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.     

A comparative study of extensive machine learning models for predicting long-term monthly rainfall with an ensemble of climatic and meteorological predictors

Rainfall prediction is of vital importance in water resources management. Accurate long-term rainfall prediction remains an open and challenging problem. Machine learning techniques, as an increasingly popular approach, provide an attractive alternative to traditional methods. The main objective of this study was to improve the prediction accuracy of machine learning-based methods for monthly rainfall, and to improve the understanding of the role of large-scale climatic variables and local meteorological variables in rainfall prediction. One regression model autoregressive integrated moving average model (ARIMA) and five state-of-the-art machine learning algorithms, including artificial neural networks, support vector machine, random forest (RF), gradient boosting regression, and dual-stage attention-based recurrent neural network, were implemented for monthly rainfall prediction over 25 stations in the East China region. The results showed that the ML models outperformed ARIMA model, and RF relatively outperformed other models. Local meteorological variables, humidity, and sunshine duration, were the most important predictors in improving prediction accuracy. 4-month lagged Western North Pacific Monsoon had higher importance than other large-scale climatic variables. The overall output of rainfall prediction was scalable and could be readily generalized to other regions.     

An explicit neural network formulation for evapotranspiration

Abstract

An explicit neural network formulation (ENNF) is developed for estimating reference evapotranspiration (ET₀) using daily meteorological variables obtained from the California Irrigation Management Information System (CIMIS) database. First, the ENNF is trained and tested using the CIMIS database, and then compared with five conventional ET₀ models, as well as the multiple linear regression method. Statistics such as average, standard deviation, minimum and maximum values, and criteria such as mean square error and determination coefficient are used to measure the performance of the ENNF. Daily atmospheric data of four climatic stations in central California are taken into consideration in the model development and those of three other stations are used for comparison purposes. The meteorological variables employed in the formulation are solar radiation, air temperature, relative humidity and wind speed. It is concluded from the results that ENNF offers an alternative ET₀ formulation, but that the gain in skill is marginal compared with simpler linear techniques. However, this finding needs to be tested using sites drawn from a wider range of climate regimes.     

Regional scale rainfall–runoff modeling using VARX–MGARCH approach

Multivariate time series modeling approaches are known as useful tools for describing, simulating, and forecasting hydrologic variables as well as their changes over the time. These approaches also have temporal and cross-sectional spatial dependence in multiple measurements. Although the application of multivariate linear and nonlinear time series approaches such as vector autoregressive with eXogenous variables (VARX) and multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models are commonly used in financial and economic sciences, these approaches have not been extensively used in hydrology and water resources engineering. This study employed VARX and VARX–MGARCH approaches in modeling mean and conditional heteroscedasticity of daily rainfall and runoff records in the basin of Zarrineh Rood Dam, Iran. Bivariate diagonal VECH (DVECH) model, as a main type of MGARCH, shows how the conditional variance–covariance and conditional correlation structure vary over the time between residuals series of the fitted VARX. For this purpose, five model fits, which consider different combinations of twofold rainfall and runoff, including both upstream and downstream stations, have been investigated in the present study. The VARX model, with different orders, was applied to the daily rainfall–runoff process of the study area in each of these model fits. The Portmanteau test revealed the existence of conditional heteroscedasticity in the twofold residuals of fitted VARX models. Therefore, the VARX–DVECH model is proposed to capture the heteroscedasticity existing in the daily rainfall–runoff process. The bivariate DVECH model indicated both short-run and long-run persistency in the conditional variance–covariance matrix related to the twofold innovations of rainfall–runoff processes. Furthermore, the evaluation criteria for the VARX–DVECH model revealed the improvement of VARX model performance.     

