Estimation of Surface Water Vapour Density and Its Variation with Other Meteorological Parameters Over Owerri, South Eastern, Nigeria

In this paper, the monthly variation of Surface Water Vapour Density (SWVD) with meteorological parameters of monthly average daily mean temperature, relative humidity, surface pressure, cloud cover and sunshine hours during the period of sixteen years (2000 – 2015) for Owerri (Latitude 5.48°N, Longitude 7.00°E, and 91m above sea level) were investigated. The daily variation of surface water vapour density for the two distinct seasons considering two typical months in each during the period of year 2015 was examined. The results showed fluctuation in the amount of surface water vapour density in each day of the month for the period under investigation. The monthly average daily values indicated that the surface water vapour densities are greater during the raining season than in the dry season. It was observed that the maximum average value of surface water vapour density of 21.002gm -3 occurred in the month of June during the raining season and minimum value of 14.653gm -3 in the month of January during the dry season. The highest value of surface water vapour density was observed on 9 th May, 2015 and the lowest on 14 th January, 2015. The comparison assessment of the developed SWVD based models was carried out using statistical indices of coefficient of determination (R 2 ), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), Nash – Sutcliffe Equation (NSE) and Index of Agreement (IA). The developed multivariate correlation regression model that relates temperature and relative humidity with R 2 =99.9% MBE=0.1259 RMSE=0.1462 MPE=-0.6739 NSE=99.8402% and IA=99.9611% was found more suitable for surface water vapour density estimation with good fitting and therefore can be used for estimating surface water vapour density in the location under investigation and region with similar climatic information. The results of the descriptive statistical analysis revealed that the surface water vapour density, mean temperature, relative humidity, cloud cover and sunshine hours data spread out more to the left of their mean value (negatively skewed), while the surface pressure data spread out more to the right of their mean value (positively skewed). The surface water vapour density data have positive kurtosis which indicates a relatively peaked distribution and possibility of a leptokurtic distribution while the mean temperature, relative humidity, surface pressure, cloud cover and sunshine hours data have negative kurtosis which indicates a relatively flat distribution and possibility of platykurtic distribution.


Introduction
The connection between the surface and the atmosphere in the hydrological cycle is normally referred to as Water vapour. Virtually all the water vapour in the atmosphere originated at the surface of the earth where water evaporates from the ocean and the continents owning to the sun's radiation and is transpired by plants and respired by animals into the atmosphere [1]. The atmosphere and the water vapour can be transported horizontally and vertically through the three-dimensional circulation of the atmosphere and may condense forming liquid water or ice crystals in clouds; when water returns to the earth's surface in different forms of precipitation such as rain or snow the cycle is said to be completed. The cycle is closely related to the atmospheric circulation and temperature patterns [2]. Approximately two third of the natural green house effect of the earth's atmosphere are caused by water vapour, as a result of this, may be considered the most important greenhouse gas [3].
As the Earth's surface temperature increases, the atmosphere tends to hold more water vapour. This atmospheric water vapour, acts as a greenhouse gas thereby absorbing energy that would otherwise cause attenuation of electromagnetic radiation travelling through the atmosphere, the consequences of these could be atmospheric or global warming. The proportion by volume of water vapour in the air at the ground level on the average changes from less than 0.001%in the arctic to more than 6% in the tropics [4]. This proportion decreases speedily with height [4].
The balance between the incoming radiation from the sun and the outgoing reflected and scattered solar radiation plus the thermal infrared emission to space is referred to as the Earth's Radiation Budget (ERB) and is significantly influenced by the Earth's surface conditions through surface water vapour and temperature variations in the thermal infrared and through a critical contribution of temperature to the planetary albedo particularly for desert areas and snow-and ice-covered polar areas [5][6]. The atmospheric water vapour content responds to variations in temperature, microphysical processes and the atmospheric circulation. An overarching consideration is that the highest quantity of water vapour air can hold increases rapidly with temperature, in accordance with the Clausius-Clapeyron equation [7]. This affects all aspects of the hydrological cycle [7].
