Growth Probability Distribution Research Articles

Monitoring Waterlogging Damage of Winter Wheat Based on HYDRUS-1D and WOFOST Coupled Model and Assimilated Soil Moisture Data of Remote Sensing

Waterlogging harms winter wheat growth. To enable accurate monitoring of agricultural waterlogging, this paper conducts a winter wheat waterlogging monitoring study using multi-source data in Guzhen County, Anhui Province, China. The hydrological model HYDRUS-1D is coupled with the crop growth model WOFOST, and the Ensemble Kalman Filter is used to assimilate Sentinel-1 inversion soil moisture data. According to the precision and continuity of soil moisture, the damage of winter wheat waterlogging were obtained. The experimental results show that the accuracy of the soil moisture is improved after data assimilation compared with that before data assimilation, and the Nash–Sutcliffe efficiency (NSE) of the simulated soil moisture values at three monitoring sites increased from 0.528, 0.541 and 0.575 to 0.752, 0.692 and 0.731, respectively. A new waterlogging identification criterion has been proposed based on the growth periods and probability distribution of soil moisture. The proportion, calculated from this identification criterion, of the waterlogging wheat farmland in total farmland shows a high correlation with the yield reduction rate. The correlation coefficient of the waterlogging farmland proportion and the yield reduction rate in 11 towns of Guzhen County reaches 0.78. Through the synchronization of geography, agriculture and meteorology, the framework shows great potential in waterlogging monitoring.

Modelling forest ruin due to climate hazards

Abstract. Estimating the risk of forest collapse due to extreme climate events is one of the challenges of adapting to climate change. We adapt a concept from ruin theory, which is widely used in econometrics and the insurance industry, to design a growth–ruin model for trees which accounts for climate hazards that can jeopardize tree growth. This model is an elaboration of a classical Cramer–Lundberg ruin model that is used in the insurance industry. The model accounts for the interactions between physiological parameters of trees and the occurrence of climate hazards. The physiological parameters describe interannual growth rates and how trees react to hazards. The hazard parameters describe the probability distributions of the occurrence and intensity of climate events. We focus on a drought–heatwave hazard. The goal of the paper is to determine the dependence of the forest ruin and average growth probability distributions on physiological and hazard parameters. Using extensive Monte Carlo experiments, we show the existence of a threshold in the frequency of hazards beyond which forest ruin becomes certain to occur within a centennial horizon. We also detect a small effect of the strategies used to cope with hazards. This paper is a proof of concept for the quantification of forest collapse under climate change.

Quantitative study on natural gas production risk of Carboniferous gas reservoir in eastern Sichuan

Quantifying natural gas production risk can help guide natural gas exploration and development in Carboniferous gas reservoirs. In this study, the Monte Carlo probability method is used to obtain the probability distribution and growth curve of each production risk factor and production in a Carboniferous gas reservoir in eastern Sichuan. In addition, the fuzzy comprehensive evaluation method is used to conduct the sensitivity analysis of the risk factors, and the natural gas production and realization probability under different risk factors are obtained. The research results show that: (1) the risk factor–production growth curve and probability distribution are calculated by the Monte Carlo probability method. The average annual production under the stable production stage under different realization probabilities is obtained. The maximum probability range of annual production is left( {43.43 - 126.35} right) times 10^{8} {text{m}}^{3} /{text{year}}, and the probability range is 14.59–92.88%. (2) The risk factor sensitivity analysis is significantly affected by the probability interval. In the entire probability interval, the more sensitive risk factors are the average production of the kilometer-deep well (D) and the production rate in the stable production stage (A). During the exploration and development of natural gas, these two risk factors can be adjusted to increase production.

An Empirical Investigation of the Effects of Rounding on the SPF Probabilities of Decline and Output Growth Histograms

I consider the possibility that respondents to the Survey of Professional Forecasters round their probability forecasts of the event that real output will decline in the future, as well as their reported output growth probability distributions. I make various plausible assumptions about respondents’ rounding practices, and show how these impinge upon the apparent mismatch between probability forecasts of a decline in output and the probabilities of this event implied by the annual output growth histograms. I find that rounding accounts for about a quarter of the inconsistent pairs of forecasts.

