Implementation of a hybrid MLP-FFA model for water level prediction of Lake Egirdir,Turkey

The predictive ability of a hybrid model integrating the Firefly Algorithm (FFA), as a heuristic optimization tool with the Multilayer Perceptron (MLP-FFA) algorithm for the prediction of water level in Lake Egirdir, Turkey, is investigated. The accuracy of the hybrid MLP-FFA model is then evaluated against the standalone MLP-based model developed with the Levenberg–Marquadt optimization scheme applied for in the backpropagation-based learning process. To develop and investigate the veracity of the proposed hybrid MLP-FFA model, monthly time scale water level data for 56 years (1961–2016) are applied to train and test the hybrid model. The input combinations of the standalone and the hybrid predictive models are determined in accordance with the Average Mutual Information computed from the historical water level (training) data; generating four statistically significant lagged combinations of historical data to be adopted for the 1-month forecasting of lake water level. The proposed hybrid MLP-FFA model is evaluated with statistical score metrics: Nash–Sutcliffe efficiency, root mean square and mean absolute error, Wilmott’s Index and Taylor diagram developed in the testing phase. The analysis of the results showed that the hybrid MLP–FFA4 model (where 4 months of lagged combinations of lake water level data are utilized) performed more accurately than the standalone MLP4 model. For the fully optimized hybrid (MLP-FFA4) model evaluated in the testing phase, the Willmott’s Index was approximately 0.999 relative to 0.988 (MLP 4) and the root mean square error was approximately 0.029 m and compared to 0.102 m. Moreover, the inter-comparison of the forecasted and the observed data with various other performance metrics (including the Taylor diagram) verified the robustness of the proposed hybrid MLP-FFA4 model over the standalone MLP4 model applied in the problem of forecasting lake water level prediction in the current semi-arid region in Turkey.     

Stream flow forecasting using neuro‐wavelet technique

This paper proposes the application of a neuro‐wavelet technique for modelling monthly stream flows. The neuro‐wavelet model is improved by combining two methods, discrete wavelet transform and multi‐layer perceptron, for one‐month‐ahead stream flow forecasting and results are compared with those of the single multi‐layer perceptron (MLP), multi‐linear regression (MLR) and auto‐regressive (AR) models. Monthly flow data from two stations, Gerdelli Station on Canakdere River and Isakoy Station on Goksudere River, in the Eastern Black Sea region of Turkey are used in the study. The comparison results revealed that the suggested model could increase the forecast accuracy and perform better than the MLP, MLR and AR models. Copyright © 2008 John Wiley & Sons, Ltd.     

Developing a hybrid multi‐model for peak flood forecasting

The present study aims to develop a hybrid multi‐model using the soft computing approach. The model is a combination of a fuzzy logic, artificial neural network (ANN) and genetic algorithm (GA). While neural networks are low‐level computational structures that perform well dealing with raw data, fuzzy logic deal with reasoning on a higher level by using linguistic information acquired from domain experts. However, fuzzy systems lack the ability to learn and cannot adjust themselves to a new environment. Moreover, experts occasionally make mistakes and thus some rules used in a system may be false. A network type structure of the present hybrid model is a multi‐layer feed‐forward network, the main part is a fuzzy system based on the first‐order Sugeno fuzzy model with a fuzzification and a defuzzification processes. The consequent parameters are determined by least square method. The back‐propagation is applied to adjust weights of network. Then, the antecedent parameters of the membership function are updated accordingly by the gradient descent method. The GA was applied to select the fuzzy rule. The hybrid multi‐model was used to forecast the flood level at Chiang Mai (under the big flood 2005) and the Koriyama flood (2003) in Japan. The forecasting results are evaluated using standard global goodness of fit statistic, efficient index (EI), the root mean square error (RMSE) and the peak flood error. Moreover, the results are compared to the results of a neuro‐genetic model (NGO) and ANFIS model using the same input and output variables. It was found that the hybrid multi‐model can be used successfully with an efficiency index (EI) more than 0·95 (for Chiang Mai flood up to 12 h ahead forecasting) and more than 0·90 (for Koriyama flood up to 8 h ahead forecasting). In general, all of three models can predict the water level with satisfactory results. However, the hybrid model gave the best flood peak estimation among the three models. Therefore, the use of fuzzy rule base, which is selected by GA in the hybrid multi‐model helps to improve the accuracy of flood peak. Copyright © 2009 John Wiley & Sons, Ltd.     

