 Solution

Weather-forecast errors arise from uncertainty in the initial atmospheric state, including measurement noise, incomplete spatial coverage and imperfect data assimilation; from model error, including unresolved clouds, convection and turbulence, approximate physical parameterizations and imperfect boundary forcing; and from discretization, time stepping and roundoff. Sensitive dependence on initial conditions amplifies suitable small errors through nonlinear dynamics, limiting deterministic predictability even with a good model. It is an amplification mechanism rather than a separate observational noise source. Ensemble forecasts sample some initial-state and model uncertainty, but their spread need not represent every systematic error.