**3. Data and methodology**

where *r* is the distance from the radar to the target, *C* is a constant depending on the radar equipment, and *Z* is the radar reflectivity factor, which is determined by the physical properties of the target. The returned power and radar reflectivity factor are usually expressed in decibels (dB) because they span a large range of values. Therefore, dBZ is the unit most frequently seen on the radar display, which stands for decibel relative to *Z* and can be estimated

10log(*Z*) = 10log(*Pr*) + 20log(*r*) − 10log(*C*) (2)

The dBZ is a basic quantity used in weather radar. Radar reflectivity (*Z*) is an inherent prop-

*Z* = ∫*N*(*D*) *D*<sup>6</sup> *dD* (3)

where *D* is the raindrop diameter and *N(D)* is raindrop size distribution. Eq. (3) is only valid if the radar wavelength is larger than the raindrop size, which is also known as Rayleigh scattering. On the other hand, if the wavelength (*λ*) is not large enough compared with the raindrop

where *σ* is the Mie scattering cross section and |*Kw*| is the complex index of refraction for

Weather radar has become essential in cloud physics, weather observation, and forecasting. Accurate estimates of both the spatial and temporal distribution of observed rainfall are important inputs for weather forecasts, river and flash flood models, and others. Unfortunately, the accuracy of rainfall estimates using weather radar is affected by multiple sources of error. The errors originate from the internal characteristics of weather radar such as the miscalibration of radar parameters in constant *C* of Eq. (2). Other error sources are from external environmental conditions such as ground clutter, partial beam blockage, signal attenuation, and the vertical profile of radar reflectivity. Most operation, ground-based radar cannot measure radar reflectivity close to the surface. The minimum effective height of radar coverage may be 1–2 km or more above the surface [18]. Thus, information about the vertical gradient of radar reflectivity

Radar reflectivity is proportional to the sixth power of the drop size (Eq. (3)), and thus, the characteristics of a raindrop have a disproportionate effect on radar reflectivity. Downward increasing or decreasing of radar reflectivity toward the surface is related to the evolution of raindrop, particularly a large-sized drop. Over the IMC, spatiotemporal variation of DSD is clearly observed, particularly for heavy rains [9, 23–25]. As the physical properties of precipitation, such as raindrops, continuously change and vary spatially and temporally due to many aspects, the vertical gradient of radar reflectivity also varies. Therefore, using a fixed vertical gradient of radar reflectivity values can result in erroneous surface reflectivity that leads to erroneous rainfall estimates from weather radar. However, a study on the vertical


*π*<sup>5</sup>

below freezing level is crucial for the estimation of the surface radar reflectivity.

profile of precipitation over the IMC remains limited to several locations.

by solving Eq. (1) as follows:

74 Engineering and Mathematical Topics in Rainfall

erty of a raindrop, which is given by the following:

size, then the radar reflectivity equation as follows:

*Z* = *<sup>λ</sup>*<sup>4</sup> \_\_\_\_\_\_\_

water [27].

In this chapter, attenuation corrected equivalent radar reflectivity from the TRMM PR 2A25 data product was used. The 2A25 has level 2 algorithms from TRMM PR, which generate products associated with radar signal processing and physical processes of storms. The TRMM PR works in the Ku band frequency with horizontal resolutions of 4.3 and 5.7 km at nadir, before and after boost, respectively [29]. The vertical resolution is 250 m with the total number of vertical range gate of 80. The height corresponds to the distance measured along the radar beam from the point of intersection between the beam and Earth's ellipsoid, and this is not to the local vertical height.

In the current study, the TRMM PR V7 data for a time span of more than 17 years, from 1998 to 2014, is examined. The PR consists of 49 angle bins with an angle-bin interval of 0.71°, which gives a maximum scan angle of 17° about the central beam. However, because the focus of this study is on vertical structure and a reduction of problems at higher scan angles is sought, such as like range-height offset, only the profiles with an incidence angle of less than 7° on either side of nadir are included, which is similar to some of the previous studies [20, 21].

The PR has a minimum sensitivity of approximately 17 dBZ [29]. In this study, only those reflectivity profiles with a Z ≥ 17 dBZ for at least seven consecutive range bins are considered. Also excluded from this study is the virga profile, where only the profile with detectable surface rainfall is analyzed. The vertical profile of radar reflectivity gradient (VPRG) is used to express the vertical gradient of precipitation. The gradient is calculated by using the linear regression as a function of dBZ and height. Negative values indicate a downward decreasing (DD) of radar reflectivity toward the surface, which is characterized a maximum rainfall rate aloft and positive rates denotes a downward increasing (DI) pattern. The gradient is calculated for the dBZ profile below the freezing level (0.75–3 km) with four consecutive range bins [18].

Separation radar reflectivity profile between convective and stratiform is important in precipitation study because each rain type is characterized by different mechanisms of precipitation growth. The TRMM PR V7 of 2A25 classifies the rain type into more than 30 subcategories which can be summarized into several major types: stratiform, stratiform maybe, convective, convective maybe, and others [30]. Simply, the bright band (BB) signature is used to identify the stratiform and convective. If BB is not detected, and yet, any value of radar reflectivity in the beam exceeds 39 dBZ, the profile is labeled convective. Furthermore, if BB is not detected, and the convective reflectivity threshold is not met, the profile is called other. In this study, only those reflectivity profiles with stratiform and convective labels are considered. The convective reflectivity profiles are then classified into deep and shallow convective. The profile with a rain top height (RTH) of less than the freezing level height is considered to be shallow rain; otherwise it is assumed to be deep convective. In this work, the RTH is assumed to be at the highest altitude with Z ≥ 18 dBZ for at least two consecutive range bins.

Of the many variations in precipitation over the IMC, characteristics of the vertical profile of radar reflectivity at seasonal and diurnal scales are the main focus of this chapter. The seasons are classified into four categories, that is, December, January, February (DJF); March, April, May (MAM); June, July, August (JJA); and September, October, November (SON). Using the aforementioned database, the spatiotemporal distribution of profile number, mean gradient and RTH are contoured on 0.25 × 0.25° boxes. Mean gradient and RTH is only calculated if the number of profiles in that box is more than three.
