A New Double-Moment Microphysics Parameterization for Application in Cloud and Climate Models. Part I: Description

2005 ◽  
Vol 62 (6) ◽  
pp. 1665-1677 ◽  
Author(s):  
H. Morrison ◽  
J. A. Curry ◽  
V. I. Khvorostyanov
Keyword(s):  
High Resolution ◽  
Vertical Velocity ◽  
Large Scale ◽  
Climate Models ◽  
The Other ◽  
Microphysics Scheme ◽  
Cloud Models ◽  
Droplet Nucleation ◽  
Double Moment ◽  
Droplet Activation

Abstract A new double-moment bulk microphysics scheme predicting the number concentrations and mixing ratios of four hydrometeor species (droplets, cloud ice, rain, snow) is described. New physically based parameterizations are developed for simulating homogeneous and heterogeneous ice nucleation, droplet activation, and the spectral index (width) of the droplet size spectra. Two versions of the scheme are described: one for application in high-resolution cloud models and the other for simulating grid-scale cloudiness in larger-scale models. The versions differ in their treatment of the supersaturation field and droplet nucleation. For the high-resolution approach, droplet nucleation is calculated from Kohler theory applied to a distribution of aerosol that activates at a given supersaturation. The resolved supersaturation field and condensation/deposition rates are predicted using a semianalytic approximation to the three-phase (vapor, ice, liquid) supersaturation equation. For the large-scale version of the scheme, it is assumed that the supersaturation field is not resolved and thus droplet activation is parameterized as a function of the vertical velocity and diabatic cooling rate. The vertical velocity includes a subgrid component that is parameterized in terms of the eddy diffusivity and mixing length. Droplet condensation is calculated using a quasi-steady, saturation adjustment approach. Evaporation/deposition onto the other water species is given by nonsteady vapor diffusion allowing excess vapor density relative to ice saturation.

scholarly journals The Response of the Northwest Atlantic Ocean to Climate Change

2020 ◽  
Vol 33 (2) ◽  
pp. 405-428 ◽  
Author(s):  
Michael A. Alexander ◽  
Sang-ik Shin ◽  
James D. Scott ◽  
Enrique Curchitser ◽  
Charles Stock
Keyword(s):  
Climate Change ◽  
High Resolution ◽  
Atlantic Ocean ◽  
Gulf Stream ◽  
Large Scale ◽  
Climate Models ◽  
Gulf Of Maine ◽  
Global Climate Models ◽  
The Other ◽  
Surface Salinity

AbstractROMS, a high-resolution regional ocean model, was used to study how climate change may affect the northwestern Atlantic Ocean. A control (CTRL) simulation was conducted for the recent past (1976–2005), and simulations with additional forcing at the surface and lateral boundaries, obtained from three different global climate models (GCMs) using the RCP8.5 scenario, were conducted to represent the future (2070–99). The climate change response was obtained from the difference between the CTRL and each of the three future simulations. All three ROMS simulations indicated large increases in sea surface temperatures (SSTs) over most of the domain except off the eastern U.S. seaboard resulting from weakening of the Gulf Stream. There are also substantial intermodel differences in the response, including a southward shift of the Gulf Stream in one simulation and a slight northward shift in the other two, with corresponding changes in eddy activity. The depth of maximum warming varied among the three simulations, resulting in differences in the bottom temperature response in coastal regions, including the Gulf of Maine and the West Florida Shelf. The surface salinity decreased in the northern part of the domain and increased in the south in all three experiments, although the freshening extended much farther south in one ROMS simulation relative to the other two, and also relative to the GCM that provided the large-scale forcing. Thus, while high resolution allows for a better representation of currents and bathymetry, the response to climate change can vary considerably depending on the large-scale forcing.

