The Global Positioning System (GPS) is a powerful atmospheric
observing system for determining precipitable water vapour (PWV). In the
detection of PWV using GPS, the atmospheric weighted mean
temperature
(

Water vapour (WV), a component of the Earth's atmosphere, plays a crucial role in global atmospheric radiation, energy equilibrium, and the hydrological cycle (Wang et al., 2007). Since the Global Positioning System (GPS) became fully operational in 1994, it has been possible to use GPS measurements to retrieve precipitable WV (PWV) information in the atmosphere (Duan et al., 1996). The main advantages of using GPS technique to derive PWV are its high quality, wide coverage, and all-time availability under all-weather conditions. These features are vital for meteorological applications of GPS such as the prediction of short-term rainstorms and rainy seasons (Song et al., 2003; Zhang et al., 2007) and the monitoring of severe weather events, including thunderstorms, hailstorms, strong winds, and hurricanes (Choy et al., 2001; Zhang et al., 2015).

PWV is defined as the equivalent height to a column of liquid water. GPS-derived PWV values above a given GPS station, i.e. GPS-PWV, are converted from the zenith tropospheric delay (ZTD) estimated from GPS measurements. The GPS-PWV can be used to compare different techniques of WV detection, such as radiosonde, WV radiometer, Moderate-Resolution Imaging Spectroradiometer (MODIS), and sun photometer (Yang et al., 1999; Li et al., 2003; Prasad and Singh, 2009; Kwon et al., 2010). It can also be used for evaluating improvements in numerical weather prediction (NWP) systems (Gutman and Benjamin, 2001; Song et al., 2004). Moreover, temporal and spatial variations in PWV can be precisely identified using GPS-PWV over GPS networks (Champollion et al., 2004; Jin and Luo, 2009; Van Baelen and Penide, 2009).

The GPS-derived ZTD (GPS-ZTD) generally consists of two components: the
zenith hydrostatic delay (ZHD) and the zenith wet delay (ZWD). The ZWD is
caused by WV in the atmosphere below

The

A list of the latest global empirical

In the Bevis formula

Table 1 summarises existing empirical

Building upon the global pressure and temperature (GPT) model proposed by
Böhm et al. (2007), Yao et al. (2012) developed the season-specific
Global Weighted Mean Temperature (GWMT) model based on radiosonde data of 135
global stations in the period 2005–2009. The RMSE of

However, given that the diurnal variation and the lapse rate of

Three data sets with various temporal and spatial resolutions are used to
calculate

A state-of-the-art analysis and forecast system has been used to assimilate
multi-source data since 1948 and the NCEP2 data set is an updated version
from its former reanalysis data (available on

Radiosondes released from ground-based stations can directly measure the
atmospheric profiles. Radiosonde records from 585 global Integrated Global
Radiosonde Archive (IGRA) stations (Fig. 1) in 2014 are utilised to validate
the new GWMT-D model. They are retrieved from the upper-air archive at the
website of University of Wyoming (available on

Distribution of the 585 radiosonde stations selected to validate the new GWMT-D model (only those data that pass a quality check are used).

In addition, raw radiosonde measurements are rejected as outliers in the
data preprocessing under the following conditions:

the height of the first data record in the profile is greater than 20 m above the ground;

the difference in height between two successive pressure levels is greater than 10 km;

the gap between two successive atmospheric pressure levels is greater than 200 hPa;

the total number of valid radiosonde levels is less than 20;

the highest humidity level (at the pressure level of 200–350 hPa)
is less than

the height of the last data record in the profile is lower than 20 km.

In this study, global surface

The NCEP2 data from the 4-year period 2010–2013 are employed to develop
the new GWMT-D (D stands for diurnal variation) model. All global

Compared with other empirical

These coefficients are estimated from the time series of

Statistical results of diurnal

Annual and semi-annual variations in a NCEP2-derived

Figure 2 shows an example of the diurnal variation at 2 km above the ground
for 30

The

Global annual mean

Four specific reference height levels (0, 2, 5, and 9 km) are selected
covering most of the troposphere in the new GWMT-D model. All global

Another important task is to determine the optimal length of reanalysis data
required for the development of empirical

Different sets of coefficients of the GWMT-D are calculated using the
NCEP2-derived

