1. Introduction
The existence of downdrafts in deep convective systems was acknowledged as early as a hundred years ago by Humphreys (1914), who also hypothesized that they are maintained by the evaporation of rain falling through unsaturated air. Since then, downdrafts have been the focus of many studies (e.g., Knupp and Cotton 1985; Cotton et al. 2011, and references therein), which have led to a considerable advancement of our understanding of these phenomena and, more generally, of precipitating convection.
Within the category of downdrafts, we would like to concentrate on precipitation-driven downdrafts, by which, following the nomenclature explained in Knupp and Cotton (1985), we mean those downdrafts that appear in the presence of precipitation and that reach the surface, injecting masses of cold and dry air in the subcloud layer (e.g., Byers and Braham 1949; Fankhauser 1976; Barnes and Garstang 1982; Knupp 1987, 1988).
From a rather practical point of view, precipitation-driven downdrafts have been of interest for some time, given their potential to generate downbursts and microbursts, very strong currents of air with vertical velocities often exceeding 10 m s−1 in magnitude (see, e.g., Fujita 1985, 1986; Proctor 1988, 1989; Wakimoto et al. 1994). These intense downdrafts can be found in cases where precipitating clouds are formed above deep and dry boundary layers—such as over the Great Plains—and constitute a serious hazard for civil aviation.
From a more conceptual perspective, throughout the years precipitation-driven downdrafts have been studied in different contexts, an important example being that of the so-called boundary layer quasi-equilibrium (BLQE) hypothesis (Emanuel 1989; Raymond 1994, 1995), proposed to explain why the moist entropy of tropical boundary layers seems to change very little with time. Simply put, according to this hypothesis, the moistening and heating of the tropical boundary layer provided by the surface fluxes are counterbalanced mainly by precipitation-driven downdrafts that bring low-entropy air from the midtroposphere to the surface. As argued by Raymond (1995), the turbulent entrainment at the top of the boundary layer plays little role in the balance. This explanation is in contrast with the hypothesis used by Arakawa and Schubert (1974) in their cumulus parameterization, where it is mixing with the environmental air and, sometimes, horizontal advection, which balance the action of surface fluxes. These two hypotheses were recently examined and tested by Thayer-Calder and Randall (2015) with a numerical model. Interestingly, their results suggest that only a small fraction of the flux of moist static energy (MSE) at the top of the boundary layer is due to precipitation-driven downdrafts.
Another framework in which precipitation-driven downdrafts are of considerable importance is that of convection triggering. The masses of air injected by downdrafts in the subcloud layer spread horizontally on the surface as density currents, usually called cold pools, which are one of the main factors responsible for maintaining deep convective systems (Purdom 1976; Weaver and Nelson 1982). In organized cases, such as squall lines or supercell thunderstorms, it has been known for a long time (see, e.g., Rotunno and Klemp 1985; Rotunno et al. 1988; Weisman et al. 1988; Weisman and Rotunno 2004) that the interaction between the gust front of cold pools and the wind shear or the collision between two or more cold pools can provide enough kinetic energy to parcels at the surface to reach their level of free convection (LFC). In nonorganized cases, parcels reach their LFC through a cooperation of the gust-front lifting and the thermodynamic effect provided by the positive moisture anomaly at the leading edge of cold pools, which reduces the convective inhibition experienced by parcels above the lifting condensation level (Tompkins 2001; Torri et al. 2015). The influence of precipitation-driven downdrafts on convection triggering is indirect but, nevertheless, strong: by controlling the initial conditions of cold pools, downdrafts effectively control the strength of the cold pools’ gust fronts and their ability to lift parcels from the surface and, potentially, also the magnitude of the thermodynamic effect.
In this study, we will consider a tropical maritime environment, and we will focus on three fundamental aspects of precipitation-driven downdraft dynamics:
What is the initial height of a precipitation-driven downdraft?
What is the contribution of precipitation-driven downdrafts to the budget of MSE in the subcloud layer?
What is the role of condensate loading versus rain evaporation in maintaining a precipitation-driven downdraft?