Mesoscale Modeling of Springtime Arctic Mixed-Phase Stratiform Clouds Using a New Two-Moment Bulk Microphysics Scheme

2005 ◽  
Vol 62 (10) ◽  
pp. 3683-3704 ◽  
Author(s):  
H. Morrison ◽  
J. O. Pinto
Keyword(s):  
Boundary Layer ◽  
Vertical Velocity ◽  
Large Scale ◽  
Ice Nucleation ◽  
Mixed Phase ◽  
The Arctic ◽  
Cloud Base ◽  
Microphysics Scheme ◽  
Stratiform Clouds ◽  
Droplet Activation

Abstract A new two-moment bulk microphysics scheme is implemented into the polar version of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) to simulate arctic mixed-phase boundary layer stratiform clouds observed during Surface Heat Budget of the Arctic (SHEBA) First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE) Arctic Cloud Experiment (ACE). The microphysics scheme predicts the number concentrations and mixing ratios of four hydrometeor species (cloud droplets, small ice, rain, snow) and includes detailed treatments of droplet activation and ice nucleation from a prescribed distribution of aerosol obtained from observations. The model is able to reproduce many features of the observed mixed-phase cloud, including a near-adiabatic liquid water content profile located near the top of a well-mixed boundary layer, droplet number concentrations of about 200–250 cm−3 that were distributed fairly uniformly through the depth of the cloud, and continuous light snow falling from the cloud base to the surface. The impacts of droplet and ice nucleation, radiative transfer, turbulence, large-scale dynamics, and vertical resolution on the simulated mixed-phase stratiform cloud are examined. The cloud layer is largely self-maintained through strong cloud-top radiative cooling that exceeds 40 K day−1. It persists through extended periods of downward large-scale motion that tend to thin the layer and reduce water contents. Droplet activation rates are highest near cloud base, associated with subgrid vertical motion that is diagnosed from the predicted turbulence kinetic energy. A sensitivity test neglecting subgrid vertical velocity produces only weak activation and small droplet number concentrations (<90 cm−3). These results highlight the importance of parameterizing the impact of subgrid vertical velocity to generate local supersaturation for aerosol-droplet closure. The primary ice nucleation mode in the simulated mixed-phase cloud is contact freezing of droplets. Sensitivity tests indicate that the assumed number and size of contact nuclei can have a large impact on the evolution and characteristics of mixed-phase cloud, especially the partitioning of condensate between droplets and ice.

scholarly journals Relationship between Shortwave Cloud Radiative Forcing and Local Meteorological Variables Compared in Observations and Several Global Climate Models

2006 ◽  
Vol 19 (17) ◽  
pp. 4344-4359 ◽  
Author(s):  
Markus Stowasser ◽  
Kevin Hamilton
Keyword(s):  
Relative Humidity ◽  
Vertical Velocity ◽  
Radiative Forcing ◽  
Large Scale ◽  
Climate Models ◽  
Grid Point ◽  
Global Climate Models ◽  
Coupled Models ◽  
Cloud Radiative Forcing ◽  
Cloud Forcing

Abstract The relations between local monthly mean shortwave cloud radiative forcing and aspects of the resolved-scale meteorological fields are investigated in hindcast simulations performed with 12 of the global coupled models included in the model intercomparison conducted as part of the preparation for Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4). In particular, the connection of the cloud forcing over tropical and subtropical ocean areas with resolved midtropospheric vertical velocity and with lower-level relative humidity are investigated and compared among the models. The model results are also compared with observational determinations of the same relationships using satellite data for the cloud forcing and global reanalysis products for the vertical velocity and humidity fields. In the analysis the geographical variability in the long-term mean among all grid points and the interannual variability of the monthly mean at each grid point are considered separately. The shortwave cloud radiative feedback (SWCRF) plays a crucial role in determining the predicted response to large-scale climate forcing (such as from increased greenhouse gas concentrations), and it is thus important to test how the cloud representations in current climate models respond to unforced variability. Overall there is considerable variation among the results for the various models, and all models show some substantial differences from the comparable observed results. The most notable deficiency is a weak representation of the cloud radiative response to variations in vertical velocity in cases of strong ascending or strong descending motions. While the models generally perform better in regimes with only modest upward or downward motions, even in these regimes there is considerable variation among the models in the dependence of SWCRF on vertical velocity. The largest differences between models and observations when SWCRF values are stratified by relative humidity are found in either very moist or very dry regimes. Thus, the largest errors in the model simulations of cloud forcing are prone to be in the western Pacific warm pool area, which is characterized by very moist strong upward currents, and in the rather dry regions where the flow is dominated by descending mean motions.

scholarly journals A New Double-Moment Microphysics Parameterization for Application in Cloud and Climate Models. Part II: Single-Column Modeling of Arctic Clouds

