Implementation of linear regression and neural network models for local climate change assessment and forecasting based on time series data

Climate change studies are based on the data processing of the following time series for number of Ukrainian cities: daily precipitation and air temperature from the site of the European Climate Assessment & Dataset (ECA&D) project and monthly carbon dioxide emissions from fossil fuels in the atmosphere from the area of one geographical degree size from the site of the Carbon Dioxide Information Analysis Center (CDIAC). Assessment of synchronous dynamics and forecasting of the air temperature, precipitation according to the period 1950–2016 and the carbon dioxide concentration in atmosphere according to the period 1951–2013 was performed using two types of models: linear regression and neural network model in the form of perceptron with one hidden neuron layer. These models implementation is based on modern approaches to the Big Data intellectual analysis: Data Mining and Knowledge Discovery in Databases. The program scenarios for processing, intelligent analysis and forecasting of the above mentioned data time series using the constructed forecasting models have been developed and implemented in the unified analytical platform Deductor. The monthly time series of the emission in atmosphere of carbon dioxide from fossil fuels to area of 1 geographical degree in 1951–2013 for number of Ukrainian cities shows clear trend, which is well approximated by the cubic polynomial and does not contain a periodic seasonal component. There is the tendency to increasing CO<sub>2</sub> emissions before 1991 and the declining tendency after 1991 with some “plateau” in the period 2000–2009 that are years of relative stability in the economic development of Ukraine. However, there is no correlation between the trend of CO<sub>2</sub> emissions and the trend of average monthly temperature in 1951–2013. The predictive model of linear regression was the most acceptable for time series of average monthly temperature in 1950–2016, which are characterized by strong seasonal component with the periodicity of 1 year. Using the predictive model of linear regression [240 × 1], trained on the dataset, constructed by the sliding window method with retrospective depth of 240 months, the consistent forecast of the average monthly temperature time series for Kyiv after 12.01.2016 with the forecast horizon of 60 months was derived. However, the application of the predictive model of linear regression is characterized by a relatively short horizon of consistent forecasting. For the time series of the average monthly temperature for Kyiv city after 12.01.2016, the predictive neural network model [360 × 5 × 1] (number of inputs is equal to the selected prehistory depth of the time series samples that is 360; number of outputs is 1; number of neurons in the hidden layer is 5; activation function type is sigmoid with the given slope 1) provided the consistent forecast with the horizon of 120 months. Low values of the maximum and average relative errors of the neural network model were achieved on the training set (4.45·10<sup>-2</sup> and 2.99·10<sup>-4</sup>, respectively) and on the test set (3.60·10<sup>-2</sup> and 5.69·10<sup>-3</sup>, respectively). Similarly, for the time series of monthly CO<sub>2</sub> emissions for the Kyiv city after December 1, 2013, the predictive neural network model [240 × 5 × 1] provided consistent forecast with the horizon of 60 months. In general, the time series of monthly CO<sub>2</sub> emission values are characterized by much smaller values of the consistent forecast horizon in comparison with the time series of the average monthly temperature, at least when using predictive neural network models.