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An Idealized 1½-Layer Isentropic Model with Convection and Precipitation for Satellite Data Assimilation Research. Part I: Model Dynamics

Luca CantarelloaSchool of Mathematics, University of Leeds, Leeds, United Kingdom

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Onno BokhoveaSchool of Mathematics, University of Leeds, Leeds, United Kingdom

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Steven TobiasaSchool of Mathematics, University of Leeds, Leeds, United Kingdom

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Abstract

An isentropic 1½-layer model based on modified shallow-water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified rotating shallow water (modRSW) model. The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic model a more suitable tool to achieve our future goal: to conduct idealized experiments for investigating satellite data assimilation. The numerical model implementation is verified against an analytical solution for stationary waves in a rotating fluid, based on Shrira’s methodology for the isopycnal case. Recovery of the equivalent isopycnal model is also verified, both analytically and numerically. With convection and precipitation added, we show how complex model dynamics can be achieved exploiting rotation and relaxation to a meridional jet in a periodic domain. This solution represents a useful reference simulation or “truth” in conducting future (satellite) data assimilation experiments, with additional atmospheric conditions and data. A formal analytical derivation of the isentropic 1½-layer model from an isentropic two-layer model without convection and precipitation is shown in a companion paper (Part II).

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Luca Cantarello, mmlca@leeds.ac.uk; Onno Bokhove, o.bokhove@leeds.ac.uk

Abstract

An isentropic 1½-layer model based on modified shallow-water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified rotating shallow water (modRSW) model. The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic model a more suitable tool to achieve our future goal: to conduct idealized experiments for investigating satellite data assimilation. The numerical model implementation is verified against an analytical solution for stationary waves in a rotating fluid, based on Shrira’s methodology for the isopycnal case. Recovery of the equivalent isopycnal model is also verified, both analytically and numerically. With convection and precipitation added, we show how complex model dynamics can be achieved exploiting rotation and relaxation to a meridional jet in a periodic domain. This solution represents a useful reference simulation or “truth” in conducting future (satellite) data assimilation experiments, with additional atmospheric conditions and data. A formal analytical derivation of the isentropic 1½-layer model from an isentropic two-layer model without convection and precipitation is shown in a companion paper (Part II).

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Luca Cantarello, mmlca@leeds.ac.uk; Onno Bokhove, o.bokhove@leeds.ac.uk
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