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NASA NTRS2017

Validation Process for LEWICE by Use of a Navier-Stokes Solver

A research project is underway at NASA Glenn to produce computer software that can accurately predict ice growth under any meteorological conditions for any aircraft surface. This report will present results from the latest LEWICE release, version 3.5. This program differs from previous releases in its ability to model mixed phase and ice crystal conditions such as those encountered inside an engine. It also has expanded capability to use structured grids and a new capability to use results from unstructured grid flow solvers. A quantitative comparison of the results against a database of ice shapes that have been generated in the NASA Glenn Icing Research Tunnel (IRT) has also been performed. This paper will extend the comparison of ice shapes between LEWICE 3.5 and experimental data from a previous paper. Comparisons of lift and drag are made between experimentally collected data from experimentally obtained ice shapes and simulated (CFD) data on simulated (LEWICE) ice shapes. Comparisons are also made between experimentally collected and simulated performance data on select experimental ice shapes to ensure the CFD solver, FUN3D, is valid within the flight regime. The results show that the predicted results are within the accuracy limits of the experimental data for the majority of cases.

large-eddy simulations↗

NASA NTRS2017

A Revised Validation Process for Ice Accretion Codes

turbulent heat flux↗

NASA NTRS2000

Continuing Measurements of CO2 Crystals with a Hand-Held 35 GHz Radiometer

In order to increase our knowledge of the Martian polar caps, an improved understanding of the behavior of both frozen H2O and CO2 in different parts of the electromagnetic spectrum is needed. The thermal microwave part of the spectrum has received relatively little attention compared to the visible and infrared wavelengths. A simple experiment to measure the brightness temperature of frozen CO2 was first performed in the winter of 1998 using a 35 GHz radiometer. in experiments performed during the winter of 1999 and 2000, passive microwave radiation emanating from within layers of manufactured CO2 (dry ice) crystals was again measured with a 35 GHz handheld radiometer. Both large (0.8 cm) and small (0.3 cm) cylindrical-shaped dry ice pellets, at a temperature of 197 K (-76 C), were measured. A 1 sq m plate of aluminum sheet metal was positioned beneath the dry ice so that microwave emissions from the underlying soil layers would be minimized. Non-absorbing foam was positioned around the sides of the plate in order to keep the dry ice in place and to assure that the incremental deposits were level. Thirty-five GHz measurements of this plate were made through the dry ice deposits in the following way. Layers of dry ice were built up and measurements were repeated for the increasing CO2 pack. First, 7 cm of large CO2 pellets were poured onto the sheet metal plate, then an additional 7 cm were added, and finally, 12 cm were added on top of the 14 cm base. Hand-held 35 GHz measurements were made each time the thickness of the deposit was increased. The same process was repeated for the smaller grain pellets. Furthermore, during the past winter, 35 GHz measurements were taken of a 25 kg (27 cm x 27 cm x 27 cm) solid cube Of CO2, which was cut in half and then re-measured. Additional information is contained in the original extended abstract.

Foster, J.↗

NASA NTRS1988

Backscatter laser depolarization studies of simulated stratospheric aerosols: Crystallized sulfuric acid droplets

The optical depolarizing properties of simulated stratospheric aerosols were studied in laboratory laser (0.633 micrometer) backscattering experiments for application to polarization lidar observations. Clouds composed of sulfuric acid solution droplets, some treated with ammonia gas, were observed during evaporation. The results indicate that the formation of minute ammonium sulfate particles from the evaporation of acid droplets produces linear depolarization ratios of beta equivalent to 0.02, but beta equivalent to 0.10 to 0.15 are generated from aged acid cloud aerosols and acid droplet crystallization effects following the introduction of ammonia gas into the chamber. It is concluded that partially crystallized sulfuric acid droplets are a likely candidate for explaining the lidar beta equivalent to 0.10 values that have been observed in the lower stratosphere in the absence of the relatively strong backscattering from homogeneous sulfuric acid droplet (beta equivalent to 0) or ice crystal (beta equivalent to 0.5) clouds.

