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Understanding cirrus clouds using explainable machine learning
- Kai Jeggle, David Neubauer, Gustau Camps-Valls, Ulrike Lohmann
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- Environmental Data Science / Volume 2 / 2023
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- 04 July 2023, e19
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Cirrus clouds are key modulators of Earth’s climate. Their dependencies on meteorological and aerosol conditions are among the largest uncertainties in global climate models. This work uses 3 years of satellite and reanalysis data to study the link between cirrus drivers and cloud properties. We use a gradient-boosted machine learning model and a long short-term memory network with an attention layer to predict the ice water content and ice crystal number concentration. The models show that meteorological and aerosol conditions can predict cirrus properties with R2 = 0.49. Feature attributions are calculated with SHapley Additive exPlanations to quantify the link between meteorological and aerosol conditions and cirrus properties. For instance, the minimum concentration of supermicron-sized dust particles required to cause a decrease in ice crystal number concentration predictions is 2 × 10−4 mg/m3. The last 15 hr before the observation predict all cirrus properties.
References
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 368-381
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3 - Atmospheric dynamics
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 68-94
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Index
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 382-391
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List of symbols and acronyms
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp xvi-xxvi
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6 - Cloud droplet formation and Köhler theory
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 155-185
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Summary
In this chapter the details of phase transitions, nucleation and cloud droplet formation are discussed. Some phase transitions require a nucleation process, for instance, ice nucleation or the gas-to-particle conversion of aerosol particles. Other phase transitions, such as cloud droplet formation, do not require a nucleation process: cloud droplets form on soluble or hydrophilic aerosol particles such as sulfate, sea salt (soluble) and mineral dust (hydrophilic) particles. These particles acquire water by condensation and hence develop a liquid phase at conditions where the nucleation of pure water droplets from vapor cannot occur. Although no nucleation process initiates the existence of a cloud droplet, the concept of nucleation is a prerequisite for the understanding of cloud droplet formation and is therefore introduced in Section 6.1. The mathematical formulation of nucleation leads to the Kelvin equation (Section 6.2). Hygroscopic growth (Section 6.3) and Raoult's law (Section 6.4) consider the contribution of aerosol particles to cloud droplet formation. Combining Raoult's law with Kelvin's equation yields the Köhler theory describing the activation of a deliquesced aerosol particle – forming an aqueous solution droplet – into a cloud droplet (Section 6.5). The chapter ends with a discussion of measurements on cloud condensation nuclei (CCN), the subset of aerosol particles that can be activated into cloud droplets (Section 6.6).
Nucleation
From thermodynamics of phase transitions (Chapter 2), we do not obtain information about how a new phase is initiated. One possibility for the initiation of a new phase is a nucleation process; nucleation denotes a phase transition where a cluster of a thermodynamically stable phase forms and grows within the surrounding metastable parent phase. In the case of aerosol nucleation this refers to the formation of a liquid phase out of the gas phase. Ice crystal formation requires the initiation of the ice phase within the liquid or vapor phase.
The nucleation of a new phase requires the parent phase to be in a metastable state, which can be a supersaturated vapor or a supercooled liquid in the atmospheric context. The transition to the new, stable, phase is not spontaneous but is inhibited by an intermediate maximum in the Gibbs free energy, a so-called energy barrier. This energy barrier is of crucial importance, as it governs the kinetics and therefore the likelihood of a specific nucleation process under given atmospheric conditions.
10 - Storms and cloud dynamics
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 285-322
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Summary
Convective precipitation originates from cumulus clouds, namely cumulus congestus (Cu con) and cumulonimbus (Cb); (Table 1.1, Figure 1.4b and Chapter 9). The prerequisite for precipitation from cumulus clouds is that the hydrometeors grow to precipitation size in a short time. This is most efficiently achieved in Cb, which by definition consists of water and ice and has the largest vertical extent and highest vertical velocities (Table 1.3). Precipitation can also fall from Cu con, but its precipitation is typically less heavy and in the form of short showers, whereas Cb has the potential to turn into a thunderstorm, owing to the coexistence of water and ice, which is a prerequisite for the formation of lightning and thunder (Section 10.2). The various types of thunderstorms can generally be grouped into three categories as follows.
