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NASA NTRS2002

A New Statistically based Autoconversion rate Parameterization for use in Large-Scale Models

The autoconversion rate is a key process for the formation of precipitation in warm clouds. In climate models, physical processes such as autoconversion rate, which are calculated from grid mean values, are biased, because they do not take subgrid variability into account. Recently, statistical cloud schemes have been introduced in large-scale models to account for partially cloud-covered grid boxes. However, these schemes do not include the in-cloud variability in their parameterizations. In this paper, a new statistically based autoconversion rate considering the in-cloud variability is introduced and tested in three cases using the Canadian Single Column Model (SCM) of the global climate model. The results show that the new autoconversion rate improves the model simulation, especially in terms of liquid water path in all three case studies.

Lin, Bing↗

NASA NTRS2011

Global Distribution of Cloud Droplet Number Concentration, Autoconversion Rate, and Aerosol Indirect Effect Under Diabatic Droplet Activation

This study presents a global assessment of the sensitivity of droplet number to diabatic activation (i.e., including effects from entrainment of dry air) and its first-order tendency on indirect forcing and autoconversion. Simulations were carried out with the NASA Global Modeling Initiative (GMI) atmospheric and transport model using climatological metereorological fields derived from the former NASA Data Assimilation Office (DAO), the NASA Finite volume GCM (FVGCM) and the Goddard Institute for Space Studies version II (GISS) GCM. Cloud droplet number concentration (CDNC) is calculated using a physically based prognostic parameterization that explicitly includes entrainment effects on droplet formation. Diabatic activation results in lower CDNC, compared to adiabatic treatment of the process. The largest decrease in CDNC (by up to 75 percent) was found in the tropics and in zones of moderate CCN concentration. This leads to a global mean effective radius increase between 0.2-0.5 micrometers (up to 3.5 micrometers over the tropics), a global mean autoconversion rate increase by a factor of 1.1 to 1.7 (up to a factor of 4 in the tropics), and a 0.2-0.4 W m(exp -2) decrease in indirect forcing. The spatial patterns of entrainment effects on droplet activation tend to reduce biases in effective radius (particularly in the tropics) when compared to satellite retrievals. Considering the diabatic nature of ambient clouds, entrainment effects on CDNC need to be considered in GCM studies of the aerosol indirect effect.

Barahona, Donifan↗

NASA NTRS2006

Model Intercomparison of Indirect Aerosol Effects

Modeled differences in predicted effects are increasingly used to help quantify the uncertainty of these effects. Here, we examine modeled differences in the aerosol indirect effect in a series of experiments that help to quantify how and why model-predicted aerosol indirect forcing varies between models. The experiments start with an experiment in which aerosol concentrations, the parameterization of droplet concentrations and the autoconversion scheme are all specified and end with an experiment that examines the predicted aerosol indirect forcing when only aerosol sources are specified. Although there are large differences in the predicted liquid water path among the models, the predicted aerosol first indirect effect for the first experiment is rather similar, about -0.6 W/sq m to -0.7 W/sq m. Changes to the autoconversion scheme can lead to large changes in the liquid water path of the models and to the response of the liquid water path to changes in aerosols. Adding an autoconversion scheme that depends on the droplet concentration caused a larger (negative) change in net outgoing shortwave radiation compared to the 1st indirect effect, and the increase varied from only 22% to more than a factor of three. The change in net shortwave forcing in the models due to varying the autoconversion scheme depends on the liquid water content of the clouds as well as their predicted droplet concentrations, and both increases and decreases in the net shortwave forcing can occur when autoconversion schemes are changed. The parameterization of cloud fraction within models is not sensitive to the aerosol concentration, and, therefore, the response of the modeled cloud fraction within the present models appears to be smaller than that which would be associated with model "noise". The prediction of aerosol concentrations, given a fixed set of sources, leads to some of the largest differences in the predicted aerosol indirect radiative forcing among the models, with values of cloud forcing ranging from -0.3 W/sq m to -1.4W/sq m. Thus, this aspect of modeling requires significant improvement in order to improve the prediction of aerosol indirect effects.

