Multivariate Similarity Metric Development for Analog Ensembles

Ensemble forecasts capture an array of possible future states of the atmosphere. They foster a quantifiable understanding of uncertainty for a given forecast which can assist in risk-based decision making and other environmental science challenges. However standard methods for ensemble generation can be computationally expensive.

One computationally efficient alternative is the Analog Ensemble (AnEn). Using a current deterministic prediction, a set of corresponding historical deterministic forecasts and observations, the AnEn Independent Search (IS) set forth by Delle Monache et al. [1] generates calibrated probabilistic predictions. The technique has been shown to perform well for wind and solar energy prediction, air quality forecasting, 2 m and 10 m wind speed, and select additional applications including the handling of rare events. However, the AnEn does not currently have the capability of generating multivariate forecasts which presents a challenge for environmental applications.

In this study, we aim to investigate a multivariate similarity metric as an improvement for the AnEn. First, this investigates a possible solution whereby the AnEn is run several times independently and examines whether the physical relationship between the multiple variables of interest, e.g., temperature and wind speed, are preserved. Another potential solution is to design a built-in multivariate similarity metric that adopts a holistic approach. This multivariate similarity metric utilizes frequency-based information, generated as a byproduct of the AnEn-IS method implementation, to inform discovery of the most similar analogs. In order to verify the members of the ensemble generated, the spatio-temporal field should be reconstructed and this can be performed using the Schaake Shuffle variant. The proposed multivariate AnEn method can be applied in environmental prediction areas requiring multivariate predictions of geophysical variables, furthering both future alternative methods to ensemble prediction and forecast verification.

[1] Delle Monache, Luca, F. Anthony Eckel, Daran L. Rife, Badrinath Nagarajan, and Keith Searight. "Probabilistic weather prediction with an analog ensemble." Monthly Weather Review 141, no. 10 (2013): 3498-3516.