Rain drop size distribution analysis at a tropical location near land-sea boundary

Rain events can be characterized by rain drop size distribution (DSD) that denotes the number of drops as a function of diameter per unit size interval and per unit volume of space. DSD (at ground level) describes the microstructure of precipitation during different phases of rain varying both spatially and temporally. DSD can be influenced by the nature and origin of rain. The present study investigates the role of continental and maritime airflow in influencing the precipitation features near the land-sea boundary. The data of the rain DSD used in the present analysis are collected from a ground-based disdrometer located at Kolkata, India, near land-sea boundary during the year of 2011–2017. The dataset is divided into two categories, namely, maritime and continental rainfall, based on the airflow trajectories associated with rain events exclusively from Bay of Bengal or land region in the west of Kolkata as derived from TRAJSTAT software. The events with trajectories extending both over land and sea region are excluded for the present study. Variations of the DSD parameters using the gamma model are presented showing the abundance of smaller drops during maritime rain events whereas dominance of larger rain drops in the case of the continental rain events. The Z-R relations are also found to be significantly different for these two types of rain. The present study reveals the microstructures of rain at a location where the influences of both land and sea climatic features prevail.


Introduction
Past studies on rain microstructures are mostly concerned with DSD variations with respect to locations and rain types (Rao et al. 2001Tokay and Short 1996;Atlas et al. 1999;Rosenfeld and Ulbrich, 2003). Precipitation process near land-sea boundary has more variability (Singh and Mulye, 1991;Chakravarty et al. 2013) compared to the land and coastal locations separately. The aerosol transports from both land and ocean have significant influence on rain climatology as reported in earlier studies (Rosenfeld and Lensky, 1998;Radhakrishna et al., 2009;Fuentes et al., 2008). Limited studies are reported on the rain DSD difference due to maritime and continental circulation from a coastal location (Das and Chatterjee, 2018). Rain classification based on land and sea airflow at the locations like the present one (Kolkata, India) has not been investigated adequately. Earlier studies (Maitra et al., 2019;Rakshit et al., 2016;Jana et al., 2018) from Kolkata suggests the location to be important for the study of DSD variations as it is situated near the land-ocean boundary and thereby experiencing a variety of atmospheric processes influencing DSD. The main objective of this study is to understand the role of continental and maritime air motion that influences the precipitation microstructure near the land-ocean boundary.
Kolkata is located in the eastern part of India which is about 70 km away from the coast of Bay of Bengal. Kolkata experiences a tropical climate with the Indian summer monsoon. Rain brought by the Bay of Bengal branch of the monsoon gives maximum rainfall which occurs during June-August, the average annual rainfall being 1,582 mm. Figure 1a gives the geographical location of the experimental site, Kolkata, India. Figure 1b depicts the average monthly variation of rainfall during the period of 7 years with rainfall occurring mainly in the months of June, July and August from Joss and Waldvogel disdrometer (JWD) dataset. The highest amount of rainfall of about 300 mm in the month July has been recorded.