To some extent, these topics have been addressed in the past in various studies, although using limited techniques that did not provide an entirely clear answer. For instance, starting from as early as Mal and Desai (1938), the typical approach to diagnose the initial height of downdrafts, sometimes referred to as source level, has been to use thermodynamic properties of downdraft air, like the wet-bulb potential temperature 
Analogously, various authors have asked what mechanisms maintain precipitation-driven downdrafts, recognizing rain evaporation and condensate loading as leading factors (Byers and Braham 1949; Braham 1952; Fankhauser 1976; Lemon 1976; Barnes and Garstang 1982; Knupp and Cotton 1985). However, the extent to which one mechanism is dominant over the other even in simple cases of unorganized convection remains unclear.
In this manuscript, we will address the two questions outlined above mainly using a Lagrangian particle dispersion model (LPDM). Compared to the techniques that have been used in the past, the LPDM provides a great deal of information. In particular, analyzing the position of millions of particles released in the simulation domain will allow us to determine the initial height of a downdraft in a clear and simple manner. Also, combining the output from the LES model that we will use with the Lagrangian history of the particles from when they enter a precipitation-driven downdraft until their exit near the surface, we will be able to quantify the importance of rain evaporation and condensate loading in driving the downdraft.
Notice that the use of particles’ trajectories to study downdrafts is a path that has been explored in the past: Miller and Betts (1977), for example, used them to illustrate the behavior of downdrafts in Venezuelan convective storms, and Knupp (1988) used them in the context of storms in the high plains. However, the computational limitations of the past did not allow for the simulation of a number of trajectories large enough to make significant statistics.
2. Methods
The model used in this study is the System for Atmospheric Modeling (SAM), version 6.8.2, which solves the anelastic equations of motion and uses liquid water static energy and nonprecipitating and precipitating total water as thermodynamic prognostic variables (Khairoutdinov and Randall 2003). The equations are solved with doubly periodic boundary conditions in the horizontal directions. A prognostic turbulent kinetic energy 1.5-order closure scheme is used to parameterize subgrid-scale effects.
We ran the model with the Lin microphysics scheme, a single-moment scheme that predicts the specific humidities of water vapor, cloud liquid water, cloud ice, rain, snow, and graupel (Lin et al. 1983). The surface fluxes are computed using the Monin–Obukhov similarity theory.
The simulations are carried out over a domain of 64 × 64 km2 in the horizontal directions and 30 km in the vertical. The grid size in the horizontal directions is 250 m, and it varies in the vertical: 500 m above 10 km, which decrease progressively to 38 m close to the model surface. The time step is 3 s. Figure 1 shows the environment vertical profiles of potential temperature (red), water vapor specific humidity (blue), and relative humidity (green), averaged over the duration of the simulation.
Time average of the vertical profiles of potential temperature (red), water vapor specific humidity (blue), and relative humidity (green).
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
We ran the model with the LPDM discussed in Nie and Kuang (2012). For every column in the domain, the LPDM is initialized with 1120 particles, their positions being distributed randomly over the bottom 18 km of the model domain, with a probability distribution that is a uniform function of pressure. A validation of the LPDM can be found in the supplemental information.
Every minute of simulated time, the positions of the Lagrangian particles and the three-dimensional model fields from SAM are recorded. A cross-comparison of Lagrangian and Eulerian data provides the complete histories of thermodynamic and dynamic properties of the particles.
Throughout the simulation, the sea surface temperature is held constant at 302.65 K, and the diurnal cycle is removed by fixing the zenith angle at 51.7° with solar constant halved to 685 W m−2. The mean winds are initialized to zero. We first ran the model for 30 days without Lagrangian particles on the same domain until radiative–convective equilibrium (RCE) is reached. At the end of this period, we restarted the simulation with the Lagrangian particles and collected data for 12 h of model time. No nudging was imposed on the horizontal winds. The precipitation rate averaged in time during the 12 h of data collection and in space over the entire domain is 3.4 mm day−1.
We define the subcloud layer as the portion of the model domain that includes the surface and in which the time- and domain-averaged cloud liquid water specific humidity 
We say that a grid box in the subcloud layer is part of the core of a cold pool if its density potential temperature 
We consider as part of a precipitation-driven downdraft all particles from any altitude that acquire and maintain negative vertical velocity until they enter the core of a cold pool. Interestingly, although we do not require the precipitation-driven downdraft to be unsaturated, most of the descent of the particles in precipitation-driven downdrafts takes place in unsaturated grid boxes.
