1National Centre for Applied Physics, King Abdulaziz City For Science and Technology, Saudi Arabia
2 National Center for Geodesy & Navigation Technology, King Abdulaziz City for Science and Technology, KSA
3Instituto D. Luiz, Universidade da Beira Interior, Portugal
4 Prince Nora University, Saudi Arabia
Submission: May 25, 2020; Published: June 08, 2020
*Corresponding author: Maghrabi AH, National Centre for Applied Physics, King Abdulaziz City For Science and Technology, P.O. Box 6086, Riyadh 11442, Saudi Arabia
How to cite this article: Maghrabi A, Alothman A, Fernandes R, Almutairi M, Aldosari A, et al.Modelling and Validation of the Precipitable Water Vapour from
Zenith Wet Delay using Radiosonde and GNSS Data in the Central Arabian Peninsula. Int J Environ Sci Nat Res. 2020; 25(1): 556152.
In this study, radiosonde observations for the period 1985 to 2016 from four sites in Saudi Arabia (Riyadh, Abha, Hail, and Dammam) were used to calculate the Zenith Wet Delay (ZWD) and Precipitable Water Vapour (PWV). Using the Asken & Nordius  approach (PWV =1/k ZWD), correlation analyses between these two variables (in mm) were carried out using data from1986-2012 for each site individually and for the combined data from all sites. The values of the conversion constant between the two variables were determined and found to lie between 0.171 and 0.178. The site-specific model and the regional developed model were used to predict the PWV values for the period between 2013 and 2016 and for the entire study period (1986 to 2016). The predictability of these models against the three datasets was excellent. The mean bias error (MBE) and root mean square error (RMSE) for the three datasets were, respectively, between 0.02mm and 0.53mm and between 1.51mm and 3.71mm.
Zenith Total Delay (ZTD) and ZWD from the GNSS receiver installed at the Geodetic Solar Village (SOLA) site for the period between2004 and 2016 were used to calculate the PWV during this period to validate the accuracies of the proposed models. Three models, dependent upon the k value, were used to obtain the PWV values. These were the regional k value (0.178), the Riyadh site k value (0.172), and the global k value (0.15). Additionally, three locally developed models to calculate the weighted mean temperatures(Tm) from the surface temperature as well as eight models previously developed by different investigators were used to calculate the PWV values. The calculated PWV values were validated against the radiosonde-derived PWV for this period of time. For all the considered models, the MBE values were less than 2mm, and the RMSE values were between 1 and 4mm.
Keywords: GPS applications; Saudi Arabia; ZWD; PWV; weighted temperature
Atmospheric Water Vapour is one of the most important and abundant greenhouse gases. Precipitable Water Vapour is an actual measure of the total moisture in the atmosphere. Knowledge of the water vapour distribution and variability is very important for several atmospheric applications, as well as meteorological and climate studies. Water vapour has a considerable impact on radiation transfer in the atmosphere by absorbing and attenuating
electromagnetic radiation, as well by influencing the environment [2-4]. Despite its importance, water vapour is difficult to measure or quantify due to its variability, both spatially and temporally [5-7].
The number of measurement techniques used for observations of PWV increased considerably in the 1990s [8-11]. A summary of these techniques and a discussion of their advantages, disadvantages, and limitations are given in Maghrabi
& Clay  and references there in. However, with advances in
satellite technology, Global Navigation Satellite System (GNSS)
observations has become are liable, accurate, high resolution, low
cost source of global PWV measurements [13-19].
The atmosphere delays GNSS signals as they pass through.
