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Coronavirus disease knocked in Wuhan city of China in December 2019 which spread quickly across the world and infected millions of people within a short span of time. COVID-19 is a fast-spreading contagious disease which is caused by SARS-CoV-2 (severe acute respiratory syndrome-coronavirus-2). Accurate time series forecasting modeling is the need of the hour to monitor and control the universality of COVID-19 effectively, which will help to take preventive measures to break the ongoing chain of infection. India is the second highly populated country in the world and in summer the temperature rises up to 50°, nowadays in many states have more than 40° temperatures. The present study deals with the development of the autoregressive integrated moving average (ARIMA) model to predict the trend of the number of COVID-19 infected people in most affected states of India and the effect of a rise in temperature on COVID-19 cases. Cumulative data of COVID-19 confirmed cases are taken for study which consists of 77 sample points ranging from 1st March 2020 to 16th May 2020 from six states of India namely Delhi (Capital of India), Madya Pradesh, Maharashtra, Punjab, Rajasthan, and Uttar Pradesh. The developed ARIMA model is further used to make 1-month ahead out of sample predictions for COVID-19. The performance of ARIMA models is estimated by comparing measures of errors for these six states which will help in understanding future trends of COVID-19 outbreak. Temperature rise shows slightly negatively correlated with the rise in daily cases. This study is noble to analyse the variation of COVID-19 cases with respect to temperature and make aware of the state governments and take precautionary measures to flatten the growth curve of confirmed cases of COVID-19 infections in other states of India, nearby countries as well.

Almost every organization around the globe is working with uncertainty due to inevitable changes and growth in every sphere of life. These changes affect directly or indirectly the stock market prices which makes forecasting a challenging task. So, the need for reliable, cost-effective, and accurate forecasting models significantly arises to reduce risk and uncertainty in stock market investment. Different time series models have been proposed by data scientists and researchers for accurate prediction of the future with the least errors. Econometric autoregressive time series models such as autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models have established forecasting models capable of generating accurate forecasts. Wavelet methods, being capable of handling nonlinear data, combined with autoregressive models generate more accurate forecasts. In this present study, soft computing models of discreet wavelet transformation and wavelet denoising combined with autoregressive models are developed to forecast the weekly and daily closing prices of the BSE100 S&P Sensex index. Statistical error analysis of the forecasting outcomes of coupled models has been made to evaluate the performance of the prediction of these models. The prediction results reveal that soft computing methods coupled with autoregressive models (wavelet-ARIMA and wavelet denoise-ARIMA) generate considerably accurate forecasts as compared to baseline models (simple regression, ARMA and ARIMA models) and coupled models (wavelet-ARMA and wavelet denoise-ARMA models).

Machine learning is an innovative approach that has extensive applications in prediction. This technique needs to be applied for the COVID-19 pandemic to identify patients at high risk, their death rate, and other abnormalities. It can be used to understand the nature of this virus and further predict the upcoming issues. This literature-based review is done by searching the relevant papers on machine learning for COVID-19 from the databases of SCOPUS, Academia, Google Scholar, PubMed, and ResearchGate. This research attempts to discuss the significance of machine learning in resolving the COVID-19 pandemic crisis. This paper studied how machine learning algorithms and methods can be employed to fight the COVID-19 virus and the pandemic. It further discusses the primary machine learning methods that are helpful during the COVID-19 pandemic. We further identified and discussed algorithms used in machine learning and their significant applications. Machine learning is a useful technique, and this can be witnessed in various areas to identify the existing drugs, which also seems advantageous for the treatment of COVID-19 patients. This learning algorithm creates interferences out of unlabeled input datasets, which can be applied to analyze the unlabeled data as an input resource for COVID-19. It provides accurate and useful features rather than a traditional explicitly calculation-based method. Further, this technique is beneficial to predict the risk in healthcare during this COVID-19 crisis. Machine learning also analyses the risk factors as per age, social habits, location, and climate.

Accurate estimation of streamflow has a vital importance in water resources engineering, management and planning. In the present study, the abilities of group method of data handling-neural networks (GMDH-NN), dynamic evolving neural-fuzzy inference system (DENFIS) and multivariate adaptive regression spline (MARS) methods are investigated for monthly streamflow prediction. Precipitation, temperature and streamflows from Kalam and Chakdara stations at Swat River basin (mountainous basin), Pakistan, are used as inputs to the applied models in the form of different input scenarios, and models’ performances are evaluated on the basis of root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE) and combined accuracy (CA) indexes. Test results of the Kalam Station show that the DENFIS model provides more accurate prediction results in comparison of GMDH-NN and MARS models with the lowest RMSE (18.9 m3/s), MAE (13.1 m3/s), CA (10.6 m3/s) and the highest NSE (0.941). For the Chakdara Station, the MARS outperforms the GMDH-NN and DENFIS models with the lowest RMSE (47.5 m3/s), MAE (31.6 m3/s), CA (26.1 m3/s) and the highest NSE (0.905). Periodicity (month number of the year) effect on models’ accuracies in predicting monthly streamflow is also examined. Obtained results demonstrate that the periodicity improves the models’ accuracies in general but not necessarily in every case. In addition, the results also show that the monthly streamflow could be successfully predicted using only precipitation and temperature variables as inputs.

