Tendency Terms Research Articles

A new algorithm inspired in the behavior of the social-spider for constrained optimization

During the past decade, solving constrained optimization problems with swarm algorithms has received considerable attention among researchers and practitioners. In this paper, a novel swarm algorithm called the Social Spider Optimization (SSO-C) is proposed for solving constrained optimization tasks. The SSO-C algorithm is based on the simulation of cooperative behavior of social-spiders. In the proposed algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviors that are typically found in the colony. For constraint handling, the proposed algorithm incorporates the combination of two different paradigms in order to direct the search towards feasible regions of the search space. In particular, it has been added: (1) a penalty function which introduces a tendency term into the original objective function to penalize constraint violations in order to solve a constrained problem as an unconstrained one; (2) a feasibility criterion to bias the generation of new individuals toward feasible regions increasing also their probability of getting better solutions. In order to illustrate the proficiency and robustness of the proposed approach, it is compared to other well-known evolutionary methods. Simulation and comparisons based on several well-studied benchmarks functions and real-world engineering problems demonstrate the effectiveness, efficiency and stability of the proposed method.

On the Use of Potential Vorticity Tendency Equations for Diagnosing Atmospheric Dynamics in Numerical Models

Abstract This study critically assesses potential vorticity (PV) tendency equations used for analyzing atmospheric convective systems. A generic PV tendency format is presented to provide a framework for comparing PV tendency equations, which isolates the contributions to PV tendency from wind and mass field changes. These changes are separated into forcing terms (e.g., diabatic or friction) and flow adjustment and evolution terms (i.e., adiabatic motions). One PV tendency formulation analyzed separates PV tendency into terms representing PV advection and diabatic and frictional PV sources. In this form the PV advection is shown to exhibit large cancellation with the diabatic forcing term when used to analyze deep convective systems, which compromises the dynamical insight that the PV tendency analysis should provide. The isentropic PV substance tendency formulation of Haynes and McIntyre does not suffer from this cancellation problem. However, while the Haynes and McIntyre formulation may be appropriate for many convective system applications, there are likely to be some applications in which the formulation is difficult to apply or is not ideal. This study introduces a family of PV tendency equations in geometric coordinates that is free from the deficiencies of the above formulations. Simpler forms are complemented by more complex forms that expand the vorticity tendency term to offer additional insight into flow dynamics. The more complex forms provide insight similar to the influential Haynes and McIntyre isentropic formulation.

Impact of a Vertical Vorticity Constraint in Variational Dual-Doppler Wind Analysis: Tests with Real and Simulated Supercell Data

Abstract One of the greatest challenges to dual-Doppler retrieval of the vertical wind is the lack of low-level divergence information available to the mass conservation constraint. This study examines the impact of a vertical vorticity equation constraint on vertical velocity retrievals when radar observations are lacking near the ground. The analysis proceeds in a three-dimensional variational data assimilation (3DVAR) framework with the anelastic form of the vertical vorticity equation imposed along with traditional data, mass conservation, and smoothness constraints. The technique is tested using emulated radial wind observations of a supercell storm simulated by the Advanced Regional Prediction System (ARPS), as well as real dual-Doppler observations of a supercell storm that occurred in Oklahoma on 8 May 2003. Special attention is given to procedures to evaluate the vorticity tendency term, including spatially variable advection correction and estimation of the intrinsic evolution. Volume scan times ranging from 5 min, typical of operational radar networks, down to 30 s, achievable by rapid-scan mobile radars, are considered. The vorticity constraint substantially improves the vertical velocity retrievals in our experiments, particularly for volume scan times smaller than 2 min.