Ordinary, isolated or pulse thunderstorms, which consist of only a single convective cell and last approximately 40 minutes to one hour.
Multicell thunderstorms, which consist of a number of cells in different stages of development and last for several hours.
Supercell thunderstorms, which also last several hours but, in contrast with multicell thunderstorms, consist of only one self-maintaining cell.
Supercell storms are the rarest type of thunderstorm, but the most violent.Whether a given thunderstorm turns out to be a single cell (Section 10.1), multicell or supercell (Section 10.3), depends on both the vertical shear of the horizontal wind (hereafter just referred to as the wind shear) and the static stability of the environment. The largest convective storms are mesoscale convective systems (Section 10.4). They include a large variety of mesoscale systems, such as squall lines, mesoscale convective complexes and tropical cyclones, which we will discuss in terms of their formation and transition into extratropical cyclones (Section 10.5). This chapter ends with a discussion of the observed changes in tropical and extratropical cyclones in the last decades and projected future changes.
Isolated thunderstorms and hail
An ordinary or isolated thunderstorm is also called a pulse storm because of its short duration (Table 1.3) and because it may generate another ordinary thunderstorm as it weakens. Thus this type of thunderstorm appears to occur in pulses. It undergoes a characteristic life cycle and is often accompanied by graupel and hail.
12 - Impact of aerosol particles and clouds on climate
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 335-367
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Summary
Aerosol particles affect the climate by scattering solar radiation and by absorbing solar and terrestrial radiation, as discussed in Chapter 11. In addition they modify cloud properties by acting as CCN (Chapter 6) and INPs (Chapter 8). These so-called aerosol–cloud interactions play a key role in the anthropogenic radiative forcing of the climate system (Boucher et al., 2013). They continue to remain the most uncertain of all forcing agents and are still associated with a low level of scientific understanding. The impact of aerosol particles on the radiative budget at TOA is expressed in terms of the radiative forcing (RF) as discussed in Section 12.1. The aerosol RF is negative and hence partly offsets the greenhouse gas warming.
Clouds have a large effect on Earth's radiative budget (Chapter 11). Vice versa, clear-sky radiative cooling and solar heating destabilize the atmosphere and thus drive convection and cloud formation. Also, the emission of longwave radiation from a cloud top destabilizes the air above it, allowing the cloud to grow vertically, while the absorption of solar radiation within the cloud can cause its dissipation. The climate impact of clouds depends on the altitude and the geographical locations where they form. These two aspects will be discussed in Section 12.2 together with the change in global cloud cover over the last 40–60 years.
The increase in greenhouse gases causes Earth's temperature to increase. In addition to the radiative forcing due to greenhouse gases, feedbacks also operate in the climate system in such a way that the water vapor mixing ratio increases or snow and ice melt. These changes in turn cause the temperature to increase even more; thus, they are positive feedbacks. How they work, and the role clouds play in a warmer climate, is the topic of Section 12.3.
Given that aerosol particles partly offset greenhouse gas warming, it has been suggested that aerosol particles should be deliberately injected into the atmosphere to cool the climate. This so-called climate engineering involving aerosol particles and clouds is discussed in Section 12.4.
Aerosol radiative forcing
Aerosol particles affect the climate directly by scattering and absorbing radiation as well as by modifying cloud properties, as shown in Figure 12.1 as quantified in terms of the RF in W m-2.
5 - Atmospheric aerosol particles
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 115-154
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Summary
Thus far we have discussed the macrophysical requirements for cloud formation. Since each cloud droplet forms on an aerosol particle, these particles will be discussed in this chapter. An aerosol is defined as a dispersed system of solid or liquid particles suspended in a carrier gas, in our case air. Although technically the term “aerosol” includes both the particles and the carrier gas, in atmospheric science it is common to use the term “aerosols” just for the solid or liquid particles and to neglect the carrier gas.
