Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “cloud microphysics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Evaluation of Cloud Microphysics in JMA-NHM Simulations Using Bin or Bulk Microphysical Schemes through Comparison with Cloud Radar Observations

Numerical weather prediction (NWP) simulations using the Japan Meteorological Agency NonhydrostaticModel (JMA-NHM) are conducted for three precipitation events observed by shipborne or spaceborneW-band cloud radars. Spectral bin and single-moment bulk cloud microphysics schemes are employed separatelyfor an intercomparative study. A radar product simulator that is compatible with both microphysicsschemes is developed to enable a direct comparison between simulation and observation with respect to theequivalent radar reflectivity factor Ze, Doppler velocity (DV), and path-integrated attenuation (PIA). Ingeneral, the bin model simulation shows better agreement with the observed data than the bulk modelsimulation. The correction of the terminal fall velocities of snowflakes using those of hail further improves theresult of the bin model simulation. The results indicate that there are substantial uncertainties in the masssizeand sizeterminal fall velocity relations of snowflakes or in the calculation of terminal fall velocity of snowaloft. For the bulk microphysics, the overestimation of Ze is observed as a result of a significant predominanceof snow over cloud ice due to substantial deposition growth directly to snow. The DV comparison shows thata correction for the fall velocity of hydrometeors considering a change of particle size should be introducedeven in single-moment bulk cloud microphysics.

cloud radar↗
DOE OSTI2024

The impact of cloud microphysics and ice nucleation on Southern Ocean clouds assessed with single-column modeling and instrument simulators

Abstract. Supercooled liquid clouds are common at higher latitudes (especially over the Southern Ocean) and are critical for constraining climate projections. We take advantage of the Macquarie Island Cloud and Radiation Experiment (MICRE) to perform an analysis of observed and simulated cloud processes over the Southern Ocean in a region and season dominated by supercooled liquid clouds. Using a single-column version of the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS), we compare two different cloud microphysical schemes to ground-based observations of cloud, precipitation, and radiation over a 2.5-month period (1 January–17 March 2017). Both schemes are able to reproduce aspects of the cloud and radiation observations during MICRE to within the uncertainty of the data when the thermodynamic profile is prescribed with relaxation. There are differences in water mass and representation of reflectivity between the schemes. A sensitivity study of the cloud microphysics schemes, one a bulk one-moment scheme and the other a two-moment scheme with prediction of mass and number, indicates that several key processes create differences between the schemes. Surface radiative fluxes and total water path are highly sensitive to the formation and fall speed of precipitation. The prediction of hydrometeor number with the two-moment scheme yields a better comparison with observed reflectivity and radiative fluxes, despite predicting higher liquid water contents than observed. With the two-moment scheme, we are also able to test the sensitivity of the results to the input of liquid cloud condensation nuclei (CCN) and ice nuclei (IN). The cloud properties and resulting radiative effects are found to be sensitive to the CCN and IN concentrations. More CCN and IN increase liquid and ice water paths, respectively. Thus, both the dynamic environment and aerosols, integrated through the cloud microphysics, are important for properly representing Southern Ocean cloud radiative effects.

58 GEOSCIENCES↗
NASA NTRS1978

Cloud microphysics - Analysis of the clouds of Earth, Venus, Mars, and Jupiter

The probable microphysics of a cloud is deduced by a described method which requires information on cloud particle mean size, composition, number density, and atmospheric structure, but does not require any additional information. The analysis is applied to the sulfuric acid clouds of Venus, the water ice and dust clouds of Mars, and the ammonia-water and ammonia ice clouds of Jupiter. The Venus cloud layer is found to have some resemblance to smog and haze layers on earth. The water ice clouds on Mars resemble tenuous nonprecipitating cirrus clouds on earth. Precipitation, vertical distribution of gases, and vertical transport of heat in the clouds on Jupiter are considered.

Rossow, W. B.↗
DOE OSTI2025

Perspectives on Systematic Cloud Microphysics Scheme Development With Machine Learning