This delay is either dry, known as the Zenith Hydrostatic Delay
(ZHD), or wet, termed the Zenith Wet Delay (ZWD). The total
delay is due to the sum of these two components; namely the
Zenith Total Delay (ZTD). The ZHD can be calculated accurately
based on the ground level temperature and pressure [20-22]. On
the other hand, ZTD can be obtained from processing the GNSS
signals using state-of-art processing software (e.g., GIPSY-OASIS,
Bernese, Gamit). Thus, by subtracting the ZHD from the ZTD,
the ZWD component can be obtained. By knowing the ZWD and
by employing a specific type of transformation, the PWV can be
The aim of this work was to provide a model to calculate the
PWV from the ZWD that could be used for several applications
without using the surface meteorological variables. To achieve
this, radiosonde data for the period between 1986 and 2016
from four sites in Saudi Arabia, were used to calculate the ZWD
and PWV. These sites were Riyadh, Hail, Dammam, and Abha
(Figure 1). Correlation analyses between these two variables were
carried out for each site and for the combined data to model the
PWV from the ZWD measurements; several models are proposed.
A regionally developed model is also proposed to calculate the
weighted temperature from the surface temperature. The GNSS
data from the SOLA site (located in Riyadh) for the period 2004-
2016 were used to validate the proposed models. Moreover, eight
previously proposed models to calculate the weighted mean
temperature were used to calculate the PWV values for this data
The experimental data and the methodologies are discussed
in section 2. In section 3, the results are presented. Conclusions
are presented in section 4.
Radiosonde observations from the record of the Saudi
Presidency of Meteorology and Environment (PME) for four
sites in Saudi Arabia during the period from1985 to 2016 were
used for the purposes of the current study. The selected sites
were Riyadh, Abha, Hail, and Dammam. These sites were chosen
because they had the longest series of observations, which are
relatively homogeneous and cover a broad range of climatic and
atmospheric conditions experienced in the region (Figure 1).
The available data were subjected to several quality
control procedures. These include the elimination of the whole
atmospheric profile if several observations of the required
variables are missing. Radiosonde observations less than 5km
were excluded from the analysis. Linear interpolation procedures
were carried out to replace up to five missing profiles to complete
the series. These interpolations were kept at a reasonable level in
order to preserve the nature of the information contained in the
According to Askne & Nordius , the relationship between
the PWV and the ZWD can be formulated as:
Where k is the proportionality coefficient, which can be
expressed according to Bevis et al.  as:
where ρ is the density of liquid water, Rv (461.518J/kg K) is
the specific gas constant for water vapour, k3 = (3.776±0.004)105
K2mbar-1, k2 = (17±10)Kmbar-1, and Tm is the mean weighted temperature of the water vapour in the atmosphere (K). The value
of k is about 0.15 globally; however, this value can vary by up to
20% due to variations in Tm [22,27]. Characteristically, the value
of k used in Eq. (1) can be obtained through several methods
[19,20,28,29]: (a) assuming the constant value of 0.15; (b) using
Eq. (2); or (c) determining it experimentally for a specific site or
region, as described below.
Using radiosonde data, the ZWD can be calculated using the
following formula [30,31]:
In this equation, Nw is the wet atmospheric refractivity
between layer i and i+1, ΔH is the height difference between the
two layers, and n is the number of layers available for a certain
profile. For a certain layer, Nw can be obtained from:
Where e is the atmospheric water vapour pressure and Zw is
the inverse of the compressibility (≈ 1) and formulated as:
Where Tc is the temperature in Celsius.
Using equation (6), the Precipitable Water Vapour (PWV)
content for each radiosonde profile can be calculated as :
Where v ρ
is the absolute humidity at sounding level z and it is
obtained from the equation of the state of an ideal gas as:
Where T is the observed absolute temperature, RH(z) is
the relative humidity, and e(z, T) is the saturation water vapour
pressure in mbar.
For each available radiosonde profile, the required
meteorological variables were extracted and the ZWD was
calculated (using equations 3-5) for each atmospheric layer
and integrated from the surface up to 300mbar. The 300mbar
data limit is due to the poor performance of the radiosonde
humidity sensors in cold temperatures (Zhai and Eskrideg 1996;
Kassomenos and McGregor 2006) . Finally, the radiosonde
derived PWV was obtained using equation (6).