Sassen, Kenneth↗

NASA NTRS1989

Backscatter laser depolarization studies of simulated stratospheric aerosols - Crystallized sulfuric acid droplets

The optical depolarizing properties of simulated stratospheric aerosols were studied in laboratory laser (0.633 micrometer) backscattering experiments for application to polarization lidar observations. Clouds composed of sulfuric acid solution droplets, some treated with ammonia gas, were observed during evaporation. The results indicate that the formation of minute ammonium sulfate particles from the evaporation of acid droplets produces linear depolarization ratios of beta equivalent to 0.02, but beta equivalent to 0.10 to 0.15 are generated from aged acid cloud aerosols and acid droplet crystalization effects following the introduction of ammonia gas into the chamber. It is concluded that partially crystallized sulfuric acid droplets are a likely candidate for explaining the lidar beta equivalent to 0.10 values that have been observed in the lower stratosphere in the absence of the relatively strong backscattering from homogeneous sulfuric acid droplet (beta equivalent to 0) or ice crystal (beta equivalent to 0.5) clouds.

Sassen, Kenneth↗

DOE OSTI2024

Molecular-Resolution Electron Imaging of Defects and Dynamics at the Ice-Water Interface

Water crystallization into hexagonal ice (type I h ) is one of the most critical processes relevant to the Earth’s environment and human activities. However, despite recent breakthroughs in imaging non-equilibrium condensed ice structures, the ice-water interface has never been imaged at a molecular resolution. This is primarily due to the low stability of the hydrogen bonds in ice under high-resolution microscopy conditions and a lack of methods to prepare compatible samples. Here, this presentation describes the first molecular-resolution imaging of ice crystallized from liquid water and the ice-water interface using high-resolution transmission electron microscopy (HRTEM). By encapsulating deionized (DI) water between two amorphous carbon (a-C) TEM grids and subsequently freezing it with liquid N 2 on a cryo sample stage, we generated two types of ice: non-equilibrium, condensed ice from the atmosphere and encapsulated ice from the DI water (Fig. 1A). Condensed ice usually shows irregular, spherulitic shapes (Fig. 1B). Selected area electron diffraction (SAED) shows that they are a mixture of cubic and hexagonal crystals (Fig. 1C). On the contrary, encapsulated ice forms thin films that contain large-area single-crystalline regions of hexagonal ice oriented along the [0001] zone axis (Fig. 1D). Differential electron energy-loss spectroscopy (EELS) confirmed the high purity of the encapsulated ice free from organic contaminations that are common in other encapsulation methods for HRTEM such as graphene liquid cells. These single-crystalline areas are robust under the electron beam up to ~100 e/Å 2 s. Aberration-corrected HRTEM imaging in these areas achieved a line resolution of ~1.3 Å (Fig. 1E and F). This platform allows us to study near-equilibrium ice structures and dynamics at an unprecedented spatial resolution (Fig. 2). For example, we discovered subdomain-rich regions near the defective crystal edges despite the structure appearing single-crystalline according to diffraction criteria. These subdomains connect via low-angle grain boundaries with flat energy landscapes as a function of tilt angles (according to simulations), showing the high tolerance of ice to defect structures. When we tuned the sample temperature and electron flux rate, we observed radiolysis-controlled bubble generation and dissolution in ice single crystals near a steady state of bubble dynamics. Furthermore, rich beam-induced melting and recrystallization dynamics were observed at the ice-water interface with lattice resolution. These data represent the first observation of the ice-water phase transformation at the sub-nanometer level. In summary, the methods developed in this work enabled molecular-resolution observations of ice and the ice-water interface and shed light on the microstructures and phase transformation pathways. Finer control on the temperature, electron irradiation profile, and imaging detector could eventually lead to real-time observation of ice nucleation in water and address long-standing questions in the nucleation pathways.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS2016

Validation Process for LEWICE Coupled by Use of a Navier-Stokes Solver

A research project is underway at NASA Glenn to produce computer software that can accurately predict ice growth for many meteorological conditions for any aircraft surface. This report will present results from the latest LEWICE release, version 3.5. This program differs from previous releases in its ability to model mixed phase and ice crystal conditions such as those encountered inside an engine. It also has expanded capability to use structured grids and a new capability to use results from unstructured grid flow solvers. An extensive comparison of the results in a quantifiable manner against the database of ice shapes that have been generated in the NASA Glenn Icing Research Tunnel (IRT) has also been performed. This paper will show the differences in ice shape between LEWICE 3.5 and experimental data. In addition, comparisons will be made between the lift and drag calculated on the ice shapes from experiment and those produced by LEWICE. This report will also provide a description of both programs. Quantitative geometric comparisons are shown for horn height, horn angle, icing limit, area and leading edge thickness. Quantitative comparisons of calculated lift and drag will also be shown. The results show that the predicted results are within the accuracy limits of the experimental data for the majority of cases.