3. Results
Having laid out the research questions in section 1, and after having explained how we pursue these questions in the section 2, we will now discuss our findings.
a. On the initial height of precipitation-driven downdrafts
Following the definition of precipitation-driven downdraft that we have given in the previous section, whenever a particle enters the core of a cold pool, we track its position back in time for every step during which the particle was in grid boxes that satisfied the condition that the vertical wind w ≤ 0 m s−1. The height of the first grid box for which the previous condition is true is taken as the initial height of the particle we sampled.
Notice that, because the coldest regions of cold pools are known to exhibit high pressure perturbations, the model outputs show that the vertical velocity of precipitation-driven downdrafts as they approach the surface decreases considerably (cf. Fig. 10 later in the text). When the vertical velocity is small enough, turbulent or wave fluctuations may cause its values in some grid boxes to oscillate between positive and negative. There follows that, if we were to apply the definition of precipitation-driven downdraft given above, a considerable number of sampled particles would appear to have originated close to the surface. To avoid this problem, whenever the vertical velocity of a particle in a downdraft turns positive, a clock is started as the particles’ positions are scanned backward in time; if the vertical velocity becomes negative again within 10 min from the start of the clock, the particle is still considered part of the downdraft; otherwise, it is dismissed. Sensitivity tests presented in the supplemental information show that the results and our conclusions are not particularly sensitive to the precise value chosen for the time threshold. Furthermore, in order to avoid interference from fast detrainment–entrainment events in cold pools, once a particle ends up in a cold pool core and its properties are recorded, the particle is flagged and discarded for the rest of the simulation.
In Fig. 2, the blue curve shows the distribution of initial heights of all particles that were injected in the core of a cold pool by a precipitation-driven downdraft. Notice that the distribution is confined almost entirely to the bottom of the troposphere: 98% of particles have initial heights lower than 2.5 km. The curve shows a pronounced peak at approximately 1 km of altitude, just a few hundred meters above the top of the subcloud layer, and a smaller one near the surface. Examination of trajectories for particles that contribute to the lower peak shows that most of these particles descended from higher altitudes with a precipitation-driven downdraft, but, near the surface, their vertical velocity, however small, was positive for more than 10 min before they entered the core of a cold pool.
Distribution of Lagrangian particles’ positions at various times before becoming part of a precipitation-driven downdraft. The red, green, and black curves refer to positions 30, 60, and 90 min before entering the downdraft, respectively. The blue curve shows the distribution of positions at the time of entrance.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
These results are nicely in accordance with existing literature, which suggested that, for tropical convection, the source level of precipitation-driven downdrafts is just above cloud base [see, e.g., Zipser (1969), Betts (1976), and Kingsmill and Houze (1999), just to cite a few].
We should point out that the initial height of a downdraft may still carry along some ambiguity. For example, it could be that a number of particles that entered the precipitation-driven downdraft at 1 km actually originated from much greater altitudes: they were transported down by another downdraft from which they eventually left, and then, after some time, they became part of the precipitation-driven downdraft that carried them down to the surface. A simple way to check whether this is the case is to ask where the particles were before entering the precipitation-driven downdraft.
The red, green, and black curves in Fig. 2 show the distribution of the sampled particles’ positions 30, 60, and 90 min before entering the precipitation-driven downdraft, respectively. They can be thought of as the evolution back in time of the blue curve. Interestingly, the red curve suggests that 61% of particles actually come from the subcloud layer, whereas the remaining seem to originate near the height where they entered the downdraft. According to the nomenclature discussed in Knupp (1988), we will refer to the former as up–down and to the latter as midlevel. Less than 2% of all particles originate from an altitude greater than 2.5 km.
To better appreciate the history of the Lagrangian particles prior to their entrance in a precipitation-driven downdraft, we can look directly at the trajectories of a few representative cases. The red lines in Fig. 3 show the time evolution of the vertical positions of three particles for the 60 min before they enter the core of a cold pool. Notice that the horizontal axis represents the time in the particles’ histories, with 0 min being the moment they enter a cold pool’s core. The particles have been selected rather arbitrarily, but an extensive scan through a large number of particles’ histories makes us confident the particular examples shown illustrate well the possible scenarios for downdrafts.
