Accounting seasonal nonstationarity in time series models for short-term ozone level forecast

Due to the nonlinear feature of a ozone process, regression based models such as the autoregressive models with an exogenous vector process (ARX) suffer from persistent diurnal behaviors in residuals that cause systematic over-predictions and under-predictions and fail to make accurate multi-step forecasts. In this article we present a simple class of the functional coefficient ARX (FARX) model which allows the regression coefficients to vary as a function of another variable. As a special case of the FARX model, we investigate the threshold ARX (TARX) model of Tong [Lecture notes in Statistics, Springer-Verlag, Berlin, 1983; Nonlinear time series: a dynamics system approach, Oxford University Press, Oxford, 1990] which separates the ARX model in terms of a variable called the threshold variable. In this study we use time of day as the threshold variable. The TARX model can be used directly for ozone forecasts; however, investigation of the estimated coefficients over the threshold regimes suggests polynomial coefficient functions in the FARX model. This provides a parsimonious model without deteriorating the forecast performance and successfully captures the diurnal nonstationarity in ozone data. A general linear F-test is used to test varying coefficients and the portmanteau tests, based on the autocorrelation and partial autocorrelation of fitted residuals, are used to test error autocorrelations. The proposed models were applied to a 2 year dataset of hourly ozone concentrations obtained in downtown Cincinnati, OH, USA. For the exogenous processes, outdoor temperature, wind speed, and wind direction were used. The results showed that both TARX and FARX models substantially improve one-day-ahead forecasts and remove the diurnal pattern in residuals for the cases considered.     

Phase-space reconstruction and self-exciting threshold modeling approach to forecast lake water levels

Lake water level forecasting is very important for an accurate and reliable management of local and regional water resources. In the present study two nonlinear approaches, namely phase-space reconstruction and self-exciting threshold autoregressive model (SETAR) were compared for lake water level forecasting. The modeling approaches were applied to high-quality lake water level time series of the three largest lakes in Sweden; Vänern, Vättern, and Mälaren. Phase-space reconstruction was applied by the k-nearest neighbor (k-NN) model. The k-NN model parameters were determined using autocorrelation, mutual information functions, and correlation integral. Jointly, these methods indicated chaotic behavior for all lake water levels. The correlation dimension found for the three lakes was 3.37, 3.97, and 4.44 for Vänern, Vättern, and Mälaren, respectively. As a comparison, the best SETAR models were selected using the Akaike Information Criterion. The best SETAR models in this respect were (10,4), (5,8), and (7,9) for Vänern, Vättern, and Mälaren, respectively. Both model approaches were evaluated with various performance criteria. Results showed that both modeling approaches are efficient in predicting lake water levels but the phase-space reconstruction (k-NN) is superior to the SETAR model.     

Identification of the best architecture of a multilayer perceptron in modeling daily total ozone concentration over Kolkata,India

Autoregressive neural network (AR-NN) models of various orders have been generated in this work for the daily total ozone (TO) time series over Kolkata (22.56°N, 88.5°E). Artificial neural network in the form of multilayer perceptron (MLP) is implemented in order to generate the AR-NN models of orders varying from 1 to 13. An extensive variable selection method through multiple linear regression (MLR) is implemented while developing the AR-NNs. The MLPs are characterized by sigmoid non-linearity. The optimum size of the hidden layer is identified in each model and prediction are produced by validating it over the test cases using the coefficient of determination (R ²) and Willmott’s index (WI). It is observed that AR-NN model of order 7 having 6 nodes in the hidden layer has maximum prediction capacity. It is further observed that any increase in the orders of AR-NN leads to less accurate prediction.     

Spatial interpolation schemes of daily precipitation for hydrologic modeling

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs.     

Selection of the data time interval for the prediction of maximum ozone concentrations

This paper highlights the problem of step-length selection for the one-step-ahead prediction of ozone called the data time interval. This is done using a case study-based comparison of two approaches for predicting the maximum daily values of tropospheric ozone. The first approach is the 1-day-ahead prediction and the second is the prediction of the maximum values based on a multi-step-ahead iteration of 1-h predictions. Gaussian process modelling is utilised for this comparison. In particular, evolving Gaussian-process models are used that update on-line with the incoming measurement data. These sorts of models have been successfully used in the past for the prediction of ozone pollution. This paper contributes an assessment of the way that the maximum ozone values are predicted. A comparison of the daily maximum ozone values forecasted by a model based on 1-day-ahead predictions with those obtained by iterated 1-h-ahead predictions of the ozone with predictions at predetermined hours of the day is given. The forecast results are in favour of the on-line model based on hourly predictions when approaching closer to the real maximum values of ozone, and in favour of the daily predictions when they are made on a daily basis.     

