Subgrid Distribution Research Articles

Deep Learning Parameterization of Vertical Wind Velocity Variability via Constrained Adversarial Training

Abstract Atmospheric models with typical resolution in the tenths of kilometers cannot resolve the dynamics of air parcel ascent, which varies on scales ranging from tens to hundreds of meters. Small-scale wind fluctuations are thus characterized by a subgrid distribution of vertical wind velocity W with standard deviation σW. The parameterization of σW is fundamental to the representation of aerosol–cloud interactions, yet it is poorly constrained. Using a novel deep learning technique, this work develops a new parameterization for σW merging data from global storm-resolving model simulations, high-frequency retrievals of W, and climate reanalysis products. The parameterization reproduces the observed statistics of σW and leverages learned physical relations from the model simulations to guide extrapolation beyond the observed domain. Incorporating observational data during the training phase was found to be critical for its performance. The parameterization can be applied online within large-scale atmospheric models, or offline using output from weather forecasting and reanalysis products. Significance Statement Vertical air motion plays a crucial role in several atmospheric processes, such as cloud droplet and ice crystal formation. However, it often occurs at scales smaller than those resolved by standard atmospheric models, leading to uncertainties in climate predictions. To address this, we present a novel deep learning approach that synthesizes data from various sources, providing a representation of small-scale vertical wind velocity suitable for integration into atmospheric models. Our method demonstrates high accuracy when compared to observation-based retrievals, offering potential to mitigate uncertainties and enhance climate forecasting.

Analysis of the Closures of Sub-grid Scale Variance of Reaction Progress Variable for Turbulent Bunsen Burner Flames at Different Pressure Levels

The statistical behaviour and modelling of the sub-grid variance of reaction progress variable have been analysed based on a priori analysis of direct numerical simulation (DNS) data of turbulent premixed Bunsen burner flames at different pressure levels. An algebraic expression for sub-grid variance, which can be derived based on a presumed bi-modal sub-grid distribution of reaction progress variable with impulses at unburned reactants and fully burned products, has been found to be inadequate for the purpose of prediction of sub-grid variance even for the flames in the wrinkled flamelets/corrugated flamelets regime. Moreover, an algebraic model, which is often used for modelling sub-grid variance of passive scalars, has been found to significantly overpredict the sub-grid variance of reaction progress variable for all the cases considered here. The modelling of the unclosed terms of the sub-grid variance transport equation has been analysed in detail. Suitable model expressions have been identified for the sub-grid flux of variance, reaction rate contribution and scalar dissipation rate based on a priori analysis of DNS data. It has been found that the alternation of pressure does not have any significant impact on the closures of sub-grid flux of variance but a model parameter for the Favre-filtered scalar dissipation rate needs to be modified to account for the variation of pressure.

Sub-grid Reaction Progress Variable Variance Closure in Turbulent Premixed Flames

The statistical behaviour and modelling of the sub-grid variance of reaction progress variable have been analysed based on a priori analysis of Direct Numerical Simulation (DNS) data of freely propagating statistically planar turbulent premixed flames with different turbulence intensities. It has been found that an algebraic expression, which can be derived based on a presumed bi-modal sub-grid distribution of reaction progress variable with impulses at unburned reactants and fully burned products, is inadequate for the purpose of prediction of sub-grid variance. An algebraic model, which is often used for modelling sub-grid variance of passive scalars, has been found to significantly overpredict the sub-grid variance of reaction progress variable for the cases considered here. The statistical behaviours of the terms of the sub-grid variance have been analysed in detail and explained based on scaling arguments. It has been found that reaction rate and molecular dissipation contributions play leading order roles in the transport of sub-grid reaction progress variable variance and they remain in approximate equilibrium for large filter widths. Suitable model expressions have been identified for the sub-grid flux of variance, reaction rate contribution and scalar dissipation rate based on a priori analysis of DNS data.