Three examples of Lagrangian particles’ histories 60 min before entering the core of a cold pool are shown with a red line. (left) An up–down downdraft, (middle) a midlevel downdraft originating at ~1 km, and (right) a hybrid between the two. The blue contours represent the specific humidity of total nonprecipitating water at increasing intervals of 1 g kg−1. The green contours show negative buoyancy in the subcloud layer at decreasing intervals of 0.02 m s−2 starting at −0.01 m s−2. The gray shading represents the specific humidity of total precipitating water. The values shown for all variables at different heights refer to the vertical column where the particle is.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
In all panels, the blue contours represent the total nonprecipitating water specific humidity 
Figure 3 (left) shows the history of a particle in an up–down downdraft. As can be seen, the particle is lifted from the surface at approximately −25 min by the gust front of an expanding cold pool, indicated by the appearance of the negative buoyancy contours in the subcloud layer, and it quickly becomes part of an updraft. As the particle ascends, it reaches lifting condensation level (LCL), and soon afterward it enters a precipitating column. The precipitation experienced by the particle is sufficient to change the sign of its buoyancy and stop its ascension. As a result, the particle leaves the updraft and enters a downdraft that becomes unsaturated almost immediately. The descent continues with no interruptions until the particle reaches the core of a cold pool. Curiously, visual inspection of the three-dimensional model output suggests that the particle enters the same cold pool that had lifted it from the surface.
Figure 3 (middle) shows the history of a particle that descends to the surface levels through a midlevel downdraft. As might be expected, the particle sits in an almost undisturbed environment for most of its life. The changes in altitude in clear sky seem to be due to random turbulent fluctuations or gravity waves. Then, at approximately −20 min, the particle is entrained into a cloud, where its buoyancy becomes negative. The particle starts descending and enters the core of a cold pool at the surface.
Finally, Fig. 3 (right) shows another possible scenario for particles entering precipitation-driven downdrafts—one that, to some extent, is a mixture of the previous two. The particle represented in the figure starts off at an altitude of approximately 1 km, subject only to random turbulence or wave motions, which cause its position to oscillate a little. At −20 min, the particle becomes part of an updraft that makes it rise to an altitude of 2 km, where, finally, its buoyancy reverses sign and the particle enters an unsaturated downdraft all the way down to the surface. This strengthens the conclusion drawn from Fig. 2 that particles with higher initial height may actually originate at much lower altitude and have, therefore, a higher MSE than what the initial height could suggest.
One of the messages that emerges from the previous discussion is that precipitation-driven downdrafts tend to have relatively low initial heights, possibly transporting parcels that originated in the bottom kilometer of the troposphere. To provide further evidence to support this statement, we will use three methods, one based on the Lagrangian and two on the Eulerian point of view.
The former one consists of changing the sampling technique we have adopted above, and, instead of considering particles that enter a downdraft and then reach the surface layers inside the core of a cold pool, we simply track all particles in downdrafts, and we follow them until they leave it, regardless of the height where this happens. To be more specific, whenever a particle enters a grid box in which w ≤ −0.5 m s−1, its positions are saved for as long as the particle is in a grid box with negative vertical velocity (i.e., w ≤ 0 m s−1).
For every particle, we collect the initial height and the final height, which, in contrast to the previous sampling of precipitation-driven downdrafts, does not necessarily have to be in a cold pool or even in the subcloud layer. We also do not allow for a temporal window between the time a particle leaves the downdraft and when its final height is recorded, as done with the other sampling technique. Nevertheless, in the supplemental information we show that considering such a window has no effect on our conclusions.
Next, we define the height matrix as the matrix where the (i, j) element contains the density of particles per meter square that entered a downdraft at height 
Logarithm of the height matrix, the (i, j) entry of which indicates the number of particles that became part of a downdraft at height 
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
The figure suggests that, although there are downdrafts at all heights, they do not travel much farther than a few hundred meters. The reason for this, as also suggested by others (see, e.g., Böing et al. 2014), is that, as downdraft parcels descend over large distances, they become dry, and, thus, they start following a dry adiabat. Because the environment above the subcloud layer remains close to a moist adiabat, these parcels quickly lose their negative buoyancy. Furthermore, because precipitating columns are not steady, the negative contributions of rain evaporation and condensate loading to the parcels’ buoyancy are also going to become insufficient to maintain the parcels’ descent.
