Abstract
Accurate calculation of precipitable water vapor (PWV) in the atmosphere has always been a matter of importance for meteorologists. Potential water vapor (POWV) or maximum precipitable water vapor can be an appropriate base for estimation of probable maximum precipitation (PMP) in an area, leading to probable maximum flood (PMF) and flash flood management systems. PWV and POWV have miscellaneously been estimated by means of either discrete solutions such as tables, diagrams or empirical methods; however, there is no analytical formula for POWV even in a particular atmospherical condition. In this article, fundamental governing equations required for analytical calculation of POWV are first introduced. Then, it will be shown that this POWV calculation relies on a Riemann integral solution over a range of altitude whose integrand is merely a function of altitude. The solution of the integral gives rise to a series function which is bypassed by approximation of saturation vapor pressure in the range of -55 to 55 degrees Celsius, and an analytical formula for POWV in an atmosphere of constant lapse rate is proposed. In order to evaluate the accuracy of the suggested equation, exact calculations of saturated adiabatic lapse rate (SALR) at different surface temperatures were performed. The formula was compared with both the diagrams from the US Weather Bureau and SALR. The results demonstrated unquestionable capability of analytical solutions and also equivalent functions.
Highlights
The distribution of water vapor in the atmosphere has always been noticed in different aspects
It was revealed that analytical computation of Potential water vapor (POWV) relies on a Riemann integral solution over a range of altitude whose integrand is merely a function of altitude
The solution yielded a series function which was circumvented by approximation of saturation vapor pressure in the range of -55 to 55 degrees Celsius, and a formula for POWV in an atmosphere of constant lapse rate was successively proposed
Summary
The distribution of water vapor in the atmosphere has always been noticed in different aspects. After the Banqiao and Shimantan dams in China were built in the 1950s, estimation methods of the inflow design flood for dam safety have greatly altered with improvements in hydrometeorological techniques These new techniques exploit meteorological theories and concepts to determine a design storm of a probable maximum precipitation (PMP) magnitude (Svensson and Rakhecha 1998). An atmospheric modeling program (ATMOS) was utilized to compute the mentioned depth, lPWV, at 3.8 km for a range of sea-level water vapor density t0. They worked out a linear fit between PWV and t0 through the following equation: lPWV = 0.174 t0. USWB (1949) has provided tables for computing precipitable water in the atmosphere over the United States
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