Wavelet regression model as an alternative to neural networks for monthly streamflow forecasting

The accuracy of the wavelet regression (WR) model in monthly streamflow forecasting is investigated in the study. The WR model is improved combining the two methods—the discrete wavelet transform (DWT) model and the linear regression (LR) model—for 1‐month‐ahead streamflow forecasting. In the first part of the study, the results of the WR model are compared with those of the single LR model. Monthly flow data from two stations, Gerdelli Station on Canakdere River and Isakoy Station on Goksudere River, in Eastern Black Sea region of Turkey are used in the study. The comparison results reveal that the WR model could increase the forecast accuracy of the LR model. In the second part of the study, the accuracy of the WR model is compared with those of the artificial neural networks (ANN) and auto‐regressive (AR) models. On the basis of the results, the WR is found to be better than the ANN and AR models in monthly streamflow forecasting. Copyright © 2009 John Wiley & Sons, Ltd.     

Short‐term inflow forecasting using an artificial neural network model

The primary objective of this study is to investigate the possibility of including more temporal and spatial information on short‐term inflow forecasting, which is not easily attained in the traditional time‐series models or conceptual hydrological models. In order to achieve this objective, an artificial neural network (ANN) model for short‐term inflow forecasting is developed and several issues associated with the use of an ANN model are examined in this study. The formulated ANN model is used to forecast 1‐ to 7‐h ahead inflows into a hydropower reservoir. The root‐mean‐squared error (RMSE), the Nash–Sutcliffe coefficient (NSC), the A information criterion (AIC), B information criterion (BIC) of the 1‐ to 7‐h ahead forecasts, and the cross‐correlation coefficient between the forecast and observed inflows are estimated. Model performance is analysed and some quantitative analysis is presented. The results obtained are satisfactory. Perceived strengths of the ANN model are the capability for representing complex and non‐linear relationships as well as being able to include more information in the model easily. Although the results obtained may not be universal, they are expected to reveal some possible problems in ANN models and provide some helpful insights in the development and application of ANN models in the field of hydrology and water resources. Copyright © 2002 John Wiley & Sons, Ltd.     

Enhancing streamflow forecasting using the augmenting ensemble procedure coupled machine learning models: case study of Aswan High Dam

ABSTRACT

The potential of the most recent pre-processing tool, namely, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), is examined for providing AI models (artificial neural network, ANN; M5-model tree, M5-MT; and multivariate adaptive regression spline, MARS) with more informative input–output data and, thence, evaluate their forecasting accuracy. A 130-year inflow dataset for Aswan High Dam, Egypt, is considered for training, validating and testing the proposed models to forecast the reservoir inflow up to six months ahead. The results show that, after the pre-processing analysis, there is a significant enhancement in the forecasting accuracy. The MARS model combined with CEEMDAN gave superior performance compared to the other models – CEEMDAN-ANN and CEEMDAN-M5-MT – with an increase in accuracy of, respectively, about 13–25% and 6–20% in terms of the root mean square error.     

西藏扎布耶盐湖水位Winters和ARIMA模型分析

由于温室效应,气温加速上升,我国西部干旱一半干旱盐湖区盐湖水位出现加速下降或上升等变化．藏北高原湖泊众多,但都缺少湖水位的人工观测记录．中国地质科学院盐湖中心自1990年始在西藏扎布耶盐湖建立了长期科学观测站,进行水位动态观测,积累了连续13年珍贵的数据．如何根据湖泊水位历史记录数据,准确的定量预测水位中短期变化,是关系着盐湖资源开发命运的大事．本文用Winters线性和季节性指数平滑法、ARIMA乘积季节模型两种时间序列分析方法,根据西藏扎布耶盐湖1991年1月-2003年12月水位变化的时间序列数据,探讨了两种时间序列数据的预测方法在盐湖水位动态变化预测中的应用．     

