Temperature dependence of the elastic constants for biaxial nematic liquid crystals

The elastic constants K ij of the Frank-Oseen energy density for uniaxial nematic liquid crystals depend on the Maier-Saupe order parameter S and hence on temperature. Longa et al. recently used an extended Landau-Ginzburg-de Gennes theory to expand the functions K ij(S) up to fourth order in S. Here, a similar procedure is applied for the elastic energy density of biaxial nematic liquid crystals. The three chiral and 15 achiral constants are expressed as fourth-order polynomials in the order parameter S and the degree of biaxiality T. Via the temperature dependence of the quantities S and T also the temperature dependence of the elastic constants is fixed.Die elastischen Konstanten K ij der Frank-Oseen-Energiedichte für einachsige nematische Flüssigkristalle hängen über den Maier-Saupe-Ordnungsparameter von der Temperatur ab. Longa et al. haben kürzlich eine erweiterte Theorie nach Landau-Ginzburg-de Gennes benutzt, um die Funktionen K ij(S) bis zur vierten Ordnung nach S zu entwickeln. Hier wird ein ähnliches Verfahren bei der elastischen Energiedichte von biaxialen nematischen Flüssigkristallen angewandt. Die drei chiralen und 15 nichtchiralen Konstanten werden als Polynome vierten Grades in Ordnungsparameter S und Biaxialitätsparameter T ausgedrückt. Durch deren Temperaturabhängigkeit ist damit das Temperaturverhalten der elastischen Konstanten bestimmt

Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory

Phase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ∂Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Using angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau-de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermo-dynamically correct way of establishing contact between the generalized de Gennes elastic free energy and other theories, like those of Oseen-Frank or Meyer, is proposed by applying fluctuation theory. Thus, the degeneracy of splay and bend elastic constants is removed even when these are calculated from the standard de Gennes free energy. Restrictions on higher order elastic constants are also obtained by comparing mean field relations and stability conditions with available experimental data

Impacts of ocean wave‐dependent momentum flux on global ocean climate

Accurate knowledge of air‐sea fluxes of momentum, heat, and carbon are central to fully understanding the evolution of the climate system. The role of ocean surface waves has been largely overlooked in global climate models despite the growing body of work elucidating the influence of ocean wave state on air‐sea fluxes. Here we account for the impact of ocean surface waves on global ocean climate using a global ocean model through implementation of wave‐dependent momentum fluxes. Wave‐dependent momentum fluxes improve the simulation of observed ocean heat content (OHC) through increasing the trend in OHC over the last three decades. Specifically, the larger increase in OHC is attributable to increased net heat flux in the Southern Hemisphere (SH). These results highlight the important role of accounting for wave‐dependent momentum transfer in terms of both simulating future climate and understanding changes over the recent historical period

Transient response of the global mean warming rate and its spatial variation

The Earth has warmed over the past century. The warming rate (amount of warming over a given period) varies in time and space. Observations show a recent increase in global mean warming rate, which is initially maintained in model projections, but which diverges substantially in future depending on the emissions scenario followed. Scenarios that stabilize forcing lead to much lower warming rates, as the rate depends on the change in forcing, not the amount. Warming rates vary spatially across the planet, but most areas show a shift toward higher warming rates in recent decades. The areal distribution of warming rates is also changing shape to include a longer tail in recent decades. Some areas of the planet are already experiencing extreme warming rates of about 1 °C/decade. The fat tail in areal distribution of warming rates is pronounced in model runs when the forcing and global mean warming rate is increasing, and indicates a climate state more prone to regime transitions. The area-proportion of the Earth displaying warming/cooling trends is shown to be directly related to the global mean warming rate, especially for trends of length 15 years and longer. Since the global mean warming rate depends on the forcing rate, the proportion of warming/cooling trend areas in future also depends critically on the choice of future forcing scenario. Keywords: Climate variability, Climate projection, Transient response, Extreme warmin

Heat stored in the Earth system:where does the energy go?