Cloud microphysics—the collection of processes that govern the small‐scale formation, evolution, and interactions of liquid droplets and ice crystals in clouds and precipitation—remains a major source of uncertainty in weather and climate models. Although too small in scale to be explicitly resolved in any large‐eddy simulation, weather, or climate model, the representation of cloud microphysical processes has significant impact at the climate scale. Current microphysical schemes are limited by both parametric uncertainty, linked to uncertainty in physical parameter values, and structural uncertainty, arising from incomplete physical understanding of the processes at play or approximations made for computational efficiency. Recent advances in the application of machine learning (ML) to the physical sciences show significant potential for minimizing these limitations by leveraging high‐fidelity simulations and observations. Here we outline the challenges that must be addressed to apply ML toward cloud microphysics scheme development. This perspectives paper synthesizes recent progress in using data‐driven methods, including ML, to improve cloud microphysics parameterizations and highlights opportunities to address key uncertainties. We discuss the roles of aleatoric (irreducible, or statistical) and epistemic (reducible, or systematic) errors in contributing to microphysics parameterization uncertainty. ML can leverage observations to improve microphysical schemes via bottom‐up and top‐down constraints. Methods such as differentiable programming and ML‐enhanced sampling strategies and the creation of large scale benchmark data sets promise to bridge the gap between observations and models and to improve the consistency of cloud microphysical representation across temporal and spatial scales.

Lamb, Kara D. [Columbia Univ., New York, NY (Unite↗
NASA NTRS2001

Cloud Microphysics Budget in the Tropical Deep Convective Regime

Cloud microphysics budgets in the tropical deep convective regime are analyzed based on a 2-D cloud resolving simulation. The model is forced by the large-scale vertical velocity and zonal wind and large-scale horizontal advections derived from TOGA COARE for a 20-day period. The role of cloud microphysics is first examined by analyzing mass-weighted mean heat budget and column-integrated moisture budget. Hourly budgets show that local changes of mass-weighted mean temperature and column-integrated moisture are mainly determined by the residuals between vertical thermal advection and latent heat of condensation and between vertical moisture advection and condensation respectively. Thus, atmospheric thermodynamics depends on how cloud microphysical processes are parameterized. Cloud microphysics budgets are then analyzed for raining conditions. For cloud-vapor exchange between cloud system and its embedded environment, rainfall and evaporation of raindrop are compensated by the condensation and deposition of supersaturated vapor. Inside the cloud system, the condensation of supersaturated vapor balances conversion from cloud water to raindrop, snow, and graupel through collection and accretion processes. The deposition of supersaturated vapor balances conversion from cloud ice to snow through conversion and riming processes. The conversion and riming of cloud ice and the accretion of cloud water balance conversion from snow to graupel through accretion process. Finally, the collection of cloud water and the melting of graupel increase raindrop to compensate the loss of raindrop due to rainfall and the evaporation of raindrop.

Li, Xiao-Fan↗
DOE OSTI2025

Advancing the Understanding of Cloud Microphysical Processes and Aerosol Indirect Effects in High-Latitude Mixed-Phase Clouds by Linking ARM Measurements with Climate Model Simulations (Final Report)

The key objectives of this project were to advance our understanding of cloud microphysical characteristics and aerosol indirect effects on mixed-phase clouds in high latitudes. To improve the representation of ice and mixed-phase clouds in Earth System Models (ESMs), we propose an integrated observation and modeling study of cloud macro- and microphysical properties, including spatial heterogeneities, mass partitioning between ice crystals and supercooled liquid water, effects of ice nucleating particles (INPs), and efficiency of secondary ice production (SIP), etc. Specifically, we took four main approaches in this project: (1) examining macro- and microphysical properties of ice and mixed-phase clouds based on in-situ and ground-based observations from multiple field campaigns funded by the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program, including the Mixed-Phase Arctic Cloud Experiment (M-PACE), Indirect and Semi-Direct Aerosol Campaign (ISDAC), Ice Nucleating Particle Sources at Oliktok Point (INPOP), ARM West Antarctic Radiation Experiment (AWARE), Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS), and Macquarie Island Cloud and Radiation Experiment (MICRE); (2) evaluating the DOE Energy Exascale Earth System Model (E3SM) simulations based on observations, particularly for ice and mixed-phase cloud microphysical properties; (3) examining the impacts of INPs on ice and mixed-phase clouds. Specifically, a series of comparisons were conducted using observations over the Arctic, Southern Ocean, and Antarctica, including comparisons between the lower and higher southern latitudes as well as comparisons between the northern and southern hemispheres. In addition, aerosol indirect effects from distinct sources of dust particles were examined; and (4) investigating the impacts of SIP. Ultimately, these results helped to improve cloud microphysics and aerosol-cloud interaction parameterizations in the E3SM model. Overall, the project provided improved understanding regarding various factors, including thermodynamic, dynamic, and aerosol conditions, on the micro- and macrophysical properties of ice and mixed-phase clouds in the high latitudes. Resulting analysis helped to provide an improved physical basis for refining the current cloud microphysics parameterizations related to ice and mixed-phase clouds in E3SM.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2008

