Influence of drop size distribution function on simulated ground precipitation for different cloud droplet number concentrations

Atmospheric Research 158–159 (2015) 36–49

Contents lists available at ScienceDirect

Atmospheric Research journal homepage: www.elsevier.com/locate/atmos

Influence of drop size distribution function on simulated ground precipitation for different cloud droplet number concentrations Nemanja Kovačević ⁎, Mladjen Ćurić Institute of Meteorology, University of Belgrade, 16 Dobračina, 11000 Belgrade, Serbia

a r t i c l e

i n f o

Article history: Received 7 December 2013 Received in revised form 31 January 2015 Accepted 7 February 2015 Available online 18 February 2015 Keywords: Cloud-resolving model Convective clouds Size distribution function Surface precipitation

a b s t r a c t A cloud-resolving mesoscale model with a two-moment bulk microphysical scheme is used to perform cloud simulations for two different modes of the liquid water spectrum: a unified Khrgian–Mazin size distribution for the entire spectrum of drops and the monodisperse size distribution for cloud droplets with the exponential Marshall–Palmer distribution for raindrops. The cloud model calculates the mixing ratios and number concentrations of the six microphysical categories: raindrops, cloud ice, snow, graupel, frozen raindrops and hail. The cloud droplet number concentration was prescribed. The main purpose of this sensitivity study was to analyse the differences in simulated surface precipitation (rain and hail) for the two assumed approaches with different values of cloud droplet number concentration. The study showed that there are significant differences in the occurrence, amount and spatial distribution of accumulated precipitation at the surface. It can be noted that the unified Khrgian–Mazin size distribution is generally more sensitive to changes in the cloud droplet number concentration than an alternative approach. The rain showers and cloud splitting are well simulated with the unified Khrgian–Mazin size distribution, especially for smaller values of cloud droplet number concentration. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Convective precipitation generated by storms is very important in many areas of the world. It is usually characterised by sudden and intense rainfall (rain showers) and the occurrence of hail. This type of precipitation can cause flash floods and hail damage, resulting in loss of property, agricultural damage and even loss of human life. Often, it is very useful to simulate convective clouds using cloud-resolving mesoscale models to obtain the necessary information about the accumulated precipitation on the ground. Therefore, forecasting the amount of accumulated surface precipitation, the time of its appearance, its duration and spatial distribution at the surface is of great importance. Cloud-resolving mesoscale models use explicit microphysics (Feingold et al., 1994; Ackerman et al., 2004; Morrison and ⁎ Corresponding author at: Institute of Meteorology, University of Belgrade, 16 Dobračina, 11000 Belgrade, Serbia. E-mail address: [email protected] (N. Kovačević).

http://dx.doi.org/10.1016/j.atmosres.2015.02.004 0169-8095/© 2015 Elsevier B.V. All rights reserved.

Grabowski, 2010; Khain et al., 2011) or bulk microphysical schemes (Mansell et al., 2010; van Weverberg, 2013; Roh and Satoh, 2014; Loftus et al., 2014). The bulk microphysical scheme assumes a size distribution function for the microphysics elements described by one or more moments of the size distribution function. One of the crucial decisions is the choice of the size distribution of the cloud and precipitating elements. In recent years, only a few papers have discussed the impact of an altered size distribution of cloud droplets and raindrops on surface precipitation (Ćurić et al., 1998, 2009, 2010). Some studies have examined the impact of the changed parameter within the same distribution function on precipitation characteristics (van den Heever and Cotton, 2004; Cohen and McCaul, 2006). Ćurić et al. (1998) investigated the influence of the chosen drop size distribution on cloud microphysics in their forced 1-D timedependent convective cloud model. They changed the liquid water spectrum by assuming the Khrgian–Mazin gamma distribution for the entire drop spectrum instead of the frequently used approach of using the monodisperse size

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

distribution for cloud droplets and Marshall–Palmer exponential size distribution for raindrops (Lin et al., 1983; Murakami, 1990; McCumber et al., 1991; Straka and Mansell, 2005; Chen and Xiao, 2010). They concluded that the unified Khrgian– Mazin size distribution gives a shower-type precipitation and prevailing solid precipitation. Obviously, the main disadvantage of this model is its dimensionality. Similarly, Ćurić et al. (2009) examined the cloud microphysics, dynamics and surface precipitation for the two previously mentioned approaches in a description of the liquid drop spectrum in a 3-D cloud-resolving mesoscale model with a single-moment bulk microphysical scheme. According to their study, it can be noted that the unified Khrgian–Mazin size distribution generates more cumulative rain over a larger area in a shorter time compared with the alternative approach. In their sensitivity study, Ćurić et al. (2010) investigated which of the two approaches in the description of the drop spectrum agrees better with the observed values of accumulated convective precipitation. They varied a mean radius of the Khrgian–Mazin distributed drops and compared the given results with the other case. They showed that the unified Khrgian–Mazin size distribution was in better accord with the mean, median and range of extreme values of the observed precipitation, whereas the alternative model version underestimated the observed accumulated precipitation. Additionally, both models generated cloud splitting in a V-shape with the storm cells characterised by rain showers. The crucial shortcomings of these studies are the use of the single-moment bulk microphysical scheme as well as the rough description of ice precipitating elements due to the absence of hailstone embryos (graupel and frozen raindrops). In this sensitivity study, we investigated the accumulated precipitation for the two previously mentioned approaches with a two-moment bulk microphysical scheme with various concentrations of cloud droplets. Therefore, we compared the results of the model version characterised by the unified Khrgian–Mazin size distribution for the entire spectrum of liquid drops with the frequently used model version with the monodisperse size distribution of cloud droplets and raindrops that obey the Marshall–Palmer size distribution. We used the unified Khrgian–Mazin size distribution to avoid the unnatural gap at the lower end of the raindrop spectrum. The Khrgian– Mazin distribution function is fitted by using the measured cloud droplets collected by aircraft (Khrgian and Mazin, 1963; Mazin et al., 1989). The Marshall–Palmer size distribution is obtained by fitting the raindrops collected on the ground (Marshall and Palmer, 1948). Despite its simplicity and frequent use in the literature, the Marshall–Palmer size distribution tends to overestimate the number of small and large raindrops (Torres et al., 1994). Zhang et al. (2006) compared the constrainedgamma (CG) and Marshall–Palmer distribution models (retrieved from radar measurements) with disdrometer observations. Their results show that the CG model agrees better with the disdrometer observations and produces more accurate forecasts than the Marshall–Palmer model parameterization. Martins et al. (2010) concluded that the Marshall–Palmer size distribution does not agree with radar and disdrometer observations of raindrop spectra over the Amazon region. Additionally, it is observed that the Marshall–Palmer size distribution tends to simulate rain on the ground for reported non-rain cases (Farley and Orville, 1986).