Human-induced atmospheric composition changes cause a radiative imbalance at the top of the atmosphere which is driving global warming. This Earth energy imbalance (EEI) is the most critical number defining the prospects for continued global warming and climate change. Understanding the heat gain of the Earth system – and particularly how much and where the heat is distributed – is fundamental to understanding how this affects warming ocean, atmosphere and land; rising surface temperature; sea level; and loss of grounded and floating ice, which are fundamental concerns for society. This study is a Global Climate Observing System (GCOS) concerted international effort to update the Earth heat inventory and presents an updated assessment of ocean warming estimates as well as new and updated estimates of heat gain in the atmosphere, cryosphere and land over the period 1960–2018. The study obtains a consistent long-term Earth system heat gain over the period 1971–2018, with a total heat gain of 358±37 ZJ, which is equivalent to a global heating rate of 0.47±0.1 W m−2. Over the period 1971–2018 (2010–2018), the majority of heat gain is reported for the global ocean with 89 % (90 %), with 52 % for both periods in the upper 700 m depth, 28 % (30 %) for the 700–2000 m depth layer and 9 % (8 %) below 2000 m depth. Heat gain over land amounts to 6 % (5 %) over these periods, 4 % (3 %) is available for the melting of grounded and floating ice, and 1 % (2 %) is available for atmospheric warming. Our results also show that EEI is not only continuing, but also increasing: the EEI amounts to 0.87±0.12 W m−2 during 2010–2018. Stabilization of climate, the goal of the universally agreed United Nations Framework Convention on Climate Change (UNFCCC) in 1992 and the Paris Agreement in 2015, requires that EEI be reduced to approximately zero to achieve Earth's system quasi-equilibrium. The amount of CO2 in the atmosphere would need to be reduced from 410 to 353 ppm to increase heat radiation to space by 0.87 W m−2, bringing Earth back towards energy balance. This simple number, EEI, is the most fundamental metric that the scientific community and public must be aware of as the measure of how well the world is doing in the task of bringing climate change under control, and we call for an implementation of the EEI into the global stocktake based on best available science. Continued quantification and reduced uncertainties in the Earth heat inventory can be best achieved through the maintenance of the current global climate observing system, its extension into areas of gaps in the sampling, and the establishment of an international framework for concerted multidisciplinary research of the Earth heat inventory as presented in this study. This Earth heat inventory is published at the German Climate Computing Centre (DKRZ, https://www.dkrz.de/, last access: 7 August 2020) under the DOI https://doi.org/10.26050/WDCC/GCOS_EHI_EXP_v2 (von Schuckmann et al., 2020)

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

Global Oceans

Global Oceans is one chapter from the State of the Climate in 2019 annual report and is avail-able from https://doi.org/10.1175/BAMS-D-20-0105.1. Compiled by NOAA’s National Centers for Environmental Information, State of the Climate in 2019 is based on contr1ibutions from scien-tists from around the world. It provides a detailed update on global climate indicators, notable weather events, and other data collected by environmental monitoring stations and instru-ments located on land, water, ice, and in space. The full report is available from https://doi.org /10.1175/2020BAMSStateoftheClimate.1

