From turbulence to cloud formation : modelling the aerosol-cloud interactions

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Acknowledgements

The work presented in this thesis was mainly done at the Finnish Meteorolog- ical Institute in Helsinki andfinalized at the Atmospheric Research Centre of Eastern Finland of the FMI in Kuopio. I am very grateful to my su- pervisors Heikki Järvinen and Petri Räisänen for giving me the opportunity to work with climate modelling and for their excellent advice and guidance throughout this work. I also thank Yrjö Viisanen and Ari Laaksonen for providing the research facilities and resources that made this work possible.

The Academy of Finland and the Finnish Academy of Science and Letters are acknowledged for theirﬁnancial support.

There are many people who have helped me with scientiﬁc as well as practi- cal issues and whose help has been priceless for making this work succesful.

I would like to thank Ewan O’Connor, Antti Hellsten, Antti-Ilari Partanen and Leif Backmann for all their help. Thanks are due also to Hannele Korho- nen, Veli-Matti Kerminen, Tommi Bergman and to the joint FMI/University earth system modelling group as well as to the FMI climate modelling group for their support. In addition I thank all the people who co-authored the papers inluded in this thesis for their much needed comments and input. This thesis was pre-examined by Professors Johannes Quaas and Kari Lehtinen to whom I express my gratitude for their eﬀorts and interest to this work.

For many discussions, encouragement and friedship I thank Tea Thum, Joni- Pekka Pietikäinen, Svante Hendriksson, Panu Lahtinen and Toni Viskari as well as all the people at the coffee table. As I have been employed in Kuopio for about a year now, I thank my new bosses Harri Kokkola and Sami Ro- makkaniemi, with whom I was involved already during my PhD studies, as well as everyone in ISI for taking me in and having such a nice atmosphere around the office.

Finally, warm thoughts and gratitude go to my parents and sister for their continuous support and to Sindi for her love and caring.

Kuopio, February 2015 Juha Tonttila

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4.1 Measurements . . . 21 4.2 Statistical properties of vertical velocity . . . 22 4.3 Parameterizing vertical velocity for cloud activation . . . 25 5 Subcolumn representation of cloud microphysics and CDNC 29 5.1 Impacts on cloud properties . . . 30 5.2 Impacts on anthropogenic aerosol eﬀects . . . 33 6 Review of papers and the author’s contribution 38

7 Discussion and conclusions 40

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List of publications

I Tonttila, J., O’Connor, E. J., Niemelä, S., Räisänen, P., Järvinen, H.:

Cloud base vertical velocity statistics: a comparison between an atmospheric mesoscale model and remote sensing observations. Atmos.

Chem. Phys., 11, 9207-9218, doi:10.5194/acp-11-9207-2011, 2011.

II Tonttila, J., Räisänen, P., Järvinen, H.: Monte Carlo-based subgrid parameterization of vertical velocity and stratiform cloud microphysics in ECHAM5.5-HAM2. Atmos. Chem. Phys., 13, 7551-7565, doi:10.5194/acp-13-7551-2013, 2013.

III Tonttila, J., O’Connor, E. J., Hellsten, A., Hirsikko, A., O’Dowd, C., Järvinen, H., Räisänen, P.: Turbulent structure and scaling of the inertial subrange in a stratocumulus-topped boundary layer observed by a Doppler lidar. Atmos. Chem. Phys. Discuss., 14, 24119-24148, doi:10.5194/acpd-14-24119-2014, 2014.

IV Tonttila, J., Järvinen, H., Räisänen, P.: Explicit representation of subgrid variability in cloud microphysics yields weaker aerosol indirect effect in the ECHAM5-HAM2 climate model. Atmos. Chem. Phys., 15, 703-714, doi:10.5194/acp-15-703-2015, 2015.

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1 Introduction

Clouds exert a significant radiative forcing on the Earth’s energy balance as they absorb and emit longwave (LW) thermal radiation as well as absorb and scatter the shortwave (SW) solar radiation. More specifically, the influence of clouds on the radiationfluxes depends strongly on the cloud type. Generally speaking, high-altitude cirrus clouds act to warm the climate. While the influence of cirrus clouds on SW radiation is weak, they efficiently absorb the outgoing LW radiation emitted at the surface and the lower atmosphere, and re-emit only a fraction of that energy due to their low temperature.

