Reverse Hydrology is a term describing methods for estimating rainfall from
streamflow. The method presented here is based on combining inversion of a causal
rainfall-runoff model with regularisation. This novel method,
termed RegDer, combines a continuous-time transfer function model with regularised
derivative estimates and is compared with an alternative method for direct inversion of
a discrete-time transfer function using sub-hourly data from two catchments with
contrasting rainfall and catchment storage characteristics. It has been demonstrated to
recover the prominent features of the observed rainfall enabling it to generate a
streamflow hydrograph indistinguishable from the observed catchment outflow. The
loss of temporal resolution of the resultant rainfall series is the price paid for the
numerical stability of the RegDer method, however this does not affect its ability to
capture the dynamics required for streamflow generation. The inferred rainfall series
was initially interpreted as an estimate of catchment rainfall but was later more
precisely described as the rainfall necessary for generating streamflow – Discharge
Generating Rainfall (DGR). The spatial aspect of the method was investigated using
data from a densely gauged catchment. Frequency domain aspects of RegDer dual
interpretation as a composite spectral decomposition method are analysed and
discussed in the context of catchment data. Potential applications and developments of
the approach include in-filling and extending rainfall records, reducing uncertainty in
both gauged and ungauged catchments by improving rainfall estimates, assessing and
refining rain gauge networks and re-evaluating areal rainfall estimation.