37

This paper is organised as follows. The model description and model setup used in this study are described in Section 2. The model results and discussion are given in Section 3. Finally, the conclusions are presented in Section 4. 2. Description of the cloud model 2.1. General model characteristics A cloud-resolving mesoscale model with the two-moment bulk microphysical scheme was used (Kovačević and Ćurić, 2013). The model integrates time-dependent, non-hydrostatic and fully compressible equations. The prognostic variables of the model are: the x, y and z components of the Cartesian velocity, perturbation potential temperature and pressure, mixing ratios for eight microphysics fields (water vapour, cloud water, rain, cloud ice, snow, graupel, frozen raindrops and hail), as well as the number concentrations of all microphysics fields excluding water vapour and cloud water. The cloud droplet number concentration was prescribed and its value varied in the different experiments. The mixing ratio and number concentration, as the two moments of the size distribution function were calculated at every grid point and at each time step in the model. The model area was 100 × 100 × 15 km. We used a horizontal grid spacing of 1000 m and a vertical grid spacing of 500 m. All simulations were terminated after 120 min. The short time step for integrating acoustic wave terms was 1 s. The large time step for the other terms was 6 s. The wave-radiating open boundary condition was used for the lateral boundaries. The turbulence was treated by a 1.5-order turbulent kinetic energy formulation. The effect of the Coriolis force was neglected in our experiments. 2.2. Model microphysics In this study, cloud droplets and raindrops are represented by the unified Khrgian–Mazin size distribution or, alternatively, the liquid drop spectrum is described using the monodisperse size distribution for cloud droplets and Marshall–Palmer size distribution for raindrops. The size distribution of cloud ice was used in agreement with Hu and He (1988). Other microphysics categories (snow, graupel, frozen raindrops and hail) were exponential (Lin et al., 1983). The terminal velocities used for hail were as proposed by Ćurić and Janc (1997) and for other elements, by Murakami (1990). Cloud water is produced by condensation using a saturation adjustment scheme derived from Tao et al. (1989). Melting of cloud ice is another source for cloud water. Rain can be initiated by the autoconversion of cloud droplets in agreement with Meyers et al. (1997), melting solid precipitating elements (snow, graupel, frozen raindrops and hail), or shedding of excess water from the surfaces of hailstones in a wet growth regime. Once created, raindrops grow mainly by the accretion of cloud droplets, or by the collision with cloud ice and snow at temperatures higher than 0 °C. Cloud ice initiation is performed through depositional nucleation and homogeneous freezing of cloud water below −40 °C. Depositional nucleation starts when water vapour is supersaturated with respect to ice at temperatures below 0 °C. The interactions of cloud elements (cloud droplets and ice crystals) as well as the immersion

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

38

freezing of cloud water are ignored. The cloud ice number concentration is equal to the concentration of active natural ice nuclei, as according to Fletcher (1962). Snow can be initiated by the Bergeron–Findeisen process and an autoconversion of cloud ice. Graupel is produced by an autoconversion of snow. Frozen raindrops are created by the immersion freezing of raindrops and by collisions of raindrops with cloud ice and snow. Hail can develop by the autoconversion of graupel and frozen raindrops. Furthermore, hail grows through collisions with cloud droplets, raindrops, ice crystals and snow. Melting and sublimation are the sinks of hail. Some microphysical processes for rain and hail are described in more detail in Appendix A. A definition of the symbols used in the microphysical parameterisation and a list of constants and variables are given in the study by Kovačević and Ćurić (2013). 2.3. Initial conditions

3. Model results and discussion We performed the model sensitivity tests using the two approaches to describe the spectrum of liquid water. In one case, the size distribution of liquid water is the unified Khrgian– Mazin size distribution for cloud droplets and raindrops with the boundary of the two spectra — Dmin = 200 μm (hereafter called KM). In the other case, we used the monodisperse size distribution (hereafter called M) for cloud droplets and Marshall–Palmer size distribution for raindrops (hereafter

z (km)

p

The reference state was horizontally homogeneous and it was obtained from a single sounding. The skewed-T/log p thermodynamic diagram for the sounding used is presented in Fig. 1. The wind direction veered sharply (from SE to NW

direction) from the surface to 1-km above ground level (AGL). The prevailing wind is from the northwest, while its speed increased with altitude from 7 ms−1 near the ground to approximately 17 ms−1 at 9 km AGL. A large amount of moisture is present until approximately 760 mb. The maximum value of the water vapour mixing ratio reaches 13.3 g kg−1 at p = 900 mb. This sounding is typical for the development of severe storms over the region of Western Serbia (Ćurić, 1982). To start convection, we used an ellipsoidal warm bubble with a maximum temperature perturbation of 2.0 K in the bubble centre. The bubble has a horizontal radius of 10 km and a vertical radius of 1.5 km. The coordinates of the bubble centre are (x, y, z) = (16, 84, 1.65) km.

Fig. 1. Initial sounding of temperature (solid line) and dew point (dashed line) plotted on skew T/log p diagram. Coordinate lines denote pressure (hPa) and temperature (°C). Height values (km) and wind barbs are shown on the right-hand side of the figure.