Data and methodology
Rain DSD analysis is done with the dataset collected from a ground-based Joss and Waldvogel (JWD) disdrometer located at the Institute of Radio Physics and Electronics of University of Calcutta (22.5° N,88.4° E), which is a tropical location near the land-sea boundary during the years 2011-2017. The range of rain drops that the JWD disdrometer measures is 0.3-5.5 mm, and it arranges them in 20 bins. JWD is considered a dependable and robust groundbased instrument based on its overall performance and is widely used around the globe (Sarkar et al., 2015;Tokay et al., 2013). The rain rate data from DSD were validated by colocated ORG (optical rain gauge) rain rate measurements (Sarkar et al., 2015). Here, untruncated disdrometer measurements are considered for DSD parameter estimation (Vivekanandan et al., 2004). As very small drops are not sensed by the present impact type disdrometer, the error due to not truncating the data is not significant. Rain in Kolkata is influenced by the wind containing moisture picked up from Bay of Bengal, or it can be generated over the Indian landmass (Das and Maitra, 2018;Tenório et al., 2012). The dataset is divided into two subsets, namely, maritime and continental rainfall. Rainfall systems coming from the continent moving eastward represent the continental subset. The other is composed of rainfall systems that developed over Bay of Bengal and moving westward representing the maritime subset. The rain events are segmented into maritime rain and continental rain using the back trajectory calculation software, namely, TRAJSTAT (Draxler and Hess, 1998). NCEP/NCAR global reanalysis data products of National Oceanic and Atmospheric Administration (NOAA) (ftp:// arlftp. arlhq. noaa. gov/ pub/ archives/ reanalysis) have been used in back trajectory analysis. The long-distance pathways of airflow responsible for each rain event are traced using the HYSPLIT model (Kassomenos et al., 2010). HYSPLIT model requires U,V (horizontal and vertical wind components), T (temperature), Z (height), P (pressure), and pressure at the surface (P 0 ) (Draxler and Hess, 1998;Stein et al., 2015). This analysis of continental and maritime rain has been done with the 5 days back trajectories at a height of 2000 m above sea level over Kolkata. For the present study, those dates are chosen where the back trajectory either fully covers the land or the sea region and the events with trajectories extending over both land and sea regions are excluded.
For comparing DSDs, the number concentration of drop (Rosenfeld and Ulbrich, 2003) is modelled with gamma distribution function (Kozu et al., 2006) given as: where N(D) (m −3 cm −1 ) is the number of drops per unit volume per unit size interval and the parameters , Λ, and N 0 signify the shape, slope, and intercept of the distribution. The gamma model has been chosen because it gives the realistic representation of rain DSD at the Indian locations Kirankumar et al., 2008;Maitra et al., 2019;Rakshit et al., 2016;Jana et al., 2018) and elsewhere (Ulbrich, 1983). The method of moment technique is used for computing the distribution parameters using the following relations (Kozu and Nakamura, 1991).
The N 0 (m −3 ) parameter is given by The slope parameter Λ (mm −1 ) is given by where μ is the shape parameter without dimensions and is given by and where M 3 , M 4 , and M 6 , are the 3rd, 4th, and 6th moments of the drop size distribution.
The rain integral parameters can be estimated using the formulas: Rain rate Radar reflectivity where A represents total area of observation, t denotes time interval between the successive observations, n i denotes total number of drops in ith drop size class, D i represents mean diameter of ith drop size class, and V(D i ) is the terminal drop velocity of class i having diameter D i . The drop velocities are calculated using the Gunn and Kinzer (1949) relationship as given below.

Results and discussions
Case studies have been made for two typical rain events in the month of October 2017 depicting maritime and continental rain as shown in Fig. 2.The red line indicates the continental airflow as the wind direction fully covers the land mass before rain occurrence at Kolkata, while the blue line corresponds to the maritime airflow as the wind contains trajectory coming from Bay of Bengal indicating that it picked up moisture from the sea surface. This analysis has been done to study the differences in rain DSD characteristics of maritime and continental rain as indicated by the wind trajectories.
In Figs. 3a and 4a, contour diagrams (Maitra et al., 2012) of the number density of various drop sizes at different time points during continental and maritime events are

