Resolution‐dependent behavior of subgrid‐scale vertical transport in the Zhang‐McFarlane convection parameterization. (18th April 2015)

• Record Type: Journal Article
• Authors: Xiao, Heng; Gustafson, William I.; Hagos, Samson M.; Wu, Chien‐Ming; Wan, Hui
• Is Part Of: Journal of advances in modeling earth systems. Volume 7:Number 2(2015:Jun.)
• Page Start: 537
• Page End: 550
• Publication Date: 2015-04-18
• Subjects: Geological modeling -- Periodicals; Climatology -- Periodicals; Geochemical modeling -- Periodicals; 551.5011
• DOI: 10.1002/2014MS000356
• Languages: English
• ISSNs: 1942-2466

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>To better understand the behavior of quasi‐equilibrium‐based convection parameterizations at higher resolution, we use a diagnostic framework to examine the resolution‐dependence of subgrid‐scale vertical transport of moist static energy as parameterized by the Zhang‐McFarlane convection parameterization (ZM). Grid‐scale input to ZM is supplied by coarsening output from cloud‐resolving model (CRM) simulations onto subdomains ranging in size from 8 × 8 to 256 × 256 km<sup>2</sup>. Then the ZM‐based parameterization of vertical transport of moist static energy for scales smaller than the subdomain size ( <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5gz" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>Z</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>) are compared to those directly calculated from the CRM simulations ( <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5j2" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>) for different subdomain sizes. The ensemble mean <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5dv" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> decreases by more than half as the subdomain size decreases from 128 to 8 km across while <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5fd" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>Z</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> decreases with subdomain size only for strong convection cases and increases for weaker cases. The resolution dependence of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5rc" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0005" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>Z</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> is determined by the positive‐definite grid‐scale tendency of convective available potential energy (CAPE) in the convective quasi‐equilibrium (QE) closure. Further analysis shows the actual grid‐scale tendency of CAPE (before taking the positive definite value) and <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5v1" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0006" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> behave very similarly as the subdomain size changes because they are both tied to grid‐scale advective tendencies. We can improve the resolution dependence of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5nq" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0007" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>Z</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> significantly by averaging the grid‐scale tendency of CAPE over an appropriately large area surrounding each subdomain before taking its positive definite value. Even though the ensemble mean <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5qt" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0008" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> decreases with increasing resolution, its variability increases dramatically. <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t51s" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:19422466:media:jame20160:jame20160-math-0009" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>w</mml:mi><mml:mo>′</mml:mo><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>Z</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> cannot capture such increase in the variability, suggesting the need for stochastic treatment of convection at relatively high spatial resolution (8 or 16 km).</p> </abstract>