Aquifers and karst springs are among the most studied and challenging topics of hydrogeology in recent years. They are difficult to model due to the aquifer's heterogeneity and anisotropy, as well as the difficulties of conventional monitoring. However, they are among the most important groundwater resources, accounting for a significant portion of freshwater intended for human consumption, especially in the EU.The study area is located in the Umbria Region in central Italy and is characterised by an elongated carbonate ridge formed by a multilayered karstified carbonate succession, locally separated by marly interbeds. Groundwater circulation is controlled by Apennine tectonics, with faults either enhancing or limiting hydraulic connectivity between hydrogeological units. Recharge occurs predominantly through diffuse but also local infiltration over carbonate outcrops and high plains.This study contributes to the understanding of hydrogeological functioning by integrating long-term monitoring data (more than 20 years) of discharge and rainfall with numerical modelling.The data reveal that the karst system exhibits highly complex hydrological behaviour, and the distinctive hydrograph shapes observed for certain springs are attributed to direct surface water inputs entering the system through local sinkholes. Modkarst Model that was applied to six major karst springs, allowed the quantification of surface water contribution.This work highlights that effective management of karst aquifers under increasing climate change effects that usually requires integrated approaches combining geological understanding, continuous monitoring, and modelling.

This paper presents a new and innovative methodology for the investigation of karst systems using spring discharge. The behaviour of springs in phase space is investigated by plotting the measurements of spring discharge versus the measurements of the water level at the spring’s outlet. Such a diagram reveals new features of the function of the karst system and the discharge pattern of the spring that are not captured by common research methods. The application of this method to the Azmak Spring in southwestern Türkiye revealed the existence of five distinct discharge subsystems that operate alternately and never simultaneously. They have a specific connection between them, while the transition from one to another is not random but follows a pattern. An attempt was made to interpret these features using concepts from percolation theory.

The MODKARST mathematical code is used to simulate both brackish and non-brackish karst springs and provides useful information on the hydrological and hydrogeological characteristics of their aquifers. Next to this, MODKARST can also explain the often peculiar behavior of these springs, inherited from the complexity of the structures that most of the times form fractures, cavities, and conduits in carbonate formations in tectonically complex areas. The simulation focuses on explaining the complex behavior of the Azmak spring. Azmak is a large brackish karst spring in SW Turkey, which displays peculiarities both in terms of its hydrograph and seawater intrusion mechanism. In particular, during the recession period, contrary to the chloride concentrations of its water which appears more or less stable, its hydrograph shows fluctuations. The MODKARST simulation showed that the discharge fluctuation during the recession period is due to the operation of a siphon, while the abnormal variation of its chloride content is due to its predominant seawater intrusion mechanism which is the Venturi effect.

A modification is proposed of Torricelli’s (1608–1647) formula for the velocity of water discharging from a small hole at the bottom of a large tank filled with fractal solid material. The new formula takes proper account of the mechanical energy losses due to flow in the solid matrix, thus expanding the area of validity of the classical Torricelli’s formula. Moreover, it offers a convenient alternative to Darcy’s law for estimating the discharge rate from an aquifer. The new formula was derived from laboratory experiments, with a low-Reynolds number discharge flow (Darcian flow). It was tested in a natural karst aquifer where the flow is non-Darcian, at Almiros spring on the island of Crete (Greece). In both cases, the predictive capability of the modified formula is established.

A method of identifying the dominant hydrodynamic sea-intrusion mechanism of brackish karst springs is presented. A karst spring becomes brackish when tubes, which bring the freshwater to the spring (freshwater discharge), intersect other tubes that come from the sea and bring saltwater to the freshwater tubes (saltwater discharge) when the saltwater pressure at the intersection is higher than the freshwater pressure. There are two potential seawater intrusion mechanisms. The first one is the difference between the freshwater density and the seawater density, and the second is the venturi effect. Both mechanisms are present but it is a matter of great significance to know which mechanism dominates. In order to find out the dominant mechanism, the seawater discharge versus the freshwater discharge was charted using the MODKARST model, which estimates these discharges. The model determines how the freshwater discharge affects the saltwater discharge estimating thereby the dominant seawater intrusion mechanism. Application was made to the “Almiros” and “Makaria” springs in Greece.

A new approach to the method of artificial upraising of the water outlet point, for management and development of brackish karst springs, uses the MODKARST model. Brackish karst springs simulation can be used to estimate the necessary upraising of the spring elevation, so that sea-water intrusion is blocked. The consequent freshwater loss to the sea, due to this upraising, can also be estimated. The method has been applied to the periodically brackish karst Almiros spring at Heraklion of Crete, Greece. The spring simulation showed that the sea-water intrusion could be prevented through an artificial upraising of the water-outlet point, realized by the construction of a dam. The exact upraising has been estimated. Freshwater loss to the sea because of this upraising has also been estimated. The model could also be used as a tool for the management of the spring. For example, it was used to assess management options for the spring during the depletion period of the year 1994. The best scenario for the development of the spring during this period has been estimated.

A new method of estimating the fractal dimension of the percolation backbone of karst systems, which are discharged through karst springs, is presented. This method is based on the simulation of the spring by the MODKARST deterministic mathematical model. Application has been made to the Psiloritis karst formation in Crete, which feeds the periodically brackish karst spring “Almiros” in Crete. Furthermore, the estimated dimension justifies an independently determined power law that quantifies the sea intrusion into the karst system.