Flow‐dependent stochastic coupling for climate models with high ocean‐to‐atmosphere resolution ratio

AbstractThis study introduces a new flow‐dependent distribution sampling (FDDS) scheme for air–sea coupling. The FDDS scheme is implemented in a climate model and used to improve the simulated mean and variability of atmospheric and oceanic surface fields and thus air–sea fluxes. Most coupled circulation models use higher resolutions in the sea ice and ocean compared to the atmospheric model component, thereby explicitly simulating the atmospheric subgrid‐scale at the interface. However, the commonly applied averaging of surface fields and air–sea fluxes tends to smooth fine‐scale structures, such as oceanic fronts. The stochastic FDDS scheme samples the resolved spatial ocean (and sea ice) subgrid distribution that is usually not visible to a coarser‐resolution atmospheric model. Randomly drawn nodal ocean values are passed to the corresponding atmospheric boxes for the calculation of surface fluxes, aiming to enhance surface flux variability. The resulting surface field perturbations of the FDDS scheme are based on resolved dynamics, displaying pronounced seasonality with realistic magnitude. The AWI Climate Model is used to test the scheme on interannual time‐scales. Our set‐up features a high ocean‐to‐atmosphere resolution ratio in the Tropics, with grid‐point ratios of about 60:1. Compared to the default deterministic averaging, changes are largest in the Tropics leading to an improved spatial distribution of precipitation with bias reductions of up to 50%. Enhanced sea‐surface temperature variability in boreal winter further improves the seasonal phase locking of temperature anomalies associated with the El Niño–Southern Oscillation. Mean 2m temperature, sea ice thickness and concentration react with a contrasting dipole pattern between hemispheres but a joint increase of monthly and interannual variability. This first approach to implement a flow‐dependent stochastic coupling scheme shows considerable benefits for simulations of global climate, and various extensions and modifications of the scheme are possible.

On the Covariability of Cloud and Rain Water as a Function of Length Scale

AbstractMicrophysics parameterizations in large-scale models often account for subgrid variability in the calculation of process rates by integrating over assumed subgrid distributions of the input variables. The variances and covariances that define distribution width may be specified or diagnosed. The correlation ρ of cloud and rain mass mixing ratio/liquid water content (LWC) is a key input for accurate prediction of the accretion rate and a constant value is typically assumed. In this study, high-frequency aircraft measurements with a spatial resolution of ≈22 cm are used to evaluate the scaling behavior of cloud and rain LWC (qc and qr, respectively) and to demonstrate how and why covariability varies with length scale ℓ. It is shown that power spectral densities of both qc and qr exhibit scale invariance across a wide range of scales (2.04–142 m for qc; 33–1.45 × 104 m for qr). Because the cloud–rain cospectrum is also scale invariant, ρ is therefore expected to vary with ℓ. Direct calculation of ρ shows that it generally increases with ℓ, but there is significant variability in the ρ–ℓ relationship that primarily depends on cloud drop number concentration N and cloud cellular organization, suggesting that ρ may also vary with cloud regime. A parameterization of ρ as a function of ℓ and N is developed from aircraft observations and implications for diagnosis of ρ from limited-area model output are also discussed.

Modeling Water Vapor and Clouds as Passive Tracers in an Idealized GCM

This paper introduces an idealized general circulation model (GCM) in which water vapor and clouds are tracked as tracers, but are not allowed to affect circulation through either latent heat release or cloud radiative effects. The cloud scheme includes an explicit treatment of cloud microphysics and diagnoses cloud fraction from a prescribed subgrid distribution of total water. The model is capable of qualitatively capturing many large-scale features of water vapor and cloud distributions outside of the boundary layer and deep tropics. The subtropical dry zones, midlatitude storm tracks, and upper-tropospheric cirrus are simulated reasonably well. The inclusion of cloud microphysics (namely rain re-evaporation) has a modest but significant effect of moistening the lower troposphere in this model. When being subjected to a uniform fractional increase of saturated water vapor pressure, the model produces little change in cloud fraction. A more realistic perturbation, which considers the nonlinearity of the Clausius–Clapeyron relation and spatial structure of CO2-induced warming, results in a substantial reduction in the free-tropospheric cloud fraction. This is reconciled with an increase of relative humidity by analyzing the probability distributions of both quantities, and may help explain partly similar decreases in cloud fraction in full GCMs. The model provides a means to isolate individual processes or model components for studying their influences on cloud simulation in the extratropical free troposphere.

