The Social Metwork

Sophie Cuckow – s.cuckow@pgr.reading.ac.uk 

Introduction 

Transient corridors of strong horizontal water vapour transport, called atmospheric rivers have been linked to flooding over Europe and the US (Ralph et al. 2004, Lavers et al. (2011), Corringham et al. (2019)). Despite this, the relationship between atmospheric rivers and the precipitation associated with extratropical cyclones is debated in literature. It is often thought that atmospheric rivers feed moisture from the tropics directly to the cyclone where it rises to form precipitation (Ralph et al. (2004), Neiman et al. 2008)). However, this would only be the case if the cyclone propagation velocity is slower than the vapour transport, which might not occur when a cyclone is developing. Thus, arises the question, where does the moisture that produces the precipitation come from? The tropics via atmospheric rivers or from another location via a different mechanism? Understanding which moisture sources contribute to extratropical precipitation would help to improve forecasts and mitigate the risk of damage from flooding events. 

Case Study – Storm Bronagh

To investigate different moisture sources, we examined our case study, storm Bronagh, in an Earth relative and system relative framework. Storm Bronagh tracked over the UK during the 20^th and 21^st September 2018 and bought over 50mm of rainfall in 24 hours to parts of Wales and England. This led to flooding in mid-Wales and Sheffield (Met Office). The Earth relative framework allows us to investigate whether the storm has an associated atmospheric river. The cyclone relative framework allows us to investigate airstreams called conveyor belts, which are moving faster than the cyclone propagation velocity. To transition to this framework, we calculated the propagation velocity of the cyclone using the tracks produced by the tracking algorithm of Hodges (1995). We then subtracted the velocity from the Earth relative wind fields (European Centre for Mid-range Weather Forecasts Re-analysis 5, ERA5) to give the cyclone relative wind fields (Carlson (1980)).

Figure 1: The 300K isentropic surface on 21^st September 2018 00:00UTC with the center of the storm (red cross, the isobars (white contours) and masked areas depicting where the surface intersects the ground are shown. Left hand side: The Earth relative moisture flux (streamlines) and the magnitude of the Earth relative moisture flux (filled contours). Right hand side: The system relative moisture flux (streamlines) and the magnitude of the system relative moisture flux (filled contours).

The Earth relative and system relative moisture flux () on the 300K isentropic surface for storm Bronagh on 21^st September 2018 00:00UTC are shown in figure 1. In the Earth relative framework on the left-hand side of this figure, there is an atmospheric river approaching from the West as shown by the blue arrow. This suggests that the source of moisture for this storm was the tropics. However, the cyclone relative framework suggests there is in fact a local source of moisture. This can be seen on the right-hand side of figure 1 where three important airstreams can be seen: the warm conveyor belt (red), the dry intrusion (blue) and the feeder airstream (green). 

The warm conveyor belt is responsible for most of the cloud and precipitation associated with the cyclone. As shown in figure 1, it ascends ahead of the cold front and turns cyclonically to form the upper part of the cloud head, resulting in the iconic comma shape. Also shown in figure 1 is the dry intrusion which descends from behind the cold front into the centre of the cyclone. As this is a dry airflow, it creates a cloud free area between the cold frontal cloud band and the cloud head.

The feeder airstream is a low-level moist airflow that supplies moisture to the base of the warm conveyor belt where it rises. This can be seen in figure 1 where an airstream approaches from the East and splits into two branches, one of which joins the base of the warm conveyor belt. Therefore, in the cyclone relative framework, the moisture originates in the environment ahead of the cyclone rather than the tropics. Furthermore, the other branch of the feeder airstream indicates that the atmospheric river is a result of the moisture being left behind by the cyclone as it propagates. This supports the findings of Dacre et al. (2019) where the feeder airstream was identified by examining 200 of the most intense winter storms over 20 years. 

Therefore, the question arises, which cyclones have a local moisture source? Is it just the intense cyclones or do weaker ones have one too? In order to answer these questions, a diagnostic that identifies the feeder airstream has been developed thus, determining whether there is a local or non-local source of moisture.  

