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Modelling of environmental processes is subject to a high degree of uncertainty due to the incorporation of random errors and a lack of knowledge about how processes operate at the scale of interest. Use of uncertain data when identifying and calibrating a model can lead to disinformative data being included in the procedure, resulting in uncertain parameter estimation and ambiguity in the outcomes. Rainfall-runoff modelling where a single rain-gauge is often assumed to be representative of the potentially highly variable (in both space and time) rainfall field is a good example. The noisy pattern of rainfall inputs is transformed by the catchment into streamflow. The streamflow pattern is dependent on the spatio-temporal pattern of rainfall and of the dominant processes operating within the catchment. Inverse modelling of the catchment dynamics, that is, inferring catchment rainfall from streamflow, provides a possible means of improving the estimated rainfall input because all rain falling on the catchment becomes streamflow, and thus, providing improved forecasts of the streamflow output. A combination of inverse modelling, time series analysis, spatial analysis and spectral analysis may also help to provide an insight into the complex processes operating within the catchment system. This paper applies a novel method for inferring true catchment rainfall from streamflow highlighting that the streamflow is better estimated using inferred rainfall than observed rainfall (from a single gauge) because a single gauge only gives a partial description of the rainfall field. However reducing uncertainty in this way comes at a price, in this case, the reduction in time-resolution of the inferred rainfall series

What Really Happens at the End of the Rainbow? – Paying the Price for Reducing Uncertainty (Using Reverse Hydrology Models)