Small-Scale Variability of the Raindrop Size Distribution and Its Effect on Areal Rainfall Retrieval

AbstractThe drop size distribution (DSD) describes the microstructure of liquid precipitation. The high variability of the DSD reflects the variety of microphysical processes controlling raindrop properties and affects the retrieval of rainfall. An analysis of the effects of DSD subgrid variability on areal estimation of precipitation is presented. Data used were recorded with a network of disdrometers in Ardèche, France. DSD variability was studied over two typical scales: 5 km × 5 km, similar to the ground footprint size of the Global Precipitation Measurement (GPM) spaceborne weather radar, and 2.8 km × 2.8 km, an operational pixel size of the Consortium for Small-Scale Modeling (COSMO) numerical weather model. Stochastic simulation was used to generate high-resolution grids of DSD estimates over the regions of interest, constrained by experimental DSDs measured by disdrometers. From these grids, areal DSD estimates were derived. The error introduced by assuming a point measurement to be representative of the areal DSD was quantitatively characterized and was shown to increase with the size of the considered area and with drop size and to decrease with the integration time. The controlled framework allowed for the accuracy of retrieval algorithms to be investigated. Rainfall variables derived by idealized simulations of GPM- and COSMO-style algorithms were compared to subgrid distributions of the same variables. While rain rate and radar reflectivity were well represented, the estimated drop concentration and mass-weighted mean drop diameter were often less representative of subgrid values.

Accurate and efficient prediction of fine‐resolution hydrologic and carbon dynamic simulations from coarse‐resolution models

AbstractThe topography, and the biotic and abiotic parameters are typically upscaled to make watershed‐scale hydrologic‐biogeochemical models computationally tractable. However, upscaling procedure can produce biases when nonlinear interactions between different processes are not fully captured at coarse resolutions. Here we applied the Proper Orthogonal Decomposition Mapping Method (PODMM) to downscale the field solutions from a coarse (7 km) resolution grid to a fine (220 m) resolution grid. PODMM trains a reduced‐order model (ROM) with coarse‐resolution and fine‐resolution solutions, here obtained using PAWS+CLM, a quasi‐3‐D watershed processes model that has been validated for many temperate watersheds. Subsequent fine‐resolution solutions were approximated based only on coarse‐resolution solutions and the ROM. The approximation errors were efficiently quantified using an error estimator. By jointly estimating correlated variables and temporally varying the ROM parameters, we further reduced the approximation errors by up to 20%. We also improved the method's robustness by constructing multiple ROMs using different set of variables, and selecting the best approximation based on the error estimator. The ROMs produced accurate downscaling of soil moisture, latent heat flux, and net primary production with O(1000) reduction in computational cost. The subgrid distributions were also nearly indistinguishable from the ones obtained using the fine‐resolution model. Compared to coarse‐resolution solutions, biases in upscaled ROM solutions were reduced by up to 80%. This method has the potential to help address the long‐standing spatial scaling problem in hydrology and enable long‐time integration, parameter estimation, and stochastic uncertainty analysis while accurately representing the heterogeneities.

