Lumped-element model for subglacial transport of solute and suspended sediment

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Abstract
Present understanding of the subglacial water system and its role in transporting solute and sediment is largely based on subglacial observations of water pressure, turbidity and electrical conductivity and on portal measurements. Such data reveal a wealth of intriguing phenomena, but convincing interpretations can be elusive. Although a proper mathematical description of the subglacial water system would unquestionably lead to a coupled system of non-linear partial differential equations, it is not fruitful to introduce this level of complexity until the important physical processes have been identified and quantified. Lumped-element models offer an efficient approach to examining the complex but dimly perceived physics of the subglacial water system. Water volume, hydraulic head, discharge and flow resistance have the respective electrical analogues of charge, voltage, current and ohmic resistance. Thus, subglacial hydraulic circuits can be approximated by electrical circuits. Mathematically, this circuit description commonly leads to a coupled system of algebraic and differential equations which can be solved numerically. It is straightforward to enrich this representation by adding sources and sinks of solute and sediment. To demonstrate the method, model results are compared to records of subglacial pressure, electrical conductivity and turbidity measured beneath Trapridge Glacier, Yukon Territory, Canada.