## 1. Introduction

[2] The total column quantity of water vapor overlying a specific point on or above the Earth's surface, expressed as the height of an equivalent column of liquid water, is known as precipitable water (PW). In the last decade the Global Positioning System (GPS) has been used to measure PW with an accuracy comparable to that achieved using radiosondes [e.g., *Duan et al.*, 1996; *Tregoning et al.*, 1998; *Gutman and Benjamin*, 2001]. The recent appearance of multiyear time series of PW measurements derived from continuous GPS networks has prompted a resurgence of interest in the statistics of PW variability. One of the most basic properties of an environmental variable is its statistical distribution. *Foster and Bevis* [2003] studied the statistical distribution of PW in Hawaii and found it to be lognormal, or very nearly so, when variability is considered over a period of several years. They analyzed PW time series derived from a network of Global Positioning System (GPS) receivers based on the Big Island of Hawaii and from a suite of radiosonde profiles associated with the Lihue radiosonde station in Kauai.

[3] The geodetic measurement of PW is achieved indirectly. What is estimated directly from the observations collected at each GPS station is the zenith neutral delay (ZND) which is a measure of the propagation delay imposed by the neutral atmosphere on GPS (radio) signals reaching that station. This delay is expressed or parameterized as the equivalent excess path length associated with a vertical path through the atmosphere. A ZND time series is transformed into a PW time series using measurements of surface temperature and pressure at each GPS station or by inferring these quantities using a numerical weather model or via objective analysis [*Bevis et al.*, 1992]. The ZND can be decomposed into the zenith hydrostatic delay (ZHD), proportional to the surface pressure [*Davis et al.*, 1985], and the zenith wet delay (ZWD) which is very nearly proportional to PW [*Bevis et al.*, 1992, 1994]. Since the temporal variability of ZND is known to be dominated by the variability of the ZWD, it is reasonable that *Foster and Bevis* [2003] found ZND in Hawaii is also lognormally distributed, or very nearly so.

[4] The lognormal nature of PW and ZND in Hawaii was a surprise to many geodesists (including us) who have typically assumed that PW and ZND have Gaussian statistics (largely for the purposes of computational convenience) if they have considered the statistical distribution at all. Also, even though many other meteorological and hydrological quantities (such as rainfall and cloud droplet size) have been characterized as lognormal, this association rarely occurs in the literature discussing the climatology of PW. Most likely this is because in many parts of the world the empirical probability density function for PW (and for ZND) is bimodal (or multimodal) or, for some other reason, has an appearance which is not strongly suggestive of lognormality. The lognormal character of PW and ZND in Hawaii is a local but not a global property of these quantities, but how common is lognormality, and is it possible that bimodal distributions of PW or ZND represent combinations of two lognormal populations?

[5] In this paper we use both GPS measurements and radiosonde measurements to survey the statistical distribution of PW and ZND in a variety of oceanic and continental settings. By including GPS measurements in addition to the direct PW measurements of radiosondes, we are able to confirm whether the ZND, the parameter of direct interest to space geodesists, reflects the same distributions as the PW. The ZND also provides an independent platform to corroborate the radiosonde results. In addition, the rapid global expansion of GPS networks means GPS data is available from many areas that have little or no coverage by traditional meteorological instruments.