As was seen in Chapter 11, one of the issues that hydrologists and engineers most frequently have to deal with is the estimation of the frequency of different discharges at a site, particularly flood discharges and low flows. In that chapter methods were presented for the analysis of the observations of discharges available at gauging sites. There are, however, only a limited number of sites where gauging station data are available, so the problem that arises in many studies is how to estimate the flood and low flow characteristics at ungauged sites. This is a global problem. The UK has a relatively large number of gauging stations for its area (some 1400 in total; Marsh, 2002); in many developing countries the network is much sparser and often being reduced further for reasons of cost, organisation or war at a time when it is more and more important to monitor the impacts of ongoing catchment change and potential climate change. The International Association of Hydrological Sciences initiated a decadal project in 2003 to address this problem, called ‘Prediction in ungauged basins’ (PUB;1 e.g. Sivapalan et al., 2006).