Precipitation Processes

Transcription

1 Precipitation Processes Dave Rahn Precipitation formation processes may be classified into two categories. These are cold and warm processes, where cold processes can only occur below 0 C and warm processes can occur above or below 0 C. Historically, the cold rain processes were closely examined first because it was believed that this was the main process that leads to the formation of rain. However, with the use of first echo studies it became clear that warm processes are also important. First echo studies examine time height radar echoes to find the time and location of the first formation of precipitation, or at least significantly large drops that are detectable by the radar. Battan (1953) found that these regions of significantly large drops can form in the warm sector, as shown below. This figure shows a first echo at about 1658 EST that is between about seven and eleven thousand feet, which corresponds to a temperature between +8 C and +13 C. From this observation, it can be concluded that warm processes must be happening and that they lead to the development of significantly large drops. The two main factors for droplet growth in warm rain processes are condensation and coalescence. Condensation is the first process that must occur in order for droplets to

2 form. Growth by condensation involves two major issues. These are the solution effect and the curvature effect, and they lead to the Köhler curve. There are several important things to mention about this curve. Given a particular curve that represents a particular solution, there is a critical radius and supersaturation at the peak of the Köhler curve. To the left of this peak toward smaller radii, the droplet is in a stable equilibrium with the environment and these are known as haze particles. To the right of this peak toward larger radii the droplet is not in a stable equilibrium and this results in spontaneous growth. The next step is connecting single drop condensation and multidrop condensation to get an expression for the condensation occurring within a cloud and how the droplets and their environment interact with each other. This is done by examining the vapor budget of an ascending air parcel. There are two factors that change the supersaturation of this parcel. The saturation is increased as the air parcel ascends and cools, lowering the saturation vapor pressure. The saturation is decreased by the condensation occurring on the droplets. This is represented by the equation below. ds dt = Q dz dt 1 Where S is the supersaturation, w is the mixing ratio of the liquid water condensate, and Q 1 and Q 2 are constants (assuming only small changes). From this relationship, setting the left hand side of the equation to zero yields the maximum supersaturation and number concentration. The relationship between the number of activated nuclei at a given supersaturation is approximated by power-law relationship that is found empirically. Given a distribution of droplets growing by condensation and no other processes, the size distribution becomes narrower over time. The reason for this narrowing is that the surface area to volume ratio slows down the growth rate of the larger droplets compared to that of the smaller droplets. This narrowing of the size distribution is an important characteristic of growth by condensation. The importance of the width of the size spectrum is discussed in detail later on. While this initial growth of the droplet after it is activated by a sufficiently high saturation ratio is important to begin the growth process, it can be shown that it is a relatively slow process at larger radii, so that if this was the Q 2 dw dt

3 sole process responsible for droplet growth, the time that it would take is far too long to form what is observed. The primary process that forms the larger droplets after condensation occurs is coalescence. Unlike condensational growth which can be a single droplet process, coalescence is necessarily a drop to drop interaction. Furthermore, it requires a significant amount of drops, or else the probability that two drops will meet is too small. The process of coalescence may be described as basically a larger drop falling through a distribution of smaller droplets. This larger droplet sweeps out a certain volume and collects some of the smaller drops as it falls since the terminal velocities of the drops are not the same. This basic idea becomes quite complicated, however, when it is examined in detail. There are many factors that determine whether two drops coalesce together. For example, smaller droplets tend to follow the streamlines of air flow around the large drop since they have a small inertia. So, even if the small droplet is in the path of the larger droplet it may be pushed to the side by the air flow, so that the actual area of collection is smaller then the geometric area. Even if a droplet does indeed make contact with the larger droplet, it may not be collected due to factors such as surface tension, electric charge, air cushion, and the angle of impact. In order to represent these complicated factors, the collision and coalescence of drops are often represented by probabilities to simplify the expression for the complicated processes listed above. The individual probabilities are coined the collision and coalescence efficiencies and together the two probabilities are called the collection efficiency. An example of how the collection efficiency behaves is given by Beard (1993), shown below, which shows collection efficiency as a function of the radius of the large and small droplets.

