Space-Time ARIMA Modeling for Regional Precipitation Forecasting

An aggregate regional forecasting model class belonging to the general family of space-time auto regressive moving average (STARMA) process is investigated. These models are characterised by autoregressive and moving average terms lagged in both time and space. The paper demonstrates an iterative procedure for buling a starima model of precipitation time series. Eleven raingage sites located in a watershed in southern Ontario, Canada, sampled at 15-day intervals for the period of 1966 to 1980 are used in the numerical analysis. The identified model is STMA($l_2)$. The model parameters are estimated by the polytope technique, a nonlinear optimization algorithm. The developed model performed well in regional forecasting and in describing the spatio-temporal characteristics of the precipitation time series.     

A dynamical model for the overland flow on an infiltrating catchment

An approximate lumped parameter model for the surface runoff phenomenon on a catchment is presented. It consists of two submodels which are spatial discretizations of the basic partial differential equations of overland flow and infiltration. The aim of the model is to describe the dynamical input-output relationship between the rainfall rate and the surface runoff from the catchment. The boundary conditions of the infiltration process are modelled in an approximate way so that the number of state variables in the model can be reduced. With the aid of a single model parameter it is possible to describe simple catchment shapes like linearly converging and diverging surfaces. The model structure is flexible so that it can also be applied to more complex catchment configurations. The simulation results show that the phenomenon under consideration can be properly described by the model structure presented.     

南通地区月降水量时间序列分析

根据南通地区1989年-2005年月降水量数据,在统计检验其平稳性、纯随机性的基础上,结合谱分析,建立该地区具有季节效应的疏系数ARIMA月降水量时间序列模型,对模型作了拟合预测检验.研究表明,多个模型的联合使用比单一模型更利于准确拟合预测.     

FLOODING ON THE EEL RIVER: SYSTEM THEORETIC TIME SERIES,TRANSFER FUNCTION TIME SERIES,AND STRUCTURAL MODEL FORECASTS

Three models are developed to forecast precipitation, stream flow, and suspended sediment load for the Middle Fork Eel River basin near Dos Rios, California. The models are a structural model, a transfer function time series model, and a multivariate time series model based on the ideas of linear systems theory. Monthly observations from 1961 through 1970 were used to specify and estimate the models, and their performance was evaluated using 36 observations from 1971 through 1973. The comparisons show that all of the models are able to simulate the general trend of the data fairly well but that the two time series models capture the detail better. The system theoretic time series model fares the best, providing consistently better forecasts of all three series. We conclude that this model would be valuable for use in planning water supply systems in the Eel River basin.     

A new integrated surface and subsurface flows model and its verification

A new coupled model for simulating surface and subsurface flows in a fully integrated way is presented. This model contains two sub-models; one is the 2D kinematic wave approximation of the Saint Venant’s equations used to model runoff, and another is Richards’ equation for variably saturated subsurface flow. In this model, boundary conditions (the conditions describing groundwater discharge at the land surface or surface water infiltration into the subsurface) could be eliminated through mathematic transformations of the governing equation of surface and subsurface flows. The solution of surface and subsurface flows could be simultaneous. And the surface domain and subsurface domain could be considered as a fully integrated domain. This approach naturally provides pressure and fluxes continuity along land surface. In order to assess this modelling approach, several classical validations, verification and application test cases are presented. For overland flow solely, the model is compared to an analytical solution and to commonly use hydrological models. The integrated model is then validated with a sandbox laboratory experiment and a soil column test. Finally, the effects of rainfall intensity, hydraulic conductivity of soils and initial bulk water content of soils to runoff and infiltration of a homogeneous soil slope are studied under different conditions.     

基于小波去噪和WNN-ARIMA组合模型的年径流预测

为解决单一的小波神经网络预测精度不高的问题,提出一种新的基于小波去噪和WNN-ARIMA组合模型,应用小波阈值去噪法对小波神经网络的输入值进行预处理,同时对模型残差值进行ARIMA模型修正.利用该组合模型对洮河流域下巴沟站年径流量进行预测,预测趋势和预测值与原始实测数据吻合度高,表明此组合模型可靠性强,可以有效预测年径...     

