Role of adjoint equations in estimating monthly mean air surface temperature anomalies

Abstract

Using the solution of a specially formulated adjoint problem an integral formula is derived for the study of linear model response. The formula relates directly every chosen characteristic of the model sensitivity to variations of initial data and forcing. By analogy with the well-known Green function, the adjoint equation solution performs here the role of a weight function (or influence function). A set of such relatively simple formulas gives an effective method for estimating the model sensitivity to different types of input data without solving every time the complicated basic problem. The simplified three-dimensional global heat interaction model of atmosphere and ocean is considered as an example. The model has been linearized by using the climatic monthly mean wind in the atmosphere and the climatic seasonal currents in the World Ocean. The time-space structures of the influence functions calculated for the December mean surface temperature anomalies of the European part of USSR and the USA territory, are demonstrated. The regions of local maxima of the influence function show the energetically active zones in the World Ocean. Within the time intervals while these local maxima exists, only the heat flux anomalies located in such zones can be responsible for the final magnitude of the mean temperature anomaly considered.