The potential of four different neuro-fuzzy embedded meta-heuristic algorithms, particle swarm optimization, genetic algorithm, harmony search, and teaching–learning-based optimization algorithm, was investigated in this study in estimating the water quality of the Yamuna River in Delhi, India. A cross-validation approach was employed by splitting data into three equal parts, where the models were evaluated using each part. The main aim of this study was to find an accurate prediction model for estimating the water quality of the Yamuna River. It is worth noting that the hybrid neuro-fuzzy and LSSVM methods have not been previously compared for this issue. Monthly water quality parameters, total kjeldahl nitrogen, free ammonia, total coliform, water temperature, potential of hydrogen, and fecal coliform were considered as inputs to model chemical oxygen demand (COD). The performance of hybrid neuro-fuzzy models in predicting COD was compared with classical neuro-fuzzy and least square support vector machine (LSSVM) methods. The results showed higher accuracy in COD prediction when free ammonia, total kjeldahl nitrogen, and water temperature were used as inputs. Hybrid neuro-fuzzy models improved the root mean square error of the classical neuro-fuzzy model and LSSVM by 12% and 4%, respectively. The neuro-fuzzy models optimized with harmony search provided the best accuracy with the lowest root mean square error (13.659) and mean absolute error (11.272), while the particle swarm optimization and teaching–learning-based optimization showed the highest computational speed (21 and 24 min) compared to the other models.

Precise estimation of water temperature plays a key role in environmental impact assessment, aquatic ecosystems’ management and water resources planning and management. In the current study, convolutional neural networks (CNN) and long short-term memory (LSTM) network-based deep learning models were examined to estimate daily water temperatures of the Bailong River in China. Two novel optimization algorithms, namely the reptile search algorithm (RSA) and weighted mean of vectors optimizer (INFO), were integrated with both deep learning models to enhance their prediction performance. To evaluate the prediction accuracy of the implemented models, four statistical indicators, i.e., the root mean square errors (RMSE), mean absolute errors, determination coefficient and Nash–Sutcliffe efficiency were utilized on the basis of different input combinations involving air temperature, streamflow, precipitation, sediment flows and day of the year (DOY) parameters. It was found that the LSTM-INFO model with DOY input outperformed the other competing models by considerably reducing the errors of RMSE and MAE in predicting daily water temperature.

Fast spreading coronavirus disease 2019 (COVID-19), originated in the Wuhan city, China in December 2019, is a contagious disease caused by Severe Acute Respiratory Syndrome-Coronavirus-2 (SARS-CoV-2). Within a short period, COVID-19 infections spread over large geographical area affecting millions of people and declared a pandemic by the World Health Organization (WHO). The fast and quick spread of the virus across the globe resulted in thousands of casualties. COVID-19 prevalence in India was reported in the late of January 2020 and the number of infections increased sharply by the end of March. In such a troublesome situation, time series analysis proves very much helpful in monitoring and assessing the growth curve of COVID-19 infections. In the present study, autoregressive integrated moving average (ARIMA) models are developed for the time series data of cumulative confirmed, recovered and causalities cases of COVID-19 in India. The data set under study is broken up into two subsets, modelling and testing data sets. After analysing the input data for stationarity using autocorrelation function (ACF) and partial correlation function (PACF) plots, different ARIMA models are estimated for confirmed, recovered and causalities’ cases of COVID-19 in India for modelling phase. ARIMA Model outputs are then compared with observed values of confirmed, recovered and casualties’ cases for the testing phase using error analysis. It has been found that ARIMA \(\left( {0,2,3} \right)\), ARIMA \(\left( {0,2,5} \right)\) and ARIMA \(\left( {1,2,1} \right)\) models are appropriate with the lowest mean absolute percentage error (MAPE) values for the data of confirmed cases, recovered cases and casualties’ cases respectively. Finally, the developed ARIMA models are used to forecast one-month ahead values of confirmed, recovered and casualties’ cases of COVID-19 in India. The predictions indicate rise in confirmed COVID-19 cases and speedy recoveries as well, whereas the casualties continue to show a constant trend in future. Based on these future trends of COVID-19 outbreak, governments and policymakers can take preventive measures to break the ongoing chain of COVID-19 infections and make necessary arrangements in the wake of an emergency.

This chapter aimed to survey some significant contributions in the field of artificial neural networks to solve the prediction problems related to finance and economics, environment, hydrology and agriculture preferably. A detailed methodology of artificial neural networks with historical background has been discussed here. The results of the survey reveal that artificial neural networks give more accurate forecasts than traditional and baseline regression, ARMA and ARIMA models, etc. The major contribution of this chapter is to provide the basic terminology of ANN architecture and methodology useful for different forecasting problems, and survey the available sources of different type of data to define a new problem in this field for future research.

In recent times, black carbon (BC) has attracted the interest of the researchers due to its adverse effect on human health, climate, rainfall, and global heating causing the melting of ice in the poles due to carbon deposition on it. Coal industry is the backbone of Indian economy and India being the world’s third largest producer of coal. Various mining activities are leading to spontaneous emission of black carbon in the atmosphere, especially in the IGP (Indo-Gangetic plain) region. Long-term studies related to black carbon emission in the coal regions of India are very rare. In the present study, a long-term datum of 38 years (1980–2018) for the amount of black carbon emission among the three important coal mines of India, namely Bokaro, Jharia, and Raniganj, is studied using correlation analysis, and time-series analysis along with a few other mathematical parameters. The comparison and forecast obtained using this study will be beneficial in the upcoming years, so as to gather the interest of the government, NGOs, and researchers in this area, so that new policies and preventive measures could be taken to curtail the black carbon concentration from the coal mines.

