•Input and output time series from the conduit system of a karst aquifer are analyzed.•A simple water-balance model of epikarst zone is proposed.•Hourly internal runoff and diffuse drainage from ...epikarst zone are estimated.•Correlation and partial correlation functions are used.•A more precise insight into the sediment transport process in aquifer is obtained.
Information about the transport of suspended sediment through a karst aquifer is obtained by the time series analysis of the input and outputs from the conduit system of vadose and phreatic zone. The input is the internal runoff from epikarst zone at the analyzed location. The outputs are the discharge from karst spring, as well as the turbidity and electrical conductivity of spring water. The diffuse drainage from epikarst zone is considered as a control process that changes the quantity of water in the conduit system, and consequently it affects the outputs. The time series of internal runoff and diffuse drainage are obtained by a simple water-balance model of epikarst zone based on the concept of saturation threshold. The proposed model has two parameters: maximal capacity of epikarst storage, and maximal diffuse drainage from epikarst storage, which are estimated by using the cumulative rainfall and turbidity data, as well as the value of runoff coefficient. The time series are analyzed by means of the correlation and partial correlation functions. The presented results show that the overall capability and accuracy of the time series analysis are significantly improved by considering the conduit system separately. It is possible to register and to characterize processes in karst aquifer that are not recognizable by using classical approaches. The results for Jadro Spring show that the memory of hypothetical discharge generated by the internal runoff is practically same as the memory of time series of turbidity. The memory of hypothetical discharge generated by the diffuse drainage is very similar to the memory of time series of discharge. The duration of turbidity response is 22 days, which entirely corresponds to the duration of fresh rainwater withdrawal from the conduit system. During the first 5 days, turbidity is generated mostly by the internal runoff from the central part of catchment. During the last 12 days, turbidity has been generated by the internal runoff from the eastern part of catchment. Two components in turbidity are recognized, which are manifested as two peaks in the turbidity graph. Both peaks are produced dominantly by autochthonous sediment.
•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.
Time 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 19years, 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 14days, the intermediate-flow duration is 80days, and the pure base flow starts after 80days. The base flow consists of an inter-catchment groundwater flow. The system memory of the spring is 80days. 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.
•Karst aquifer sediment transport is investigated by partial correlation functions.•Hourly temperature, conductivity, and turbidity of karst spring water are analyzed.•Contribution of subbasins is ...estimated using rain-gauge data.•Remobilized autochthonous sediment dominates in the water from Jadro Spring.
The process of sediment transport through a karst aquifer is investigated by means of time series analysis. The correlation and spectral analyses are used for determination of the temporal characteristics of this process, such as timing, synchronization with discharge from spring, and time delay between arrivals of sediment and infiltrated rainwater to spring. The partial correlation analysis is used for the spatial characterization. The study area is the catchment of Jadro Spring in Croatia. The analyzed hourly time series are discharge, water temperature, electrical conductivity, and nephelometric turbidity recorded at the source of this spring, as well as the rainfall collected at three locations in the catchment of spring. They cover the period of four years, from 2017 to 2020. The main aims of this research are (1) presentation of the methods of time series analysis that can be used for the investigation of sediment transport through karst aquifer, (2) analysis of the applicability of partial cross-correlation functions for the spatial characterization of sediment transport process, and (3) extension of the existing knowledge about the sediment in water from karst springs with a special reference to the Jadro Spring. The obtained results show that the partial cross-correlation function can be very useful in the investigation of mass transport through the karst aquifer. They enable identification of the specific contribution of each rain-gauge location to the quantity and quality of spring water. Specifically, the origin of sediment in water from Jadro Spring is determined in this study, as well as the origin of quick-flow and baseflow component in discharge from this spring, including the timing of fresh rainwater arrival, rainwater withdrawal, and emptying of previously accumulated water in vadose and phreatic zone. The sediment transport through the karst aquifer of Jadro Spring is initiated after heavy rainfall in the central and eastern part of the catchment. The origin of sediment in spring water is dominantly the remobilized autochthonous sediment from aquifer, and possible limited contribution of allochthonous sediment from the part of catchment located in hinterland of spring.
•A new method for groundwater recharge estimation in karst is proposed.•A simple conceptual model of soil cover, epikarst and vadose zone is developed.•Partial cross-correlation function is used as ...objective function.•Applicability of five existing empirical models to the Dinaric karst is analyzed.
Aquifers with time variant catchment boundaries, regional flows, and inflows from surface streams and accumulations are common in karst areas. Due to the lack of reliable methods for determination of water balance in the phreatic zone of such aquifers, groundwater recharge estimation is a challenge task. This paper introduces a new method for estimation of groundwater recharge in karst – the so-called partial correlation method (PCM). The basic hypothesis is that the groundwater recharge rates can be determined from the time series of precipitation, air temperature, relative humidity, and spring discharge, by using a partial cross-correlation function as objective function. Following this hypothesis, a simple conceptual model of water balance in the soil cover, epikarst and vadose zone is developed, and an objective function for estimation of the optimal value of parameter of this model is proposed. PCM is applied on the catchment of Žrnovnica Spring located in the Dinaric karst area of Croatia. The results of application are compared with the results of previous studies, as well as with the results obtained by five empirical models that have been used for estimation of groundwater recharge in the Mediterranean karst. The effective infiltration coefficients obtained by PCM for the Žrnovnica Spring are generally in accordance with the previously published ones.
