Under typical marine conditions of about 80% relative humidity, evaporation of water from the ocean is an irreversible process accompanied by entropy production. In this article, equations are derived for the latent heat of irreversible evaporation and the related nonequilibrium entropy balance at the sea surface. To achieve this, linear irreversible thermodynamics is considered in a conceptual ocean evaporation model. The equilibrium thermodynamic standard TEOS-10, the International Thermodynamic Equation of Seawater—2010, is applied to irreversible evaporation under the assumption of local thermodynamic equilibrium. The relevance of local equilibrium conditions for irreversible thermodynamics is briefly explained. New equations are derived for the mass flux of evaporation and for the associated nonequilibrium enthalpies and entropies. The estimated entropy production rate of ocean evaporation amounts to 0.004 W m−2 K−1 as compared with the average terrestrial global entropy production of about 1 W m−2 K−1.

A sign error has been found in Equation (32) of the paper [...]JW=−Dfln1+SMW1−SMS+ln⁡ψfxV,T,p[...]

At an energy flux imbalance of about 1 W m−2, the ocean stores 90% of the heat accumulating by global warming. However, neither the causes of this nor the responsible geophysical processes are sufficiently well understood. More detailed investigations of the different phenomena contributing to the oceanic energy balance are warranted. Here, the role of low-level marine clouds in the air–sea interaction is analysed. TEOS-10, the International Thermodynamic Equation of State of Seawater—2010, is exploited for a rigorous thermodynamic description of the climatic trends in the lifted condensation level (LCL) of the marine troposphere. Rising sea surface temperature (SST) at a constant relative humidity (RH) is elevating marine clouds, cooling the cloud base, and reducing downward thermal radiation. This LCL feedback effect is negative and counteracts ocean warming. At the current global mean SST of about 292 K, the net radiative heat flux from the ocean surface to the LCL cloud base is estimated to be 24 W m−2. Per degree of SST increase, this net flux is expected to be enhanced by almost 0.5 W m−2. The climatic LCL feedback effect is relevant for the ocean’s energy balance and may be rigorously thermodynamically modelled in terms of TEOS-10 equations. LCL height may serve as a remotely measured, sensitive estimate for the sea surface’s relative fugacity, or conventional relative humidity.

In this study, we analyze the transition of a stable atmospheric boundary layer (ABL) with a low-level jet (LLJ) to a traditional stable ABL with a classic Ekman helix in the late-winter central Arctic. Vertical profiles in the ABL were measured with a hot-wire anemometer on a tethered balloon during a 15 h period in March 2018 in northeast Greenland. The tethered balloon allows high-resolution turbulence observations from the ground to the top of the ABL. The core of the LLJ was observed at about 150 m altitude, and its height and strength were associated with the temperature inversion. Increased turbulence was observed in the vicinity of the LLJ, but most of the turbulence does not reach down to the surface, thus decoupling the LLJ from the surface. Only when the LLJ collapses and the ABL again exhibits a more classical Ekman spiral is a coupling to the surface re-established. The LLJ might enhance both advective and turbulent vertical transport of passive tracers such as aerosol particles or moisture in the often stably stratified Arctic ABL.

Adopted by the Intergovernmental Oceanographic Commission (IOC) of UNESCO in 2010 and the International Union of Geodesy and Geophysics (IUGG) in 2011, the Thermodynamic Equation of Seawater 2010 (TEOS-10) is the current geophysical standard for the thermodynamic properties of humid air, seawater and ice. TEOS-10 equations for evaporation and sublimation enthalpies are derived mathematically from the thermodynamic potential of a »sea air« model, denoting a multi-phase equilibrium composite of the geophysical aqueous mixtures. To estimating evaporation rates from the ocean, Dalton equations in various versions are implemented in numerical climate models. Some of those equations appear to be biased on climatic time scales if compared with proper thermodynamic driving forces. Such equations may lead to a spurious amplification of the hydrological cycle and an implied effect of cooling oceans. As an unbiased alternative, Dalton equations are proposed in terms of TEOS-10 relative fugacity (RF) or its conventional relative humidity (RH) approximations. With respect to RH uncertainties or trends, the substantial sensitivity of the evaporation flux may be estimated to be as much as 5 W m−2 per 1 %rh. Within a maximum error of only 0.04 %rh, sea-surface RF may be approximated in terms of dew-point or frost-point temperatures using a simple formula.