Table 1 gives the mean values of meteorological variables,
the number of radiosonde profiles, and the calculated values of
the PWV and the ZWD for each site individually and for all the
The data were divided into two groups, namely the modelling
and validation groups. The modelling dataset (set 1) covers
the period between 1985 and 2016, whereas the validation
dataset (set 2) covers the period between 2013 and2016, where
independent estimatives obtained from GNSS observations were
available. The combined data for the entire period of study is
called set 3.
The statistical indicators used here were the mean bias error
(MBE) and the root mean square error (RMSE). Their functional
forms are given as follows:
Where ximeas is the ith measured value, xcal is the ith predicted
value, and N is the total number of observations. Furthermore, a
t-statistic Student’s test was used to test the significance of the
proposed regressions. According to Stone , the t-value can be
calculated as follows:
Additionally, the relationship between the predicted and
measured data was examined using linear regression analysis, as
represented by equation (11):
For better prediction by the proposed models, the MBE and
RMSE values need be as small as possible, the t-value must be less
than the critical value, the correlation coefficient r must be close
to 1, intercept (b) close to zero, and the best-fit slope (a) must be
close to 1.
Figure 2 shows the variations in mean PWV and ZWD values
from all stations during the considered period. It is clearly evident
that both variables exhibited seasonal variation with a maximum
reached in summer months and minimum in winter months.
During this period, the PWV showed a minimum value of about
2mm in January of 1987 and February 2008. The highest PWV
(34.7mm) was recorded in May 1988, followed by September
2013 (34mm) and August 2003, when it reached a value of 32mm.
ZWD attained a maximum value of 0.2m in September 1986 and
May 1987. The minimum ZWD of 0.01m was reached in January
1987 and February 2008.
The relationships between the calculated PWV and the ZWD
for each site for the period between 1986 and 2012 are depicted
in Figure 3.While there is spread in the data, Figure 3 shows that
the PWV was correlated with the ZWD, with different degrees of
Regression analyses between the two variables for this period
of time were carried out and the constant (k) values of equation (1)
were obtained for each site individually and for the combined data
from all sites. Moreover, the predictability of the site-developed
model was tested against the independent data set (covering the
period 2013-2016) and against data for the whole period (1985-
2016) for the corresponding site. The results of these regression
analyses are presented in Table 2
The regression equation between the combined PWV and the
ZWD data from all the considered sites (regional model) for the
period between 1985 and 2012 was:
This equation has a correlation coefficient of 0.94, MBE of
0.017mm, and RMSE of 1.55mm. Using the validation dataset, the
MBE and RMSE values for this model were -0.61mm and 1.34mm
respectively. The RMSE and MBE values of this model, when is
tested against the measured PWV data for each site individually
for the whole period of the study (1985-2016),are given in the
last column of the Table 2. It can be seen that the obtained MBE
values between the prediction of equation (12) and the measured
PWV values were less than 1mm. The model underestimated the
measured data by 0.081mm, 0.002mm, and -0.28mm for Riyadh,
Hail, and Dammam respectively. The model presented RMSE
values of 2.09mm, 1.52mm, 1.51mm, and 3.92mm for Abha,
Riyadh, Hail, and Dammam, respectively.
The value of the constant k was about 0.177 for both Abha and
Hail, with correlation coefficients between the PWV and the ZWD
of0.93 and 0.94, respectively. For the Riyadh site, it was 0.175
with a correlation coefficient of 0.96. This value was 0.171 with a
correlation coefficient of 0.88 for the Dammam site.
The site-specific developed model, when tested against
the measured data from the modelling data (third column),
independent data (fourth column), and the data combined from
all the sites (fifth column), presented MBE values less than 1mm all cases. However, the RMSE values were different from one
dataset to another. For the dataset covering the whole period of
the study (1986-2016), all the site-specific models showed RMSE
values less than 2mm, in which the Hail model had the highest
value (1.76mm) and Riyadh model had the lowest value (1.51mm).
For the other two datasets, i.e. 1986 to 2012 and 2013 to 2016,
the Dammam developed model presented the highest RMSE
values of 3.71mm for the former dataset and 3.1mm for the latter.