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

called MP); therefore, hereafter, this model version is called MMP. We conducted four sensitivity tests (for the KM and MMP model versions) called A, B, C and D, which are characterised by the corresponding values of the cloud droplet number concentration: 50, 200, 500 and 1000 cm−3, respectively. Thereby, these values cover a range of characteristic values of cloud droplet number concentration from maritime to typical continental clouds. The KM size distribution and the exponential MP size distribution (Marshall and Palmer, 1948) are two special cases of generalized gamma size distribution (Cotton et al., 2003). The KM size distribution is described in more detail (Kovačević and Ćurić, 2013). Fig. 2 illustrates the size distributions of the cloud droplets (M and KM size distribution) and raindrops (KM and MMP size distribution) for the four values of the cloud droplet number concentration. We can see that the M size distribution generates higher concentrations of the cloud droplets compared with the KM size distribution (Fig. 2a). The MP size distribution generates a significant concentration of raindrops with a diameter of up to about 10 mm, as opposed to the KM distributed raindrops that are characterised by minor drop concentrations over 1–2 mm in diameter. We examined the sensitivity of the rain and hail accumulation at the surface depending on the proposed size distribution of liquid water at different cloud droplet number concentrations. The time evolution of the rain accumulation on the ground is presented in Fig. 3. It can be seen that the amount of surface rain for the KM model version is larger than that of the MMP model version. This difference decreases as the cloud droplet number concentration grows. Additionally, rainfall is observed approximately 10 min earlier for the KM model version. Ćurić and Janc (2011) compared the arealaccumulated convective precipitation (AACP) from observations with the KM and MMP single-moment schemes during a 15-year period using a statistical analysis. They prescribed a mean radius of drop spectrum of 10 and 50 μm (KM10 and KM50, respectively). Their results showed that the MMP model version simulated significantly lower values of the AACP. Additionally, the KM50 microphysical scheme better simulates the AACP values than the other schemes.

(a)

39

Fig. 4 shows the total amount of hail accumulation at the surface depending on time. It can be seen that hail accumulation on the ground is reduced as the cloud droplet number concentration increases for the MMP model version. The time of hail occurrence at the surface is not sensitive to changes of cloud droplet number concentration. In the KM model version, the amount of surface hail increases with higher cloud droplet number concentration. Additionally, there is greater sensitivity in the appearance of hail on the ground for the KM model version. Therefore, higher values of cloud droplet number concentration lead to an earlier appearance of hail at the surface. In test A, the surface hail occurred after 80 min, whereas in test D, it was approximately 20 min. We will prove the cause of this phenomenon of simulated precipitation on the ground for the two different models. The total amounts of surface rain and hail are summarized in Table 1. We analysed the ratio of mass contribution of the production terms for the KM and MMP model versions as
k ¼ log10

 M KM : MMMP

ð1Þ

Positive values of k-ratios mean that the mass contribution of the production term for the KM model version is greater than its MMP counterpart; contrarily, negative values indicate the opposite relation. In addition to the k-ratios of the mass contribution on the current time step, we examined the kratios for the corresponding cumulative values. Fig. 5 illustrates the k-ratios for the autoconversion process of cloud droplets to raindrops (Praut) on the current time step (Fig. 5a) and for their cumulative values (Fig. 5b). In this case, the KM transfer rates of cloud droplets to raindrops are mainly several orders of magnitude greater than the MMP ones. This difference is greatest at lower cloud droplet number concentrations (tests A and B), whereas in case D, the MMP rate is somewhat higher than in the case of the KM model version. This fact is a consequence of the characteristics of the cloud droplet distribution. In the case of the M distribution, cloud droplets are of the same dimensions and their transfer to the raindrops is slowed, whereas with the M distribution, the KM size distribution generates a significant number of larger cloud

(b)

Fig. 2. Size distribution function for cloud droplets (a) and raindrops (b). M size distribution (single symbols), KM size distribution (solid line) and MP size distribution (dashed line) are presented for different cloud droplet number concentrations. Distributions are presented for Q = 10−2 kgkg−1.

40

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

(a)

(b)

(c)

(d)

Fig. 3. Mass M (in tonnes) of accumulated rain on the ground as a function of time for: nc = 50 cm−3 (a); nc = 200 cm−3 (b); nc = 500 cm−3 (c); and nc = 1000 cm−3 (d). Rain accumulation at the surface is presented for the KM and MMP model versions.

droplets. This leads to an increase in the probability of random collisions between cloud droplets and the rapid creation of raindrops. In the early stages of the cloud's life, there is a sharp peak of the k-ratio values. Later, the interaction of the cloud droplets with the other microphysics elements leads to a smoothing of the cloud water field and the minimising of the differences between the M and KM size distributions; thus, the absolute values of the k-ratio decrease rapidly. However, except for test D, the k-ratio remains positive, which indicates that the KM conversion rates are larger than the MMP ones. Similar behaviour of the k-ratio as a function of time is observed in the following figures for other microphysical processes. The time dependence of the k-ratio for the collection of cloud droplets by raindrops (Pracw) is presented in Fig. 6. In this case, the MMP collection rates are greater than their KM counterparts. Unrealistically large raindrops generated by the MP size distribution lead to an overriding of the accretion rates of the cloud droplets compared with the KM size distribution. Fig. 7 shows the k-ratio for the overall sink of rain depending on time. The sink of rainwater is the summary contribution by evaporation of raindrops and their collisions with ice categories. The sink of rain can be presented as:

P sink ¼ P revp þ P i f r þ P iacr þ P sacr þ P gacr þ P facr þ Dhacr þ W hacr :

ð2Þ

In Fig. 7, it can be seen that the MMP model version is characterised by rapid consumption of rainwater compared with the KM model version. The presence of super-large raindrops in significant concentrations, generated by the MP size distribution, leads to their evaporation and to the rapid mass transfer of rainwater to other microphysics categories, such as hailstone embryos (graupel and frozen raindrops) and hail. Zhang et al. (2006) noted that the MP model parameterization overestimates the evaporation and accretion rates for stratiform rain compared with the disdrometer data set. Our results show that the MMP version is able to simulate only stratiform precipitation, which will be discussed later. In summary, both the slower autoconversion of cloud droplets to raindrops and a stronger sink of rain for the MMP model version lead to a lower amount of the surface rain compared with the KM model version. Initially, hail is formed by the autoconversion of graupel and frozen raindrops. Fig. 8 demonstrates the time dependence of the k-ratio based on initial hail production. It can be noted that initially, the MMP model version generates more hail than its KM counterpart at lower cloud droplet number concentrations. As the cloud droplet number concentration increases, the KM initial production of hail overrides the MMP one. This means that the KM initial production of hail describes the process of creating hailstones better because it is positively correlated with the increase in cloud droplet number concentration. Namely, a higher cloud droplet number concentration provides more frequent collisions of cloud droplets with hailstone