In effect, cirrus clouds thus mask out some of the outgoing LW radiation which explains their warming effect. Low-altitude clouds instead act to cool the climate. Unlike high-altitude clouds, they do not have as strong an impact on the outgoing LW radiation because their temperature is close to the surface temperature of the Earth and the lower atmosphere. However, they reflect significant amounts of solar radiation back to space due to their high albedo at SW wavelengths. Combining the effects of low- and high-level clouds, their global mean net radiative effect in the LW is 26.2 W m⁻² and

−47.3 W m⁻² in the SW (Stephens et al., 2012; Boucher et al., 2013). The total impact of all clouds on the Earth’s energy budget is therefore negative,

−21.1 W m⁻². The uncertainty in these estimates is on the order of a few W m⁻².

Compared to the magnitude of the current anthropogenic radiative forcing caused by increased atmospheric CO2 concentration (≈1.82 W m⁻², Myhre et al., 2013), even rather small changes in the properties of clouds or in their extent could yield signiﬁcant eﬀects in terms of the global climate.

Such changes can take place e.g. due to anthropogenic aerosol emissions.

Atmospheric aerosol particles, deﬁned as liquid or solid particles suspended in the atmosphere (Hinds, 1999), can act as condensation nuclei for cloud droplets as well as freezing nuclei for ice crystals in cold clouds. Therefore, changes in the amount and composition of aerosol particles emitted in the atmosphere can alter the cloud radiative properties and aﬀect the projections of anthropogenic climate change (Makkonen et al., 2012).

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The effects of aerosols on clouds, known as aerosol-cloud interactions, consti- tute a long-standing challenge in thefield of climate modelling. Cloud-related processes act at a very wide range of scales, extending from microscopic to scales of several hundreds of kilometers in the atmosphere. The difficulty of the subject then arises from the need to realistically reproduce the effects of these processes in global-scale climate models, which at the same time are severely constrained by limited computational resources.

The purpose of this thesis is to present an experimental climate model version where a stochastic subgrid framework is used as a basis for describing the small-scale variability in cloud microphysical processes, which is then used to improve the model representation of aerosol-cloud interactions. This work focuses on aerosol eﬀects in warm lower-tropospheric clouds (e.g. stratocumulus) and thus ice clouds are left beyond the scope of this thesis. The work also comprises investigation of the turbulent variation of vertical wind, which is a key subject in terms of modelling the formation of cloud droplets.

The main questions behind this work include

• What are the statistical properties of vertical motions in cloud-topped boundary layers and can they be adequately represented in atmospheric models?

• How does parameterizing the subgrid variability of cloud microphysical processes in a stochastic subgrid framework aﬀect the simulated present-day cloud properties?

• What is the impact of the subgrid variability in cloud microphysics on the simulated eﬀect of anthropogenic aerosols on clouds and radiation?

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2 Modelling tools

2.1 ECHAM5.5-HAM2

The primary research tool used in this thesis is the ECHAM5.5 general circulation model (GCM) (Roeckner et al., 2003, 2006), coupled with the second- generation aerosol module HAM2 (Zhang et al., 2012). ECHAM5.5 is a spectral model, i.e. the main prognostic variables (the atmospheric circulation in terms of vorticity and divergenceﬁelds, temperature, pressure and humidity) are solved in spectral space using spherical harmonic functions. The so-called model physics, i.e. parameterizations describing radiation, cloud processes, turbulence and surface processes, are solved in a regular Gaussian grid. For the vertical levels, the model uses a hybrid-sigma coordinate system, which follows the terrain close to the surface, and approaches isobaric coordinates at the highest model levels. The model top is set at the 10 hPa pressure level.

The HAM2-aerosol model dynamically prognoses the size distribution and composition of atmospheric aerosol particles coupled with the atmospheric conditions simulated by ECHAM5.5. The size distribution of the main aerosol species included in the model (sulphates, sea salt, mineral dust, black carbon and organic compounds) is represented by seven lognormal modes in the M7 aerosol microphysics model (Vignati et al., 2004) embedded inside HAM2. The M7 also solves the aerosol dynamical processes such as nucleation, condensational growth and coagulation. The aerosol properties simulated by HAM2 thus provide an interactive basis also for describing aerosol-cloud interactions in the coupled ECHAM5.5-HAM2 conﬁguration.

In addition to the interactive treatment of aerosols, the initial model version used inPapers IIand IVwas augmented by a stochastic cloud generator (SCG) (R¨ais¨anen et al., 2004) and the Monte-Carlo Independent Column Approximation-method (McICA) for radiation computations (Pincus et al., 2003). The SCG is an algorithm that divides each grid-column of the parent GCM to several subcolumns (50 are used in Papers II and IV) in which

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cloud structure is described based on statistical information about the subgrid distribution of total water amount (vapour + condensate) in the model grid box. The cloud fraction in each subcolumn at each model level is set to 0 or 1 and varying cloud liquid water content is assigned for the cloudy subcolumns at each model level. In the case of ECHAM5.5, the subgrid distribution of the total water is obtained from the Tompkins (2002) large-scale condensation scheme, based on a semiprognostic Beta-function.