Intraseasonal moist static energy budget in reanalysis data

[1] The vertically integrated moist static energy (MSE) budget and moisture budgets of the Madden-Julian oscillation (MJO) are studied using 16 years of National Centers for Environmental Prediction Reanalysis II data and European Centre for Medium Range Weather Forecasts interim reanalysis data. Longitudinal distributions of vertically integrated MSE and latent heat (Lq) anomalies as well as their advective tendency terms are studied as a function of MJO phase. They are shown to have similar patterns and magnitudes, indicating that variations in MSE are mainly governed by moisture on intraseasonal time scales. MSE anomalies are approximately in phase with precipitation. Reanalysis MSE budget results are compared with the general circulation model results of Maloney (2009) (hereinafter M09). Many aspects of the reanalysis MSE budget resemble those of M09, with strong contributions from horizontal advection in increasing (decreasing) column MSE before (after) peak MJO convection. Other terms in the vertically integrated MSE budget, including vertical advection, are relatively larger in the reanalysis compared to M09 model results. Vertical advection contributes as much or more than horizontal advection to MSE buildup in advance of MJO convection in the reanalysis data sets. A large budget residual also exists which appears to suggest a missing moistening source in advance of MJO convection that provides a caveat to the results derived here. A positive covariance between radiative and surface fluxes and precipitation anomalies indicates that these flux terms slow the discharge of column MSE during an MJO event and may help to destabilize the MJO. As in the work of M09, variability in synoptic eddy activity as a function of the MJO phase dominates the meridional advection term. Suppression of synoptic eddies appears to contribute to anomalous moistening of the atmospheric column in advance of MJO convection.

Influence of Gravity Waves in the Tropical Upwelling: WACCM Simulations

Abstract The annual cycle of tropical upwelling and contributions by planetary and gravity waves are investigated from climatological simulations using the Whole Atmosphere Community Climate Model (WACCM) including three gravity wave drag (GWD) parameterizations (orographic, nonstationary background, and convective GWD parameterizations). The tropical upwelling is estimated by the residual mean vertical velocity at 100 hPa averaged over 15°S–15°N. This is well matched with an upwelling estimate from the balance of the zonal momentum and the mass continuity. A clear annual cycle of the tropical upwelling is found, with a Northern Hemispheric (NH) wintertime maximum and NH summertime minimum determined primarily by the Eliassen–Palm flux divergence (EPD), along with a secondary contribution from the zonal wind tendency. Gravity waves increase tropical upwelling throughout the year, and of the three sources the contribution by convective gravity wave drag (CGWD) is largest in most months. The relative contribution by all three GWDs to tropical upwelling is not larger than 5%. However, when tropical upwelling is estimated by net upward mass flux between turnaround latitudes where upwelling changes downwelling, annual mean contribution by all three GWDs is up to 19% at 70 hPa by orographic and convective gravity waves with comparable magnitudes. Effects of CGWD on upwelling are investigated by conducting an additional WACCM simulation without CGWD parameterization. It was found that including CGWD parameterization increases tropical upwelling not only directly by adding CGWD forcing, but also indirectly by modulating EPD and zonal wind tendency terms in the tropics.

An alternate and robust approach to calibration for the estimation of land surface model parameters based on remotely sensed observations

[1] Atmospheric models include land surface parameterizations of heat and moisture fluxes. Most parameterizations derive from early models of layered soil and vegetation canopy that account for liquid, vapor and heat diffusion, radiation processes, and surface turbulence. The number of parameters in these models ranges roughly from 10 to 50. Some parameters are known to vary over a small range and/or not significantly impact predictions. Others are highly influential (e.g., Leaf Area Index), but are currently well estimated from satellite data. Many parameters, however, are highly influential, vary over a large dynamic range, cannot be estimated from satellite data, and cannot be readily upscaled from in-situ measurements. For such parameters (e.g., maximum stomatal conductance and soil hydraulic conductivity), values are assigned based on look-up tables sorted by land cover and soil texture. Here we present a method for estimating these parameters by minimizing a measure of nonstationarity of model-predicted moisture state variable tendencies. This method has advantages over calibration: 1) it does not require flux data (e.g., evapotranspiration); and 2) the tendency terms are evaluated at the model grid and thus yield parameters that are effective for that scale. The method is demonstrated with the Noah Land Surface Model, using remotely-sensed soil moisture, at a site in California. Preliminary results indicate that the method is robust and performs better than both: 1) calibration to soil moisture observations, which can lead to large, compensating errors in drainage and evaporation; and 2) minimizing the sum of squares of innovations of soil moisture updates.