Water is the basic need for life to exist on this planet earth; rivers play a vital role to fulfill this need for the supply of freshwater. Due to spontaneous growth of industrialization and urbanization near the important rivers, most of them have been polluted to a severe extent and the future of these rivers and living organism depending on the water from them is on threat. Thus, various prediction models have been developed by researchers to build an accurate forecasting model to access the future quality of rivers with least forecasting error. Time series models have been developed to form such prediction, but most of them were unsuccessful in handling nonlinear problems. Artificial neural network (ANN) and adaptive neuro-fuzzy interface system have proven to be an efficient tool to handle such nonlinear situations. In this study, in addition to the above methods, wavelet transformation has been used to develop a forecasting model to generate forecasts close to actual values. The biochemical oxygen demand of river Yamuna at sample site of Nizamuddin (Delhi) is predicted using the past monthly averaged data. Statistical analysis has been used to study the nature of the wavelet domain constitutive series considered. The results obtained indicate that the neuro-fuzzy-wavelet-coupled model leads to considerably superior outcomes compared to neuro-fuzzy, ANN and regression models.

Biomass-derived biogas is a very promising alternative energy source because of its renewable and clean combustion characteristics compared to fossil petroleum diesel fuel. The forecasting of emiss...

The accurate estimation of suspended sediments (SSs) carries significance in determining the volume of dam storage, river carrying capacity, pollution susceptibility, soil erosion potential, aquatic ecological impacts, and the design and operation of hydraulic structures. The presented study proposes a new method for accurately estimating daily SSs using antecedent discharge and sediment information. The novel method is developed by hybridizing the multivariate adaptive regression spline (MARS) and the Kmeans clustering algorithm (MARS–KM). The proposed method’s efficacy is established by comparing its performance with the adaptive neuro-fuzzy system (ANFIS), MARS, and M5 tree (M5Tree) models in predicting SSs at two stations situated on the Yangtze River of China, according to the three assessment measurements, RMSE, MAE, and NSE. Two modeling scenarios are employed, data are divided into 50–50% for model training and testing in the first scenario, and the training and test data sets are swapped in the second scenario. In Guangyuan Station, the MARS–KM showed a performance improvement compared to ANFIS, MARS, and M5Tree methods in term of RMSE by 39%, 30%, and 18% in the first scenario and by 24%, 22%, and 8% in the second scenario, respectively, while the improvement in RMSE of ANFIS, MARS, and M5Tree was 34%, 26%, and 27% in the first scenario and 7%, 16%, and 6% in the second scenario, respectively, at Beibei Station. Additionally, the MARS–KM models provided much more satisfactory estimates using only discharge values as inputs.

Water is the most important substance for life on earth and every living being need freshwater to survive. Besides various sources of water, river water is all-important source of freshwater. Due to rapid urbanization, industrialization, religious and social practices on the banks of rivers, the river water gets polluted and it is one of the major issues in India. So, the need of hour is to keep a continuous check on the quality of river water parameters. Various researchers have developed accurate prediction models to estimate the future quality of river water with least forecasting errors. Autoregressive time series models have been developed to generate linear forecast only and most of them are unable to handle nonlinear problems. To handle such nonlinear problems, artificial neural network (ANN) and adaptive neuro-fuzzy interface system are found to be most efficient tool for accurate prediction. Besides these methods, wavelet decomposition tool for analyzing nonlinear situations has been used to generate forecast values close enough to observed values. The biochemical oxygen (BOD) of river Yamuna at sample site of Nizamuddin (Delhi) is predicted using the past monthly averaged data. Statistical analysis provides basis to understand the nature of wavelet domain constitutive series. The prediction results obtained using neuro-fuzzy-wavelet coupled model generates more accurate outcomes as compared to neuro-fuzzy, ANN and regression models.

Air pollution became a major problem, which is directly impacting on the health of humans by affecting the respiratory system and lungs. Air pollution is a major environmental health problem affecting emerging and established countries. Air pollutants contain gaseous pollutants (SO2, NO2, CO, etc.), suspended particulate matter (SPM), and odors like as dust, mist, fumes, and smoke. This chapter examines the role of soft computing techniques such as the Adaptive Neuro-Fuzzy Inference System (ANFIS), Artificial Neural Networks (ANNs), Wavelet, Auto-Regressive Integrated Moving Average (ARIMA), Fuzzy Logic (FL), and their hybrids in air pollution meteorology. In this chapter, a comprehensive review of the soft computing techniques using both ground-based and satellite-based datasets to study the different parameters like PM10, PM2.5, SOx, NOx, Aerosol Optical Depths (AOD) characteristics concerning the air pollution is reported. The advantages and limits of techniques are discussed and important problems that need future attention are identified.