2005 ◽  
Vol 62 (6) ◽  
pp. 1678-1693 ◽  
Author(s):  
H. Morrison ◽  
J. A. Curry ◽  
M. D. Shupe ◽  
P. Zuidema
Keyword(s):  
Climate Models ◽  
Heat Budget ◽  
Number Concentration ◽  
The Arctic ◽  
Liquid Water Path ◽  
Microphysics Scheme ◽  
Radiative Fluxes ◽  
Arctic Clouds ◽  
Single Column ◽  
Double Moment

Abstract The new double-moment microphysics scheme described in Part I of this paper is implemented into a single-column model to simulate clouds and radiation observed during the period 1 April–15 May 1998 of the Surface Heat Budget of the Arctic (SHEBA) and First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment–Arctic Clouds Experiment (FIRE–ACE) field projects. Mean predicted cloud boundaries and total cloud fraction compare reasonably well with observations. Cloud phase partitioning, which is crucial in determining the surface radiative fluxes, is fairly similar to ground-based retrievals. However, the fraction of time that liquid is present in the column is somewhat underpredicted, leading to small biases in the downwelling shortwave and longwave radiative fluxes at the surface. Results using the new scheme are compared to parallel simulations using other microphysics parameterizations of varying complexity. The predicted liquid water path and cloud phase is significantly improved using the new scheme relative to a single-moment parameterization predicting only the mixing ratio of the water species. Results indicate that a realistic treatment of cloud ice number concentration (prognosing rather than diagnosing) is needed to simulate arctic clouds. Sensitivity tests are also performed by varying the aerosol size, solubility, and number concentration to explore potential cloud–aerosol–radiation interactions in arctic stratus.

scholarly journals An evaluation of the importance of spatial resolution in a global climate and hydrological model based on the Rhine and Mississippi basin

2017 ◽  
Author(s):  
Imme Benedict ◽  
Chiel C. van Heerwaarden ◽  
Albrecht H. Weerts ◽  
Wilco Hazeleger
Keyword(s):  
High Resolution ◽  
Spatial Resolution ◽  
Large Scale ◽  
Climate Models ◽  
Hydrological Cycle ◽  
Global Climate ◽  
Global Scale ◽  
Global Climate Models ◽  
Convective Processes ◽  
Parameter Values

Abstract. The hydrological cycle of river basins can be simulated by combining global climate models (GCMs) and global hydrological models (GHMs). The spatial resolution of these models is restricted by computational resources and therefore limits the processes and level of detail that can be resolved. To further improve simulations of precipitation and river-runoff on a global scale, we assess and compare the benefits of an increased resolution for a GCM and a GHM. We focus on the Rhine and Mississippi basin. Increasing the resolution of a GCM (1.125° to 0.25°) results in more realistic large-scale circulation patterns over the Rhine and an improved precipitation budget. These improvements with increased resolution are not found for the Mississippi basin, most likely because precipitation is strongly dependent on the representation of still unresolved convective processes. Increasing the resolution of vegetation and orography in the high resolution GHM (from 0.5° to 0.05°) shows no significant differences in discharge for both basins, because the hydrological processes depend highly on other parameter values that are not readily available at high resolution. Therefore, increasing the resolution of the GCM provides the most straightforward route to better results. This route works best for basins driven by large-scale precipitation, such as the Rhine basin. For basins driven by convective processes, such as the Mississippi basin, improvements are expected with even higher resolution convection permitting models.

scholarly journals Indian Summer Monsoon Precipitation Climatology in a High-Resolution Regional Climate Model: Impacts of Convective Parameterization on Systematic Biases

2010 ◽  
Vol 25 (2) ◽  
pp. 369-387 ◽  
Author(s):  
P. Mukhopadhyay ◽  
S. Taraphdar ◽  
B. N. Goswami ◽  
K. Krishnakumar
Keyword(s):  
High Resolution ◽  
Regional Climate Model ◽  
Vertical Velocity ◽  
Rain Rate ◽  
Climate Model ◽  
Regional Climate ◽  
The Other ◽  
Monsoon Precipitation ◽  
Percentage Contribution ◽  
Systematic Biases