Researches on climate models have shown that an increase in atmospheric humidity by 12 -25% will have the same global average radiative effect than doubling the Carbon (iv) oxide concentration [5]. On the contrary to the homogeneous distribution of long-lived Carbon (iv) oxide, water vapour distribution is highly variable in space and time. Apart from its direct radiative effect, water vapour acts indirectly by interacting with aerosols, clouds and precipitation [8][9]. This indirect effect of surface cooling offers one of the largest uncertainties in the understanding of the radiative balance of the earth's atmosphere [10].
The aim of this study was to investigate the daily and monthly variation of surface water vapour density and to examine the monthly variation with meteorological parameters of mean temperature, relative humidity, surface pressure, cloud cover and sunshine hours for Owerri located in South Eastern, Nigeria. The study also developed new model for estimating surface water vapour density and descriptive statistical analysis was carried out for the location under investigation. Figure 1 shows the study area under investigation. Imo is a state in Nigeria located in south eastern Nigeria. Owerri (Latitude 5.48°N, Longitude 7.00°E, and 91m above sea level) is the capital city of Imo and one of the largest in the state. The State is bordered by Abia State on the East, River Niger and Delta State to the West, Anambra State on the North and Rivers State to the South. The changes that occur as a result of rising surface temperature and rainfall, the area is likely vulnerable to the consequences of global warming [11]. Two seasons are identified, wet and dry seasons. The rainy season is from April to October while the dry season is from November to March. Double maxima, with the first maximum in June and the second in September also characterized the climate. There is therefore a "little dry season" in-between known as "August Break" brought about by the seasonal north and southward movement of the ITCZ (Inter-Tropical Convergence Zone). An average annual temperature above 20°C (68.0°F) creates an annual relative humidity of 75%, with humidity reaching 90% in the rainy season [11]. The dry season experiences two months of Harmattan from late December to late February. January and March are the hottest months [11].

Study Area
Imo state has three main political zones; this are, Okigwe (Imo North), Orlu (Imo West) and Owerri (Imo East). According to Okorie [12], the state has a population of about 3,927,563 with male, 1,976,471 and female 1,951,092. The state is blessed with natural resources which include crude oil, natural gas, lead and zinc. Economically exploitable flora like the iroko, mahogany, obeche, bamboo, rubber tree and oil palm predominate [11].

Methodology
The daily and monthly average minimum temperature, maximum temperature, relative humidity, surface pressure, cloud cover and sunshine hours meteorological data used in this study were obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) at 2m height for Owerri, Imo state located in the South Eastern, Nigeria during the period of sixteen years (2000 -2015).
The surface water vapour density (SWVD), vapour pressure (e) and mean temperature (T) are related by the following expression [2,4] as: The vapour pressure was obtained using the expression given by Adeyemi and Ogolo [2] as: (2) where and are the relative humidity and saturated vapour pressure respectively. The saturated vapour pressure was evaluated using the Claussius Clapeyron equation defined as: The mean temperature, T was obtained using where " )*+ and " ),-are the maximum and minimum temperatures respectively. The is in . / , and in millibars 0.12 , " in Kelvin 032 and in percentage 0%2.
In this study, the regression models for SWVD estimations are of the forms 5 6 1" ) *-6 7 (5) The Nash-Sutcliffe equation (NSE) is given by the expression The Index of Agreement (IA) is given as From equations (9) - (13) ,,) * , ,,H*I and B are respectively the =`a measured and =`a calculated values of daily surface water vapour density and the total number of observations, also [[[[[[[[[ ,,) * is the mean surface water vapour density.
Chen et al. [14] have recommended that a zero value for MBE is ideal and a low RMSE is desirable. Similarly, the smaller the value of the MBE and RMSE the better is the performance of the model, a positive MPE and MBE values provide the averages amount of overestimation in the calculated values, while the negative values gives underestimation. A low value of MPE is desirable. The percentage error between −10% and +10% is considered acceptable [15]. High values of R 2 , NSE and IA are desirable. The MBE and the RMSE are in gm -3 , while R 2 , MPE, NSE and IA are in percentage (%).