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

(a)

(b)

(c)

(d)

41

Fig. 4. Mass M (in tonnes) of accumulated hail on the ground as a function of time for: nc = 50 cm−3 (a); nc = 200 cm−3 (b); nc = 500 cm−3 (c); and nc = 1000 cm−3 (d). Hail accumulation at the surface is presented for the KM and MMP model versions.

embryos (graupel and frozen raindrops) and therefore, riming is pronounced. This leads to the rapid transfer of hailstone embryos into hail. The MMP model version does not simulate the increased production of hailstones at higher concentrations of cloud droplets. This is also reflected in the time occurrence of surface hail, because the hail reaches the ground earlier as the cloud droplet number concentration grows due to the pronounced riming of the cloud droplets. It can be noted that k values depend greatly on the cloud droplet number concentration. At higher concentrations of cloud droplets (tests C and D), the k values have positive values. In these cases, there are many of the KM distributed cloud droplets that are larger than the M distributed ones; hence, the growth rate of the hailstone embryos is much larger in the KM case, via riming of cloud droplets. The excess of hailstone embryos above a given threshold is converted automatically into hail. Table 1 The total amounts of surface rain and hail for all experiments.

nc (cm Rain Hail

−3

)

MKM (kt) MMMP (kt) MKM (kt) MMMP (kt)

A

B

C

D

50

200

500

1000

9651.06 2126.45 0.02 864.33

7612.93 2313.13 521.85 1242.79

5479.81 2750.23 736.58 395.21

3780.54 2819.34 1444.53 451.27

Similar relations between the two model versions, described by the k-ratio as a function of time, can be seen in Fig. 9. This describes the k-ratio for the accretion of cloud droplets by hailstones (Dhacw), which is the most important mechanism for the growth of hailstones (Kovačević and Ćurić, 2014). Similarly, it can be noted that the growth rate of hail is higher for the KM model version at higher cloud droplet number concentrations. A higher concentration of cloud droplets leads to numerous KM distributed cloud droplets that are larger than the M distributed ones, which increase the hail amount due to the freezing of cloud droplets onto the surfaces of the hail. Fig. 10 represents a spatial distribution of the cumulative surface precipitation (in mm) for all experiments in the KM model case. It can be noted that lower cloud droplet number concentrations favour the development of expressed storm cells that cause cloud splitting in a V-shape and which are characterised by rain showers. At higher concentrations of cloud droplets, the weakening of the storm cells can be observed, the precipitation is more uniform and it extends over a larger horizontal area. Ćurić et al. (2009) showed that the KM model version is capable of creating more rain in a shorter time for the single-moment bulk microphysical scheme. In contrast to the KM model version, the spatial distribution of the accumulated precipitation on the ground for the MMP model case (Fig. 11) shows little sensitivity to changes in cloud droplet number concentration. This model

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

42

(a)

(b)

Fig. 5. The k-ratios for autoconversion of cloud droplets to raindrops (Praut) as a function of time (a) and their cumulative values (b) for all experiments.

version does not generate storm cells with rain showers as well as storm splitting. Accumulated precipitation at the surface is distributed uniformly over the entire precipitating area, similar to the precipitation from stratiform clouds. The reasons for these facts can be found in the transfers among the microphysics categories. For the MMP model version, a slower autoconversion of cloud droplets to raindrops (Praut) with pronounced gravity collection of cloud droplets (Pracw) compared with the KM model version, causes a population of super-large raindrops. A rapid consumption of rainwater through evaporation and collisions with ice categories (see Fig. 7) leads to a lowering of the precipitation rate and its surface accumulation for all experiments. On the other hand, the appearance of rain showers in the KM model version can be explained by the rapid autoconversion of cloud droplets to raindrops and slower sinks of rainwater. Additionally, as the cloud droplet number concentration increases, narrow bands of intense rainfall are weaker and disappear for experiment D. In this case, a strong sink of cloud water due to increased riming and a smaller average size of cloud droplets that reduce autoconversion are the primary causes for the weakening of the intense rain bands for the KM model version. The occurrence of rain showers can be explained in another way. Observations indicate that the rain showers occur after

(a)

strong thunder (Moore and Vonnegut, 1977). Some studies (Ćurić and Vuković, 1991; Vuković and Ćurić, 1998) have examined this phenomenon in more detail. When electrical discharge occurs, an acoustic front is formed that extends radially from the lightning channel. We assume that the lightning channel is set vertically. Under the influence of the acoustic wave from the thunder, the air accelerates rapidly and carries drops horizontally. Smaller water drops have low inertia, so they move more in the horizontal direction. Therefore, faster and smaller drops catch up with bigger ones and collide with them. For the M size distribution, cloud droplets shift the same distance (having the same dimensions) in the horizontal direction and they can only collide with raindrops (generated by the MP size distribution). The mass contribution of these droplets for raindrops is very small due to their size. Compared to the M size distribution, the KM distributed cloud droplets are of different sizes, which therefore causes a greater probability of acoustic coagulation (with other cloud droplets and raindrops) to form drops that will be effective for gravitation coagulation. Additionally, large raindrops (generated by the MP size distribution) are very inert, and are therefore not greatly influenced by the acoustic coagulation. Hence, the observed occurrence of rain showers after lightning may be evidence that the KM size distribution

(b)

Fig. 6. The k-ratios for accretion of cloud droplets by rain (Pracw) as a function of time (a) and their cumulative values (b) for all experiments.

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

(a)

43

(b)

Fig. 7. The k-ratios based on overall sink of rain as a function of time (a) and their cumulative values (b) for all experiments.

