The major properties of a heat wave are its duration and intensity and they were used to characterize the strength of hot events. A bivariate probability distribution of duration and relative intensity, and the corresponding marginal distributions, as well as the conditional probability distribution were developed. These distributions were used to derive practical applications. It was found the average duration was 2.57 days and standard deviation of 0.76 days. The maximum value of relative intensity during heat waves shows an average of 4.3 °C and standard deviation of 2.16 °C; where, relative intensity is the excess of heat index over the maximum threshold. It was found that 78% of heat waves last equal or less than 3 days, and 60% exhibit a relative intensity equal or fewer 4 °C. The accumulated heat wave intensity (AHWI) was introduced in this work as a parameter that takes into accounts both duration and intensity to accurately measure the strength of a heat wave. The AHWI parameter can especially be used to rank a set of heat waves that have occurred in different parts of the world. Although, it is recommended to apply the definition of heat wave based on heat index, a similar definition base only in air temperature is also provided. The correlation analysis shows that the duration and relative intensity exhibit a correlation of 0.52 indicating that if the duration of a heat wave increases (reduces) the relative intensity will also increases (reduces). The probability distributions suggest that an extreme heat wave can be defined as an extraordinary hot event that stay in the category of heat wave for more than 4 consecutive days or exhibits 8 °C or more of relative intensity. It was detected 2 extreme heat waves, one exceed the duration and the other the relative intensity threshold. The heat wave that exceeds duration occurred in July 16, 1995 in the station located in Antigua & Barbuda with a 5 days and 7 °C of relative intensity. The extreme heat wave that exceeds the relative intensity threshold occurred in October 23, 2003 in Colombia with 8 °C and 3 days of duration. NARR data were also used to study the spatial distribution of the atmospheric variables during heat wave episodes. This exercise shows that the air temperature, the relative humidity, and the heat index start rising in the previous days to the hot event and increases to the maximum values during the event, and then reduces their values after the heat wave.
It was postulate that the increments observed in heat waves are a response of the global warming. To test this hypothesis is very important to determine the time when the heat waves and global warming parameter exhibit the significant change. A sequential statistical test was introduced and the test shows that a significant increment of heat waves occurred in 1995 and coincides with a significant increment in global air temperature. Hence, there is a high possibility that the increasing frequency of heat waves in the MAC region may be a direct consequence of the global warming.