^{1}

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^{2}

^{3}

The diabatic heating is calculated, using the thermodynamic equation in isobaric coordinates, of a heavy rainstorm that developed over Jeddah, Saudi Arabia on 25 November 2009. Throughout the period of study, the horizontal heat advection is the dominant term and the vertical advection term is opposed by the adiabatic one. The contribution of the local temperature term to the change in diabatic heating is relatively very minimal. The presence of the Red Sea and its adjacent mountains suggest that the diabatic heating in the lower atmosphere on that rainy day is primarily due to the latent heat released by convection. The dynamics of the studied case is also investigated in terms of isobaric Potential Vorticity (PV). The results show that the heating region coincides with the location of the low-level PV anomaly. Ertel’s Potential Vorticity (EPV) generation estimates imply that condensation supplies a large enough source of moisture to account for the presence of the low-level EPV anomaly. The low-level diabatic heating-produced PV assisted in amplifying the surface thermal wave early in the rainstorm development and in the upper-level wave during the later stages of the system’s growth.

Diabatic heating is the essential force driving atmospheric circulation. The diabatic heating of the atmosphere consists of the release of latent heat, sensible heating and radiative heating as well as cooling. However, the understanding of diabatic heating has been hindered because atmospheric heating cannot be directly measured and must be estimated indirectly from other variables. Many investigations have examined the influence of moisture on the intensity of mature cyclones. However, an issue of considerable importance is how cyclone structure and propagation are altered by the presence of moisture throughout its phases of development. This issue was partly addressed theoretically by [

Previous case studies have shown that diabatic potential vorticity (PV) maxima in the lower troposphere can influence on the evolution of extratropical cyclones [

Many studies attribute the PV concentration to the diabatic heating gradients that are present in the stratiform precipitation region of a mesoscale convective system [

From elementary thermodynamic we find that

where _{p} the

specific heat at constant pressure, and ω = dP/dt. Expanding dT/dt and rearranging the terms in Equation (1), the thermodynamic energy equation in isobaric coordinates per unit mass is given by

where V is the horizontal wind vector and Ñ the two-dimensional del operator on the isobaric surface. According

to Equation (2),

Thus, diabatic heating changes are determined by quasi-horizontal temperature advection (V.ÑT), adiabatic temperature changes associated with work done on (ω > 0) or by (ω < 0) the air parcel on the environment during vertical displacements (−ωα/C_{p}), local temperature changes, (

(

vapour, turbulent flux and short-long wave radiations.

Potential vorticity fields were calculated from the available meteorological parameters, namely temperature and the horizontal wind components on constant pressure surface. In isobaric coordinates the potential vorticity was approximated by the product of the vertical components of absolute vorticity and potential temperature gradients as

where f is the coriolis parameter, q is the potential temperature u the wind in x-direction of the grid (W-E in principle) and v the wind in y-direction. Following [^{−7} Kpa^{−1}∙s^{−1} = 1.6 PVU, where, for convenience, the potential vorticity unit (PVU) is set as 10^{−7} Kpa^{−1}∙s^{−1}.

The data used in this study have been taken from the archives of the European Centre for Medium-Range Weather Forecasts (ECMWF; http://www.ecmwf.int/). They consist of the horizontal wind components (u- eastward, v-northward), the temperature (T) and the geopotential height (z) on regular latitude-longitude grid points (resolution 2.5˚ × 2.5˚) for the isobaric levels 1000, 850, 700, 500, 400, 300, 250, 200, 150 and 100 hPa. The data used are at 00:00, 06:00, 12:00 and 18:00 GMT during the period 23 to 26 November 2009. The study domain extends from 10˚W to 60˚E and from 10˚N to 60˚N.

