A new trend analysis for seasonal time series with consideration of data dependence

Trend analysis has been an important tool in assessing hydrological process. However, statistical approaches employed for trend analysis frequently assume independence in hydrological time series. To satisfy the independence assumption, the hydrological series of interest are usually summarized to large scale data (e.g. annual) for long-term trend. To assess intra-annual variability, the hydrological series are summarized to several periods within a year (e.g. season or month) and then analyzed separately for each period over different years (e.g. each month over different years). Unfortunately, for those seasonal and monthly data, the trend analysis must be conducted separately for individual periods in order to avoid data dependence. However, the setting of periodic models cannot guarantee the smoothness in model coefficients from period to period (e.g. month to month). In this paper, we develop a trend analysis tool by including a period component in the method. By doing this, the data dependence and seasonality will not be issues but become advantages as information gain for each period. The proposed method treats the change in hydrological series as the interaction between long-term trend and seasonal variation. The functional coefficient model with a periodic component is used for model development. Unlike the traditional functional coefficient models which extend the threshold regression model, our functional coefficient model with periodic components enjoys smoothing changes from year to year. As case studies, the models are applied to Australian streamflows in three typical climate conditions.