Alexakis, A., and L. Biferale, 2018: Cascade and transitions in turbulence flows. Phys. Rep., 1228 769–769, 1–101. 1229 Arakawa, A., 2004: The cumulus parameterization problem: Past, present, and future. J. Cli1230 mate, 17, 2493–2525. 1231 Augier, P., and E. Lindborg, 2013: A new formulation of the spectrum energy budget of the 1232 atmosphere, with application to two high–resolution general circulation models. J. At1233 mos. Sci., 70, 2293–2308. 1234 Bartello, P., 2000: Potential vorticity, resonance and dissipation in rotating convective tur1235 bulence. in Geophysical and Astrophysical Convection, Eds., R. H. Kerr, P. Fox, and C.- 1236 H. Moeng, 309–321. 1237 Billant, P., and J.–M. Chomaz, 2001: Self–similarity of strongly stratified flows. Phys. Flu1238 ids, 13, 1645–1651. 1239 Bretherton, C. S., and P. K. Smolarkiewicz, 1989: Gravity waves, compensating subsidence 1240 and detrainment around cumulus clouds. J. Atmos. Sci., 46, 740-759. 1241 Bretherton, C. S., P. N. Blossey, M. Khairoutdinov, 2005: An energy-balance analysis of deep 1242 convective self-aggregation above uniform SST. J. Atmos. Sci., 62, 4273-4292. 1243 Charney, J. G., and A. Eliassen, 1964: On the Growth of the Hurricane Depression. J. At1244 mos. Sci., 21, 68–75. 1245 Cho, J. Y–K., L. M. Polvani, 1996: The emergence of jets and vortices in freely evolving, shallow1246 water turbulence on a sphere. Phys. Fluids, 8, 1531–1552. 1247 Cullen, M. J. P., 2017: The impact of high vertical resolution in the Met Office Unified Model. 1248 Quart. J. Roy. Meteor. Soc., 143, 278–287. 1249 Davies, T., M. J. P. Cullen, A. J. Malcolm, M. H. Mawson, A. Staniforth, A. A. White, and 1250 N. Wood, 2005: A new dynamical core for the Met Office’s global and regional modelling 1251 of the atmosphere. Quart. J. Roy. Meteor. Soc., 131, 1759–1782. 1252 Deusebio, E., P. Augier, and E. Lindborg, 2014: Third–order structure functions in rotating 1253 and stratified turbulence: a comparison between numerical, analytical and observational 1254 results. J. Fluid Mech., 755, 294–313. 1255 Emanuel, K. A., 1987: An air–sea interaction model of intraseasonal oscillations in the trop1256 ics, J. Atmos. Sci., 44, 2324–2340. 1257 Finnigan, J. J., F. Einaudi, 1981: The interaction between an internal gravity wave and the 1258 planetary boundary layer. Part II: Effect of the wave on the turbulence structure. Quart. 1259 J. Roy. Meteor. Soc., 107, 807–832. 1260 Finnigan, J. J., 1988: Kinetic energy transfer between internal gravity waves and turbulence. 1261 J. Atmos. Sci., 45, 486–505. 1262 Fournier, A., 2002: Atmospheric energetics in the wavelet domain. Part I: Governing equa1263 tions and interpretation for idealized flows. J. Atmos. Sci., 59, 1182–1197. 1264 Fournier, A., 2003: Atmospheric energetics in the wavelet domain. Part II: Time-averaged 1265 observed atmospheric blocking. J. Atmos. Sci., 60, 319–338. 1266 Fournier, A., 2005: Instantaneous wavelet energetic transfers between atmospheric blocking 1267 and local eddies. J. Climate, 18, 2151–2171. 1268 Fraedrich, K., and J. L. McBride, 1989: The physical mechanism of CISK and the free-ride 1269 balance. J. Atmos. Sci., 46, 2642–2648. 1270 Gregory, D., and P. R. Rowntree, 1990: A mass flux convection scheme with representation 1271 of cloud ensemble characteristics and stability-dependent closure. Mon. Wea. Rev., 118, 1272 1483–1506. –44– manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) 1273 Hayashi, Y., 1970: A theory of large—scale equatorial waves generated by condensation heat 1274 and accelerating the zonal wind. J. Met. Soc. Japan, 48, 140–160. 1275 Held, I. M., R. S. Hemler, and V. Ramaswamy, 1993: Radiative-convective equilibrium with 1276 explicit two–dimensional moist convection. J. Atmos. Sci., 50, 3909-3927. 