System dynamics of euthrophication processes in lakes

Eutrophication is the phenomenon observed in the bodies of water that receive large influxes of nutrients due to agricultural runoff or urban waste disposal. It is characterized by blooms of either green or blue-green algae (often noxious smelling) and by a drastic reduction in dissolved oxygen and often makes it impossible for many species of fish and zooplankton to live in the water. The objective was to examine the effects of eutrophication on plankton seasonal dynamics. Simulation models have been used primary tool in the study of eutrophication in lakes. Many eutrophication models have been developed both to predict the effect of nutrient additions on lake biota and to examine how effective various nutrient diversions alternatives might be improved water quality. Systems dynamics was studied using the model, which is expressed as a series of four differential equations as its state variables for the rates of change of phytoplankton, zooplankton, nitrogen and phosphorus. Influence of the phosphorus concentration on eutrophication was treated and studied as the one of the most important process in the lake ecosystem.     

Synoptic airflow and UK daily precipitation extremes

We develop a vector generalised linear model to describe the influence of the atmospheric circulation on extreme daily precipitation across the UK. The atmospheric circulation is represented by three covariates, namely synoptic scale airflow strength, direction and vorticity; the extremes are represented by the monthly maxima of daily precipitation, modelled by the generalised extreme value distribution (GEV). The model parameters for data from 689 rain gauges across the UK are estimated using a maximum likelihood estimator. Within the framework of vector generalised linear models, various plausible models exist to describe the influence of the individual covariates, possible nonlinearities in the covariates and seasonality. We selected the final model based on the Akaike information criterion (AIC), and evaluated the predictive power of individual covariates by means of quantile verification scores and leave-one-out cross validation. The final model conditions the location and scale parameter of the GEV on all three covariates; the shape parameter is modelled as a constant. The relationships between strength and vorticity on the one hand, and the GEV location and scale parameters on the other hand are modelled as natural cubic splines with two degrees of freedom. The influence of direction is parameterised as a sine with amplitude and phase. The final model has a common parameterisation for the whole year. Seasonality is partly captured by the covariates themselves, but mostly by an additional annual cycle that is parameterised as a phase-shifted sine and accounts for physical influences that we have not attempted to explicitly model, such as humidity.     

Modeling the depletion of dissolved oxygen due to algal bloom in a lake by taking Holling type-III interaction

In this paper a non-linear mathematical model for depletion of dissolved oxygen due to algal bloom in a lake is proposed and analyzed. The model is formulated by considering four variables namely, cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen. In the modeling process it is assumed that nutrients are continuously coming with a constant rate to the lake through water runoff from agricultural fields and domestic drainage. The Holling type-III interaction between nutrients and algal population is considered. Equilibrium values have been obtained and their stability analysis has also been performed. Numerical simulations are carried out to explain the mathematical results.     

A rain water infiltration model with unilateral boundary condition: qualitative analysis and numerical simulations

We present a rigorous mathematical treatment of a model describing rain water infiltration through the vadose zone in case of runoff of the excess water. The main feature of the mathematical problem emerging from the model lies on the boundary condition on the ground surface which is in the form of a unilateral constraint. Existence and uniqueness of a weak solution is proved under general assumptions. We present also the results of a numerical study comparing the proposed model with other models which approach in a different way the rain water infiltration problem. Copyright © 2006 John Wiley & Sons, Ltd.     

基于模糊聚类分析的小波神经网络模型在径流预测中的应用

提出了一种在对预报因子集进行模糊聚类分析基础上构建径流预测模型的新方法:先通过模糊C-均值聚类将历史径流数据进行分类,然后利用小波神经网络分别建立预报因子集类别变量特征值与观测值之间的局部预测模型,并设计了特征值分类识别器,自动搜寻相适应的局部网络模型进行预测.通过西南某水库2011年日平均入库来流的计算实例对简单小波神经网络预测模型和所建的基于FCM与小波神经网络的预测模型进行了比较,结果较为满意.     

A comparison study of extreme precipitation from six different regional climate models via spatial hierarchical modeling

We analyze output from six regional climate models (RCMs) via a spatial Bayesian hierarchical model. The primary advantage of this approach is that the statistical model naturally borrows strength across locations via a spatial model on the parameters of the generalized extreme value distribution. This is especially important in this application as the RCM output we analyze have extensive spatial coverage, but have a relatively short temporal record for characterizing extreme behavior. The hierarchical model we employ is also designed to be computationally efficient as we analyze RCM output for nearly 12000 locations. The aim of this analysis is to compare the extreme precipitation as generated by these RCMs. Our results show that, although the RCMs produce similar spatial patterns for the 100-year return level, their characterizations of extreme precipitation are quite different. Additionally, we examine the spatial behavior of the extreme value index and find differing spatial patterns for the point estimates for the RCMs. However, these differences may not be significant given the uncertainty associated with estimating this parameter.     