Aerosol particles can be classified in terms of their chemical composition and according to their physical characteristics such as size, shape, density and mass, as will be discussed in Section 5.1. Because aerosol particles vary in size from a few nanometers to several micrometers, it has been found useful to describe their number, surface and mass concentrations in terms of size ranges, called modes, using log-normal size distributions (Section 5.2). Aerosol particles can be directly emitted into the atmosphere or form by gasto- particle conversion. These mechanisms and the emissions of the most important aerosol types are the subject of Section 5.3. Aerosol particles are removed from the atmosphere by dry and wet scavenging (Section 5.4). The difference between their formation and removal rates determines their abundance (burden) in the atmosphere as well as their atmospheric lifetime. Their lifetime is strongly dependent on their size but also on the altitude in the atmosphere (Section 5.5). The chapter concludes with a summary of the most important aerosol processes in Section 5.6.
Chemical and physical characteristics of aerosol particles
Depending on the type of particle, aerosols have differing properties that determine their role in atmospheric processes. A number of fundamental properties can be used to characterize aerosol particles; these include chemical and physical properties.
Chemical characteristics
The chemical characterization of an aerosol particle at the level of chemical compounds would usually be too complicated. Whereas a sulfuric acid particle nucleated from its gaseous precursors can be described by a single chemical formula, a mineral dust particle or a combustion-generated carbonaceous particle consists of a vast multitude of different chemical compounds.
9 - Precipitation
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 251-284
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Summary
In the previous three chapters we discussed on the microscale how cloud droplets and ice crystals form and how they can grow and reach precipitation size. In this chapter we take a more macroscopic perspective and start with an overview of observed precipitation rates (Section 9.1). Raindrop and snowflake size distributions have been observed to be exponential, as discussed in Section 9.2. At Earth's surface, rainfall and snowfall rates are measured with rain gauges. In the atmosphere they are estimated from radar reflectivity. In fact, radars are irreplaceable for the short-term forecast, called “nowcast”, of precipitation events. We discuss how estimates of precipitation rates can be obtained from radar measurements and how radar images can be interpreted (Section 9.3). Next we discuss how precipitation can be classified into stratiform and convective precipitation (Section 9.4) and explain its mesoscale structure (Section 9.5). This chapter concludes with a discussion of the geographical distribution of precipitation in the present climate, how it has changed since the 1950s and how it is projected to change until the end of this century (Section 9.6).
Precipitation rates
As discussed in Chapter 7, precipitation in warm clouds involving only the liquid phase forms via collision–coalescence. Collision–coalescence is favored in clouds which have a large liquid water content with relatively few cloud droplets. Therefore clouds which form precipitation involving only the liquid phase are mainly convective clouds over the tropical oceans. However, even in the tropics only 31% of the total precipitation is “warm rain” (Lau and Wu, 2003). Warm-phase precipitation often produces light precipitation (drizzle) because it is less efficient than precipitation formation involving the ice phase. An exception are tropical islands such as Hawaii, where significant warm rain has been observed due to orographic forcing.
After hydrometeors are formed, they can continue to grow by collisions with other hydrometeors such as cloud droplets (Section 7.2) or ice crystals (Section 8.3) as illustrated in Figures 8.18 and 8.19. All collision processes that involve hydrometeors of either different sizes or different phases are summarized as growth by accretion (Section 8.3.3). Depending on the phases of the hydrometeors involved, accretion leads to raindrops, snowflakes, graupel or hailstones. Regardless of how precipitation is initiated inside clouds, over a large part of Earth's surface it reaches the ground as rain because the average surface temperature of Earth is +15°C.
8 - Microphysical processes in cold clouds
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 218-250
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Summary
As discussed in Chapter 7, warm rain formation is not sufficient to explain most global precipitation. Globally 50% of all precipitation events of more than 1 mm d-1 involve the formation and growth of ice crystals somewhere in the cloud (Field and Heymsfield, 2015). In the tropics, precipitation via the ice phase accounts for 69% of the total precipitation (Lau and Wu, 2003). In mid-latitudes, warm rain is even less prevalent, especially over land. Here it accounts for less than 10% of the total precipitation because of the smaller cloud droplets in continental clouds as compared with marine clouds (Mülmenstädt et al., 2015).
