Precipitable Water Comparisons Over Ghana using PPP Techniques and Reanalysis Data

Atmospheric Water vapor is an important greenhouse gas and contributes greatly in maintaining the Earth’s energy balance. This critical meteorological parameter is not being sensed by any of the 22 synoptic weather stations in Ghana. This study presents a highly precise tool for water vapor sensing based on the concept Global Navigation Satellite Systems (GNSS) meteorology and tests the computed results against global reanalysis data. Conventional approaches used to sense the atmospheric water vapor or Precipitable Water (PW) such as radiosondes, hygrometers, microwave radiometers or sun photometers are expensive and have coverage and temporal limitations. Whereas GNSS meteorological concept offers an easier, inexpensive and all-weather technique to retrieve PW or Integrated Water Vapor (IWV) from zenith tropospheric delays (ZTD) over a reference station. This study employed precise point positioning (PPP) techniques to quantify the extend of delays on the signal due to the troposphere and stratosphere where atmospheric water vapor resides. Stringent processing criteria were set using an elevation cut-off of 5 degrees, precise orbital and clock products were used as well as nominal tropospheric corrections and mapping functions implemented. The delays which are originally slanted are mapped unto the zenith direction and integrated with surface meteorological parameters to retrieve PW or IWV. The gLAB software, Canadian Spatial Reference System (CSRS) and Automatic Precise Positioning Service (APPS) online PPP services were the approaches used to compute ZTD. PW values obtained were compared with Japanese Metro Agency Reanalysis (JRA), European Centre for Medium-Range Weather Forecasts Reanalysis (ERA-interim) and National Center for Environmental Prediction (NCEP) global reanalysis data. Correlation analysis were run on the logged station data using the three approaches and global reanalysis data. The obtained results show stronger correlation between the retrieved PW values and those provided by the ERA-interim. Finally, the study results indicate that with a more densified network of GNSS base stations the retrieved PW or IWV will greatly improve numerical weather predictions in Ghana.


Introduction
As a major constituent in the atmospheric greenhouse gases, water vapour concentration is not significantly influenced by direct anthropogenic activities (USGS-Editors, 2011;Seidel, 2002). This is because water vapour contributes to weather phenomena through natural evolution and feedback mechanism. Again its contents in the atmosphere is highly variable both in space and in time due to temperature changes, atmospheric circulation and micro-physical processes (Pottiaux, 2010;Zebker et al., 1997;Rocken et al., 1993). According to Solomon et al. (2007), an estimated 70% of the recent rises in atmospheric temperature are attributed to water vapour feedback. Additionally, the long-term surface warming under an assumed doubling of the atmospheric carbon dioxide are as a result of enhanced radiation dependent cloud and water vapour feedbacks (IPCC, 2014).
The amount and distribution of water vapour in space (horizontal and vertical) is a major parameter in the development of Numerical Weather Prediction (NWP) models and its importance cannot be underestimated. Sensing and measurement of water vapour by conventional methods such as radiosondes, hygrometers, microwave radiometers, sun photometers are affected by meteorological conditions (Maghrabi and Al Dajani, 2013;Pérez-Ramírez et al., 2012;England et al., 1992). In addition, they are expensive and have coverage limitations. Again water vapour is under sampled in current operational meteorological and climate observing systems (Pichelli et al., 2010;Pierdicca et al., 2009;Gendt et al., 2003). The timely delivery and availability of fine-resolution and accurate 3D water vapour field measurements would lead to substantial improvements in NWP model initialization (Andersson, 2014;Sahoo et al., 2013). The Ghana Meteorological Agency (GMet), the institute responsible for weather forecasting has 22 synoptic stations but unfortunately none is equipped to sense atmospheric water vapour. GMet instead uses most products from the European Center for Medium-Range Weather Forecasts (ECMWF) and other global numerical weather prediction models for their activities. These NWP server products are very good but there still exhibits substantial data gaps with respect to ground-based GNSS observational networks for the African region (refer Figure 1). Seidel et al., 2009 andTeunissen, 2003 have reported of densification of stations of the Global Climate Observing System (GCOS) Upper-Air Network (GUAN) with greater availability and improved data accessed for weather forecasting. With these modernization efforts being carried-out, are aimed at improving coverage and data availability which will go a long way to improve and enhance global weather forecasting.  Bevis et al. (1992) and patented by Solheim and Ware (1997). This GNSS technique estimates the propagation delays on the signals caused by the neutral atmosphere and the magnitude of the delayed component is directly proportional to the atmospheric water vapour. Tropospheric delays are estimated using either double differencing based on Differential GNSS (DGNSS) for a network of stations or Precise Point Positioning (PPP) for single stations. PPP approach was used for the study because data from a single base station were processed. GNSS Meteorological method is highly accurate irrespective of adverse meteorological conditions, inexpensive and with modelling capabilities to estimate errors with high temporal and spatial resolutions. There is an added advantage that retrieved precipitable water or integrated water vapour can be directly assimilated into NWP models (Bennitt and Jupp, 2012;Bengtsson et al., 2003;van der Marel et al., 2003;Johnsen and Kidder, 2002).