Fig. 2
Back trajectories of wind regenerated by TRAJSTAT for a single day of maritime (October 20, 2017) and continental rain (October 25, 2017) presented. It is seen from Figs. 3a and b and 4a and b that for similar rain rates which are around 40-60 mm/h, the rain drop size distributions do not show similar patterns. In Figs. 3a and 4a, the colour bar indicates the number density of rain drops in log scale N(D) ( mm −1 m −3 ). The DSD variation pattern shows the abundance of drop sizes from 1 to 2 mm, and the presence of drop sizes above 3 mm is marginal for the maritime event on October 20, 2017. This clearly indicates that this particular rain event has abundance of small rain drops compared with large rain drops. On October 25, 2017, when the back trajectory from the present location covered the landmass, the rain event is identified as the continental type for which DSD variation is shown in Fig. 4a.
The contour diagram of drop number density for the convective event shows significant presence of large rain drops above 3 mm size, and rain drops as large as 5 mm also occur. This indicates that the event has higher number of larger drops compared to the earlier maritime rain event. This analysis of two rain events of continental and maritime Again, maritime rain has been considered on those days on which wind trajectories are from Bay of Bengal and Indian Ocean during 2011-2017 as shown in Fig. 6, trajectories on different days being indicated by different colours.
Rain drops in continental rainfall grow in the form of ice particles. On the other hand, rain drops of maritime rainfall grow by the collision-coalescence mechanism (Suh et al. 2016). So, the mass-weighted drop diameter of continental rainfall observed on the ground is larger than that of maritime rainfall. Specific heat is a major climatological feature that creates differences between DSDs in maritime and continental regions. As these two regions have different thermal capacities, there might be significant variations of DSDs in these two types of rain. Distinguishable DSD variations for maritime and continental rain are studied for different rain rates for the period 2011-2017.
To investigate the DSD differences between maritime and continental rainfall, six rain rate classes (namely, 0 < RR < 2, 2 < RR < 4, 4 < RR < 8, 8 < RR < 16, 16 < RR < 32, and RR > 32 mm/h) are considered by following the rain rate classification criterion of Tokay and Short (1996). For each rain rate class, DSD variations are depicted in Fig. 7. In the first rain rate class (Fig. 7a), 0 < RR < 2 mm/h, small-size drops (D < 1 mm) have higher concentration in maritime than in continental rain, and a reverse pattern is observed for the midsize to large drops (D > 1 mm). Rain drops of diameter smaller than 1 mm have a lower concentration, and rain drops larger than 1.2 mm have a higher concentration in continental as compared to maritime rainfall in the second rain rate class 2 < RR < 4 mm/h (Fig. 7b). In third rain rate class 4 < RR < 8 mm/h, rain drops of diameter less than 1.4 mm are more abundant in maritime than continental rainfall, and rain drops with diameter above 1.4 mm diameter are more in continental than maritime. Rain drops above 1.6 mm diameter have a higher concentration in continental than maritime in the fourth rain rate class 8 < RR < 16 mm/h. In the remaining two rain rate classes 16 < RR < 32 mm/h and RR > 32 mm/h, continental rainfall has a higher concentration than maritime for the rain drops above 2-mm diameter. For both cases, with the increase in rain rate, the breadth of DSD shape increases, the tail of DSD shifts toward the larger diameter, and the concentration of small drops decreases (Fig. 7). It may also be noted that the difference of DSD in continental and maritime rain reduces with increase of rain rate. The decrease of number density of very small drop sizes has been reported from the measurements by other types of disdrometer that includes an optical disdrometer (Sarkar et al., 2015). Since very small drops do not significantly impact the rain integral parameters, a possible underestimation of such drops by the impact type of disdrometer will not affect the main contentions of the study. Figure 8 illustrates the distribution curve of massweighted mean diameter ( D m ). Mass-weighted drop diameter, D m (Suh et al. 2016), is obtained using method of moments (Bringi et al. 2003) and is defined as the ratio of fourth to third moment of DSD (Seela et al. 2018).
The distribution of occurrence of D m for maritime and continental rain events has been investigated in terms of probabilty density function (PDF). Essentially, PDF represents the probability of occurrence of a certain D m value per unit size interval. The PDF of D m is calculated by using a kernel density function (Jones, 1990) in MATLAB that returns a probability density estimate in vector form for sample data. The PDFs are evaluated at equally spaced points that cover the range of D m values. Figure 8 shows that the peak PDF value for maritime rain is around 0.8 mm, while the peak value for continental rain is nearly 1.4 mm (Tenorio et al., 2012;Seela et al. 2018). PDF analyses indicate a relative abundance of smaller drops during maritime events and larger drops during continental events. The broader peak of occurrence probability for continental rain also shows that this type of precipitation is subject to wider atmospheric variation compared to maritime rain.

Z-R relation for continental and maritime data subsets
The Z-R relation can indicate microphysical process involved with rain drops. A difference in the DSD between continental and maritime rainfall event implies that the parameter A and b of the radar rainfall estimation relation Z = AR b will also vary due to geographic location, atmospheric condition, and type of instrument (Campos and Zawadzki, 2000;Rosenfeld and Ulbrich, 2003;Das and Maitra, 2018).
The coefficient A infers the overall presence of smaller or larger rain drops (larger A for larger drops), and the power b reflects the microphysical processes involving drop size evolution. A value b greater than 1 signifies size or mixed controlled cases, namely, collision and coalescence, whereas b ~ 1 signifies number-controlled cases (collision, coalescence and breakup) that produce equilibrium DSD (Seela et al., 2018;Atlas et al., 1999;Rosenfeld and Ulbrich, 2003;Steiner et al., 2004).
A clear difference in coefficient (A) and exponent (b) values of Z-R relations can be noticed between continental  Fig. 9a and maritime rainfall in Fig. 9b. For clarity two (continental and maritime) curves are shown together in Fig. 9c.The radar rainfall relation for continental rain is Z = 446.4R 1.261 , and that of maritime rain is Z = 270.7R 1.267 which shows that continental rain has higher A value than Maritime Rain Continental Rain maritime rain. This reveals that continental rain mainly is mostly composed of moderate to large drop size rain drops and higher rain rates, while small drops are dominant in maritime rain which has low intensity rain.