Predicting river water temperatures using stochastic models: case study of the Moisie River (Québec,Canada)

Successful applications of stochastic models for simulating and predicting daily stream temperature have been reported in the literature. These stochastic models have been generally tested on small rivers and have used only air temperature as an exogenous variable. This study investigates the stochastic modelling of daily mean stream water temperatures on the Moisie River, a relatively large unregulated river located in Québec, Canada. The objective of the study is to compare different stochastic approaches previously used on small streams to relate mean daily water temperatures to air temperatures and streamflow indices. Various stochastic approaches are used to model the water temperature residuals, representing short‐term variations, which were obtained by subtracting the seasonal components from water temperature time‐series. The first three models, a multiple regression, a second‐order autoregressive model, and a Box and Jenkins model, used only lagged air temperature residuals as exogenous variables. The root‐mean‐square error (RMSE) for these models varied between 0·53 and 1·70 °C and the second‐order autoregressive model provided the best results. A statistical methodology using best subsets regression is proposed to model the combined effect of discharge and air temperature on stream temperatures. Various streamflow indices were considered as additional independent variables, and models with different number of variables were tested. The results indicated that the best model included relative change in flow as the most important streamflow index. The RMSE for this model was of the order of 0·51 °C, which shows a small improvement over the first three models that did not include streamflow indices. The ridge regression was applied to this model to alleviate the potential statistical inadequacies associated with multicollinearity. The amplitude and sign of the ridge regression coefficients seem to be more in agreement with prior expectations (e.g. positive correlation between water temperature residuals of different lags) and make more physical sense. Copyright © 2006 John Wiley & Sons, Ltd.     

One-day-ahead prediction of maximum carbon monoxide concentration in urban environments

The adverse health effects associated with exposure to CO range from the more subtle cardiovascular effects at low concentrations to death after acute or chronic exposure to higher concentrations. The forecasting of the daily CO maximum levels is therefore essential in every attempt for protecting and improving public health in urban areas. The objective of this work is to create a suite of statistical models for predicting the one-day-ahead maximum CO levels based on both the meteorological and the pollutant data recorded in six monitoring sites in the greater area of Athens, Greece. The meteorological variables used as input consist of hourly values of the surface air Temperature, the Relative Humidity, the Wind Speed and the Wind Direction, while the pollutant parameters consist of hourly concentrations of nitrogen oxide, nitric dioxide, ozone and sulfur dioxide, all corresponding to the 7-year-period between 2001 and 2007. The models were developed on a seasonal (warm vs. cold period) and hebdomadal (workdays vs. weekends) basis and revealed that the influence of the air pollution levels recorded one day before (day m?1) on the maximum CO concentrations of day m is quite variable and depends on the site/type of the station, the local meteorology and the emission sources. Additionally, the analysis revealed that the CO concentrations are influenced by both local and/or wider area CO sources, suggesting a strong persistence of the CO levels, while only local meteorology (e.g. in the vicinity of the station and especially during working days) plays a role in the formation of present day’s CO levels. The derived models were validated against an independent yearlong data set (2008) through the use of a classical set of validation parameters known as the Model Validation Kit. Indices assessing the ability of the models to predict the CO exceedances of the EC limit value were also used. On the whole, it was found that the prognostic models introduced here manage to predict the CO maximum daily values in a satisfactory level, with Pearson’s correlation coefficients ranging between 0.62 and 0.76 during the warm period and between 0.51 and 0.80 during the cold period of the year. Similarly the index of agreement ranges between 0.50–0.95 during the warm period and 0.57–0.81 during the cold period of the year, revealing a rather adequate model performance.     

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.     

Comparison of non-parametric and parametric water temperature models on the Nivelle River,France

Abstract

Water temperature is an important abiotic variable in aquatic habitat studies and may be one of the factors limiting the potential fish habitat (e.g. salmonids) in a stream. Stream water temperatures are modelled using statistical approaches with air temperature and streamflow as exogenous variables in the Nivelle River, southern France. Two different models are used to model mean weekly maximum temperature data: a non-parametric approach, the k-nearest neighbours method (k-NN) and a parametric approach, the periodic autoregressive model with exogenous variables (PARX). The k-NN is a data-driven method, which consists of finding, at each point of interest, a small number of neighbours nearest to this value, and the prediction is estimated based on these neighbours. The PARX model is an extension of commonly-used autoregressive models in which parameters are estimated for each period within the years. Different variants of air temperature and flow are used in the model development. In order to test the performance of these models, a jack-knife technique is used, whereby model goodness of fit is assessed separately for each year. The results indicate that both models give good performances, but the PARX model should be preferred, because of its good estimation of the individual weekly temperatures and its ability to explicitly predict water temperature using exogenous variables.     

Multi-step SETARMA predictors in the analysis of hydrological time series

The performance of the self-exciting threshold autoregressive moving average model in forecasting river flow data is investigated. Multi-step forecasts of two daily time series are generated through three different nonlinear predictors. The model adequacy to capture the main features of the data under study and its forecasting performance are analysed and discussed.     