Highlights • The study is about the prediction of COVID-19 cases in major countries around the globe. Its Noble study. • It will help the different countries to make the decision on this virus. • ARIMA and LSSVM are the machine learning models, which computes accurate prediction with the least error. • The model provides the 99% approximate accuracy. • This manuscript will also help to all governments for preparing isolation wards, availability of medical staff, medicines requirement, the decision on lock down, economic plans, etc., Discussions about the recently identified deadly coronavirus disease (COVID-19) which originated in Wuhan, China in December 2019 are common around the globe now. This is an infectious and even life-threatening disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It has rapidly spread to other countries from its originating place infecting millions of people globally. To understand future phenomena, strong mathematical models are required with the least prediction errors. In the present study, autoregressive integrated moving average (ARIMA) and least square support vector machine (LS-SVM) models are applied to the data consisting of daily confirmed cases of SARS-CoV-2 in the most affected five countries of the world for modeling and predicting one-month confirmed cases of this disease. To validate these models, the prediction results were tested by comparing it with testing data. The results revealed better accuracy of the LS-SVM model over the ARIMA model and also suggested a rapid rise of SARS-CoV-2 confirmed cases in all the countries under study. This analysis would help governments to take necessary actions in advance associated with the preparation of isolation wards, availability of medicines and medical staff, a decision on lockdown, training of volunteers, and economic plans.

Dissolved oxygen (DO) concentration is an important water-quality parameter, and its estimation is very important for aquatic ecosystems, drinking water resources, and agro-industrial activities. In the presented study, a new support vector machine (SVM) method, which is improved by hybrid firefly algorithm–particle swarm optimization (FFAPSO), is proposed for the accurate estimation of the DO. Daily pH, temperature (T), electrical conductivity (EC), river discharge (Q) and DO data from Fountain Creek near Fountain, the United States, were used for the model development. Various combinations of pH, T, EC, and Q were used as inputs to the models to estimate the DO. The outcomes of the proposed SVM–FFAPSO model were compared with the SVM–PSO, SVM–FFA, and standalone SVM with respect to the root mean square errors (RMSE), the mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and determination coefficient (R2), and graphical methods, such as scatterplots, and Taylor and violin charts. The SVM–FFAPSO showed a superior performance to the other methods in the estimation of the DO. The best model of each method was also assessed in multistep-ahead (from 1- to 7-day ahead) DO, and the superiority of the proposed method was observed from the comparison. The general outcomes recommend the use of SVM–FFAPSO in DO modeling, and this method can be useful for decision-makers in urban water planning and management.

Long-term aerosol climatology is derived using Terra MODIS (Collection 6) enhanced Deep Blue (DB) AOD retrieval algorithm to investigate decadal trend (2006–2015) in columnar aerosol loading, future scenarios and potential source fields over the Indo-Gangetic Plain (IGP), South Asia. Satellite based aerosol climatology was analyzed in two contexts: for the entire IGP considering area weighted mean AOD and for nine individual stations located at upper (Karachi, Multan, Lahore), central (Delhi, Kanpur, Varanasi, Patna) and lower IGP (Kolkata, Dhaka). A comparatively high aerosol loading (AOD: 0.50 ± 0.25) was evident over IGP with a statistically insignificant increasing trend of 0.002 year−1. Analysis highlights the existing spatial and temporal gradients in aerosol loading with stations over central IGP like Varanasi (decadal mean AOD±SD; 0.67 ± 0.28) and Patna (0.65 ± 0.30) exhibit the highest AOD, followed by stations over lower IGP (Kolkata: 0.58 ± 0.21; Dhaka: 0.60 ± 0.24), with a statistically significant increasing trend (0.0174–0.0206 year−1). In contrast, stations over upper IGP reveal a comparatively low aerosol loading, having an insignificant increasing trend. Variation in AOD across IGP is found to be mainly influenced by seasonality and topography. A distinct “aerosol pool” region over eastern part of Ganges plain is identified, where meteorology, topography, and aerosol sources favor the persistence of airborne particulates. A strong seasonality in aerosol loading and types is also witnessed, with high AOD and dominance of fine particulates over central to lower IGP, especially during post-monsoon and winter. The time series analyses by autoregressive integrated moving average (ARIMA) indicate contrasting patterns in randomness of AOD over individual stations with better performance especially over central IGP. Concentration weighted trajectory analyses identify the crucial contributions of western dry regions and partial contributions from central Highlands and north-eastern India, in regulating AOD over stations across IGP. Although our analyses provide some attributes to the observed changes in aerosol loading, we conclude that the spatial and temporal pattern of aerosol properties is highly complex and dynamic over IGP, and require further investigation in order to reduce uncertainty in aerosol-climate model.

Air pollution is a major issue in all around world, it directly impact on human health, which affecting the lungs and respiratory system. This deposited on soil, plants and in the water, further contributing to human exposure and It mixes in the blood and pumped all-around the body. The most important air pollutants found over Delhi were sulfur dioxide (SO2), nitrogen dioxides (NO2) and suspended particulate matter (SPM). Statistical and wavelet analysis of these air pollutants at three different sample sites two residential namely Janakpuri, Nizamuddin, and one industrial namely Shahazada Bagh over Delhi for the more than 20 year period from 1987 to 2010 in India have been studied. The results shown that the mean concentration of SO2 decreased for both residential (Janakpuri, Nizamuddin) as well as industrial (Shahzada Bagh) area, whereas NO2 increased but it is under the prescribed limits of National Ambient Air Quality Standards (NAAQS). Janakpuri and Nizamuddin represent almost equal but lower mean values of SO2 concentration than Shahzada Bagh. SO2, NO2 and SPM at all sites depicts symmetrical and platykurtic behaviour except Shahzada bagh, for that it follows leptokurtic. Discrete wavelet analysis of air pollutants using Daubechies wavelet (level 5) have been calculated for the study. It is also observed that the values at five different levels of signal data for all air pollutants varies between −225 and +225.

