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At least 163 records · Page 9

Investigation into alternative statistical auroral oval models, stage 1

The statistical model sensitivity to different methods of binning the NOAA/TIROS data base was examined. Each partial auroral pass was analyzed to locate the latitude of peak electron energy flux. Then using this location as the final reference latitude, all other data was binned relative to it. The next line of attack was to bin according to where the latitudinal profile center of gravity lay. This procedure overcomes the problem of very narrow intense features controlling the binning. Again the same data sets were analyzed and a binning made. These profiles look better and indeed look similar to the original auroral model. The passes were then binned relative to the equatorward boundary. The problems associated with the equatorward edge were resolved.

Bowline, M.↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e.,pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.A spectral-bin microphysical model is very expensive from a from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region using identical thermodynamic conditions but with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. Besides the initial differences in aerosol concentration, preliminary results indicate that the low CCN concentration case produces rainfall at the surface sooner than the high CCN case but has less cloud water mass aloft. Because the spectral-bin model explicitly calculates and allows for the examination of both the mass and number concentration of species in each size categor, a detailed analysis of the instantaneous size spectrum can be obtained for the two cases. It is shown that since the low CCN case produces fewer droplets, larger sized develop due to the greater condensational and collectional growth, leading to a broader size spectrum in comparison to the high CCN case.

Tao, Wei-Kuo↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-resolving Model Simulations

Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, r d a U production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembe1 (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and platelike), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and in the mid-latitude continent with different concentrations of CCN: a low "c1ean"concentration and a high "dirty" concentration. In addition, differences and similarities between bulk microphysics and spectral-bin microphysical schemes will be examined and discussed.

Tao, Wei-Kuo↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembel (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and in the mid-latitude continent with different concentrations of CCN: a low "c1ean"concentration and a high "dirty" concentration. In addition, differences and similarities between bulk microphysics and spectral-bin microphysical schemes will be examined and discussed.

Tao, Wei-Kuo↗

Evaluating Nighttime CALIOP 0.532 micron Aerosol Optical Depth and Extinction Coefficient Retrievals

NASA Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) Version 3.01 5-km nighttime 0.532 micron aerosol optical depth (AOD) datasets from 2007 are screened, averaged and evaluated at 1 deg X 1 deg resolution versus corresponding/co-incident 0.550 micron AOD derived using the US Navy Aerosol Analysis and Prediction System (NAAPS), featuring two-dimensional variational assimilation of quality-assured NASA Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging Spectroradiometer (MISR) AOD. In the absence of sunlight, since passive radiometric AOD retrievals rely overwhelmingly on scattered radiances, the model represents one of the few practical global estimates available from which to attempt such a validation. Daytime comparisons, though, provide useful context. Regional-mean CALIOP vertical profiles of night/day 0.532 micron extinction coefficient are compared with 0.523/0.532 micron ground-based lidar measurements to investigate representativeness and diurnal variability. In this analysis, mean nighttime CALIOP AOD are mostly lower than daytime (0.121 vs. 0.126 for all aggregated data points, and 0.099 vs. 0.102 when averaged globally per normalised 1 deg. X 1 deg. bin), though the relationship is reversed over land and coastal regions when the data are averaged per normalised bin (0.134/0.108 vs. 0140/0.112, respectively). Offsets assessed within single bins alone approach +/- 20 %. CALIOP AOD, both day and night, are higher than NAAPS over land (0.137 vs. 0.124) and equal over water (0.082 vs. 0.083) when averaged globally per normalised bin. However, for all data points inclusive, NAAPS exceeds CALIOP over land, coast and ocean, both day and night. Again, differences assessed within single bins approach 50% in extreme cases. Correlation between CALIOP and NAAPS AOD is comparable during both day and night. Higher correlation is found nearest the equator, both as a function of sample size and relative signal magnitudes inherent at these latitudes. Root mean square deviation between CALIOP and NAAPS varies between 0.1 and 0.3 globally during both day/night. Averaging of CALIOP along-track AOD data points within a single NAAPS grid bin improves correlation and RMSD, though day/night and land/ocean biases persist and are believed systematic. Vertical profiles of extinction coefficient derived in the Caribbean compare well with ground-based lidar observations, though potentially anomalous selection of a priori lidar ratios for CALIOP retrievals is likely inducing some discrepancies. Mean effective aerosol layer top heights are stable between day and night, indicating consistent layer-identification diurnally, which is noteworthy considering the potential limiting effects of ambient solar noise during day.