One of the most curious features of Fig. 4 that jumps out at the viewer is that downdrafts originating between 3 and 5 km seem to be able to travel a greater distance than those originating at other heights. The average profile of rain evaporation rate shown by the blue curve in Fig. 5, and that of the graupel melting rate shown in green, suggests that particles in downdrafts that cross the levels between 2 and 4 km would experience significant evaporation of rain and melting of graupel, which could provide extra kinetic energy to travel a longer distance than particles that descended from much higher or lower altitudes. Notice that, although the peak in melting rate of graupel is almost an order of magnitude higher than the rain evaporation rate at the same altitude, the latent heat of fusion is roughly a factor of 8 smaller than the latent heat of vaporization, so melting of graupel is less efficient in cooling the parcels, and thus in driving the downdraft, than rain evaporation. Finally, we should note that the minimum of evaporation rate between 1 and 2 km is the result of high relative humidity, and thus low saturation deficit, at these altitudes.
Time averages of the vertical profiles of rain evaporation rate (blue), graupel melting rate (green), and total precipitating water specific humidity (red) for the bottom 5 km of the model domain.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
The second consistency check that we perform is based on the distribution of MSE in cold pool cores, by which, we remind the reader, we mean those grid cells with a 
Time average of the vertical profile of MSE in the environment (blue) and cumulative distribution function of MSE in cold pool cores (red).
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
Finally, the third method that we use to check the consistency of our claim that initial heights of precipitation-driven downdrafts are very low is based on the joint distribution of MSE and vertical velocity at a given height. In particular, Fig. 7 (left) shows the logarithm of the time-averaged joint distribution of MSE anomaly—computed at each time step with respect to the horizontal average—and the vertical velocity at 531 m near the top of the subcloud layer. The black curve highlights the contour corresponding to the value 4.5 of the logarithm of the distribution, which encloses 99.7% of the total number of grid boxes sampled and 87.5% of the total flux of MSE. The contour line shows that most of the MSE flux is given by grid boxes with an MSE anomaly higher than −6 K and relatively small vertical velocities, which suggests that downdrafts from the midtroposphere do not inject much air in the boundary layer.
(left) Logarithm of the joint distribution of vertical velocity and MSE anomaly at 531 m. The black contour corresponds to the isopleth −1 of the logarithmic distribution. (right) Sinks of MSE at the top of the subcloud layer divided by three transport categories: updraft, downdraft, and environment. The blue (green) bars show the rates according to the broad (narrow) definition of the categories introduced in Thayer-Calder and Randall (2015), whereas the red bars show the results obtained using the definition we have given using Lagrangian particles.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
b. On the contribution of precipitation-driven downdrafts to the subcloud-layer MSE
The choice of substituting h with 
Another source of arbitrariness that we have deliberately left vague in our derivation is the definition of the three transport categories. As is well known, the lines between the three categories are blurry enough to allow for multiple ways to address this issue. For example, Thayer-Calder and Randall (2015) used two different definitions to compute the budget of MSE at the top of the boundary layer. In the first one, called broad, each grid box at 500-m height is considered a downdraft (updraft) box if it contains any cloud ice, water, or precipitation and has a negative (positive) velocity; if the box does not contain any condensate, it is considered as environment. In the second, called narrow, a grid box is considered a downdraft (updraft) box if the vertical velocity is below −1 m s−1 (above 1 m s−1) for two continuous levels, above and below 500 m, and if it contains any condensate; all other grid boxes are considered environment.
A potential problem with this approach is that some of the properties of a parcel, like its vertical velocity or its liquid water specific humidity, near the top of the boundary layer or cloud base are not necessarily indicative of what transport category the parcel belongs to. For instance, a parcel that will enter a convective updraft might have an LCL at a higher altitude than 500 m, or it might encounter significant convective inhibition, which will then sensibly reduce its vertical velocity, before reaching its LFC. A similar story could also hold true for parcels in downdrafts. We have tried reproducing the results of Thayer-Calder and Randall (2015) at various heights around 500 m and found the conclusions, particularly the contribution by updrafts, to change according to which height is being used.