Use of daily precipitation uncertainties in streamflow simulation and forecast

Among other sources of uncertainties in hydrologic modeling, input uncertainty due to a sparse station network was tested. The authors tested impact of uncertainty in daily precipitation on streamflow forecasts. In order to test the impact, a distributed hydrologic model (PRMS, Precipitation Runoff Modeling System) was used in two hydrologically different basins (Animas basin at Durango, Colorado and Alapaha basin at Statenville, Georgia) to generate ensemble streamflows. The uncertainty in model inputs was characterized using ensembles of daily precipitation, which were designed to preserve spatial and temporal correlations in the precipitation observations. Generated ensemble flows in the two test basins clearly showed fundamental differences in the impact of input uncertainty. The flow ensemble showed wider range in Alapaha basin than the Animas basin. The wider range of streamflow ensembles in Alapaha basin was caused by both greater spatial variance in precipitation and shorter time lags between rainfall and runoff in this rainfall dominated basin. This ensemble streamflow generation framework was also applied to demonstrate example forecasts that could improve traditional ESP (Ensemble Streamflow Prediction) method.     

Advances in shot noise modeling of daily streamflows

Univariate shot noise models for streamflow generation at short time scales are examined in detail, to reconsider the verification of the basic hypotheses behind the models, the problem of objectively evaluating their performances, and the importance of model parsimony. The classical approach to model estimation is shown to produce some inconsistencies in the inverse evaluation of the model input, in particular regarding the assumed independence and Poissonianity of the pulses; an alternative procedure for pulses identification is proposed, which enables the mentioned hypotheses to be respected. To evaluate model performances, two indices are proposed, respectively based on the comparison of real and generated flow duration curves (I₁) and annual maxima statistics (I₂). A method for explicitly accounting for the dependence of I₁ and I₂ on the number of model parameters is described. An application to seven daily streamflow time series in northern Italy demonstrates the validity of the proposed procedure for the identification of the input and the usefulness of the performance indices in discerning among competing models.     

Evaluation of weather forecast systems for storm surge modeling in the Chesapeake Bay

Accurate forecast of sea-level heights in coastal areas depends, among other factors, upon a reliable coupling of a meteorological forecast system to a hydrodynamic and wave system. This study evaluates the predictive skills of the coupled circulation and wind-wave model system (ADCIRC+SWAN) for simulating storm tides in the Chesapeake Bay, forced by six different products: (1) Global Forecast System (GFS), (2) Climate Forecast System (CFS) version 2, (3) North American Mesoscale Forecast System (NAM), (4) Rapid Refresh (RAP), (5) European Center for Medium-Range Weather Forecasts (ECMWF), and (6) the Atlantic hurricane database (HURDAT2). This evaluation is based on the hindcasting of four events: Irene (2011), Sandy (2012), Joaquin (2015), and Jonas (2016). By comparing the simulated water levels to observations at 13 monitoring stations, we have found that the ADCIR+SWAN System forced by the following: (1) the HURDAT2-based system exhibited the weakest statistical skills owing to a noteworthy overprediction of the simulated wind speed; (2) the ECMWF, RAP, and NAM products captured the moment of the peak and moderately its magnitude during all storms, with a correlation coefficient ranging between 0.98 and 0.77; (3) the CFS system exhibited the worst averaged root-mean-square difference (excepting HURDAT2); (4) the GFS system (the lowest horizontal resolution product tested) resulted in a clear underprediction of the maximum water elevation. Overall, the simulations forced by NAM and ECMWF systems induced the most accurate results best accuracy to support water level forecasting in the Chesapeake Bay during both tropical and extra-tropical storms.     

一次显著的远场水位短临异常

2012年2月2日辽宁营口发生了M4.3和M4.1地震。震前距震中468km的河北省黄骅井水位出现了显著的短临下降异常变化,异常过程演化与震级较小的营口地震序列发展具有完整的可对比性。本文从地质、构造、震源机制等方面,分析判断该异常与构造活动应有一定的相关性,是一次显著的远场水位短临异常。     

Alternating Gaussian process modulated renewal processes for modeling threshold exceedances and durations