Penner, J. E.↗

NASA NTRS2004

Warm Rain Processes Over the Tropical Oceans and Implications on Climate Change

In this talk, we will first show results from TRMM regarding the characteristics of warm rains over the tropical oceans, and the dependence of rate of warm rain production on sea surface temperature. Results lead to the hypothesis that warm rain production efficiency, i.e., autoconversion, may be increased in a warm climate. We use the GEOS-II GCM to test this hypothesis. Our modeling results show that in a climate with increased rate of autoconversion, the total rain amount is increased, with warm rain contributing to a larger portion of the increase. The abundant rainout of warm precipitation at middle to low levels causes a reduction of high cloud cover due to the depletion of water available for ice-phase rain production. As a result, more isolated, but more intense penetrative convection develops. Results also show that increased autoconversion reduces the convective adjustment time scale tends, implying a faster recycling of atmospheric water. Most interestingly, the increased low level heating associated with warm rain leads to more energetic Madden and Julian oscillations in the tropics, with well-defined eastward propagation. While reducing the autoconversion leads to an abundant mix of westward and eastward tropical disturbance on daily to weekly time scales. The causes of the sensitivity of the dynamical regimes to the microphysics parameterization in the GCM will be discussed.

Lau, William K. M.↗

NASA NTRS2004

Warm Rain Processes Over the Tropical Oceans and Implications on Climate Change: Results from TRMM and GOES GCM

In this talk, we will first show results from TRMM data regarding the characteristics of warm rains over the tropical oceans, and the dependence of rate of warm rain production on sea surface temperature. Results lead to the hypothesis that warm rain production efficiency, i.e., autoconversion, may be increased in a warm climate. We use the GEOS-II GCM to test this hypothesis. Our modeling results show that in a climate with increased rate of autoconversion, the total rain amount is increased, with warm rain contributing to a larger portion of the increase. The abundant rainout of warm precipitation causes a reduction of low and middle cloud amount due to rainout, and reduced high clouds due to less water vapor available for ice-phase convection. However, clod radiation feedback caused by the increased rainfall efficiency, leads to differential vertical heating/cooling producing a more unstable atmosphere, allowing, more intense, but isolated penetrative convection, with contracted anvils to develop. Results also show that increased autoconversion reduces the convective adjustment time scale, resulting in faster recycling of atmospheric water. Most interestingly, the increased low level heating associated with warm rain leads to more energetic Madden and Julian oscillations in the tropics, with well-defined eastward propagation. While reducing the autoconversion leads to an abundant mix of westward and eastward tropical disturbances on daily to weekly time scales. The crucial link of precipitation microphysical processes to climate change including the effects of aerosols will be discussed.

Lau, William K. M.↗

NASA NTRS2004

Warm Rain Processes over the Tropical Oceans and Implications on Climate Change: Results from TRMM and GEOS GCM

In this talk, we will first show results from TRMM data regarding the characteristics of warm rains over the tropical oceans, and the dependence of rate of warm rain production on sea surface temperature. Results lead to the hypothesis that warm rain production efficiency, i.e., autoconversion, may be increased in a warm climate. We use the GEOS-II GCM to test this hypothesis. Our modeling results show that in a climate with increased rate of autoconversion, the total rain amount is increased, with warm rain contributing to larger portion of the increase. The abundant rainout of warm precipitation causes a reduction of low and middle cloud amount due to rainout, and reduced high clouds due to less water vapor available for ice-phase convection. However, clod radiation feedback caused by the increased rainfall efficiency, leads to differential vertical heating/cooling producing a more unstable atmosphere, allowing, more intense, but isolated penetrative convection, with contracted anvils to develop. Results also show that increased autoconversion reduces the convective adjustment time scale, resulting in faster recycling of atmospheric water. Most interestingly, the increased low level heating associated with warm rain leads to more energetic Madden and Julian oscillations in the tropics, with well-defined eastward propagation. While reducing the autoconversion leads to an abundant mix of westward and eastward tropical disturbances on daily to weekly time scales. The crucial link of precipitation microphysical processes to climate change including the effects of aerosols will be discussed.

Lau, William K. M.↗

NASA NTRS2007

Cloud Condensation Nuclei Prediction Error from Application of Kohler Theory: Importance for the Aerosol Indirect Effect

In situ observations of aerosol and cloud condensation nuclei (CCN) and the GISS GCM Model II' with an online aerosol simulation and explicit aerosol-cloud interactions are used to quantify the uncertainty in radiative forcing and autoconversion rate from application of Kohler theory. Simulations suggest that application of Koehler theory introduces a 10-20% uncertainty in global average indirect forcing and 2-11% uncertainty in autoconversion. Regionally, the uncertainty in indirect forcing ranges between 10-20%, and 5-50% for autoconversion. These results are insensitive to the range of updraft velocity and water vapor uptake coefficient considered. This study suggests that Koehler theory (as implemented in climate models) is not a significant source of uncertainty for aerosol indirect forcing but can be substantial for assessments of aerosol effects on the hydrological cycle in climatically sensitive regions of the globe. This implies that improvements in the representation of GCM subgrid processes and aerosol size distribution will mostly benefit indirect forcing assessments. Predictions of autoconversion, by nature, will be subject to considerable uncertainty; its reduction may require explicit representation of size-resolved aerosol composition and mixing state.