This study investigates the applicability of three different soft computing methods, least square support vector regression (LSSVR), multivariate adaptive regression splines (MARS), and M5 Model Tree (M5-Tree), in forecasting SO2 concentration. These models were applied to monthly data obtained from Janakpuri, Nizamuddin, and Shahzadabad, located in Delhi, India. The models were compared with each other using the cross validation method with respect to root mean square error, mean absolute error, and correlation coefficient. According to the comparison, LSSVR provided better accuracy than the other models, while the MARS model was found to be the second best model in forecasting monthly SO2 concentration. Results indicated that the applied models gave better forecasting accuracy in Janakpuri station than the other stations. The results were also compared with previous studies and satisfactory results were obtained from three methods in modeling SO2 concentrations.

Modeling pan evaporation (Epan) estimation is a vital issue in water resources management because it directly affects water reservoir and water supply systems. In the developing countries (e.g., India), Epan data are generally limited, and in such a circumstance, theoretical estimates from available climatic data could be beneficial. The study investigates the capability of three adaptive neuro-fuzzy methods, adaptive neuro-fuzzy inference system (ANFIS)–embedded grid partition (GP), subtractive clustering (SC), and fuzzy c-means clustering (FCM), in estimation of monthly pan evaporation using climatic inputs of minimum and maximum air temperatures, wind speed, sunshine hours, and relative humidity obtained from two stations, Uttarakhand, India. Cross validation method is applied by dividing data into three equal parts, and methods are tested using each part. Methods are evaluated by applying various combinations of inputs and using root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and determination coefficient (R2) criteria. The ANFIS-FCM is found to be superior to the ANFIS-GP and ANFIS-SC methods in Epan modeling. Cluster-based proposed neuro-fuzzy method increases performance of the best ANFIS-GP and ANFIS-SC models with respect to RMSE by about 9–14% for the both stations. The three ANFIS methods are also compared with each other and Stephen Stewart (SS) method by dividing data into three stages, training, validation, and test. The results indicate the superior accuracy of the ANFIS methods to SS for the same input variables. The ANFIS-FCM generally produces better Epan estimates than the other two ANFIS methods.

The paper analyzes the long-term noise monitoring data using autoregressive integrated moving averages (ARIMA) modeling technique and artificial neural networks (ANNs) methodology. Box-Jenkins ARIMA and ANN approach have been utilized to simulate daily equivalent LDay (06-22h) and LNight (22-06h) in A and C weightings for a period of 1 year. The forecasting performance is ascertained using the statistical tests. The work draws a comparison of time-series ARIMA and ANN approach for ascertaining their suitability for traffic noise modeling and forecasting. It is observed that the artificial neural network (ANN) models outperform the ARIMA models so developed. The pattern of ARIMAf orecasting models is directional and as such the time-series predictive model utilizing ANN approach has demonstrated superior performance over the ARIMA model.

Summary This study investigates the accuracy of least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5Tree) in modeling river water pollution. Various combinations of water quality parameters, Free Ammonia (AMM), Total Kjeldahl Nitrogen (TKN), Water Temperature (WT), Total Coliform (TC), Fecal Coliform (FC) and Potential of Hydrogen (pH) monitored at Nizamuddin, Delhi Yamuna River in India were used as inputs to the applied models. Results indicated that the LSSVM and MARS models had almost same accuracy and they performed better than the M5Tree model in modeling monthly chemical oxygen demand (COD). The average root mean square error (RMSE) of the LSSVM and M5Tree models was decreased by 1.47% and 19.1% using MARS model, respectively. Adding TC input to the models did not increase their accuracy in modeling COD while adding FC and pH inputs to the models generally decreased the accuracy. The overall results indicated that the MARS and LSSVM models could be successfully used in estimating monthly river water pollution level by using AMM, TKN and WT parameters as inputs.

Time series display irregular patterns and self-similar microstructures usually termed as fractals over a period of time, depending on several factors like climate, season, market fluctuations, growth cycles etc. Various methods are developed in mathematical modeling to investigate such trends in the time series. Black carbon is one of the major air pollutants released during several mining activities having dangerous effect on climate and human health. In this paper we aim to study the behavioral pattern and trends in the time series of black carbon concentration over the three major coal mines of India namely Raniganj, Jharia and Bokaro considering a long term time series data of past 38 years using regression and fractal dimensional analysis of black carbon between the major coal mines with the help statistical tools like Hurst exponent, predictability index and trend percent. In this comparative study it is observed that the time series display anti persistent behavior with positive and large variation then the past time. The results and comparisons obtained will be helpful in studying the behavior and trends in the concentration of black carbon over the coal mines regions. The significance of the study will be helpful to gather the interest of researcher’s, NGO’s and government towards the black carbon concentration over the coal mines so that preventive measures and new policies be framed to keep a check on black carbon concentration in these areas.