Aerosol and Cloud Microphysical Characteristics of Rifts and Gradients in Maritime Stratocumulus Clouds

A cloud rift is characterized as a large-scale, persistent area of broken, low reflectivity stratocumulus clouds usually surrounded by a solid deck of stratocumulus. A rift observed off the coast of Monterey Bay, California on 16 July 1999 was studied to compare the aerosol and cloud microphysical properties in the rift with those of the surrounding solid stratus deck. Variables measured from an instrumented aircraft included temperature, water vapor, and cloud liquid water. These measurements characterized the thermodynamic properties of the solid deck and rift areas. Microphysical measurements made included aerosol, cloud drop and drizzle drop concentrations and cloud condensation nuclei (CCN) concentrations. The microphysical characteristics in a solid stratus deck differ substantially from those of a broken, cellular rift where cloud droplet concentrations are a factor of 2 lower than those in the solid cloud. Further, CCN concentrations were found to be about 3 times greater in the solid cloud area compared with those in the rift and aerosol concentrations showed a similar difference as well. Although drizzle was observed near cloud top in parts of the solid stratus cloud, the largest drizzle rates were associated with the broken clouds within the rift area. In addition to marked differences in particle concentrations, evidence of a mesoscale circulation near the solid cloud rift boundary is presented. This mesoscale circulation provides a mechanism for maintaining a rift, but further study is required to understand the initiation of a rift and the conditions that may cause it to fill.

Sharon, Tarah M.↗
NASA NTRS1993

Comparison of cloud microphysical parameters derived from surface and satellite measurements during FIRE phase 2

Cloud microphysical properties are an important component in climate model parameterizations of water transport, cloud radiative exchange, and latent heat processes. Estimation of effective cloud particle size, liquid or ice water content, and optical depth from satellite-based instrumentation is needed to develop a climatology of cloud microphysical properties and to better understand and model cloud processes in atmospheric circulation. These parameters are estimated from two different surface data sets taken at Coffeyville, Kansas, during the First ISCCP Regional Experiment (FIRE) Phase-2 Intensive Field Observation (IFO) period (November 13 - December 7, 1991). Satellite data can also provide information about optical depth and effective particle size. This paper explores the combination of the FIRE-2 surface and satellite data to determine each of the cloud microphysical properties.

Young, David F.↗
NASA NTRS2022

The Radiative Effect on Cloud Microphysics from the Arctic to the Tropics

Cloud representation is one of the largest uncertainties in the current weather and climate models. In this article, the observations and modeling of the radiative effect on (cloud) microphysics (REM) from the Arctic to the Tropics are overviewed, providing a new direction to meet the challenge of cloud representation. REM deals with the radiation-induced temperature difference between cloud particles and air. It leads to two common phenomena observed at the surface—dew and frost—and impacts clouds aloft significantly, which is noticed via the wide occurrence of horizontally oriented ice crystals (HOICs). However, REM has been overlooked by all of the operational weather and climate models. Based on the bin model of REM and the global distribution of radiative cooling/warming, the observations of REM from several platforms (e.g., aircrafts, field campaigns, and satellites) are coordinated in this article, yielding a global picture on REM. As a result, the picture is compatible with the global distribution of HOICs and other ice crystal characteristics obtained from various clouds on the globe, such as diamond dust (or clear-sky precipitation) in the Arctic, sub-visual cirrus clouds in the tropical tropopause layer, and other cirrus clouds from the low to high latitudes. In addition, ice crystals possess relatively strong REM compared to liquid drops because their aspect ratio is usually not one. The global picture on REM can be used by the weather and climate modelers to diagnose their cloud representation biases. It can also be used to improve the atmospheric ice retrieval algorithm from satellite observations.

cloud microphysics↗
DOE OSTI2025

Uncertainty quantification and optimization of precipitating hydrometeor parameters for winter precipitation in a cloud microphysics scheme

The precipitating hydrometeor parameters used in cloud microphysics schemes carry inherent uncertainties. The quantification of these uncertainties, together with parameter optimization, can significantly improve precipitation forecasts. This study investigates the effects of 13 parameters in the Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) microphysics scheme, which define the hydrometeor characteristics such as fall velocity–diameter and mass–diameter relationships, as well as the shape parameter of the drop size distribution for precipitating particles such as rain, snow, and graupel on simulated winter precipitation. A comparison between the model's pre-defined parameters and observations from the International Collaborative Experiments for the PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign reveals that the fall velocity–diameter relationship for rain, the mass–diameter relationships for snow and graupel, and the shape parameters for all precipitating particles in the WDM6 scheme deviate from the median values observed by the two-dimensional video disdrometer (2DVD). To quantify parameter sensitivities, a perturbed parameter ensemble (PPE) of 256 simulations was conducted within parameter ranges constrained by 2DVD observations for three winter precipitation cases. Bayesian optimization was then applied to identify parameter sets that minimized the root mean square error (RMSE) for each case, achieving reductions of up to 30.2 %. These results demonstrate that ensemble-based uncertainty quantification and parameter optimization can help identify key parameters and provide a pathway to improving precipitation simulation performance. In addition, measurement sites can be strategically selected based on regions that show high sensitivity to variations in hydrometeor characteristic parameters.