aerosol optical depth↗

A direct detection method of galaxy intrinsic ellipticity-gravitational shear correlation in non-linear regimes using self-calibration

Intrinsic alignment (IA) of galaxies is a challenging source of contamination in the Cosmic shear (GG) signals. The galaxy intrinsic ellipticity-gravitational shear (IG) correlation is generally the most dominant component of such contamination for cross-correlating redshift bins. One of the most effective techniques to mitigate such contamination is the self-calibration (SC) method which extracts the IG correlation and allows for its removal from the GG signal. In a photometric survey, the SC method first extracts the galaxy number density-galaxy intrinsic ellipticity (gI) correlation from the observed galaxy-galaxy lensing correlation using the redshift dependence of lens-source pairs. The IG correlation is computed through a scaling relation using the gI correlation and other lensing observables. The applicability of the SC method has so far been focused on the linear IA scales and the linear galaxy bias. We extend the SC method beyond the linear regime by modifying its scaling relation which can account for the non-linear galaxy bias model and various IA models. In this study, we provide a framework to detect the IG correlation for the redshift bins for source galaxies for the proposed year 1 survey of the Rubin Legacy Survey of Space and Time (LSST Y1). We tested the method for the tidal alignment and tidal torquing (TATT) model of IA and we found that the scaling relation is accurate within 10% and 20% for cross-correlating and auto-correlating redshift bins, respectively. Hence the suppression of IG contamination in observed GG correlation can be accomplished with a factor of 10 and 5, for cross-correlating and auto-correlating redshift bins, respectively. We tested the method's robustness and found that the suppression of IG contamination by a factor of 5 is still achievable for all combinations of cross-correlating bins even with the inclusion of a moderate amount of uncertainties on IA and bias parameters, respectively. We also make available, a branch of the code FAST-PT to provide gI correlations up to 1-loop order term used by the new SC method.

gravitational lensing↗

The Atacama Cosmology Telescope: SZ-based masses and dust emission from IR-selected cluster candidates in the SHELA survey

Here we examine the stacked thermal Sunyaev–Zel’dovich (SZ) signals for a sample of galaxy group and cluster candidates from the 24 deg 2 infrared Spitzer-HETDEX Exploratory Large Area (SHELA) survey. We identify the objects in combination with optical data using the redMaPPer algorithm, and divide them into three richness bins (λ in 10–20, 20–30, and 30–76 with average photometric redshifts of 0.80, 0.73, and 0.70, respectively). All richness bins show evidence for dust emission, which we fit using stacked profiles from Herschel Stripe 82 data. We fit for synchrotron emission using stacked profiles created by binning source fluxes from NRAO VLA Sky Survey data. We can confidently detect the SZ decrement only in the highest richness bin, finding M SZ,500 = $8.7^{+1.7}_{-1.3} \times 10^{13}\, \mathrm{ M}_\odot$. Neglecting the correction for dust and synchrotron depresses the inferred mass by 26 percent, indicating a partial fill-in of the SZ decrement from dust and synchrotron emission. We compare our corrected SZ masses to two redMaPPer mass–richness scaling relations and find that the SZ mass is lower than predicted by the richness. For the lower richness bins, mass bias factors as low as 1 – b = 0.6 are not enough to bring the mass limits into agreement. We discuss possible explanations for this discrepancy. The SHELA richnesses may differ from previous richness measurements due to the inclusion of infrared data in redMaPPer. To connect the SZ signal to the mass, we use a universal gas pressure profile that is calibrated to massive clusters at low redshift. It may not be applicable to our lower mass, higher redshift sample.