Abstract In an attempt to develop a better simulation of the climatology of monsoon precipitation in climate models, this paper investigates the impacts of different convective closures on systematic biases of an Indian monsoon precipitation climatology in a high-resolution regional climate model. For this purpose, the Weather Research Forecast (WRF) model is run at 45- and 15-km (two-way nested) resolution with three convective parameterization schemes, namely the Grell–Devenyi (GD), the Betts–Miller–Janjić (BMJ), and the Kain–Fritsch (KF), for the period 1 May–31 October 2001–07. The model is forced with the NCEP–NCAR reanalysis data as the initial and boundary conditions. The simulated June–September (JJAS) mean monsoon rainfall with the three convective schemes is compared with the observations. KF is found to have a high moist bias over the central and western coastal Indian region while GD shows the opposite. Among the three, BMJ is able to produce a reasonable mean monsoon pattern. In an attempt to get further insight into the seasonal bias and its evolution, the probability distribution function (PDF) of different rain-rate categories and their percentage contribution to the seasonal total are computed. BMJ and KF underestimate the observations for lighter rain rates and overestimate for rain-rate categories of more than 10 mm day−1. GD shows an overestimation for lighter rain and an underestimation of PDF for moderate categories. The seasonal patterns of evolution of PDF plots of three rain-rate categories are analyzed to determine whether the convective schemes show any systematic bias throughout the season or if they have problems during certain phases of the monsoon. This shows that the GD systematically overestimates the lighter rain rate and underestimates the moderate rain rate throughout the season, whereas BMJ and KF have problems in the initial stages. The heavy rain category is systematically overestimated by the KF compared to the other two. To further evaluate the proportionate contribution of each rain-rate bin to the total rain, the percentage contribution of each rain rate to the seasonal total is computed. Analyzing all the rain-rate simulations produced by the three schemes, it is found that KF has a moist bias and GD has a dry bias in the spatiotemporal distribution of the monsoon precipitation. Further, this paper investigates the causes behind the mean monsoon precipitation bias. It is shown that GD produces a model climate where the vertical velocity is less than that of the observations up to 500 hPa and the vertically integrated moist instability is also weaker. KF, on the other hand, shows a higher than the observed vertical velocity and a stronger moist instability. Along with this, the vertical profile of heating suggests a warmer middle level in the KF case and significantly reduced midlevel heating for GD. Thus, KF (GD) has produced a model atmosphere that has a stronger (weaker) convective instability to produce the observed bias in the model precipitation. BMJ is found to simulate a reasonable heating profile, along with the realistic moist instability and seasonal cycle of evaporation and condensation. Insight derived from the analysis is expected to help improve the convective parameterizations.

Mass-Flux Characteristics of Tropical Cumulus Clouds from Wind Profiler Observations at Darwin, Australia

2015 ◽  
Vol 72 (5) ◽  
pp. 1837-1855 ◽  
Author(s):  
Vickal V. Kumar ◽  
Christian Jakob ◽  
Alain Protat ◽  
Christopher R. Williams ◽  
Peter T. May
Keyword(s):  
Vertical Velocity ◽  
Mass Flux ◽  
Large Scale ◽  
Climate Models ◽  
Convective Available Potential Energy ◽  
Area Fraction ◽  
High Temporal Resolution ◽  
Marginal Effect ◽  
Cumulus Clouds ◽  
Average Mass

Abstract Cumulus parameterizations in weather and climate models frequently apply mass-flux schemes in their description of tropical convection. Mass flux constitutes the product of the fractional area covered by convection in a model grid box and the vertical velocity in cumulus clouds. However, vertical velocities are difficult to observe on GCM scales, making the evaluation of mass-flux schemes difficult. Here, the authors combine high-temporal-resolution observations of in-cloud vertical velocities derived from a pair of wind profilers over two wet seasons at Darwin with physical properties of precipitating clouds [cloud-top heights (CTH), convective–stratiform classification] derived from the Darwin C-band polarimetric radar to provide estimates of cumulus mass flux and its constituents. The length of this dataset allows for investigations of the contributions from different cumulus cloud types—namely, congestus, deep, and overshooting convection—to the overall mass flux and of the influence of large-scale conditions on mass flux. The authors found that mass flux was dominated by updrafts and, in particular, the updraft area fraction, with updraft vertical velocity playing a secondary role. The updraft vertical velocities peaked above 10 km where both the updraft area fractions and air densities were small, resulting in a marginal effect on mass-flux values. Downdraft area fractions are much smaller and velocities are much weaker than those in updrafts. The area fraction responded strongly to changes in midlevel large-scale vertical motion and convective inhibition (CIN). In contrast, changes in the lower-tropospheric relative humidity and convective available potential energy (CAPE) strongly modulate in-cloud vertical velocities but have moderate impacts on area fractions. Although average mass flux is found to increase with increasing CTH, it is the environmental conditions that seem to dictate the magnitude of mass flux produced by convection through a combination of effects on area fraction and velocity.

