Sinuosity: A robust measure of mid-tropospheric waviness

High impact, mid-latitude weather events are very often associated with increases in the amplitude of planetary waves, as such increases are dynamically linked to robust cyclogenesis and anticyclogenesis. However, no widely accepted metric exists for quantifying the waviness of the circulation. Here we appropriate a measure common in geomorphology, - sinuosity - to measure the waviness of the mid-tropospheric flow using 500 hPa geopotential height contours. Every such contour encloses a certain amount of area. That same area is contained poleward of what we term its equivalent latitude. The sinuosity of that contour is the ratio of its curvilinear length to the length of its equivalent latitude circle. We describe a method of calculation of this quantity applicable to analysis of the middle tropospheric flow and describe elements of the 66-year time series of cold season (DJF) sinuosity calculated using the NCAR/NCEP Reanalysis data set. The data suggest no trend in either seasonally averaged sinuosity or the number of unusually wavy days since 1948-49, although wintertime sinuosity has been increasing since the late 1980s. The analysis suggests a strong relationship exists between the daily Arctic Oscillation (AO) index and the daily sinuosity. In fact, comparison of the seasonal average AO index to the seasonally averaged sinuosity demonstrates that enhanced waviness in the flow is unmistakably associated with a negative AO. The implications of these findings on the plausibility of a connection between Arctic amplification, increased waviness, and an increased frequency of high-impact weather are considered.