The end users of hydrological models may be justified for being tired of the excessive uncertainty of these models, not to mention their simplistic approximations and crude modelling. The ever-increasing sophistication of model parameter fitting is simply a smoke-screen that hides the models' lack of physical basis, their scale dependence, and their inability to fit widely diverse behaviours. More generally, we have to admit a lack of qualitative improvement in hydrological modelling in recent times. In fact, operational hydrology may have suffered for some time from ignoring the advances in theoretical hydrology, which have, in contrast, greatly stimulated the nonlinear sciences. For instance, more than a century ago fractals were considered as geometrical monsters, whereas decades ago river networks became classical fractal objects, and rainfall and discharges are now classical examples of multifractal fields. These hydrological characteristics are still often ignored by operational hydrology, whereas they explain not only its current limitations, but also how to overcome them. To illustrate these problems, this paper focuses on the fact that hydrological fields are most likely singular with respect to measures of time and volume. This would not only explain the ubiquitous scale dependence of hydrological observations, but would also give the possibility to transform them into scale-independent quantities. The upscaling of a rainfall time series from an hour to a year is therefore discussed in detail, and enables us to quickly introduce other examples.