A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

Modelling nutrient uptake by crops implies considering and integrating the processes controlling the soil nutrient supply, the uptake by the root system and relationships between the crop growth response and the amount of nutrient absorbed. We developed a model that integrates both dynamics of maize growth and phosphorus (P) uptake. The crop part of the model was derived from Monteith's model. A complete regulation of P-uptake by the roots according to crop P-demand and soil P-supply was assumed. The soil P-supply to the roots was calculated using a diffusion equation and assuming that roots behave as zero-sinks. The actual P-uptake and crop growth were calculated at each time step by comparing phosphate and carbohydrate supply–demand ratios. Model calculations for P-uptake and crop growth were compared to field measurements on a long term P-fertilization trial. Three P-fertilization regimes (no P-fertilization, 42.8 kg P ha⁻¹ year⁻¹ and 94.3 kg P ha⁻¹ year⁻¹) have led to a range of P-supply. Our model correctly simulated both the crop development and growth for all P-treatments. P-uptake was correctly predicted for the two non-limiting P-treatments. Nevertheless, for the limiting P-treatment, P-uptake was correctly predicted during the early period of growth but it was underestimated at the last sampling date (61 day after sowing). Several arguments for under-prediction were considered. However, most of them cannot explain the observed magnitude in discrepancy. The most likely reason might be the fact that biomass allocation between shoot and root must be modelled more precisely. Despite this mismatch, the model appears to provide realistic simulations of the soil–plant dynamic of P in field conditions.     

A simple Lagrangian model to simulate temporal variability of algae in the Elbe River

We present a five-year (1997–2001) numerical simulation of daily mean chlorophyll a concentrations at station Geesthacht Weir on the lower Elbe River (Germany) using an extremely simple Lagrangian model driven by (a) water discharge, global radiation, water temperature, and (b) silica observations at station Schmilka in the upper reach of the Elbe River. Notwithstanding the lack of many mechanistic details, the model is able to reproduce observed chlorophyll a variability surprisingly well, including a number of sharp valleys and ascents/descents in the observed time series. The model's success is based on the assumption of three key effects: prevailing light conditions, sporadic limitation of algal growth due to lack of silica and algae loss rates that increase above an empirically specified temperature threshold of 20 °C. Trimmed-down model versions are studied to analyse the model's success in terms of these mechanisms.In each of the five years the model consistently fails, however, to properly simulate characteristic steep increases of chlorophyll a concentrations after pronounced spring minima. Curing this model deficiency by global model re-calibration was found to be impossible. However, suspension of silica consumption by algae for up to 10 days in spring is shown to serve as a successful placeholder for processes that are disregarded in the model but apparently play an important role in the distinctly marked period of model failure. For the remainder of the year the very simple model was found to be adequate.     

A two-dimensional stochastic model of downy mildew of radish

A two-dimensional stochastic model that simulates the spread of disease over space and time was recently proposed by Xu and Ridout [Xu, X.M., Ridout, M.S., 1998. Effects of initial epidemic conditions, sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. Phytopathology 88, 1000–1012]. In a theoretical study, the authors showed the ability of their model to generate a broad range of disease patterns and disease progress rates. The objective of our study was to test if this theoretical approach was able to describe disease progress and the disease pattern of a specific disease, downy mildew (Peronospora parasitica) of radish (Raphanus sativus L.). Two field experiments with artificial inoculation were carried out and disease incidence and spatial pattern were assessed twice a week until disease incidence was greater than 0.25. Four model parameters were estimated by an algorithm that uses a least square regression together with an evolutionary optimisation strategy. Moran's I indices of spatial autocorrelation calculated both for measured und simulated data were significantly correlated (α = 0.05, r = 0.61). Also observed variances in measurements and in simulations were closely and significantly correlated (α = 0.05, r = 0.95). Thus, disease pattern (as assessed in terms of variance inflation and spatial autocorrelation) was well described by the model. The model accounted for 94% of the variation in the disease incidence data. It has, therefore, the potential to be developed into a forecast model for risk analysis and for decision support in plant protection. However, in the specific case of downy mildew on radish more experimental data are required for model validation and to parameterise the effects of environment on infection, sporulation and spore dispersal.     