Wright, William B.↗

NASA NTRS2023

The CHROMA Cloud-Top Pressure Retrieval Algorithm for the Plankton, Aerosol, Cloud, Ocean Ecosystem (PACE) Satellite Mission

This paper provides the theoretical basis and simulated retrievals for the Cloud Height Retrieval from O2 Molecular Absorption (CHROMA) algorithm. Simulations are performed for the Ocean Color Instrument (OCI), which is the primary payload on the forthcoming NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, and the Ocean Land Colour Instrument (OLCI) currently flying on the Sentinel 3 satellites. CHROMA is a Bayesian approach which simultaneously retrieves cloud optical thickness (COT), cloud-top pressure and height (CTP and CTH respectively), and (with a significant prior constraint) surface albedo. Simulated retrievals suggest that the sensor and algorithm should be able to meet the PACE mission goal for CTP error, which is ±60 mb for 65 % of opaque (COT ≥3) single-layer clouds on global average. CHROMA will provide pixel-level uncertainty estimates, which are demonstrated to have skill at telling low-error situations from high-error ones. CTP uncertainty estimates are well-calibrated in magnitude, although COT uncertainty is overestimated relative to observed errors. OLCI performance is found to be slightly better than OCI overall, demonstrating that it is a suitable proxy for the latter in advance of PACE's launch. CTP error is only weakly sensitive to correct cloud phase identification or assumed ice crystal habit/roughness. As with other similar algorithms, for simulated retrievals of multi-layer systems consisting of optically thin cirrus clouds above liquid clouds, retrieved height tends to be underestimated because the satellite signal is dominated by the optically thicker lower layer. Total (liquid plus ice) COT also becomes underestimated in these situations. However, retrieved CTP becomes closer to that of the upper ice layer for ice COT ≈3 or higher.

PACE↗

NASA NTRSDate not supplied

Towards an Optimal Estimation Retrieval of Cirrus Cloud Optical and Microphysical Properties Using Hyperspectral Shortwave Instruments and A Fast Radiative Transfer Algorithm

Cirrus cloud retrieval products (here, cloud optical depth, effective particle size, and cloud top height) are important inputs into numerical weather and climate models. Uncertainties in such retrieval products, as a matter of course, propagate downstream, impacting model calculations. Improvements in high-quality global cirrus cloud optical and microphysical data products from satellite observations are needed to understand and reduce retrieval uncertainties. Hyperspectral shortwave instruments produce high-resolution and information-dense spectra, thus offering the opportunity to reduce uncertainties in retrieval products. We are in the process of developing a retrieval that uses the very fast Principal Component Radiative Transfer Model in the solar spectral region (PCRTM-Solar) in the forward model calculations. This retrieval will use measured reflectances from the NASA Earth Surface Mineral Dust Source Investigation (EMIT) and the forthcoming Climate Absolute Radiance and Refractivity Observatory Pathfinder (CLARREO-Pathfinder) instruments. In this manuscript we present progress towards a reference retrieval employing a widely used, verified, accurate, yet computationally slower radiative transfer modeling technique. The reference retrieval, while too slow for using the complete hyperspectral measurement, will allow us to study the behavior of retrieval products and help us verify results from our in-development fast retrieval. Both retrievals will use the optimal estimation retrieval framework. In this manuscript we present results from an uncertainty analysis considering three uncertainty sources for a cirrus cloud retrieval in the form of error covariance matrices: reflectance uncertainty due to water vapor, the reflectance uncertainty due to ice crystal scattering assumptions, and the instrument measurement uncertainty. Results show that the uncertainty due to habit selection is the largest, while that due to water vapor is at most 0.6% relative to channel reflectance. As a first step, the retrieval is being designed for single layer ice clouds over open ocean water.