79 ASTRONOMY AND ASTROPHYSICS↗

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear two-point correlation functions

Here, we perform a blinded cosmology analysis with cosmic shear two-point correlation functions measured from more than 25 million galaxies in the Hyper Suprime-Cam three-year shear catalog in four tomographic redshift bins ranging from 0.3 to 1.5. After conservative masking and galaxy selection, the survey covers 416 deg 2 of the northern sky with an effective galaxy number density of 15 arcmin –2 over the four redshift bins. The 2PCFs adopted for cosmology analysis are measured in the angular range; 7.1 <θ/arcmin < 56.6 for ξ + and 31.2 < θ/arcmin < 248 for ξ – , with a total signal-to-noise ratio of 26.6. We apply a conservative, wide, flat prior on the photometric redshift errors on the last two tomographic bins, and the relative magnitudes of the cosmic shear amplitude across four redshift bins allow us to calibrate the photometric redshift errors. With this flat prior on redshift errors, we find Ω m = 0.25⁢6$^{+0.056}_{–0.044}$ and S 8 ≡ σ 8 ⁢$\sqrt{Ω_{m}/0.3}$ = 0.76⁢9$^{+0.031}_{–0.034}$ (both 68% C.I.) for a flat Λ cold dark matter cosmology. We find, after unblinding, that our constraint on S 8 is consistent with the Fourier space cosmic shear and the 3 × 2 pt analyses on the same HSC dataset. We carefully study the potential systematics from astrophysical and systematic model uncertainties in our fiducial analysis using synthetic data, and report no biases (including projection bias in the posterior space) greater than 0.5σ in the estimation of S 8 . Our analysis hints that the mean redshifts of the two highest tomographic bins are higher than initially estimated. In addition, a number of consistency tests are conducted to assess the robustness of our analysis. Comparing our result with Planck-2018 cosmic microwave background observations, we find a ~2σ tension for the Λ ⁢CDM model.

79 ASTRONOMY AND ASTROPHYSICS↗

Measurements of jet cross-section ratios in 13 TeV proton-proton collisions with ATLAS

Measurements of jet cross-section ratios between inclusive bins of jet multiplicity are performed in 140 fb -1 of proton-proton collisions with √s = 13 TeV center-of-mass energy, recorded with the ATLAS detector at CERN’s Large Hadron Collider. These ratios are constructed from double-differential cross-section measurements that are made in bins of jet multiplicity and other observables that are sensitive the energy scale and angular distribution of radiation due to the strong interaction in the final state. Additionally, the scalar sum of the two leading jets’ transverse momenta is measured triple differentially, in bins of the third jet’s transverse momentum and of jet multiplicity. These measurements are unfolded to account for acceptance and detector-related effects. The measured distributions are used to construct ratios of the inclusive jet-multiplicity bins, which have been shown to be sensitive to the strong coupling Formula Presented while being less sensitive than other observables to systematic uncertainties and parton distribution functions. The measured distributions are compared with state-of-the-art QCD calculations, including next-to-next-to-leading-order predictions for two- and three-jet events. These predictions are generally found to model the data well and perform best in bins with a modest requirement on the third jet’s transverse momentum. Significant differences between data and Monte Carlo predictions are observed in events with large rapidity gaps and invariant masses of the leading jet pair. Studies leading to reduced jet energy scale uncertainties significantly improve the precision of this work and are documented herein.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Atacama Cosmology Telescope DR6 and DESI: Structure growth measurements from the cross-correlation of DESI legacy imaging galaxies and CMB lensing from ACT DR6 and 𝑃⁢𝑙⁢𝑎⁢𝑛⁢𝑐⁢𝑘 PR4