Sotiropoulou, Rafaella-Eleni P.↗

NASA NTRS2004

Effects of Cloud-Microphysics on Tropical Atmospheric Hydrologic Processes in the GEOS GCM

The sensitivity of tropical atmospheric hydrologic processes to cloud-microphysics is investigated using the NASA GEOS GCM. Results show that a faster autoconversion - rate produces more warm rain and less clouds at all levels. Fewer clouds enhances longwave cooling and reduces shortwave heating in the upper troposphere, while more warm rain produces increased condensation heating in the lower troposphere. This vertical heating differential destablizes the tropical atmosphere, producing a positive feedback resulting in more rain over the tropics. The feedback is maintained via a two-cell secondary circulation. The lower cell is capped by horizontal divergence and maximum cloud detrainment near the melting/freezing, with rising motion in the warm rain region connected to descending motion in the cold rain region. The upper cell is found above the freezing/melting level, with longwave-induced subsidence in the warm rain and dry regions, coupled to forced ascent in the deep convection region. The tropical large scale circulation is found to be very sensitive to the radiative-dynamic effects induced by changes in autoconversion rate. Reduced cloud-radiation processes feedback due to a faster autoconversion rate results in intermittent but more energetic eastward propagating Madden and Julian Oscillations (MJO). Conversely,-a slower autconversion rate, with increased cloud radiation produces MJO's with more realistic westward propagating transients, resembling a supercloud cluster structure. Results suggests that warm rain and associated low and mid level clouds, i.e., cumulus congestus, may play a critical role in regulating the time-intervals of deep convections and hence the fundamental time scales of the MJO.

Lau, K. M.↗

NASA NTRS1992

Frequency up-conversion of a high-power microwave pulse propagating in a self-generated plasma

In the study of the propagation of a high-power microwave pulse, one of the main concerns is how to minimize the energy loss of the pulse before reaching the destination. A frequency autoconversion process that can lead to reflectionless propagation of powerful electromagnetic pulses in self-generated plasmas is studied. The theory shows that, under the proper condition, the carrier frequency omega of the pulse shifts upward during the growth of local plasma frequency omega(pe). Thus, the self-generated plasma remains underdense to the pulse. A chamber experiment to demonstrate the frequency autoconversion during the pulse propagation through the self-generated plasma is conducted. The detected frequency shift is compared with the theoretical result calculated by using the measured electron density distribution along the propagation path of the pulse. Good agreement is obtained.

Kuo, S. P.↗

NASA NTRS1990

Observation of frequency up-conversion in the propagation of a high-power microwave pulse in a self-generated plasma

A chamber experiment is conducted to study the propagation of a high-power microwave pulse. The results show that the pulse is experiencing frequency up-shift while ionizing the background air if the initial carrier frequency of the pulse is higher than the electron plasma frequency at the incident boundary. Such a frequency autoconversion process may lead to reflectionless propagation of a high-power microwave pulse through the atmosphere.

Kuo, S. P.↗

NASA NTRS1990

Diabatic forcing and initialization with assimilation of cloud and rain water in a forecast model: Methodology

The focus of this part of the investigation is to find one or more general modeling techniques that will help reduce the time taken by numerical forecast models to initiate or spin-up precipitation processes and enhance storm intensity. If the conventional data base could explain the atmospheric mesoscale flow in detail, then much of our problem would be eliminated. But the data base is primarily synoptic scale, requiring that a solution must be sought either in nonconventional data, in methods to initialize mesoscale circulations, or in ways of retaining between forecasts the model generated mesoscale dynamics and precipitation fields. All three methods are investigated. The initialization and assimilation of explicit cloud and rainwater quantities computed from conservation equations in a mesoscale regional model are examined. The physical processes include condensation, evaporation, autoconversion, accretion, and the removal of rainwater by fallout. The question of how to initialize the explicit liquid water calculations in numerical models and how to retain information about precipitation processes during the 4-D assimilation cycle are important issues that are addressed. The explicit cloud calculations were purposely kept simple so that different initialization techniques can be easily and economically tested. Precipitation spin-up processes associated with three different types of weather phenomena are examined. Our findings show that diabatic initialization, or diabatic initialization in combination with a new diabatic forcing procedure, work effectively to enhance the spin-up of precipitation in a mesoscale numerical weather prediction forecast. Also, the retention of cloud and rain water during the analysis phase of the 4-D data assimilation procedure is shown to be valuable. Without detailed observations, the vertical placement of the diabatic heating remains a critical problem.