Cirrus cloud↗

NASA NTRS2012

Simulation Tools Model Icing for Aircraft Design

Here s a simple science experiment to try: Place an unopened bottle of distilled water in your freezer. After 2-3 hours, if the water is pure enough, you will notice that it has not frozen. Carefully pour the water into a bowl with a piece of ice in it. When it strikes the ice, the water will instantly freeze. One of the most basic and commonly known scientific facts is that water freezes at around 32 F. But this is not always the case. Water lacking any impurities for ice crystals to form around can be supercooled to even lower temperatures without freezing. High in the atmosphere, water droplets can achieve this delicate, supercooled state. When a plane flies through clouds containing these droplets, the water can strike the airframe and, like the supercooled water hitting the ice in the experiment above, freeze instantly. The ice buildup alters the aerodynamics of the plane - reducing lift and increasing drag - affecting its performance and presenting a safety issue if the plane can no longer fly effectively. In certain circumstances, ice can form inside aircraft engines, another potential hazard. NASA has long studied ways of detecting and countering atmospheric icing conditions as part of the Agency s efforts to enhance aviation safety. To do this, the Icing Branch at Glenn Research Center utilizes a number of world-class tools, including the Center s Icing Research Tunnel and the NASA 607 icing research aircraft, a "flying laboratory" for studying icing conditions. The branch has also developed a suite of software programs to help aircraft and icing protection system designers understand the behavior of ice accumulation on various surfaces and in various conditions. One of these innovations is the LEWICE ice accretion simulation software. Initially developed in the 1980s (when Glenn was known as Lewis Research Center), LEWICE has become one of the most widely used tools in icing research and aircraft design and certification. LEWICE has been transformed over the years from strictly a research tool to one used routinely by industry and other government agencies. Glenn contractor William Wright has been the architect of this development, supported by a team of researchers investigating icing physics, creating validation data, and ensuring development according to standard software engineering practices. The program provides a virtual simulation environment for determining where water droplets strike an airfoil in flight, what kind of ice would result, and what shape that ice would take. Users can enter geometries for specific, two-dimensional cross sections of an airfoil or other airframe surface and then apply a range of inputs - different droplet sizes, temperatures, airspeeds, and more - to model how ice would build up on the surface in various conditions. The program s versatility, ease of use, and speed - LEWICE can run through complex icing simulations in only a few minutes - have contributed to it becoming a popular resource in the aviation industry.

Source record↗

NASA NTRS2026

Ice in Convective Storm Environments: Assessing Impacts of Microphysics on Simulated Reflectivities

Satellite radar retrievals of clouds and precipitation rely on assumptions about the microphysical properties of hydrometeors such as particle size distributions (PSDs) and massdimensional relationships, which have been shown to vary in distinct environments. A deeper understanding of linkages between mass-dimensional relationships, ice crystal shape, and radar reflectivities across cloud and precipitation regimes is necessary for developing new retrievals for upcoming satellite radar missions, including the INvestigation of Convective UpdraftS (INCUS), as well as future missions that will feature space-borne radars observing clouds, convection, and precipitation. This study investigates ice microphysical characteristics through aircraft in-situ and remote sensing observations from two convective events during the Mid-latitude Continental Convective Clouds Experiment (MC3E) in the Southern Great Plains, and tests implications for ice particle habit in forward modeled radar observations. During MC3E, the Ka/Ku- band High Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) was onboard the NASA ER-2 aircraft, while in-situ measurements were taken onboard the University of North Dakota Citation. In-situ PSDs and particle shape information from optical array probe data are used to forward model radar reflectivities from particle scattering databases and are compared against HIWRAP reflectivities. Various particle combinations can be used to find agreement with HIWRAP observations, and the forward modeled reflectivities were sensitive to particle type. Varying the riming on the aggregate and graupel particles resulted in larger than 10 dB differences in reflectivities. The in-situ and radar observations imply the occurrence of aggregation, size sorting and lofting particles.