To remove this ambiguity, we propose a slightly different approach using the Lagrangian particles. Let us go back to the joint distribution of vertical velocity and MSE anomaly shown in Fig. 7 (left). Whenever a particle reaches the top of the subcloud layer, its vertical velocity and the future 60 min of its history are considered. If the particle has positive vertical velocity and, within the specified time frame, acquires positive buoyancy at an altitude higher than 1.5 km, the particle is considered an updraft particle; if the particle has negative vertical velocity and enters a grid box with a density potential temperature anomaly lower than −0.5 K in less than an hour, the particle is considered a downdraft particle. If none of the above conditions are true, the particle is considered an environment particle.
In Fig. 7 (right), we show the contributions to the budget of MSE by the three transport categories. To compare our method with those of Thayer-Calder and Randall (2015), we measure the fluxes of MSE at 531 m, which, in our model, is the height closest to 500 m and also corresponds to the top of the subcloud layer. The blue (green) bars refer to the results obtained using the broad (narrow) definitions explained above, whereas the red bars refer to the method using Lagrangian particles explained above. Like Thayer-Calder and Randall (2015), we find turbulent mixing in the environment to be the biggest contributor to the total MSE sinks, although the contribution from updrafts and downdrafts is not negligible. The export of high MSE air by convective updrafts provides a sink of MSE of 2.43 K day−1, which is 16% of the total, amounting to 15.51 K day−1, whereas the low-MSE air injected in the subcloud layer by precipitation-driven downdrafts reduces MSE at the rate of 1.81 K day−1, 12% of the total. As documented in the supplemental information, we have also tested the sensitivity of the results to the sampling height and found that our conclusions are robust. Of all the heights where we have tested our results, 531 m is the one where the three methods are closest to each other, especially in predicting the contribution by downdrafts. Finally, we want to note that the surface sensible and latent heat fluxes contribute to the budget of MSE with a source equal to 16.28 K day−1, whereas radiative effects provide a sink of 0.86 K day−1.
c. On the maintenance of precipitation-driven downdrafts
The next question that we want to focus on in the present work is how to quantify the importance of rain evaporation and whether it is bigger than that of condensate loading in maintaining precipitation-driven downdrafts. Because we are concerned with the role of rain evaporation from the dynamical point of view, we propose using a purely dynamical quantity such as work to address the problem.
The definition we have given above will provide us with a way to quantify the importance of each mechanism in maintaining a downdraft. Considering again the Lagrangian particles we sampled earlier to construct Fig. 2, we compute the two types of work for each particle and average together the values for particles with the same initial height with the assumption that they have a comparable history and experienced the same phenomena. Figure 8 shows a comparison of the average work done on particles with different initial heights by condensate loading (solid red) and by rain evaporation (solid blue). Notice that, apart from the bottom 300 m, the contribution due to evaporation is smaller than that due to loading by a factor of approximately 0.4.
Comparison between the total work done on Lagrangian particles with different initial heights by different contributions to buoyancy (solid lines) and total buoyancy (dashed lines). Line colors refer to the contributions by condensate loading (red) and the contribution by rain evaporation (blue).
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
In this way, we can reconstruct the various contributions to the buoyancy-related pressure gradients very simply, and the calculation of the work done by these contributions is straightforward.
The two contributions to the work done by total buoyancy—by which we mean the sum of the Archimedean buoyancy and the buoyancy-related pressure gradients (Torri et al. 2015)—are shown by the dashed lines in Fig. 8, and they suggest that our conclusions are robust, even when buoyancy-related pressure gradients are taken into account. A close inspection of the vertical profiles of buoyancy ratio (not shown) suggests that this quantity tends to be maximum in magnitude in the subcloud layer, with values approaching −1, and becomes closer to 0 with increasing height. This explains why the particles that seem most affected by the correction are those with an initial height smaller than 1 km.