1277 Holloway, C. E., and S. J. Woolnough, 2016: The sensitivity of convective aggregation to di1278 abatic processes in idealized radiative-convective equilibriums. J. Adv. Model. Earth Syst., 1279 8, 166-195. 1280 Holloway, C. E., A. A; Wang, S. Bony, C. Muller, H. Masunaga, T. S. L’Ecuyer, D. D. Turner, 1281 P. Zuidema, 2017: Observing convective aggregation. Surv. Geophys., 38, 1199-1236. 1282 Holloway, C. E., S. J. Woolnough, and G. M. S. Lister, 2013: The effects of explicit versus 1283 parameterized convection on the MJO in a large–domain high–resolution tropical case 1284 study. Part I: Characterization of large–scale organization and propagation. J. Atmos. 1285 Sci., 70, 1342–1369. 1286 Houze, R. A., Jr., and A. K. Betts, 1981: Convection in GATE. Rev. Geophys. Space Phys., 1287 19, 541-576. 1288 Houze, R. A., Jr., 2018: 100 years of research on mesoscale convective systems. Meteorolog1289 ical Monographs, 59 17.1–17.54, doi:10.1175/AMSMONOGRAPHS-D-18-0001.1 1290 Lai, K. W., and M. L. Waite, 2023: Kinetic energy spectra and spectral budget of radiative– 1291 convective equilibrium. J. Atmos. Sci., 80, 1953–1970. 1292 Lean, H. W., P. A. Clark, M. Dixon, N. M. Roberts, A. Fitch, R. Forbes, and C. Halliwell, 1293 2008: Characteristics of high-resolution versions of the Met Office Unified Model for fore1294 casting convection over the United Kingdom, Mon. Wea. Rev., 136, 3408–3424. 1295 Lin, H., 2022: The Madden-Julian Oscillation. Atmos.–Ocean, 60, 338–359. 1296 Lindborg, E., 1999: Can the atmospheric kinetic energy spectrum be explained by two–dimensional 1297 turbulence? J. Fluid Mech., 388, 259–288. 1298 Lindborg, E., 2006: The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550, 1299 207–242. 1300 Lindborg, E., 2007: Horizontal wavenumber spectra of vertical velocity and horizontal diver1301 gence in upper troposphere and lower stratosphere. J. Atmos. Sci., 64, 1017–1025. 1302 Lindzen, R. S., 1974: Wave-CSIK in the tropics. J. Atmos. Sci., 31, 156-179. 1303 Lilly, D. K., 1962: On the numerical simulation of buoyant convection. Tellus, 14, 148–172. 1304 Lilly, D. K., 1983, Stratified turbulence and the mesoscale variability of the atmosphere. J. 1305 Atmos. Sci., 40, 749–761. 1306 Lilly, D. K., G. Bassett, K. Droegemeier, and P. Bartello, 1998: Stratified turbulence in the 1307 atmospheric mesoscales. Theor. Comp. Fluid Dyn., 11, 139–153. 1308 Lindzen, R. S., and M. Fox–Rabinovits, 1989: Consistent vertical and horizontal resolution. 1309 Mon. Wea. Rev., 117, 2575–2583. 1310 Lorenz, E.N., 1955: Available potential energy and the maintenance of the general circula1311 tion. Tellus, 7, 157–167. 1312Mallat, S., 1998: A Wavelet Tour of Signal Processing. 2nd Ed., Academic Press, 637pp. 1313Mapes, B. E., 1993: Gregarious tropical convection. J. Atmos. Sci., 50, 2026–2037. 1314Marsham, J. H., and Parker, D. J., 2006: Secondary initiation of multiple bands of cumulonim1315 bus over southern Britain. Part II: Dynamics of secondary initiation. Quart. J. Roy. Me1316 teor. Soc., 132, 1053–1072. 1317Meneveau, C., 1991: Analysis of turbulence in the orthonormal wavelet. J. Fluid Mech., 232, 1318 469–520. –45– manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) 1319Meyer, Y., 1992: Wavelets and Operators. Cambridge University Press, 223pp. 1320Morcrette, C. J., K. A. Browning, A. M. Blyth, K. E. Bozier, P. A. Clark, D. Ladd, E. G. 1321 Norton, and E. Pavelin, E., 2006: Secondary initiation of multiple bands of cumulonim1322 bus over southern Britain. Part I: An observational case study. Quart. J. Roy. Meteor. 1323 Soc., 132, 1021–1051. 1324Muller, C., D. Yang, G. Craig, T. Cronin, B. Fildier, J. O. Haerter, C. Hohenegger, B. Mapes, 1325 D. Randall, S. Shamekh, and S. C. Sherwood, 2022: Spontaneous Aggregation of Con1326 vective Storms. Ann. Rev. Fluid Mech., 54, 133–157. 