A Quantile-Conserving Ensemble Filter Framework. Part III: Data Assimilation for Mixed Distributions with Application to a Low-Order Tracer Advection Model

Jeffrey Anderson aNSF NCAR/CISL/TDD/DAReS, Boulder, Colorado, jla@ucar.edu

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Chris Riedel bCooperative Programs for the Advancement of Earth System Science, University Corporation for Atmospheric Research

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Molly Wieringa cUniversity of Washington, Department of Atmospheric Sciences, Seattle, Washington

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Fairuz Ishraque dDepartment of Geosciences, Princeton University, Princeton, New Jersey

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Marlee Smith aNSF NCAR/CISL/TDD/DAReS, Boulder, Colorado, jla@ucar.edu

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Helen Kershaw aNSF NCAR/CISL/TDD/DAReS, Boulder, Colorado, jla@ucar.edu

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Abstract

The uncertainty associated with many observed and modeled quantities of interest in Earth system prediction can be represented by mixed probability distributions that are neither discrete nor continuous. For instance, a forecast probability of precipitation can have a finite probability of zero precipitation, consistent with a discrete distribution. However, nonzero values are not discrete and are represented by a continuous distribution; the same is true for rainfall rate. Other examples include snow depth, sea ice concentration, amount of a tracer or the source rate of a tracer. Some Earth system model parameters may also have discrete or mixed distributions. Most ensemble data assimilation methods do not explicitly consider the possibility of mixed distributions. The Quantile Conserving Ensemble Filtering Framework (Anderson 2022, 2023) is extended to explicitly deal with discrete or mixed distributions. An example is given using bounded normal rank histogram probability distributions applied to observing system simulation experiments in a low-order tracer advection model. Analyses of tracer concentration and tracer source are shown to be improved when using the extended methods. A key feature of the resulting ensembles is that there can be ensemble members with duplicate values. An extension of the rank histogram diagnostic method to deal with potential duplicates shows that the ensemble distributions from the extended assimilation methods are more consistent with the truth.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Abstract

The uncertainty associated with many observed and modeled quantities of interest in Earth system prediction can be represented by mixed probability distributions that are neither discrete nor continuous. For instance, a forecast probability of precipitation can have a finite probability of zero precipitation, consistent with a discrete distribution. However, nonzero values are not discrete and are represented by a continuous distribution; the same is true for rainfall rate. Other examples include snow depth, sea ice concentration, amount of a tracer or the source rate of a tracer. Some Earth system model parameters may also have discrete or mixed distributions. Most ensemble data assimilation methods do not explicitly consider the possibility of mixed distributions. The Quantile Conserving Ensemble Filtering Framework (Anderson 2022, 2023) is extended to explicitly deal with discrete or mixed distributions. An example is given using bounded normal rank histogram probability distributions applied to observing system simulation experiments in a low-order tracer advection model. Analyses of tracer concentration and tracer source are shown to be improved when using the extended methods. A key feature of the resulting ensembles is that there can be ensemble members with duplicate values. An extension of the rank histogram diagnostic method to deal with potential duplicates shows that the ensemble distributions from the extended assimilation methods are more consistent with the truth.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

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