Methods and Data
To ascertain the accuracies and precision of estimates provided by the Precise Point Positioning techniques for the computation of zenith tropospheric delays, three (3) Mireault et al., 2008;T´etreault et al., 2005). PPP processing technique was used because datasets for the study came from a single station in Kumasi, Ghana. PPP implementation is based on carrier phases (Kouba and H´eroux, 2001). The knowledge of the precise coordinates of the reference receiver, inter-station distance limitation and simultaneous observations as required in doubledifferenced differential techniques are not needed. These facts make PPP techniques more advantageous for single-station GNSS Meteor assignments. Following Misra and Enge (2011), the GNSS carrier phase observable equation is given as: where R is the true range, Iϕ and Tϕ are the delays associated with signal transmission through the ionosphere and troposphere delays, ερ are measurement noise, c is speed of light in vacuum, (δtr − δt s ) are receiver and satellite clock biases respectively. ϕ, is carrier phase, λ is wavelength, N is integer ambiguity. However, the PPP dual-frequency functional model for carrier phases, Φ s r, from satellite, s, to receiver, r, as given by Subriana et al. (2013) is: The true range, ρ, can hardly be obtained as its adulterated with offsets caused by satellite and receiver clocks, c∆tr and c∆t s , ionospheric and tropospheric delays, αr and α s are phase biases for receiver and satellite, ∆ρrel is range correction due to relativistic effects, ω is a phase wind-up correction, λ is wavelength, N is ambiguity for the carrier frequency. ∆dpcv is frequency dependent delay due to the phase center variations, ∆dmp is delay due to multipath, ερ and εΦ are the remaining un-modelled errors in the measurements. Accounting for all these errors in Equation 2 Bevis et al. (1992) gives IWV as: where pv is the partial density of water vapour in kg/m 3 ; e is water vapour pressure; T is temperature in kelvin; the height h in metres and Rw is the specific gas constant for water vapour in J/(kgK). PW relates to IWV by diving with the density of liquid water, ρw. PW = IWV/ρw. Again IWV is related to the ZWD using a dimensionless quantity as conversion factor, Π: Introducing a mean temperature, Tm, which is defined as: Tm = 0.72Ts + 70.2, where Ts is the surface temperature. The conversion factor finally becomes: The dimensionless constant computed using Equation 5 ranged between 0.1598 to 0.1665, with an average value of 0.1629 and a standard deviation of 0.0013. The average value of 0.1629 was used for PW computations in the study. Bevis et al. (1994) computed the dimensionless constant to be approximately 0.15, and they found Π to be a function of season and location. The computed Π for this study falls within the 20% recommended range variation identified by Liou et al. (2001) and Bevis et al. (1994).
In this study, GPS data was collected from a Base Station on the campus of Kwame Nkrumah  (Dee et al., 2011). The downloaded data were in the netCDF formats and climate data operators (CDO) software (Schulzweida et al., 2009) was used for data manipulation and extraction for further processing and analysis.

Data Processing
An a priori or possibly the precise knowledge of the Base station's antenna position must be known in a specific reference datum before data can be processed using PPP techniques. For this study the ITRF2008 reference frame was used (Altamimi et al., 2011). The precise coordinates of the antenna position were determined by comparing GNSS Baseline Differential processing with data submitted to APPS and CSRS-PPP online servers. The final result was fed into the gLAB for ZTD estimations.
The criteria set in gLAB were an elevation mask of 5 o , modified Niell mapping functions for mapping slant delays unto the zenith and L1-C1 differences for cycle-slip detections. The rest are data decimation of 300secs, Klobuchar model for ionospheric correction (Klobuchar, 1996) and corrections for relativistic, antenna phase centres and ocean tidal loading effects (Subriana et al., 2013).
Processing with the online servers were done by first registering with the services and formatting data to meet the input requirements. Data were subsequently uploaded via the web. Output results were downloaded in a compressed format and extracted then files containing ZTD were identified.
Using the GREP command in UNIX, ZTDs at hourly time-marks were extracted from the output reports. Some key features of the online services used are given in Table 1.

Results
Computed ZTDs for the three processing approaches were matched against Day-of-year (DoY) and descriptive statistics were run to determine how the 3 results are related. Table 2 shows the results with a corresponding box plot in Figure 2 showing the spread and outliers. The results show the means, µ, of the software agree to the second decimals, same with standard deviation, σ, but gLAB gave a wider range with some multiple outliers.  A C A plot showing computed PW using ZTD from the three software against the data extracted from the reanalysis models are shown in Figure 4. Comparative analysis for the different methods used in deriving PW for the study area were done and the resulting correlation coefficients, r matrix is given in Table 3. Precipitable Water (PW) quantities report by NCEP reanalysis were the highest for the reporting period, followed by ERA-Interim with JRA giving the least values. Values retrieved from the GPS signals gave the smallest ranges of ≈6mm in PW over the study period whilst JRA recorded the highest range of ≈23mm. Comparing PW retrieved from GPS signals with the reanalysis models, APPS gave the highest correlation for all the three reanalysis models followed by CSRS and gLAB (refer Table 2

Conclusions
GNSS signals coupled with surface meteorological data can be utilized to derive tropospheric delays and PW with high accuracy. We have shown that when IGS precise products are applied, whichever PPP approach used in computing ZTD, the retrieved PW will compare favourably with other remote water vapour sensing devices. While GNSS-sensed PW is found to generally agree and positively correlates with Reanalysis models, the findings show that ERA-Interim is the best.
However, these findings are not to rate one reanalysis over the other but to point that for atmospheric water vapour sampling over Kumasi, ERA-Interim samples better. Summing up, GNSS measurements can be logged as frequently at a rate of 1sec making the concept of GNSS meteorology much more advantageous in sampling temporal variability of atmospheric water vapour.

Acknowledgements
Funds for this study were partly provided by DANIDA through Building Stronger Universities' Environment & Climate Platform (www.bsuec.org).