The McICA radiation scheme employs the cloudy subcolumns for radiative transfer using the methods by Fouquart and Bonnel (1980) and Mlawer et al.

(1997) for shortwave and longwave calculations, respectively. McICA treats each subcolumn independently and they are randomly sampled to handle each sub-band in the spectral integration (Räisänen et al., 2007). Therefore, the method potentially adds statistical noise to the simulation, which, however, has been found to be negligible for climate simulations, except when the number of subcolumns is very low (Räisänen et al., 2005; Räisänen et al.

, 2008).

A distinct limitation of the implementation of the SCG-McICA framework into ECHAM5 described in R¨ais¨anen et al. (2007) is that the cloud droplet number concentration (CDNC) is given by parameterizations operating at GCM grid-scale and is thus assumed uniform inside the cloudy portion of a model grid-box. Accordingly, cloud microphysical processes do not account for any subgrid variability in that model version. Subgrid parameterized components for CDNC and cloud microphysics were implemented and tested inPapers II andIV, the results of which are summarized in Section 5 of this thesis.

All the simulations with ECHAM5.5-HAM2 used inPapers IIandIVwere performed with a relatively coarse T42 spectral resolution due to the computational expense of the HAM2 module. This corresponds to a horizontal grid spacing of about 2.8 degrees. 19 vertical levels in the hybrid-sigma coordinates between the surface and the model top were used. The sea surface temperatures were prescribed to their climatological monthly mean values, which simpliﬁes the interpretation of the model results.

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2.2 The numerical weather prediction model AROME

The AROME mesoscale numerical weather prediction (NWP) model (Seity et al., 2011) was used inPaper Ito quantify the statistics of cloud-base vertical velocities compared with observations from a Doppler radar. During the writing ofPaper I, the AROME was still in experimental use at the Finnish Meteorological Institute (FMI), and since then it has become an operational forecast model at the FMI. Similar to ECHAM5.5, AROME calculates the model dynamics in spectral space and switches to a regular spatial grid for calculation of model physics. The horizontal resolution of the model is 2.5 km. At such a high spatial resolution, deep convection can be resolved in the model grid instead of being parameterized as in the larger-scale models.

Moreover, unlike in most larger-scale models, a non-hydrostatic set of equa- tions is solved in AROME, allowing non-zero vertical acceleration of theﬂow which is important for resolving deep convective motions.

3 Aerosol-cloud interactions

3.1 Formation of cloud droplets

At the heart of this work is parameterizing the formation of cloud droplets and calculating the CDNC in GCMs. Cloud droplets are created through the process of nucleation, where molecules of supersaturated water vapour form stable clusters that can grow into droplets. Nucleation can generally occur as a homogeneous or heterogeneous process, of which only the latter is possible for water in atmospheric conditions. In homogeneous nucleation, water molecules inside the vapour collide as a result of their random relative motions to form clusters which can grow if the saturation ratio of the vapour is suﬃciently large. It turns out that preventing the initial cluster of water molecules from breaking requires a very large saturation ratio for water vapour (>2, Hinds, 1999)) because of the energy needed to support the surface tension of the emerging droplet. Such high saturation ratios never occur naturally in the atmosphere. This energetic constraint can be expressed as

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the Kelvin equation that gives the equilibrium saturation ratio over a curved surface, such as a spherical droplet (Pruppacher and Klett, 1997) (the smaller the radius of curvature, the larger the equilibrium supersaturation).

In the heterogeneous nucleation, the initial condensation of water occurs on the surface of existing aerosol particles in the atmosphere, that have suitable properties to act as cloud condensation nuclei (CCN). An eﬃcient CCN is (1) suﬃciently large and (2) at least partially consists of water soluble material, although also originally insolube particles can be transformed to be active CCN (for example due to ageing of the particles; Dusek et al., 2006; Shilling et al., 2007). In the case of soluble CCN, the particle dissolves as water condenses on it, forming a solution above which the equilibrium saturation ratio is typically lower than that for pure water, as described by Raoult’s law.

Combining the Kelvin eﬀect with Raoult’s law yields the K¨ohler equation, which gives the equilibrium saturation ratioSeqfor heterogeneously nucleated droplet as a function of the droplet diameterDp

ln(Seq) = A Dp − B

D³_p, (1)

whereAandBare coeﬃcients depending on the properties of water and the condensation nucleus.