Highlights • The study is about the forecasting the deaths because of COVID-19 in major countries around the globe. Its noble study. • It will help the different countries to make the decision on this coronavirus disease. • Wavelet and ARIMA are coupled to develop new hybrid model, which computes accurate prediction with the least error. • The model provides the 99% approximate accuracy. • The manuscript will also help to all for preparing isolation wards and strategy for the newly infected patients., Everywhere around the globe, the hot topic of discussion today is the ongoing and fast-spreading coronavirus disease (COVID-19), which is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-COV-2). Earlier detected in Wuhan, Hubei province, in China in December 2019, the deadly virus engulfed China and some neighboring countries, which claimed thousands of lives in February 2020. The proposed hybrid methodology involves the application of discreet wavelet decomposition to the dataset of deaths due to COVID-19, which splits the input data into component series and then applying an appropriate econometric model to each of the component series for making predictions of death cases in future. ARIMA models are well known econometric forecasting models capable of generating accurate forecasts when applied on wavelet decomposed time series. The input dataset consists of daily death cases from most affected five countries by COVID-19, which is given to the hybrid model for validation and to make one month ahead prediction of death cases. These predictions are compared with that obtained from an ARIMA model to estimate the performance of prediction. The predictions indicate a sharp rise in death cases despite various precautionary measures taken by governments of these countries.

In this paper, new prediction model introduced by coupling of neural networks model, fuzzy model and wavelet model for the water resources management. Artificial neural network (ANN), fuzzy, wavelet and adaptive neuro-fuzzy inference system (ANFIS) are found to be a sturdy tool to model many non-linear hydrological processes. Wavelet transformation will improve the ability of a prediction model by capturing valuable information on different resolution levels. The target of this research is to compare our model with other famous data-driven models for monthly forecasting of water quality parameter chemical oxygen demand (COD) level monitored at Nizamuddin station, New Delhi, India of river Yamuna based on the past history. The data has been decomposed into wavelet domain constitutive sub series using Daubechies wavelet at level 8 (Db8). Statistical behavior of wavelet domain constitutive series has been studied. The foretelling performance of the wavelet coupled model has been compared with classical neuro fuzzy, artificial neural network and regression models. The result shows that the wavelet coupled model produces considerably higher leads to comparison to neuro fuzzy, neural network, regression models.

Long-term observations and modeling of aerosol loading over the Indo-Gangetic plains (IGP), the Indian desert region and Himalayan slopes are analyzed in the present study. The Box–Jenkins popular ARIMA (AutoRegressive Integrated Moving Average) model was applied to simulate the monthly-mean Terra MODIS (MODerate Resolution Imaging Spectroradiometer) Aerosol Optical Depth (AOD 550 nm) over eight sites in the region covering a period of about 13 years (March 2000–May 2012). The autocorrelation structure has been analyzed indicating a deterministic pattern in the time series that it regains its structure every 24 month period. The ARIMA models namely ARIMA(2,0,12), ARIMA(1,0,6), ARIMA(3,0,0), ARIMA(2,0,13) ARIMA(0,0,12), ARIMA(2,0,2), ARIMA(1,0,12) and ARIMA(0,0,1) have been developed as the most suitable for simulating and forecasting the monthly-mean AOD over the eight selected locations. The Stationary R-squared, R-squared, Root Mean Square Error (RMSE) and Normalized BIC (Bayesian Information Criterion) are used to test the validity and applicability of the developed ARIMA models revealing adequate accuracy in the model performance. The values of Hurst Exponent, Fractal Dimension and Predictability Index for AODs are about 0.5, 1.5 and 0, respectively, suggesting that the AODs in all sites follow the Brownian time-series motion (true random walk). High AOD values (> 0.7) are observed over the industrialized and densely-populated IGP sites associated with low ones over the foothills/slopes of the Himalayas. The trends in AOD during the ~ 13-year period differentiates depending on season and site. During post-monsoon and winter accumulation of aerosols and increasing trends are shown over IGP sites, which are neutralized in pre-monsoon and become slightly negative in monsoon. The AOD over the Himalayan sites does not exhibit any significant trend and seems to be practically unaffected by the aerosol built-up over IGP.

River water is a major resource of drinking water on earth. Management of river water is highly needed for surviving. Yamuna is the main river of India, and monthly variation of water quality of river Yamuna, using statistical methods have been compared at different sites for each water parameters. Regression, correlation coefficient, autoregressive integrated moving average (ARIMA), box-Jenkins, residual autocorrelation function (ACF), residual partial autocorrelation function (PACF), lag, fractal, Hurst exponent, and predictability index have been estimated to analyze trend and prediction of water quality. Predictive model is useful at 95% confidence limits and all water parameters reveal platykurtic curve. Brownian motion (true random walk) behavior exists at different sites for BOD, AMM, and total Kjeldahl nitrogen (TKN). Quality of Yamuna River water at Hathnikund is good, declines at Nizamuddin, Mazawali, Agra D/S, and regains good quality again at Juhikha. For all sites, almost all parameters except potential of hydrogen (pH), water temperature (WT) crosses the prescribed limits of World Health Organization (WHO)/United States Environmental Protection Agency (EPA).