Joint time–frequency sparse estimation of large-scale network traffic

When 3G, WiFi, and WiMax technologies are successfully applied to access networks, current communication networks become more and more complex, more and more heterogeneous, and more difficult to manage. Moreover, network traffic exhibits the increasing diversities and concurrently shows many new characteristics. The real-time end-to-end demand urges network operators to learn and grasp traffic matrix covering their networks. However, unfortunately traffic matrix is significantly difficult directly to attain. Despite many studies made previously about traffic matrix estimation problem, it is a significant challenging to obtain its reliable and accurate solution. Here we propose a novel approach to solve this problem, based on joint time–frequency analysis in transform domain. Different from previous methods, we analyze the time–frequency characteristics about traffic matrix and build the time–frequency model describing it. Generally, traffic matrix can be divided into tendency terms and fluctuation terms. We find that traffic matrix in time–frequency domain owns the more obvious sparsity than in time domain. Obviously, its tendency terms and fluctuation terms also have the lower dimensions in time–frequency domain. This brings us into the field of compressive sensing that is a generic technique for data reconstruction. Additionally, we take into account updating time–frequency model presented with link loads to make our model adaptive. Finally, comparative analysis in two real backbone networks confirms that the accuracy, stability, and effectiveness of our approach.

Parameter estimation of coupled water and energy balance models based on stationary constraints of surface states

We use a conditional averaging approach to estimate the parameters of a land surface water and energy balance model and then use the estimated parameters to partition net radiation into latent, sensible, and ground heat fluxes and precipitation into evapotranspiration and drainage plus runoff. Through conditional averaging of the modeled fluxes with respect to soil moisture and temperature, we write an objective function that approximates the temperature‐ and moisture‐dependent errors of the modeled fluxes in terms of atmospheric forcing (e.g., precipitation and radiation), surface states (moisture (S) and temperature (Ts)), and model parameters. The novelty of the approach is that the error term is estimated without comparison to measured fluxes. Instead, it is inferred from the deviation of the conditionally averaged tendency terms (expectation and expectation ) from zero since each of these terms equals zero in stationary systems but diverges from zero in the presence of misspecified parameters. Minimization of the approximated error yields parameters for model applications. This strategy was previously studied for simple water balance models using soil moisture conditional averaging. Here we extend the idea to include energy balance fluxes and surface temperature conditioning. The method is tested at two AmeriFlux sites, Vaira Ranch (California) and Kendall Grassland (Arizona). The estimated fluxes (using only observed forcing and state variables) are in reasonable agreement with field measurements. Because this method is based on conditional averages, it can be applied to situations with subsampled or missing data; that is, continuous integration in time is not required.

Analysis of prognostic cloud scheme increments in a climate model

AbstractAn analysis of a cloud scheme is presented, which can aid the development of climate and weather forecasting models. Budget tendency terms, or cloud increment diagnostics, are analysed to show the relative importance of the various physical processes in creating the cloud fields simulated by a climate model. When looking at time‐averaged diagnostics, the use of mean positive and mean negative increments separately, as well as mean net increments, is shown to be informative in understanding how the model is behaving. Maps of vertically integrated tendency terms illustrate how the dominant cloud production terms vary geographically. A cross‐section through the Hadley Circulation shows how the tendency terms vary across a transition region as the clouds change from stratocumulus to shallow cumulus and then to cumulonimbus. Although there are no observations against which these increment diagnostics can be compared, identification of the key cloud formation and dissipation processes highlights the parts of the cloud scheme where further work should be focussed in order to improve the climatological cloud fields. Simulations with changes to a part of the cloud parametrization are analysed using the increment diagnostics and the change in the relative importance of the different processes highlights some of the feedbacks present in the model. While our detailed findings are model specific, the analysis technique could be used in the development of any weather forecasting or climate model. © Crown Copyright 2010. Published by John Wiley & Sons, Ltd.

Trends in the North Atlantic carbon sink: 1992–2006

A biogeochemical general circulation model is used to assess the impact of climate variability from 1992 to 2006 on air‐sea CO2 fluxes and ocean surface pCO2 in the North Atlantic and to understand trends in the North Atlantic carbon sink over this time period. The model indicates that the North Atlantic carbon sink increased from the mid‐1990s to the mid‐2000s. Consistent with observations, the model output indicates large changes in the physical and chemical systems of the basin. An analysis of the changes in dissolved inorganic carbon (DIC), alkalinity (ALK), and sea‐surface temperature (SST), combined with model‐derived DIC tendency terms, allow for an investigation of the mechanisms that dominate the spatial variability and magnitude of the trends in the air‐sea fluxes and pCO2. Modeled parameters compare favorably with available data from the Bermuda Atlantic Time Series in the subtropical gyre and the SURATLANT volunteer observation ship data in the subpolar gyre. Subtropical changes are controlled primarily by changes in sea‐surface temperature. Subpolar changes in pCO2 are instead driven dynamically, primarily through changing vertical supply of DIC. The amplitude of the ocean pCO2 and air‐sea flux trends are largely related to the increase in atmospheric CO2, but changes to the forcing and circulation of the North Atlantic during this period set the spatial patterns. Model changes are consistent with variation in the North Atlantic Oscillation over the period of study.