Once a cloud extends to altitudes where the temperature is below 0°C, ice crystals may form by the homogeneous freezing of cloud droplets or by the heterogeneous ice nucleation, as discussed below in Section 8.1. Heterogeneous ice nucleation takes place with the help of ice nucleating particles (INPs) and can occur via different pathways depending on the temperature and supersaturation (Section 8.1.2).
Once nucleated, the ice crystals can grow by diffusion from the vapor phase (Section 8.3). As long as they keep their identity, they are called pristine crystals. They can also grow by aggregation to form snowflakes or by riming to form graupel and hail. The counterpart of raindrop break-up is ice multiplication, which also occurs upon collision and drastically enhances the number concentration of ice crystals in the cloud. The melting of ice and snow and the sublimation of snow (Section 8.4.2) complete our discussion of these microphysical processes; a summary is given in Section 8.5.
Ice nucleation
As discussed in Section 6.1, nucleation denotes a phase transition where a cluster of a thermodynamically stable phase forms and grows within the surrounding metastable parent phase. Ice crystals can form by the direct deposition of water vapor on an INP (deposition nucleation) or by the freezing of a cloud droplet or solution droplet (Section 6.4). The term solution droplet refers to a liquid aerosol, such as sulfuric acid or sodium chloride, that has undergone hygroscopic growth (Section 6.3). A cloud droplet, however, is sufficiently large that the amount of solute is negligible and it can be regarded as a pure water droplet.
Frontmatter
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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2 - Thermodynamics
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- An Introduction to Clouds
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- 23 June 2016, pp 26-67
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Summary
Thermodynamics describes the behavior of matter on a macroscopic scale, looking at it as a continuum rather than the sum of its atomic or molecular constituents. In this chapter we review the thermodynamics necessary for the understanding of cloud formation. We start by defining in Section 2.1 some fundamental terms, which will be used throughout the textbook. We discuss the physical laws that describe processes in dry air and introduce the concept of air parcels in Section 2.2. Since thermodynamic processes that involve adiabatic changes can best be visualized with the help of thermodynamic charts, the use of tephigrams is introduced in Section 2.3.We then move to moist air, i.e. a mixture of dry air and water vapor. Water is a unique substance because it exists in all three phases (ice, liquid water and water vapor) in the atmosphere. The transitions between its different phases are crucial for the understanding of liquid and ice cloud formation and microphysical processes inside clouds. They are the subject of Section 2.4. We end the chapter by extending the laws introduced for dry air to moist air, in order to analyze how water vapor influences certain processes; this enables us to predict the conditions under which a cloud is formed (Section 2.5).
Basic definitions
Thermodynamic states and variables of state
The aim of thermodynamics is to describe the spatially and temporally averaged properties of macroscopic systems of gases, liquids or solids. The concepts of thermodynamics are suitable for systems containing a number of molecules on the order of the Avogadro constant (NA = 6.022 x1023 mol-1) and changing slowly in time. Considering a large, macroscopic, quantity Q of a substance also justifies the assumption of negligible edge effects, which is usually made in thermodynamics.
In reality the quantity Q consists of a large number of molecules N each of whose instantaneous state can be described by 6N coordinates (three for the spatial position x, y, z, and three for the momentum components of each molecule, mu, mv, mw). Such a state is called a “microstate” of the system. For most practical purposes, to describe a system in terms of its microstates is too complicated, i.e. to solve the equations of motion with 6N degrees of freedom. Furthermore, it would be meaningless because microstates cannot be directly observed.