Julia A. Shates↗

NASA NTRS1982

The mechanisms of fine particle generation and electrification during Mount St. Helens volcanic eruption

Microscopical investigation of volcanic ash collected from ground stations during Mount St. Helens eruptions reveal a distinctive bimodel size distribution with high concentrations of particle ranges at (1) 200-100 microns and (2) 20-0.1 microns. Close examination of individual particles shows that most larger ones are solidified magma particles of porous pumice with numerous gas bubbles in the interior and the smaller ones are all glassy fragments without any detectable gas bubbles. Elemental analysis demonstrates that the fine fragments all have a composition similar to that of the larger pumice particles. Laboratory experiments suggest that the formation of the fine fragments is by bursting of glassy bubbles from a partially solidified surface of a crystallizing molten magma particle. The production of gas bubbles is due to the release of absorbed gases in molten magma particles when solubility decreases during phase transition. Diffusion cloud chamber experiments strongly indicate that sub-micron volcanic fragments are highly hygroscopic and extremely active as cloud condensation nuclei. Ice crystals also are evidently formed on those fragments in a supercooled (-20 C) cloud chamber. It has been reported that charge generation from ocean volcanic eruptions is due to contact of molten lava with sea water. This seems to be insufficient to explain the observed rapid and intense lightning activities over Mount St. Helens eruptions. Therefore, a hypothesis is presented here that highly electrically charged fine solid fragments are ejected by bursting of gas bubbles from the surface of a crystallizing molten magma particles.

Cheng, R. J.↗

NASA NTRS2004

Examination of Surface Roughness on Light Scattering by Long Ice Columns by Use of a Two-Dimensional Finite-Difference Time-Domain Algorithm

Natural particles such as ice crystals in cirrus clouds generally are not pristine but have additional micro-roughness on their surfaces. A two-dimensional finite-difference time-domain (FDTD) program with a perfectly matched layer absorbing boundary condition is developed to calculate the effect of surface roughness on light scattering by long ice columns. When we use a spatial cell size of 1/120 incident wavelength for ice circular cylinders with size parameters of 6 and 24 at wavelengths of 0.55 and 10.8 mum, respectively, the errors in the FDTD results in the extinction, scattering, and absorption efficiencies are smaller than similar to 0.5%. The errors in the FDTD results in the asymmetry factor are smaller than similar to 0.05%. The errors in the FDTD results in the phase-matrix elements are smaller than similar to 5%. By adding a pseudorandom change as great as 10% of the radius of a cylinder, we calculate the scattering properties of randomly oriented rough-surfaced ice columns. We conclude that, although the effect of small surface roughness on light scattering is negligible, the scattering phase-matrix elements change significantly for particles with large surface roughness. The roughness on the particle surface can make the conventional phase function smooth. The most significant effect of the surface roughness is the decay of polarization of the scattered light.

Sun, W.↗

NASA NTRS2020

Particle Size Measurements from the 2018 Honeywell Uncertified Research Engine Test in the NASA Propulsion Systems Laboratory

The particle size measurements from the Honeywell Uncertified Research Engine Icing Test in the NASA Propulsion Systems Laboratory conducted in 2018 are presented. This work focuses on describing the experimental arrangement, the processing and analysis methods, and final results for select cases acquired during ice crystal cloud conditions. The measurements presented will include data acquired by two High Speed Imaging instruments located both upstream and downstream of the fan, in the engine bypass section. Experimental results demonstrate the expected downward shift in the particle size distribution as the cloud passes through the engine fan and the ice particles break-up. This work also demonstrates the feasibility of acquiring particle size distributions in the environment of a running engine.

Engine icing↗

NASA NTRS2000

Occurrence of Ice Supersaturations, Ice Clouds, and Ternary Aerosols in the Arctic Lowermost Stratosphere

Relative humidity, aerosol concentration, and ice crystals all have important impacts on chemistry and radiative transfer in the lowermost stratosphere. In this study, we have combined SOLVE measurements with meteorological analyses to investigate the statistics of humidity, aerosols, and clouds in the arctic lower stratosphere. First, we will present a statistical analysis of relative humidity with respect to ice in the lowermost stratosphere, used on the DC-8 in situ measurements. We will show examples of ice supersaturation well within the stratosphere. Generally, these cases were associated with extremely low temperatures near the tropopause. Next, we will discuss the climatological occurrence frequency of tropopause temperatures low enough for ice saturation even with typically low stratospheric water vapor mixing ratios. Really, we will examine case studies of ice clouds observed in the lowermost stratosphere during SOLVE. We will discuss the possible origin of these clouds (i.e., precipitation from higher type II PSCs, injection of tropospheric air into the lower stratosphere, etc.).