Indian Ocean sea surface salinity variations in a coupled model

The variability of the sea surface salinity (SSS) in the Indian Ocean is studied using a 100-year control simulation of the Community Climate System Model (CCSM 2.0). The monsoon-driven seasonal SSS pattern in the Indian Ocean, marked by low salinity in the east and high salinity in the west, is captured by the model. The model overestimates runoff into the Bay of Bengal due to higher rainfall over the Himalayan–Tibetan regions which drain into the Bay of Bengal through Ganga–Brahmaputra rivers. The outflow of low-salinity water from the Bay of Bengal is too strong in the model. Consequently, the model Indian Ocean SSS is about 1 less than that seen in the climatology. The seasonal Indian Ocean salt balance obtained from the model is consistent with the analysis from climatological data sets. During summer, the large freshwater input into the Bay of Bengal and its redistribution decide the spatial pattern of salinity tendency. During winter, horizontal advection is the dominant contributor to the tendency term. The interannual variability of the SSS in the Indian Ocean is about five times larger than that in coupled model simulations of the North Atlantic Ocean. Regions of large interannual standard deviations are located near river mouths in the Bay of Bengal and in the eastern equatorial Indian Ocean. Both freshwater input into the ocean and advection of this anomalous flux are responsible for the generation of these anomalies. The model simulates 20 significant Indian Ocean Dipole (IOD) events and during IOD years large salinity anomalies appear in the equatorial Indian Ocean. The anomalies exist as two zonal bands: negative salinity anomalies to the north of the equator and positive to the south. The SSS anomalies for the years in which IOD is not present and for ENSO years are much weaker than during IOD years. Significant interannual SSS anomalies appear in the Indian Ocean only during IOD years.

A New Metric for Estimating the Influence of Evaporation on Seasonal Precipitation Rates

Abstract The objective of this paper is to introduce a diagnostic metric—termed the local-convergence ratio—that can be used to quantify the contribution of evaporation (and transpiration) to the atmospheric hydrologic cycle, and precipitation in particular, over a given region. Previous research into regional moisture (or precipitation) recycling has produced numerous methods for estimating the contributions of “local” (i.e., evaporated) moisture to climatological precipitation and its variations. In general, these metrics quantify the evaporative contribution to the mass of precipitable water within an atmospheric column by comparing the vertically integrated atmospheric fluxes of moisture across a region with the fluxes via evaporation. Here a new metric is proposed, based on the atmospheric moisture tendency equation, which quantifies the evaporative contribution to the rate of precipitation by comparing evaporative convergence into the column with large-scale moisture-flux convergence. Using self-consistent, model-derived estimates of the moisture-flux fields and the atmospheric moisture tendency terms, the authors compare estimates of the flux-based moisture-recycling ratio with the newly introduced local-convergence ratio. Differences between the two ratios indicate that they can be considered complementary, but independent, descriptors of the atmospheric hydroclimatology for a given region.

Diagnosing Summertime Mesoscale Vertical Motion: Implications for Atmospheric Data Assimilation

Abstract Balance omega equations have recently been used to try to improve the characterization of balance in variational data assimilation schemes for numerical weather prediction (NWP). Results from Fisher and Fillion et al. indicate that a quasigeostrophic omega equation can be used adequately in the definition of the control variable to represent synoptic-scale balanced vertical motion. For high-resolution limited-area data assimilation and forecasting (1–10-km horizontal resolution), such a diagnostic equation for vertical motion needs to be revisited. Using a state-of-the-art NWP forecast model at 2.5-km horizontal resolution, these issues are examined. Starting from a complete diagnostic partial differential equation for omega, the rhs forcing terms were computed from model-generated fields. These include the streamfunction, temperature, and physical time tendencies of temperature in gridpoint space. To accurately compute one term of second-order importance (i.e., the ageostrophic vorticity tendency forcing term), a special procedure was used. With this procedure it is shown that Charney’s balance equation brings significant information in order to deduce the geostrophic time tendency term. Under these conditions, results show that for phenomena of length scales of 15–100 km over convective regions, a diagnostic equation can capture the major part of the model-generated vertical motion. The limitations of the digital filter initialization approach when used as in Fillion et al. with a cutoff period reduced to 1 h are also illustrated. The potential usefulness of this study for mesoscale atmospheric data assimilation is briefly discussed.

