present in synforms between granitoid diapirs. The infrastructure has been subjected to ultrametamorphism, and the second and third generation palingenetic magmas so formed have intruded the suprastructure. The granitoid association contains widespread migmatized relicts of the greenstone-belt association, indicating that the latter originally covered much larger areas, but the granitoids are also thought to be partly transformed primitive ensialic crust on which rocks of the greenstone-belt association were deposited. The Archean rocks have been deformed in at least four subsequent phases, of which part developed in Proterozoic time. The youngest deformation is the overthrust of the granulite belt of Lapland towards SSW. NWSE striking transcurrent faults played a major role in Proterozoic time and affected cratonized Archean crust. On the whole the greenstone belts in eastern and northern Finland form a NNW-trending zone 750 km long. On a geochemical basis the volcanic rocks of the greenstone belts can be divided into two groups: tholeiites with a low potassium content and extremely low aluminium content and a calc-alkalic group with some alkalic affinities.     

Anisotropic gravitational radiation in the problems of three and four black holes

The momentum flux in merging binary black holes is rediscussed using the actual orbit integrations. The terminal velocity acquired by the centre of mass of the system is found to be greater than the estimate of Fitchett (1983) by a factor of 1.45. The actual value in km s^–1 is still uncertain but may be as high as 2000 km s^–1. The centre of mass velocity kick at a black hole merger is incorporated in the orbit integration of few black hole systems. Assuming that the symmetric break-up mode of such systems corresponds to the classical double radio sources, we determine that the centre of mass velocity kick can be about 1000 km s^–1 at most.     

Simple derivation of Symplectic Integrators with First Order Correctors

In this paper we consider almost integrable systems for which we show that there is a direct connection between symplectic methods and conventional numerical integration schemes. This enables us to construct several symplectic schemes of varying order. We further show that the symplectic correctors, which formally remove all errors of first order in the perturbation, are directly related to the Euler—McLaurin summation formula. Thus we can construct correctors for these higher order symplectic schemes. Using this formalism we derive the Wisdom—Holman midpoint scheme with corrector and correctors for higher order schemes. We then show that for the same amount of computation we can devise a scheme which is of order O(h ⁶)+(² h ²), where is the order of perturbation and h the stepsize. Inclusion of a modified potential further reduces the error to O(h ⁶)+(² h ⁴).This revised version was published online in October 2005 with corrections to the Cover Date.     

Changed thinning regimes may increase carbon stock under climate change: A case study from a Finnish boreal forest

A physiological growth and yield model was applied for assessing the effects of forest management and climate change on the carbon (C) stocks in a forest management unit located in Finland. The aim was to outline an appropriate management strategy with regard to C stock in the ecosystem (C in trees and C in soil) and C in harvested timber. Simulations covered 100 years using three climate scenarios (current climate, ECHAM4 and HadCM2), five thinning regimes (based on current forest management recommendations for Finland) and one unthinned. Simulations were undertaken with ground true stand inventory data (1451 hectares) representing Scots pine (Pinus sylvestris), Norway spruce (Picea abies) and silver birch (Betula pendula) stands. Regardless of the climate scenario, it was found that shifting from current practices to thinning regimes that allowed higher stocking of trees resulted in an increase of up to 11% in C in the forest ecosystem. It also increased the C in the timber yield by up to 14%. Compared to current climatic conditions, the mean increase over the thinning regimes in the total C stock in the forest ecosystem due to the climate change was a maximum of 1%; but the mean increase in total C in timber yield over thinning regimes was a maximum of 12%.     

