Early recession behaviour of spring hydrographs

Abstract

The long-term flow recession of many springs can be approximated by an exponential function. However, the early recession often exhibits a different behaviour. The exponential recession function represents a long-term approximation of analytical solutions of the flow equation of fissured matrix blocks draining toward a fixed-head boundary. Thus, early deviations from the exponential behaviour potentially originate from the inappropriateness of this approximation at short times. We therefore examine the properties of the exact analytical solutions and make comparisons with field data. If hydraulic heads are initially constant within the matrix blocks the flow recession exhibits a power-law decrease at short times. Both from steady-state initial conditions and after finite recharge pulses the early flow recession follows a power law, too, if discharge is appropriately shifted and rescaled. If the catchment is composed of multiple blocks drained by highly conductive conduits the recession behaviour of the spring is identical to that of the individual blocks if the blocks are of the same size. The recession curves of the published hydrograph of Cheddar spring (Great Britain) are found to be in good agreement with this model if reasonable initial conditions are assumed. A brief look at recession curves from other springs suggests that the model might be applicable to most of them, too. The model also provides satisfactory fits to the flow recession of the Gallusquelle (Germany). However, the observed power-law exponent differs from that predicted by the analytical model. A consistent interpretation of the shape of several recession curves from this spring is provided by a more general fractal approach, which assumes that the catchment is composed of blocks of strongly different sizes.