Gamma model parameter analysis
As already mentioned, the gamma DSD parameters ( N 0 , , and Λ ) could be effectively used to study the natural variations in the characteristics of precipitation (Seela et al., 2018). Variations of the gamma parameters with rain rate have been studied to inquire the difference between continental and maritime rain and are shown below.

Variation of N 0 with rain rate
The scatter plots N 0 with R for continental and maritime rains are presented in Fig. 10a and b, respectively. A power law relation N 0 = AR b can be fitted in which A depends on the total number of drops and b reflects the microphysical process. From Fig. 10c it is seen that coefficient A is 0.4002 for continental rain and 0.7311 for maritime rain, indicating that more number of drops are present in maritime than in continental rain. The values of b also differ for both the rain types showing the difference in microphysical process (Table 1).

Variation of and 3 with rain rate
The μ parameter describes the breadth and the shape of the DSD spectrum, and the value of μ less (greater) than 1 denotes concave upward (downward) shape and equal to zero gives an exponential shape (Ulbrich, 1983). The Λ parameter describes the slope of the distribution of rain DSD. Larger values of Λ and μ in maritime compared to continental rains, as shown in Fig. 11a and b, indicate a narrower distribution of rain drop sizes in the maritime rain compared to the convective type. The μ-R curve for Kolkata compares well with that for Gadanki (Kozu et al., 2006). As Kozu et al. (2006) reported, large μ values indicate an inhibition of the growth of drop sizes due to weak convective activity. The present study shows larger μ values for maritime rain indicating the dominance of smaller rain drops. The smaller values of Λ point to a more gradual decay of DSD spectrum towards the larger drop sizes. Therefore, the continental rain has greater presence of large drops, while the maritime rain has an abundance of smaller rain drops (Seela et al., 2018).

Conclusion
In this study, maritime and continental rainfall showed some contrasting characteristics. The dataset of DSD spanning over 7 years during 2011-2017 from measurements with a disdrometer over Kolkata revealed less intense rainfall occurring in maritime rain compared to continental rain. Mean raindrop concentration of both the rain clearly shows a demarcation with dominance of smaller drops in maritime and midsize and larger drops in continental rainfall. The radar reflectivity against rain rate relation yields Z = 446.4R 1.261 for continental rain and Z = 270.7R 1.267 for maritime rain, supporting this fact. Strong convective activity occurring due to heating of earth's surface results in the formation of continental clouds where water vapour gets transferred to higher altitude resulting in rapid development of ice crystals above the melting layer. Vapour deposition, aggregation and riming process make the ice crystals to grow into large snowflakes occurring in convective clouds of continental rain. These bigger ice crystals melt to precipitate as bigger raindrops, which are able to fall, and smaller drops, on the other hand, are lifted up by strong updrafts. An increase in the collision-coalescence process aided by updraft by holding the small drops aloft results in large values D m at the ground. In contrast, since maritime rainfall is linked with small updraft and downdraft and formation of low melting layer heights (Seela et al., 2018), there is no adequate time for the drops to grow bigger in size as in the continental rainfall, causing smaller size rain drops to dominate compared to continental rainfall. However, maritime rainfall mostly occurred in post monsoon periods (October-December) when the temperature is cooler, and usually strong convection does not occur. As reported (Seela et al., 2018), the rainfall during this period is associated with low melting layer heights and weak updrafts and downdrafts, which are not conducive to let drop sizes grow bigger. It should be noted that continental and maritime events are not connected on a one-to-one basis with convective and stratiform types of rain. Usually, continental rains are associated with strong convective activities producing large rain drops, whereas maritime rains are accompanied by small vertical drafts and low melting layer formation which result in an abundance of small rain drops. The present location provides an opportunity to study the microphysics of rain of different origins that are influenced by atmospheric conditions over land and sea. This has Fig. 11 Variation of Λ versus R and μ versus R for both continental and maritime rain applications in radar-based measurements of rainfall and in indicating changes in regional climate scenarios.