Extreme events of precipitation have a potential for impacting our social and economic activities. It is therefore essential to determine if there has been a systematic increase in the extremes over the past years and what awaits us in the future. Studies indicate that there has been an increasing trend in the extremes of precipitation over the past few decades. It has also been argued that global warming induced by anthropogenic forcings may lead to an increase in the extremes of precipitation. In this study, we examine the statistical significance of the observed trends in the extremes of monthly precipitation over the US over the past century using a Monte Carlo approach. A multivariate stochastic model is constructed to estimate the 95% confidence limit simulation envelope for the trends in the extremes of monthly precipitation. The stochastic model incorporates statistical characteristics of precipitation, namely log-normal probability distribution and spatial correlation. Trends in precipitation extremes in data from various global General Circulation Models (GCMs) simulating the 20th century and those projecting into the 21st century are also investigated. The results from the Monte Carlo approach are compared to the non-parametric Kendall's tau test for trends and are found to be similar.

Two different observational datasets are used to test for trends. An upward trend in the extremes of monthly precipitation over the US is observed over the past century in both the datasets. Although the trends in the extremes of monthly precipitation in both the datasets are found to be statistically similar to each other, a marginal statistical significance is observed in one dataset but is not replicated in the other. GCM integrations simulating the 20th century demonstrate both upwards and downwards trends in the extremes. None but one of these trends are statistically significant.

However, GCM projections of the 21st century generally display statistically significant upward trends implying a role for anthropogenic forcing. An analysis of the mean and variance of the GCM integrations revealed that this upward trend in extremes appears to be associated primarily with an increase in the variance of the precipitation, rather than an increase in the mean precipitation.

Another approach to the analysis of extremes of precipitation is also undertaken. The probability distribution of the extremes of precipitation is approximated using the Generalized Extreme Value (GEV) distribution. Parameters of the GEV fit of observational data and the GCM simulations of the 20th century are compared to those of the 21st century GCM projections. In addition, an asymptotic model of the extremes of precipitation created using the GEV parameters from the observational data of the 20th century is used to forecast for the extremes of precipitation in the 21st century. These forecasts are compared to the extremes observed in the GCM integrations of the 21st century.