A statistical framework to assess time trend and predict near-future climatic conditions

A statistical framework to assess the long-term climatic water balance changes includes the following phases of the data analysis and predictions: (1) Preparation of daily, monthly, and yearly averaged time series of meteorological parameters (temperature, relative humidity, precipitation, wind speed, etc.), and an evaluation of the temporal structural breakpoints (breakthroughs) of meteorological parameters trends, (2) calculations of potential evapotranspiration, aridity index, actual evapotranspiration (ET), Standard Precipitation Index (SPI), and Standard Precipitation-Evapotranspiration Index (SPEI), as well as an evaluation of breakthroughs of their trends, (3) climatic zonation based on the application of the hierarchical k-means and Principal Component Analysis (PCA) clustering of temporal trends of ET and SPEI for the periods before and after the breakthroughs, and (4) simple forecasting hierarchical time series for different forecasting situations.

The statistical framework was applied to 17 locations at the East River watershed for the period from 1966 to 2020. Structural changes of time trends of measured and calculated water balance parameters are used to determine the time of abrupt climatic changes and breakthroughs. Calculations of the evapotranspiration are conducted using the Budyko model, with the potential/reference evapotranspiration (ETo) calculated using the Penman-Monteith (PM) equation. The results of calculations of ETo based on the PM model were compared to the ETo calculated using the Thornthwaite and Hargreaves equations. The results of the hierarchical clustering using ET and SPEI are illustrated using the tree dendrograms and the PCA plots of clusters of the studied sites for the periods of before and after the breakthroughs. A significant shift in the cluster arrangements for the time periods before and after the temporal structural breakpoints indicate that zonation patterns are driven by dynamic climatic processes, which are variable through time, and the watershed zonation requires periodic re-evaluation. Examples of time series forecasting are also shown.