11 - Global energy budget
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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4 - Mixing and convection
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- 23 June 2016, pp 95-114
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Summary
In this chapter we discuss the mixing of air masses (Section 4.1) and convection (Section 4.2). Mixing can either occur isobarically, i.e. at constant pressure, or adiabatically, when air parcels repeatedly move up- and downward. The isobaric mixing of different air masses can lead to fog formation when the air is sufficiently moist. In contrast, adiabatic mixing occurs when air parcels or air masses are mixed with the potential temperature constant. Adiabatic mixing can be observed when thermals rise from a hot surface in summer or when smoke from chimneys disperses.
Convection in the atmosphere refers to vertical motions of air parcels. Atmospheric convection may be divided into (i) (mechanically) forced convection and (ii) free convection, which is also referred to as thermal, gravitational or buoyant convection. An example of forced convection is the lifting of air along a cold or warm front or because of the orography. Here we are mainly interested in buoyant convection. This is best described in terms of the elementary parcel theory, which we will use to introduce the convectively available potential energy (CAPE) and the level of free convection (LFC). Because elementary parcel theory is rather simplified, its modifications, including entrainment, aerodynamic drag, compensating downdrafts and the weight of hydrometeors, are discussed at the end of this chapter.
Mixing
Isobaricmixing
Isobaric mixing provides one possibility for fog formation, creating the so-called “mixing fog”. Mixing fog is most commonly observed if warm and cold air is mixed, when both air masses are close to saturation with respect to liquid water. An example of mixing fog is “steam fog” (Figure 4.1), which can often be observed in autumn when cool air moves over warm water. When the cool air mixes with warm moist air over the water, the warm moist air cools. If its RH reaches 100% then condensation sets in and fog forms. Other examples of isobaric mixing occur when you see your breath on a cold winter day or the steam above a hot cup of tea.
Let us consider two air masses with mass, temperature and specific humidity given by m1, T1, qv1 and m2, T2, qv2. If these air masses are well mixed at constant pressure, we obtain a mixture that is the mass-weighted mean of their individual properties.
7 - Microphysical processes in warm clouds
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- 23 June 2016, pp 186-217
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Summary
In Chapter 6 we discussed how cloud droplets are activated. Both before and after a droplet reaches its critical size, it grows by the uptake of water molecules from the vapor phase. Water vapor molecules are transported by diffusion towards the droplet where condensation takes place at the droplet surface. This is called diffusional or condensational growth (Section 7.1). Additional processes involving collisions with other droplets are required for the droplets to reach precipitation size, since diffusion of water vapor alone can be too slow to produce precipitation-sized drops on the time scales observed in the atmosphere. This growth is referred to as growth by collision–coalescence. It is induced by the difference in terminal velocity of the larger and smaller drops. Diffusional growth (and evaporation) and growth by collision–coalescence (Section 7.2), along with evaporation and the breakup of raindrops, which limits raindrops to a maximum equivalent radius of around 5 mm (Section 7.3), are discussed in this chapter.
Figure 7.1 shows typical sizes for a CCN, a cloud droplet, a drizzle drop and a raindrop, along with their typical concentrations in the marine atmosphere: typical marine CCN concentrations range between 102 and 103 cm-3 while that for cloud droplets is only around 102 cm-3 (Kubar et al., 2009). This shows that for typical supersaturations (0.1%–1.6%) in the atmosphere not all CCN are activated to become cloud droplets (Chapter 6), i.e. the number of cloud droplets is less than the number of CCN.
After activation a cloud droplet must grow by two orders of magnitude in radius in order to reach the size of a raindrop, with typical radius 1 mm. Put differently, it requires a million cloud droplets to form one raindrop. Raindrops are large enough to overcome the updraft velocities within a cloud and leave the cloud as precipitation. Their large sizes explain their typical concentration, of only 10-4 cm-3 (100 m-3), which is six orders of magnitude smaller than that of cloud droplets. Drizzle drops have sizes in between cloud droplets and raindrops, with radii between 25 µm and 0.25 mm (Table 1.2). Their typical concentration in marine clouds is 0.1 cm-3, which is three orders of magnitude smaller than that of cloud droplets (Wood et al., 2009) and three orders of magnitude larger than that of raindrops.
