Dependence of Mass–Dimensional Relationships on Median Mass Diameter
Retrievals of ice cloud properties require accurate estimates of ice particle mass. Empirical mass–dimensional (<i>m</i>–<i>D</i>) relationships in the form <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> &l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Atmosphere |
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| Online Access: | https://www.mdpi.com/2073-4433/11/7/756 |
| _version_ | 1797562093081198592 |
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| author | Saisai Ding Greg M. McFarquhar Stephen W. Nesbitt Randy J. Chase Michael R. Poellot Hongqing Wang |
| author_facet | Saisai Ding Greg M. McFarquhar Stephen W. Nesbitt Randy J. Chase Michael R. Poellot Hongqing Wang |
| author_sort | Saisai Ding |
| collection | DOAJ |
| description | Retrievals of ice cloud properties require accurate estimates of ice particle mass. Empirical mass–dimensional (<i>m</i>–<i>D</i>) relationships in the form <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>=</mo> <mi>a</mi> <msup> <mi>D</mi> <mi>b</mi> </msup> </mrow> </semantics> </math> </inline-formula> are widely used and usually universally applied across the complete range of particle sizes. For the first time, the dependence of <i>a</i> and <i>b</i> coefficients in <i>m–D</i> relationships on median mass diameter (<i>D<sub>mm</sub></i>) is studied. Using combined cloud microphysical data collected during the Olympic Mountains Experiment and coincident observations from Airborne Precipitation Radar Third Generation, <i>D<sub>mm</sub></i>-dependent (<i>a</i>, <i>b</i>) coefficients are derived and represented as surfaces of equally plausible solutions determined by some tolerance in the chi-squared difference <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> that minimizes the difference between observed and retrieved radar reflectivity. Robust dependences of <i>a</i> and <i>b</i> on <i>D<sub>mm</sub></i> are shown with both parameters significantly decreasing with <i>D<sub>mm</sub></i>, leading to smaller effective densities for larger <i>D<sub>mm</sub></i> ranges. A universally applied constant <i>m–D</i> relationship overestimates the mass of large aggregates when <i>D<sub>mm</sub></i> is between 3–6 mm and temperatures are between −15–0 °C. Multiple <i>m–D</i> relations should be applied for different <i>D<sub>mm</sub></i> ranges in retrievals and simulations to account for the variability of particle sizes that are responsible for the mass and thus for the variability of particle shapes and densities. |
| first_indexed | 2024-03-10T18:23:42Z |
| format | Article |
| id | doaj.art-63ff77ed79004fab8fcd44f828ae4ef8 |
| institution | Directory Open Access Journal |
| issn | 2073-4433 |
| language | English |
| last_indexed | 2024-03-10T18:23:42Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
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| series | Atmosphere |
| spelling | doaj.art-63ff77ed79004fab8fcd44f828ae4ef82023-11-20T07:09:12ZengMDPI AGAtmosphere2073-44332020-07-0111775610.3390/atmos11070756Dependence of Mass–Dimensional Relationships on Median Mass DiameterSaisai Ding0Greg M. McFarquhar1Stephen W. Nesbitt2Randy J. Chase3Michael R. Poellot4Hongqing Wang5Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing 100871, ChinaCooperative Institute of Mesoscale Meteorological Studies, Norman, OK 73072, USADepartment of Atmospheric Sciences, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USADepartment of Atmospheric Sciences, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USADepartment Atmospheric Sciences, University of North Dakota, Grand Forks, ND 58202, USADepartment of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing 100871, ChinaRetrievals of ice cloud properties require accurate estimates of ice particle mass. Empirical mass–dimensional (<i>m</i>–<i>D</i>) relationships in the form <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>=</mo> <mi>a</mi> <msup> <mi>D</mi> <mi>b</mi> </msup> </mrow> </semantics> </math> </inline-formula> are widely used and usually universally applied across the complete range of particle sizes. For the first time, the dependence of <i>a</i> and <i>b</i> coefficients in <i>m–D</i> relationships on median mass diameter (<i>D<sub>mm</sub></i>) is studied. Using combined cloud microphysical data collected during the Olympic Mountains Experiment and coincident observations from Airborne Precipitation Radar Third Generation, <i>D<sub>mm</sub></i>-dependent (<i>a</i>, <i>b</i>) coefficients are derived and represented as surfaces of equally plausible solutions determined by some tolerance in the chi-squared difference <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> that minimizes the difference between observed and retrieved radar reflectivity. Robust dependences of <i>a</i> and <i>b</i> on <i>D<sub>mm</sub></i> are shown with both parameters significantly decreasing with <i>D<sub>mm</sub></i>, leading to smaller effective densities for larger <i>D<sub>mm</sub></i> ranges. A universally applied constant <i>m–D</i> relationship overestimates the mass of large aggregates when <i>D<sub>mm</sub></i> is between 3–6 mm and temperatures are between −15–0 °C. Multiple <i>m–D</i> relations should be applied for different <i>D<sub>mm</sub></i> ranges in retrievals and simulations to account for the variability of particle sizes that are responsible for the mass and thus for the variability of particle shapes and densities.https://www.mdpi.com/2073-4433/11/7/756mass–dimensional relationshipmedian mass diameterradar reflectivityequally plausible surface |
| spellingShingle | Saisai Ding Greg M. McFarquhar Stephen W. Nesbitt Randy J. Chase Michael R. Poellot Hongqing Wang Dependence of Mass–Dimensional Relationships on Median Mass Diameter Atmosphere mass–dimensional relationship median mass diameter radar reflectivity equally plausible surface |
| title | Dependence of Mass–Dimensional Relationships on Median Mass Diameter |
| title_full | Dependence of Mass–Dimensional Relationships on Median Mass Diameter |
| title_fullStr | Dependence of Mass–Dimensional Relationships on Median Mass Diameter |
| title_full_unstemmed | Dependence of Mass–Dimensional Relationships on Median Mass Diameter |
| title_short | Dependence of Mass–Dimensional Relationships on Median Mass Diameter |
| title_sort | dependence of mass dimensional relationships on median mass diameter |
| topic | mass–dimensional relationship median mass diameter radar reflectivity equally plausible surface |
| url | https://www.mdpi.com/2073-4433/11/7/756 |
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