Influence of stress on single-cell lag time and growth probability for Listeria monocytogenes in half Fraser broth.

The impacts of 12 common food industry stresses on the single-cell growth probability and single-cell lag time distribution of Listeria monocytogenes were determined in half Fraser broth, the primary enrichment broth of the International Organization for Standardization detection method. First, it was determined that the ability of a cell to multiply in half Fraser broth is conditioned by its history (the probability for a cell to multiply can be decreased to 0.05), meaning that, depending on the stress in question, the risk of false-negative samples can be very high. Second, it was established that when cells are injured, the single-cell lag times increase in mean and in variability and that this increase represents a true risk of not reaching the detection threshold of the method in the enrichment broth. No relationship was observed between the impact on single-cell lag times and that on growth probabilities. These results emphasize the importance of taking into account the physiological state of the cells when evaluating the performance of methods to detect pathogens in food.

Visualization of a general family of growth functions and probability distributions – The Growth-curve Explorer

A variety of growth-curve functions are used in many areas of environmental science. Closely related probability distributions are useful in simulation modelling. A model that includes many of these functions and distributions as special cases is discussed, and an interactive Java applet that facilitates the visual exploration of the various curve characteristics and interrelationships is presented.

Estimation of crystallization kinetics for an organic fine chemical using a modified continuous cooling mixed suspension mixed product removal (MSMPR) crystallizer

The crystallization kinetics of an important organic fine chemical was determined using a modified laboratory scale continuous cooling mixed suspension mixed product removal (MSMPR) crystallizer with a product recycle loop designed for use with limited quantities of available material. A convenient method of monitoring steady state in the MSMPR using lasentec focussed beam reflectance measurement (FBRM) is also described. The effect of supersaturation, suspension density of the crystallizer content, impeller velocity (turnover time) and configuration on the growth and nucleation rates was studied. An observed deviation from the McCabe Δ L law for small crystal sizes was attributed to either size-dependent growth (SDG) or growth rate dispersion (GRD) mechanisms and hence complicated the estimation of growth and nucleation rates. SDG was successfully modelled using a three-parameter exponential SDG model. Growth rates estimated from the SDG model were compared to a GRD model using discrete growth probability distributions.

Extinction Rate of a Population under both Demographic and Environmental Stochasticity

We examined the asymptotic rate of population extinctionβwhen the population experiences density-dependent population regulation, demographic stochasticity, and environmental stochasticity. We assume discrete-generation population dynamics, in which some parameters fluctuate between years. The fluctuation of parameters can be of any magnitude, including both fluctuation traditionally treated as diffusion processes and fluctuation from catastrophes within a single scheme. We develop a new approximate method of calculating the asymptotic rate of population extinction per year,β=∫∞0exp(−x)u(x)dx, whereu(x) is the stationary distribution of adult population size from the continuous-population model including environmental stochasticity and population-regulation but neglecting demographic stochasticity. The method can be regarded as a perturbation expansion of the transition operator for population size. For several sets of population growth functions and probability distributions of environmental fluctuation, the stationary distributions can be calculated explicitly. Using these, we compare the predictions of this approximate method with that using a full transition operator and with the results of a direct Monte Carlo simulation. The approximate formula is accurate when the intrinsic rate of population increase is relatively large, though the magnitude of environmental fluctuation is also large. This approximation is complementary to the diffusion approximation.

Two representations in multifractal analysis

Two representations in multifractal analysis, the so-called q and tau representations, are discussed theoretically and computed practically. Complementary to the standard q-representation, the so-called tau -representation is especially suited to resolving the most rarified subsets of the distributed measure. Moreover, these two representations are especially adapted, respectively, to the well known fixed-size and fixed-mass box-counting algorithms. Both strategies are first applied to iteratively constructed mathematical measures. Once tested in this way, we use them to analyse the mass distribution and the growth probability distribution of an experimental electrodeposited pattern.

