Investigating relationships between rainfall and karst-spring discharge by higher-order partial correlation functions

- Higher-order partial correlation functions are applied in karst hydrology.
- The effects of evapotranspiration are removed from correlation functions.
- Specific contributions of different parts of the catchment to spring discharge can be identified.
- An alternative method for the estimation of karst-system memory is proposed.
- Seasonal effects of inter-catchment groundwater flows can be detected.

SummaryTime series of rainfall and karst-spring discharge are influenced by various space-time-variant processes involved in the transfer of water in hydrological cycle. The effects of these processes can be exhibited in auto-correlation and cross-correlation functions. Consequently, ambiguities with respect to the effects encoded in the correlation functions exist. To solve this problem, a new statistical method for investigating relationships between rainfall and karst-spring discharge is proposed. The method is based on the determination and analysis of higher-order partial correlation functions and their spectral representations. The study area is the catchment of the Jadro Spring in Croatia. The analyzed daily time series are the air temperature, relative humidity, spring discharge, and rainfall at seven rain-gauges over a period of 19 years, from 1995 to 2013. The application results show that the effects of spatial and temporal variations of hydrological time series and the space-time-variant behaviours of the karst system can be separated from the correlation functions. Specifically, the effect of evapotranspiration can be separated to obtain the forms of correlation functions that represent the hydrogeological characteristics of the karst system. Using the proposed method, it is also possible to separate the effects of the process of groundwater recharge that occurs in neighbouring parts of a catchment to identify the specific contribution of each part of the catchment to the karst-spring discharge. The main quantitative results obtained for the Jadro Spring show that the quick-flow duration is 14 days, the intermediate-flow duration is 80 days, and the pure base flow starts after 80 days. The base flow consists of an inter-catchment groundwater flow. The system memory of the spring is 80 days. The presented results indicate the far-reaching applicability of the proposed method in the analyses of relationships between rainfall and karst-spring discharge; e.g., the method can be used for (1) the identification of effects of various time series on the quick-flow, intermediate-flow and base-flow components of the discharge, (2) the detection of the seasonal effect of inter-catchment groundwater flows in the discharge, and (3) the estimation of the karst system memory. Generally, the presented approach can be applied to the qualitative analyses of the relationships between two time series whenever appropriate control time series are available.