scholarly journals The Earth Model Column Collaboratory (EMC<sup>2</sup>) v1.1: An Open-Source Ground-Based Lidar and Radar Instrument Simulator and Subcolumn Generator for Large-Scale Models

2021 ◽  
Author(s):  
Israel Silber ◽  
Robert C. Jackson ◽  
Ann M. Fridlind ◽  
Andrew S. Ackerman ◽  
Scott Collis ◽  
...  
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Climate Models ◽  
Earth Model ◽  
Model Output ◽  
The Earth ◽  
Scale Models ◽  
Flexible Framework ◽  
Ground Based Lidar

Abstract. Climate models are essential for our comprehensive understanding of Earth's atmosphere and can provide critical insights on future changes decades ahead. Because of these critical roles, today's climate models are continuously being developed and evaluated using constraining observations and measurements obtained by satellites, airborne, and ground-based instruments. Instrument simulators can provide a bridge between the measured or retrieved quantities and their sampling in models and field observations while considering instrument sensitivity limitations. Here we present the Earth Model Column Collaboratory (EMC2), an open-source ground-based lidar and radar instrument simulator and subcolumn generator, specifically designed for large-scale models, in particular climate models, but also applicable to high-resolution model output. EMC2 provides a flexible framework enabling direct comparison of model output with ground-based observations, including generation of subcolumns that may statistically represent finer model spatial resolutions. In addition, EMC2 emulates ground-based (and air- or space-borne) measurements while remaining faithful to large-scale models' physical assumptions implemented in their cloud or radiation schemes. The simulator uses either single particle or bulk particle size distribution lookup tables, depending on the selected scheme approach, to perform the forward calculations. To facilitate model evaluation, EMC2 also includes three hydrometeor classification methods, namely, radar- and sounding-based cloud and precipitation detection and classification, lidar-based phase classification, and a Cloud Feedback Model Intercomparison Project Observational Simulator Package (COSP) lidar simulator emulator. The software is written in Python, is easy to use, and can be straightforwardly customized for different models, radars and lidars. Following the description of the logic, functionality, features, and software structure of EMC2, we present a case study of highly supercooled mixed-phase cloud based on measurements from the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) West Antarctic Radiation Experiment (AWARE). We compare observations with the application of EMC2 to outputs from four configurations of the NASA Goddard Institute for Space Studies (GISS) climate model (ModelE3) in single-column model (SCM) mode and from a large-eddy simulation (LES) model. We show that two of the four ModelE3 configurations can form and maintain highly supercooled precipitating cloud for several hours, consistent with observations and LES. While our focus is on one of these ModelE3 configurations, which performed slightly better in this case study, both of these configurations and the LES results post-processed with EMC2 generally provide reasonable agreement with observed lidar and radar variables. As briefly demonstrated here, EMC2 can provide a lightweight and flexible framework for comparing the results of both large-scale and high-resolution models directly with observations, with relatively little overhead and multiple options for achieving consistency with model microphysical or radiation scheme physics.