State of the climate in 2018

In 2018, the dominant greenhouse gases released into Earth’s atmosphere—carbon dioxide, methane, and nitrous oxide—continued their increase. The annual global average carbon dioxide concentration at Earth’s surface was 407.4 ± 0.1 ppm, the highest in the modern instrumental record and in ice core records dating back 800 000 years. Combined, greenhouse gases and several halogenated gases contribute just over 3 W m−2 to radiative forcing and represent a nearly 43% increase since 1990. Carbon dioxide is responsible for about 65% of this radiative forcing. With a weak La Niña in early 2018 transitioning to a weak El Niño by the year’s end, the global surface (land and ocean) temperature was the fourth highest on record, with only 2015 through 2017 being warmer. Several European countries reported record high annual temperatures. There were also more high, and fewer low, temperature extremes than in nearly all of the 68-year extremes record. Madagascar recorded a record daily temperature of 40.5°C in Morondava in March, while South Korea set its record high of 41.0°C in August in Hongcheon. Nawabshah, Pakistan, recorded its highest temperature of 50.2°C, which may be a new daily world record for April. Globally, the annual lower troposphere temperature was third to seventh highest, depending on the dataset analyzed. The lower stratospheric temperature was approximately fifth lowest. The 2018 Arctic land surface temperature was 1.2°C above the 1981–2010 average, tying for third highest in the 118-year record, following 2016 and 2017. June’s Arctic snow cover extent was almost half of what it was 35 years ago. Across Greenland, however, regional summer temperatures were generally below or near average. Additionally, a satellite survey of 47 glaciers in Greenland indicated a net increase in area for the first time since records began in 1999. Increasing permafrost temperatures were reported at most observation sites in the Arctic, with the overall increase of 0.1°–0.2°C between 2017 and 2018 being comparable to the highest rate of warming ever observed in the region. On 17 March, Arctic sea ice extent marked the second smallest annual maximum in the 38-year record, larger than only 2017. The minimum extent in 2018 was reached on 19 September and again on 23 September, tying 2008 and 2010 for the sixth lowest extent on record. The 23 September date tied 1997 as the latest sea ice minimum date on record. First-year ice now dominates the ice cover, comprising 77% of the March 2018 ice pack compared to 55% during the 1980s. Because thinner, younger ice is more vulnerable to melting out in summer, this shift in sea ice age has contributed to the decreasing trend in minimum ice extent. Regionally, Bering Sea ice extent was at record lows for almost the entire 2017/18 ice season. For the Antarctic continent as a whole, 2018 was warmer than average. On the highest points of the Antarctic Plateau, the automatic weather station Relay (74°S) broke or tied six monthly temperature records throughout the year, with August breaking its record by nearly 8°C. However, cool conditions in the western Bellingshausen Sea and Amundsen Sea sector contributed to a low melt season overall for 2017/18. High SSTs contributed to low summer sea ice extent in the Ross and Weddell Seas in 2018, underpinning the second lowest Antarctic summer minimum sea ice extent on record. Despite conducive conditions for its formation, the ozone hole at its maximum extent in September was near the 2000–18 mean, likely due to an ongoing slow decline in stratospheric chlorine monoxide concentration. Across the oceans, globally averaged SST decreased slightly since the record El Niño year of 2016 but was still far above the climatological mean. On average, SST is increasing at a rate of 0.10° ± 0.01°C decade−1 since 1950. The warming appeared largest in the tropical Indian Ocean and smallest in the North Pacific. The deeper ocean continues to warm year after year. For the seventh consecutive year, global annual mean sea level became the highest in the 26-year record, rising to 81 mm above the 1993 average. As anticipated in a warming climate, the hydrological cycle over the ocean is accelerating: dry regions are becoming drier and wet regions rainier. Closer to the equator, 95 named tropical storms were observed during 2018, well above the 1981–2010 average of 82. Eleven tropical cyclones reached Saffir–Simpson scale Category 5 intensity. North Atlantic Major Hurricane Michael’s landfall intensity of 140 kt was the fourth strongest for any continental U.S. hurricane landfall in the 168-year record. Michael caused more than 30 fatalities and $25 billion (U.S. dollars) in damages. In the western North Pacific, Super Typhoon Mangkhut led to 160 fatalities and$6 billion (U.S. dollars) in damages across the Philippines, Hong Kong, Macau, mainland China, Guam, and the Northern Mariana Islands. Tropical Storm Son-Tinh was responsible for 170 fatalities in Vietnam and Laos. Nearly all the islands of Micronesia experienced at least moderate impacts from various tropical cyclones. Across land, many areas around the globe received copious precipitation, notable at different time scales. Rodrigues and Réunion Island near southern Africa each reported their third wettest year on record. In Hawaii, 1262 mm precipitation at Waipā Gardens (Kauai) on 14–15 April set a new U.S. record for 24-h precipitation. In Brazil, the city of Belo Horizonte received nearly 75 mm of rain in just 20 minutes, nearly half its monthly average. Globally, fire activity during 2018 was the lowest since the start of the record in 1997, with a combined burned area of about 500 million hectares. This reinforced the long-term downward trend in fire emissions driven by changes in land use in frequently burning savannas. However, wildfires burned 3.5 million hectares across the United States, well above the 2000–10 average of 2.7 million hectares. Combined, U.S. wildfire damages for the 2017 and 2018 wildfire seasons exceeded $40 billion (U.S. dollars)