一套格点化的中国区域逐日观测资料及与其它资料的对比

为高分辨率气候模式检验等的需要,基于2400余个中国地面气象台站的观测资料,通过插值建立了一套0.25°×0.25°经纬度分辨率的格点化数据集(CN05.1).CN05.1包括日平均和最高、最低气温,以及降水4个变量.插值通过常用的"距平逼近"方法实现,首先将计算得到的气候平均场使用薄板样条方法进行插值,随后使用"角距权重法"对距平场进行插值,然后将两者叠加,得到最终的数据集.将CN05.1与CN05、EA05和APHRO三种日气温和降水资料(四种资料的分析时段统一为1961-2005年)进行对比,分析了它们对气候平均态和极端事件描述上的不同,结果表明几者总体来说在中国东部观测台站密集的地方差别较小,而在台站稀疏的西部差别较大,相差最大的是青藏高原北部至昆仑山西段等地形起伏较大而很少或没有观测台站的地方,反映了格点化数据在这些地区的不确定性,在使用中应予以注意.     

Comparison between gene expression programming and traditional models for estimating evapotranspiration under hyper arid Conditions

Gene Expression Programming (GEP) was used to develop new mathematical equations for estimating daily reference evapotranspiration (ET _ref) for the Kingdom of Saudi Arabia. The daily climatic variables were collected by 13 meteorological stations from 1980 to 2010. The GEP models were trained on 65% of the climatic data and tested using the remaining 35%. The generalised Penman-Monteith model was used as a reference target for evapotranspiration (ET) values, with h _c varies from 5 to 105 cm with increment of a centimetre. Eight GEP models have been compared with four locally calibrated traditional models (Hargreaves-Samani, Irmak, Jensen-Haise and Kimberly-Penman). The results showed that the statistical performance criteria values such as determination coefficients (R ²) ranged from as low as 64.4% for GEP-MOD1, where the only parameters included (maximum, minimum, and mean temperature and crop height), to as high as 95.5% for GEP-MOD8 with which all climatic parameters included (maximum, minimum and mean temperature; maximum, minimum and mean humidity; solar radiation; wind speed; and crop height). Moreover, an interesting founded result is that the solar radiation has almost no effect on ET _ref under the hyper arid conditions. In contrast, the wind speed and plant height have a great positive impact in increasing the accuracy of calculating ET _ref. Furthermore, eight GEP models have obtained better results than the locally calibrated traditional ET _ref equations.     

Fuzzy logic model approaches to daily pan evaporation estimation in western Turkey / Estimation de l’évaporation journalière du bac dans l’Ouest de la Turquie par des modèles à base de logique floue

Abstract

Abstract Evaporation is one of the fundamental elements in the hydrological cycle, which affects the yield of river basins, the capacity of reservoirs, the consumptive use of water by crops and the yield of underground supplies. In general, there are two approaches in the evaporation estimation, namely, direct and indirect. The indirect methods such as the Penman and Priestley-Taylor methods are based on meteorological variables, whereas the direct methods include the class A pan evaporation measurement as well as others such as class GGI-3000 pan and class U pan. The major difficulty in using a class A pan for the direct measurements arises because of the subsequent application of coefficients based on the measurements from a small tank to large bodies of open water. Such difficulties can be accommodated by fuzzy logic reasoning and models as alternative approaches to classical evaporation estimation formulations were applied to Lake Egirdir in the western part of Turkey. This study has three objectives: to develop fuzzy models for daily pan evaporation estimation from measured meteorological data, to compare the fuzzy models with the widely-used Penman method, and finally to evaluate the potential of fuzzy models in such applications. Among the measured meteorological variables used to implement the models of daily pan evaporation prediction are the daily observations of air and water temperatures, sunshine hours, solar radiation, air pressure, relative humidity and wind speed. Comparison of the classical and fuzzy logic models shows a better agreement between the fuzzy model estimations and measurements of daily pan evaporation than the Penman method.     