The diabatic heating is calculated using Equation (3) at 00:00, 06:00, 12:00 and 18:00 GMT. Therefore, time derivatives evaluated by centered finite difference spanning 12 hours provide a reasonable indication of the time variation of heating. Centered finite differences were used to compute horizontal derivatives and all vertical derivatives except those at 1000 and 100 hPa, where non-centered differences were employed. The inner domain used for calculating the terms of the thermodynamic Equation 3 extends from 37.5˚E to 47.5˚E and from 17.5˚N to 27.5˚N. Each term in the Equation (3) is diagnostically calculated. In the present study, the vertically inte-

grated diabatic heating term

heating rate is evaluated using a residual, by summing all the terms in the Equation (3). The tendency term is calculated as a centered finite differences scheme. The diabatic heating, evaluated in terms of the thermodynamic equation in isobaric coordinates, is affected by the evaluation of the vertical motion (ω). This motion is computed using the Q-vector representation of the quasi-geostrophic ω equation [^{−1} = 86 K∙d^{−1}. Centered finite differences were also used to compute horizontal derivatives and all the vertical derivatives of the potential vorticity Equation (4) except those at 1000 and 100 hPa.

On 25 November 2009, heavy rainstorms hit Jeddah, Makkah and other regions in the western Saudi Arabia, as seen from the high-resolution (25 km × 25 km) Tropical Rainfall Measuring Mission satellite and observed rainfall merged product (not shown). The Jeddah station recorded 74.0 millimeters of rain in just four hours. This amount of rainfall in Jeddah is nearly twice the average for an entire year and the heaviest rainfall in Saudi Arabia in a decade. The dynamics of this 25 November 2009 heavy rainstorm case is studied through the winter depression that developed over the Mediterranean Sea for the period 00:00 GMT (03:00 local time) on 23 November to 12:00 GMT on 26 November 2009. Based on 1000 hPa and 700 hPa charts, the lifecycle of this studied case can be divided into two periods. The first period (growth) is from 00:00 GMT on 23 November to 12:00 GMT on 25 November while the second period (decay) is from 06:00 GMT on 26 November to 12:00 GMT on 27 November.

Geopotential height in meters (gpm) and temperature in ˚C on the 1000 hPa and 700 hPa charts at 00:00 and 12:00 GMT on each day of the period 23-26 November are shown in

During the next 12 hours (12:00 GMT on 24 November), the inverted v-shaped trough associated with the Sudan low oscillates northward and in the upper atmosphere (700 hPa), the cut-off low also moves eastward to reach just northeast of Egypt. During the period 18:00 GMT on 24 November to 12:00 GMT on 25 November (the rainy period), a strong interaction occurs between the inverted v-shaped troughs extending from the tropical region and from mid-latitude region. The two depressions merge to form a single system. The most interesting features are the strong northward warm advection from the tropical region associated with the air flow around the Sudan low, and the strong southward cold advection. The interaction between these two air masses causes a great deal of instability over the East Mediterranean and the west of Saudi Arabia.

After 12:00 GMT on 25 November, the inverted v-shaped trough of the Sudan low moves south-westward while the upper air trough retreats westward where the associated cut-off low is centered over the northwest of Egypt, and the interaction between the two troughs vanishes. During the next day (26 November), the depression starts to weaken and its central pressure increases gradually. On the other hand, the subtropical high pressure over North Africa and the western Mediterranean is extended with a major ridge that joins the Siberian high on 27 November. In other words, no more cold advection is permitted to the system. While the Siberian high pressure propagates westward, the horizontal extension of the system decreases and moves slowly eastward. It becomes a stationary vortex rotating above the northeast of the Mediterranean (

The results of the diabatic heating rate in 8 time steps starting from 06:00 GMT on 24 November to 00:00 GMT on 26 November 2009 are presented. As the interest is to examine the time variations of the diabatic heating for the studied case,

1000 hPa diabatic heating in

there is a region of diabatic cooling, and at the eastern side of the trough (the area of upward vertical motion), there is a dominant region of diabatic heating. In other words, the diabatic heating behaves like warm advection, and the diabatic cooling behaves like cold advection. Therefore, diabatic heating/cooling in the vicinity of developing convection is usually associated with rising/sinking motions, respectively. Strictly speaking, a relative maximum in diabatic heating is associated with rising motion while a relative minimum in diabatic heating is associated with sinking motion.