Dual-Doppler Analysis of Winds and Vorticity Budget Terms near a Tornado

Abstract Three-dimensional dual-Doppler observations with unprecedented finescale spatial and temporal resolution are used to characterize the vector wind field and vorticity generation terms in and near a weak, short-lived tornado. The beam widths of the two Doppler on Wheels (DOW) mobile radars, at the range of the tornado, are 250 m with gate lengths of 75 m, resulting in a resolution of less than 107 m3. One of the DOWs collected data during the 240 s prior to the formation of the tornado, enabling examination of the genesis process. A single set of volumetric scans suitable for dual-Doppler analyses were completed by both DOWs, permitting the calculation of vertical and horizontal vorticity, divergence, and stretching and tilting terms in the vorticity budget of the large but weak tornado and its surroundings, but no local tendency terms. Analyses of the dual-Doppler vector wind fields document, for the first time in a supercellular tornado, revealed several structures expected to be associated with tornadoes, including the tilting of horizontal vorticity into the vertical near the tornado, and stretching of vertical vorticity in the region of the tornado. The analyses are compared to conceptual and computer models of tornadic storms, confirming the existence of various phenomena and processes, although some model predictions, particularly those concerning the distribution of horizontal vorticity, could not be verified through these analyses. The observed magnitudes of stretching of vertical vorticity and tilting of horizontal vorticity are consistent with those necessary for generating the observed vorticity near the tornado.

The Diurnal Cycle of Water and Energy over the Continental United States from Three Reanalyses

The Continental United States summertime diurnal surface and column-integrated atmospheric water and energy components are compared among three reanalyses. The strengtJh of the diurnal solar forcing leads to consistent phases among surface energy components across the continent and all reanalyses, but the amplitudes vary widely. This forcing has a particularly strong and direct impact on the surface energy cycle, but interacts with many aspects of the surface and column-integrated water and energy cycles through dynamical convergence, leading to large diurnal fluctuations in the atmospheric reservoir of water vapor and total dry energy. Although they are negligible on timescales greater than a year, the tendency terms of the water and energy budgets at the surface and in the atmosphere are important on the diurnal scale. The North American Regional Reanalysis (NARR) displays a diurnal circulation pattern centered over Northern Texas that links together regional patterns in the diurnal cycles of assimilated precipitation. Constructed vapor flux convergences from the National Centers for Environmental Prediction/Department of Energy (NCEP/DOE) Reanalysis-2 Global Spectral Model and the Experimental Climate Prediction Center’s reanalysis using an updated Seasonal Forecast Model reproduce many of the observed regional circulation and convergence patterns, but fail to generate the appropriate diurnal precipitation, presumably due to inadequate convective parameterizations. Diurnal variations in atmospheric energy respond not only to the direct solar forcing, but also to the resulting dynamically-forcedsemidiurnal thermal tide.

Determination of 3D Cloud Ice Water Contents by Combining Multiple Data Sources from Satellite, Ground Radar, and a Numerical Model

Abstract This study aims at determining the three-dimensional distribution of ice water content over a broad area near the Atmospheric Radiation Measurement Program Southern Great Plains site, where cloud radar and meteorological observations have been routinely conducted. Together with wind fields from other measurements, the ice water content retrievals can be used to derive the cloud ice water advective tendency terms needed for single-column model simulations. In this study, a Bayesian retrieval algorithm has been developed that combines multiple data sources from satellite high-frequency microwave radiometry, ground cloud radar observations, and mesoscale numerical model analysis. The cloud radar observations allow the characteristics of vertical ice water content structures to be inferred. The numerical model data are used to locate the cloud height. The satellite data provide information on the integrated ice water path, its horizontal distribution over a broad area, and, to a lesser extent, the vertical structure of ice water content. The approach herein is to retrieve the three-dimensional cloud ice water content in a 10° × 10° area surrounding the cloud radar site by combining all the information contained in the above datasets through a Bayesian framework. Validation of the algorithm has been done by comparing the retrievals with measurements from two ground radars. The comparison shows that the mean ice water content profiles and the two-dimensional (height–ice water content) probability density functions retrieved for 19 coincident cases agree fairly well with the validation data. However, the retrieved ice water contents generally lack detailed vertical structures because of the low sensitivity of satellite data to the vertical variation of cloud ice.