1 - Clouds
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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- 23 June 2016, pp 1-25
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Summary
Clouds are fascinating to watch for their myriad of shapes. They are also scientifically challenging because their formation requires both knowledge about the large-scale meteorological environment as well as knowledge about the microphysical processes involved in cloud droplet and ice crystal formation.
In this chapter we introduce clouds. In Section 1.1 we highlight their importance for Earth's energy budget and the hydrological cycle. In Section 1.2 we discuss the main cloud types, with their macroscopic properties, as defined by the World Meteorological Organization (WMO), and other, less common cloud types. After this macroscopic description of clouds, we turn to their microphysical properties in Section 1.3.
Definition and importance of clouds
A cloud is an aggregate of cloud droplets or ice crystals, or a combination of both, suspended in air. For a cloud to be visible, the cloud particles need to exist in a sufficiently large concentration. This definition has its origin in operational weather forecasting, where observers indicate the fraction of the sky that is covered with clouds. A more precise definition of cloud cover is used when the information is derived from satellite data, which nowadays provide a global picture of the total cloud cover. Satellites define clouds on the basis of their optical depth, which is the amount of radiation (in our case from the Sun) removed from a light beam by scattering and absorption (Chapter 12).
There are several global cloud climatologies; most of them derived from satellite data, so-called satellite retrievals (Stubenrauch et al., 2009). In the global annual average, roughly 70% of Earth's surface is covered with clouds. The cloud cover is 5%–15% higher over oceans than over land (Table 1.1). The oldest satellite data are from the International Satellite Cloud Climatology Project (ISCCP) (Rossow and Schiffer, 1999), which has cloud information dating back to 1983. The ISCCP satellite picture (Figure 1.1) shows that clouds cover more than 90% of the sky in the storm tracks of the Southern Ocean and the semi-permanent Aleutian and Icelandic low pressure regions in the north Pacific and north Atlantic, respectively, as shown in Figure 1.2.
Preface
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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Summary
Clouds, in their various forms, are a vital part of our lives. They are a crucial part of the global hydrological cycle, redistributing water to Earth's surface in the form of precipitation. In addition, they are a key element for the global energy budget since they interact with both shortwave (solar) and longwave (terrestrial) radiation. These so-called cloud–radiation interactions depend strongly on the type of cloud. Clearly clouds affect the global climate and thus understanding clouds is an important factor for future climate projections. The effects on Earth's energy budget and on the hydrological cycle both depend on processes on the microphysical scale, encompassing the formation of cloud droplets, ice crystals, raindrops, snowflakes, graupel and hailstones.
Establishing an understanding of clouds and precipitation requires a knowledge of the environment in which they form, i.e. the atmosphere, with all the gases and airborne particles present there. The latter are usually referred to as aerosol particles and encompass a wide range of solid and liquid particles suspended in air. Some aerosol particles can act as nuclei to form cloud droplets or ice crystals and thus initiate the formation of clouds or change their phase from liquid to solid. Thus they influence the microphysical properties of clouds. In turn aerosol particles are removed from the atmosphere when clouds precipitate. In order to gain a complete picture of the behavior of clouds in the atmosphere, the strong interplay between aerosol particles and clouds requires one to tackle the subject in an integrated approach.
This book is intended to offer a fundamental understanding of clouds in the atmosphere. It is primarily written for students at an advanced undergraduate level who are new to the field of atmospheric sciences. The content of this book evolved from the atmospheric physics lectures held at ETH Zurich. This book is intended to serve students with a multidisciplinary background as an introduction to cloud physics, assuming that most readers will have a basic understanding of physics.
The book is organized into 12 chapters, each focusing on a particular topic. Chapter 1 introduces the major cloud types found in the atmosphere and discusses them from a macroscopic point of view. Chapters 2–4 focus on the meteorological conditions and atmospheric dynamics needed for cloud formation and the thermodynamic principles needed to describe atmospheric processes, including phase transitions.
Contents
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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Dedication
- Ulrike Lohmann, Felix Lüönd, Fabian Mahrt
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