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Atmospheric warming is projected to intensify heat wave events, as quantified by multiple descriptors, including intensity, duration, and frequency. While most studies investigate one feature at a time, heat wave characteristics are often interdependent and ignoring the relationships between them can lead to substantial biases in frequency (hazard) analyses. We propose a multivariate approach to construct heat wave intensity, duration, frequency (HIDF) curves, which enables the concurrent analysis of all heat wave properties. Here we show how HIDF curves can be used in various locations to quantitatively describe the likelihood of heat waves with different intensities and durations. We then employ HIDF curves to attribute changes in heat waves to anthropogenic warming by comparing GCM simulations with and without anthropogenic emissions. For example, in Los Angeles, CA, HIDF analysis shows that we can …