Bayesian optimization↗
NASA NTRS2012

Performance of McRAS-AC in the GEOS-5 AGCM: Part 1, Aerosol-Activated Cloud Microphysics, Precipitation, Radiative Effects, and Circulation

A revised version of the Microphysics of clouds with Relaxed Arakawa-Schubert and Aerosol-Cloud interaction (McRAS-AC), including, among others, the Barahona and Nenes ice nucleation parameterization, is implemented in the GEOS-5 AGCM. Various fields from a 10-year long integration of the AGCM with McRAS-AC were compared with their counterparts from an integration of the baseline GEOS-5 AGCM, and with satellite data as observations. Generally using McRAS-AC reduced biases in cloud fields and cloud radiative effects are much better over most of the regions of the Earth. Two weaknesses are identified in the McRAS-AC runs, namely, too few cloud particles around 40S-60S, and too high cloud water path during northern hemisphere summer over the Gulf Stream and North Pacific. Sensitivity analyses showed that these biases potentially originated from biases in the aerosol input. The first bias is largely eliminated in a sensitivity test using 50% smaller aerosol particles, while the second bias is much reduced when interactive aerosol chemistry was turned on. The main drawback of McRAS-AC is dearth of low-level marine stratus clouds, probably due to lack of dry-convection, not yet implemented into the cloud scheme. Despite these biases, McRAS-AC does simulate realistic clouds and their optical properties that can improve with better aerosol-input and thereby has the potential to be a valuable tool for climate modeling research because of its aerosol indirect effect simulation capabilities involving prediction of cloud particle number concentration and effective particle size for both convective and stratiform clouds is quite realistic.

Sud, Y. C.↗
DOE OSTI2025

Dependence of Convective Cloud Microphysical Properties on Environmental Conditions during the TRACER and ESCAPE Field Campaigns: A Synergistic Approach of Observations, Machine Learning and Parcel Models

The sensitivity of convective clouds to aerosols and their interactions with environment, combined with limited observational constraints in parameterizations, introduces significant uncertainties in atmospheric models. Here, this study investigates the dependence of convective cloud microphysical properties on environmental conditions using a synergistic approach that combines unique observations from the TRACER and ESCAPE field campaigns, machine learning techniques, and parcel model simulations with a super-droplet microphysics scheme. A random forest algorithm identifies in-situ vertical velocity (w), temperature (T), and surface fine-mode aerosol mass concentration as the three most important environmental conditions influencing cloud properties including liquid water content (LWC), number concentration for particles with D max < 50 μm (N c ,<50), 50 μm ≤ D max ≤ 3000 μm (N c,50–3000 ), and droplet effective diameter (D e ). Results show that LWC, N c,<50 , and N c,50–3000 significantly increase with w in updrafts. Across w bins, as T decreases, LWC, D e , and N c,50–3000 increase, while N c,<50 decreases, which are closely linked to the distance above cloud bases. Warmer cloud bases yield higher LWC, greater N c,50–3000 , and smaller N c,<50 , while polluted environments produce greater N c,<50 . Parcel model simulations successfully replicate these observed dependencies. The simulation results indicate that warmer cloud bases enhance condensation generating larger droplets, and differences in droplet sizes are then amplified through collision-coalescence, resulting in a greater N c,50–3000 . Polluted conditions result in a greater N c,<50 primarily due to enhanced cloud condensation nuclei activation despite increased collision-coalescence rates compared to pristine conditions. This study provides observed quantitative patterns characterizing cloud microphysical properties as a function of key environmental parameters, offering valuable constraints for improving physics parameterizations and numerical models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2000

The Influence of Microphysical Cloud Parameterization on Microwave Brightness Temperatures

