The models that are able to appropriately study the temporal and spatial dependence structure of water quality and hydrological time series are the essential tools to evaluate the future state of water availability, pollution loading, and best watershed management options. The mass-balance model is one of the current approaches for modeling water quality. However, it has the following limitations: extensive data for inputs, limited effectiveness for many water quality parameters, and ineffectiveness for long-term forecasts. To address the above limitations, statistical and stochastic models, such as classical ARIMA, ANN, and TFN modeling approaches have also been applied to investigate water quality and hydrological time series. However, they also have the some limitations, i.e., Gaussian process and/or linear dependence.
Thereby, this study proposes to investigate the water quality and hydrological time series with the use of the following methodologies: (1) applying the order series transformation method to fulfill the assumptions and to address the limitations of the classic (F)AR(I)MA time series modeling approach; (2) applying the copula theory to investigate the spatial dependence pattern for water quality and hydrological time series at the different locations within the same watershed; (3) investigating the temporal dependence for the observed sequences with the use of copula-based Markov process to address the limitations existed in the classic Markov process.
To valid the proposed approaches, three watersheds (i.e., Stillaguamish and Snohomish watersheds in Washington: Forest watershed, Chattahoochee River Watershed in Georgia: Urban Watershed, and Cuyahoga River Watershed in Ohio: watershed with mixed LULC) are selected as case-studies. The findings of this study showed: (1) the order series transformation may successfully transform the heavy-skewed and/or fat-tailed univariate time series to Gaussian process to fulfill the assumptions of (F)AR(I)models; (2) the length of records should be considered in evaluating the Hurst phenomenon, if it is existed; (3) the copula theory is an efficient tool in modeling the spatial dependence pattern of water quality and hydrological time series by relaxing the assumptions of classic multivariate analysis; (4) the copula-based Markov processes are able to successfully model the temporal dependence of the observed water quality and hydrological time series by relaxing the assumptions of classic Markov process modeling approach; (5) the estimated VaRs may provide valuable information for risk analysis and management; and (6) the proposed procedures can be adopted by other watersheds for watershed management and decision making.