On Modelling and Pricing Rainfall Derivatives with Seasonality

Abstract

We are interested in pricing rainfall options written on precipitation at specific locations. We assume the existence of a tradeable financial instrument in the market whose price process is affected by the quantity of rainfall. We then construct a suitable ‘Markovian gamma’ model for the rainfall process which accounts for the seasonal change of precipitation and show how maximum likelihood estimators can be obtained for its parameters.

We derive optimal strategies for exponential utility from terminal wealth and determine the utility indifference price of the claim. The method is illustrated with actual measured data on rainfall from a location in Kenya and spot prices of Kenyan electricity companies.     

Predictive accuracy determination applied to a linear model phosphorus loading resulting from urban runoff

A case study of the application of an iterative technique for determination of predictive accuracy is presented. The method uses Monte Carlo simulations and split sampling techniques to verify model accuracy. Examination of the ability of a linear parametric runoff loading model's ability to project total phosphorus loadings reveals the sensitivity of the model to calibration procedures. Predictive reliability was found to vary widely as the number of rainfall events considered in the calibration process changed. Predictive reliability was substantially increased by imposing calibration constraints which ensured that a wide distribution of values of the independent variable were presented in the calibration pool.Although the linear model is theoretically weak in its representation of the runoff loading phenomenon, it displays relatively stable predictive capabilities which warrant its consideration for use in management studies. The predictive errors associated with loading projections limit the linear model's value to applications insensitive to errors in the loading projections for individual storm events. This study provides further evidence of the need to consider uncertainties associated with the modelling of water quality phenomena.     

Construction and selection of quantitative planning models — a general procedure illustrated with models for stock control

The paper investigates the process of quantitative model construction when for a particular realworld decision problem different quantitative models are available. It develops first some general features for constructing a model hierarchy comprising all quantitative models which should be taken into consideration. The main objective is an investigation into the selection process giving the best quantitative model for the particular decision problem at hand. This selection, however, can be performed in different ways possibly ending up with different models. A myopic selection principle is suggested which leads to a class of strategies. Different strategies within this class are discussed showing the complexity of the selection procedure. The investigations are illustrated using inventory models particularly stressing the role of cost parameters.     

径流中长期预报模糊识别优化模型及应用

对水文中长期预报模糊识别方法进一步研究,基于模糊环境下的目标函数,提出了具有主观监督因子和稳定系数的模糊识别预报模型.根据已知样本的最优模糊划分建立预报模型,利用已知样本的指标和样本的最优模糊划分计算预报模型的参数,给定模型的稳定系数,再通过调整主观监督因子对预报模型参数进行优化.径流中长期预报实例的模型检验平均相对误差为7.84%.     

Introduction to the Special Issue on Discrete Event Models of Continuous Systems

Automatic control systems rely on models to predict the near future and identification algorithms to adapt the models to changing process behaviour. The traditionally highly complex models of the activated sludge process developed for scientific purposes cannot be identified from on-line measurements and are not suited for process control purposes in their present form. Model decoupling based on the different time scales of the dynamic processes is one possible way of attacking this problem. It allows the implementation of more simple and realistically applicable controllers in combination with predictions based on simplified models in hierarchical control structure. This paper discusses these concepts and presents a reduced order model describing carbonaceous removal, nitrification, and denitrification in a medium time scale (several hours/days). The model parameters are identifiable from available on-line measurements and the dynamic behaviour is verified against computer simulations of the IAWQ activated sludge model no. 1.     

Simultaneous engineering approach to an integrated design and process planning

To support integration of design and process planning, a reference model has been developed. This reference model represents the basis for a new methodology for integrated design and process planning which enables a Simultaneous Engineering approach in the early stages of product development. The reference model consists of four partial models. These are the activity model, the information model, the technical system model and the model of integrating methods. Using these models, the methodology enables a concurrent processing of design and process planning activities with regard to different components of a product. Furthermore, the methodology covers planning methods as well as execution methods, to support early transmission of information to downstream activities and a feedback of information to upstream activities within the process chain of design and process planning.     

Nonparametric Bayesian topic modelling with the hierarchical Pitman–Yor processes

The Dirichlet process and its extension, the Pitman–Yor process, are stochastic processes that take probability distributions as a parameter. These processes can be stacked up to form a hierarchical nonparametric Bayesian model. In this article, we present efficient methods for the use of these processes in this hierarchical context, and apply them to latent variable models for text analytics. In particular, we propose a general framework for designing these Bayesian models, which are called topic models in the computer science community. We then propose a specific nonparametric Bayesian topic model for modelling text from social media. We focus on tweets (posts on Twitter) in this article due to their ease of access. We find that our nonparametric model performs better than existing parametric models in both goodness of fit and real world applications.