Toward Form-Function Relationships for Mesoscale 3 Structure in Convection

Mesoscale patterns in atmospheric convection (between the inner scale of convecting-layer 30 depth and the outer scales of domain constraints) are fascinating and ubiquitous. This review 31 asks whether some aspects of that form (normalized for a given amount of convective activity) 32 play a meaningful role or function in the total flow, especially in its more-predictable larger 33 scales. Do some mesoscale features deserve to be called organization in its stronge sense, acting 34 like multi-cellular organs in an organism? After enumerating hypotheses from null (mesoscale 35 arrangement doesn't matter) to various detailed ideas (rectification of nonlinear processes with 36 spatial agglomeration, size-dependent top-heaviness of heating, vertical momentum flux effects, 37 adjustment roles, and the character of stochastic noise), a tabular framework for categorizing 38 form-function research is offered. Function measures are divided into micro (mere quantification 39 of budget terms averaged over mesoscale patches) vs. macro (roles played through time in 40 larger-scale phenomena). Tools and approaches are arrayed from literal and explicit (case 41 observations) to conceptualized (models, ranging from theory to numerical to statistical 42 depictions), on timelines both historical (contacting case observations in some way) and 43 synthetic (theory, simulation, and composites). Efforts are further distinguished by whether their 44 inferences are associative (derived from conditional sampling of either form or function) or 45 causal (involving controlled experimentation). Literature examples are surveyed, albeit 46 incompletely, and future research strategies are suggested across this tabular landscape or 47 framework. One spotlighted result is an apparent internal optimum in the horizontal geometry 48 continuum between isotropic horizontal two-dimensionality and horizontally one-dimensional 49 squall lines. Form-function questions could help justify, orient, and capitalize scientifically on 50 the field’s costly multiscale activities (requiring both coverage and resolution) in both 51 observational and modeling realms. Data assimilation is a motivating application, and also a 52 potentially powerful research tool for achieving greater synthesis. An observant human 53 sensibility remains crucial for discovering and interpreting form-function relationships, at the very least to design more salient algorithms in the age of big data and computing.


Corrigendum: Water Vapor Retrieval by Shipboard Lidar
The authors of Katsumata et al. (2020) (hereafter KTN2020) have discovered an 28 error to process the lidar data. The error is on the length of the raw data bin along the ray 29 direction (hereafter "bin length") at a part of the channels to archive Raman backscattered 30 signals. KTN2020 erroneously set the value as 7.5 meters at all wavelengths in both 31 MR15-04 and MR17-08. The correct bin length is 3.75 meters, for data at 607 and 387 32 nm (for nitrogen) in MR15-04 and MR17-08, and for data at 660 and 408 nm (for water 33 vapor) in MR17-08. Meanwhile at 660 nm (for water vapor) in MR15-04, correct bin 34 length is 7.5 meters as identical to that in KTN2020. The differences between correct bin 35 length and those in KTN2020 are summarized in Table C1. These errors came by 36 confusing specifications of hardware used before and after 2015 (i.e. before and after 37 adding capability to receive Raman signals). Note that the error was only for the Raman 38 signals, while the other data (at Mie scattering channels) were unaffected.

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Using the correct bin lengths, we re-calculate K(r) in Eq. (1) in KTN2020, which is 40 the coefficient at range distance r to convert the observed signal at the Raman channels to   On the scatter diagrams comparing ql and radiosonde-observed water vapor mixing 48 ratio qrs (Fig. 2), panels for MR17-08 ( Fig. 2b and 2c) show that the data points are better 49 confined along ql = qrs line than those of KTN2020. The statistical parameters are also 50 improved from those in KTN2020, as in the correlation coefficients (~ 0.9) and the root 51 mean squared differences (RMSDs) (~ 0.5 g/kg, which corresponds ~ 3 % of qrs (and ql)). 52 In contrast, the results for MR15-04 are not improved as those for MR17-08, with the 53 correlation coefficients of 0.67 and the RMSD is approximately 1.2 g/kg which 54 corresponds to approximately 7 % of qrs (and ql). These differences are probably resulted 55 by the larger number of the raw data bin in a resampled data grid point (with the size of 56 120 meters and 10 minutes) in the corrected data for MR17-08 than in KTN2020.

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On the panels comparing vertical profiles of ql and qrs (Fig. 3), the data available 58 height range is lower than those in KTN2020 for all panels, by reflecting the correction of 59 the range distance of the raw data. For MR17-08, ql532 and ql355 are available up to 0.45 60 and 0.85 km height, respectively. Below 0.6 km height where MABL generally exists, the 61 RMSD and the quartiles of ql -qrs are smaller than 0.7 g/kg which is improved than those 62 in KTN2020. On the other hands for MR15-04, the RMSD and the quartiles of ql -qrs are 63 generally ≥ 1.0 g/kg, which is comparable to those in KTN2020.

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On the case study (Fig. 4), the available height range of ql532 and ql355 become lower The conclusions of KTN2020 are found to be basically unchanged with the corrected 69 data, while the data-available height range is generally shortened. Reflecting the 70 corrected results, we correct the former part in "5. Summary" as follows: to estimate water vapor mixing ratio (ql) by referring the radiosonde-observed water 75 vapor mixing ratio (qrs). Our demonstration involves data from two special observations, 76 "MR15-04" cruise during "Pre-YMC" and "MR17-08" cruise during "YMC-Sumatra".

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The obtained ql by using 355 nm laser (received signal at 387 and 408 nm) are shown to 78 be quantitatively reasonable up to 0.6 km height that covers the MABL, and to be feasible 79 to study meso-scale features of MABL. With the present Mirai lidar system, ql from 355 80 nm laser is advantageous to analyze up to higher altitude and better quality than that from 81 532 nm laser (received signal at 607 and 660 nm)."

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The bin length is also described in the Supplement of KTN2020. In the Supplement,    Figure 2: Scattering plots comparing lidar-derived water vapor mixing ratio q l (in ordinate) and radiosonde-observed one q rs (in abscissa). (a) q l532 for MR15-04, (b) q l532 for MR17-08, and (c) q l355 for MR17-08, respectively. "points", "RMSD" and "cor" stands for number of data points, root mean square difference, and correlation coefficient, respectively. and (g) ) are for the averaged profile of q l (red) and q rs at corresponding time (black). Panels in the middle column are for the q l -q rs , as in the average (thick black), average ± standard deviation (gray), median (thick red), and 1st and 3rd quartiles (thin red), respectively. Panels in the right column are number of available pairs of ql and q rs . Top panels are for q l532 in MR15-04, middle panels are for q l532 in MR17-08, and bottom panels are for q l355 in MR17-08. (c-e) Surface meteorological parameters obtained by instruments onboard R/V Mirai, for (c) pressure (blue) and temperature (red), (d) rain rate (red), relative humidity (blue) and water vapor mixing ratio (green), and (e) wind speed (black), zonal wind speed (red), meridional wind speed (blue) and wind vector at every hour. (f) time-height cross section of normalized backscatter signal received at 1064 nm.