We measure the growth of cosmic density fluctuations on large scales and across the redshift range 0.3 < 𝑧 < 0.8 through galaxy clustering and the cross-correlation of the ACT data release 6 cosmic microwave background (CMB) lensing map and galaxies from the Dark Energy Spectroscopic Instrument Legacy Survey, using three galaxy samples spanning the redshifts of 0.3 ≲ 𝑧 ≲ 0.45, 0.45 ≲ 𝑧 ≲ 0.6, 0.6 ≲ 𝑧 ≲ 0.8. We adopt a scale cut where nonlinear effects are negligible, so that the cosmological constraints are derived from the linear regime. We determine the amplitude of matter fluctuations over all three redshift bins using Atacama Cosmology Telescope (ACT) data alone to be 𝑆 8 ≡ 𝜎 8 ⁢(Ω 𝑚 /0.3) 0.5 =0.772 ± 0.040 in a joint analysis combining the three redshift bins and ACT lensing alone. Using a combination of ACT and Planck data we obtain 𝑆 8 = 0.765 ± 0.032. The lowest redshift bin used is the least constraining and exhibits a ∼2⁢𝜎 tension with the other redshift bins; thus we also report constraints excluding the first redshift bin, giving 𝑆 8 = 0.785 ± 0.033 for the combination of ACT and Planck. This result is in excellent agreement at the 0.3⁢𝜎 level with measurements from galaxy lensing, but is 1.8⁢𝜎 lower than predictions based on Planck primary CMB data. Understanding whether this hint of discrepancy in the growth of structure at low redshifts arises from a fluctuation, from systematics in data, or from new physics is a high priority for forthcoming CMB lensing and galaxy cross-correlation analyses.

cosmic microwave background↗

Mbin v1.0

The Mbin software, is a software toolkit that implements the IMG metagenome binning pipeline. The software allows the user to process input metagenome contigs, and produces metagenome assembled genomes (metagenome bins) and valuation metrics per bin including completion and contamination estimates, quality assignment, predicted lineage and eukaryotic potential. It is currently packed as a portable docker container and provides the advantage of running the process of binning and analysis of the bins generated, using a suite of tools run sequentially with controls in place to capture errors and optional arguments to run a modified version depending on individual needs and capabilities.

Varghese, Neha↗

Effects of finite sampling on fatigue damage estimation of wind turbine components: A statistical study

The variability of the wind turbine loads complicates fatigue assessment in the design phase, as performing simulations covering the entire lifetime is computationally expensive. The current work provides important information for assessing the uncertainty in fatigue damage estimation due to finite data. Here we study the sample size effect on mean, variance, and skewness of damage in each wind bin, identify the important wind bins, and study the uncertainty propagation from each wind bin to the lifetime damage using 3600 aeroelastic simulations and bootstrapping. To achieve less than 1% error in the damage estimation across all load channels in the current case study, at least 100 turbulence seeds are needed. Damage in different wind bins follows a lognormal distribution when using the conventional approach of six seeds. The provided insights and information allow the designer to achieve a specific level of accuracy for a given computational cost using strategic bin sampling.

17 WIND ENERGY↗

End-Use Savings Shapes Measure Documentation: Dispatch Schedule Generation for Demand Flexibility Measures

