John Keller, Peter Dailey and Michele Fischer highlight advances made in physically-based numerical weather prediction for European windstorms..

While earthquakes and tropical hurricanes usually receive considerably more media attention, mid-latitude winter-season storms can be the cause of a significant amount of damage. Indeed, some of the costliest events over the past quarter century (in terms of insured losses) have resulted from strong winds associated with extratropical cyclone systems affecting northwestern Europe. Thanks to advances in meteorology, in particular physically- based numerical weather prediction (NWP), computer hardware, and high-speed networks, it is becoming possible to model these complex systems with increasing accuracy and realism.

The complexity of these systems calls for the use of more sophisticated modeling techniques than the standard approach that uses a parameterised model with a simple polynomial horizontal structure. Parameterised models are suitable for simple spatial structure and unambiguous storm tracks, such as those of tropical storms. However, they can fall short when it comes to effectively and efficiently capturing the complex structures of extratropical cyclones. For example, some modelers define an extratropical storm's intensity by its nadir, or lowest recorded pressure. It is then assumed that the highest wind speeds correspond to the nadir. There are several problems with using this approach. First, extratropical cyclone systems often have more than one area of low pressure. Furthermore, frequently the highest wind speed areas do not necessarily correspond to the lowest pressure areas. Finally, unlike in a tropical storm, wind speed cannot be effectively captured based on distance from the storm centre.

Problem solving
AIR solved these problems by introducing physical modeling of the atmosphere to catastrophe modeling in the autumn of 1999. The latest version of AIR's European extratropical cyclone model, released in July 2003, builds on this technology to bring an even higher level of detail into the modeling process. AIR' s expanded use of numerical weather prediction incorporates the high resolution mesoscale model called MM5 that effectively captures the localised effects - in three dimensions and over time - that drive the strongest winds at the surface, resulting in increased realism in the wind field and increased accuracy in loss estimates.

Technology
After decades of government investment of billions of dollars, NWP models have become the workhorses of modern operational weather forecasting. Government forecasts in every industrialised nation rely on 'guidance charts' produced from their own, and increasingly, through collaborative agreements, other nations' NWP models.

Furthermore, NWP models now are used for many applications in the public interest other than traditional weather forecasting. With the rapid decrease in computing and networking costs compared to 10 to 15 years ago, NWP technology began to migrate into the private sector to address specific economic interests, including air quality, agriculture, transport and energy.

Given the current three-dimensional state of the atmosphere, NWP models are designed to predict how it will change with time. Since we are concerned with variation in both space and time, these are often referred to as 'state-of-the-atmosphere variables' (SAVs). In practice, SAVs are environmental data that may include air pressure, air and sea surface temperatures, moisture and wind.

The NWP modeling process begins with an initial three-dimensional 'snapshot' of these SAVs. Operationally, this initial snapshot of the atmosphere is provided by the Global Reanalysis Model (GRM), where the GRM is simply an NWP model that includes sensor observations. Not only is GRM data being continuously created in real time, it also exists as a continuous record of the atmosphere's evolution since the late 1940s. The existence of this data set is a rich resource for studying significant historical European windstorm events. The three-dimensional SAVs (including the wind field) are moved forward in time through the application of a set of coupled, partial differential equations governing fluid flow. They are referred to as the 'primitive equations' and have as their basis the physical laws conserving momentum, mass and energy.

Mesoscale NWP model
Traditional highly parameterised 'engineering models' have attempted to model the storm's wind footprints by using simple relationships between central pressure, storm track and the wind field. As noted earlier, engineering models can still be a practical tool for symmetric storms (e.g., tropical cyclones), but are inadequate for more spatially complex mid-latitude frontal cyclone systems. For example, Figure 1 shows a wind field for Daria created from an engineering model (a) and provided from GRM data (b). These figures clearly illustrate how physically-based NWP technology captures the complex structure of extratropical cyclones and the damaging winds associated with these storms. NWP technology represents a major advance over the conventional approach many catastrophe modelers have taken in the past and still use today.

One important role of NWP models is to 'downscale' these systems, as originally resolved in the GRM data set, to a sufficiently high resolution that the features important to the strongest surface winds can be accurately determined. AIR selected the MM5 system as the NWP modeling technology to downscale European windstorms. Starting in the late 1970s, MM5 has been undergoing development as a joint project of the National Center for Atmospheric Research (NCAR) and the Pennsylvania State University (PSU). MM5 is one of a relatively small number of 'comprehensive mesoscale' models capable of realistically simulating atmospheric phenomena with spatial scales in the order of a few metres.

