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Optimal Estimation Retrievals and Their Uncertainties: What Every Atmospheric Scientist Should Know

Maximilian MaahnCooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and NOAA/Physical Sciences Lab, Boulder, Colorado

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David D. TurnerNOAA/Global Systems Lab, Boulder, Colorado

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Ulrich LöhnertInstitute for Geophysics and Meteorology, University of Cologne, Cologne, Germany

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Derek J. PosseltJet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Kerstin EbellInstitute for Geophysics and Meteorology, University of Cologne, Cologne, Germany

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Gerald G. MaceDepartment of Atmospheric Science, University of Utah, Salt Lake City, Utah

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Jennifer M. ComstockPacific Northwest National Laboratory, Richland, Washington

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Abstract

Remote sensing instruments are heavily used to provide observations for both the operational and research communities. These sensors do not provide direct observations of the desired atmospheric variables, but instead, retrieval algorithms are necessary to convert the indirect observations into the variable of interest. It is critical to be aware of the underlying assumptions made by many retrieval algorithms, including that the retrieval problem is often ill posed and that there are various sources of uncertainty that need to be treated properly. In short, the retrieval challenge is to invert a set of noisy observations to obtain estimates of atmospheric quantities. The problem is often complicated by imperfect forward models, by imperfect prior knowledge, and by the existence of nonunique solutions. Optimal estimation (OE) is a widely used physical retrieval method that combines measurements, prior information, and the corresponding uncertainties based on Bayes’s theorem to find an optimal solution for the atmospheric state. Furthermore, OE also allows the relative contributions of the different sources of error to the uncertainty in the final retrieved atmospheric state to be understood. Here, we provide a novel Python library to illustrate the use of OE for inverse problems in the atmospheric sciences. We introduce two example problems: how to retrieve drop size distribution parameters from radar observations and how to retrieve the temperature profile from ground-based microwave sensors. Using these examples, we discuss common pitfalls, how the various error sources impact the retrieval, and how the quality of the retrieval results can be quantified.

Supplemental material on Python code belonging to all shown retrieval examples available at https://github.com/maahn/pyOptimalEstimation_examples

Corresponding author: Maximilian Maahn, maximilian.maahn@uni-leipzig.de

Abstract

Remote sensing instruments are heavily used to provide observations for both the operational and research communities. These sensors do not provide direct observations of the desired atmospheric variables, but instead, retrieval algorithms are necessary to convert the indirect observations into the variable of interest. It is critical to be aware of the underlying assumptions made by many retrieval algorithms, including that the retrieval problem is often ill posed and that there are various sources of uncertainty that need to be treated properly. In short, the retrieval challenge is to invert a set of noisy observations to obtain estimates of atmospheric quantities. The problem is often complicated by imperfect forward models, by imperfect prior knowledge, and by the existence of nonunique solutions. Optimal estimation (OE) is a widely used physical retrieval method that combines measurements, prior information, and the corresponding uncertainties based on Bayes’s theorem to find an optimal solution for the atmospheric state. Furthermore, OE also allows the relative contributions of the different sources of error to the uncertainty in the final retrieved atmospheric state to be understood. Here, we provide a novel Python library to illustrate the use of OE for inverse problems in the atmospheric sciences. We introduce two example problems: how to retrieve drop size distribution parameters from radar observations and how to retrieve the temperature profile from ground-based microwave sensors. Using these examples, we discuss common pitfalls, how the various error sources impact the retrieval, and how the quality of the retrieval results can be quantified.

Supplemental material on Python code belonging to all shown retrieval examples available at https://github.com/maahn/pyOptimalEstimation_examples

Corresponding author: Maximilian Maahn, maximilian.maahn@uni-leipzig.de
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