基于随机森林的内陆湖泊水体有色可溶性有机物(CDOM)浓度遥感估算

水体中的有色可溶性有机物(CDOM)是湖泊生态系统中氮、磷等有机营养物质的重要来源,利用卫星遥感数据反演内陆水体中CDOM浓度一直是个挑战.因此本文基于滇池2009年9月、2017年4月以及太湖2016年7月的现场原位观测和室内实验,在分析水体固有光学特性的基础上,引入机器学习算法,建立了基于哨兵-3A OLCI传感器的我国内陆湖泊水体CDOM浓度随机森林反演模型.利用独立的验证数据集对所构建的随机森林模型及常用的波段比值模型、一阶微分模型、半分析模型、BP神经网络模型等的反演精度进行评价.结果表明:随机森林模型的均方根误差为0.14 m-1,平均相对误差为21%,与反演效果相对较好的BP神经网络模型相比,均方根误差降低了50%,平均相对误差降低了38%,反演精度得到了显著的提高.根据随机森林算法的特征重要性参数提供的各自变量影响力结果,发现B11(709 nm)和B6(560 nm)波段贡献率最大,是反演CDOM的敏感波段.最后将随机森林模型应用到滇池2017年4月12日、太湖2017年5月18日的哨兵-3A OLCI影像上,得到滇池、太湖水体CDOM浓度分布图.滇池CDOM浓度的分布特征大致符合东北、西南高,中西部低的趋势,且河口处的CDOM浓度高于湖泊水体,表明径流的输入给滇池水体带来了大量的CDOM.太湖CDOM浓度的分布特征大致符合西部高,湖心区和东部低的趋势.太湖西部以及北部梅梁湾受入湖河流影响较大,CDOM浓度较高,太湖开敞区远离河口处,受外源河流的影响逐渐减小,且由于湖水的不断稀释,CDOM浓度不断降低.太湖东部水生植物很多,湖水较为清澈,CDOM浓度较低.     

Effects of changing climate on ice cover in three morphometrically different lakes

A one‐dimensional hydrodynamic lake model (DYRESM‐WQ‐I) is employed to simulate ice cover and water temperatures over the period 1911–2014. The effects of climate changes (air temperature and wind speed) on ice cover (ice‐on, ice‐off, ice cover duration, and maximum ice thickness) are modeled and compared for the three different morphometry lakes: Fish Lake, Lake Wingra, and Lake Mendota, located in Madison, Wisconsin, USA. It is found that the ice cover period has decreased due to later ice‐on dates and earlier ice‐off dates, and the annual maximum ice cover thickness has decreased for the three lakes during the last century. Based upon simulated perturbations of daily mean air temperatures across the range of ?10°C to +10°C of historical values, Fish Lake has the most occurrences of no ice cover and Lake Wingra still remains ice covered under extreme conditions (+10°C). Overall, shallower lakes with larger surface areas appear more resilient to ice cover changes caused by climate changes.     

A two‐step‐ahead recurrent neural network for stream‐flow forecasting

In many engineering problems, such as flood warning systems, accurate multistep‐ahead prediction is critically important. The main purpose of this study was to derive an algorithm for two‐step‐ahead forecasting based on a real‐time recurrent learning (RTRL) neural network that has been demonstrated as best suited for real‐time application in various problems. To evaluate the properties of the developed two‐step‐ahead RTRL algorithm, we first compared its predictive ability with least‐square estimated autoregressive moving average with exogenous inputs (ARMAX) models on several synthetic time‐series. Our results demonstrate that the developed two‐step‐ahead RTRL network has efficient ability to learn and has comparable accuracy for time‐series prediction as the refitted ARMAX models. We then investigated the two‐step‐ahead RTRL network by using the rainfall–runoff data of the Da‐Chia River in Taiwan. The results show that the developed algorithm can be successfully applied with high accuracy for two‐step‐ahead real‐time stream‐flow forecasting. Copyright © 2003 John Wiley & Sons, Ltd.     