An assessment of the impact of local processes on dust lifting in martian climate models

Simulation of the lifting of dust from the planetary surface is of substantially greater importance on Mars than on Earth, due to the fundamental role that atmospheric dust plays in the former’s climate, yet the dust emission parameterisations used to date in martian global climate models (MGCMs) lag, understandably, behind their terrestrial counterparts in terms of sophistication. Recent developments in estimating surface roughness length over all martian terrains and in modelling atmospheric circulations at regional to local scales (less than O(100km)) presents an opportunity to formulate an improved wind stress lifting parameterisation. We have upgraded the conventional scheme by including the spatially varying roughness length in the lifting parameterisation in a fully consistent manner (thereby correcting a possible underestimation of the true threshold level for wind stress lifting), and used a modification to account for deviations from neutral stability in the surface layer. Following these improvements, it is found that wind speeds at typical MGCM resolution never reach the lifting threshold at most gridpoints: winds fall particularly short in the southern midlatitudes, where mean roughness is large. Sub-grid scale variability, manifested in both the near-surface wind field and the surface roughness, is then considered, and is found to be a crucial means of bridging the gap between model winds and thresholds. Both forms of small-scale variability contribute to the formation of dust emission ‘hotspots’: areas within the model gridbox with particularly favourable conditions for lifting, namely a smooth surface combined with strong near-surface gusts. Such small-scale emission could in fact be particularly influential on Mars, due both to the intense positive radiative feedbacks that can drive storm growth and a strong hysteresis effect on saltation. By modelling this variability, dust lifting is predicted at the locations at which dust storms are frequently observed, including the flushing storm sources of Chryse and Utopia, and southern midlatitude areas from which larger storms tend to initiate, such as Hellas and Solis Planum. The seasonal cycle of emission, which includes a double-peaked structure in northern autumn and winter, also appears realistic. Significant increases to lifting rates are produced for any sensible choices of parameters controlling the sub-grid distributions used, but results are sensitive to the smallest scale of variability considered, which high-resolution modelling suggests should be O(1km) or less. Use of such models in future will permit the use of a diagnosed (rather than prescribed) variable gustiness intensity, which should further enhance dust lifting in the southern hemisphere in particular.

Monte Carlo-based subgrid parameterization of vertical velocity and stratiform cloud microphysics in ECHAM5.5-HAM2

Abstract. A new method for parameterizing the subgrid variations of vertical velocity and cloud droplet number concentration (CDNC) is presented for general circulation models (GCMs). These parameterizations build on top of existing parameterizations that create stochastic subgrid cloud columns inside the GCM grid cells, which can be employed by the Monte Carlo independent column approximation approach for radiative transfer. The new model version adds a description for vertical velocity in individual subgrid columns, which can be used to compute cloud activation and the subgrid distribution of the number of cloud droplets explicitly. Autoconversion is also treated explicitly in the subcolumn space. This provides a consistent way of simulating the cloud radiative effects with two-moment cloud microphysical properties defined at subgrid scale. The primary impact of the new parameterizations is to decrease the CDNC over polluted continents, while over the oceans the impact is smaller. Moreover, the lower CDNC induces a stronger autoconversion of cloud water to rain. The strongest reduction in CDNC and cloud water content over the continental areas promotes weaker shortwave cloud radiative effects (SW CREs) even after retuning the model. However, compared to the reference simulation, a slightly stronger SW CRE is seen e.g. over mid-latitude oceans, where CDNC remains similar to the reference simulation, and the in-cloud liquid water content is slightly increased after retuning the model.

Object-Based Evaluation of MERRA Cloud Physical Properties and Radiative Fluxes during the 1998 El Niño–La Niña Transition