(a)

(b)

Fig. 8. The k-ratios for overall initial production of hail as a function of time (a) and their cumulative values (b) for all experiments.

describes more realistically the liquid water spectrum in the clouds. We conclude that the acoustic coagulation has little impact in the case of the MMP model. This is another proof of the lack of rain showers in this case.

(a)

Consider how the KM and MMP microphysical schemes affect the vertical motions in the cloud. Fig. 12 presents maximum updrafts and downdrafts with time for all experiments. Updrafts increase quickly at the early stage

(b)

Fig. 9. The k-ratios for accretion of cloud droplets by hail (Dhacw) as a function of time (a) and their cumulative values (b) for all experiments.

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

44

surface rain and reduced amounts of ice (hailstone embryos and hail) on the ground for both models. Increased vertical resolution causes slower riming of hailstone embryos. These ice elements are smaller, and they therefore melt faster and form raindrops below 0 °C and increase the amount of surface rain. A lower content of hailstone embryos leads to reduced hail formation. The impact of the increased vertical resolution on ground precipitation may be the subject of future study.

100

of the time integration. Generally, the MMP model version simulates lower values of the vertical velocity (updraft and downdraft) compared to the KM scheme. The presence of large raindrops slows updrafts in the MMP model version. The differences between the two microphysical schemes are reduced by increasing the concentration of the cloud droplets. In downdrafts, the rapid mass transfer of the MP distributed raindrops to ice precipitating categories (see Fig. 7) causes significant release of latent heat, which leads to weaker downdrafts compared with the KM model. In previous experiments, we used a 500 m grid interval in the vertical direction. This is necessary to examine the impact of altered vertical grid spacing on precipitation characteristics on the ground. We performed sensitivity experiments with an increased vertical grid resolution. We used 200 and 300 m grid intervals with the large time step of 3 s. The grid intervals remain unchanged in the horizontal direction. Generally, increased vertical resolution leads to greater amounts of

6

11

16

31

60

(b)

16

21

11

41

80

In this sensitivity study, we simulated convective clouds to investigate the precipitation characteristics (amount, time of occurrence and spatial distribution) for two approaches for the description of the liquid drop spectrum. We used the twomoment bulk microphysical scheme, in which the cloud droplet number concentration is suppositional. The occurrence, amount and spatial distribution of accumulated rain and hail at

(a)

16

21 46

4. Conclusion

51

6

6 11

11

46

y (km)

21 11

40

41

20

36

100 0

31

(c)

11 11

80

31

(d)

26

6

6

21

6

y (km)

60

6

16

11

40

6

20

11

1

0

y

6

0

x

20

40

60

x (km)

80

100

0

20

40

60

80

100

x (km)

Fig. 10. Spatial distribution of the total surface precipitation of the KM model version at t = 120 min for: nc = 50 cm−3 (a); nc = 200 cm−3 (b); nc = 500 cm−3 (c); and nc = 1000 cm−3 (d). Isohyets are drawn at 5 mm; the base isohyet is 1 mm. The amount of accumulated precipitation on the ground is represented using a scale on the right-hand side of the figure.

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

100

45

(b)

80

(a)

51

6 6 11

y (km)

60

46

40

41

20

36

100 0

31

(d)

26

80

(c) 6

21

6

6

60

6

40

y (km)

16

20

11

0

y

6

0

x

20

40

60

80

100

x (km)

0

20

40

60

80

100

1

x (km) Fig. 11. As in Fig. 10 but for the MMP model version.

the surface were investigated for different values of cloud droplet number concentration. We compared the results for the two different models, which are characterised by the frequently used approach (monodisperse size distribution for cloud droplets and Marshall–Palmer size distribution for raindrops) and the unified Khrgian–Mazin size distribution for the entire spectrum of liquid water. Our conclusions are as follows: • The larger amounts of accumulated rain in the KM model version are caused mainly by the rapid autoconversion of the KM distributed cloud droplets to raindrops and slower transfer of rain to other microphysics categories. • The KM model initial production of hail is positively correlated with the increase in cloud droplet number concentration. A higher cloud droplet number concentration leads to rapid hail production, causing larger amounts of accumulated hail on the ground and the earlier appearance of surface hail for the KM model version. This reason for this phenomenon lies in the fact that the KM model version simulates well the pronounced riming due to the larger concentration of cloud droplets. • The KM model version shows substantial differences in the spatial distribution of surface precipitation for different cloud

droplet number concentrations. A low concentration of cloud droplets causes the presence of narrow rain bands with intense precipitation (rain showers); in contrast, the MMP model version does not simulate rain showers. This is a consequence of the reduced autoconversion of the M distributed cloud droplets as well as the faster consumption of the MP distributed raindrops through evaporation and their collisions with ice elements. • The large MP distributed raindrops slow updrafts, whereas, in downdrafts, rapid freezing causes significant release of latent heat, which leads to weaker downdrafts compared with the KM model. • Generally, it can be said that the KM model version is more sensitive to changes in cloud droplet number concentration. Acknowledgements This research was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (grant no. 176013). We gratefully acknowledge the help of Mr Dragomir Bulatović for the technical preparation of the figures.

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

46

(a)

(b)

(c)

(d)

Fig. 12. Maximum values of updrafts and downdrafts (in ms−1) as a function of time for: nc = 50 cm−3 (a); nc = 200 cm−3 (b); nc = 500 cm−3 (c); and nc = 1000 cm−3 (d). The vertical velocities are presented for the KM and MMP model versions.