Raymond, William H.↗

NASA NTRS1990

Initialization and assimilation of cloud and rainwater in a regional model

The initialization and assimilation of cloud and rainwater quantities in a mesoscale regional model was examined. Forecasts of explicit cloud and rainwater are made using conservation equations. The physical processes include condensation, evaporation, autoconversion, accretion, and the removal of rainwater by fallout. These physical processes, some of which are parameterized, represent source and sink in terms in the conservation equations. The question of how to initialize the explicit liquid water calculations in numerical models and how to retain information about precipitation processes during the 4-D assimilation cycle are important issues that are addressed.

Raymond, William H.↗

NASA NTRS2001

GCM Simulations of the Aerosol Indirect Effect: Sensitivity to Cloud Parameterization and Aerosol Burden

We describe the coupling of the Goddard Institute for Space Studies (GISS) general circulation model (GCM) to an online sulfur chemistry model and source models for organic matter and sea-salt that is used to estimate the aerosol indirect effect. The cloud droplet number concentration is diagnosed empirically from field experiment datasets over land and ocean that observe droplet number and all three aerosol types simultaneously; corrections are made for implied variations in cloud turbulence levels. The resulting cloud droplet number is used to calculate variations in droplet effective radius, which in turn allows us to predict aerosol effects on cloud optical thickness and microphysical process rates. We calculate the aerosol indirect effect by differencing the top-of-the-atmosphere net cloud radiative forcing for simulations with present-day vs. pre-industrial emissions. Both the first (radiative) and second (microphysical) indirect effects are explored. We test the sensitivity of our results to cloud parameterization assumptions that control the vertical distribution of cloud occurrence, the autoconversion rate, and the aerosol scavenging rate, each of which feeds back significantly on the model aerosol burden. The global mean aerosol indirect effect for all three aerosol types ranges from -1.55 to -4.36 W/sq m in our simulations. The results are quite sensitive to the pre-industrial background aerosol burden, with low pre-industrial burdens giving strong indirect effects, and to a lesser extent to the anthropogenic aerosol burden, with large burdens giving somewhat larger indirect effects. Because of this dependence on the background aerosol, model diagnostics such as albedo-particle size correlations and column cloud susceptibility, for which satellite validation products are available, are not good predictors of the resulting indirect effect.

Menon, Surabi↗

NASA NTRS2001

GCM Simulations of the Aerosol Indirect Effect: Sensitivity to Cloud Parameterization and Aerosol Burden

We describe the coupling of the Goddard Institute for Space Studies (GISS) general circulation model (GCM) to an online sulfur chemistry model and source models for organic matter and sea-salt that is used to estimate the aerosol indirect effect. The cloud droplet number concentration is diagnosed empirically from field experiment datasets over land and ocean that observe droplet number and all three aerosol types simultaneously; corrections are made for implied variations in cloud turbulence levels. The resulting cloud droplet number is used to calculate variations in droplet effective radius, which in turn allows us to predict aerosol effects on cloud optical thickness and microphysical process rates. We calculate the aerosol indirect effect by differencing the top-of-the-atmosphere net cloud radiative forcing for simulations with present-day vs. pre-industrial emissions. Both the first (radiative) and second (microphysical) indirect effects are explored. We test the sensitivity of our results to cloud parameterization assumptions that control the vertical distribution of cloud occurrence, the autoconversion rate, and the aerosol scavenging rate, each of which feeds back significantly on the model aerosol burden. The global mean aerosol indirect effect for all three aerosol types ranges from -1.55 to -4.36 W m(exp -2) in our simulations. The results are quite sensitive to the pre-industrial background aerosol burden, with low pre-industrial burdens giving strong indirect effects, and to a lesser extent to the anthropogenic aerosol burden, with large burdens giving somewhat larger indirect effects. Because of this dependence on the background aerosol, model diagnostics such as albedo-particle size correlations and column cloud susceptibility, for which satellite validation products are available, are not good predictors of the resulting indirect effect.