A two-dimensional numerical model for eutrophication in Baiyangdian Lake

Hydrodynamic, physical, and biochemical processes in the Baiyangdian Lake water environment were analyzed comprehensively. An eutrophication ecodynamics model including the effects of reed resistance on flow was coupled with the hydrodynamics governing equations. An improvement on the Water Quality Analysis Simulation Program (WASP, a modeling system introduced by the US Environmental Protection Agency) is established, which uses the zooplankton kinetic equation. The model simulates water quality constituents associated with eutrophication in the lake, including phytoplankton, zooplankton, nitrogen, phosphorus, dissolved oxygen, and others. Various kinetic coefficients were calibrated using measured data or information from relevant literature, to study eutrophication in the lake. The values calculated by the calibrated model agree well with field data, including ammonia nitrogen, total nitrogen, total phosphorus and dissolved oxygen. Changes related to nutrition and dissolved oxygen during the processes were simulated. The present model describes the temporal variation of water quality in Baiyangdian Lake with reasonable accuracy. Deviations between model-simulated and observed values are discussed. As an ideal tool for environmental management of the lake, this model can be used to predict its water quality, and be used in research to examine the eutrophication process.     

A simulation model for the management of low density recreational areas

In order to take account of the congestion externalities associated with increased use intensity during a given period at a low density recreational resource, it is necessary to determine the effects of alternative use levels on the expected quality of each individual's experience. This paper describes a simulation model for wilderness recreation designed to provide such measures. In order to illustrate the model it is applied to the Spanish Peaks Areas in Montana.     

A simulation model of the effects of vertical mixing on primary productivity

A random walk stimulation model was developed to explore the effects of variations in light regimes due to vertical mixing on primary productivity. Cells were allowed to light-shade adapt on some time scale by altering chl:carbon ratios in response to variations in light regimes. Photosynthetic response was adjusted according to variations in chl: carbon ratios by either varying the initial slopes of photosynthesis-irradiance curves, or varying photosynthetic capacities. The model suggests that despite physiological adaptation to light, vertical mixing may have little effect on the integrated water column primary productivity. It is suggested that if photoinhibition does not have a pronounced effect, the average distribution of primary production in a water column is not related to variations in light regimes arising from turbulent diffusion processes.This research was performed under the auspices of the US Department of Energy under Contract No. DE-ACO2-76CH00016 and partially supported by the International Decade of Ocean Exploration (IDOE), NSF, as part of the Coastal Upwelling Ecosystems Analysis (CUEA) program.     

A semi-coupled model for determining the distribution of two-dimensional coherent structures in open channel flow

Environmental Fluid Mechanics - Mixing layers and associated large-scale turbulent structures are some of the most common features of turbulent shallow water flow. Due to their...     

A simulation model for the management of vicuña populations

The population dynamics of the vicuña was modelled based on field data from the Central Galeras Sector, Perú. Rains were simulated in order to obtain net primary productivity and grass availability which act upon density-dependent fecundity and mortality. The model produces a population growth curve that tends to stabilize at densities around 100 vicuñas per km². Harvest and shearing processes were simulated as part of the vicuña population management model. Harvest was based upon a fixed threshold density D_e below which no harvest occurs; for densities above D_e harvesting is applied at a rate proportional to the difference between D_e and the current population density (fixed escapement or ‘bang-bang’ harvest rule). Management optimization was analyzed by determining the optimal escapement density D_e, which maximized either net profits or the number of animals harvested. Analyzing the results as cumulative totals over 20 years of simulation, an optimum harvest production was obtained for a D_e of about 40 vicuñas per km², and maximum profit was obtained for a D_e around 70 vicuñas per km². Analyzing the results of 20 years of simulation as annual averages with an original population density of 40 vicuñas per km², the harvest production and profits were maximized for a D_e of 40 and 60 vicuñas per km², respectively.The model was validated using data from the Reserva Nacional San Guillermo, Argentina, where vicuña and guanaco populations coexist (although their interaction was not modelled). The sensitivity analysis was performed with three different techniques: (a) stepwise multiple linear regression, (b) visual graphic analysis based on a polar coordinates system, and (c) direct evaluation of the effect on management decisions. The curve shape parameters of the fecundity and mortality functions proved to be the most important ones in determining the outcome of the model.     