Annual streamflow modelling with asymmetric distribution function

Classical autoregressive models (AR) have been used for forecasting streamflow data in spite of restrictive assumptions, such as the normality assumption for innovations. The main reason for making this assumption is the difficulties faced in finding model parameters for non‐normal distribution functions. However, the modified maximum likelihood (MML) procedure used for estimating autoregressive model parameters assumes a non‐normally distributed residual series. The aim in this study is to compare the performance of the AR(1) model with asymmetric innovations with that of the classical autoregressive model for hydrological annual data. The models considered are applied to annual streamflow data obtained from two streamflow gauging stations in K?z?l?rmak Basin, Turkey. Copyright © 2008 John Wiley & Sons, Ltd.     

Using the Climate Forecast System Reanalysis as weather input data for watershed models

Obtaining representative meteorological data for watershed‐scale hydrological modelling can be difficult and time consuming. Land‐based weather stations do not always adequately represent the weather occurring over a watershed, because they can be far from the watershed of interest and can have gaps in their data series, or recent data are not available. This study presents a method for using the Climate Forecast System Reanalysis (CFSR) global meteorological dataset to obtain historical weather data and demonstrates the application to modelling five watersheds representing different hydroclimate regimes. CFSR data are available globally for each hour since 1979 at a 38‐km resolution. Results show that utilizing the CFSR precipitation and temperature data to force a watershed model provides stream discharge simulations that are as good as or better than models forced using traditional weather gauging stations, especially when stations are more than 10 km from the watershed. These results further demonstrate that adding CFSR data to the suite of watershed modelling tools provides new opportunities for meeting the challenges of modelling un‐gauged watersheds and advancing real‐time hydrological modelling. Copyright © 2013 John Wiley & Sons, Ltd.     

Long-term changes (1980–2003) in total ozone time series over Northern Hemisphere midlatitudes

Long-term changes in total ozone time series for Arosa, Belsk, Boulder and Sapporo stations are examined. For each station we analyze time series of the following statistical characteristics of the distribution of daily ozone data: seasonal mean, standard deviation, maximum and minimum of total daily ozone values for all seasons. The iterative statistical model is proposed to estimate trends and long-term changes in the statistical distribution of the daily total ozone data. The trends are calculated for the period 1980–2003. We observe lessening of negative trends in the seasonal means as compared to those calculated by WMO for 1980–2000. We discuss a possibility of a change of the distribution shape of ozone daily data using the Kolmogorov-Smirnov test and comparing trend values in the seasonal mean, standard deviation, maximum and minimum time series for the selected stations and seasons. The distribution shift toward lower values without a change in the distribution shape is suggested with the following exceptions: the spreading of the distribution toward lower values for Belsk during winter and no decisive result for Sapporo and Boulder in summer.     

Spatial distribution of monthly potential evaporation over mountainous regions: case of the Lhasa River basin,China

Abstract

This paper develops an algorithm for computing spatially-distributed monthly potential evaporation (PE) over a mountainous region, the Lhasa River basin in China. To develop the algorithm, first, correlation analysis of different meteorological variables was conducted. It was observed that PE is significantly correlated with vapour pressure and temperature differences between the land surface and the atmosphere. Second, the Dalton model, which was developed based on the mass transfer mechanism, was modified by including the influence of the related meteorological variables. Third, the influence of elevation on monthly temperature, vapour pressure and wind velocity was analysed, and functions for extending these meteorological variables to any given altitude were developed. Fourth, the inverse distance weighting method was applied to integrate the extended meteorological variables from five stations adjacent to and within the Lhasa River basin. Finally, using the modified Dalton model and the integrated meteorological variables, we computed the spatially-distributed monthly PE. This study indicated that spatially-distributed PE can be obtained using data from sparse meteorological stations, even if only one station is available; the results show that in the Lhasa River basin PE decreases when elevation increases. The new algorithm, including the modified model and the method for spatially extending meteorological variables can provide the basic inputs for distributed hydrological models.

