Research Study: Re-simulating Hurricane Katrina

1. Introduction

Hurricane Katrina, in August 2005, was the costliest natural disaster in history to hit the United States, with an estimated $108 billion of damage to property, as well as 1833 deaths (FEMA, 2007). It had become a hurricane ( winds > 33m/s) just before making landfall in Florida on the 25th. As the hurricane passed over the warm waters of the Gulf of Mexico, it rapidly intensified. As Fig.1a shows, by 0000UTC on the 28th, maximum wind speeds were above 50m/s, hence a category 3 hurricane. The hurricane deepened further - shown by decreasing pressure in Fig.1b – and wind speeds also increased. A maximum wind speed of 78m/s was recorded at 18000UTC on the 29th, although this is not present in Fig.1a. A minimum hourly surface pressure of 941hPa was also simulated at this time (Fig.1b). This value is much higher than the 902hPa minimum observed (NOAA, 2005). These underestimations are discussed in Sec. 4.2.

Fig.1 a) Maximum and minimum wind speeds, b) Minimum surface pressure, in the vicinity of the hurricane on 28th and 29th August 2005.

2. Method

The WRF model was used to simulate the progress of Hurricane Katrina. Using ‘ncview’ to plot the water vapour mixing ratio (QVAPOR), the hurricane’s synoptic-scale structure could be interpreted (Fig.2). From this, the hurricane was considered to be strongest, whilst still approximately symmetrical, at 1000UTC on the 29th. This time is therefore used in the subsequent analysis. The model is initialised at 2005-08-28_00:00 UTC.

Coordinates were then taken in the zonal, west-to-east direction through the centre of the hurricane, which were used in cross sections of various quantities. Potential temperature contours were overlaid on each vertical cross section to allow for easy identity of the location of the eye column.
Plan views of cloud types were also plotted, using the assumptions:
• Stratiform cloud where w < 1 m/s, with liquid or mixed-phase cloud and precipitation hydrometeors.
• Cirriform cloud where w < 1 m/s, with ice-only cloud.
• Convective cloud where w > 1 m/s.

All scripts were then re-ran under a new parameterisation scheme (Sec.4.2). The coordinates used in the cross section plots were changed, in order to transect through the eye of the storm for comparison of the different schemes. Although this will capture the hurricane in a different stage of its development, simple comparisons of the hurricane’s structure can be made.

3. Results and analysis

3.1 Structure

Katrina had a classic hurricane structure. In the northern hemisphere, the flow around a surface low pressure is cyclonic (Fig.3a). Gradient wind balance exists, but this is disrupted by turbulent friction at low levels, causing the flow to be deflected towards the low pressure at the centre of the system. The low-level winds spiral towards the low-pressure centre, causing large horizontal convergence in the eye wall. By the conservation of mass, this leads to strong ascent in this region (Fig.3b), setting up a thermal direct circulation: the ascending air rises and flows outwards in the upper levels. Fig.3a-b can be used to interpret that the radial velocity would be large and positive where there is the inflow, decreases with height, and would become negative where there is the outflow.

The kink in the potential temperature contours (Fig.3c) indicates the upward advection of ascending air in the eye wall and the downward advection of descending air in the eye. As the air rises in the eye wall, it rapidly cools, allowing relative humidity to increase to, or close to, 100% (Fig.3d). This initiates the rapid growth of the cloud-liquid amount (Fig.4a), and deep convective cloud forms (Fig.4c), producing a very high total precipitation hydrometeor amount in the eye wall region (Fig.4b).
 

Fig.3 West-east vertical cross section (looking north) of a) horizontal velocity, b) vertical velocity, c) potential temperature, and d) relative humidity, valid at 2005-08-29_10:00UTC. Horizontal velocity is negative to the west of the eye and positive to the east of the eye – hence cyclonic flow.

Fig.4 West-east vertical cross section (looking north) of a) cloud-liquid amount, b) total precipitation hydrometeor amount, and c) a plan view of convective cloud, valid at 2005-08-29_10:00UTC.

      3.2 Dynamics

In the Northern Hemisphere, the Coriolis force causes low pressure systems to have cyclonic flow, which is seen in the lower levels on Hurricane Katrina (Fig.5a). However, latent heat release and warming builds high pressure aloft, generating a strong upper level pressure gradient. This causes the upper level outflow to become anti-cyclonic. This can be seen in Fig.5b by observing the clockwise outward-spiralling wind barbs. This process also results in the strongest winds being close to the surface and decreasing with height, which can be seen in Fig.3a and by comparing the magnitude of the wind barbs in Fig.5.

   

Fig.5 Plan view of wind barbs at a) 950hPa and b) 200hPa, valid at 2005-08-29_10:00UTC.