A general bioeconomic simulation model for annual-crop marine fisheries

A generalized bioeconomic simulation model of annual-crop marine fisheries is described and its use in marine fisheries management is demonstrated. The biological submodel represents the recruitment of new organisms into the fishery, the movement of organisms from one fishing area to another and from one depth to another, the growth of organisms and the mortality of organisms resulting both from natural causes and from fishing. The economic submodel represents the fishing effort exerted on each resource species, the monetary costs of fishing, the value of the harvest and the rent (or excess profits) to the fishery.Basic dynamics of the model results from changes in the number of organisms in the fishery over time, which can be summarized as a set of difference equations of the general form ΔN/Δt = R + I ? E ? M ? F where ΔN/Δt is the net change in number of organisms in the fishery over time, R is recruitment, I is immigration, E is emigration, M is natural mortality and F is fishing mortality. R is a driving variable, whereas I, E, M and F are functions of the state of the system at any given point in time. The model can be run in a deterministic or stochastic mode. Values for parameters affecting rates of recruitment, movement, growth, natural mortality and fishing mortality can be selected from uniform, triangular or normal distributions.Use of the model within a fisheries-management framework is demonstrated by evaluating several management alternatives for the pink shrimp (Penaeus duorarum) fishery on the Tortugas grounds in the Gulf of Mexico. Steps involved in use of the model, including parameterization, validation, sensitivity analysis and stochastic simulations of management policies, are explained.     

A simulation model for lead movement in a watershed

A simulation model of the movement and accumulation of automotively emitted lead in a watershed of Central Illinois is presented. The model is composed of four parallel terrestrial subsystems or zones based on traffic volume, and an aquatic system in series. The model is used to estimate historical accumulations of lead within the watershed and to compare different scenarios of reductions of lead emissions. Since the introduction of leaded gasoline an estimated 570, 000 kg of lead has been emitted in the watershed. Of this total about 36% remained airborne and left the watershed, and 3% left the watershed via the quatic system.Lead is found to be a significant pollutant in urban areas and near major highways. Without emission controls lead is expected to cause environmental problems after about 25 years.     

A simulation model of management alternatives in a freshwater fishery

A model for investigating management alternatives on the Pyramid Lake-Truckee River system of Nevada and California is presented. Cutthroat trout, Cui-ui, Tahoe Sucker and Tui Chub are modeled with special emphasis on river spawning by trout. Management decision variables include hatchery input, water flow control, and diversion screening. Preliminary results indicate that some hatchery input will be needed to support the trout even with the best river management.     

Characterization of bedload intermittency near the threshold of motion using a Lagrangian sediment transport model

At the smallest scales of sediment transport in rivers, the coherent structures of the turbulent boundary layer constitute the fundamental mechanisms of bedload transport, locally increasing the instantaneous hydrodynamic forces acting on sediment particles, and mobilizing them downstream. Near the critical threshold for initiating sediment motion, the interactions of the particles with these unsteady coherent structures and with other sediment grains, produce localized transport events with brief episodes of collective motion occurring due to the near-bed velocity fluctuations. Simulations of these flows pose a significant challenge for numerical models aimed at capturing the physical processes and complex non-linear interactions that generate highly intermittent and self-similar bedload transport fluxes. In this investigation we carry out direct numerical simulations of the flow in a rectangular flat-bed channel, at a Reynolds number equal to Re = 3632, coupled with the discrete element method to simulate the dynamics of spherical particles near the bed. We perform two-way coupled Lagrangian simulations of 48,510 sediment particles, with 4851 fixed particles to account for bed roughness. Our simulations consider a total of eight different values of the non-dimensional Shields parameter to study the evolution of transport statistics. From the trajectory and velocity of each sediment particle, we compute the changes in the probability distribution functions of velocities, bed activity, and jump lengths as the Shields number increases. For the lower shear stresses, the intermittency of the global bedload transport flux is described by computing the singularity or multifr actal spectrum of transport, which also characterizes the widespread range of transport event magnitudes. These findings can help to identify the mechanisms of sediment transport at the particle scale. The statistical analysis can also be used as an ingredient to develop larger, upscaled models for predicting mean transport rates, considering the variability of entrainment and deposition that characterizes the transport near the threshold of motion.     

Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model

We present a method for estimating the upper bound of the horizontal eddy diffusivity using a non-stationary Lagrangian stochastic model. First, we identify a mixing barrier using a priori evidence (e.g., aerial photographs or satellite imagery) and using a Lagrangian diagnostic calculated from observed or modeled spatially non-trivial, time-dependent velocities [for instance, the relative dispersion (RD) or finite time Lyapunov exponent (FDLE)]. Second, we add a stochastic component to the observed (or modeled) velocity field. The stochastic component represents sub-grid stochastic diffusion and its mean magnitude is related to the eddy diffusivity. The RD of Lagrangian trajectories is computed for increasing values of the eddy diffusivity until the mixing barrier is no longer present. The value at which the mixing barrier disappears provides a dynamical estimate of the upper bound of the eddy diffusivity. The erosion of the mixing barrier is visually observed in numerical simulations, and is quantified by computing the kurtosis of the RD at each value of the eddy diffusivity. We demonstrate our method using the double gyre circulation model and apply it to high frequency (HF) radar observations of surface currents in the Gulf of Eilat.     

A dry deposition scheme for particulate matter coupled with a well-known Lagrangian Stochastic model for pollutant dispersion

Environmental Fluid Mechanics - A 3D dry deposition scheme for particulate matter (PM) is presented as a Free-Libre and Open-Source Software (FOSS) library, DePaSITIA (RSE SpA). This combines some...     

A survival-analysis-based simulation model for Russian wheat aphid population dynamics

A simulation model for Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), populations is built by integrating survival-analysis-based development and survivor functions and the same-shape reproduction distribution model in the framework of Leslie [Leslie, P.H., 1945. On the use of matrices in certain population mathematics. Biometrika 33, 183–212] matrix structure. Survival analysis is utilized to model both the development and survival of RWA populations, and the Cox (1972) proportional hazards model is fitted with the data sets from our laboratory observation of 1800 RWA individuals under 25 factorial combinations of five temperature regimes and five barley plant-growth stages. Rather than using simple age-specific survivor rates as in the traditional Leslie matrix, the survivor functions based on survival analysis describe age-specific, temperature and plant stage-dependent RWA survival probabilities. Similarly, a probability model from survival analysis to estimate the probability that an individual will reach mature adult stage is utilized to describe the development process; this makes the transition from nymphal stage to mature adult stage dependent on RWA age as well as temperature and plant-growth stage.Inspired by the same-shape distribution and rate-summation approach for modeling insect development, a similar approach for modeling insect reproduction under variable temperature is developed. This new same-shape reproduction distribution model incorporates individual variation in reproduction capability, as well as the effects of RWA age, temperature and plant-growth stage. Consequently, the same-shape reproduction distribution model replaces the simple age-specific fecundities in Leslie matrix model. To the best of our knowledge, this work is the first to introduce survival analysis to simulation modeling in entomology and ecology and also the first to integrate our newly developed same-shape reproduction distribution model into application.     

A simulation model of carbon and oxygen dynamics in a reservoir

The CORES model represents the long-term carbon and oxygen dynamics of the Conowingo Reservoir. The model, formulated using subsetted historical data, is readily validated using the remaining historical data for all state variables of importance. Sensitivity analyses make it clear that the flux of particulate organic carbon from upstream sources and its subsequent “trapping” and metabolism in the deeper regions of the reservoir are the major factors controlling the oxygen declines historically observed in the summer months. Increased natural vertical mixing (i.e., transport of oxygen from shallow to deep waters) can increase deep-water oxygen concentrations to some extent, but not to the degree necessary to meet water quality standards. Air-to-water diffusion adds substantial quantities of oxygen to surface waters in these mixing events. Simple solutions, such as requiring continuous flow, do not appear to adequately increase the dissolved oxygen levels in the deeper portion of the reservoir.     

A simulation model to evaluate the impacts of invasive earthworms on soil carbon dynamics

