The ice cover on small and large lakes: scaling analysis and mathematical modelling

Lake ice cover is described by its thickness, temperature, stratigraphy and overlying snow layer. When the ratio of ice thickness to lake size is above ～10^?5, the ice cover is stable; otherwise, mechanical forcing breaks the ice cover, and ice drifting takes place with lead-opening and ridging. This transition enables a convenient distinction to be made between small and large lakes. The evolution of the ice cover on small lakes is solved by a wholly thermodynamic model, but a coupled mechanical–thermodynamic model is needed for large lakes. The latter indicates a wide distribution of ice thickness, and frazil ice may be formed in openings. Ecological conditions in large lakes differ markedly from those in small lakes because vertical mixing and oxygen renewal may take place during the ice season, and the euphotic zone penetrates well into the water column in thin ice regions. Mesoscale sea ice models are applicable to large lakes with only minor tuning of the key parameters. These model systems are presented and analysed using Lake Peipsi as an example. As the climate changes, the transition size between small and large lake ice cover will change.     

The dynamic evolution of the power exponent in a universal growth model of tumors

We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo after an initial exponential growth phase. In contrast to the assumption of a fixed power exponent p (assumed by West et al. to be equal to 3/4), we propose in this paper a dynamic evolution of p, using experimental data from the cancer literature. In analogy with results obtained by applying scaling laws to the study of fragmentation of solids, the dynamic behaviour of p is related to the evolution of the fractal topology of neoplastic vascular systems. Our model might be applied for diagnostic purposes to mark the emergence of an efficient neo-angiogenetic structure if the results of our in silico experiments are confirmed by clinical observations.     

结构函数的标度律

分析了GOY模型结构函数的标度律．指出结构函数的振荡涨落导致非线性标度律。     

Scaling exponents and rank-size distributions as indicators of landscape character and change

I used a rank-size distribution model and its associated scaling exponents to describe the organization of Yellowstone National Park before and after the 1988 fire season using the statistical distribution of patch sizes. Rank-size distributions indicate the relative effect of patch size on landscape structure, and whether the size of patches differs from what is expected from the model. Scaling exponents describe the distribution and magnitude of change in patch size, and may indicate the effect of fire on ecological processes including succession and resource distribution. The results of my analysis suggest that fires during the 1988 fire-season substantially affected the distribution of patch size in Yellowstone National Park, where large patches have a disproportionate effect on landscape character. For example, patches ≥100 ha occupy a majority of the area even though they represent a minority number of patches in the landscape. Additionally, rank-size distributions indicate fractal properties existed over several orders of magnitude, signifying that processes acting at one level of the landscape hierarchy may be acting similarly at other levels of the hierarchy. This has implications for linking the scaling properties of patch size with other scale-based phenomena including allometry. Finally, the distribution of patch sizes in conjunction with fire-return interval may be useful in assessing the likelihood of landscape-level disturbances.     

The Visually Mediated Escape Response in Fish: Predicting Prey Responsiveness and the Locomotor Behaviour of Predators and Prey

The outcome of predator-prey encounters is determined by a number of factors related to the locomotor and sensory performance of the animals. Escape responses can be triggered visually, i.e. by the magnifying retinal image of an approaching object (i.e. a predator), called the looming effect, and calculated as the rate of change of the angle subtended by the predator frontal profile as seen by the prey. A threshold of looming angle (ALT, the Apparent Looming Threshold) determines the reaction distance of a startled fish, which is proportional to the attack speed of the predator and its apparent frontal profile. Optimal tactics for predator attacks as well as consideration on their functional morphology are discussed in relation to ALT. Predator optimal attack speeds depend on predator morphology as well as the prey ALT. Predictions on the scaling of ALT suggest that ALT may increase (i.e. implying a decrease in reaction distance) with prey size in cases in which predator attack speeds are high (i.e. > 4 L/s in a 1-m long predator), while it may be relatively independent of prey size when predators attack at lower speeds. The issue of scaling of ALT is discussed using examples from field and laboratory studies. While the timing of the escape is a crucial issue for avoiding being preyed upon, the direction of escape manoeuvres may also determine the success of the escape. A simple theoretical framework for optimal escape trajectories is presented here and compared with existing data on escape trajectories of fish reacting to startling stimuli.     

Combining stratification and up-scaling method-block cokriging with remote sensing imagery for sampling and mapping an erosion cover factor

When a ground and vegetation cover factor related to soil erosion is mapped with the aid of remotely sensed data, a cost-efficient sample design to collect ground data and to obtain an accurate map is required. However, the supports used to collect ground data are often smaller than the desirable pixels used for mapping, which leads to complexity in developing procedures for sample design and mapping. For these purposes, a sampling and mapping method was developed by integrating stratification and an up-scaling method in geostatistics — block cokriging with Landsat Thematic Mapper imagery. This method is based on spatial correlation and stratified sampling. It scales up not only the ground sample data but also the uncertainties associated with the data aggregation from smaller supports to larger pixels or blocks. This method uses the advantages of both stratification and block cokriging variance-based sample design, which leads to sample designs with variable grid spacing, and thus significantly increases the unit cost-efficiency of sample data in sampling and mapping. This outcome was verified by the results of this study.     

Support vector machine-based open crop model (SBOCM): Case of rice production in China

Existing crop models produce unsatisfactory simulation results and are operationally complicated. The present study, however, demonstrated the unique advantages of statistical crop models for large-scale simulation. Using rice as the research crop, a support vector machine-based open crop model (SBOCM) was developed by integrating developmental stage and yield prediction models. Basic geographical information obtained by surface weather observation stations in China and the 1:1000000 soil database published by the Chinese Academy of Sciences were used. Based on the principle of scale compatibility of modeling data, an open reading frame was designed for the dynamic daily input of meteorological data and output of rice development and yield records. This was used to generate rice developmental stage and yield prediction models, which were integrated into the SBOCM system. The parameters, methods, error resources, and other factors were analyzed. Although not a crop physiology simulation model, the proposed SBOCM can be used for perennial simulation and one-year rice predictions within certain scale ranges. It is convenient for data acquisition, regionally applicable, parametrically simple, and effective for multi-scale factor integration. It has the potential for future integration with extensive social and economic factors to improve the prediction accuracy and practicability.