4 This distribution of probabilities is affected by two main concepts. The first is that for a given small droplet as the size of the large droplet increases, the collection efficiency tends to increase. This is because larger drops have a larger area of collection that they sweep out. The second point is that as the size of the smaller drops increases so does the collection efficiency, but only to a point, then the efficiency begins to decrease, as the small droplet size increases. This is because smaller sizes have small inertia so they follow the streamlines of air flow around the larger droplet. As the size increases they have more inertia so they tend to resist the airflow more and collide with the larger droplets. At some point the radius of the small droplet becomes large enough so that the terminal velocity is relatively fast. This makes the difference of the terminal velocities between the drops smaller and prevents the two drops from colliding as hard and allows more time for horizontal forces due to the air flow around the larger droplet to keep the drops apart. Even at the most optimal of sizes, the collection efficiency is just above 70%.

5 A contrary topic to droplet collection that is worth mentioning concerns the breakup of a drop. This breakup can occur either spontaneously through hydrodynamic stress or through collisions. These processes are affected by the size of the drop, shape of the drop, fall velocity, size distribution, electric charges, aerodynamics, and turbulence of the air. This breakup basically provides an upper limit to the size distribution of rain and is a source that contributes to the number of smaller droplets present in a given size distribution if there are sufficiently large drops present to breakup and create smaller drops. A model of the growth by coalescence is referred to as the stochastic collection equation. This equation expresses the change of the size distribution over time due to collision and coalescence. The change of size distribution comes from the addition of larger drops due to collecting smaller droplets and from the removal of smaller droplets due to being collected by the larger drops. The equation is stochastic in the sense that the collection is represented as a probability, but deterministic in the sense that it gives only the average value if many samples are taken. Scott (1968) shows how these coalescence calculations change the size distribution over time by using the stochastic collection equation with an initial Gaussianlike distribution. Berry and Reinhardt (1974) also did this same type of analysis using different integration schemes in a series of papers that show how different initial size distributions change over time due to collection. An example of a particular size distribution from Berry and Reinhardt (1974) is shown below. This plot shows a bimodal

6 size distribution developing over 30 minutes from an initial, unimodal size distribution. How this initial size distribution changes over time is shown to be dependent on the mean mass and standard deviation of the initial size distribution. This initial spread of the size distribution affects the size distribution greatly later on and influences whether the cloud forms precipitation or not. Also, it is shown in this series of papers that just a small tail of larger size droplets can have a strong influence on later size distributions. Since this tail is important, the factors affecting the initial size distribution observed in clouds needs to be discussed. However, before this discussion happens some observation and modeling data is discussed in order to find the factors that may lead to the initial and subsequent size spectrums. Yum and Hudson (2005) compare adiabatic predictions and observations of droplet spectral broadening. This comparison demonstrated that the modeled theory can explain most of the observed trends, but not all. This is because the modeled theory does not take into account all possible factors such as entrainment, mixing, and gravitational collection, which all modify the cloud droplet size spectra. There is one significant discrepancy between the model and the observation. The model and the observations show opposite trends regarding the standard deviation of the cloud droplet diameter compared with maximum supersaturation, activated cloud droplet concentration, cloud droplet mean diameter, and average CCN concentration at 1% S(N CCN ). Another study by Brengnier and Chaumet (2001) examines the spectrum by looking at just the narrowest part of the spectrum observed from a flight, but while these segments of the spectrum are narrower then most observations, there is still more broadening occurring then the adiabatic models indicate. There are several possibilities that may lead to these discrepancies between observations and modeling results that show up in studies such as Yum and Hudson (2005) and Brengnier and Chaumet (2001). There are two observational errors that would tend to broaden the spectrum. These errors are from the forward-scattering spectrometer probe s (FSSP) uncertainties in measuring the spectrum and also from averaging the data, especially important for non-linear processes. However, these errors have been shown to be minimal. There are also several physical processes that would tend to affect the spectrum. These are the condensation coefficient, the inhibition of

7 growth, mixing, turbulence, and giant and ultra giant aerosols. The condensation coefficient and inhibition of growth are admittedly not well-understood, but are suspected to have only minor roles. The first important topic concerns how giant (1-10 µm diameter) and ultra giant aerosols (>10 µm diameter) affect the change in the size distribution over time. Feingold, et al (1999) studied the impact of these giant aerosols in stratocumulus. It is shown that the time for 10% of the liquid water content to be converted to a radius greater then 20 µm (drizzle) as a function of initial drop density is greatly effected by the presence of these giant aerosols, most notably affecting the concentration of the larger droplets. This result is shown in the figure below. Including these large particles demonstrates a reduction in time to drizzle. This reduction in time is a function of the liquid water content and the initial drop number. For example, for a liquid water content of 0.6 g m -3 and an initial drop number of 100 cm -3, there is only a 1% difference. However, for the same liquid water content but an initial drop number of 300 cm -3, the difference jumps to