By looking at the time variation of heating and cooling over the inner domain, which is used for the present calculation, two main features of the horizontal distribution of heating rates at 06:00 GMT on 24 November 2009 can be seen (

The estimation of the atmospheric diabatic heating in terms of the isobaric thermodynamic method allows the individual contribution of each effect to be examined [

The vertical transport of the diabatic heating through time-pressure cross-sections is shown in

In the vertically averaged sense, the adiabatic term (−ωα/C_{P}) and vertical advection (ωϑT/ϑP) work in opposite senses, which imply that these two terms numerically cancel each other out when viewed in the time-pressure plane. However, these two terms do not balance each other exactly. _{P}) tends to decrease the temperature throughout the period of study. The maximum cool contribution of this term occurs at 06:00 and 18:00 GMT on 24 November, and 12:00 GMT on 25 November between 500 and 200 hPa.

The outstanding features here are the heating at all levels during the period of study. The existence of the Red Sea and its adjacent mountains supports the suggestion that the diabatic heating in the lower atmosphere is primarily due to latent heat being released from the developed convection.

Usually, intense low-level Ertel’s potential vorticity (EPV) anomalies have been observed in cyclone cases [

of low-level EPV anomaly (

For a more in-depth understanding, the EPV generation rate from latent heat release is estimated. Following [

where the subscript LH refers only to condensational heating. The regions of reduced static stability are initially unknown and are found through iteration during the ω-equation inversion. The horizontal gradients of heating in this calculation were included, which can be significant in frontal zones. In addition, the non-conservative generation term is free to feedback on the flow tendency and vertical velocity.

The results of the above discussion indicate that the heating region coincides with the location of the low-level PV anomaly and the EPV generation estimates, and implies that condensation provides a large enough source to account for the presence of the low-level EPV anomaly. The condensation produces a low-level EPV anomaly that adds directly to the low-level PV anomaly, which in turn is strongly influenced by moisture processes.

The low-level diabatically produced PV assists in amplifying the surface thermal wave early in the development of the studied system and in the upper-level wave during the later growth stages. A further application of the quantitative diagnostics discussed in this work is recommended, continuing into the dynamics of synoptic and large-scale systems. This promises to provide a common ground through which observational, numerical and theoretical work may be easily compared.

The aim of this paper has been to study the relationship between the diabatic processes and the generation of the low-level potential vorticity anomaly throughout the lifecycle of a rainstorm, which developed in Saudia Arabia on 25 November 2009 when Jeddah, Makkah and other regions received heavy rainfall. Calculations of the diabatic heating have been made using the thermodynamic equation in isobaric coordinates. The horizontal heat advection is the dominant term during the lifecycle of the system. This means that the diabatic heating is strongly associated with the warm air advected into the region. The analyses of the time-height variations of the terms illustrate that the contribution of vertical temperature advection and the adiabatic term are opposite to each other, which means that there is a strong negative correlation between the patterns of the adiabatic and the vertical temperature advection terms. The contributions of the term of local temperature changes to the diabatic heating rates are very small with respect to all the other terms. The presence of the Red Sea and its adjacent mountains supports the suggestion that the diabatic heating in the lower atmosphere is primarily due to the latent heat release on the rainy day.

The dynamics of the rainstorm system have been investigated also in terms of isobaric potential vorticity. On the whole, this approach seems to identify the same features for rainstorm initiation: an isobaric PV anomaly at the lower levels with a low-level baroclinic zone (with a shallow frontal system). The PV analysis identified possible effects at low levels in the central Red Sea (where the positive lower PV anomaly resulted from the

condensation of water vapor), an area where the diabatic processes appear to play an important role in convection development. It is also found that the heating region coincides with the location of the low-level PV anomaly and the EPV generation estimates, which implies that condensation provides a large enough source to account for the presence of the low-level EPV anomaly. The condensation produces a low-level EPV anomaly that adds directly to the low-level PV anomaly, which in turn is strongly influenced by moisture processes. The low- level diabatically produced PV assisted in amplifying the surface thermal wave early in the convection development and in the upper-level wave during the later stages of the system’s growth.

The authors would like to acknowledge the support of the King Abdulaziz University (KAU) and the Presidency of Meteorology and Environment in Saudi Arabia (PME). The NCEP data are obtained from their website.

H.Abdel-Basset,A. K.AL-Khalaf,A.Albar, (2015) Diabatic Processes and the Generation of the Low-Level Potential Vorticity Anomaly of a Rainstorm in Saudi Arabia. Atmospheric and Climate Sciences,05,275-291. doi: 10.4236/acs.2015.53021