This may be due to the considerable variations in atmospheric
conditions in Dammam and due to its proximity to the sea. The
Abha specific model presented the second highest RMSE values
when it was used to predict the PWV for these two datasets. The
Riyadh and Hail models had RMSE values of 1.54mm and 1.78mm,
respectively, when they were used to predict the PWV for all data
between 1986 and 2012. For the second dataset (2013-2016), the
RMSE values were 0.83mm and 0.81mm, respectively, when the
Riyadh and Hail specific models were used.
Figure 4 indicates the measured PWV data plotted against the
predicted PWV values using the regional model (equation 12) and
the site-specific model for the independent dataset (2013-2016)
for each site. It can be clearly seen that most of the data points
lie far from the 1:1 line, but the majority of them are distributed
Regression analyses between the measured and the predicted
PWV values, for all panels in Figure 4, showed slope values from
1 for Abha, Hail, and Riyadh to 0.93 for the Dammam site and the
combined data from all sites. The intercepts of these regression
lines were 0.004mm for Riyadh, 0.08mm for Hail, 0.28mm for
Abha, 1.7mm for Dammam, and 1.25mm for the combined data
from all sites. Apart from the Dammam site (correlation coefficient
0.91), the correlation coefficients for all the cases ranged between
0.94 and 0.99. Additionally, Student’s t-tests at a confidence level
of 95% showed that the developed models were statistically
significant for (n-1) degrees of freedom.
The values of the k constant obtained in this study are within
the range previously reported by several investigators. Liu et
al.  found that the values of the k constant ranged between
0.17 and 0.182 for different Chinese regions. Singh (2015), when
studying the relationship between the ZWD and the PWV in the
Indian region, reported k constant values between 0.166 and
0.162. However, these values are slightly higher than the typical
value reported for American stations (about 0.15) [20,27].
Variations in the k value are attributed to several factors, such as
the season and the latitude of the site [23,30,32].
Several investigators have found that accurate determination
of the PWV depends on the accuracy of estimating the k
value which, as a consequence, depends upon variations in
the atmospheric weighted temperature . Knowledge of
the weighted temperature is of a great importance for PWV
estimations from ground-based GNSS receivers [23,29,30,35].
Weighted temperature determinations require detailed
information on the upper air regarding both temperature and
water, which is usually unavailable and difficult to obtain. Instead,
several empirical models have been developed to calculate the
weighted temperature from easy-to-measure meteorological data
such as surface temperature, pressure, and humidity (Yanxin et
al. 2013; Sapucci 2014) [13,22,23]. The most commonly used and
easy to use method to determine the weighted temperature is
the Bevis method. This method is based on the linear correlation
between the weighted temperature and surface temperature (Ts).
The weighted mean temperature of the atmosphere can be
Where ei and Ti are the water vapour pressure (in mbar) and
the atmospheric temperature (in K), respectively, at height hi [29-
In this section, using the available radiosonde profiles from
the selected sites for the period between 1986 and 2016, the
weighted temperature (Tm) was calculated for each atmospheric
layer and integrated from the surface up to 300mbar .
Regression analyses between the calculated Tm and the Ts from
all sites were conducted, as shown in Figure 5.
The regression equation for this plot was:
The correlation coefficient, MBE and RMSE were 0.86, -0.01
K, and 4.32 K, respectively.The calculated Tm will be used in the
calculations of the PWV discussed in the following section
In 2004, King Abdulaziz City for Science and Technology
(KACST) established a GNSS network for geodetic and geophysical
applications to contribute to the International GNSS Service (IGS).
In this study, we use the data from covering the period between
2004 and 2016.
The ZTD values for this station were directly obtained from
the analysis of the GNSS data using the GIPSY/OASIS software
package . GIPSY/OASIS processes the daily files for each
station individually using a strategy called PPP – Precise Point
Positioning . Satellite orbit and clock parameters are provided
by the Jet Propulsion Laboratory (JPL) and kept fixed in order to
estimate the ZTD and other parameters of interest (in particular
the daily positions) simultaneously. One estimate for ZTD was
obtained every 5 minutes. In order to remove the jumps at 00h00
UTC (since each daily file is computed separately), we used a
methodology developed at SEGAL that computes the ZTD values
using files with 30h (from 21h00 from day before to 03h00 of the
following day) and uses a transference function to remove these jumbs .