Model Computations on the Effects of Elevating Temperature and Atmospheric CO2 on the Regeneration of Scots Pine at the Timber Line in Finland

Based on model computations, the regeneration of Scots pine (Pinus sylvestris L.) was studied at the northern timber line in Finland (70°N) in relation to elevating temperature and atmospheric CO₂. If a transient increase of 4°C was assumed during the next 100 years, the length of growing season increased from the current 110–120 days to 150–160 days. This was associated with ca. 5°C increase in the soil temperature over June–August with larger variability in temperature and deeper freezing of the soil due to the reduced depth and duration of the snow cover. At the same time, the moisture content of the surface soil decreased ca. 10% and was more variable, due to less infiltration of water into the soil as a consequence of the enhanced evapotranspiration and deeper freezing of the soil. The temperature elevation alone, or combined with elevating CO₂, increased flowering and the subsequent seed crop of Scots pine with a decrease in the frequency of zero crops. In both cases, temperature elevation substantially increased the success of regeneration in terms of the number of seedlings produced after each seed crop. The increasing number of mature seeds was mainly responsible for the enhanced regeneration, but increasing soil temperature also increased the success of regeneration. The soil moisture was seldom limited for seed germination. In terms of the density of seedling stands, and the height and diameter growth of the seedlings, the establishment of a seedling stand was substantially improved under the combined elevation of temperature and CO₂ in such a way that the temperature increased the number of mature seeds and enhanced germination of seeds and CO₂ increased seedling growth. Even under the changing climatic conditions, however, the growth of the seedling stands was slow, which indicated that the northward advance of the timber line would probably be very slow, even though regeneration was no longer a limiting factor.     

Non-canonical perturbations in symplectic integration

The inclusion of non-canonical perturbations in symplectic integration schemes has been discussed. A rigorous derivation of an analog for theWisdom–Holman (1991) method, such that velocity dependent forces can be included, has been outlined. This is done both by using the δfunction formalism and also by means of formal Hamiltonization. Application to the relativistic corrections in Solar System integrations is discussed as an example. Numerical experiments confirm the usefulness of the method. This revised version was published online in July 2006 with corrections to the Cover Date.     

Carbon balance in the forest sector in Finland during 1990–2039

In this study we estimated the amount of carbon (C) stored in the forest growing stock and in wood-based products, and the C-sequestration capacity of the forest sector in Finland. Comparison of different management and utilization options for forest resources over the period 1990-2039 indicates that C is stored more efficiently in standing timber than in wood-based products. This implies that an appropriate increase in the length of the rotation in forestry could be optimal for balancing the needs of forest resources for C sequestration and timber production. Increased use of wood, based on sustainable use of forest resources, to substitute for fossil fuels and materials, could decrease the overall C emissions. Release of sequestered C back to the atmosphere can be delayed by prolonging product lifespans, by increasing recycling, or by disposing of discarded products in landfills. To delay C release, and affect the C balance, however, these changes should be substantial.In 1990, the net C balance of the growing stemwood stock was 5.5 Tg C/a, which increased to 16.3 Tg C/a by 2039 if in the future the use of wood would be at the level of the late 1980s. Increased use of wood resulted in a balance of 6.6 Tg C/a or -0.2 Tg C/a, depending on the extent of the use of wood. The average C balance in wood products for the whole period was 3.9, 5.6 or 6.6 Tg C/a, respectively. Changes in production capacity, and consideration of timber and product import and export decreased the average balance from 6.6 Tg C/a to 0.9–1.3 Tg C/a. By comparison, emission from the use of fossil fuels in 1990 C was 14.5 Tg C/a.     

Explicit Symplectic Algorithms For Time‐Transformed Hamiltonians

By Hamiltonian manipulation we demonstrate the existence of separable time‐transformed Hamiltonians in the extended phase‐space. Due to separability explicit symplectic methods are available for the solution of the equations of motion. If the simple leapfrog integrator is used, in case of two‐body motion, the method produces an exact Keplerian ellipse in which only the time‐coordinate has an error. Numerical tests show that even the rectilinear N‐body problem is feasible using only the leapfrog integrator. In practical terms the method cannot compete with regularized codes, but may provide new directions for studies of symplectic N‐body integration. This revised version was published online in July 2006 with corrections to the Cover Date.