Time averaging for tendency budget analysis

Abstract. Climate models can be used to quantify the processes that contribute to a property's change through analysis of the tendency terms in the budget of the property. For example, a heat budget can be performed to understand the processes driving an increase in the ocean's heat content under climate change. However, conventional budget analyses in climate models are typically performed without proper consideration of their relationship to the property of interest. Specifically, most studies consider standard arithmetic time-averages of budget terms. For the tendency term, this average is related to the difference between two time instants (snapshots) of the property and thus is strongly impacted by rapid fluctuations, or "weather".  Such an approach to budget analysis is thus less relevant to the "climate change" problem, that is, the difference between two long-term averages, or "epochs", of the property. Here we present a time-averaging method, referred to as the hat average, which exactly relates the processes contributing to a property's tendency budget to the epoch difference, or "climate change", of that property.  We demonstrate the utility of this method by applying it to the horizontally integrated heat budget of a global ocean model. We find that the hat average removes high-frequency variability, typically associated with rapid and noisy advective processes, and so allows for a clear measure of how processes contribute to changes in climate.