Simulating water temperatures and stratification of a pre‐alpine lake with a hydrodynamic model: calibration and sensitivity analysis of climatic input parameters

We report on the calibration of the one‐dimensional hydrodynamic lake model Dynamic Reservoir Simulation Model to simulate the water temperature conditions of the pre‐alpine Lake Ammersee (southeast Germany) that is a representative of deep and large lakes in this region. Special focus is given to the calibration in order to reproduce the correct thermal distribution and stratification including the time of onset and duration of summer stratification. To ensure the application of the model to investigate the impact of climate change on lakes, an analysis of the model sensitivity under stepwise modification of meteorological input parameters (air temperature, wind speed, precipitation, global radiation, cloud cover, vapour pressure and tributary water temperature) was conducted. The total mean error of the calibration results is ?0.23 °C, the root mean square error amounts to 1.012 °C. All characteristics of the annual stratification cycle were reproduced accurately by the model. Additionally, the simulated deviations for all applied modifications of the input parameters for the sensitivity analysis can be differentiated in the high temporal resolution of monthly values for each specific depth. The smallest applied alteration to each modified input parameter caused a maximum deviation in the simulation results of at least 0.26 °C. The most sensitive reactions of the model can be observed through modifications of the input parameters air temperature and wind speed. Hence, the results show that further investigations at Lake Ammersee, such as coupling the hydrodynamic model with chemo‐dynamic models to assess the impact of changing climate on biochemical conditions within lakes, can be carried out using Dynamic Reservoir Simulation Model. Copyright © 2012 John Wiley & Sons, Ltd.     

Adjusting wavelet‐based multiresolution analysis boundary conditions for long‐term streamflow forecasting

We propose a novel technique for improving a long‐term multi‐step‐ahead streamflow forecast. A model based on wavelet decomposition and a multivariate Bayesian machine learning approach is developed for forecasting the streamflow 3, 6, 9, and 12 months ahead simultaneously. The inputs of the model utilize only the past monthly streamflow records. They are decomposed into components formulated in terms of wavelet multiresolution analysis. It is shown that the model accuracy can be increased by using the wavelet boundary rule introduced in this study. A simulation study is performed to evaluate the effects of different wavelet boundary rules using synthetic and real streamflow data from the Yellowstone River in the Uinta Basin in Utah. The model based on the combination of wavelet and Bayesian machine learning regression techniques is compared with that of the wavelet and artificial neural networks‐based model. The robustness of the models is evaluated. Copyright © 2015 John Wiley & Sons, Ltd.     

Wavelet–copula‐based mutual information for rainfall forecasting applications

Under a climate change, the physical factors that influence the rainfall regime are diverse and difficult to predict. The selection of skilful inputs for rainfall forecasting models is, therefore, more challenging. This paper combines wavelet transform and Frank copula function in a mutual information‐based input variable selection (IVS) for non‐linear rainfall forecasting models. The marginal probability density functions (PDFs) of a set of potential rainfall predictors and the rainfall series (predictand) were computed using a wavelet density estimator. The Frank copula function was applied to compute the joint PDF of the predictors and the predictand from their marginal PDFs. The relationship between the rainfall series and the potential predictors was assessed based on the mutual information computed from their marginal and joint PDFs. Finally, the minimum redundancy maximum relevance was used as an IVS stopping criterion to determine the number of skilful input variables. The proposed approach was applied to four stations of the Nigerien Sahel with rainfall series spanning the period 1950–2016 by considering 24 climate indices as potential predictors. Adaptive neuro‐fuzzy inference system, artificial neural networks, and random forest‐based forecast models were used to assess the skill of the proposed IVS method. The three forecasting models yielded satisfactory results, exhibiting a coefficient of determination between 0.52 and 0.69 and a mean absolute percentage error varying from 13.6% to 21%. The adaptive neuro‐fuzzy inference system performed better than the other models at all the stations. A comparison made with KDE‐based mutual information showed the advantage of the proposed wavelet–copula approach.     

基于小波神经网络耦合模型对云南星云湖富营养化气象驱动因子的分析

气象因子是影响湖泊富营养化的重要因素,而湖泊富营养化对人群健康、生态系统和社会经济等均有负面影响.本文基于统计资料及遥感数据,结合Morlet小波分析和BP多层前馈神经网络(BP神经网络)构建了不同时间尺度下的小波神经网络耦合模型,分析了19862011年云南星云湖水华强度变化与月降雨量、月平均气温、月平均风速、月日照...     