Power law tail in the radial growth probability distribution for DLA

Using both analytic and numerical methods, we study the radial growth probability distribution $P(r,M)$ for large scale off lattice diffusion limited aggregation (DLA) clusters. If the form of $P(r,M)$ is a Gaussian, we show analytically that the width $\xi(M)$ of the distribution {\it can not} scale as the radius of gyration $R_G$ of the cluster. We generate about $1750$ clusters of masses $M$ up to $500,000$ particles, and calculate the distribution by sending $10^6$ further random walkers for each cluster. We give strong support that the calculated distribution has a power law tail in the interior ($r\sim 0$) of the cluster, and can be described by a scaling Ansatz $P(r,M) \propto {r^\alpha\over\xi}\cdot g\left( {r-r_0}\over \xi \right)$, where $g(x)$ denotes some scaling function which is centered around zero and has a width of order unity. The exponent $\alpha$ is determined to be $\approx 2$, which is now substantially smaller than values measured earlier. We show, by including the power-law tail, that the width {\it can} scale as $R_G$, if $\alpha > D_f-1$.

Multifractal analysis of two-dimensional carbon clusters

The multifractality of graphite and amorphous carbon fractal clusters with distinct morphologies was studied by analysing the growth probability distribution (GPD) using the harmonic measure. The results showed that the multifractality of the graphite clusters is similar to that of diffusion-limited aggregation (DLA), and that a single phase transition to non-multifractals occurred at a negative scaling factor, beta . However, two critical points at which the multifractality was broken down were observed in the GPD of the multifractal-like amorphous carbon clusters. Such a multifractal behaviour was also found in the GPD of dissolution patterns generated by etching of porous materials, and the GPD of magnetic-microsphere aggregates, which suggests that the behaviour is common to many fractal clusters.

Theory of branched growth.

We present a theory of branched growth processes, notably diffusion-limited aggregation (DLA). Using a simple model of the dynamics of screening of competing branches, we compute statistics of the growth probability distribution. These statistics are multifractal only for stochastic models. Applying this general approach to diffusion-limited aggregation, we obtain results for the dimension D of a DLA cluster that are extremely close to the Muthukumar formula, D=(${\mathit{d}}^{2}$+1)/(d+1), in spatial dimensionality d [Phys. Rev. Lett. 50, 839 (1983)]. This formula is believed to be accurate for DLA clusters in dimensions dg2. The maximum growth probability of the cluster scales as ${\mathit{p}}_{\mathrm{max}}$\ensuremath{\sim}${\mathit{r}}^{1\mathrm{\ensuremath{-}}\mathit{D}}$, with r the cluster radius, as predicted by Turkevich and Scher [Phys. Rev. Lett. 55, 1026 (1985); Phys. Rev. A 33, 786 (1986)]. We also discuss the scaling of the minimum growth probability, the behavior of nonstochastic models, and possible approaches to direct computation of the screening dynamics. Our results are in good qualitative, and in some cases good quantitative, agreement with numerical studies of the screening dynamics.

Structural five-fold symmetry in the fractal morphology of diffusion-limited aggregates

The statistical self-similarity of the geometry of diffusion-limited aggregates and the multifractal nature of the growth probability distribution on the surface of the growing clusters are investigated using the wavelet transform. This study reveals the existence of a predominant structural five-fold symmetry in the internal frozen region as well as in the active outer region of the interface. This observation is corroborated by a statistical analysis of the screening effects that govern diffusion-limited aggregation (DLA) growth in linear and sector-shaped cells. The existence of this symmetry is likely to be a clue to a hierarchichal fractal ordering. We report on the discovery of Fibonacci sequences in the inner extinct region of large mass off-lattice DLA clusters, with a branching ratio which converges asymptotically to the golden mean. We suggest an interpretation of the DLA morphology as a “quasifractal” counterpart of the well-ordered snowflake fractal architecture.

Fractal and Multifractal Properties of Poissonian Growth

A growth model governed by the Poisson equation is presented to simulate the aggregation process in sputter (or vapor)-deposited thin films. By using computer simulation, it is found that the fractal dimension of the aggregates is consistent with that of diffusion-limited aggregation (DLA) at an initial stage and increases with time. The multifractal structure of the growth probability distribution is derived by making use of the Monte Carlo estimation. It is shown that the Poissonian growth pattern has characteristic fractal and multifractal properties.