Editor Z.W. Kundzewicz     

A Gridded Daily Min/Max Temperature Dataset With 0.1° Resolution for the Yangtze River Valley and its Error Estimation

The minimum/maximum (Min/Max) temperature in the Yangtze River valley is decomposed into the climatic mean and anomaly component. A spatial interpolation is developed which combines the 3D thin-plate spline scheme for climatological mean and the 2D Barnes scheme for the anomaly component to create a daily Min/Max temperature dataset. The climatic mean field is obtained by the 3D thin-plate spline scheme because the relationship between the decreases in Min/Max temperature with elevation is robust and reliable on a long time-scale. The characteristics of the anomaly field tend to be related to elevation variation weakly, and the anomaly component is adequately analyzed by the 2D Barnes procedure, which is computationally efficient and readily tunable. With this hybridized interpolation method, a daily Min/Max temperature dataset that covers the domain from 99°E to 123°E and from 24°N to 36°N with 0.1° longitudinal and latitudinal resolution is obtained by utilizing daily Min/Max temperature data from three kinds of station observations, which are national reference climatological stations, the basic meteorological observing stations and the ordinary meteorological observing stations in 15 provinces and municipalities in the Yangtze River valley from 1971 to 2005. The error estimation of the gridded dataset is assessed by examining cross-validation statistics. The results show that the statistics of daily Min/Max temperature interpolation not only have high correlation coefficient (0.99) and interpolation efficiency (0.98), but also the mean bias error is 0.00 °C. For the maximum temperature, the root mean square error is 1.1 °C and the mean absolute error is 0.85 °C. For the minimum temperature, the root mean square error is 0.89 °C and the mean absolute error is 0.67 °C. Thus, the new dataset provides the distribution of Min/Max temperature over the Yangtze River valley with realistic, successive gridded data with 0.1° × 0.1° spatial resolution and daily temporal scale. The primary factors influencing the dataset precision are elevation and terrain complexity. In general, the gridded dataset has a relatively high precision in plains and flatlands and a relatively low precision in mountainous areas.     

Deep echo state network: a novel machine learning approach to model dew point temperature using meteorological variables

ABSTRACT

The potential of different models – deep echo state network (DeepESN), extreme learning machine (ELM), extra tree (ET), and regression tree (RT) – in estimating dew point temperature by using meteorological variables is investigated. The variables consist of daily records of average air temperature, atmospheric pressure, relative humidity, wind speed, solar radiation, and dew point temperature (T_dew) from Seoul and Incheon stations, Republic of Korea. Evaluation of the model performance shows that the models with five and three-input variables yielded better accuracy than the other models in these two stations, respectively. In terms of root-mean-square error, there was significant increase in accuracy when using the DeepESN model compared to the ELM (18%), ET (58%), and RT (64%) models at Seoul station and the ELM (12%), ET (23%), and RT (49%) models at Incheon. The results show that the proposed DeepESN model performed better than the other models in forecasting T_dew values.     

Evaporation process modelling over northern Iran: application of an integrative data-intelligence model with the krill herd optimization algorithm

ABSTRACT

An integrated data-intelligence model based on multilayer perceptron (MLP) and krill herd optimization – the MLP-KH model – is presented for the estimation of daily pan evaporation. Daily climatological information collected from two meteorological stations in the northern region of Iran is used to compare the potential of the proposed model against classical MLP and support vector machine models. The integrated and the classical models were assessed based on different error and goodness-of-fit metrics. The quantitative results evidenced the capacity of the proposed MLP-KH model to estimate daily pan evaporation compared to the classical ones. For both weather stations, the lowest root mean square error (RMSE) of 0.725 and 0.855 mm/d, respectively, was obtained from the integrated model, while the RMSE for MLP was 1.088 and 1.197, and for SVM it was 1.096 and 1.290, respectively.     

Modeling and Prediction of Monthly Total Ozone Concentrations by Use of an Artificial Neural Network Based on Principal Component Analysis

In the work discussed in this paper we considered total ozone time series over Kolkata (22°34′10.92″N, 88°22′10.92″E), an urban area in eastern India. Using cloud cover, average temperature, and rainfall as the predictors, we developed an artificial neural network, in the form of a multilayer perceptron with sigmoid non-linearity, for prediction of monthly total ozone concentrations from values of the predictors in previous months. We also estimated total ozone from values of the predictors in the same month. Before development of the neural network model we removed multicollinearity by means of principal component analysis. On the basis of the variables extracted by principal component analysis, we developed three artificial neural network models. By rigorous statistical assessment it was found that cloud cover and rainfall can act as good predictors for monthly total ozone when they are considered as the set of input variables for the neural network model constructed in the form of a multilayer perceptron. In general, the artificial neural network has good potential for predicting and estimating monthly total ozone on the basis of the meteorological predictors. It was further observed that during pre-monsoon and winter seasons, the proposed models perform better than during and after the monsoon.