Secondary Ice Production in Antarctic Clouds: a process neglected in large-scale models

2020 ◽  
Author(s):  
Georgia Sotiropoulou ◽  
Etienne Vignon ◽  
Gillian Young ◽  
Thomas Lachlan-Cope ◽  
Alexis Berne ◽  
...  
Keyword(s):  
Large Scale ◽  
Climate Models ◽  
Weather Prediction ◽  
Wrf Model ◽  
Weddell Sea ◽  
Microphysics Scheme ◽  
Ice Multiplication ◽  
Ice Production ◽  
Low Sensitivity ◽  
The Impact

&lt;p&gt;In-situ measurements of Antarctic clouds frequently show that ice crystal number concentrations &amp;#160;are much higher than the available ice-nucleating particles, suggesting that Secondary Ice Production (SIP) may be active. Here we investigate the impact of two SIP mechanisms, Hallett-Mossop (H-M)and collisional break-up (BR), on a case from the Microphysics of Antarctic Clouds (MAC) campaign in Weddell Sea using the Weather and Research Forecasting (WRF) model. H-M is already included in the default version of the Morrison microphysics scheme in WRF; for BR we implement different parameterizations and compare their performance. H-M alone is not effective enough to reproduce the observed concentrations. In contrast, BR can result in realistic ice multiplication, independently of whether H-M is active or not. In particular, the Phillips parameterization results in very good agreement with observations, but its performance depends on the prescribed rimed fraction of the colliding ice particles. Finally, our results show low sensitivity to primary ice nucleation, as long as there are enough primary ice crystals to initiate ice-ice collisions. Our findings suggest that BR is a potentially important SIP mechanism in the pristine Antarctic atmosphere that is currently not represented in weather-prediction and climate models.&lt;/p&gt;

Simulation of subtropical marine stratocumulus clouds in convection-resolving models

2020 ◽  
Author(s):  
Christoph Heim ◽  
Laureline Hentgen ◽  
Nikolina Ban ◽  
Christoph Schär
Keyword(s):  
Cloud Cover ◽  
Large Scale ◽  
Climate Models ◽  
Inversion Layer ◽  
Heat Fluxes ◽  
Global Climate Models ◽  
The Other ◽  
Limited Area ◽  
Stratocumulus Clouds ◽  
The Mean

&lt;p&gt;Even though the complexity and resolution of global climate models (GCMs) has increased over the last decades, the inter-model spread of equilibrium climate sensitivity has not narrowed. The representation of subtropical low-level clouds and their associated radiative feedbacks in climate models still poses a major challenge. A fundamental problem underlying the simulation of such clouds is their multiscale nature. On the one hand, current GCMs allow to capture the large-scale processes but are too coarse to represent the mesoscale and microscale dynamical processes governing their formation and dissipation. On the other hand, large eddy simulations (LES) resolving the micro scale are bound to small domains and thus lack a robust representation of the large-scale flow and the mesoscale organisation of the clouds. Convection-resolving models (CRMs) are an attractive compromise between the former two since they allow for simulations at much higher resolution than in conventional GCMs and on larger domains than in LES.&lt;/p&gt;&lt;p&gt;Here we analyse how CRMs simulate stratocumulus decks and investigate causes for inter-model differences. We consider a set of ten CRMs (nine GCMs that are run at convection-resolving resolution during a short time period as part of the pioneering DYAMOND initiative, and the limited area model COSMO run by ourselves) used to simulate stratocumulus clouds over the South-East Atlantic during a 40 day period. The simulations cover a range of horizontal grid spacings between 5 and 1 km.&lt;/p&gt;&lt;p&gt;We find pronounced differences in the mean cloud cover among the analysed CRMs. In comparison to observed radiation (CERES), most of them underestimate cloud cover, in particular the low-lying stratus decks close to the African coast. Nevertheless, the simulated mesoscale cloud organisation is realistic and similar in the set of CRMs, with few exceptions showing organisation on larger scales than in the other models. In general, the simulated cloud field appears to be more sensitive to the model choice than to the horizontal resolution.&lt;/p&gt;&lt;p&gt;Despite the differences in the cloud cover, most models capture the subtropical inversion and its spatial structure relatively well. Therefore, differences in the inversion strengths do not suffice to explain variability in the simulated cloud cover fraction between models. However, we find a relation between the mean height of the stratocumulus layer (or inversion layer) and its cloud cover fraction: Models with higher inversions tend to simulate a higher cloud cover fraction, bringing them closer to observations. Similarly, stronger vertical mixing within the boundary layer and enhanced surface latent heat fluxes appear to be related to higher cloud cover. Such relations may help to determine the physical processes responsible for the differences among CRMs in the simulated stratocumulus field.&lt;/p&gt;

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