• uncertainty;
  • time-trend;
  • regional streamflow

[1] An expression is derived for the variance of a regional linear trend in annual runoff (units: mm of runoff per km2 per year), averaged over P gauging sites, where the P individual runoff sequences are subject to both year-to-year and site-to-site correlations. At each site, it is assumed that mean annual runoff has a linear trend with serially correlated residuals modeled by an ARMA(1,1) process which can represent both short-term and long-term persistence in annual runoff. Extension to ARMA(p,q) processes is straightforward, and the procedure is also adapted to the case where runoff exhibits long-term persistence. In the case of the ARMA(1,1) model, the expression obtained for the variance of the regional trend need not assume Gaussianity, but if the assumption of Gaussianity is tenable, the note shows how the following hypotheses can be tested: (i) that the linear trend is zero at all P sites; (ii) that the linear trend is equal at all P sites.