The ZWD for each estimate was obtained by subtracting the
hydrostatic part (ZHD) from the ZTD [25,38]:
Where ZHD is almost constant over time and it was modelled
in the GPS processing using the Vienna Mapping Function .
Radiosonde observations for the considered period (2004-
2016) were used to calculate the PWV, and these values were
considered as the reference for further comparisons. The ZWD
values used in this section are those calculated by the software
(equation 15). Using equation (1), the PWV was calculated using
six different approaches. Three of them were based on using the
value of the transforming constant (k) between the PWV and
the ZWD. The remaining three approaches were based on using
the mean weighted temperature in calculating the value of the
constant k. The methods are:
a) The regional k value (0.178) developed in this study.
b) The Riyadh-specific k value (0.175) developed here.
c) Assuming a value of 0.15 for the k constant as adopted
by several investigators [25,27].
d) Calculating the k constant (equation 2) using the
mean weighted temperature (Tm), calculated from radiosonde
observations using equation (13); namely the measured Tm
e) Calculating the k constant (equation 2) using Tm
obtained from equation (14).
f) Calculating the k constant (equation 2) using Tm
calculated using the Riyadh-specific temperature model :
The mean values of the radiosonde-derived PWV and the PWV
values calculated using the six methods as well as the GPS-derived
ZTD and ZWD are given in Table 3. It can be seen that the PWV
obtained using the global and site-specific k values presented the
highest PWV, whereas the site-specific Tm model provided the
minimum value. The radiosonde-derived mean PWV for this data
set was almost same as the mean for the entire period (Table 1).
The software-derived mean ZWD value was almost the same as
that calculated using equation (3).
The least square fits between the measured and the predicted
PWV values using the six approaches were assessed; the results are
depicted in Figure 6. The MBE and RMSE values of these analyses
are presented in the last two columns of Table 3. It is clear that all
the models predicted the measured data with good accuracy. The
obtained RMSE and MBE values using method 3 were 3.48mm
and 1.83mm, respectively. For the rest of the methods, the MBE
values were less than 1mm and the RMSE values were about
3mm. The slopes of the regression lines between the measured
and predicted values were between 0.85 and 0.88. Moreover, the
correlation coefficients for the measured and predicted data, in
all the cases, were about 0.91 and the intercept values ranged
between 2.42mm and 3.14mm. Student’s t-tests were conducted
and showed that the t values for all the regressions were below
the critical value (1.64) at the 95% level of significance for (n-
1) degrees of freedom. It is obvious that, in some situations, the
methods either over-or underestimated the measured data, which
may be due to the uncertainties, associated with measurements
of meteorological variables and/or PWV estimations from the
radiosonde data. Other atmospheric parameters, such as the
effects of wind speed and day/night variations in the atmospheric
boundary layer, which may affect the distribution of atmospheric
water, may have some influence on PWV estimations in some
Several empirical models from different regions around the
world have been developed to estimate the Tm (i.e. the Bevis
method) according to the surface temperature, and to use this
relationship to calculate the PWV. In this section, eight previously
established models (Table 4) were used to calculate the Tm for
the Riyadh site based on the surface temperature. The obtained Tm temperatures from each model were used to calculate the k
values, which were then used to transform the GPS ZWD data to
PWV data. The RMSE and the MBE values between the radiosondederived
PWV data and those obtained from the selected models
are also given in Table 4. It can be seen that the overall predictions
of the selected models for the measured data appear to be
adequate. They showed sub-millimetre MBE values and RMSE
values of about 3mm.
Figure 7 shows the measured data plotted against the predicted
PWV values using the selected models. It can be seen that the data
are distributed very close to the 1:1 line. For all the considered
models, the correlation coefficients between the measured and
predicted PWV values were between 0.87 and 0.89. The slopes
of the regression lines ranged between 0.77 and 0.79 and the
intercept values ranged between 2.8 and 3mm. Student’s t-tests
were carried out and showed that the overall predications of the
selected models were significant at a 95% level of significance for
(n-1) degrees of freedom.
