Towards detection and attribution of multivariate phenomena

Certain high impact weather events are inherently multivariate. For instance, hot, moist, stagnant heat events are different than hot, dry, windy events. Not only are the impacts different; in this case human health vs. wildfire risk, the fundamental meteorology is also different. Generally, univariate indices have been constructed to be characterize impacts.  However, nuances in changes in the multivariate nature of such events is lost with that practice. We present a methodology to calculate iso-surfaces of constant probability of rare combinations of meteorological variables. Key to the detection and attribution of changes in probabilities is quantifying the uncertainty in these iso-surfaces. If changes in iso-surfaces are found to be outside “confidence tubes” in the multivariate space, statistically significant changes can be said to be detected at a given confidence level. As an example, we consider the two dimensional case of temperature and relative humidity at various cities in the US and Mexico.