1327 Nakajima, K., and T. Matsuno, 1988: Numerical experiments concerning the origin of cloud 1328 clusters in the tropical atmosphere. J. Met. Soc. Japan, 66, 309-329. 1329 Nakazawa, T., 1988: Tropical super clusters within interaseasonal variations over the west1330 ern Pacific. J. Met. Soc. Japan, 66, 823-839. 1331 Neelin, J. D., I. M. Held, and K. H. Cook, 1987: Evaporation-Wind Feedback and Low-Frequency 1332 Variability in the Tropical Atmosphere. J. Atmos. Sci., 44, 2341–2348. 1333 Nicholls, M. E. R. A. Pielke, and W. R. Cottons, 1991: Thermally forced gravity waves in 1334 an atmosphere at rest. J. Atmos. Sci., 48, 1869-1884. 1335 Oort, A.H., 1964: On the energetics of the mean and eddy circulations in the lower strato1336 sphere. Tellus, 16, 309–327. 1337 Oort, A.H., J. P. Peixoto, 1974: The annual cycle of the energetics of the atmosphere on a 1338 planetary scale. J. Geophys. Res., 79, 2705–19. 1339 Ooyama, K. V., 1982: Conceptual evolution of the theory and modeling of the tropical cy1340 clone, J. Meteor. Soc. Jpn., 60, 369–380. 1341 Pandya, P., D. Durren, and C. S. Bretherton, 1993: Comments on “Thermally forced grav1342 ity waves in an atmosphere at rest”. J. Atmos. Sci., 50, 4097-4101. 1343 Riley, J. J., and E. Lindborg, 2008: Stratified turbulence: a possible interpretation of some 1344 geophysical turbulence measurements. J. Atmos. Sci., 65, 2416–2424. 1345 Saltsman, B., 1957: Equations governing the energetics of the larger scales of atmospheric 1346 turbulence in the domain of wave number. J. Atmos. Sci., 14, 513–523. 1347 Saltzman, B., 1958: Some hemispheric spectral statistics. J. Atmos. Sci., 15, 259–263. 1348 Scorer, R. S., and F. H. Ludlam, 1953: Bubble theory of penetrative convection. Quart. J. 1349 Roy. Meteor. Soc., 79, 94-103. 1350 Skamarock, W. C., C. Snyder, J. B. Klemp, and S.–H. Park, 2019: Vertical resolution require1351 ments in atmospheric simulation. Mon. Wea. Rev., 147, 2641–2656. 1352 Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Mon. 1353 Wea. Rev., 91, 99–164. 1354 Smith, R. K., and M. T. Montgomery, 2023: Tropical Cyclones. Elsevier, 600pp. 1355 Sobel, A. H., J. Nilssson, and L. M. Polvani, 2001: The weak temperature gradient approx1356 imation and balanced moisture waves. J. Atmos. Sci., 58, 3650-3665. 1357 Su, H., C. S. Bretherton, and S. S. Chen, 2000: Self-aggregation and large-scale control of 1358 tropical deep convection: A modeling study. J. Atmos. Sci., 57, 1797-1816. 1359 Sun, Y. Q., R. Rotunno, and F. Zhang, 2017: Contributions of moist convection and inter1360 nal gravity waves to building the atmospheric -5/3 kinetic energy spectra. J. Atmos. Sci., 1361 74, 185–201. 1362 Tennekes, H., 1978: Turbulent flow in two and three dimensions. Bull. Amer. Meteor. Soc., 1363 59, 22–28. –46– manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) 1364 Thorpe, S. A., 1971: Experiments on the instability of stratified shear flows: miscible fluids. 1365 J. Fluid Mech., 46, 299–319. 1366 Tompkins, A. M., 2001a: Organization of tropical convection in low vertical wind shears: The 1367 role of water vapor. J. Atmos. Sci., 58, 529-545. 1368 Tompkins, A. M., 2001b: Organization of tropical convection in low vertical wind shears: The 1369 role of cold pools. J. Atmos. Sci., 58, 1650–1672. 1370 Turner, J. S., 1973: Buoyancy Effects in Fluids, Cambridge University Press, 367pp. 1371 Uccellini, L. W., and S. E. Koch, 1987: The synoptic setting and possible sources for mesoscale 1372 wave disturbances. Mon. Wea. Rev., 115, 721–729. 1373Waite, M. L., 2016: Dependence of model energy spectra on vertical resolution. Mon. Wea. 1374 Rev., 1442016, 1407–1421. 1375Wheeler, M., and G. N. Kiladis, 1999: Convectively-coupled equatorial waves: analysis of clouds 1376 and temperature in the wavenumber-frequency domain. J. Atmos. Sci., 56, 374–399. 