How is hydrology improving?

There are as many ways of evaluating performances of hydrological models as purposes to represent phenomena of interest and aspects of water cycle which to focus on. There is no single criterion satisfying all assessment practices. Despite this obvious limitation, the article attempts to identify some statistical indicators with which to answer the general question: whether it is progressing and how the effectiveness of hydrological modelling at large. From examples published on international journals and from case studies taken from documents by the main international hydrological organizations, spanning over a period of about 35 years, a statistical analysis is made separately for models predicting 1) low flows, 2) peak events, 3) whole cycle. The reported performance indexes (mainly determination or correlation coefficients) are plotted against time, to check the overall trend. Time is not the best explanatory variable but, although linearly, it summarizes the non linear increase of means: numerical codes, data availability from new gauging tools, human and financial resources, attention and effort paid to this branch of science. The overall trend is of course positive but less than expected and, moreover, in the last 15 years, in spite of new analysis techniques, it seems to show an asymptote far from unity. Is this a boundary provided by the mathematical representation or by the description of physical systems and their forcing actions? Has the knowableness of a hydrological system an upper limit which cannot be exceeded by the usual methods of numerical simulation? Has the calibration-validation approach to be revised? How is hydrological modelling effective in practice? Is there an ideal set of data and of experiments which allows a given model to perform at its best? How far are we usually from this optimal condition when running hydrological codes? How can this distance be measured from the very beginning of the task? Some tentative hypotheses are made to answer these questions.