This supplemental document describes the methodology used for determining the dispatch timing of various EUSS demand flexibility measures. Demand flexibility measures are designed to reduce/dispatch electricity demand in buildings during especially beneficial/critical times. The method used in this work utilizes predictions of building loads to generate a schedule that reflects the periods when the building's daily peak load occurs to support decision making in demand flexibility measures. The dispatch schedule generation method described in this document creates an hourly schedule that includes a load dispatch (peak) window for each day for a whole year based on load prediction, with options using different prediction methods: perfect prediction, bin-sampling method, fixed schedule, and outdoor air temperature (OAT)-based prediction method. The perfect prediction method performs a simulation to obtain the annual load profile as predicted load, representing the scenario of perfect load prediction. The bin-sampling method (1) categorizes days into representative bins by temperature characteristics, (2) performs simulations on sample days from each of those bins to create representative (or predicted) load, and (3) assigns representative loads for all days in a year based on the bin categorization. The fixed schedule method defines uniform start and end time of peak window with assumed fixed daily peak time, for all days in a season or a year. The OAT-based prediction method uses the statistics of OAT (minimum and maximum) as the indicators of peak load, with specified delay response time from building loads to temperature. Given the load prediction, daily peak periods are determined as a time window with specified length in each day that include the predicted daily peak load and with a secondary rule such as maximizing energy saving potential. The dispatch schedule generation method is not a standalone measure and is intended to be combined with other demand flexibility measures that could leverage the peak schedule and apply demand controls on specific systems or devices for demand response, such as measures described in "Measure Documentation - Thermostat Control for Load Shedding" and "Measure Documentation - Thermostat Control for Load Shifting".

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

97 MATHEMATICS AND COMPUTING↗

Atacama Cosmology Telescope DR6 and DESI: Structure growth measurements from the cross-correlation of DESI legacy imaging galaxies and CMB lensing from ACT DR6 and P l a n c k PR4

We measure the growth of cosmic density fluctuations on large scales and across the redshift range 0.3 < z < 0.8 through galaxy clustering and the cross-correlation of the ACT data release 6 cosmic microwave background (CMB) lensing map and galaxies from the Dark Energy Spectroscopic Instrument Legacy Survey, using three galaxy samples spanning the redshifts of 0.3 ≲ z ≲ 0.45 , 0.45 ≲ z ≲ 0.6 , 0.6 ≲ z ≲ 0.8 . We adopt a scale cut where nonlinear effects are negligible, so that the cosmological constraints are derived from the linear regime. We determine the amplitude of matter fluctuations over all three redshift bins using Atacama Cosmology Telescope (ACT) data alone to be S 8 ≡ σ 8 ( Ω m / 0.3 ) 0.5 = 0.772 ± 0.040 in a joint analysis combining the three redshift bins and ACT lensing alone. Using a combination of ACT and Planck data we obtain S 8 = 0.765 ± 0.032 . The lowest redshift bin used is the least constraining and exhibits a ∼ 2 σ tension with the other redshift bins; thus we also report constraints excluding the first redshift bin, giving S 8 = 0.785 ± 0.033 for the combination of ACT and Planck. This result is in excellent agreement at the 0.3 σ level with measurements from galaxy lensing, but is 1.8 σ lower than predictions based on Planck primary CMB data. Understanding whether this hint of discrepancy in the growth of structure at low redshifts arises from a fluctuation, from systematics in data, or from new physics is a high priority for forthcoming CMB lensing and galaxy cross-correlation analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

Intercomparison of global SST fields derived from satellite sensors and ship observations

Near global comparisons were made between binned forms of SST obtained from different instruments, ship meteorological observations, and the output of a meteorological model. Binning hereinafter means gridding by simple summation of data values in a bin, which in this study was a 2 deg. x 2 deg. box or a 10 deg. x 10 box surrounding a grid node. In the binned comparisons, the question is asked: are the binned data from two instruments drawn from the same population? The first two measures of statistical moments of the populations are used to test the hypothesis that they are. Comparisons were also attempted between raw forms of the various SST retrievals, using a structure function analysis. The results of this analysis were relatively uninteresting and are therefore omitted.

Pazan, S. E.↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles (i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail). Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep cloud systems in the west Pacific warm pool region, in the sub-tropics (Florida) and in the mid-latitude using identical thermodynamic conditions but with different concentrations of CCN: a low 'clean' concentration and a high 'dirty' concentration.

Tao, Wei-Kuo↗