The basic approach AIR has used is to employ MM5 to refine the GRM data set to provide high-resolution information about storm structure and evolution. In our implementation of MM5 we use fine horizontal resolution with over 20 vertical levels stretched from the surface to the model top. We have found that this implementation of MM5, initialised and bounded with GRM data, generally captures the three-dimensional evolution of most notorious historic European windstorms quite well.

Extreme surface winds
Of course, it is the strength of the wind near the earth's surface with which we are most concerned. As mentioned before, winds associated with extratropical cyclone systems are occurring in three-dimensional space, including the surface. While explaining most of the spatial structure of the surface wind field seen with these systems, the evolving pressure field at this scale often cannot explain the most extreme wind gusts. Meteorologists are now coming to understand that the most damaging surface winds are associated with coherent 'mesoscale substructures' embedded within extratropical cyclone systems. These substructures can be the result of some rather exotic phenomena and include:

Gravity waves - atmospheric gravity waves are also observed in a significant fraction of strong extratropical cyclones. With horizontal wavelengths between 50-500km, MM5 can model atmospheric gravity waves directly.

Kelvin-Helmholtz instabilities - eddies with wavelengths of a few kilometres that can occur when the horizontal wind increases too rapidly with height. This phenomenon is commonly observed in strong windstorms, especially at the lower levels of the atmosphere. These instabilities act to transfer momentum directly from higher levels to the surface. The contribution of Kelvin-Helmholtz instabilities in European windstorms is handled using a specialised algorithm that post-processes MM5 model output. The algorithm is an implementation of a Monte Carlo ensemble technique called 'StormSim', adaptable to the NWP simulated events

'Sting Jet' - another, newly discovered, mechanism for producing extreme wind gusts near the surface, called a 'sting jet', has recently been proposed by researchers at the UK Meteorological Office. Sting jets appear to be a larger-scale variant of the evaporation-driven microburst phenomenon known to occur in strong thunderstorms. As air exits the base of elevated convection it is accelerated downward as its density increases due to evaporative cooling. Winds at the level of the cloud need not initially be strong. The contribution of the sting jet phenomenon is also handled using StormSim.

Studies of Lothar using MM5 suggest that some if not all of these phenomena were occurring during this event. For example, Figure 2(a) shows the horizontal wind speed just above the surface (1.5-2.0km) at the time Lothar was affecting Paris (violet indicates urban areas). Figure 2(b) shows a vertical cross-section indicated by a broken line running east to west (a) through Paris. Grey hatching indicates cloud while the coloured shading portrays precipitation, with snow at higher altitudes becoming rain below. Arrows show the movement of the wind through the depth of the atmosphere shown. The complexity and scale of the structures are consistent with elevated convection (thunderstorms) triggered by gravity waves. Because of the existence of strong winds near the surface, Lothar's strong surface gusts are likely tied to the existence of one or more of the mesoscale substructures mentioned above.

Insured loss
To verify the applicability of AIR's implementation of MM5 for modeling severe wind events, one must keep in mind the limitations and implicit error associated with both observations and model data. As we perform verification analysis on storms occurring more than ten years ago, the temporal and spatial coverage of the observations declines. Model grid points do not coincide with observation locations and are representative of an area-averaged field. Moreover, wind observations are typically a snapshot of winds occurring at the time of the observation and do not reflect the strongest wind that has occurred since the last observation. As well, a high wind observation at a particular sensor site may only be representative of a relatively small area.

Fortunately, there is at least one other source of verification for historical storm events. Once a representation of the time- dependent behaviour of the surface wind for an event is obtained, this information can be used as input to an impact model to estimate damages and losses dependent upon insured exposures. Figure 3 shows for Lothar the modeled maximum wind-speed footprint (a), and the corresponding distribution of insured losses in terms of its industry-wide total (b). The path of strongest winds for this storm passed through northern France and southern Germany. The model shows a region of intense winds over the boundary of France and Switzerland, indicative of the interaction of Lothar with the Alps. The regions showing large losses are consistent with what was observed for Lothar.

This NWP model lost calculation process can be applied not only to historical storms for verification purposes, but also to potential future extreme windstorms. In effect, NWP modeling technology is the foundation of a 'regional storm-wind climate model' for northwestern Europe. The heart of the regional climate model system comprises the integration of the GRM data set, with the well-established mesoscale model MM5. By using StormSim, we have simulated hundreds of potential storms to provide a profile of the financial vulnerability associated with the current climate. In the end, it is this information which is key to insurers and reinsurers assessing their portfolio risk to severe windstorms.

By John L Keller, Peter S Dailey and Michele D Fischer

John L Keller, PhD, CCM, Peter S Dailey, PhD and Michele D Fischer of AIR Worldwide Corp.