Statistical and balance features of forecast errors are generally incorporated in the background constraint of variational data assimilation. Forecast error covariances are here estimated with a spectral approach and from a set of forecast differences; autocovariances are calculated with a nonseparable scheme, and multiple linear regressions are used in the formulation of cross covariances. Such an approach was first developed for global models; it is here adapted to ALADIN, a bi-Fourier high-resolution limited-area model, and extended to a multivariate study of humidity forecast errors. Results for autocovariances confirm the importance of nonseparability, in terms of both vertical variability of horizontal correlations and dependence of vertical correlations with horizontal scale; high-resolution spatial correlations are obtained, which should enable a high-resolution analysis. Moreover nonnegligible relationships are found between forecast errors of humidity and those of mass and wind fields.