Assuming

Two nearest reference height levels close to

where

For each of the four reference time, a vertical interpolation
is performed for the four grid points at the height of

The

Now

After the aforementioned spatial interpolations, a spline interpolation
in the time domain is carried out to find the

Spatial interpolation for the target point located at (

The global mean RMSE of various GWMT–D models built with different
lengths of time periods (2005–2013) of NCEP2 data at five pressure levels
(in K). The reference

The global RMSE distribution of the differences between the

Different empirical

The globally mean biases and RMSEs of the differences between the

The global RMSE distribution of the differences between the

Due to the fact that GTm_X is unavailable to the public and GWMT and
GTm-II have been proven inferior to GTm-III, GWMT-IV, and GTm_N, only
GTm-III, GWMT-IV, GTm_N, and the new GWMT-D model are assessed. The
methodologies for obtaining

The globally mean biases and RMSEs of the differences between NCEP2-derived
and model-derived

Figures 5–6 illustrate the distribution of the RMSE (not the mean RMSE of all
grid points listed in Table 3) of the differences between the

Global statistics of the differences between the surface

The global RMSE distribution of the differences between surface

It is worth pointing out that all these four models have relatively low RMSE
values near the tropical areas, and all have a similar performance globally
except for the Antarctic. This finding is consistent with recent studies,
(e.g. He et al., 2013; Chen et al., 2014; Yao et al., 2014a). It may be
explained by the fact that the

The GGOS surface grid

Nevertheless, the good performance of GWMT-D indicates that the modelling
method of

These four empirical

Surface

The accuracy of the

RMSE of model-derived surface

Figure 8 illustrates the RMSE of model-derived surface

Statistics of the differences between model-derived and
radiosonde-derived

Histogram of model-derived

Figure 9 shows the histogram of the difference (i.e. model-derived

The entire radiosonde-derived

RMSE profile of the

Figure 11 shows the monthly or seasonal performance of these four selected models. The monthly-mean RMSEs of all the models vary with month (or season) and only the GTm_N shows a variation pattern opposite to that of the other three models. The GWMT-D and GWMT-III present very similar results in both pattern of variation and monthly-mean RMSEs. The GWMT-IV performs the worst and GWMT-D performs the best among all these four models.

Monthly-mean RMSE of the

The purpose of determining

The theoretical RMSE

Figure 12 illustrates the global distribution of both

Moreover, comprehensive comparisons with GTm-III, GWMT-IV, and GTm_N show
that GWMT-D is unbiased and can achieve a RMSE accuracy of 4–5 K for
different seasons and locations. The improvement of the new model is around
25 % over the other three models when using NCEP2- and radiosonde-derived

It is suggested that the sets of coefficient for empirical

NCEP2:

This appendix presents the calculation of

Note that the height used in NCEP2 and radiosonde data is the geopotential
height, which is widely used in meteorology, whilst the height used in the
Eq. (A1) is a geometric height. The equations for the conversion of a
geopotential height to a geometric height (ellipsoidal height) are (Ge,
2006)

Since the humidity in layered, meteorological data are recorded as dew point
temperature (

Strictly, the UNB3m model is not a specific

The UNB3m model neglects the longitudinal variations in

The GPT2w, an improved GPT model, was developed by Böhm et al. (2015).
This empirical model can provide pressure, temperature, tropospheric delay, and

The GWMT series models are global models developed and consistently improved by Yao et al. using the state-of-the-art data sources and improved methodologies (Yao et al., 2015, 2014a, b, 2013, 2012).

The GWMT model was based on spherical harmonics of degree nine and order
nine and is a function of the geodetic coordinates of the site, as expressed
below:

The GTm-II and GWMT models are developed using the same methodology but with different data.

Considering the semi-annual and diurnal variations in

Since the adjustment model in Eq. (B4) for the GTm-III is non-linear, the
coefficients determined may be unstable or biased. Chen et al. (2014)
established the GTm_N model with a global grid of
2.5

Given a series of observations

The authors declare that they have no conflict of interest.

We would like to thank the NOAA/OAR/ESRL PSD (Boulder, Colorado, USA) for
providing NCEP-DOE Reanalysis 2 data (2010–2014), the Department of
Atmospheric Science in the University of Wyoming for providing access to
radiosonde data in 2014, the GGOS (Global Geodetic Observing System)
Atmosphere for providing 2014 surface