Recent studies have reported that earthworm invasions alter native communities and impact nutrient cycling in terrestrial ecosystems. We developed a simulation model to evaluate the potential impacts of earthworm invasions on carbon dynamics, taking into consideration earthworm feeding strategies and priming effects on the microorganisms through their casting activities. Responses of carbon stocks (forest litter, soil organic matter, microbial biomass and earthworm populations) and carbon fluxes (litter decomposition, earthworm consumption, and microbial respiration) were used to evaluate an earthworm invasion of a forest ecosystem. Data from a northern temperate forest (Arnot Forest, New York) were adapted for model calibration and evaluation. Simulation results suggest that the impact and outcome of earthworm invasions are affected by pre-invasion resource availability (litter and soil organic matter), invasive earthworm assemblages (particularly feeding strategy), and invasion history (associated with earthworm population dynamics). The abovementioned factors may also determine invasion progress of earthworm species. The accuracy of the model could be improved by the addition of environmental modules (e.g., soil water regimes), precise parameters accounting for individual species attributes under different environmental conditions (e.g. utilization ability of different types of food resources), as well as earthworm population dynamics (size and structure) and interactions with predators and other invasive/indigenous species during the invasion progress. Such an earthworm invasion model could provide valuable evaluation of the complicated responses of carbon dynamics to earthworm invasions in a range of forest ecosystems, particularly under global change scenarios.     

A simulation model of population dynamics of the codling moth, Cydia pomonella

A simulation model has been developed that predicts numbers and phenology of a population of codling moth, Cydia pomonella (L.), in an apple orchard. The model is a general insect population model based on the interative-cohort technique. It operates at two time scales: a fine time scale (1 h) for temperature-dependent physiological processes, and a coarse time scale (1 day) for population processes. The population is divided into a specifiable number of stages, and each stage is described by four process functions, which may be of any convenient mathematical form, and may differ among stages. Each stage is divided into cohorts of individuals born or emerged on the same day, and individuals within a cohort are considered probabilistically identical. The model simulates the processes of development, transition among stages, and mortality by using probability distributions representing these processes, and incorporates the effects of pesticides on mortality of the insect. Model output was evaluated by comparison with records of pheromone trap catches of codling moths in commercial apple orchards in North Carolina. The model predicts timing of the first spring flight well, depending on the initial age distribution used. Time between peaks of numbers of adults in the model is about 15 days longer than the observed period between flight peaks in orchards. Sensitivity analysis indicates that this discrepancy may be related to differences between measured ambient temperature and tree canopy temperature. The sensitivities of numbers of insects produced by the model, and timing of peaks in numbers present were determined for each of the parameters in the model. The parameters with greatest effect on the model output were those which control the locations of developmental rate functions and survival functions on the temperature scale. In the model, pesticides had a much larger effect on numbers of adults present than records of moths caught in pheromone traps indicate actually occurred, suggesting that moths caught in traps in commercial orchards where effective pesticides are applied may be largely immigrants.     

A simple model for simulation of insect pheromone dispersion within forest canopies

Synthetic pheromones and other behavioral chemicals are used by land managers to prevent insect-caused tree mortality or crop failure in forest and agricultural systems. Currently, no method exists to continuously measure pheromone concentration or movement in real-time. To improve our understanding of pheromone fate and transport under different forest canopies, results from a set of surrogate pheromone (sulfur hexafluoride tracer) experimental trials were used to evaluate a simple, instantaneous, three-dimensional Lagrangian dispersion model. The model was designed to predict both instantaneous and time-averaged pheromone concentrations. Overall, the results from the model show simulated time-averaged arc maximum concentrations within a factor of two of the observed data. The model correctly matched the sharp peaks and narrow widths of the meandering plumes observed in the instantaneous data, however the magnitude of the instantaneous peaks was often under-estimated. This model and evaluation provide the basis for a tool that can be used to guide deployment of synthetic pheromones or other semiochemicals for monitoring, mass trapping, or disruption of mating or aggregation.     

A simulation model for organic phosphorus transformation in a forest soil ecosystem

A numerical model which simulates the decomposition of litter and mineralization and immobilization of P in the humus layer of a temperate forest (beech site of Solling) is described. The model takes into account the effect of moisture, temperature and C/N ratio. The simulated concentration of P in the effluent of the humus layer agrees well with the measured values. The model predicts an increase in the C/P ratio of the unde-composed litter with time and that there is no direct mineralization of P from litter without passing through a microbial body. The net rate of mineralization is, however, always positive with its highest peak in July. Maximum immobilization of P from solution occurs in June and the minimum in January.The model is stable against changes in the litter input, its C/P ratio and other initial conditions, but it is very sensitive to changes in the efficiency factor which represents the fraction of decomposed C incorporated into microbial tissue. This is a site-specific model but can be used for grassland or agricultural systems with changes in certain parameters.