There are a couple of reasons to stimulate a discussion about the definition of clouds. One reason is that the American Meteorological Society (AMS) and the World Meteorological Organization (WMO) define clouds differently, and that in two aspects. AMS defines clouds as visible objects, and WMO as perceivable objects. Furthermore, AMS includes all minute particles independent of their nature and composition whereas WMO considers only such minute particles that consist of water, ice, or a mixture of both. Additionally, the so- called invisible or subvisible clouds are perceivable objects in the definition of WMO but not of AMS. Clouds can be observed by humans and be detected by active and passive sensors from ground and space. The detection limits of instruments span more than two orders of magnitude in visible optical thickness ranging from about 0.001 from satellite lidar (in case of horizontal and vertical averaging or 0.07 for single lidar shots) to about 0.3 to 0.45 for multispectral satellite imaging spectrometers. Human observers see clouds when their optical thickness is larger than about 0.03 at day and 0.05 at night. This paper gives a brief overview of cloud detection from ground and space and of the occurrence, characteristics, and impacts of subvisible clouds. Pros and cons of these definitions are discussed, followed by a proposal for a more precise definition. This definition is, like those of AMS and WMO, a one-parametric definition and does not cover all aspects of clouds.

Relative humidity (RH) is a fundamental quantity used in many fields of engineering and science, and in particular in meteorology and climate research. Relative fugacity (RF) and, equivalently, relative activity of water vapour in humid air have recently been proposed as a physically well-founded, unambiguous common metrological reference quantity for several conventional but mutually inconsistent definitions of RH. The RF definition is valid is valid under real-gas conditions and above boiling and sublimation temperatures. While differences between RH and RF mostly remain within uncertainties of typical present-day RH measurements, such systematic discrepancies are expected to be of substantial climatological relevance. Consequently, interdisciplinary harmonisation of RH definitions is overdue within the SI framework. Dew-point and frost-point temperatures are preferred measurands in humidity metrology using, for example, chilled-mirror hygrometers. Here, relations are presented for estimating RF from those temperatures, based on equations of state of the 2011 IUGG(6) standard TEOS-10, the 'international thermodynamic equation of seawater-2010'. Recommendations are given for numerically computing RF using the open-source TEAS-10 SIA library(6). The asymptotic limiting laws of RF for nearly saturated humid air exhibit the familiar form of Clausius-Clapeyron-like equations, despite departing from ideal-gas assumptions. Under various practical conditions, these simple equations may cover the full humidity range with only minor residuals compared to the full numerical TEAS-10 solution for RF.

The differences between one classical and three state-of-the-art formulations of the mass density of humid air were quantified. Here, we present both the calculi for direct determination of the humid-air mass density employing the virial form of the thermodynamic equation of state, and a sufficiently accurate look-up-table for the quick-look determination of the humid-air mass density, which is based on the advanced Thermodynamic Equation of Seawater 2010.

In the words of Heinrich Hertz in 1885, the Earth is a “gigantic steam engine”. On average, of the planet’s cross section exposed to sunlight, 72 % belong to the global ocean. With a delay of only 2-3 months, most of the heat absorbed there is released by evaporation rather than by thermal radiation. Water vapour is the dominating “greenhouse gas” of the marine troposphere with a typical relative humidity (RH) of 80 % at the surface. Observing the heat transport across the ocean surface permits insight in the powerhouse of the “steam engine”, controlled by the RH at the surface, a quantity that is often considered the “Cinderella” among the climate data. RH of the troposphere also controls cloud formation that is equally fundamental as challenging for climate research. As a precise and perfectly consistent thermodynamic basis for the description of such processes, the new oceanographic standard TEOS-10 was introduced by UNESCO/IOC in 2010 and IUGG in 2011. Its equations cover all thermodynamic properties of liquid water, seawater, ice and humid air, as well as their mutual equilibria and phase transitions. For harmonisation of the inconsistent RH definitions of humid air between meteorology and climatology, the relative fugacity has been defined as a physically more reasonable RH substitute that does not rely on the approximation of ideal gases. Doi: 10.28991/HEF-2021-02-02-06 Full Text: PDF

