The operation of ancient reclamation works at Lake Copais in Greece

Abstract

Water has played a vital role in life in Greece during its long history. Ancient Greek societies were very active in the field of water management, resulting in an impressive variety of hydraulic works. The main purpose of this paper is to discuss the operation of one of the most ancient and extended hydraulic works, the drainage project of Lake Copais in Central Greece. The project was developed and operated by the Minyans, a powerful Mycenaean group. The Minyans partially diverted two large rivers which fed the lake. The water was conveyed towards labyrinthine natural sinkholes, which were formed in limestone terrain. Through the sinkholes, water slowly discharged to the sea. This impressive ancient water management system has gained the attention of many scientists and has been extensively studied by archaeologists and engineers. Still, important questions remain about the way the hydro-system worked. Trying to provide some reliable answers, we have studied the Minyans’ interventions from a hydraulic engineering perspective. Available archeological, hydrological and geological data of the area were used to evaluate the operation of the system. The main elements of the hydro-system are presented and their purposes examined. For this, (i) a water balance model was developed and (ii) the hydro-system was simulated using synthetic time series of the hydrological processes. Several operational cases were examined in order to define critical parameters of the system, such as water level variation and water accumulation in the sinkholes. The analysis reveals some significant factors, which could be related to archaeological findings and the hydro-system’s performance.

Appendix

Hydrological model equations

For each monthly time step n the following components of the hydrosystem are defined:

• Qkif_n, the monthly discharge of Boiotikos Kephisos river in hm³

• Qmel_n, the monthly discharge of Melas river in hm³

• Qepl_n, the total monthly discharge of Erkynas, Pontzas and Lofis rivers in hm³

• Qsink_n, the monthly discharge capacity of sinkholes in hm³

• Virr_n, the monthly irrigation needs in hm³

• Wcop_n, the monthly withdrawal from Copais lake in case that irrigation needs are not satisfied in hm³

• Skop_n, the storage of Copais lake at the end of the month n in hm³

• Ssink_n, the storage of sinks lake at the end of the month n in hm³

• Acop_n, the mean monthly area of Copais lake in km²

• P_n, The monthly areal precipitation in mm

• E_n, the monthly areal lake evaporation in mm

The operational rules of the hydrosystem are the following:

A portion a _i of the monthly discharges of Boiotikos Kephisos and Melas discharges flow to Lake Copais and the remaining water is diverted to the sinkhole area. The storage of the lake formulated in front of the sinks at the end of the month is given by the equation

$${\text{Ssink}}_{\text{n}} \,{=}\,{\text{Ssink}}_{{{\text{n}} - 1}} \,{ + }\,\left( { 1- {\text{a}}_{\text{i}} } \right)\, *\,\left( {{\text{Qkif}}_{\text{n}} \,{ + }\,{\text{Qmel}}_{\text{n}} } \right)\,{ + }\,{\text{P}}_{\text{n}} \,\, *\,{\text{Asink}}_{\text{n}} - \,{\text{E}}_{\text{n}} *\,{\text{Asink}}_{\text{n}} \, - \,{\text{Qsink}}_{\text{n}}$$

(1)

The irrigation needs are satisfied by the remaining monthly discharges of Boiotikos Kephisos and Melas rivers and from the total monthly discharges of Erkynas, Pontzas and Lofis streams. In case that the river discharges are less than irrigation needs a withdrawal from lake Copais is performed.

The withdrawal from Lake Copais is given by the equation

$${\text{if}}\,{\text{a}}_{\text{i}} \, *\,\left( {{\text{Qkif}}_{\text{n}} \,{ + }\,\,{\text{Q}}\,{\text{mel}}_{\text{n}} } \right)\,{ + }\,{\text{Qepl}}_{\text{n}} \,\, \ge \,\,{\text{Virr}}_{\text{n}} \,\,\,\,{\text{Wcop}}_{{{\text{n}}\,}} \,{ = }\, 0$$

$${\text{Else:}}\,\,{\text{Wcop}}_{n} \, = \,\,Virr_{n} - \,{\text{a}}_{\text{i}} \, *\,\left( {{\text{Qkif}}\,\,{ + }\,\,{\text{Qmel}}_{\text{n}} } \right)\, - \,\,{\text{Qepl}}_{\text{n}}$$

$${\text{Wcop}}_{n} = \left[ {\begin{array}{*{20}l} {0,} \hfill & {{\text{a}}_{{\text{i}}} *\left( {{\text{Qkif}}_{{\text{n}}} + {\text{Qmel}}_{{\text{n}}} } \right) + {\text{Qepl}}_{{\text{n}}} \ge {\text{Virr}}_{{\text{n}}} } \hfill \\ {Virr_{n} - {\text{a}}_{{\text{i}}} *\left( {{\text{Qkif}}_{{\text{n}}} + {\text{Qmel}}_{{\text{n}}} } \right) - {\text{Qepl}}_{{\text{n}}} ,} \hfill & {{\text{a}}_{{\text{i}}} *\left( {{\text{Qkif}}_{{\text{n}}} + {\text{Qmel}}_{{\text{n}}} } \right) + {\text{Qepl}}_{{\text{n}}} < {\text{Virr}}_{{\text{n}}} } \hfill \\ \end{array} } \right]$$

(2)

The storage of lake Copais at the end of the month is given by the equation

$${\text{Scop}}_{\text{n}} \,{ = }\,{\text{Scop}}_{{{\text{n}} - 1\,}} \, + \,\,{\text{a}}_{\text{i}} \, *\,\left( {{\text{Qkif}}_{\text{n}} \,{ + }\,{\text{Qmel}}_{\text{n}} } \right)\,\,{ + }\,\,{\text{Qepl}}_{\text{n}} \,{ + }\,\,{\text{P}}_{\text{n}} \, *\,{\text{Acop}}_{\text{n}} \, - \,\,{\text{E}}_{{{\text{n}}\,}} \, *\,\,{\text{Acop}}_{\text{n}} \, - {\text{Virr}}_{\text{n}}$$

(3)

Simulation procedure

The hydrosystem was simulated for fixed initial conditions and for two different sink capacities that are presented in Table 2.