Multifractality of growth probability distribution in diffusion-limited-corrosion pit.

The multifracfal structure of the growth probability distribution on theperimeter of a pit in the diffusion-limited pitting corrosion is derived by making use of the Monte Carlo estimation of the hitting probabilities by successive launching of a large number of random walkers. The multifractal spectrum a-f(a) is determined, and compared with that of the diffusion-limited aggregation. If is found that the scaling exponent β of width w of the corrosion pit (w≃n β , where n is the particle number removed from metal) is given by β=D n (1) where D n (1) is the information dimension

Fixed scale transformation approach to the multifractcal properties of the growth probabilities in the dielectric breakdown model

The separation of the properties of the growth probability distribution in two different contributions, as discussed in the previous paper, corresponds naturally to the approximation scheme of the fixed scale transformation (FST) method. The growth probabilities used to compute the FST matrix elements represent the essential elements of the multiplicative process that gives rise to the regular part (the only one relevant to the growth process) of the multifractal spectrum. The FST uses these probabilities directly without the need of introducing a multifractal spectrum explicitly. This, however, can be obtained as a by-product of the FST method. We present here analytical calculations for the regular part of the multifractal spectrum of the dielectric breakdown model with different values of the parameter ν. The results are good for η ⩾ 1 and less accurate for η < 1. In fact for small η values, and in order to recover the Eden limit, it is necessary to go to higher order and possibly to include self-affine properties explicitly.

Deterministic model for left-sided multifractality in generalized diffusion-limited aggregation

An exactly solvable deterministic model on a hierarchical lattice is presented for the left-sided multifractality of the growth probability distribution in a generalized diffusion-limited aggregation ( eta model). The exactly renormalizable growth probability is given by a multiplicative process. It predicts the tip behaviour (the maximum growth probability is a power law) and the fjord behaviour (the minimum growth probability has a logarithmic singularity). An analytical form of a 'left-sided' generalized dimension D(q) is shown for any eta .

Diffusion-Limited Aggregation on Percolating Cluster: Crossover and Multifractal Structure

Viscous fingering in porous media is considered as the diffusion-limited aggregation (DLA) on the percolating cluster. The crossover between percolation and DLA is studied by using a three-parameter position-space renormalization-group approach. The global flow diagram in the two-parameter space is obtained. It is found that there are two nontrivial fixed points, the percolation point and the DLA point. Above the percolation threshold, the system crosses eventually over to the DLA fractal on the perfect lattice. The fractal nature and the multifractal structure of the growth probability distribution are derived from the position-space renormalization-group method. The multifractal structure at the percolation threshold is compared with that at the perfect lattice.

Growth probability distribution in percolation

The authors study the growth probability distribution for a single cluster growth process for percolation at the percolation threshold. They find that this distribution is indistinguishable from the chemical path distribution on the percolation cluster as studied by Havlin et al. (1985). They also study the density profile of the percolation cluster. Using the multiscaling idea of Coniglio and Zannetti (1989), they calculate the fractal dimension of the percolation clusters from the density profile and report df=1.895+or-0.005 for two dimensions and 2.50+or-0.01 for three dimensions. However they do not find any evidence of multifractal or multiscaling behaviour.

The interpretation and measurement of the f(α) spectrum of a multifractal measure

The authors analyse the growth probability distribution for differential limited aggregates (DLA) in terms of its f(α) curve, and f and α computed independently as generalized entropies, using data from 10 clusters of 10000 to 100000 particles. The growth probability is obtained by solving the Laplace equations numerically with a hierarchical method which improves accuracy and speed. Two additional methods are used to compare results for DLA clusters and for a few objects with simple geometry and known f(α) spectrum. These comparisons reinforce their results for the part of the DLA spectrum corresponding to q0. They also bring to light some unexpected features for q-0.1, which suggest a non-universality of the scaling exponents in this region in two dimensions.