A conceptual rainfall–runoff model is proposed for the estimation of groundwater balance components including the influences of time-variant catchment boundaries and intercatchment groundwater flows. ...Karst underground is considered as a lumped system that contains: (1) soil cover, (2) epikarst zone and (3) vadose and phreatic zones. The soil cover receives an average rainfall in catchment as the input into the system. The epikarst zone is composed of a production store and a routing store. The production store contributes to the loss of water in process of evapotranspiration. The routing store contributes to the retention of percolated water and the lateral distribution of groundwater recharge between internal runoff and diffuse infiltration. The vadose and phreatic zones accumulate groundwater in fissures, fractures and vertical shafts, and produce the vadose seepage, vadose flow and shaft flow components of the karst spring discharge. The parameter estimation and calculation procedure assemble the moisture balance and the groundwater-balance approaches. The rainfall–runoff model is divided in two sub-models. The sub-model based on the moisture balance of soil cover and epikarst production store calculates effective rainfalls. The sub-model based on the groundwater balance of vadose and phreatic zone calculates groundwater recharges. The difference between the effective rainfalls and the groundwater recharges represents the contribution of epikarst zone and non-conservative and time-variant components to the groundwater balance. The proposed methodology is applied to the Jadro Spring located near the city of Split in Croatia. The calculated groundwater balance shows that the Jadro Spring aquifer contains a significant storage capacity in the vadose and phreatic zones. During the year, the aquifer may accumulate up to 140 millions m
3. The variability of calculated catchment area is explained with the time-variant catchment boundary dependent on groundwater levels and the intercatchment groundwater flows from neighboring catchments. The average catchment area of 396
km
2 is estimated by using the average monthly effective rainfalls and the average monthly groundwater recharges.
Various methods of time series analysis have been used in studies of karst hydrological systems. Among these methods, correlation and spectral analysis have had an important role. The correlation ...analysis most often has been based on determination of correlation coefficients and correlation functions. Partial correlation functions (PCF) are a mathematical tool of the correlation analysis which practical applicability in karst hydrology is insufficiently explored. In this study, the correlation and spectral analysis are applied on the catchment of Rumin Springs located in the Dinaric karst area between Croatia and Bosnia and Herzegovina. The available daily data are the rainfall, air temperature and relative humidity from three locations, as well as the discharge from two springs. The periods before and after the construction of HPP Orlovac in 1973 are analyzed. The basic hypothesis is that a difference between PCF obtained for two neighboring karst springs describe a difference in their functioning. The results of application show that PCF can resolve some ambiguities concerning the effects included in correlation functions and can provide the additional information that cannot be obtained by other methods of time series analysis. The obtained results are mostly in accordance with the present knowledge, and they support the existing hypotheses about the functioning of Rumin Springs.
The relationship between karst spring discharge and turbidity during periods where the turbidity exceeds the permitted value of 4 NTU is analyzed by means of classical hydrological methods including ...hysteresis loops. The Williams method (1989) is adjusted by replacing river discharge with karst spring discharge, and sediment concentration with exceeding turbidity. The study’s first part focuses on the general hydrological characteristics of cumulative rainfall, turbidity, and discharge during each period. In the second part, four major types of hysteresis loops are identified, classified, and hydrologically explained. The study area is the karst catchment of the Jadro Spring in Croatia. The obtained results show that hysteresis loops can be very useful in analyses of water turbidity from karst springs. A relationship between the type of loop, intensity of discharge, and size of the secondary peak in turbidity is identified. The major types of hysteresis loops were clockwise, counterclockwise, figure-eight and complex loops, and their main characteristics were summarized. The results gave a new insight into the behavior of the turbidity of the Jadro Spring.
Abstract
The objective of this work is the study of two adjacent karst springs, Jadro and Žrnovnica, in Croatia. This work focuses on the effects of temperature, relative humidity, rainfall and ...discharges on the hydrological behavior and relations of two adjacent karst springs. Partial correlation analysis reveals the type of the control signal that affects the cross-correlation function between an input and output signal. It has been confirmed that in the case of the adjacent karst springs Jadro and Žrnovnica, the discharge of the Žrnovnica Spring has an impact on the rainfall-discharge relation of the Jadro Spring. The demonstrated approach represents an improvement in investigating the relations of adjacent karst springs and could be used as an integral part of their hydrological and hydrogeological investigations, considering that the necessary data can occur in a relatively simple and inexpensive manner.
This paper presents a form of kernel function for karst aquifers derived from the time-invariant and non-anticipatory Volterra series. The shape of the kernel function depends on the current value of ...an index of antecedent recharge that is considered as an indicator of groundwater levels and vadose zone saturation. The proposed nonlinear form preserves specific characteristics of instantaneous unit hydrographs. By using analogies with the conceptual model of nonlinear reservoir, it is shown that the second component of the kernel function characterizes the prevailing type of groundwater flow. If the second component is positive, the free-surface flow is dominant, whereas the negative value indicates that the flow under pressure prevails. Groundwater recharge rates are calculated by using a groundwater recharge model based on the Palmer’s soil-moisture balance method. The values of parameters of the groundwater recharge model are estimated by the spectral method which is modified to avoid the assumption about exponential forms of autocorrelation functions of input and output time series. This paper analyzes also the practical applicability of nonlinear kernels for the preliminary characterization of karst aquifers and the karst springs discharge modeling. The results of applications on the springs zones of the rivers Krka and Krčić are in accordance with previous assumptions that the Main Krka Spring is an ascending karst spring which aquifer is situated deeply inside the karst underground, whereas the Main Krčić Spring function as a descending karst spring.
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