. Extracting filtered characteristics of short time series

Abstract
Convectively coupled equatorial waves (CCEWs) are important modes of tropical variability. They have long time and large spatial scales and are thought to be central to improving tropical weather forecasts. However, current operational numerical weather prediction (NWP) models lack skill in predicting CCEWs past a few days lead time. Traditional methods of identifying CCEWs and their activity in observations or climate models rely on long time series (on the order of a few decades) to assess space- time characteristics of CCEWs. These methods are not easily applicable to NWP forecasts because when developing or improving weather models it is rare that long time series are available. This makes it difficult to assess the models’ performance related to CCEWs and other phenomena with time scales longer than a few days. Novel diagnostics of CCEWs are therefore needed, in particular those designed to identify long time scale phenomena from short time series. Here we present two methods to evaluate model behavior on particular time and length scales without the need of long model runs. The first uses observed EOFs of CCEWs derived from filtered precipitation data. Projection of the model output onto the observational EOFs allows the instantaneous evaluation of CCEW activity. The second method evaluates model predictions based on their spectral coherence with observational fields filtered for modes of CCEWs. These analyses allow for insights in the relationship between moist convective processes and CCEW vertical structure.