A Smart Extension of the Search Space for Use with the Analog Ensemble Technique

A number of scientific and technical fields require historical repositories of data in order to execute a task, learn a pattern, enable a prediction, or accomplish a function. For example, artificial neural networks used in artificial intelligence or machine learning, require historical data to establish a relationship and determine a prediction or a next step. Another example is the development of model output statistics for meteorological applications. However, an adequate historical repository at a specific location of interest is not always available for experimentation or analysis. The analog ensemble technique is a technique that also requires a search history (sometimes called a training dataset) and can suffer from inadequate historical data. The analog ensemble technique is used to determine a probabilistic outcome based on a historical repository of corresponding numerical weather prediction forecasts and observations.

Currently, the analog ensemble only considers only historical data for each point in the domain (single location or grid). This research explores the use of additional historical repositories from nearby, similar, or smartly chosen sites (points) or areas (grids) in order to wisely expand the potential search space (training dataset) for the analog ensemble technique. This research uses a mathematical approach to provide an error decomposition of the components involved in the original analog ensemble technique plus new terms to handle the inclusion of additional historical repositories of data from an extended search space. Next, this research executes the analysis developed around the mathematical decomposition of the error in order to investigate the search space extension for the analog ensemble technique. This research has potential applications for machine learning, artificial intelligence, model output statistics, and research areas where additional search histories or training datasets are needed.