the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Submitted as: development and technical paper 18 Feb 2021
Submitted as: development and technical paper | 18 Feb 2021
On numerical broadening of particle size spectra: a condensational growth study using PyMPDATA 1.0
- 1Jagiellonian University, Kraków, Poland
- 2Zentrum für Datenverarbeitung, Johannes Gutenberg University Mainz, Germany
- 3Institute for Atmospheric Physics, Johannes Gutenberg University Mainz, Germany
- 4German Aerospace Center (DLR), Oberpfaffenhofen, Germany
- 1Jagiellonian University, Kraków, Poland
- 2Zentrum für Datenverarbeitung, Johannes Gutenberg University Mainz, Germany
- 3Institute for Atmospheric Physics, Johannes Gutenberg University Mainz, Germany
- 4German Aerospace Center (DLR), Oberpfaffenhofen, Germany
Abstract. The work discusses the diffusional growth in particulate systems such as atmospheric clouds. It focuses on the Eulerian modeling approach in which the evolution of the probability density function describing the particle size spectrum is carried out using a fixed-bin discretization. The numerical diffusion problem inherent to the employment of the fixed-bin discretization is scrutinized. The work focuses on the applications of MPDATA family of numerical schemes. Several MPDATA variants are explored including: infinite-gauge, non-oscillatory, third-order-terms and recursive antidiffusive correction (double pass donor cell, DPDC) options. Methodology for handling coordinate transformations associated with both particle size distribution variable choice and numerical grid layout are expounded. The study uses PyMPDATA – a new open-source Python implementation of MPDATA. Analysis of the performance of the scheme for different discretization parameters and different settings of the algorithm is performed using an analytically solvable test case pertinent to condensational growth of cloud droplets. The analysis covers spatial and temporal convergence, computational cost, conservativeness and quantification of the numerical broadening of the particle size spectrum. Presented results demonstrate that, for the problem considered, even a tenfold decrease of the spurious numerical spectral broadening can be obtained by a proper choice of the MPDATA variant (maintaining the same spatial and temporal resolution).
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Michael Olesik et al.
Status: final response (author comments only)
- RC1: 'Comment on gmd-2020-404', Josef Schröttle, 24 Feb 2021
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RC2: 'Comment on gmd-2020-404', Anonymous Referee #2, 01 May 2021
This study examined performance of various MPDATA variants in solving drop size distribution evolution by condensation. The authors reviewed many previous studies in the context of improving MPDATA and showed that MPDATA with three anti-diffusive iterations, third order term, infinite gauge, and the non-oscillatory option reduces the numerical diffusion to roughly a tenth compared to that of the upwind scheme, although it requires ~10 times longer than the upwind scheme.
Although this study examined the performance of MPDATA variants systematically, I would raise two serious problems this study bears. At the current stage, my recommendation is to reject the manuscript for publishing on GMD, and encouraging the authors to improve the manuscript accordingly.
1. Somewhat outdated
I can find several recent papers closely related to the topic this study focuses on: Morrison et al. (2018, doi: 10.1175/JAS-D-18-0055.1), Pardo et al. (2020, doi:10.1175/JAS-D-20-0099.1), and Lee et al. (2021, doi:10.1175/JAS-D-20-0213.1). All those papers already pointed out that drop condensation itself can be sufficiently converged with better schemes or better designed grids, but it is the condensation w/ vertical advection or w/ collision-coalescence that causes serious problems. Furthermore, those studies utilized LES model results in explaining their results, whereas this study only showed the box model results. This study clearly exhibited the performance of MPDATA variants in solving drop condensation, but only the convergence test in solving drop condensation is somewhat outdated compared to the studies I mentioned. I strongly suggest the authors to improve their study by including vertical advection, collision-coalescence, and/or something we do not know its effects.
2. Experimental setting
In the authors’ experimental setting, supersaturation is fixed so the liquid water content increases up to 10 g kg–1, which is almost unrealistic except for tropical cyclones. I strongly suggest the authors to modify the experimental setting so the results become more realistic. For example, Morrison et al. (2018) and Lee et al. (2021) fixed the vertical velocity to be 1 m s–1 for ~ 20 min rather than fixed the supersaturation.
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RC3: 'Comment on gmd-2020-404', Anonymous Referee #3, 04 May 2021
This manuscript examines the fidelity of various flavors of the MPDATA advection scheme for solving condensation of the drop size distribution. The writing style is clear and concise, the historical review of bin scheme and MPDATA development was illuminating, and the figures were simple and easy to understand. That said, the study suffers from a few key flaws that lead me to suggest the paper be rejected.
First, the authors recognize that the difficulty of numerically modeling condensation/evaporation is that drop growth processes (in the mass dimension) are fundamentally coupled to spatial advection. Yet the test case, which if I understand correctly was chosen because a reference analytical solution can be obtained, either did not include a spatial advection component or this was not discussed. Morrison et al. (2018) and Lee et al. (2021) both point out that satisfactory solutions can be obtained by a number of schemes in the absence of transport; it is when they are coupled that special consideration must be taken. Secondly, the physical feasibility of the test case is dubious; in any warm cloud, a mass mixing ratio of 10 g/kg is nigh impossible. Finally, another important aspect (in particular, of Lee et al., 2021) was not covered: the effect of refining grid spacing vs. refining algorithm formulation. These three factors combined leave me with the impression that this study, while rigorous, is not relevant to the current state of the field.
I strongly encourage the authors to reconsider the paper by formulating a test case that would demonstrate the relevance of the algorithms tested in dynamical models, and evaluating the tradeoff of increased algorithmic accuracy versus refined size grid.
Michael Olesik et al.
Michael Olesik et al.
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