The microphysical parameterization of clouds and rain-cells plays a central role in atmospheric forward radiative transfer models used in calculating passive microwave brightness temperatures. The absorption and scattering properties of a hydrometeor-laden atmosphere are governed by particle phase, size distribution, aggregate density., shape, and dielectric constant. This study identifies the sensitivity of brightness temperatures with respect to the microphysical cloud parameterization. Cloud parameterizations for wideband (6-410 GHz observations of baseline brightness temperatures were studied for four evolutionary stages of an oceanic convective storm using a five-phase hydrometeor model in a planar-stratified scattering-based radiative transfer model. Five other microphysical cloud parameterizations were compared to the baseline calculations to evaluate brightness temperature sensitivity to gross changes in the hydrometeor size distributions and the ice-air-water ratios in the frozen or partly frozen phase. The comparison shows that, enlarging the rain drop size or adding water to the partly Frozen hydrometeor mix warms brightness temperatures by up to .55 K at 6 GHz. The cooling signature caused by ice scattering intensifies with increasing ice concentrations and at higher frequencies. An additional comparison to measured Convection and Moisture LA Experiment (CAMEX 3) brightness temperatures shows that in general all but, two parameterizations produce calculated T(sub B)'s that fall within the observed clear-air minima and maxima. The exceptions are for parameterizations that, enhance the scattering characteristics of frozen hydrometeors.

Skofronick-Jackson, Gail M.↗
NASA NTRS1999

Analysis of Cirrus Cloud Microphysical Data

The First International Satellite Cloud Climatology Regional Experiment (FIRE) program has the goal of improving our capabilities to understand, model and detect the properties of climatically-important clouds. This is being undertaken through a three-pronged effort of modeling, long-term observations and short-term intensive field studies. Through examination of satellite and other data it is apparent that stratus and cirrus cloud types have the greatest impact on climate due to their radiative effects and ubiquitous nature. As a result, the FIRE program has developed two paths of investigation, each having its own subset of research objectives and measurement programs. The work conducted under this grant was directed toward furthering our understanding of cirrus cloud systems. While it is known that cirrus are climatically important, the magnitude and even sign of the impact is unclear. Cirrus clouds affect the transfer of radiation according to their physical depth and location in the atmosphere and their microphysical composition. However, significant uncertainties still exist in how cirrus clouds form and how they are maintained, what their physical properties are and how they can be parameterized in numerical models. Better remote sensing techniques for monitoring cirrus cloud systems and improved modeling of radiative transfer through ice particles are also needed. A critical element in resolving these issues is a better understanding of cirrus cloud microphysical properties and how they vary. The focus of the research to be conducted under this grant was th data collected in situ by the University of North Dakota Citation aircraft. The goals of this research were to add to the body of knowledge of cirrus cloud microphysics, particularly at the small end of the size spectrum; and analyze the spatial variation of cirrus clouds.

Poellot, Michael R.↗
NASA NTRS1988

Theory on the uncertainty in cloud microphysical processes and climate

The interactive role of clouds and precipitation processes in a climate model is investigated. The basic model structure and parameterizations for condensation, evaporation, and precipitation are outlined. Results simulated from the cloud-climate model are discussed. The potential link between microphysical cloud processes and climate is theorized. The need to develop a climatology of the mean particle radius for clouds at the global scale, in order to understand the role of clouds in climate is stressed.

Liou, Kuo-Nan↗
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 NTRS2010

Comparison of GOES-Retrieved and In Situ Measurements of Deep Convective Anvil Cloud Microphysical Properties During the Tropical Composition, Cloud and Climate Coupling Experiment (TC(sup 4))

One of the main goals of the Tropical Composition, Cloud and Climate Coupling Experiment (TC(sup 4)) during July and August 2007 was to gain a better understanding of the formation and life cycle of cirrus clouds in the upper troposphere and lower stratosphere and how their presence affects the exchange of water vapor between these layers. Additionally, it is important to compare in situ measurements taken by aircraft instruments with products derived from satellite observations and find a meaningful way to interpret the results. In this study, cloud properties derived using radiance measurements from the Geostationary Operational Environmental Satellite (GOES) imagers are compared to similar quantities from aircraft in situ observations and are examined for meaningful relationships. A new method using dual \angle satellite measurements is used to derive the ice water content (IWC) for the top portion of deep convective clouds and anvils. The results show the in situ and remotely sensed mean microphysical properties agree to within approx.10 microns in the top few kilometers of thick anvils despite the vastly different temporal and spatial resolutions of the aircraft and satellite instruments. Mean particle size and IWC are shown to increase with decreasing altitude in the top few kilometers of the cloud. Given these relationships, it may be possible to derive parameterizations for effective particle size and IWC as a function of altitude from satellite observations

Yost, Christoher R.↗