Jensen, Eric↗

DOE OSTI2021

Ice and Supercooled Liquid Water Distributions over the Southern Ocean based on In Situ Observations and Climate Model Simulations

Three climate models are evaluated using in situ airborne observations from the Southern Ocean Clouds, Radiation, Aerosol Transport Experimental Study (SOCRATES) campaign. The evaluation targets cloud phases, microphysical properties, thermodynamic conditions, and aerosol indirect effects from –40°C to 0°C. Compared with 580-s averaged observations (i.e., 100 km horizontal scale), the Community Atmosphere Model version 6 (CAM6) shows the most similar result for cloud phase frequency distribution and allows more liquid-containing clouds below –10°C compared with its predecessor—CAM5. The Energy Exascale Earth System Model (E3SM) underestimates (overestimates) ice phase frequencies below (above) –20°C. CAM6 and E3SM show liquid and ice water contents (i.e., LWC and IWC) similar to observations from –25°C to 0°C, but higher LWC and lower IWC than observations at lower temperatures. Simulated in-cloud RH shows higher minimum values than observations, possibly restricting ice growth during sedimentation. As number concentrations of aerosols larger than 500 nm (Na 500 ) increase, observations show increases of LWC, IWC, liquid, and ice number concentrations (N liq , N ice ). Number concentrations of aerosols larger than 100 nm (Na 100 ) only show positive correlations with LWC and N liq . From –20°C to 0°C, higher aerosol number concentrations are correlated with lower glaciation ratio and higher cloud fraction. From –40°C to –20°C, large aerosols show positive correlations with glaciation ratio. CAM6 shows small increases of LWC and N liq with Na 500 and Na 100 . E3SM shows small increases of N ice with Na 500 . Altogether, CAM6 and E3SM underestimate aerosol indirect effects on ice crystals and supercooled liquid droplets over the Southern Ocean.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1989

Cirrus crystal nucleation by homogeneous freezing of solution droplets

A numerical model consisting of a system of differential equations is used to study cirrus crystal nucleation in a rising parcel containing a distribution of cloud condensation nuclei. The evolution of the particle population and the thermodynamic variables in the parcel are examined. The results suggest that, if homogeneous freezing is not considered, liquid water should be detected below -40 C. If homogeneous freezing is considered, the rapid growth of ice crystals and vapor depletion prevent water saturation from being reached. It is shown that the likelihood of a droplet being frozen is increased by lower temperatures, larger droplet diameter, or lower solution density.

Heymsfield, Andrew J.↗

DOE OSTI2026

Aerosol-deep convection interaction based on joint cell-thermal tracking in Large Eddy Simulations during the TRACER campaign

In cumulus clouds, aerosol concentrations control cloud droplet concentrations, modifying cloud radiative properties, precipitation processes, and cloud electrification. However, mechanisms of aerosol-deep convection interactions are not well understood due to complex cloud dynamics and microphysics. We investigate the interaction of aerosols with isolated deep convection using Large Eddy Simulations of two cases during the TRacking Aerosol Convection interactions ExpeRiment (TRACER) near Houston, Texas, using a joint cell-thermal tracking algorithm. Cumulus thermals are droplet generators, since supersaturation and droplet nucleation coincide with thermal centers, where the strongest updrafts occur. Primary ice crystal formation does not take place inside thermals, but at layers where previous thermals detrained moisture. As subsequent thermals containing supercooled droplets penetrate these layers, hail and graupel form at or near these thermals. Higher aerosol concentrations result in higher droplet concentrations that suppress drizzle, delay warm rain processes, and transport more moisture aloft. This increases snow and ice amount, as well as graupel and hail, leading to more lightning. Polluted thermals initiate at slightly higher altitudes, and are slightly larger and faster, suggesting a weak invigoration. We also find more thermals per cell, but fewer isolated cells, since convection is more aggregated and intense, especially near the end of the 24 h simulation. Non-linear mesoscale feedback likely triggered by temperature and moisture responses to aerosol-thermal interactions causes the aggregation. Time-lagged aerosol-reinitialization experiments show that the mesoscale response is the predominant forcing for the invigoration. These changes happen within one day, on a smaller scale than previously suggested.

54 ENVIRONMENTAL SCIENCES↗