Estimating daily inflows of large lakes using a water‐balance‐based runoff coefficient scaling approach

Daily river inflow time series are highly valuable for water resources and water environment management of large lakes. However, the availability of continuous inflow data for large lakes is still relatively limited, especially for large lakes situated within humid plain regions with tens or even hundreds of tributaries. In this study, we choose the fifth largest freshwater Lake Chaohu in China as our study area to introduce a new approach to reconstruct historical daily inflows at ungauged subcatchments of large lakes. This approach makes use of water level, lake surface rainfall, evaporation from the lake, and catchment rainfall observations. Rainfall–runoff relationship at a reference catchment was analysed to select rainfall input and estimate run‐off coefficient firstly, and the run‐off coefficient was then transferred to ungauged subcatchments to initially estimate daily inflows. Run‐off coefficient was scaled to adjust daily inflows at ungauged subcatchments according to water balance of the lake. This approach was evaluated using sparsely measured inflows at eight subcatchments of Lake Chaohu and compared with the commonly used drainage area ratio method. Results suggest that the inflow time series reconstructed from this approach consistent well to corresponding observations, with mean R² and Nash–Sutcliffe efficiency values of 0.69 and 0.6, respectively. This approach outperforms drainage area ratio method in terms of mean R² and Nash–Sutcliffe efficiency values. Accuracy of this approach holds well when the number of water‐level station being used decreased from four to one.     

Environmental isotope study on hydrodynamics of Lake Naini,Uttar Pradesh,India

Environmental isotopes (δ¹⁸O, δD and ³H) were used to understand the hydrodynamics of Lake Naini in the State of Uttar Pradesh, India. The data was correlated with the in situ physico‐chemical parameters, namely temperature, electrical conductivity and dissolved oxygen. The analysis of the data shows that Lake Naini is a warm monomictic lake [i.e. in a year, the lake is stratified during the summer months (March/April to October/November) and well mixed during the remaining months]. The presence of a centrally submerged ridge inhibits the mixing of deeper waters of the lake's two sub‐basins, and they exhibit differential behaviour. The rates of change of isotopic composition of hypolimnion and epilimnion waters of the lake indicate that the water retention time of the lake is very short, and the two have independent inflow components. A few groundwater inflow points to the lake are inferred along the existing fractures, fault planes and dykes. In addition to poor vertical mixing of the lake due to the temperature‐induced seasonal stratification, the lake also shows poor horizontal mixing at certain locations of the lake. The lake–groundwater system appears to be a flow‐through type. Also, a tritium and water‐balance model was developed to estimate the water retention time of well‐mixed and hydrologically steady state lakes. The model assumes a piston flow of groundwater contributing to the lake. The developed model was verified for (a) Finger Lakes, New York; (b) Lake Neusiedlersee, Austria; and (c) Blue Lake, Australia based on literature data. The predicted water retention times of the lakes were close to those reported or calculated from the hydrological parameters given in the references. On application of this model to Lake Naini, a water retention time of ～2 years and age of groundwater contributing to the lake ～14 years is obtained. Copyright © 2001 John Wiley & Sons, Ltd.     

Quantitative comparison of river inflows to a rapidly expanding lake in central Tibetan Plateau

The recent rapid expansion of inland lakes on the Tibetan Plateau (TP) are a good indicator of the consequences of climate change. Quantifying the hydrological cycle of the lake basin is fundamentally important to understand the causes of lake growth. However, the hydrological processes of the TP interior are very complex and difficult to investigate because of the lack of observations. This is especially true for estimating the lake changes when run‐off inflows are affected by small lakes located in the flow routes within drainage areas. We used an integrated hydrological model, in combination with glacier melt and lake retention models, to analyse the run‐off inflows to Lake Siling Co, the largest endorheic lake in Tibet. It includes four subdrainage basins: Zhajiazangbu, Zhagenzangbu, Alizangbu, and Boquzangbu. Lake Siling Co was characterized by considerable increases during warm season from 1981 to 2012, due to the increased run‐off from Zhajiazangbu accounting for about 51–62% of the total run‐off inflows. Moreover, the dramatic increases exhibited during cold seasons were related to the increased retention water released from the small lakes within Zhagenzangbu and Alizangbu. Of the studied subdrainage basins, Boquzangbu contributed the least during both warm and cold seasons. On average, the annual amount of evaporation from lakes within the drainage area was about 2 times greater than that of glacier melt run‐off. Our results suggest that the retention effects of lakes on river inflows should receive more attention, because understanding these effects is potentially crucial to improved understanding of lake variations in the TP.     