Nonlinear shallow-water solutions using the weak temperature gradient approximation

A form of the weak temperature gradient (WTG) approximation, in which the temperature tendency and advection terms are neglected in the temperature equation so that the equation reduces to a diagnostic balance between heating and vertical motion, is applied to a two-dimensional nonlinear shallow-water model with the heating (mass source) parameterized as a Newtonian relaxation on the temperature (layer thickness) towards a prescribed function of latitude and longitude, containing an isolated maximum or minimum, as in the classic linear Gill problem. In this model, temperature variations are retained in the Newtonian heating term, so that it is not a pure WTG system. It contains no free unbalanced modes, but reduces to the Gill model in the steady linear limit, so that steady solutions may be thought of as containing components corresponding to unbalanced modes in the same sense as the latter. The equations are solved numerically and are compared with full shallow-water solutions in which the WTG approximation is not made. Several external parameters are varied, including the strength, location, sign, and horizontal scale of the mass source, the Rayleigh friction coefficient, and the time scale for the relaxation on the mass field. Indices of the Walker and Hadley circulations are examined as functions of these external parameters. Differences between the WTG solutions and those from the full shallow-water system are small over most of the parameter regime studied, which includes time-dependent as well as steady solutions.

Vertically integrated sensible‐heat budgets for stable nocturnal boundary layers

AbstractThe stable nocturnal boundary layer is commonly viewed or modelled as a balance between the temperature tendency (cooling) and vertical heat‐flux divergence. Sometimes the radiative‐flux divergence is also included. This perspective has dictated the design of field experiments for investigating stable nocturnal boundary layers.Tower‐based micrometeorological data from three field campaigns are analysed to evaluate the vertically integrated sensible‐heat budget for nocturnal stable conditions. Our analysis indicates frequent occurrence of large imbalance between the temperature tendency and vertical heat‐flux divergence terms. The values of the radiative‐flux divergence are generally too small and sometimes of the wrong sign to explain the residual. An analysis of random flux errors and uncertainties in the tendency term indicate that such errors cannot explain large imbalances, suggesting the importance of advection of temperature or possibly the divergence of mesoscale fluxes. The implied role of advection is consistent with circumstantial evidence. Even weak surface heterogeneity can create significant horizontal gradients in stable boundary layers. However, it is shown that existing field data and observational strategy do not allow adequate evaluation of advection and mesoscale flux divergence terms. Copyright © 2006 Royal Meteorological Society

An improved method for doppler wind and thermodynamic retrievals

A variational method is developed to retrieve winds in the first step and then thermodynamic fields in the second step from Doppler radar observations. In the first step, wind fields are retrieved at two time levels: the beginning and ending times of the data assimilation period, simultaneously from two successive volume scans by using the weak form constraints provided by the mass continuity and vorticity equations. As the retrieved wind fields are expressed by Legendre polynomial expansions at the beginning and ending times, the time tendency term in the vorticity equation can be conveniently formulated, and the retrieved winds can be compared with the radar observed radial winds in the cost function at the precise time and position of each radar beam. In the second step, the perturbation pressure and temperature fields at the middle time are then derived from the retrieved wind fields and the velocity time tendency by using the weak form constraints provided by the three momentum equations. The merits of the new method are demonstrated by numerical experiments with simulated radar observations and compared with the traditional least squares methods which consider neither the precise observation times and positions nor the velocity time tendency. The new method is also applied to real radar data for a heavy rainfall event during the 2001 Meiyu season in China.

Sensitivities of Cumulus-Ensemble Rainfall in a Cloud-Resolving Model with Parameterized Large-Scale Dynamics

Abstract The problem of closure in cumulus parameterization requires an understanding of the sensitivities of convective cloud systems to their large-scale setting. As a step toward such an understanding, this study probes some sensitivities of a simulated ensemble of convective clouds in a two-dimensional cloud-resolving model (CRM). The ensemble is initially in statistical equilibrium with a steady imposed background forcing (cooling and moistening). Large-scale stimuli are imposed as horizontally uniform perturbations nudged into the model fields over 10 min, and the rainfall response of the model clouds is monitored. In order to reduce a major source of artificial insensitivity in the CRM, a simple parameterization scheme is devised to account for heating-induced large-scale (i.e., domain averaged) vertical motions that would develop in nature but are forbidden by the periodic boundary conditions. The effects of this large-scale vertical motion are parameterized as advective tendency terms that are ap...