Menon, Surabi↗

NASA NTRS2011

Physical Validation of GPM Retrieval Algorithms Over Land: An Overview of the Mid-Latitude Continental Convective Clouds Experiment (MC3E)

The joint NASA Global Precipitation Measurement (GPM) -- DOE Atmospheric Radiation Measurement (ARM) Midlatitude Continental Convective Clouds Experiment (MC3E) was conducted from April 22-June 6, 2011, centered on the DOE-ARM Southern Great Plains Central Facility site in northern Oklahoma. GPM field campaign objectives focused on the collection of airborne and ground-based measurements of warm-season continental precipitation processes to support refinement of GPM retrieval algorithm physics over land, and to improve the fidelity of coupled cloud resolving and land-surface satellite simulator models. DOE ARM objectives were synergistically focused on relating observations of cloud microphysics and the surrounding environment to feedbacks on convective system dynamics, an effort driven by the need to better represent those interactions in numerical modeling frameworks. More specific topics addressed by MC3E include ice processes and ice characteristics as coupled to precipitation at the surface and radiometer signals measured in space, the correlation properties of rainfall and drop size distributions and impacts on dual-frequency radar retrieval algorithms, the transition of cloud water to rain water (e.g., autoconversion processes) and the vertical distribution of cloud water in precipitating clouds, and vertical draft structure statistics in cumulus convection. The MC3E observational strategy relied on NASA ER-2 high-altitude airborne multi-frequency radar (HIWRAP Ka-Ku band) and radiometer (AMPR, CoSMIR; 10-183 GHz) sampling (a GPM "proxy") over an atmospheric column being simultaneously profiled in situ by the University of North Dakota Citation microphysics aircraft, an array of ground-based multi-frequency scanning polarimetric radars (DOE Ka-W, X and C-band; NASA D3R Ka-Ku and NPOL S-bands) and wind-profilers (S/UHF bands), supported by a dense network of over 20 disdrometers and rain gauges, all nested in the coverage of a six-station mesoscale rawinsonde network. As an exploratory effort to examine land-surface emissivity impacts on retrieval algorithms, and to demonstrate airborne soil moisture retrieval capabilities, the University of Tennessee Space Institute Piper aircraft carrying the MAPIR L-band radiometer was also flown during the latter half of the experiment in coordination with the ER-2. The observational strategy provided a means to sample the atmospheric column in a redundant framework that enables inter-calibration and constraint of measured and retrieved precipitation characteristics such as particle size distributions, or water contents- all within the umbrella of "proxy" satellite measurements (i.e., the ER-2). Complimenting the precipitation sampling framework, frequent and coincident launches of atmospheric soundings (e.g., 4-8/day) then provided a much larger mesoscale view of the thermodynamic and winds environment, a data set useful for initializing cloud models. The datasets collected represent a variety cloud and precipitation types including isolated cumulus clouds, severe thunderstorms, mesoscale convective systems, and widespread regions of light to moderate stratiform precipitation. We will present the MC3E experiment design, an overview of operations, and a summary of preliminary results.

Petersen, Walter A.↗

NASA NTRS2014

Modeling the Influences of Aerosols on Pre-Monsoon Circulation and Rainfall over Southeast Asia

We conduct several sets of simulations with a version of NASA's Goddard Earth Observing System, version 5, (GEOS-5) Atmospheric Global Climate Model (AGCM) equipped with a two-moment cloud microphysical scheme to understand the role of biomass burning aerosol (BBA) emissions in Southeast Asia (SEA) in the pre-monsoon period of February-May. Our experiments are designed so that both direct and indirect aerosol effects can be evaluated. For climatologically prescribed monthly sea surface temperatures, we conduct sets of model integrations with and without biomass burning emissions in the area of peak burning activity, and with direct aerosol radiative effects either active or inactive. Taking appropriate differences between AGCM experiment sets, we find that BBA affects liquid clouds in statistically significantly ways, increasing cloud droplet number concentrations, decreasing droplet effective radii (i.e., a classic aerosol indirect effect), and locally suppressing precipitation due to a deceleration of the autoconversion process, with the latter effect apparently also leading to cloud condensate increases. Geographical re-arrangements of precipitation patterns, with precipitation increases downwind of aerosol sources are also seen, most likely because of advection of weakly precipitating cloud fields. Somewhat unexpectedly, the change in cloud radiative effect (cloud forcing) at surface is in the direction of lesser cooling because of decreases in cloud fraction. Overall, however, because of direct radiative effect contributions, aerosols exert a net negative forcing at both the top of the atmosphere and, perhaps most importantly, the surface, where decreased evaporation triggers feedbacks that further reduce precipitation. Invoking the approximation that direct and indirect aerosol effects are additive, we estimate that the overall precipitation reduction is about 40% due to the direct effects of absorbing aerosols, which stabilize the atmosphere and reduce surface latent heat fluxes via cooler land surface temperatures. Further refinements of our two-moment cloud microphysics scheme are needed for a more complete examination of the role of aerosol-convection interactions in the seasonal development of the SEA monsoon.