The Modern-Era Retrospective Analysis for Research and Application (MERRA) is a reanalysis designed to produce an improved representation of the Earth’s hydrologic cycle. This study examines the representation of deep convective clouds in MERRA, comparing analyzed liquid and ice clouds with deep convective cloud objects observed by instruments on the Tropical Rainfall Measuring Mission satellite. Results show that MERRA contains deep convective cloud in 98.1% of the observed cases. MERRA-derived probability density functions (PDFs) of cloud properties have a similar form as the observed PDFs and exhibit a similar trend with changes in object size. Total water path, optical depth, and outgoing shortwave radiation (OSR) in MERRA are found to match the cloud object observations quite well; however, there appears to be a bias toward higher-than-observed cloud tops in the MERRA. The reanalysis fits the observations most closely for the largest class of convective systems, with performance generally decreasing with a transition to smaller convective systems. Comparisons of simulated total water path, optical depth, and OSR are found to be highly sensitive to the assumed subgrid distribution of condensate and indicate the need for caution when interpreting model-data comparisons that require disaggregation of grid-scale cloud to satellite pixel scales.

중/도시규모 기상모델을 이용한 고층건물군이 연안도시기상장에 미치는 영향 수치모델링

Modeling the effects of high-rise buildings on thermo-dynamic conditions and meteorological fields over a coastal urban area was conducted using the modified meso-urban meteorological model (Urbanized MM5; uMM5) with the urban canopy parameterization (UCP) and the high-resolution inputs (urban morphology, land-use/land-cover sub-grid distribution, and high-quality digital elevation model data sets). Sensitivity simulations was performed during a typical sea-breeze episode (4~8 August 2006). Comparison between simulations with real urban morphology and changed urban morphology (i.e. high-rise buildings to low residential houses) showed that high-rise buildings could play an important role in urban heat island and land-sea breeze circulation. The major changes in urban meteorologic conditions are followings: significant increase in daytime temperature nearly by due to sensible heat flux emitted from high density residential houses, decrease in nighttime temperature nearly by because of the reduction in the storage heat flux emitted from high-rise buildings, and large increase in wind speed (maximum 2 m ) during the daytime due to lessen drag-force or increased gradient temperature over coastal area.

Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments

A novel approach is presented for combining spatial and temporal detail from newly available TRMM-based data sets to derive hourly rainfall intensities at 1-km spatial resolution for hydrological modelling applications. Time series of rainfall intensities derived from 3-hourly 0.25° TRMM 3B42 data are merged with a 1-km gridded rainfall climatology based on TRMM 2B31 data to account for the sub-grid spatial distribution of rainfall intensities within coarse-scale 0.25° grid cells. The method is implemented for two dryland catchments in Tunisia and Senegal, and validated against gauge data. The outcomes of the validation show that the spatially disaggregated and intensity corrected TRMM time series more closely approximate ground-based measurements than non-corrected data. The method introduced here enables the generation of rainfall intensity time series with realistic temporal and spatial detail for dynamic modelling of runoff and infiltration processes that are especially important to water resource management in arid regions. Editor D. Koutsoyiannis Citation Tarnavsky, E., Mulligan, M. and Husak, G., 2012. Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments. Hydrological Sciences Journal, 57 (2), 248–264.

Characterization of cloud liquid water content distributions from CloudSat

The development of realistic cloud parameterizations requires accurate characterizations of subgrid distributions of thermodynamic variables. To this end, cloud liquid water content (CLWC) distributions are characterized with respect to cloud phase, cloud type, precipitation occurrence, and geolocation using CloudSat radar measurements. The probability density function (PDF) of CLWC is estimated using maximum likelihood estimation. The best‐estimated PDF of CLWC is found to follow either a gamma or a lognormal distribution depending on temperature (cloud phase), cloud type, the occurrence of precipitation, and geolocation. The data sampling with respect to cloud phase and precipitation significantly affects the distributional characteristics of CLWC in some regions. In the lower to midtroposphere (altitudes of 1–6 km) in the tropics and subtropics, where nonprecipitating and pure liquid phase clouds are dominant, the PDFs of CLWC are best described by lognormal distributions. In contrast, at altitudes above 6 km and in regions poleward of the midlatitudes, the CLWC more closely resembles a gamma distribution that coincides with a high frequency of occurrence of supercooled liquid clouds containing low CLWC values. When the contributions of supercooled water and precipitation are removed, the CLWC PDFs transition from gamma to lognormal distributions in two areas: (1) the high altitude and middle‐to‐polar latitude regions where the contribution of supercooled cloud is significant and (2) in the lower troposphere where precipitation is frequently detected. Although the CloudSat radar does not sample all cloud hydrometeors, coherent regional and cloud type dependence of CLWC distributional characteristics are observed that may provide useful constraints for cloud parameterizations in climate models.

