This paper investigates the effectiveness of copula models for understanding, estimating, and predicting compound climate extreme events. It focuses on the bivariate temperature-humidity, temperature-wind speed, and wind speed-humidity distributions within the Boulder County, Colorado region. Climate model simulation data is bootstrapped to investigate the variability of the choice of copula families and accuracy of extreme event probability predictions given different lengths and internal variability of climate data. This showed that longer data records have lower bias and variance than shorter data records in estimating the true probability of a compound extreme event. Fitting the ideal copula models to daily summary data from the region revealed that although there has been a slight increase in the frequency of the compound extreme events, this increase is within the expected range of sampling variability.