Stage level,volume and time‐frequency information content of Lake Tana using stochastic and wavelet analysis methods

Lake Tana is the largest fresh water body situated in the north‐western highlands of Ethiopia. In addition to its ecological services, it serves for local transport, electric power generation, fishing, recreational purposes, and source of dry season irrigation water supply. Evidence shows that the lake has dried at least once at about 15,000–17,000 before present owing to a combination of high evaporation and low precipitation events. Past attempts to understand and simulate historical fluctuation of Lake Tana based on simplistic water balance approach of inflow, outflow, and storage have failed to capture well‐known events of drawdown and rise of the lake that have happened in the last 44 years. This study tested different stochastic methods of lake level and volume simulation for supporting Lake Tana operational planning decision support. Three stochastic methods (perturbations approach, Monte Carlo methods, and wavelet analysis) were employed for lake level and volume simulation, and the results were compared with the stage level measurements. Forty‐four years of daily, monthly, and mean annual lake level data have shown a Gaussian variation with goodness of fit at 0.01 significant levels of the Kolmogorov–Smirnov test. The stochastic simulations predicted the lake stage level of the 1972, 1984, and 2002/2003 historical droughts 99% of the time. The information content (frequency) of fluctuation of Lake Tana for various periods was resolved using Wigner's Time‐Frequency Decomposition method. The wavelet analysis agreed with the perturbations and Monte Carlo simulations resolving the time (1970s, 1980s, and 2000s) in which low frequency and high spectral power fluctuation has occurred. The Monte Carlo method has shown its superiority for risk analysis over perturbation and deterministic method whereas wavelet analysis reconstructed historical record of lake stage level at daily and monthly time scales. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling hydrodynamics in Yachiyo Lake using a non‐hydrostatic general circulation model with spatially and temporally varying meteorological conditions

In this study, a three‐dimensional (3D) non‐hydrostatic circulation model was applied to study the thermal structure, its evolution and water circulation of Yachiyo Lake in Hiroshima, Japan. The simulations were conducted for 1 month during July 2006. The meteorological forcing variables such as wind stress, surface atmospheric pressure and heat flux transfer through the lake surface were provided by an atmospheric mesoscale model run. The vertical mixing process of the lake was calculated using the Mellor‐Yamada turbulence model. The 1‐month numerical simulation revealed the wind‐induced currents of the lake, two gyres in the mid‐layer, and depth‐averaged monthly mean currents. Further numerical experiments studying the mechanism of the two gyres in the lake showed the important role of topography in gyre formation. The thermal structure of the lake and its evolution both in space and in time as predicted by the model showed very good agreement with the observed values and characteristics of Yachiyo Lake. The internal gravity waves, which are crucial for mixing in the stratified lake, are depicted by the vertical fluctuation of isotherms. Using the non‐dimensional gradient Richardson number, Yachiyo Lake was determined to be stable under strong stratification during the study period, and therefore very sensitive to wind stress. Copyright © 2009 John Wiley & Sons, Ltd.     

A theoretical study on terrestrial gravimetric data refinement by Earth gravity models

The idea of this paper is to present estimators for combining terrestrial gravity data with Earth gravity models and produce a high‐quality source of the Earth's gravity field data through all wavelengths. To do so, integral and point‐wise estimators are mathematically developed, based on the spectral combination theory, in such a way that they combine terrestrial data with one and/or two Earth gravity models. The integral estimators are developed so that they become biased or unbiased to a priori information. For testing the quality of the estimators, their global mean square errors are generated using an Earth gravity model08 model and one of the recent products of the gravity field and steady‐state ocean circulation explorer mission. Numerical results show that the integral estimators have smaller global root mean square errors than the point‐wise ones but they are not efficient practically. The integral estimator of the biased type is the most suited due to its smallest global root mean square error comparing to the rest of the estimators. Due largely to the omission errors of Earth gravity models the point‐wise estimators are not sensitive to the Earth gravity model commission error; therefore, the use of high‐degree Earth gravity models is very influential for reduction of their root mean square errors. Also it is shown that the use of the ocean circulation explorer Earth gravity model does not significantly reduce the root mean square errors of the presented estimators in the presence of Earth gravity model08. All estimators are applied in the region of Fennoscandia and a cap size of 2° for numerical integration and a maximum degree of 2500 for generation of band‐limited kernels are found suitable for the integral estimators.