A two nested grid WRF model was used to simulate landfall of hurricane Katrina. The resolution of the finest and the outer grid was 3 km and 9 km, respectively. A modified version of the bulk-parameterization by Thompson et al. (2006) was applied. The WRF lateral boundary conditions were updated every six hours using Global Forecast System Reanalysis data. The Gulf of Mexico's surface water temperatures were initialized at 28 August 12 Z, and were not updated during the experiments described below. The number of vertical levels was 31 with the distances between the levels increasing with height.
Because of computer limitations, the simulations were performed in two stages. At first stage the transport of continental aerosols by the TC circulation was calculated. Aerosols were considered as a passive scalar in the run. The TC was simulated beginning with 27 August 6 Z (when it was located to the south of Florida) till 28 August 12 Z. The purpose of the simulation was to check whether continental aerosols located initially over the land can be involved into the TC circulation and penetrate to the distances of about 300 km to the TC center toward the beginning of lightning in the Mexican Gulf (Fig. 1). The simulation showed that aerosols indeed penetrate in the lower troposphere of the TC ''in time'' (Fig. 5). Toward 28 August 12 Z aerosols form a concentric front of radius of about 250-300 km with a quite sharp gradient of aerosol concentration: while at the radii r >250 km concentration in the lower atmosphere was actually similar to that over the land, the central TC zone with radius below 250 km was free from the continental aerosols. Figure 5 (left) shows that the aerosols penetrate closer toward the TC center on the south side. This effect can be attributed to the fact that aerosols are advected along spirals by the TC wind. Aerosols starting their motion at the continent (to the north of the TC) should approach the TC center during their motion along the spirals because of the radial wind directed inward. Thus, aerosols should be closer to the TC center on the southern and the eastern sides of TCs then in the west side. However, the AP concentration decreases along the stream limes. Hence, the concentration on the south side turns out to be higher than on the east side. It is interesting to note that the spatial distribution of the AP concentration obtained in the simulation resembles the locations of negative ground flashes observed during hurricane stage in the nine storms in the Western Atlantic (see Fig. 5 (right) adopted from Molinari et al. 1999), composited with respect to the hourly center position of each hurricane. One can see a good correlation between the distribution of aerosols and the lightning density. The similarity of the fields may be interpreted as some evidence of the validity of the aerosol hypothesis (at least, it does not contradict the hypothesis). These results indicate that while lightning at the distances of a few hundred km from the TC center may be related to aerosols as it is hypothesized here, lightning in the TC eye wall seen in Fig. 1 is not related to effects of continental aerosols. Note that developed rain bands form in the TC within zone of about 300 km radius. Thus, we suppose that one the concentric lightning ring seen in Fig. 1 is that this ring forms in zone of the aerosol "front", which invigorates the convection transferring the maritime clouds into thunderstorms.
In the simulation, in which aerosols are treated as a passive scalar (tracer) the aerosol front approaches TC center in the inflow layer quite slowly, with the velocity close to the radial velocity of the flow. Passive aerosols reach the central TC toward the time, when Katrina was quite close to the land and lightning in its eye wall has already terminated (Fig. 1, right panel) In case cloud-aerosol interaction is taken into account, the concentration of continental aerosols must decrease from the TC periphery toward the TC center even much stronger because of the wash out of aerosols in TC rain bands. The results indicate that:
a) The lightning in the TC eye wall is not related to aerosols and caused by dynamical reasons. To reach a significant concentration of supercooled droplets above the — 13°C level in the TC eye wall (where concentration of continental CCN is small) vertical velocities must be especially high. At the same time the conditions at the TC periphery where concentration of continental CCN is high remain favorable for flash formation during the whole time period when the TC approaches or penetrates the land. This result allows one to explain why lightning in TC eye wall takes place only during TC deepening, while the lightning is permanent at the TC periphery (see e.g., Fig. 1).
b) The problem whether giant CCN arise in zone of maximum winds or not is not very important for our purposes, because continental aerosols do not reach TC center (at least, in TC simulated in the study).
At the second stage, the calculations of the TC were performed for cases when the aerosol effects on TC clouds were taken into account. The calculation was performed for the period from 28 Aug. 12 Z to 30 Aug. 6 Z. The way how the aerosol effects were accounted for requires some preliminary comments. The 3-km resolution and relatively crude vertical resolution does not allow one to reproduce the fine features discussed in the Section 2.3. It is well known that crude resolution decreases vertical velocities, which values are of crucial importance for simulation of cloud dynamics, microphysics and precipitation. As discussed by Khain et al. (2004), the utilization of crude resolution in cloud resolving models leads to the simulation of clouds with characteristics similar to those of maritime clouds, even if the concentration of droplets (either calculated with a model like HUCM or prescribed in a bulk scheme) is high.
Khain and Lynn (2008) describe another problem related to the utilization of the bulk parameterizations (including the Thompson bulk scheme 2006) for the simulation of the aerosol effects on precipitation. They used WRF to simulate super-cell storms with the scheme as well as with the spectral microphysics. They found that the microphysical structure of super-cell storms simulated by the bulk scheme was not very sensitive to large changes in initial cloud drop concentration, at least when compared to results of corresponding simulations with the spectral (bin) micro-physics. Thus, the direct simulation of clouds with the bulk parameterization scheme, just by presetting different droplet concentrations at cloud base would most likely misrepresent fine aerosol effects in cloud microphysics in the 3-km resolution model. To "sidestep" this problem, we simulated effects of continental aerosols in the simulations by preventing warm rain altogether in the Thomson scheme. As seen in Fig. 3, it is hardly possible to prevent warm rain in maritime deep clouds by an increase in aerosol concentration to the magnitudes typical of continental conditions. However, small aerosols significantly decrease the warm rain amount, and even more relevantly, the prevention of warm rain in the 3-D model allows reproduction of the aerosol effects qualitatively similar to those obtained in the 2-D 250 m resolution cloud model, namely, a substantial transport of large CWC upward and increase in the ice content.
The following simulations have been performed with the 3-D WRF model. The control run allowed for warm rain (WR) formation by drop-drop collisions (the WR run). In this run droplet concentration at cloud base Nd was set equal 30 cm~3. This case corresponds to the M-run with the 2D model, where CCN concentration (at S = 1%) was assumed to be 60 cm~3 (usually about half of the available CCN are activated). In the second run referred to as No Warm Rain at the Periphery (NWRP-30), aerosol effects were parameterized by shutting off the drop-drop collisions only on the hurricane periphery, where the surface wind was smaller than 35 ms~\ This threshold was chosen because the continental aerosol concentration in the TC central zone where wind speed exceeds 35 ms_1 should be negligibly small, as it was discussed above. Besides, very high wind speed supposedly is able to produce a significant amount of giant CCN in the eye wall which most likely render ineffective any effects of small aerosols. Hence, warm rain is shut off only in that part of the hurricane that has winds speeds less than the threshold value. Similar approach has been used by Rosenfeld et al. (2008).
The third simulation, referred to as NWRP-1000, is similar to NWRP-30, but the droplet concentration at cloud base was set to 1000 cm~3. This is a supplemental run, which purpose is the illustration of difficulties to simulate properly the continental aerosol effects on maritime convection using the model with the crude horizontal and vertical resolution and changing only the droplet concentration.
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