Identification Diagnostic

As seen in figure 1, the feeder airstream is synonymous with a saddle point where it splits into two branches. Therefore, the basis of the feeder airstream’s identification is a saddle point in the system relative moisture flux on an isentropic surface. Utilising theory from non-linear dynamics, the flow around a minimum or fixed point can be identified. Taking the Jacobian matrix of a field and Taylor expanding around a fixed-point, results in a quadratic equation which includes the determinant and trace of the field. By solving this equation and plotting the trace and determinant of the field gives insight into how each flow can be characterised (Drazin (1992)). This is shown in figure 2 where positive values of determinant of the field characterises spiral sources and sinks, whereas the negative values of determinant of the field characterises a saddle point. The determinant of a field is calculated using an equation which calculates the gradient of the field around the fixed point. Therefore, the feeder airstream can be identified by a minimum in the system relative moisture flux field coinciding with an area of negative determinant of the system relative moisture flux field.  Applying this theory to the case study, the feeder air stream for storm Bronagh was successfully identified for 21^st September 2018 at 00:00UTC.

Figure 2: Poincare diagram based on Hundley (2012). This diagram describes how the flow around a fixed point in field A can be characterised using the determinant and trace of the field.

Conclusion and Future Work

In conclusion, the moisture source for the precipitation associated with storm Bronagh on 21^st September 2018 00:00UTC is ahead of the environment rather than the tropics. This moisture is transported to the base of the warm conveyor belt via one branch of a low-level moist airflow called the feeder airstream. The second branch forms the atmospheric river which is a result of moisture being left behind by the cyclone as it propagates. To determine the source of moisture associated with Bronagh in an objective manner, an identification diagnostic has successfully been developed using the determinant of the system relative moisture flux field on an isentropic surface.

In order to develop the identification diagnostic further, it will be adapted to identify the feeder airstream in different stages of storm Bronagh’s evolution. This would verify whether the diagnostic is successfully identifying the feeder airstream and will give us more insight into the relative sources of moisture as the storm evolves. Future work would involve applying the identification diagnostic to a climatology of cyclones with varying intensity, genesis location and durations so that we can ascertain the dependance of the moisture sources on these parameters.

References

Carlson, T. N. (1980), ‘Airflow Through Midlatitude Cyclones and the Comma Cloud Pattern’, Monthly Weather Review

Corringham, T. W., Martin Ralph, F., Gershunov, A., Cayan, D. R., & Talbot, C. A. (2019).

Atmospheric rivers drive flood damages in the western United States. Science Advances, 5(12). https://doi.org/10.1126/sciadv.aax4631

Dacre, H. F., Martınez-Alvarado, O. & Mbengue, C. O. (2019), ‘Linking Atmospheric Rivers and Warm Conveyor Belt Airflows’, Journal of Hydrometeorology

Douglas R. Hundley. “Poincare Diagram: Classification of phase portraits in (detA, TrA) – plane.” Whitman College, WA, Fall 2012. http://people.whitman.edu/~hundledr/ courses/M244F12/M244/PoincareDiagram.jpg

Drazin, P. G. (1992), Nonlinear Systems, Cambridge Texts in Applied Mathematics, Cambridge University Press

Hodges, K. I. (1995), ‘Feature Tracking on the Unit Sphere’, Monthly Weather Review 123(12)

Lavers, D. A., Villarini, G., Allan, R. P., Wood, E. F. & Wade, A. J. (2012), ‘The detection of atmospheric rivers in atmospheric reanalyses and their links to British winter floods and the large-scale climatic circulation’, Journal of Geophysical Research Atmospheres

Neiman, P. J., Ralph, F. M., Wick, G. A., Lundquist, J. D. & Dettinger, M. D. (2008), ‘Meteorological Characteristics and Overland Precipitation Impacts of Atmospheric Rivers Affecting the West Coast of North America Based on Eight Years of SSM/I Satellite Observations’, Journal of Hydrometeorology

Met Office – “Strong Winds and Heavy Rain from Storms Ali and Bronagh” https://www.metoffice.gov.uk/binaries/content/assets/metofficegovuk/pdf/weather/learn-about/uk-past-events/interesting/2018/strong-winds-and-heavy-rain-from-storms-ali-and-bronagh—met-office.pdf

Ralph, F. M., Neiman, P. J. & Wick, G. A. (2004), ‘Satellite and CALJET Aircraft Observations of Atmospheric Rivers over the Eastern North Pacific Ocean during the Winter of 1997/98’, Monthly Weather Review