Statistical Modelling of Atmospheric Mean Temperature in sub-Sahel West Africa
Falaiye Oluwasesan Adeniran Sukam Yakubu Musa Abimbola Oladiran Johnson













 






 
 
 


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[C]Falaiye et al.: Weighted Atmospheric Mean Temperature 

 
 
 
 
 
 


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*]Falaiye O. A.
*]Sukam Y. M.
**]Abimbola O. J.
[*]Department of Physics, Faculty of Physical Sciences, University of Ilorin, Nigeria
[**]Department of Physics, Faculty of Science, Federal University Lafia, Nigeria



 





Statistical Modeling of Atmospheric Mean Temperature in sub-Sahel West Africa
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§ 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 <cit.> model. The delay error introduced by the water vapor in the atmosphere, called the zenith wet delay (ZWD) is calculated thus:


    ZWD=ZTD-ZHD


The ZWD is usually transformed into the PWV using the transformation equation as given below


    PWV=Π× ZWD


The transformation constant Π, is given by


    Π = [ 10^-6( k_3/T_m + k^'_2) ρ_v R_v] ^-1


here, ρ_v is the liquid water density = 1000 kgm^-3, R_v is water vapor gas constant = 461.524 JK^-1kg^-1, k_3 = 377600 K^2hPa, k^'_2 = 22.1 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


    T_m=∫^p_1_p_2Td(lnp)/∫^p_1_p_2d(lnp)=∫^∞_ze/Tdz/∫^∞_ze/T^2dz


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.<ref>.  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.<cit.> 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.<cit.> model was adopted in many studies (e.g., Raju et al.<cit.>; Fernandez et al.<cit.>; Musa et al.<cit.>; Abimbola et al.<cit.>) across the globe despite the fact that it was obtained for the USA region. Mendes et al.<cit.> and Solbrig<cit.>, using radiosonde data, obtained similar linear relation for Germany, Raju et al.<cit.> for Indian sub-continent, Shoji<cit.> for Japan and Isioye et al.<cit.> for West Africa. Meanwhile, Schuler et al.<cit.>, 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.<ref>


    T_m=0.65T_s + 86.9


From satellite data: which is of higher resolution spatio-temporally than the radiosonde data, it is the aim of this work to find a suitable statistical model for the evaluation of atmospheric mean temperature T_m in West African region.





§ METHODOLOGY
 


 §.§ Study Area
 
This study was conducted for locations in West African region as shown in Figure<ref>. The selected locations in West Africa for this research work are: Dakar (14.76 ^oN Latitude, 17.36  ^oW Longitude), Conakry (9.64  ^oN Latitude, 13.57  ^oW Longitude), Bamako (12.63  ^oN Latitude, 8.00  ^oW Longitude), Abidjan (5.36  ^oN Latitude, 4.00  ^oW Longitude), Niamey (13.51  ^oN Latitude, 12.12  ^oE Longitude), and Abuja (90.07  ^oN Latitude, 7.39  ^oE Longitude).



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 <ref>.





 §.§ Data Analysis

The data used in this work was obtained from the archive of the Climate Monitoring Satellite Application Facilities (CM-SAF) of the European Meteorological Satellites (EUMETSAT) at https://www.cmsaf.eu/EN/Home/home_node.htmlhttps://www.cmsaf.eu. The data was obtained as a monthly average for a time period spanning from 2004 to 2016 in Network Common Data Format (netCDF).  The data obtained at six different pressure levels (level1 = 200 hPa; level2 = 300 hPa; level3 = 500 hPa; level4 = 700 hPa; level5 = 850 hPa and level6 (surface) = 1000 hPa). are the specific humidity q_m (g/kg) and the ambient temperature T (K). The vapor pressure e (in hPa) was estimated from the specific humidity using:


    e=0.5q_m/10^-3q_m + 0.622


Panoply (v4.3.1), open source software from NOAA was used for the processing of the data while Jupyter notebook, an environment for running Python code, was used for data plotting, curve fittings and other statistical analysis.

Goodness of fit and correlational analysis of the derived empirical equations were done using coefficient of determination (R^2), mean-biased error (MBE) and root-mean-square error (RMSE).





§ 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<ref>. All the stations considered show good linear correlations between T_m and T_sExcept for Conakry with a below average coefficient of determination. It will be observed from Table<ref> that the coastal region generally does not show good linear correlation between T_m and T_s, whereas the hinterland region shows very good linear correlation: also it was observed that the ambient surface temperature at the coast is generally much lower than that at the hinterland of West Africa.


Figures<ref> and <ref> show the combined plot and linear fit to the dataset of coastal and hinterland respectively. For these figures empirical equations Eq.<ref> and Eq.<ref> were derived for the coastal and hinterland respectively. It will be observed again from Figures<ref> and<ref> as well as the derived Eqs.<ref> and <ref> that the model fit to the hinterland data has better correlation than the fit to the coastal data.




    T_m=0.60T_s + 112.73       R^2 = 0.459


 


    T_m=0.72T_s + 77.89       R^2 = 0.752


Figure<ref> shows a plot of all the combined data for West Africa. The statistical model derived from Figure<ref> is given in Eq.<ref> with the corresponding coefficient of determination:


    T_m=0.617T_s + 108.49       R^2 = 0.709


Isioye et. al.<cit.> using radiosonde data covering 2009 to 2013 for West Africa obtained a corresponding statistical model as given in Eq.<ref>:


    T_m=0.5743T_s + 116.60       R^2 = 0.436


It will be noted that Eq.<ref> shows a better statistical performance than Eq.<ref>, though the two statistical models could be observed to be quite similar. A statistical comparison of Eq.<ref> with Eq.<ref> yields root-mean-square error (RMSE) of 1.189 and mean-biased error (MBE) of 0.0953, further showing that the two statistical models are comparable. Satellite data has wider spatio-temporal coverage than radiosonde data hence, the better coefficient of determination R^2, observed for Eq.<ref> as compared to Eq.<ref>.

 





§ 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.

AcknowledgmentThis work was done using data from EUMETSAT’s Satellite Application Facility on Climate Monitoring (CM SAF). DOI: 10.5676/EUM_SAF_CM/WVT_ATOVS/V001. 





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