Reconstructing tephra fall deposits via ensemble-based data assimilation techniques

In recent years, there has been a growing interest in ensemble-based based approaches for modeling volcanic plumes. The development of advanced ensemble modeling techniques enables the exploration of novel methods for the incorporation of real observations into tephra dispersal models using ensemble- based data assimilation techniques. However, traditional data assimilation algorithms, including ensemble Kalman filter methods, can yield suboptimal state estimates for positive-definite variables such as volcanic aerosols and tephra deposits. We present two new ensemble-based data assimilation techniques for semi- positive-definite variables with highly skewed uncertainty distributions, such as deposit mass loading. The proposed methods are applied to reconstruct the tephra fallout deposit resulting from the 2015 Calbuco eruption and the 946 CE eruption of Baekdu volcano, the so-called Millennium eruption, one of the largest eruptions in historic times based on widespread tephra dispersal. The FALL3D dispersal model was used to perform an ensemble of runs in order to simulate the transport and deposition of tephra for different model configurations. Subsequently, deposit thickness measurements are assimilated to reconstruct the tephra deposit and improve the first-guess results, obtained from a simple ensemble forecast. An assessment of the assimilation methods is carried out using an independent dataset of observations in terms of different evaluation metrics. The methodologies presented here represent promising alternatives for the assimilation of real observations in operational models.