Köhler curves derived from Eq. (1) are depicted schematically in Fig 1, where the equilibrium supersaturation over the droplet surface is given as a function of the droplet diameter. If the saturation ratio of water vapour is high enough, the droplet can grow past the peak of the curve, i.e. where the droplets become strongly dilute and Raoult effect becomes weak relative to the Kelvin effect. The droplet diameter corresponding to the peak in the Köhler curve is known as the critical diameter, above which the equilibrium saturation ratio decreases with increasing droplet diameter. Droplets larger than the critical diameter can then continue to grow spontaneously, without increasing the ambient water vapour saturation ratio. This type of formation of a stable droplet is known as the cloud droplet activation, as it is subsequently referred to in this thesis. The critical radius and the corresponding critical supersaturation required to activate a droplet depend on

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Figure 1: Schematic set of K¨ohler curves for consecutively larger soluble aerosol particles (Dp refers to the dry particle diameter) acting as CCN.

the properties of the aerosol particles. The smaller the initial aerosol particle, the larger water vapour supersaturation is needed for it to activate as CCN, as illustrated in Figure 1. Given that the formation of droplets and their subsequent growth after activation reduce the amount of water vapour due to condensation, and that there practically always is a suﬃcient number of particles capable to act as CCN, the water vapor supersaturation in the atmosphere does not usually exceed 1 %.

3.2 Indirect radiative eﬀects of aerosols

Aerosol particles impose their own radiative forcing on the Earth’s energy budget. This occurs directly by scattering and absorbing of SW and LW radiation by aerosols, which is relatively well known (Haywood and Boucher, 2000). In addition, aerosols aﬀect Earth’s radiation balance also indirectly by inﬂuencing cloud properties (Lohmann and Feichter, 2005). Although

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aerosols also affect other types of clouds, including deep convective and ice clouds (e.g. Hoose and Möhler, 2012; Koren et al., 2010), the focus ofPapers I-IVpresented in this thesis is on the low-level stratiform clouds that consist of liquid water droplets and have a strong influence on global climate (Chen et al., 2000).

The indirect effects of aerosols have been divided into two main subprocesses in the literature. First, increasing the number of CCN generally increases CDNC which increases the cloud albedo, given that the cloud liquid water content (LWC) is kept constant (Twomey, 1974). Thus, a larger portion of the incoming solar radiation is scattered back to space, reducing the amount of energy reaching the Earth’s surface. Second, it has been theorized (Al- brecht, 1989) that increasing CCN reduces the formation of drizzle and rain in warm clouds, thus increasing the LWC and cloud lifetime. Again, the impact is to reduce the net absorbed solar radiation at the Earth’s surface. Even though these conceptual models appear straightforward, in reality the magnitude and sometimes even the basic mechanism of the anthropogenic aerosol effects on cloud properties and radiation is rather difficult to disentangle because of a variety of non-linear feedbacks and overlapping effects (Ruckstuhl et al., 2010; Chen et al., 2011; Stevens and Feingold, 2009; Wang et al., 2012;

Hudson and Noble, 2014; Jiang and Wang, 2014). Moreover, uncertainty in the size distribution and composition of the aerosol particles themselves may yield results that are unexpected based on the simple archetypes of the indirect eﬀects (Lance et al., 2004; Roesler and Penner , 2010; Lehahn et al., 2011). Nevertheless, many studies have provided evidence of the aerosol indirect eﬀects (Feingold et al., 2003; Penner et al., 2004; Hegg et al., 2012), an interesting example being ship tracks (e.g. Baker and Peter, 2008; Lu et al., 2009), where the particles from ship exhaust cause local brightening in the stratocumulus clouds above the ocean.

Separating the aerosol indirect effects into different sub-processes is anything but unambiguous. Therefore, the radiative effects of anthropogenic aerosols studied inPaper IV are considered as the total indirect radiative effect of aerosols, thus including the changes in cloud albedo, lifetime, and precipita- tion formation caused by the aerosol-cloud interaction. This is achieved by

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calculating the radiativeﬂux perturbation between pre-industrial (PI) and present-day (PD) aerosol conditions (Lohmann et al., 2010; Makkonen et al., 2012), i.e.