Analysis of sub-grid PDF of a progress variable approach using a hybrid LES/TPDF method

In the present study, the sub-grid PDF of a progress variable approach has been investigated, in order to evaluate the capability of common sub-grid PDF models for the mixture fraction as well as a reactive progress variable. Hybrid LES/Monte-Carlo-transported PDF (MC-TPDF) simulations using a flamelet generated manifolds (FGM) progress variable approach have been performed of a non-premixed bluff-body stabilized CH4/H2 flame. Time averaged results of velocities, mixture fraction, temperature and OH mass fraction are shown and compared with presumed PDF results and experimental data. Furthermore, in order to assess the suitability of β-shaped PDF, especially for the reactive progress variable, instantaneous sub-grid distributions and third central moments of MC-TPDF and presumed β-PDF are compared. The obtained results show, that a presumed β-PDF is not a feasible model for the sub-grid PDF of the progress variable.

건물효과를 고려한 연안도시지역 고해상도 기상모델링

A meso-urban meteorological model (Urbanized MM5; uMM5) with urban canopy parameterization (UCP) was applied to the high-resolution simulation of meteorological fields in a complex coastal urban area and the assessment of urban impacts. Multi-scale simulations with the uMM5 in the innermost domain (1-km resolution) covering the Busan metropolitan region were performed during a typical sea breeze episode (4~8 August 2006) with detailed fine-resolution inputs (urban morphology, land-use/land-cover sub-grid distribution, and high-quality digital elevation model data sets). An additional simulation using the standard MM5 was also conducted to identify the effects of urban surface properties under urban meteorological conditions. Results showed that the uMM5 reproduced well the urban thermal and dynamic environment and captured well the observed feature of sea breeze. When comparison with simulations of the standard MM5, it was found that the uMM5 better reproduced urban impacts on temperature (especially at nighttime) and urban wind flows: roughness-induced deceleration and UHI (Urban Heat Island)-induced convergence.

Conservative cascade interpolation on the sphere: An intercomparison of various non‐oscillatory reconstructions

AbstractVarious new polynomial and non‐polynomial approximations to a subgrid distribution have been adapted for use in the conservative cascade scheme (CCS) and applied to conservative grid‐to‐grid interpolation on a latitude‐‐longitude grid. These approximations include the following: piecewise parabolic method (PPM), piecewise hyperbolic method (PHM), piecewise double hyperbolic method (PDHM), power‐limited piecewise parabolic method (P‐PPM), piecewise rational method (PRM), third‐order weighted essentially non‐oscillatory (WENO23), fifth‐order weighted essentially non‐oscillatory (WENO35), and a modified piecewise parabolic method (M‐PPM). A series of test cases are performed in which initial gridded data are interpolated between T42 and 2° grids and compared against analytical values. Four initial data profiles are used: smooth harmonic, high‐frequency harmonic, quasi‐polar vortex data and slotted cylinder data. In general, PDHM (WENO35) had the lowest error norms of the three‐(five‐)cell stencil methods. Quite often, M‐PPM gave accuracy comparable to WENO35 at significantly lower cost. Monotonicity violations generally only occurred when interpolating to a finer grid with a maximum violation of 1.8% of the data range. Copyright © 2009 Royal Meteorological Society

Representing the effects of subgrid variability of soil moisture on runoff generation in a land surface model