SE Asia Monsoon↗

NASA NTRS2013

Development of Two-Moment Cloud Microphysics for Liquid and Ice Within the NASA Goddard Earth Observing System Model (GEOS-5)

This work presents the development of a two-moment cloud microphysics scheme within the version 5 of the NASA Goddard Earth Observing System (GEOS-5). The scheme includes the implementation of a comprehensive stratiform microphysics module, a new cloud coverage scheme that allows ice supersaturation and a new microphysics module embedded within the moist convection parameterization of GEOS-5. Comprehensive physically-based descriptions of ice nucleation, including homogeneous and heterogeneous freezing, and liquid droplet activation are implemented to describe the formation of cloud particles in stratiform clouds and convective cumulus. The effect of preexisting ice crystals on the formation of cirrus clouds is also accounted for. A new parameterization of the subgrid scale vertical velocity distribution accounting for turbulence and gravity wave motion is developed. The implementation of the new microphysics significantly improves the representation of liquid water and ice in GEOS-5. Evaluation of the model shows agreement of the simulated droplet and ice crystal effective and volumetric radius with satellite retrievals and in situ observations. The simulated global distribution of supersaturation is also in agreement with observations. It was found that when using the new microphysics the fraction of condensate that remains as liquid follows a sigmoidal increase with temperature which differs from the linear increase assumed in most models and is in better agreement with available observations. The performance of the new microphysics in reproducing the observed total cloud fraction, longwave and shortwave cloud forcing, and total precipitation is similar to the operational version of GEOS-5 and in agreement with satellite retrievals. However the new microphysics tends to underestimate the coverage of persistent low level stratocumulus. Sensitivity studies showed that the simulated cloud properties are robust to moderate variation in cloud microphysical parameters. However significant sensitivity in ice cloud properties was found to variation in the dispersion of the ice crystal size distribution and the critical size for ice autoconversion. The implementation of the new microphysics leads to a more realistic representation of cloud processes in GEOS-5 and allows the linkage of cloud properties to aerosol emissions.

Aerosol-Cloud Interactions↗

NASA NTRS2015

A Linearized Prognostic Cloud Scheme in NASAs Goddard Earth Observing System Data Assimilation Tools

A linearized prognostic cloud scheme has been developed to accompany the linearized convection scheme recently implemented in NASA's Goddard Earth Observing System data assimilation tools. The linearization, developed from the nonlinear cloud scheme, treats cloud variables prognostically so they are subject to linearized advection, diffusion, generation, and evaporation. Four linearized cloud variables are modeled, the ice and water phases of clouds generated by large-scale condensation and, separately, by detraining convection. For each species the scheme models their sources, sublimation, evaporation, and autoconversion. Large-scale, anvil and convective species of precipitation are modeled and evaporated. The cloud scheme exhibits linearity and realistic perturbation growth, except around the generation of clouds through large-scale condensation. Discontinuities and steep gradients are widely used here and severe problems occur in the calculation of cloud fraction. For data assimilation applications this poor behavior is controlled by replacing this part of the scheme with a perturbation model. For observation impacts, where efficiency is less of a concern, a filtering is developed that examines the Jacobian. The replacement scheme is only invoked if Jacobian elements or eigenvalues violate a series of tuned constants. The linearized prognostic cloud scheme is tested by comparing the linear and nonlinear perturbation trajectories for 6-, 12-, and 24-h forecast times. The tangent linear model performs well and perturbations of clouds are well captured for the lead times of interest.

Precipitation↗