Faie= (F_{P D}^{SW cre}+F_{P D}^{LW cre})−(F_{P I}^{SW cre}+F_{P I}^{LW cre}), (2) whereF^{SW cre} and F^{LW cre} are the shortwave and longwave cloud radiative effects, respectively. The results of the indirect radiative effect obtained this way are close to the concept ”Effective radiative forcing due to aerosol-cloud interactions“ adopted in the latest IPCC report (Boucher et al., 2013).

The latest best estimate of the global-mean total radiative effect of the anthropogenic aerosols (direct and indirect effects combined) based on expert knowledge is−0.9 W m⁻² (Boucher et al., 2013). Despite the fact that the knowledge of the aerosol-cloud interactions has increased substantially during the past years, this estimate is still subject to a large uncertainty, ranging from−0.1 W m⁻²to−1.9 W m⁻²(corresponding to a 5 to 95 % uncertainty range), and is therefore one of the great challenges in improving the projections of the climate change. In particular, estimates of the aerosol indirect effect differ quite substantially between models and observations as models tend to produce a stronger coupling between aerosols and cloud properties than observations (Quaas et al., 2009). The best estimate of the indirect radiative forcing of aerosols, supported by satellite measurements and expert knowledge, is−0.45 W m⁻², while the median forcing obtained from GCMs is−1.4 W m⁻² (Boucher et al., 2013). Although the reasons for this discrepancy are not well known, many explanations have been suggested. For example, non-adiabatic effects in clouds could offset the modelled aerosol- cloud interactions, as they contradict the assumptions in most current climate models (e.g. Romakkaniemi et al., 2009). The discrepancy between models and observations is further discussed inPaper IV.

3.3 Parameterizing cloud droplet activation in large- scale models

It was explained in Section 3.1 that the maximum supersaturationSmax for an air parcel and the size and composition of an aerosol particle are the key

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pieces of information needed to determine whether the particle will activate as CCN. The number of cloud droplets can therefore be physically calculated in atmospheric models if the size distribution and the chemical composition of the particle population as well as the thermodynamic conditions of the surrounding air are known. The maximum value of Eq. (1) is the critical supersaturationScrit for each particle size in the size distribution which is solved as (by the notation of Eq. 1)

Scrit=

�4A³

27B. (3)

The coeﬃcient B is proportional to the amount of soluble material in an aerosol particle. Thus, a larger number of moles of soluble material yields lowerScrit, as expected by the discussion in Section 3.1. It is then assumed in the parameterizations for cloud droplet activation that all particles for which Scrit < Smax activate as CCN. Therefore, calculating cloud droplet number concentration in atmospheric models depends ultimately on the estimation ofSmax, assuming that the properties of the aerosol particle population are known. According to the current paradigm,Smax is dictated by the balance between

• production of supersaturation by adiabatic cooling due to the ascending motion of an air parcel, and

• the sink of moisture due to condensation of water vapour on aerosol particles.

The former depends essentially on the vertical velocity of air.

Early parameterizations for calculating CDNC in GCMs were mainly empir- ical formulae relating the mass, or number of aerosol particles with vertical velocity, serving as a proxy for the production of supersaturation. A widely used example of such a parameterization is based on Lin and Leaitch (1997), where the number of newly formed droplets is given simply by

N_c^nucl= 0.1

� Naw w+αNa

�1.27

. (4)

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HereNa is the number concentration of aerosol particles, w is the vertical velocity andα= 0.023 cm⁴ s⁻¹is a constant based on observations (Lin and Leaitch, 1997).

In later years, more physically based formulations have been published, (to name but a few Abdul-Razzak and Ghan, 2000; Fountoukis and Nenes, 2005;

Ming et al., 2006; Kivek¨as et al., 2008). A thorough presentation and comparison between these and other parameterizations is given in Ghan et al.

(2011). These parameterizations are in general based on using diﬀerent ap- proximative methods and assumptions to solveSmaxfrom a budget equation for the water vapour saturation ratioS(Leaitch et al., 1986)

dS

dt =α(T)w−β(p, T)dql

dt, (5)

where α and β are functions of temperature T and pressure p, w is the vertical velocity andqlis the liquid water mixing ratio. Time is indicated as t. Theﬁrst term on the right hand side represents the increase in saturation ratio caused by adiabatic cooling and the second is the reduction inSdue to condensation of water vapour on the aerosol particles. Eq. (5) thus illustrates the importance of vertical velocity in estimation ofSmaxand ultimately in the calculation of CDNC. The model experiments inPapers IIandIVuse the solution method and parameterization by Abdul-Razzak and Ghan (2000) for multimodal lognormal aerosol size distribution. Additional details are also provided in Abdul-Razzak et al. (1998).