Appendix A. Some production terms for rain and hail In this appendix production terms for the KM and MMP model version are given. Some of the production terms for the KM model version (Piacr, NPiacr, Psacr, NPsacr, D(W)hacr, ND(NW)hacr, Pifr, NPifr, Dhacw and NQhacw) are already presented in the study (Kovačević and Ćurić, 2013). 1. Collection of cloud water by rain • For the KM model version:

P racw ¼






 3 16 2 ρ 2X 1:74a ρ0 0:5 BD BD BD 4e BD π Erw w A Ei Γ 9−i; rmin Γ 2:8 þ i; rmax −Γ 2:8 þ i; rmin − 13 Γ 11−i; rmin 11:8 3 ρ ρ 2 2 2 2 B B i¼1 

 BDrmax BDrmin −Γ 2 þ i; : Γ 2 þ i; 2 2

ðA1Þ

• For the MMP model version:

P racw

(
 ) 3 X π ρ0 0:5 D3−i D5−i c c ¼ Erw qc N0r Ei a ½Γ ð0:8 þ i; λr Drmax Þ−Γ ð0:8 þ i; λr Drmin Þ−e i ½Γ ði; λr Drmax Þ−Γ ði; λr Drmin Þ : 4 ρ λ0:8þi λr r i¼1

ðA2Þ

2. Collection of rain by cloud ice (for the MMP model version)

P iacr ¼

(

0:3 3 X π2 ρ ρ 0:5 Γ ð1 þ i; λi Dimax Þ p0 Γ ð1:33 þ i; λi Dimax Þ Eri w N0r N 0i Ei a 0 ½ ð D Þ−Γ ð 7:8−i; λ D Þ −A Γ 7:8−i; λ r rmax r rmin vi 1þi 7:8−i 24 ρ ρ p λ λ7−i λ λ1:33þi r r i¼1 i ) i ðA3Þ ½Γ ð7−i; λr Drmax Þ−Γ ð7−i; λr Drmin Þ

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

NP iacr

47

(

0:3 3 X π ρ 0:5 Γ ð1 þ i; λi Dimax Þ p0 Γ ð1:33 þ i; λi Dimax Þ ¼ Eri N0r N0i Ei a 0 ½ ð D Þ−Γ ð 4:8−i; λ D Þ −A Γ 4:8−i; λ r rmax r rmin vi 4:8−i 4 ρ p λ4−i λ1þi λ1:33þi r i¼1 i λr i )

ðA4Þ

½Γ ð4−i; λr Drmax Þ−Γ ð4−i; λr Drmin Þ : 3. Collection of rain by snow (for the MMP model version) (
 3 X π2 ρw ρ0 0:5 Γ ði; λs Dsmax Þ Γ ð0:25 þ i; λs Dsmax Þ ½Γ ð7:8−i; λr Drmax Þ−Γ ð7:8−i; λr Drmin Þ−c E N0r N0s Ei a P sacr ¼ i 7:8−i 24 rs ρ ρ λ λ0:25þi λ λ7−i s r s r i¼1 )

ðA5Þ

½Γ ð7−i; λr Drmax Þ−Γ ð7−i; λr Drmin Þ

NP sacr ¼

(
0:5 3 X π ρ Γ ði; λs Dsmax Þ Γ ð0:25 þ i; λs Dsmax Þ Ers 0 N0r N 0s Ei a ½Γ ð4:8−i; λr Drmax Þ−Γ ð4:8−i; λr Drmin Þ−c 4 ρ λis λ4:8−i λ0:25þi λ4−i r s r i¼1 )

ðA6Þ

½Γ ð4−i; λr Drmax Þ−Γ ð4−i; λr Drmin Þ : 4. Collection of rain by graupel • For the KM model version:

P gacr

  8
 
 < 3 Γ 0:64 þ i; λg Dhmin 
Γ i; λg Dhmin X 2 2 ρw ρ0 0:5 BDrmax BDrmin Γ 9−i; −Γ 9−i; −1:74a ¼ π Egr AN0g F i Avg : 3 ρ ρ 2 2 λ0:64þi λig B9:8−i B9−i g i¼1 

 BD BD Γ 9:8−i; rmax −Γ 9:8−i; rmin 2 2

NP gacr

  8
0:5 
 < 3 Γ 0:64 þ i; λg Dhmin 
Γ i; λg Dhmin X π ρ0 BDrmax BDrmin Γ 6−i; −Γ 6−i; −1:74a ¼ Egr AN0g F i Avg : 2 ρ 2 2 λ0:64þi λig B6:8−i B6−i g i¼1 

 BD BD : Γ 6:8−i; rmax −Γ 6:8−i; rmin 2 2

ðA7Þ

ðA8Þ

• For the MMP model version:

P gacr

  8
 2 < 3 Γ 4:64−i; λg Dhmin Γ 4−i; λg Dhmin X π ρw ρ0 0:5 E ¼ N0r N0g Ei Avg ½Γ ð5 þ i; λr Drmax Þ−Γ ð5 þ i; λr Drmin Þ−1:74a 3:8þi : 24 gr ρ ρ λ4:64−i λ4−i λ5þi g r g λr i¼1 ðA9Þ ) ½Γ ð3:8 þ i; λr Drmax Þ−Γ ð3:8 þ i; λr Drmin Þ

NP gacr

  8
0:5 3 < Γ 4:64−i; λg Dhmin Γ 4−i; λg Dhmin X π ρ0 ½Γ ð2 þ i; λr Drmax Þ−Γ ð2 þ i; λr Drmin Þ−1:74a ¼ Egr N0r N0g Ei Avg : 4 ρ λ4:64−i λg4−i λ0:8þi λ2þi g r r i¼1 ðA10Þ ) ½Γ ð0:8 þ i; λr Drmax Þ−Γ ð0:8 þ i; λr Drmin Þ :

5. Collection of rain by frozen raindrops • For the KM model version:

P facr

 8 

 3 <
4gρ 0:5 Γ 0:5 þ i; λ f Dhmin 
X 2 2 ρw BDrmax BDrmin 1:74a ρ0 0:5 h AN0 f −Γ 9−i; − ¼ π Efr Fi Γ 9−i; : 3C D ρ 3 ρ 2 2 λif B9:8−i ρ λ0:5þi B9−i i¼1 f ) 

   BD BD Γ i; λ f Dhmin Γ 9:8−i; rmax −Γ 9:8−i; rmin 2 2

ðA11Þ

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

48

NP facr

 8 

 <
4gρ 0:5 Γ 0:5 þ i; λ f Dhmin 
3 X π BD BD 1:74a ρ0 0:5  h ¼ E f r AN0 f Fi Γ i; λ f Dhmin Γ 6−i; rmax −Γ 6−i; rmin − i 6:8−i 0:5þi 6−i : 3C D ρ 2 2 2 ρ λf B λf B i¼1 ðA12Þ 