A natural question that arises now is whether condensate loading dominates over rain evaporation at any moment during the particle’s descent in the downdraft or if the two mechanisms are important at different stages. To investigate this, instead of considering an integrated quantity such as the work, we look directly at the contributions to buoyancy given by the two mechanisms. We present the results in Fig. 9, with Fig. 9 (left) referring to the contribution from condensate loading and Fig. 9 (right) referring to that from rain evaporation.
Vertical profiles of the time-averaged change of buoyancy due to (left) condensate loading and (right) rain evaporation for Lagrangian particles in precipitation-driven downdrafts with different initial heights.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
As for the construction of Fig. 8, we use the initial height of a particle as a sampling criterion: the histories of particles with the same initial height are averaged together, and the results are presented for each value of initial height. Thus, each column in Fig. 9 represents the vertical profile of the average contribution to the buoyancy of particles having an initial height given by the abscissa of the column in the figure.
In comparing the two plots, one should be careful to notice that the color bars differ by a factor of 2.5. This was done to make it possible for the eye to easily distinguish the main features of each contribution at every height for different types of particles. Therefore, in spite of the immediate appearance, condensate loading contributes to buoyancy more than evaporation almost everywhere, except for very near the surface, where both contributions seem of equal magnitude.
Another interesting feature of the two plots is that, for any initial height, the altitude where each contribution is maximum is different: for loading, the peak tends to be in the initial stages of the downdraft, whereas for evaporation the maximum is in the subcloud layer.
For the condensate loading, the peak is essentially due to two factors: the first is that rain columns are not steady but, rather, quickly grow to a maximum and then decay over time; the second is the fact that precipitating water in a rain column flows through the Lagrangian particles or, in other words, the vertical velocity of the particles is typically smaller than the terminal velocity of raindrops.
To check that the latter is true, we can consider Fig. 10, which shows the average vertical velocity experienced by particles of various initial heights at different stages of their descent. Above the bottom few hundred meters, where the hydrostatic pressure perturbation in the core of cold pools causes the downdraft to slow down, the vertical velocities experienced by the descending particles are roughly between −0.5 and −1.5 m s−1. Considering the precipitation rate and the precipitating liquid water content in the grid boxes of the bottom 3 km of the model, we can estimate that the average terminal velocities of raindrops are between −5 and −6 m s−1, well outside the range of average velocities of Lagrangian particles within precipitation-driven downdrafts. As a side note, we want to point out that the terminal velocities diagnosed from the model are consistent with data from observations: the terminal velocities for raindrops with diameters between 1 and 5 mm go from −4.03 to −9.09 m s −1 (Gunn and Kinzer 1949).
Vertical profiles of time-averaged vertical velocities for Lagrangian particles in precipitation-driven downdrafts with different initial heights.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
Profiles of the time average of the cubic root of liquid water specific humidity multiplied by the saturation deficit for Lagrangian particles in precipitation-driven downdrafts.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0222.1
Given the crude assumptions that we have made to derive Eq. (24), it is not surprising that the agreement between Fig. 11 and Fig. 9 (right) is only partial: unlike the profiles of the contribution by evaporation, the magnitude of the product seems generally to decrease for particles with increasing initial height. We expect that accounting for a distribution of radii and by allowing the number of raindrops N to vary with height and initial height would improve the agreement. However, we want to stress that this mismatch does not change our conclusions.
4. Conclusions
We have used an LPDM to address two important aspects regarding the dynamics of precipitation-driven downdrafts: namely, their initial height and the role played by rain evaporation in maintaining them. By sampling all the Lagrangian particles that are injected in the coldest regions of cold pools in the subcloud layer by downdrafts, we have determined that the vast majority of such particles start descending from a height lower than 2.5 km in the model domain. Looking at the position of the particles at times prior to their entrance in a precipitation-driven downdraft, we have shown that most of them originate in the subcloud layer; almost none come from high altitudes.
As a further check, we have broadened our sampling criterion and considered all particles that are part of downdrafts at any height, regardless of whether they will be injected in a cold pool or not. With this, we have shown that downdrafts exist at all heights in the model but a few hundred meters past their initial height. This provided additional support to the claim that precipitation-driven downdrafts originate at very low altitudes and do not, therefore, bring very cold and dry air into the subcloud layer.