Different representations of runoff generation processes were implemented in the MOSES land surface model which is used with mesoscale and global atmospheric models. The standard model was compared with versions in which runoff generation was described by parameterizations based on either the Probability Distributed Model (PDM) or modified forms of TOPMODEL, all of which used probability functions to describe the subgrid distribution of soil moisture. The model results were compared with observed streamflow in three catchments in southern France. After calibration, the PDM‐ and TOPMODEL‐based parameterizations performed substantially better than the standard model. The TOPMODEL approach gave the best results through allowing a more responsive subsurface flow that contributed to peak flows and also better captured the slower changes during recessions. This approach was sensitive to uncertainty in the value of the topographic index. The PDM‐based model only changed the calculation of surface runoff and retained the standard description of subsurface runoff, and this limited the possible improvement in performance. In principle the values of the new parameters can be determined from observations, but in practice calibration is likely to be required. However, for each new parameterization, a single set of parameter values was found that performed well in all catchments. The simulated soil moisture and surface heat fluxes during summer dry periods were affected by the choice of runoff parameterization.

The streamline subgrid integration method: I. Quasi-monotonic second-order transport schemes

A new finite-volume method has been developed for conservative and monotonic transport in multiple dimensions without any sort of dimension splitting to emphasize the space–time integrity of the fluid system. The streamline subgrid integration (SSI) method is a combination of the semi-Lagrangian and the finite-volume methods with generalized multidimensional subgrid distributions. Second-order transport schemes are constructed in two dimensions, and their extensions to three dimensions are also discussed. Spurious divergence is rigorously controlled with Lagrangian control volumes, monotonicity is well preserved for both compressible and incompressible flows, and positive-definiteness is always guaranteed. The accuracy and the numerical properties of these schemes are evaluated with both continuous and discontinuous solutions in flows of rigid motion and incompressible deformation where analytic solutions are available. Icosahedral geodesic grids are selected to demonstrate the general nature of the SSI method in spherical geometry that the numerical solutions are virtually not affected by the irregularity of grid structure. We have found that the numerical solutions converge quickly to the analytic solutions, and the SSI second-order schemes are relatively more beneficial for high-resolution applications.

Predicting cloud droplet number concentration in Community Atmosphere Model (CAM)‐Oslo

A new framework for calculating cloud droplet number, including a continuity equation for cloud droplet number concentration, has been developed and implemented in an extended version of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model version 2.0.1 (CAM‐2.0.1). The new continuity equation for cloud droplet number concentration consists of a nucleation term and several microphysical sink terms. The nucleation term is calculated on the basis of a parameterization of activation of cloud condensation nuclei (CCN). A subgrid distribution of vertical velocity is used to calculate the range of supersaturations determining the activation within each model grid box. The aerosol types considered in this study are sea salt, sulfate, black carbon, organic carbon, and mineral dust. The horizontal and vertical distributions of sulfate and carbonaceous aerosols are calculated on the basis of AEROCOM (http://nansen.ipsl.jussieu.fr/AEROCOM) sources. Microphysical sink terms for cloud droplets are obtained from a prognostic cloud water scheme, assuming a direct proportionality between loss of cloud water and loss of cloud droplets. On the basis of the framework described above, the cloud droplet number concentration and cloud droplet effective radius are determined. Cloud microphysical and radiative properties compare reasonably well with satellite observations, giving an indication of the soundness of our approach. Our method of fitting the aerosol size distribution with lognormal modes has been evaluated and was found not to introduce systematic errors in our approach. The aerosol indirect effect estimated in the new framework ranges from −0.13 W/m2 to −0.72 W/m2, which is significantly smaller than in most other comparable studies. This is largely due to the introduction of microphysical sinks for cloud droplets and a cloud droplet activation scheme which accounts for the so‐called competition effect among CCN. As we are not allowing aerosol effects on cloud microphysics and radiation to feed back on the model meteorology, our estimates of the aerosol indirect effect do not include changes in relative humidity and cloud cover.