Analytical Solutions to Predict the Long‐Term Surface Energy Balance Components and Temperatures of a Bare Soil

A periodic analytical theory previously tested only against diurnal variations is applied to a 66‐day springtime period at Agassiz, British Columbia. Comparison is made with daily average values of the surface energy balance components, soil temperatures, and near‐surface atmospheric potential temperatures and water vapor densities measured throughout this period. It is shown that the inability of the periodic theory to predict the measured warming trend at the 0.5 m depth in the soil can be overcome by applying the theory to the whole of 1978, i.e., by imbedding the period of interest in a longer period. A new analytical theory that accounts for aperiodic transient effects is also described and compared with measured soil temperatures. This theory can also account for the observed soil wanning trend but is sensitive to small errors in the prescribed soil surface heat flux density. Additional analytical calculations show that advection of heat within the soil associated with evaporation and rainfall could have significantly influenced the long‐term temperature trends observed at Agassiz. The poorer success with the analytical approach when applied to long‐term rather than diurnal variations suggests that to predict the former accurately a numerical model is required.