It can be seen that the predictions of these models provided
realistic estimates of measured PWV values and showed
fairly consistent results with the regional and local weighted
temperatures used in the previous section. The selected models
failed to predict the PWV value in some situations. This may be
due to the failure of the model in predicting the exact weighted
temperature and/or to the uncertainties associated with
measuring the meteorological variables used in the calculations.
Thirty-one years (1985-2016) of radiosonde observations
from four sites in Saudi Arabia were used to calculate the zenith
wet delay (ZWD) and Precipitable Water Vapour (PWV) for each
site individually, and using the entire data set from all four sites.
Several conclusions may be drawn from these analyses.
a) Using the Asken & Nordius  approach (PWV =
k-1 PWV), the relationship between these two variables was
investigated and established for each site individually and for the
combined data from all sites. Several PWV models based on the
ZWD were developed and tested using the dataset covering the
period from 1985 to 2012.The values of the conversion constants
between the two variables were determined and were found to lie
between 0.17 and 0.178, and were within the range of previously
b) The site-specific model and the regionally developed
model were validated against the measured PWV values for the
period between 2013 and2016 and for the entire study period
(1986 to 2016). The predictability of these models against the
three datasets was excellent. The mean bias errors (MBE) and
root mean square errors (RMSE) for the three datasets were,
respectively, between 0.02mm and 0.53mm and between 1.51mm
c) The mean weighted temperatures (Tm) for the
considered sites were calculated and a regional Tm model
based on the surface temperature was developed for further
calculations. The model had MBE and RMSE values of -0.01K and
d) ZWD data obtained from GPS receiver installed at the
GNSS Solar Village (SOLA) site for the period between 2004 and
2016 were used to calculate the PWV during this period and
validate the accuracy of the proposed models.
e) Six approaches were considered in calculating the PWV
for this dataset. Three of them were based on using different
values for the constant k value; specifically, the regionally
obtained k value (0.178), Riyadh site value (0.172), and the global
value of k(0.15). The remaining three approaches depended on
calculating the weighted temperature from locally developed
models. Except for the model that used the global value of k (0.15),
all the considered models showed MBE values of less than 1mm.
The RMSE value for all the models was about 3mm.
f) Eight models previously developed by different
investigators to calculate the weighted temperature from the
surface temperature were used to derive the PWV values. The
predictions of these models were comparable with the models
developed in this study. For all eight models, the MBE value was
less than 1mm and the RMSE value was about 3mm.
g) Despite considerable efforts to establish regional and
global PWV models using data from all over the world, very few
of these studies have been conducted in this region of world.
Therefore, the sites and regional PWV-ZWD models developed
in this study will be useful for space science, meteorology,
climatology, and GPS applications.
Fernandes RMS, Sá A, Miranda P, Bos MS, Martins J, et al. (2015) Signature on GNSS PWVestimates of relevant storms affecting Iberia in recent years. IUGG General Assembly, IUGG-G07, Prague, Czech Republic, p. 372.
Mendes VB, Prates G, Santao L, Langley RB (2000) An evaluation of the accuracy of models for the determination of weighted mean temperature of the atmo sphere. In: Proceedings of the ION 2000, National Technical Meeting, Anaheim, CA, USA, pp. 433-438.
Solbrig P (2000) Untersuchungen uber die Nutzung numerischer Wettermodelle zur Wasserdampfbestimmung mit Hilfe des Global Positioning Systems. Diploma Thesis. Institute of Geodesy and Navigation, University FAF Munich, Germany.
Feng Y, Bai Z, Fang P, Williams A (2001) GPS water vapour experimental results from observations of the Australian Regional GPS Network (ARGN). 2001-A Spatial Odyssey: 42nd Australian Surveyors Congress, Brisbane, Australia, Institute of Surveyors.