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Lévy processes are useful tools for analysis and modeling of jump‐diffusion processes. Such processes are commonly used in the financial and physical sciences. One approach to building new Lévy processes is through subordination, or a random time change. In this work, we discuss and examine a type of multiply subordinated Lévy process model that we term a deep variance gamma (DVG) process, including estimation and inspection methods for selecting the appropriate level of subordination given data. We perform an extensive simulation study to identify situations in which different subordination depths are identifiable and provide a rigorous theoretical result detailing the behavior of a DVG process as the levels of subordination tend to infinity. We test the model and estimation approach on a data set of intraday 1‐min cryptocurrency returns and show that our approach outperforms other state‐of‐the‐art subordinated Lévy process models.

 

We develop a space‐time Bayesian hierarchical modeling (BHM) framework for two flood risk attributes—seasonal daily maximum flow and the number of events that exceed a threshold during a season (NEETM)—at a suite of gauge locations on a river network. The model uses generalized extreme value (GEV) and Poisson distributions as marginals for these flood attributes with non‐stationary parameters. The rate parameters of the Poisson distribution and location, scale, and shape parameters of the GEV are modeled as linear functions of suitable covariates. Gaussian copulas are applied to capture the spatial dependence. The best covariates are selected using the Watanabe‐Akaike information criterion (WAIC). The modeling framework results in the posterior distribution of the flood attributes at all the gauges and various lead times. We demonstrate the utility of this modeling framework to forecast the flood risk attributes during the summer peak monsoon season (July‐August) at five gauges in the Narmada River basin (NRB) of West‐Central India for several lead times (0–3 months). As potential covariates, we consider climate indices such as El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Pacific Warm Pool Region (PWPR) from antecedent seasons, which have shown strong teleconnections with the Indian monsoon. We also include new indices related to the East Pacific and West Indian Ocean regions depending on the lead times. We show useful long lead skill from this modeling approach which has a strong potential to enable robust risk‐based flood mitigation and adaptation strategies 3 months before flood occurrences.

 

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix.When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.