Detection of nonstationarity in series of flow records is of vast scientific and practical significance. In order to develop guidance as to the choice of an appropriate test, among the many candidates, one has recourse to analysis of a controlled trend artificially introduced to generated data mimicking river flow observations. Raw series of good quality flow data were normalized and de-seasonalized and subsequently transformed to the Fourier spectral domain. Keeping the power spectrum preserved, the phase spectrum was subjected to randomization. After transformation back to the temporal domain, the data were contaminated with trends and step changes in a controlled way. The results evaluate the detectability of nonstationarity by particular tests as a quasi-continuous function of magnitude of the contaminating change. A method is devised to compare the tests' performance, with the objective of choosing an appropriate tool. Analysis of detectability versus change magnitude gives a new insight, of direct practical applicability, into the properties of the tests. Further insight is provided by examining over 200 real series of river flow records.