) BDrmax BDrmin −Γ 6:8−i; : Γ 6:8−i; 2 2

• For the MMP model version:

P facr

  8
0:5 Γ 4−i; λ D 2 <
4gρ 0:5 Γ 4:5−i; λ f Dhmin 3 X f hmin π ρw ρ h E N N ¼ E ½Γ ð3 þ i; λr Drmax Þ−Γ ð3 þ i; λr Drmin Þ−a 0 3:8þi 24 f r ρ 0r 0 f i¼1 i : 3C D ρ ρ λ3þi λ4:5−i λ4−i r f f λr ðA13Þ ) ½Γ ð3:8 þ i; λr Drmax Þ−Γ ð3:8 þ i; λr Drmin Þ

NP facr

 8 <
4gρ 0:5 Γ 4:5−i; λ f Dhmin 3 X π h ¼ E f r N0r N0 f Ei ½Γ ði; λr Drmax Þ−Γ ði; λr Drmin Þ : 3C D ρ 4 λir λ4:5−i f i¼1  )
0:5 Γ 4−i; λ D f hmin ρ ½ ð Þ−Γ ð Þ  Γ 0:8 þ i; λ D D 0:8 þ i; λ : −a 0 r rmax r rmin 0:8þi ρ λ4−i f λr

ðA14Þ

6. Collection of rain by hail (for the MMP model version) DðW Þhacr ¼

(
 2 3 X π ρ 4gρh 0:5 1 Ehr w N0r N0h Ei ½Γ ð0:5 þ i; λh Dhmax Þ−Γ ð0:5 þ i; λh Dhmin Þ½Γ ð7−i; λr Drmax Þ−Γ ð7−i; λr Drmin Þ 24 ρ 3C D ρ λh0:5þi λr7−i i¼1 ) ðA15Þ
0:5 ρ0 1 ½Γ ði; λh Dhmax Þ−Γ ði; λh Dhmin Þ ½Γ ð7:8−i; λr Drmax Þ−Γ ð7:8−i; λr Drmin Þ −a i 7:8−i ρ λh λr

NDðNW Þhacr

(
 3 X π 4gρh 0:5 1 ¼ Ehr N0r N 0h Ei ½Γ ð0:5 þ i; λh Dhmax Þ−Γ ð0:5 þ i; λh Dhmin Þ½Γ ð4−i; λr Drmax Þ−Γ ð4−i; λr Drmin Þ 0:5þi 4−i 4 3C ρ λr λ D i¼1 h ) ðA16Þ
0:5 ρ0 1 ½Γ ði; λh Dhmax Þ−Γ ði; λh Dhmin Þ ½Γ ð4:8−i; λr Drmax Þ−Γ ð4:8−i; λr Drmin Þ : −a i 4:8−i ρ λh λr

7. Immersion freezing of rain (for the MMP model version) Pi f r ¼

0 

π2 ρw 0 N 0r B 7 exp A ðT 0 −T Þ −1 ½Γ ð7; λr Drmax Þ−Γ ð7; λr Drmin Þ 36 ρ λr

ðA17Þ

0 

π 0 N 0r B exp A ðT 0 −T Þ −1 ½Γ ð4; λr Drmax Þ−Γ ð4; λr Drmin Þ: 6 λ4r

ðA18Þ

NP i f r ¼

8. Rain evaporation • For the KM model version:

P revp

)  

 

1  1
1 
πð1−SÞ ρw 6:24 BDrmax BDrmin ν 3 a 2 ρ0 4 BDrmax BDrmin −4:9 A −Γ 4; þ4:63 −Γ 4:9; B ¼ Γ 4; Γ 4:9; : Fk þ Fd ρ Dv ν 2 2 ρ 2 2 B4 ðA19Þ

• For the MMP model version:

P revp

)
1 
1 2π ð1−SÞ ρw 0:78 0:308 ν 3  a 12 ρ0 4 N ¼ ½Γ ð2; λr Drmax Þ−Γ ð2; λr Drmin Þþ 2:9 ½Γ ð2:9; λr Drmax Þ−Γ ð2:9; λr Drmin Þ ðA20Þ F k þ F d ρ 0r λ2r Dv ν ρ λr

NP revp ¼

P revp nr : qr

ðA21Þ

N. Kovačević, M. Ćurić / Atmospheric Research 158–159 (2015) 36–49

49

9. Collection of cloud water by hail (for the MMP model version)

Dhacw ¼

(
)  3−i 5−i 3 X π 4gρh 0:5 Dc Dc ðA22Þ Γ 0:5 þ i; λ Ehw qc N0h Ei ½ ð D Þ−Γ ð 0:5 þ i; λ D Þ −e ½ Γ ð i; λ D Þ−Γ ð i; λ D Þ  h hmax h hmin h hmax h hmin 4 3C D ρ λih λ0:5þi i¼1 h