It is often of interest to model the incidence and duration of threshold exceedance events for an environmental variable over a set of monitoring locations. Such data arrive over continuous time and can be considered as observations of a two-state process yielding, sequentially, a length of time in the below threshold state followed by a length of time in the above threshold state, then returning to the below threshold state, etc. We have a two-state continuous time Markov process, often referred to as an alternating renewal process. The process is observed over a truncated time window and, within this window, duration in each state is modeled using a distinct cumulative intensity specification. Initially, we model each intensity over the window using a parametric regression specification. We extend the regression specification adding temporal random effects to enrich the model using a realization of a log Gaussian process over time. With only one type of renewal, this specification is referred to as a Gaussian process modulated renewal process. Here, we introduce Gaussian process modulation to the intensity for each state. Model fitting is done within a Bayesian framework. We clarify that fitting with a customary log Gaussian process specification over a lengthy time window is computationally infeasible. The nearest neighbor Gaussian process, which supplies sparse covariance structure, is adopted to enable tractable computation. We propose methods for both generating data under our models and for conducting model comparison. The model is applied to hourly ozone data for four monitoring sites at different locations across the United States for the ozone season of 2014. For each site, we obtain estimated profiles of up-crossing and down-crossing intensity functions through time. In addition, we obtain inference regarding the number of exceedances, the distribution of the duration of exceedance events, and the proportion of time in the above and below threshold state for any time interval.     

Using maximum likelihood to derive various distance-based goodness-of-fit indicators for hydrologic modeling assessment

Currently used goodness-of-fit (GOF) indicators (i.e. efficiency criteria) are largely empirical and different GOF indicators emphasize different aspects of model performance; a thorough assessment of model skill may require the use of robust skill matrices. In this study, based on the maximum likelihood method, a statistical measure termed BC-GED error model is proposed, which firstly uses the Box–Cox (BC) transformation method to remove the heteroscedasticity of model residuals, and then employs the generalized error distribution (GED) with zero-mean to fit the distribution of model residuals after BC transformation. Various distance-based GOF indicators can be explicitly expressed by the BC-GED error model for different values of the BC transformation parameter λ and GED kurtosis coefficient β. Our study proves that (1) the shape of error distribution implied in the GOF indicators affects the model performance on high or low flow discharges because large error-power (β) value can cause low probability of large residuals and small β value will lead to high probability of zero value; (2) the mean absolute error could balance consideration of low and high flow value as its assumed error distribution (i.e. Laplace distribution, where β = 1) is the turning point of GED derivative at zero value. The results of a study performed in the Baocun watershed via comparison of the SWAT model-calibration results using six distance-based GOF indicators show that even though the formal BC-GED is theoretically reasonable, the calibrated model parameters do not always correspond to high performance of model-simulation results because of imperfection of the hydrologic model. However, the derived distance-based GOF indicators using the maximum likelihood method offer an easy way of choosing GOF indicators for different study purposes and developing multi-objective calibration strategies.     

Depression threshold control proxy to improve HEC-HMS modeling of depression-dominated watersheds

ABSTRACT

Many hydrologic models utilize delineation results from traditional methods which create a hydrologically connected drainage system. In depression-dominated areas, topographic characteristics of depressions are vital to modeling unique hydrologic processes associated with puddle-to-puddle (P2P) filling-spilling dynamics. The objective of this study is to evaluate the impacts of the P2P processes and dynamic changes in contributing area on outlet discharge. To do so, an improved HEC-HMS model is developed by incorporating a depression threshold control proxy (DTCP) and an improved conceptual framework. The DTCP uses a storage–discharge function to simulate the P2P dynamics. The improved conceptual framework counteracts the effect of full hydrologic connectivity created by traditional delineation methods by introducing depressional and non-depressional areas to each sub-basin. Application of the improved HEC-HMS model demonstrated that it was capable of accurately simulating outlet discharge and providing the details on surface connectivity and depression storage.     

Multiple model combination methods for annual maximum water level prediction during river ice breakup

The Athabasca River is the largest unregulated river in Alberta, Canada, with ice jams frequently occurring in the vicinity of Fort McMurray. Modelling tools are desired to forecast ice‐related flood events. Multiple model combination methods can often obtain better predictive performances than any member models due to possible variance reduction of forecast errors or correction of biases. However, few applications of this method to river ice forecasting are reported. Thus, a framework of multiple model combination methods for maximum breakup water level (MBWL) Prediction during river ice breakup is proposed. Within the framework, the member models describe the relations between the MBWL (predicted variable) and their corresponding indicators (predictor variables); the combining models link the relations between the predicted MBWL by each member model and the observed MBWL. Especially, adaptive neuro‐fuzzy inference systems, artificial neural networks, and multiple linear regression are not only employed as member models but also as combining models. Simple average methods (SAM) are selected as the basic combining model due to simple calculations. In the SAM, an equal weight (1/n) is assigned to n member models. The historical breakup data of the Athabasca River at Fort McMurray for the past 36 years (1980 to 2015) are collected to facilitate the comparison of models. These models are examined using the leave‐one‐out cross validation and the holdout validation methods. A SAM, which is the average output from three optimal member models, is selected as the best model as it has the optimal validation performance (lowest average squared errors). In terms of lowest average squared errors, the SAM improves upon the optimal artificial neural networks, adaptive neuro‐fuzzy inference systems, and multiple linear regression member models by 21.95%, 30.97%, and 24.03%, respectively. This result sheds light on the effectiveness of combining different forecasting models when a scarce river ice data set is investigated. The indicators included in the SAM may indicate that the MBWL is affected by water flow conditions just after freeze‐up, overall freezing conditions during winter, and snowpack conditions before breakup.     

Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls

Abstract

A procedure is presented for using the bivariate normal distribution to describe the joint distribution of storm peaks (maximum rainfall intensities) and amounts which are mutually correlated. The Box-Cox transformation method is used to normalize original marginal distributions of storm peaks and amounts regardless of the original forms of these distributions. The transformation parameter is estimated using the maximum likelihood method. The joint cumulative distribution function, the conditional cumulative distribution function, and the associated return periods can be readily obtained based on the bivariate normal distribution. The method is tested and validated using two rainfall data sets from two meteorological stations that are located in different climatic regions of Japan. The theoretical distributions show a good fit to observed ones.     

Estimation of instantaneous peak flows from maximum mean daily flows using the HBV hydrological model

The record length and quality of instantaneous peak flows (IPFs) have a great influence on flood design, but these high resolution flow data are not always available. The primary aim of this study is to compare different strategies to derive frequency distributions of IPFs using the Hydrologiska Byråns Vattenbalansavdelning (HBV) hydrologic model. The model is operated on a daily and an hourly time step for 18 catchments in the Aller‐Leine basin, Germany. Subsequently, general extreme value (GEV) distributions are fitted to the simulated annual series of daily and hourly extreme flows. The resulting maximum mean daily flow (MDF) quantiles from daily simulations are transferred into IPF quantiles using a multiple regression model, which enables a direct comparison with the simulated hourly quantiles. As long climate records with a high temporal resolution are not available, the hourly simulations require a disaggregation of the daily rainfall. Additionally, two calibrations strategies are applied: (1) a calibration on flow statistics; (2) a calibration on hydrographs. The results show that: (1) the multiple regression model is capable of predicting IPFs with the simulated MDFs; (2) both daily simulations with post‐correction of flows and hourly simulations with pre‐processing of precipitation enable a reasonable estimation of IPFs; (3) the best results are achieved using disaggregated rainfall for hourly modelling with calibration on flow statistics; and (4) if the IPF observations are not sufficient for model calibration on flow statistics, the transfer of MDFs via multiple regressions is a good alternative for estimating IPFs. Copyright © 2015 John Wiley & Sons, Ltd.     

强矿震地球物理过程及短临阶段预测的研究

基于中尺度地震实验场高密度数字地震和前兆台网对抚顺老虎台矿两次强矿震进行连续的现场观测,用地震学方法和小波工具分析强矿震孕震过程采集到的数据,提取短临阶段的异常信息;用区域强震震源机制解、强矿震的震源机制解、极近场震源调查、震源高精度定位、现场绝对地应力测量、三维有限差分数值试验方法,分析强矿震的孕震应力场环境和震源机制;通过定量观察采矿与矿震活动的相关性,分析强矿震的直接诱发原因．提出地质构造环境、地应力场和采矿活动共同作用诱发强矿震的机理和局部应力场在孕育该震过程起主导作用、卸荷重力应力场抑或耦合了高压瓦斯的膨胀起主要诱发作用的观点;发现煤炭深部开采条件下,矿震和瓦斯存在密切的相关性,有可能存在一种开采卸荷和高压瓦斯气体膨胀耦合作用诱发的新型矿震——卸胀耦合型矿震;提取到震前短临阶段存在的b值、η值、频次、波速比等可信的地震学异常和定点潮汐形变前兆异常,对异常信息的提取方法和强矿震短临阶段的预测进行了探讨．     

Effect of ENSO on annual maximum floods and volume over threshold in the southwestern region of Iran

In this paper, the effects of the El Niño-Southern Oscillation (ENSO) on the annual maximum flood (AMF) and volume over threshold (VOT) in two major neighbouring river basins in southwest Iran are investigated. The basins are located upstream of the Dez and Karun-I dams and cover over 40?000 km² in total area. The effects of ENSO on the frequency, magnitude and severity (frequency times magnitude) of flood characteristics over the March–April period were analysed. ENSO indices were also correlated with both AMF and VOT. The results indicate that, in the Dez and Karun basins, the El Niño phenomenon intensifies March–April floods compared with neutral conditions. The opposite is true in La Niña conditions. The degree of the effect is more intense in the El Niño period.