Simulation of inertia-gravity waves using WRF model over Iran: a case study

A fluid, which is stable under the action of buoyancy, can oscillate under the influence of buoyancy and Coriolis forces. The resulting ageostrophic oscillations with a frequency between Coriolis and buoyancy frequencies are called inertia-gravity waves, hereafter IGWs.
In this study we investigate the generation and propagation of IGWs over Iran. To this end, the Weather Research and Forecasting (WRF) mesoscale model is used to simulate an event with noticeable IGWs within a synoptic system accompanied by rain and snow, from 6 to 9 February, 2012. The NCEP FNL data (final analyses) are used for this simulation in a domain of 8000 km × 6375 km extent and a medium resolution (grid interval Δs=25 km). The model has 35 levels in vertical direction with its top at 10 hPa (~30 km). A time step of 150 seconds is used and the model is run for 72 hours initialized at 12UTC 6 February and continued until 12UTC 9 February 2012. An implicit Rayleigh damping layer is used to prevent unphysical wave reflection from the upper boundary of the computational domain (Klemp et al, 2008). In order to investigate generation and propagation of IGWs and to determine the effects of each of energy sources in the region, four different model runs are designed and performed with/without orography/moisture.
In order to facilitate the conduct of the study, the main area of interest is classified into three regions where the IGWs are most active. The first area is located in the northwest of the country, in the vicinity of the maximum wind speed of the midlatitude jet stream and the left side of the jet streak. The second area, including the central and southern Zagros Mountain, is located in the vicinity of unbalanced flow and the right side of the jet streak. The third area is located geographically at the conjunction of Zagros and Alborz mountain ranges, is at the exit region of the jet stream and along a rain belt with significant cloud coverage as in the second area.
The fundamental quantities of wave like the wave frequency and periods, the intrinsic phase speed, the group velocity and horizontal and vertical wavelengths are obtained based on the horizontal divergence field as the main quantity. This is possible, because the procedure avoids explicit treatment of the background field, which has zero divergence, and is applicable to waves of arbitrary wavelength. Previous studies have shown that the most important energy sources for IGWs are: jet streams, fronts, convection and orography. Furthermore, the IGWs propagate in the atmosphere with a phase speed of 15 to 35 ms^-1, vertical wavelength of 500 m to 15 km and horizontal wavelength of 50 to 1000 km.
In the reference run (with the topography and moisture included), the distribution of the horizontal divergence clearly shows the waves closely follow the major topography and propagate nearly perpendicular to it. Estimation of wave properties shows that a high- frequency wave with  is emitted in this case. The quantity  is the estimate for wave frequency scaled by inertial frequency. In the first and second areas, the typical values of the horizontal wavelengths are from 150 to 175 km, the vertical wavelength from 5 to 6 km and intrinsic phase speed from 15 to 19 ms^-1. In the third area, the IGWs travel with a phase speed of about 15 to 21 ms^-1 and horizontal and vertical wavelengths of 100 to 120 km and 5 to 6 km, respectively.
Based on the characteristics of the IGWs and their propagation, it can be inferred that the waves are generated in the troposphere by jet-front mechanisms due to topography and then undergo deformation. Some of the waves generated in the upper troposphere cross the tropopause and propagate well into the stratosphere. Disregard of the way wave are generated, this transfer of activity from troposphere to the stratosphere is a common phenomena.
 The results of this study are in good agreement with those obtained by Zhang and Koch in 2000 who studied simulation over Rockies Mountain in Montana and Dakota. They estimated a single wave packet with 3 or 4 waves, a wavelength of 150 km and phase speed of 15.2 ms^-1.  Zulick and Peters in 2006 identified two wave packets in their study. The first wave packet included large waves with wavelengths of about 500 km and period of approximately 10 hour which were classified as sub-synoptic (or meso-α). The second wave packet, however, consisted of small waves with much higher frequency than the first wave packet, and wavelengths of almost 200 km and period of nearly 5 hour, which were classified as meso-β (mesoscale-β).
Having investigated the possible energy sources in the region, the following conclusions can be made. In the run without either orography or moisture, large-amplitude waves are observed that carry energy upward to the stratosphere and downward to the troposphere. Entering a positive feedback, the downward propagating waves emitted by the jet can facilitate convective activity at lower levels and play a role in enhancing precipitation. Although adding mountains to the physics of the model affects wave characteristics like intensity, amplitude, and direction of propagation, the presence of all of the factors is necessary for describing the actual wave generation and propagation processes.