{ "slug": "2026-09-09-warm-rain-initiation", "condensation": { "G_m2_s": 1e-10, "shared_S": 0.002, "initial_radii_um": [ 8, 12 ], "final_radii_um": [ 17.435595774162696, 19.595917942265423 ], "ten_to_twenty_um_time_s": 750.0000000000001, "pair": { "small_radius_um": 10, "large_radius_um": 12, "number_density_cm3": 100, "rho_water_kg_m3": 1000.0, "rho_air_kg_m3": 1.2, "dynamic_viscosity_Pa_s": 1.8e-05, "Stokes_velocities_m_s": [ 0.012096577777777777, 0.017419072 ], "max_Re": 0.027870515199999998, "geometric_kernel_m3_s": 8.09301663369681e-12, "waiting_time_E1_s": 1235.6331949650398, "waiting_time_E01_s": 12356.331949650397, "radius_after_one_merger_um": 13.97273605563622, "limits": "Chosen air/water parameters; low-Re rigid-sphere Stokes approximation for this small pair only. E=.1 is illustrative, not a Hall-table value. No turbulence, Brownian motion, relative-flow modification or full growth history." } }, "chamber": { "rows": [ { "injection_cm3_min": 1.0, "interstitial_cm3": 2.0, "cloud_number_cm3": 21.3, "mean_diameter_um": 16.6, "diameter_sd_um": 6.7, "reported_relative_sd": 0.4, "phase_relaxation_s": 58.1, "reported_Da": 0.03, "recomputed_relative_sd": 0.40361445783132527, "number_diameter_relaxation_product": 20542.998000000003 }, { "injection_cm3_min": 2.0, "interstitial_cm3": 10.0, "cloud_number_cm3": 76.9, "mean_diameter_um": 15.1, "diameter_sd_um": 5.7, "reported_relative_sd": 0.38, "phase_relaxation_s": 17.6, "reported_Da": 0.11, "recomputed_relative_sd": 0.3774834437086093, "number_diameter_relaxation_product": 20436.944000000003 }, { "injection_cm3_min": 4.0, "interstitial_cm3": 36.0, "cloud_number_cm3": 201.2, "mean_diameter_um": 12.7, "diameter_sd_um": 4.5, "reported_relative_sd": 0.35, "phase_relaxation_s": 8.0, "reported_Da": 0.25, "recomputed_relative_sd": 0.35433070866141736, "number_diameter_relaxation_product": 20441.92 }, { "injection_cm3_min": 12.0, "interstitial_cm3": 372.0, "cloud_number_cm3": 564.6, "mean_diameter_um": 8.6, "diameter_sd_um": 2.4, "reported_relative_sd": 0.28, "phase_relaxation_s": 4.2, "reported_Da": 0.5, "recomputed_relative_sd": 0.27906976744186046, "number_diameter_relaxation_product": 20393.352000000003 }, { "injection_cm3_min": 1515.0, "interstitial_cm3": 22000.0, "cloud_number_cm3": 1944.3, "mean_diameter_um": 7.6, "diameter_sd_um": 2.1, "reported_relative_sd": 0.28, "phase_relaxation_s": 1.4, "reported_Da": 1.5, "recomputed_relative_sd": 0.27631578947368424, "number_diameter_relaxation_product": 20687.351999999995 } ], "phase_product_relative_range": 0.01434110439732761, "limits": "Reported time-averaged chamber conditions. SD bars are distribution widths, not standard errors or confidence intervals; no new significance test, independent replication or fixed-water estimate from mean diameter cubed." }, "stochastic_condensation": { "G_m2_s": 1e-10, "turbulent_correlation_s": 2.0, "cloud_free_S_sd": 0.004, "forcing_equilibrium_S": 0.002, "duration_s": 600.0, "exact_step_s": 1.0, "samples_per_condition": 30000, "rows": [ { "tau_c_s": 1.4, "tau_effective_s": 0.8235294117647058, "mean_S": 0.0008235294117647058, "minimum_grid_radius_squared_um2": 85.74496419427183, "analytical_sd_radius_squared_um2": 16.126736002213228, "sampled_sd_radius_squared_um2": 16.185493684897978, "variance_relative_check": 0.007300265142242246, "long_time_variance_relative_excess": 0.0013744354997056174 }, { "tau_c_s": 4.2, "tau_effective_s": 1.3548387096774195, "mean_S": 0.0013548387096774196, "minimum_grid_radius_squared_um2": 75.8108749394516, "analytical_sd_radius_squared_um2": 26.519316213962064, "sampled_sd_radius_squared_um2": 26.570567424573255, "variance_relative_check": 0.0038689334387711494, "long_time_variance_relative_excess": 0.002263174911089516 }, { "tau_c_s": 8.0, "tau_effective_s": 1.6, "mean_S": 0.0016, "minimum_grid_radius_squared_um2": 75.54310183894697, "analytical_sd_radius_squared_um2": 31.311636175709506, "sampled_sd_radius_squared_um2": 31.383095329688338, "variance_relative_check": 0.004569591657165306, "long_time_variance_relative_excess": 0.002673796791443861 }, { "tau_c_s": 17.6, "tau_effective_s": 1.7959183673469388, "mean_S": 0.0017959183673469388, "minimum_grid_radius_squared_um2": 70.9072158425422, "analytical_sd_radius_squared_um2": 35.1399601855604, "sampled_sd_radius_squared_um2": 35.03373051418007, "variance_relative_check": 0.006036950656528983, "long_time_variance_relative_excess": 0.003002183406113579 }, { "tau_c_s": 58.1, "tau_effective_s": 1.9334442595673877, "mean_S": 0.0019334442595673879, "minimum_grid_radius_squared_um2": 64.85161547124102, "analytical_sd_radius_squared_um2": 37.82652113947884, "sampled_sd_radius_squared_um2": 37.72610106566867, "variance_relative_check": 0.005302458462402182, "long_time_variance_relative_excess": 0.0032328245761439334 } ], "limits": "Chosen stationary OU illustration based on the published mechanism, not a fit to the chamber. tau_c values are taken from the table but held fixed; source, temperature, droplet count/radius feedback, exit/evaporation at zero and actual mixing geometry are not solved. Only the finite-time distribution is checked; Gaussian extreme tails are not a physical negative-radius prescription." }, "mass_endpoints": { "initial_count": 1000000, "small_radius_um": 10.0, "large_radius_um": 100.0, "small_drop_volumes_per_large": 1000, "rows": [ { "stage": "initial", "small_drops": 1000000, "large_drops": 0, "large_mass_fraction": 0.0 }, { "stage": "first_large_drop", "small_drops": 999000, "large_drops": 1, "large_mass_fraction": 0.001 }, { "stage": "ten_percent_mass", "small_drops": 900000, "large_drops": 100, "large_mass_fraction": 0.1 } ], "limits": "No time prediction, added liquid, air motion or ground rainfall. Size cutoffs are chosen bookkeeping examples; paper t100 and t10% must retain their own definitions." } }