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4 Vertical motions in the atmosphere

As explained in Section 3.3, parameterizing the vertical velocity of air is an important factor in the calculation of cloud droplet activation due to its impact on Smax. Vertical motions in the atmosphere can be roughly divided into turbulent motions, strong convective up- and downdrafts and large- scale vertical motions that are associated with the circulation in transient synoptic weather systems and, in even larger scale, to the planetary general circulation. The vertical motions resolved by a typical global climate model mainly correspond to the two latter categories. However, in terms of cloud droplet activation in stratiform clouds, the main interest lies in the turbulent motions, taking place in scales down to a few meters. Therefore parameterizations are needed to account for the eﬀect of small-scale vertical motions in large-scale climate models with horizontal resolution typically on the order of 200 km. However, the same also holds true for regional-scale models, operating at horizontal resolutions down to a few kilometers. Such an example was described inPaper I, where the vertical velocityﬁelds resolved by the AROME weather prediction model operating at 2.5 km resolution were evaluated with observations from a Doppler radar. Even though AROME’s horizontal resolution is high enough to adequately resolve updraft-downdraft structure of deep convection, the vertical velocity for cloud activation in stratiform clouds should still be parameterized.

For the most part, turbulent motions take place in the boundary layer, which is the lowest portion of the troposphere. The thickness of the boundary layer varies from less than a hundred meters to a few kilometers, depending on the environmental conditions and the stability of the atmosphere. In stable conditions, which often take place close to the polar regions, it is sometimes very difficult to define a robust boundary layer height. Low-level clouds, such as stratocumulus, often reside at the top of a well-mixed boundary layer, which is typically separated from the free troposphere by a sharp temperature inversion (Stull, 1988). However, more complex boundary layer structures, such as decoupled mixed layers driven by turbulence generated due to cloud top radiative cooling (Harvey et al., 2013) are possible and impose significant challenges on representing the turbulent vertical motions in GCMs.

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4.1 Measurements

In order to understand the behaviour of vertical wind velocities and their statistical properties in the turbulent boundary layer, measurements are a critical source of information. At the same time, obtaining robust observations with good temporal and spatial coverage is not straightforward. Many observational studies have relied on instruments mounted on research aircraft, which enables measurements at different levels inside the boundary layer as well as inside clouds (e.g. Duynkerke et al., 1995; Nicholls, 1984, 1989; Rodts et al., 2003; Snider et al., 2003). Although generally useful, aircraft observations usually lack in spatial and temporal coverage, as most of the measurements are performed as parts of intensive campaigns cover- ing a limited time frame and spatial regime. Moreover, in order to study the vertical structure of the turbulent flow in the boundary layer, tempo- rally collocated measurements from consecutive altitudes are needed, which is difficult to achieve by in-situ observations.

Doppler cloud radars and lidars offer this capability and provide data at high enough temporal and spatial resolutions for robust investigations of turbulence properties (Gal-Chen et al., 1992; Banakh et al., 1999). The instruments are usually placed in a vertically pointed configuration in order to measure the entire vertical column simultaneously. The radial speed of the backscattering particles with respect to the instrument can be determined using the Doppler phenomenon, which in the case of a vertically pointed instrument provides a useful estimate of the vertical velocity of air. The quality of this estimate depends on the properties of the backscattering particles and the instrument. Small particles, i.e. aerosols and cloud droplets, are good tracers of the turbulentflow, while e.g. drizzle droplets are large enough to bias the vertical velocity estimates obtained by a Doppler cloud radar due to their fall speeds. This issue is somewhat alleviated with Doppler lidars.

Doppler cloud radars operate at millimeter wavelengths. At these wavelengths, the scattering from both the cloud and drizzle droplets lies within the Rayleigh regime, where the reﬂectivity factor is proportional to the sixth moment of the particle size distribution according to

Z=

�

D_p⁶n(Dp)dDp, (6)

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wheren(Dp) is the distribution of the particle number concentration as a function of the particle diameterDp. The vertical velocity measurement is weighted by the reﬂectivity, which causes the results to be dominated by the contribution of large particles, even if their number concentration is low. For lidar, cloud and especially drizzle droplets are much larger than the laser wavelength, so for them the scattering is in the geometric optics regime. The velocity measurements are weighted by the lidar backscatter power, which in case of large particles is proportional to the area of the particle cross- section, and thusD²_p. Hence, the Doppler velocity measurements from lidar are weighted more towards the peak in the particle size distribution, and thus smaller particles than with the radar (O’Connor et al., 2005). InPaper I a bias on the order of −0.1 to −0.2 m s⁻¹ caused by drizzle was seen in Doppler radar measurements. However, it was shown that the drizzle does not signiﬁcantly alter the retrieved vertical velocity variance, and thus further analysis was still meaningful.