      3.3 Potential vorticity

Potential vorticity (PV) is the absolute circulation of an air parcel that is enclosed between two isentropic surfaces. It is dependent on the static stability and absolute vorticity. PV on the 320K isentropic level (~600hPa using Fig.3c), in the eye wall, has values greater than 6PVU (Fig.6a), due to cyclonic flow and very large absolute vorticity here. Away from the vicinity of hurricane centre, PV is positive but close to zero, suggesting weak cyclonic flow here at this level. This plot can be compared to the PV on the 360K isentropic level (~230hPa using Fig.3c). At this level, negative PV values exist (Fig.6b) in the hurricane’s vicinity, away from the hurricane eye and eye wall (where PV has decreased to ~4PVU). Negative PV is indicative of anticyclonic flow at this upper level. This supports the analysis of radial velocity in Sec. 3.1 and the plots of wind barbs in Fig.5.

 Fig.6 Plan view of potential vorticity on the a) 320K and b) 360K isentropic level, valid at 2005-08-29_10:00UTC.

4. WRF model errors

4.1 Sources of error

NWP models such as WRF are not perfect and contain many sources of error that can significantly affect the results model output. The chaotic nature of the atmosphere amplifies any sources of error, so it is important to limit any uncertainties to avoid error growth. Firstly, the model contains truncation errors, introduced by the discretisation of partial differential equations. Unresolved parameterisations also add error, which arise due to an insufficient understanding of the processes taking place. The increased resolution of models is not matched by increasing resolution of observations, and so surface representation errors remain. The most significant contributors to model error are believed to be in the physics parameterisations (WRF-RAB, 2006). In particular, the cloud microphysics contains significant sources of uncertainty for explicit prediction of convective cells. Secondly, uncertainty arises through imperfect initial conditions. Observational data contain errors and few measurements are taken over the Ocean.

      4.2 Kain-Fritsch convection/cumulus parameterisation scheme

In Sec. 1-3, the Morrison 2-moment microphysics scheme (mp_physics=10) and the Betts-Miller-Janjic (BMJ) convection parameterisation scheme (cu_physics=2) was used. Re-running the model under the Kain-Fritsch (KF) convection parameterisation scheme (cu_physics=1) outputted noticeable differences to the simulation of the hurricane. Firstly, the new scheme resulted in a faster tracking system and hence a different hurricane location at 2005-08-29_10:00UTC (Fig.7) - the hurricane is estimated to be 120km further north than under the BMJ scheme. Comparison with observational surface pressure charts suggests that the KF scheme better estimates the location of the hurricane. Fig.7 shows a lower central surface pressure under the KF scheme than under the BMJ scheme. This may help explain why the maximum wind speed and the minimum surface pressure plotted in Fig.1 are underestimations under the BMJ ‘adjustment’ scheme. As a result, PV is greater in the lower levels. In addition, the deep convective cells within the eye wall are in different relative locations (Fig.7).

Fig.7 Plan view of convective cloud valid at 2005-08-29_10:00UTC under a) the Betts-Miller-Janjic and b) the Kain-Fritsch, convection parameterisation schemes. Surface pressure contours are overlaid.

The vertical cross section plots in Sec. 3 were repeated with the new scheme and with corrected coordinates. Kerkhoven et al. (2006) found that the BMJ scheme had difficulty representing vertical velocities accurately, but this is difficult to assess in our analysis because we do not know what the ‘true’ profiles should look like. The most noticeable difference is the structure and magnitude of the downdrafts within the eye appear more realistic under the KF scheme (Fig.8). In the KF scheme, all cloud systems are represented through a 1D cloud model, which accounts for up-/down-drafts, en-/de-trainment, and other cloud processes, and so better simulates profile changes, such as the development of the eye’s downdraft column. Also noticeable is the weaker updraft existing to the east of the eye (Fig.8b). The different structure to the east of the eye is also present for other variables.
                       

Fig.8 West-east vertical cross section (looking north) of vertical velocity valid at 2005-08-29_10:00UTC under a) the Betts-Miller-Janjic and b) the Kain-Fritsch, convection parameterisation schemes.

5. References

• FEMA (2007), Federal Disaster Declarations, FEMA, Hyattsville, MD, available at: www.fema.gov/news/disasters.fema#sev1.

• Kerkhoven, E., Gan, T. Y., Shiiba, M., Reuter, G. and Tanaka, K. (2006), A comparison of cumulus parameterization schemes in a numerical weather prediction model for a monsoon rainfall event. Hydrol. Process., 20: 1961–1978. doi:10.1002/hyp.5967

• National Oceanic and Atmospheric Administration (NOAA), 2005a: Post Storm Data Acquisition, Aerial Wind Analysis and Damage Assessment, Hurricane Katrina, 11 pp. [Available online at: http://www.weather.gov/om/data/pdfs/KatrinaPSDA.pdf]

• WRF-RAB, 2006. RESEARCH-COMMUNITY PRIORITIES FOR WRF-SYSTEM DEVELOPMENT. Pre-pared by the WRF Research Applications Board, December 2006 Executive Summary.