Statistical Modelling of Atmospheric Mean Temperature in sub-Sahel West Africa

Atmospheric mean temperature T_m, is a vital parameter in the evaluation of precipitable water vapor (PWV) through the analysis of GPS signal, it is, therefore, important to have a good way of evaluation of T_m for the eventual accurate evaluation of PWV using GPS. Simple statistical models exist for various regions of the world for the evaluation of T_m using surface temperature T_s, in the form T_m=aT_s+b where a and b are constants. For West Africa, where atmospheric data is usually very scarce, there is a minimal attempt at finding a statistical model for T_m, as a function of T_s. In this work, attempt has been made to find such a model using data from the Climate Monitoring Satellite Facilities (CM-SAF) of the European Meteorological Satellites (EUMETSAT). The model derived was found to compare well with that obtained using radiosonde data with root-mean-square error of 1.189 and mean-biased error of 0.0952 between the two models.


I. Introduction
Preciptable water vapor (PWV) is an important atmospheric parameter essential in both weather and climatic prediction. Knowledge of the variability of PWV is also very important in astronomy as water vapor interact with the incoming electromagnetic waves in the atmosphere.
GPS meteorology offers a real-time continuous measurement of PWV. From the GPS data, it is possible to estimate the zenith total delay (ZTD). The zenith hydrostatic delay (ZHD), which is the delay error caused by the dry component of the atmosphere could be estimated using models such as the Saastamoinen [7] model. The delay error introduced by the water vapor in the atmosphere, called the zenith wet delay (ZWD) is calculated thus: The ZWD is usually transformed into the PWV using the transformation equation as given below The transformation constant Π, is given by here, ρ v is the liquid water density = 1000 kgm −3 , R v is water vapor gas constant = 461.524 JK −1 kg −1 , 1 KhPa −1 and T m is called weighted atmospheric mean temperature determination of which is very crucial to accurate transformation of ZWD into the PWV.
The weighted mean atmospheric temperature T m , could be defined as where p 1 and p 2 are pressures at two different layers of the atmosphere. T is the ambient temperature. e is the vapor pressure while z is the height above the ground. From Eq. 4. T m could be estimated from the radiosonde data taken at different layers of the atmosphere. However, such radiosonde data are usually not readily available across the globe, especially Africa, hence several attempts have been made to statistically relate T m with the surface temperature T s which is readily available as a basic meteorological parameter at any weather observing station. Bevis et al. [1] used 8700 radiosonde profiles from 13 stations in the United States of America (USA) to obtain a statistical model of the form T m = aT s + b. The Bevis et al. [1] model was adopted in many studies (e.g., Raju et al. [2]; Fernandez et al. [3]; Musa et al. [4]; Abimbola et al. [5]) across the globe despite the fact that it was obtained for the USA region. Mendes et al. [6] and Solbrig [8], using radiosonde data, obtained similar linear relation for Germany, Raju et al. [2] for Indian sub-continent, Shoji [9] for Japan and Isioye et al. [10] for West Africa. Meanwhile, Schuler et al. [11], using a numerical weather prediction data, obtained a model which is more global in outlook relating T m to T s as shown in Eq. 5  For ease of analysis of the data sets and climatic consideration, the study locations were further divided into (1) Hinterland, that is those locations in the interior of the study region and (2) Coastal, that is those regions close to the Atlantic Ocean. These divisions are shown in Table 1. 3

III. Results and Discussion
The derived empirical equations relating the mean atmospheric temperature T m to the surface temperature T s for each of the locations considered in this work within the West African region are shown in Table 2. All the stations considered show good linear correlations between T m and T s Except for Conakry with a below average coefficient of determination. It will be observed from Isioye et. al. [10] using radiosonde data covering 2009 to 2013 for West Africa obtained a corresponding statistical model as given in Eq. 10: It will be noted that Eq. 9 shows a better statistical performance than Eq. 10, though the two statistical models could be observed to be quite similar. A statistical comparison of Eq. 9 with Eq. 10 yields root-mean-square error (RMSE) of 1.189 and mean-biased error (MBE) of 0.0953, 6 Falaiye et al.: Weighted Atmospheric Mean Temperature further showing that the two statistical models are comparable. Satellite data has wider spatiotemporal coverage than radiosonde data hence, the better coefficient of determination R 2 , observed for Eq. 9 as compared to Eq. 10.

IV. Conclusion
Using satellite data from the Satellite Application Facility (CM-SAF) of the EUMETSAT a suitable statistical model has been derived to estimate weighted atmospheric mean temperature T m . The statistical model derived is a simple linear model of T m as a function of surface temperature T s .
The derived model was compared with a similar statistical model which had earlier been derived from the radiosonde data in West Africa. The correspondence between the two models were found to be significant.