Statistical modelling, analysis of physico-chemical parameters chemical oxygen demand (COD), biochemical oxygen demand (BOD), dissolved oxygen (DO), water temperature (WT), free ammonia (AMM), total Kjeldahl nitrogen (TKN), total coliform (TC), fecal coliform (FC) and potential of hydrogen (pH) monitored at the Hathnikund barrage (Haryana) sample site of river Yamuna in India have been studied. It has been observed that water-quality parameters such as COD-BOD, AMM-TKN, WT-pH and TC-FC are positively correlated whereas COD-DO, BOD-DO, TKN-FC and DO-WT are negatively correlated. For water-quality parameters such as pH, AMM, TC and FC no seasonal pattern is observed. Parameters such as COD, BOD, TKN, DO and WT follow a six-month seasonal pattern. All the parameters except DO and WT follow a positive trend for monthly and annual variations. BOD, AMM and TKN have anti-persistence behaviour for both monthly and yearly variations. For parameters COD (+27.83%), BOD (+42.36%), AMM (+49.63%), TKN (+22.71%)...

This paper deals with water quality management using statistical analysis and time-series prediction model. The monthly variation of water quality standards has been used to compare statistical mean, median, mode, standard deviation, kurtosis, skewness, coefficient of variation at Yamuna River. Model validated using R-squared, root mean square error, mean absolute percentage error, maximum absolute percentage error, mean absolute error, maximum absolute error, normalized Bayesian information criterion, Ljung–Box analysis, predicted value and confidence limits. Using auto regressive integrated moving average model, future water quality parameters values have been estimated. It is observed that predictive model is useful at 95 % confidence limits and curve is platykurtic for potential of hydrogen (pH), free ammonia, total Kjeldahl nitrogen, dissolved oxygen, water temperature (WT); leptokurtic for chemical oxygen demand, biochemical oxygen demand. Also, it is observed that predicted series is close to the original series which provides a perfect fit. All parameters except pH and WT cross the prescribed limits of the World Health Organization /United States Environmental Protection Agency, and thus water is not fit for drinking, agriculture and industrial use.

Statistical and wavelet analysis of water quality parameters COD (chemical oxygen demand), BOD (biochemical oxygen demand), DO (dissolved oxygen), WT (water temperature), AMM (free ammonia), TKN (total kjeldahl nitrogen), TC (total coliform), FC (fecal coliform) and pH (potential of hydrogen) monitored at Nizamuddin bridge-mid stream (Delhi) of Yamuna River in India have been studied. It has been observed that COD is highly correlated with BOD, AMM and TKN. Daubechies wavelet at level 5 (Db"5) have been calculated for each water quality parameters as it gives the finer scale approximation and decomposition of each water parameters. Wavelet decomposition and approximation using Db"5 of each parameters presented in seven parts namely s, a"5, d"1, d"2, d"3, d"4 and d"5 where ''s'' represents signal or raw data; low frequency part ''a"5'' gives an approximate of signal at level 5; high frequency parts d"1, d"2, d"3, d"4 and d"5 contains the detail of ''s'' at different levels respectively.

Statistical analysis of the water quality parameters COD (Chemical Oxygen Demand), BOD (Biochemical Oxygen Demand), DO (Dissolved Oxygen), WT (Water Temperature), AMM (Free Ammonia), TKN (Total Kjeldahl Ni- trogen), TC (Total Coliform), FC (Fecal Coliform) and pH (Potential of Hydrogen) monitored at Hathni Kund Dam (Haryana) Yamuna River in India have been studied. It has been observed that water quality parameter have positive correlation be- tween COD-BOD; AMM-TKN; WT-pH; TC-FC; and negatively correlation between COD-DO; BOD-DO; TKN-FC; DO-WT. Discrete wavelet analyses of water quality parameter using Daubechies wavelet at level 5 have been calculated. It has been observed that the values of signal data at five different levels for AMM, BOD, COD, DO, FC, pH, TC, TKN, WT varies between -1 to 1, -2 to 2, -20 to 20, -2 to 2, -5 to 5, -1 to 1, -2 to 2, -5 to 5, -10 to 10 respectively.