1377Wilson, D. R., and S. P. Ballard, 1999: A microphysically based precipitation scheme for the 1378 UK Meteorological Office Unified Model. Quart. J. Roy. Meteor. Soc., 125, 1607–1636. 1379Wing, A. A., 2019: Self-Aggregation of Deep Convection and its Implications for Climate. 1380 Curr. Clim Change Rep., 5, 258, 1–11. 1381Wing, A. A., K. Emanuel, C. E. Holloway, and C. Muller, 2017: Convective Self-Aggregation 1382 in Numerical Simulations: A Review. Surv. Geophys., 38, 1173–1197. 1383 Yang, D., 2018: Boundary layer diabatic processes, the virtual effect, and convective self-aggregation. 1384 J. Adv. Model. Earth Syst., 10, 2163-2176. 1385 Yang, D., 2019: Convective heating leads to self–aggregation by generating available poten1386 tial energy. Geophys. Res. Lett., 46, 10687–10696. 1387 Yang, D., 2021: A shallow–water model for convective self–aggregation. J. Atmos. Sci., 78, 1388 571–582. 1389 Yano, J.–I., 1998b: Planetary–scale coherent structures of tropical moist convection. Aus1390 tralian Journal of Physics, 51, 865–874. 1391 Yano, J.–I., 2003: The cumulus parameterization problem in the context of MJO simulations. 1392 Proceedings for the MJO workshop, ECMWF, 2–5 November 2003, 115–127. http://www.ecmwf.int/publications/library/1393 Yano, J.–I., 2023: Geophysical Convection Dynamics, Elsevier, 302pp. 1394 Yano, J.–I., and D. Buniol, 2010: A minimum bulk microphysics. Atmos. Chem. Phys. Dis1395 cuss., 10, 30305–30345, doi:10.5194/acpd-10-30305-2010. 1396 Yano, J.–I., and K. A. Emanuel, 1991: An improved model of the equatorial troposphere and 1397 its coupling with the stratosphere, J. Atmos. Sci., 48, 377–389. 1398 Yano, J.–I., and B. Jakubiak, 2016: Wavelet-Based Verification of the Quantitative Precip1399 itation Forecast. Dyn. Atmos. Ocean, 74, 14–29. 1400 Yano, J.-I., and E. Ouchtar, 2017: Convective Initiation Uncertainties Without Trigger or 1401 Stochasticity: Probabilistic Description by the Liouville Equation and Bayes’ Theorem. 1402 Quart. J. Roy. Meteor. Soc., 143, 2015–2035. 1403 Yano, J.-I., and R. S. Plant, 2012a: Finite Departure from Convective Quasi-Equilibrium: 1404 Periodic Cycle and Discharge-Recharge Mechanism. Quart. J. Roy. Meteor. Soc., 138, 1405 626–637. 1406 Yano, J.-I., and R. S. Plant, 2012b: Interactions between shallow and deep convection un1407 der a finite departure from convective quasi–equilibrium. J. Atmos. Sci., 69, 3463–3470. 1408 Yano, J.–I., J. C. McWilliams, M. W. Moncrieff, and K. A. Emanuel, 1995: Hierarchical trop1409 ical cloud systems in an analog shallow water model, J. Amos. Sci, 52, 1723–1742. –47– manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) 1410 Yano, J.–I., J. C. McWilliams, and M. W. Moncrieff, 1996: Fractality in Idealized Simula1411 tions of Large–Scale Tropical Cloud Systems, Mon. Wea. Rev., 124, 838–848. 1412 Yano, J.–I., M. W. Moncrieff, X. Wu, and M. Yamada, 2001a: Wavelet Analysis of Simulated 1413 Tropical Convective Cloud Systems Part I: Basic Analysis. J. Atmos. Sci., 58, 850-867. 1414 Yano, J.–I., M. W. Moncrieff, and X. Wu, 2001b: Wavelet Analysis of Simulated Tropical Con1415 vective Cloud Systems Part II: Decomposition of Convective-scale and Mesoscale struc1416 tures. J. Atmos. Sci., 58, 868-876. 1417 Yano, J.–I., P. Bechtold, J.-L. Redelsperger, and F. Guichard, 2004a: Wavelet–Compressed 1418 Representation of deep moist convection. Mon. Wea. Rev., 132, 1472–1486. 1419 Yano, J.–I., R. Blender, Chidon Zhang, and K. Fraedrich, 2004b: 1/f Noise and Pulse–like 1420 Events in the Tropical Atmospheric Surface Variabilities. Quart. J. Roy. Meteor. Soc., 1421 300, 1697–1721. 1422 Zhang, C., 2005: Madden–Julian oscillation, Rev. Geophys, 43, RG2003, doi:10.1029/2004RG000158.