8 about 40%, which produces precipitation about 35 minutes earlier for the 10-3 GCCN case, which is quite significant. Also, just a few of these giant aerosols in a smaller mean diameter distribution has a greater impact then larger mean diameter distribution, since they create a larger spread for the smaller average radius. These particles have been shown to indeed exist naturally but there are two major problems observing them. The first problem is that there are relatively few of them to measure in a given size distribution, and the second problem is that there are issues with detecting them with an instrument since they are so much bigger then typical aerosols. These particles do indeed seem to have quite an impact on the size distribution if they are present, and cannot be neglected. The next issue that affects the drop size spectrum is turbulence. It is shown that turbulence does have quite an impact on the localized distribution of droplets, which increases the amount of collisions and coalescence in some areas and decreases it in others. This turbulent motion is demonstrated by Shaw et al (1998) in the figure below. As is rather evident from the figure below, there is quite a different spatial distribution of droplets due to this turbulent motion which changes the local microphysics due to the new spatial distribution of droplets. This would have a tendency of broadening the spectrum due to an increased chance of collision in the areas of dense distribution and decreasing the chance in areas of sparse distribution. This broadening by turbulent air motion ultimately speeds up the formation of larger droplets.

9 Looking a bit deeper into the cloud dynamics it is clear from Warner (1977) that clouds have complicated structures within them, as shown by the inhomogeneous vertical velocity of cumulus clouds in time and space shown below. The initial strong updraft is a spike in the middle of the cloud, accompanied with two minima adjacent to it and then somewhat variable vertical motions elsewhere. Over time the initial updraft is gone and there is downward vertical motion in the region of the visible cloud. This suggests that since there is so much variability in the air motions within the cloud, things such as the updraft velocity are not uniform at all and this would tend to complicate the microphysics. This complexity of air motion is also show by other studies such as MacPherson and Isaac (1977) that shows the wind vectors within a cloud. This provides not only information on the variability of the vertical motion but also the variability of a component of the horizontal motion. These upward vertical motions are often associated with convective vertical motion. This convection is often described as either a steady jet or as a bubble. A steady jet is formed by usually injecting heat at a low level and allowing it to rise. As the jet rises, its width widens as it mixes somewhat with the environment. This type of convection assumes that the area inside and outside of the jet are individually well-mixed. The other way is by convective bubbles that are more like a single entity that rises, expands, and mixes somewhat with the environment while it ascends. While these two

10 are both plausible convective motions, but are somewhat different dynamically. Also, the observed convective motions are quite variable. Often it is a combination of the two that is observed and modeled. The most common representation of convection is a steady jet at the surface that breaks off into convective bubbles after some height. The mixing that occurs with either jets, bubbles, or any type of air parcel affects the properties and therefore the microphysics occurring within a parcel. This mixing can happen in several ways and comes from several sources. A penetrative downdraft is modeled by Squires (1958) and later observed by Paluch (1979). Squire models a penetrative downdraft using four major points. These points are that a parcel of dry air is entrained from cloud top, this dry parcel mixes with the cloudy parcel, the cloud droplets evaporate instantly, and the motion of the parcel is predicted from the rate of mixing and not from the perturbed pressure field between the parcel and environmental pressure. Using these assumptions, he was able to construct a model that was able to provide reasonable results that were close to observed cloud properties. While Squires model provided the theoretical basis for describing the penetrative downdraft, Paluch (1979) developed a procedure that uses measurements within a cloud to observe this penetrative downdraft. First he determined the wet equivalent potential temperature, θ q, and the total water mixing ratio, Q, at different levels. These are then plotted together with an environmental sounding to create what is called a Paluch diagram. Since θ q and Q are conserved and if these mix linearly primarily from vertical exchanges from two levels, then the results of mixing these conserved variables will tend to fall upon a line. If this is the case then mixing is mostly due to a penetrative downdraft. While this provides evidence that mixing can come from primarily the top of the cloud, this is not always the case. For example, mixing may occur in other ways including penetration into the cloud from the side. The last topic of precipitation process concerns a couple of parameterizations that are introduced in order to improve model run times. These parameterizations are important when one considers the complexity of the dynamically and microphysically coupled system, which can all lead to excessive computational requirements. Using a parameterization helps to simplify and reduce these requirements while still maintaining a reasonable representation of the physical process.