Another advantage of the lidar is that, due to its sensitivity to aerosols, velocity measurements can often be obtained throughout the boundary layer depth, which is not obtained by cloud radars. In contrast, the lidar beam is quickly attenuated by clouds. Because of this, the lidar usually only sees the lowest levels inside even a thin stratocumulus cloud, whereas the radar can often observe multiple overlapping cloud layers.

4.2 Statistical properties of vertical velocity

The turbulent variability of vertical velocity in a stratocumulus-topped boundary layer can most often be described by a probability density function (PDF) with a mean close to 0 m s⁻¹and standard deviation (σw) on the order of 0.5−1.0 m s⁻¹ (Papers IandIII). With the exception of the mean, the statistical moments of vertical velocity are highly scale dependent, which has to be taken into account when analysing simulated or observed data.

This is demonstrated forσw in Figure 2, based on the analysis in Paper I. It is shown that the resolved grid-scale vertical velocity sampled at the cloud-base in the AROME model drastically underestimates the width of

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the vertical velocity PDF as compared to radar measurements. The results suggest that model grid spacing even below a hundred meters is required for σwto be accurately sampled, which is why simpliﬁed assumptions about the distribution of small-scale variability of vertical velocity are necessary even in relatively high-resolution models.

Modelling studies often assume a simple Gaussian PDF to describe the vertical velocity variability in the boundary layer (e.g. Paper IIand Ghan et al., 1997). However, non-Gaussian features, most notably non-zero skewness, have been observed (Hogan et al., 2009; Ansmann et al., 2010; Lenschow et al., 2012). In its simplest form, the physical interpretation for the skewness of vertical velocity is that, for positive skewness, vigorous and narrow updrafts are balanced by weaker and widespread downdrafts, and vice versa.

Another interpretation is that positive skewness indicates upwards vertical transport of turbulent kinetic energy. Consequently, positive skewness is often observed in convective boundary layers, typically driven by buoyancy generated due to the heating of the surface by solar radiation. Negative skewness has been observed as well, mostly in stratocumulus topped boundary layers, where it has been attributed to turbulent mixing driven by cloud top radiative cooling. It has also been shown that the structure of the cloud- driven mixed layer closely resembles an upside-down convective boundary layer extending downwards from the cloud deck (Hogan et al., 2009). An example of stratocumulus-driven turbulent boundary layer is shown in Figure 3, where the proﬁles of vertical velocity statistics clearly show a region below the cloud deck with negative skewness and the peak ofσw close to the cloud deck indicated by the attenuated backscatter of the lidar. These measurements were made with the Finnish Meteorological Institute’s Doppler lidar at Mace Head observatory in coastal Ireland in early 2012, and were analysed in Paper III. The case comprised both coupled and decoupled boundary layer structure, although cloud-top radiative cooling was the dominant source of mixing throughout the analysed period. The impact of cloud top radiative cooling on the boundary layer dynamics is a common phenomenon for the marine stratocumulus-topped boundary layer, especially during night-time, when the eﬀect is not compensated by absorbed solar radiation at cloud top (Fang et al., 2014).

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�2.0^�1.5^�1.0^�0.5 0.0 0.5 1.0 1.5 2.0 [m s^�¹]

10^�² 10^�¹ 10⁰ 10¹

Frequency density [s m

�1 ]

Lindenberg

Figure 2: Comparison of the vertical velocity probability distribution width at cloud base between the AROME model (solid black line), Doppler radar measurements in their native resolution (dash-dotted line) and those aver- aged to the 2.5 km length scale (grid resolution of AROME; grey line). Figure taken fromPaper I.

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Paper IIIalso analysed the scaling of the inertial subrange in coupled and decoupled cloud driven mixed layers. The hypothesis behind this investigation was that the maximum wavelength that belongs to the inertial subrange would depend on the thickness of the decoupled layer. The inertial subrange can be identiﬁed from the power spectrum of vertical velocity as the wavelengths for which the spectral density follows the Kolmogorov’s powerlaw.