The algorithm for and results of a newly developed multivariate non-parametric model, the Euclidean distance model (EDM), for the hourly disaggregation of daily climate data are presented here. The EDM is a resampling method based on the assumption that the day to be disaggregated has already occurred once in the past. The Euclidean distance (ED) serves as a measure of similarity to select the most similar day from historical records. EDM is designed to disaggregate daily means/sums of several climate elements at once, here temperature ( T ), precipitation ( P ), sunshine duration ( SD ), relative humidity ( rH ), and wind speed ( WS ), while conserving physical consistency over all disaggregated elements. Since weather conditions and hence the diurnal cycles of climate elements depend on the weather pattern, a selection approach including objective weather patterns (OWP) was developed. The OWP serve as an additional criterion to filter the most similar day. For a case study, EDM was applied to the daily climate data of the stations Dresden and Fichtelberg (Saxony, Germany). The EDM results agree well with the observed data, maintaining their statistics. Hourly results fit better for climate elements with homogenous diurnal cycles, e.g., T with very high correlations of up to 0.99. In contrast, the hourly results of the SD and the WS provide correlations up to 0.79. EDM tends to overestimate heavy precipitation rates, e.g., by up to 15% for Dresden and 26% for Fichtelberg, potentially due to, e.g., the smaller data pool for such events, and the equal-weighted impact of P in the ED calculation. The OWPs lead to somewhat improved results for all climate elements in terms of similar climate conditions of the basic stations. Finally, the performance of EDM is compared with the disaggregation tool MELODIST (Förster et al. 2015). Both tools deliver comparable and well corresponding results. All analyses of the generated hourly data show that EDM is a very robust and flexible model that can be applied to any climate station. Since EDM can disaggregate daily data of climate projections, future research should address whether the model is capable to respect and (re)produce future climate trends. Further, possible improvements by including the flow direction and future OWP s should be investigated, also with regard to reduce the overestimation of heavy rainfall rates.

Subcooled water is the primordial matrix for ice embryo formation by homogeneous and heterogeneous nucleation. The knowledge of the specific Gibbs free energy and other thermodynamic quantities of subcooled water is one of the basic prerequisites of the theoretical analysis of ice crystallization in terms of classical nucleation theory. The most advanced equation of state of subcooled water is the IAPWS G12-15 formulation. The determination of the thermodynamic quantities of subcooled water on the basis of this equation of state requires the iterative determination of the fraction of low-density water in the two-state mixture of low-density and high-density subcooled water from a transcendental equation. For applications such as microscopic nucleation simulation models requiring highly frequent calls of the IAPWS G12-15 calculus, a new two-step predictor-corrector method for the approximative determination of the low-density water fraction has been developed. The new solution method allows a sufficiently accurate determination of the specific Gibbs energy and of all other thermodynamic quantities of subcooled water at given pressure and temperature, such as specific volume and mass density, specific entropy, isothermal compressibility, thermal expansion coefficient, specific isobaric and isochoric heat capacities, and speed of sound. The misfit of this new approximate analytical solution against the exact numerical solution was demonstrated to be smaller than or equal to the misprediction of the original IAPWS G12-15 formulation with respect to experimental values.

A recently developed thermodynamic theory for the determination of the driving force of crystallization and the crystal–melt surface tension is applied to the ice-water system employing the new Thermodynamic Equation of Seawater TEOS-10. The deviations of approximative formulations of the driving force and the surface tension from the exact reference properties are quantified, showing that the proposed simplifications are applicable for low to moderate undercooling and pressure differences to the respective equilibrium state of water. The TEOS-10-based predictions of the ice crystallization rate revealed pressure-induced deceleration of ice nucleation with an increasing pressure, and acceleration of ice nucleation by pressure decrease. This result is in, at least, qualitative agreement with laboratory experiments and computer simulations. Both the temperature and pressure dependencies of the ice-water surface tension were found to be in line with the le Chatelier–Braun principle, in that the surface tension decreases upon increasing degree of metastability of water (by decreasing temperature and pressure), which favors nucleation to move the system back to a stable state. The reason for this behavior is discussed. Finally, the Kauzmann temperature of the ice-water system was found to amount T K = 116 K , which is far below the temperature of homogeneous freezing. The Kauzmann pressure was found to amount to p K = − 212 MPa , suggesting favor of homogeneous freezing on exerting a negative pressure on the liquid. In terms of thermodynamic properties entering the theory, the reason for the negative Kauzmann pressure is the higher mass density of water in comparison to ice at the melting point.

Previous cloud chamber experiments on freezing of supercooled cloud droplets with single immersed, size-selected 400 nm and 800 nm kaolinite particles revealed a sigmoidal increase of the fraction of frozen cloud droplets with decreasing temperature in the range from 243 to 236 K. Assuming uniformity of the particle composition and horizontal homogeneity of the phase compatibility, applying classical nucleation theory (CNT), and fitting the microscopic "ice contact angle" to these experimental freezing probabilities disclosed a negative temperature coefficient of the ice contact angle, revealing an apparent increase of the cryophobia of the freezing catalyzer. On the basis of Derjaguin's thermomechanic concept of the disjoining pressure, a conceptual model is proposed that links the semi-empirical ice contact angle to its generating molecular interaction forces by extrapolating macroscopic relations to microscopic scales. Within the framework of a closure study with consideration of a comprehensive set of physical constraints for the water/ice/kaolinite system, this model is used to determine the residual molecular interaction force, which is necessary to reproduce the experimentally derived ice contact angles. The residual interaction force is on the order of magnitude of steric oscillation forces at the kaolinite/ice interfacial layer and corresponds to a temperature-dependent negative line tension of -(5-28)pN. The line tension behavior is discussed in the light of previous findings on heterogeneous water nucleation on solid surfaces and computer simulations of the water/ice/kaolinit system. Uncertainties originating from the employed model assumptions, especially interference due to interparticle variability are analyzed. Finally, observational requirements for a conclusive discrimination between inter- and intraparticle effects are discussed.

Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth's radiation balance, atmospheric water vapour is the strongest 'greenhouse' gas, and non-equilibrium relative humidity at the air–sea interface drives evaporation and latent heat export from the ocean. In this paper, we examine the climatologically relevant atmospheric relative humidity, noting fundamental deficiencies in the definition of this key observable. The metrological history of this quantity is reviewed, problems with its current definition and measurement practice are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures (BIPM), in cooperation with the International Association for the Properties of Water and Steam (IAPWS), along with other international organizations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions, such as are suggested here, for what are long-standing metrological problems.

Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth's radiation balance, atmospheric water vapour is the strongest 'greenhouse' gas, and non-equilibrium relative humidity at the air–sea interface drives evaporation and latent heat export from the ocean. On climatic time scales, melting ice caps and regional deviations of the hydrological cycle result in changes of seawater salinity, which in turn may modify the global circulation of the oceans and their ability to store heat and to buffer anthropogenically produced carbon dioxide. In this paper, together with three companion articles, we examine the climatologically relevant quantities ocean salinity, seawater pH and atmospheric relative humidity, noting fundamental deficiencies in the definitions of those key observables, and their lack of secure foundation on the International System of Units, the SI. The metrological histories of those three quantities are reviewed, problems with their current definitions and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures, BIPM, in cooperation with the International Association for the Properties of Water and Steam, IAPWS, along with other international organizations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for these long standing metrological problems in climatology.

Fugacity is considered the proper real-gas substitute for the partial pressure commonly used to describe ideal-gas mixtures. However, in several fields such as geophysics, meteorology, or air conditioning, partial pressure is still preferred over fugacity when non-equilibrium conditions of humid air are quantified. One reason may be that for ambient air, the deviations from ideal-gas behavior are small, another that explicit correlation equations for the fugacity of water vapor in humid air are scarce in the literature. This situation has improved with the publication of the new oceanographic standard TEOS-10, the International Thermodynamic Equation of Seawater 2010, which provides highly accurate values for the chemical potential and the fugacity of water vapor in humid air over wide ranges of pressure and temperature. This paper describes the way fugacity is obtained from the fundamental equations of TEOS-10, and it derives computationally more convenient virial approximations for the fugacity, consistent with TEOS-10. Analytically extracted from the TEOS-10 equation of state of humid air, equations for the 2nd and 3rd virial coefficients are reported and compared with correlations available from the literature. The virial fugacity equation is valid in the temperature range between \({-}80\,^{\circ }\hbox {C}\) and +200 \(^{\circ }\hbox {C}\) at pressures up to 5 MPa, and between \({-}130\,^{\circ }\hbox {C}\) and +1000 \(^{\circ }\hbox {C}\) at low pressures such as those encountered in the terrestrial atmosphere at higher altitudes.

Thermodynamic and kinetic peculiarities of nucleation, deliquescence and efflorescence transitions in the ensemble of droplets formed on soluble condensation nuclei from a solvent vapor have been considered. The interplay of the effects of solubility and the size of condensation nuclei has been analyzed. Activation barriers for the deliquescence and phase transitions and for the reverse efflorescence transition have been determined as functions of the relative humidity of the vapor-gas atmosphere, initial size, and solubility of condensation nuclei. It has been demonstrated that, upon variations in the relative humidity of the atmosphere, the crossover in thermodynamically stable and unstable variables of the droplet state takes place. The physical meaning of stable and unstable variables has been clarified. The kinetic equations for establishing equilibrium and steady distributions of binary droplets have been solved. The specific times for relaxation, deliquescence and efflorescence transitions have been calculated.

The multiscale model system LM-MUSCAT consists of two online coupled codes. The operational forecast model LM (Local Model) of the German Weather Service and the chemistry transport model MUSCAT (Multi-Scale Atmospheric Transport Model). The coupler provides MUSCAT with meteorological fields like temperature, humidity and density from LM. An improved coupling scheme was developed to optimize the parallel efficiency of the model system.