This led us to the question of what balances the surface fluxes and keeps the boundary layer MSE relatively steady in time. Using a definition of the three transport categories—updraft, downdraft, and environment—based on the Lagrangian particles, we have concluded that most of the MSE sink is to be attributed to turbulent mixing or wave activity in the environment, although the contributions by updrafts and downdrafts are nonnegligible, their sum accounting for 28% of the total.
We then proceeded to quantify the role of rain evaporation in maintaining the precipitation-driven downdrafts. By looking at the total work done on each Lagrangian particle that is injected in the core of a cold pool by a downdraft and distinguishing the contribution due to condensate loading from that due to rain evaporation, we showed that the latter is smaller than the former, roughly by a factor of 0.4.
Considering the change of the Lagrangian particles’ buoyancy due to condensate loading and rain evaporation, we showed that the former is bigger than the latter at all heights and tends to be maximum in the first part of the downdraft descent; on the other hand, the latter is highest in the second part of the descent, when the particles are in the subcloud layer.
We interpreted the first effect as due to the fact that the terminal velocity of rain droplets is higher in magnitude than the vertical velocity of the descending Lagrangian particles and that the liquid water content associated with each rain shaft is not constant in time.
As for rain evaporation, we have argued that its maximum in the subcloud layer is simply the combination of saturation deficit and the liquid water specific humidity, which enters the equation for evaporation rates only in a cubic root. In particular, even though the precipitation experienced by Lagrangian particles is largest in the initial stages of the downdraft, the small saturation deficit does not allow for large amounts of rain to be evaporated. Only in the subcloud layer is the saturation deficit large enough to make the contribution of rain evaporation in maintaining the downdraft more significant.
Since the dynamics of downdraft maintenance is tightly related to microphysical processes such as rain evaporation, it seems natural to ask how sensitive our conclusions are to the microphysics scheme. For this reason, we have run the same simulation described in section 2 using the two-moment microphysics scheme introduced in Morrison et al. (2005) and have carried out the same analysis described in the previous section. Apart from some slight differences, we found that the conclusions of this study are robust.
Although this robustness gives us some confidence over the generality of our findings, we want to stress that we have only considered an oceanic case in RCE with no wind shear and, a priori, we do not expect our results to hold for other cases. For instance, it is very well possible that, in a continental case with a much drier boundary layer, evaporation of rain will play a much bigger role in maintaining the downdraft. This could also be the case in the presence of wind: a considerable vertical wind shear might change the geometry of a precipitating cloud, exposing a larger part of a precipitating column to an unsaturated environment.
Finally, the conceptual framework that emerges from this manuscript can have important consequences for climate models. In particular, our findings suggest that the premises on which the BLQE hypothesis is founded—that downdrafts are responsible for most of the MSE sink in the boundary layer—may not be realized in nature. Although some models have been shown to better reproduce certain features of the tropical climate, such as the MJO, when strong convective downdrafts are included (Mishra and Sahany 2011), we suggest that the key for a more accurate simulation of the tropical atmosphere is in improving parameterizations of the transport due to turbulent mixing or wave activity in the environment. Mesoscale organization of convective systems, absent in this study, may also affect the results. Notwithstanding these additional scenarios, which clearly warrant further investigations, our analysis of the oceanic RCE case addresses a basic scenario that is potentially representative of large areas over the tropical oceans with modest wind shears.
Although they play only a secondary role in the MSE budget of the tropical boundary layer, downdrafts still remain an important component of convective systems that should be included in convective parameterizations. Our results could also be useful for this task: first, they indicate the initial height tends to be in the lower troposphere; second, the fact that rain evaporation contributes much less than condensate loading in maintaining the downdraft indicates that downdrafts might be more sensitive to the model precipitation rate rather than to the relative humidity.
Acknowledgments
The authors thank Marat Khairoutdinov for access to the SAM code and Paul Edmon for precious and tireless assistance with the Harvard Odyssey cluster on which the simulations were run. This research was partially supported by the Office of Biological and Environmental Research of the U.S. Department of Energy under Grant DE-SC0008679 as part of the ASR program and by NSF Grants AGS-1062016 and AGS-1260380.
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For brevity, whenever a particle enters a grid box that is part of the core of a cold pool, we will simply say that “the particle enters/belongs to the core of a cold pool.”