11 The first parameterization was proposed by Kessler (1969) and is shown below: dm dt = k( m a) Where M is the precipitation water content, m is the cloud water content, k is the autoconversion rate, and a is the autoconversion threshold. If the amount of cloud water is less then the threshold then there is no precipitation water going to form because there needs to be a certain density of cloud droplets in order to create precipitation. Otherwise, this excess of cloud water is converted to precipitable water at a rate of k, the autoconversion rate. It is important to note that this expression assumes a linear relationship between the amount of water in a cloud and the rate at which precipitation grows, which is valid for a monodisperse distribution of cloud droplets. The second parameterization is from Berry (1968) and is shown below. dm dt 2 m = N 60(5+ md where M and m are as above, N b is the droplet number density at cloud base and D b is the droplet relative dispersion at cloud base. The important distinction between this scheme and Kessler s scheme is the inclusion of the droplet number density at cloud base and the dispersion at cloud base. As discussed previously the larger that the initial size distribution is, the greater is the precipitation production, and this agrees with Berry s formulation. Also, the initial number density would also affect the precipitation. A larger number of the droplets would tend to slow down the rate at which precipitation forms, since there will be a larger number of smaller droplets. There are many factors influencing warm rain processes. It begins with condensational activation of haze particles that initiates droplet growth and the collision and coalescence of larger drops, which incorporates a large range of factors that change the size distribution over time and is strongly dependent on the initial size distribution. These initial and subsequent size distributions are sensitive to many factors including mixing, turbulence, and giant aerosol particles. All of which contribute to ultimately the formation of rain. b b )

12 References Battan, L.J., 1953: Observations on the formation and spread of precipitation in convective clouds. Journal of the Atmospheric Sciences 10, Beard, K.V. and H.T. Ochs III, 1993: Warm-rain initiation: an overview of microphysical mechanisms. Journal of Applied Meteorology 32, Berry, E.X., 1968: Modification of the warm rain process. Proceedings of the First National Conference on Weather Modification, Albany, New York, April 28-May 1, American Meteorological Society, Boston, Mass., Berry, E.X. and R.L. Reinhardt, 1974: An analysis of cloud drop growth by collection: Part II. single initial distributions. Journal of the Atmospheric Sciences 31, Brenguier, J. and L. Chaumat, 2001: Droplet spectra broadening in cumulus clouds. Part I: broadening in adiabatic cores. Journal of the Atmospheric Sciences 58, Cotton, W.R., 1975: On parameterization of turbulent transport in cumulus clouds. Journal of the Atmospheric Sciences 32, Feingold, G., W.R. Cotton, S.M. Kreidenweis, and J.T. Davis, 1999: The impact of giant cloud condensation nuclei on drizzle formation in stratocumulus: implications for cloud radiative properties. Journal of the Atmospheric Sciences 56, Kessler, E., 1969: On the distribution and continuity of water substance on atmospheric circulation. Meteorological Monograms 10, 84 pp.

13 MacPherson, J.I. and G.A. Isaac, 1977: Turbulent characteristics of some Canadian cumulus clouds. Journal of Applied Meteorology 16, Paluch, I.R., 1979: The entrainment mechanism in Colorado Cumuli. Journal of Atmospheric Sciences 36, Scott, W.T., 1968: Analytic studies of cloud droplet coalescence I. Journal of the Atmospheric Sciences 25, Shaw, R.A., W.C. Reade, L.R. Collins, and J. Verlinde, 1998: Preferential concentration of cloud droplets by turbulence: effects on the early evolution of cumulus cloud droplet spectra. Journal of the Atmospheric Sciences 55, Squires, P., 1958: Penetrative downdraughts in Cumuli. Tellus 3, Warner, J., 1977: Time variation of updraft and water content in small cumulus clouds. Journal of the Atmospheric Sciences 34, Yum, S.S. and J.G. Hudson, 2005: Adiabatic predictions and observations of cloud droplet spectral broadness. Atmospheric Research 73,