A study of the assessment and management of air quality was carried out at 11 coal mines in India. Long-term observations (about 13 years, March 2000–December 2012) and modeling of aerosol loading over coal mines in India are analyzed in the present study. In this respect, the Box-Jenkins popular autoregressive integrated moving average (ARIMA) model was applied to simulate the monthly mean Terra Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD550 nm) over 11 sites in the coal mines region. The ARIMA model was found as the most suitable model with least normalized Bayesian information criterion (BIC) and root mean square error and high value of R 2. Estimation was done with the Ljung-Box test. Finally, a forecast for a 3-year period from January 2013 to December 2015 was calculated which showed that the model forecasted values are following the observed trend quite well over all mining areas in India. The average values of AOD for the next 3 years (2013–2015) at all sites are found to be 0.575 ± 0.13 (Raniganj), 0.452 ± 0.12 (Jharia), 0.339 ± 0.13 (Bokaro), 0.280 ± 0.09 (Bishrampur), 0.353 ± 0.13 (Korba), 0.308 ± 0.08 (Talcher), 0.370 ± 0.11 (Wardha), 0.35 ± 0.10 (Adilabad), 0.325 ± 0.09 (Warangal), 0.467 ± 0.09 (Godavari Valley), and 0.236 ± 0.07 (Cuddapah), respectively. In addition, long-term lowest monthly mean AOD550 values are observed over Bishrampur followed by Cuddapah, Talcher, Warangal, Adilabad, Korba, Wardha, Godavari Valley, Jharia, and Raniganj. Raniganj and Jharia exhibit the highest AOD values due to opencast mines and extensive mining activities as well as a large number of coal fires. Similarly, the highest AOD values are observed during the monsoon season among all four seasons over all the mining sites. Raniganj exhibits the highest AOD value at all seasons and at all sites. In contrast, the lowest seasonal AOD values are observed during the post-monsoon season over Raniganj, Talcher, Wardha, Adilabad, Warangal, and Godavari Valley. Similarly, over Jharia, Bokaro, Bishrampur, Korba, and Cuddapah, the lowest AOD values are found in the winter season. Increasing trends in AOD550 have been observed over Raniganj, Bokaro, Bishrampur, Korba, Talcher, and Wardha as well as over Adilabad and Godavari Valley, which is in agreement with previous works. Negative or decreasing AOD trend is found only over Jharia, Warangal, and Cuddapah without being statistically significant. Seasonal trends in AODs have also been studied in the present paper.

Time series, trend, wavelet and statistical analysis of water quality parameters Chemical Oxygen Demand (COD), Biochemical Oxygen Demand (BOD), Dissolved Oxygen (DO) monitored for river Yamuna in India have been studied. It is observed that COD is highly correlated with BOD. For all auto regressive integrated moving average model (p,d,q) value of “d,” i.e. middle value is zero thus process is stationary. It is also observed that RMSE values are comparatively very low, thus dependent series is closed with the model predicted level. MAPE, MaxAPE, MAE, MaxAE, Normalized BIC are calculated and have low value for all parameters. Trend is calculated by using auto correlation function, partial auto correlation function, and lag. Thus the predictive model is useful at 95 % confidence limits. 1-D discrete and continuous Daubechies Wavelet analysis explains that the parameters COD, BOD, DO have the maximum value 120, 50, 8 and amplitude (a5) varies between 52 to 78, 10 to 30, 0.2 to 1.4, respectively. The scale values of Db5, i.e. d5, d4, d3, d2, and d1 range between − 20 and + 20 for all parameters. All parameters cross the prescribed limits of WHO/EPA, thus water is not fit for drinking, agriculture, and industrial use.

Natural and anthropogenic aerosols over coal mines regions in India play a significant role in influencing the regional radiation budget, causing climate implications to the overall hydrological cycle of India. In the reference of regional climate change and air quality, we discuss aerosol optical depth (AOD) variability and long-term trends (from Mar 2000–Dec 2012) over eastern, southeast, and south coalfield regions in India. The present work analyses the variations and trends in aerosol loading using Terra-MODIS (Moderate-Resolution Imaging Spectroradiometer) AOD550 data in the period 2000–2012. Overall, an increasing trend in AOD550 has been observed over all regions namely Raniganj (7.31 %) in eastern and Korba (5.0 %) in southeast, and Godavari Valley (32 %) in the south coalfield region in India. This increasing trend predominantly owes to a constant increase in the seasonal/monthly averaged AOD during the winter (Dec–Feb) and post-monsoon (Oct–Nov) seasons dominated by anthropogenic emissions. In contrast, a decreasing trend is observed during pre-monsoon (Mar–May) season over eastern coalfield region (−13 %), while at south coalfield region (44 %) and southeastern coalfield region (0.8 %), increasing trends are observed. Similarly, increasing trends is observed over all regions in monsoon (Jun–Sep) months. Furthermore, the values of Hurst exponent, fractal dimension, and predictability index for AODs are 0.5, 1.5, and 0, respectively suggesting that the AODs in all sites follow the Brownian time series motion (true random walk). High AOD values (0.59 ± 0.21) are observed over eastern region Raniganj.

Time series, trend and wavelet analysis of water quality parameters Chemical Oxygen Demand (COD), Biochemical Oxygen Demand (BOD), Dissolved Oxygen (DO) monitored at Nizamuddin bridge mid-stream of river Yamuna in India have been studied. In Auto Regressive Integrated Moving Average (ARIMA) model (p, d, q) value of ‘d’ is zero thus process is stationary. It is observed that Root Mean Square Error (RMSE) value are comparatively very low thus dependent series is closed with the model predicted level. The Mean Absolute Percentage Error (MAPE), MaxAPE, MAE, MaxAE, normalized Bayesian Information Criterion (BIC) are calculated and have low value. Trend is calculated by using Auto correlation function (ACF), Partial auto correlation function (PACF) and lag. The predictive model is useful at 95% confidence limits. The 1-D discrete and continuous Daubechies wavelet analysis explains that the parameters COD, BOD, DO have the maximum value 120, 50, 8; the value of a5 varies between 52 to 78, 10 to 30, 0.2 to 1.4 and the scale values of Db5, i.e., d5 ranges between −10 to 10; −5 to 5 and −0.5 to 0.5, respectively. It is concluded that as the value of COD, BOD increases and value of DO decreases, water is not fit for drinking, agriculture and industrial use.