This appears as a−5/3-slope in the logarithmic scale, shown schematically in Figure 4. Physically, it depicts the range of scales for turbulent eddies, over which a cascade of turbulent kinetic energy takes place according to the similarity theory (Stull, 1988). In other words, energy input in the large- scale eddies is balanced out by the dissipation of turbulent energy in the smallest eddies due to viscous forces. Consequently, knowing the cut-off wavelengths of the inertial subrange is important e.g. for calculating the turbulence dissipation rate (O’Connor et al., 2010) or the turbulent kinetic energy from Doppler measurements. It was concluded in Paper III that the inertial subrange presents significant changes in its cut-off length-scale related to transitions between coupled and decoupled mixing and changes in the turbulent intensity of the cloud-driven layer. However, no robust scaling according to the fractional depths of the cloud driven and surface based mixing regimes was found. Nevertheless, the scaling does provide information about the structure of the boundary layer in complex situations and may thus be useful as an additional diagnostic, as well as for screening data for analysis and derived observational products.

4.3 Parameterizing vertical velocity for cloud activa- tion

The most widely used methods to parameterize the eﬀects of small-scale variability of vertical velocity in GCMs can be divided into two main groups:

• Calculating an eﬀective vertical velocity which is a single value assumed to be valid for the entire grid-cell of the model,

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Figure 3: Time-height cross-sections of the lidar backscatter, vertical velocity along with its standard deviation and skewness (σwandγw, respectively) and the turbulence dissipation rate for a two-day case with stratocumulus-topped boundary layer. Figure taken fromPaper III.

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Figure 4: Schematic representation of a typical vertical velocity power spectrum displaying the inertial subrange as the region with a -5/3-slope (red dashed line) in logarithmic coordinates. kis the wavenumber andS(k) is the powerspectrum density. λ0 is the wavelength where the slope of the spectrum deviates from the -5/3-powerlaw and thus represents the largest scale of motion inside the inertial subrange. Figure taken fromPaper III.

• a statistical representation for the subgrid variability of vertical velocity using a PDF.

The former has been regarded as thede facto standard since the introduction of the parameterization in Lohmann et al. (1999) in the ECHAM model family. A common feature for the state-of-the-art parameterizations of cloud activation in large-scale models according to the current paradigm is that they assume cloud droplet formation to take place only in regions with upwards vertical motion due to adiabatic cooling. The parameterizations of

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vertical velocity for cloud activation are thus generally designed to account only for the positive branch of the turbulent vertical motions.

In ECHAM5.5-HAM2, the eﬀective vertical velocity for stratiform clouds is given by Lohmann et al. (2007):

w^{ef f}=w+ 1.33√

TKE, (7)

wherewis the resolved GCM-mean vertical velocity and TKE is the turbulent kinetic energy. Other similar suggestions include parameterizations where the effective vertical velocity is based on the turbulent diffusion coefficient (K), e.g. (Morrison and Gettelman, 2008)

w^{ef f} =K lt

, (8)

wherelt= 30 m is the turbulent mixing length scale. The effective velocity approach is appealing especially for climate modelling because of its simplic- ity and computational efficiency. However, as shown in Paper IV and in Section 5 of this summary, it can not sufficiently account for the non-linear effects of the small-scale variability of vertical velocity on clouds.

Another popular approach used in many global models is the statistical approach, where a PDF is used to represent the subgrid vertical velocity variability (Chuang et al., 1997; Ghan et al., 1997; Storelvmo et al., 2006; Golaz et al., 2011). Typically, a Gaussian PDF is assumed, whose variance is es- timated by various methods using the turbulence parameters available from the host model, often similar to the expressions forw^{ef f} (Ghan et al., 1997).

CDNC based on cloud droplet activation can then be calculated by integrat- ing over the positive vertical velocities:

N_c^nucl=

�_∞

0 P(w)N(w)dw

�_∞

0 P(w)dw , (9)

whereP(w) represents the probability density function for vertical velocity andN(w) represents the cloud droplet activation parameterization, for which everything except w is kept constant during the integration. Some studies have also used additional weighting of the integral withwitself in an attempt to account for higher mass-ﬂux across the cloud base height with strong updrafts (Conant et al., 2004; Meskhidze et al., 2005; Romakkaniemi et al., 2009).

From turbulence to cloud formation : modelling the aerosol-cloud interactions

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Acknowledgements

Contents

List of publications

1 Introduction

2 Modelling tools

2.1 ECHAM5.5-HAM2

2.2 The numerical weather prediction model AROME

3 Aerosol-cloud interactions

3.1 Formation of cloud droplets

3.2 Indirect radiative eﬀects of aerosols

3.3 Parameterizing cloud droplet activation in large- scale models

4 Vertical motions in the atmosphere

4.1 Measurements

4.2 Statistical properties of vertical velocity

4.3 Parameterizing vertical velocity for cloud activa- tion

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