NQ hacw ¼

Q hacw nh ; Q hacw ¼ Dhacw ; TN273:16 K: qh

References Ackerman, A.S., Kirkpatrick, M.P., Stevens, D.E., Toon, O.B., 2004. The impact of humidity above stratiform clouds on indirect aerosol climate forcing. Nature 432, 1014–1017. Chen, B., Xiao, H., 2010. Silver iodide seeding impact on the microphysics and dynamics of convective clouds in the high plains. Atmos. Res. 96, 186–207. Cohen, C., McCaul Jr., E.W., 2006. The sensitivity of simulated convective storms to variations in prescribed single-moment microphysics parameters that describe particle distributions, sizes, and numbers. Mon. Weather Rev. 134, 2547–2565. Cotton, W.R., Pielke Sr., R.A., Walko, R.L., Liston, G.E., Tremback, C.L., Jiang, H., McAnelly, R.L., Harrington, J.Y., Nicholls, M.E., Carrio, G.G., McFadden, J.P., 2003. RAMS 2001: current status and future directions. Meteorol. Atmos. Phys. 82, 5–29. Ćurić, M., 1982. The development of the cumulonimbus clouds which moves along a valley. In: Asai, T., Agee, E.M. (Eds.), Cloud Dynamics. Reidel, Dordrecht, pp. 259–272. Ćurić, M., Janc, D., 1997. On the sensitivity of hail accretion rates in numerical modeling. Tellus 49A, 100–107. Ćurić, M., Janc, D., 2011. Comparison of modeled and observed accumulated convective precipitation in mountainous and flat land areas. J. Hidrometeor. 12, 245–261. Ćurić, M., Vuković, Z.R., 1991. The influence of thunderstorm-generated acoustic waves on coagulation. Part I: mathematical formulation. Z. Meteorol. 41 (3), 164–168. Ćurić, M., Janc, D., Vučković, V., 1998. On the sensitivity of cloud microphysics under influence of cloud drop size distribution. Atmos. Res. 47–48, 1–14. Ćurić, M., Janc, D., Vučković, V., Kovačević, N., 2009. The impact of the choice of the entire drop size distribution function on Cumulonimbus characteristics. Meteorol. Z. 18 (2), 207–222. Ćurić, M., Janc, D., Veljović, K., 2010. Dependence of accumulated precipitation on cloud drop size distribution. Theor. Appl. Climatol. 102 (3–4), 471–481. Farley, R.D., Orville, H.D., 1986. Numerical modeling of hailstorms and hailstone growth. Part I: preliminary model verification and sensitivity tests. J. Clim. Appl. Meteorol. 25, 2014–2035. Feingold, G., Stevens, B., Cotton, W.R., Walko, R.L., 1994. An explicit cloud microphysical/LES model designed to simulate the Twomey effect. Atmos. Res. 33, 207–233. Fletcher, N.H., 1962. The Physics of Rain Clouds. Cambridge University Press, Cambridge (390 pp.). Hu, Z., He, G., 1988. Numerical simulation of microphysical processes in cumulonimbus. Part I: microphysical model. Acta Meteorol. Sin. 2, 471–489. Khain, A., Rosenfeld, D., Pokrovsky, A., Blahak, U., Ryzhkov, A., 2011. The role of CCN in precipitation and hail in a mid-latitude storm as seen in simulations using a spectral (bin) microphysics model in a 2D dynamic frame. Atmos. Res. 99, 129–146. Khrgian, A., Mazin, I.P., 1963. Cloud Physics. Israel Prog. Sci. Transl., Jerusalem (392 pp.). Kovačević, N., Ćurić, M., 2013. The impact of the hailstone embryos on simulated surface precipitation. Atmos. Res. 132–133, 154–163.

ðA23Þ

Kovačević, N., Ćurić, M., 2014. Sensitivity study of the influence of cloud droplet concentration on hail suppression effectiveness. Meteorol. Atmos. Phys. 123, 195–207. Lin, Y.-L., Farley, R.D., Orville, H.D., 1983. Bulk parameterization of the snow field in a cloud model. J. Clim. Appl. Meteorol. 22, 1065–1092. Loftus, A.M., Cotton, W.R., Carrió, G.G., 2014. A triple-moment hail bulk microphysics scheme. Part I: description and initial evaluation. Atmos. Res. 149, 35–57. Mansell, E.R., Ziegler, C.L., Bruning, E.C., 2010. Simulated electrification of a small thunderstorm with two-moment bulk microphysics. J. Atmos. Sci. 67, 171–194. Marshall, J.S., Palmer, W. McK, 1948. The distribution of raindrops with size. J. Meteorol. 5, 165–166. Martins, R.C.G., Machado, L.A.T., Costa, A.A., 2010. Characterization of the microphysics of precipitation over Amazon region using radar and disdrometer data. Atmos. Res. 96, 388–394. Mazin, I.P., Khrgian, A.K., Imianitov, I.M., 1989. Clouds and Cloud Atmosphere (in Russian). Gidrometeoizdat, Leningrad (648 pp.). McCumber, M., Tao, W.K., Simpson, J., Penc, R., Soong, S.T., 1991. Comparison of ice-phase microphysical parameterization schemes using numerical simulations of tropical convection. J. Appl. Meteorol. 30, 985–1004. Meyers, M.P., Walko, R.L., Harrington, J.Y., Cotton, W.R., 1997. New RAMS cloud microphysics parameterization. Part II: the two-moment scheme. Atmos. Res. 45, 3–39. Moore, C.B., Vonnegut, B., 1977. The thunder cloud. In: Golde, R.H. (Ed.), Lightning 1. Academic, San Diego, USA, pp. 51–98. Morrison, H., Grabowski, W.W., 2010. An improved representation of rimed snow and conversion to graupel in a multicomponent bin microphysics scheme. J. Atmos. Sci. 67, 1337–1360. Murakami, M., 1990. Numerical modeling of dynamical and microphysical evolution of an isolated convective cloud — the 19 July 1981 CCOPE cloud. J. Meteorol. Soc. Jpn. 68, 107–127. Roh, W., Satoh, M., 2014. Evaluation of precipitating hydrometeor parameterizations in a single-moment bulk microphysics scheme for deep convective systems over the tropical Central Pacific. J. Atmos. Sci. 71, 2654–2673. Straka, J.M., Mansell, E.R., 2005. A bulk microphysics parameterization with multiple ice precipitation categories. J. Appl. Meteorol. 44, 445–466. Tao, W.K., Simpson, J., McCumber, M., 1989. An ice–water saturation adjustment. Mon. Weather Rev. 117, 231–235. Torres, D.S., Porra, J.M., Creutin, J.-D., 1994. A general formulation for raindrop size distribution. J. Appl. Meteorol. 33, 1494–1502. van den Heever, S.C., Cotton, W.R., 2004. The impact of hail size on simulated supercell storms. J. Atmos. Sci. 61, 1596–1609. van Weverberg, K., 2013. Impact of environmental instability on convective precipitation uncertainty associated with the nature of the rimed ice species in a bulk microphysics scheme. Mon. Weather Rev. 141, 2841–2849. Vuković, Z.R., Ćurić, M., 1998. The acoustic–electric coalescence and the intensification of precipitation radar echoes in clouds. Atmos. Res. 47–48, 113–125. Zhang, G., Sun, J., Brandes, E.A., 2006. Improving parameterization of rain microphysics with disdrometer and radar observations. J. Atmos. Sci. 63, 1273–1290.