The skewness and kurtosis tests were studied in this present work. The skewness test 0b c 2 measures the asymmetry of the parameters data around their mean value; it is a measure of symmetry, or more precisely, the lack of symmetry [16]. It informs us about the direction of variation of the dataset [16]. If b c = 0 , the data have a Gaussian distribution (normal distribution), while b c < 0indicates that the data are spread out more to the left of the mean value than to its right (negatively skewed), when b c > 0indicates that data are spread out more to the right than to its left (positively skewed) [17].
The Kurtosis test 0? f 2 describes the shape of a random variable's probability distribution, that is it characterizes the relative peakedness or flatness of a distribution compared to the normal distribution [16]. It measures the degree of normality of each of the meteorological parameters under investigation [17]. For ? f = 0 the data have normal distribution, for ? f > 0 the data have positive kurtosis which implies peaked distribution, that is, leptokurtic distribution (that is, too tall), when ? f < 0the data have negative kurtosis signifying flat distribution, that is, platykurtic distribution (that is, too flat, or even concave if the value is large enough).  Figure 2 shows the monthly variation of Surface Water Vapour Density (SWVD) during the period under investigation for the study area. The result revealed that the SWVD during the raining season is greater than in the dry season. It was observed that the maximum average value of SWVD of 21.002gm -3 and minimum value of 14.653gm -3 occurred during the raining and dry seasons in the months of June and January respectively. It was observed that the values of SWVD decreases in the month of July and August immediately after its maximum value in the month of June and later increases in the month of September; this observation is in line with the result reported by Adeyemi and Ogolo [2] for Ikeja and Ibadan located in the Southern zone of Nigeria.            Figure 9 shows the monthly variation of SWVD with mean temperature for the location under study. The SWVD at Owerri increases gradually from a minimum value of 14.653gm -3 in the month of January until it gets to its peak value of 21.002gm -3 in the month of June and decreases to August with a dip downward which suddenly increases to September and then drop to December. The mean temperature increases with the SWVD from January and attained its maximum value of 27.813°C in the month of March which then decreases continuously to its minimum value in the month of August and increases subsequently to December. The drop in the SWVD as observed in the month of August may be as a result of August break, which is a period of short dryness; it is obvious that it corresponds to the period when the minimum temperature was observed in the study area. The results showed that high and low values of SWVD were observed during the raining and dry seasons respectively; the reverse is the case for the mean temperature.   Figure 10 shows the monthly variation of SWVD with relative humidity for the location under study. The relative humidity increases with SWVD from their minimum values in the month of January to June while the relative humidity extends to July. A little dip downward was observed both for the relative humidity and SWVD in the month of August which then increases slightly to September and then drop to December. The observed drop in the values of the relative humidity and SWVD in the month of August may be due to short period of dryness (August break) which is common in the coastal region and most parts of Nigeria. The high values of SWVD observed during the raining season are due to high air humidity (close to 90%) observed in this part of Nigeria, when the city of Owerri is under the influence of a large quantity of moisture-laden tropical maritime air resulting from continuous migration of inter-tropical discontinuity (ITD) with the sun. Generally, when the dry and dust -laden north-east winds become dominant in December, the dry harmattan season sets in, resulting in lower values of SWVD. The result revealed that high values of SWVD and relative humidity were observed during the raining season and low values during the dry season. Figure 11. Monthly variation of SWVD with surface pressure at Owerri, Nigeria. Figure 11 shows the monthly variation of SWVD with surface pressure for the location under study. It was observed that as the SWVD increases from its minimum value in January and attained its maximum value in June; the surface pressure decreases from January and attained its minimum value in March which then increases until it gets to its peak value in the month of July and then decreases to December. The result revealed that high values of SWVD and surface pressure were observed during the raining season and low values during the dry season.  Figure 12 shows the monthly variation of SWVD with cloud cover for the location under study. The cloud cover increases with the SWVD from January to April and maintain almost a constant value from April to May and increases from May and attained its maximum values in the month of September; the cloud cover and SWVD drop from September to December in which the minimum value of cloud cover is in December. The result revealed that high values of SWVD and cloud cover were observed during the raining season and low values during the dry season.  Figure 13 shows the monthly variation of SWVD with sunshine hours for the location under study. The sunshine hours decreases and increases at almost an equal interval from January to May and then decreases to its minimum value in the month of August which corresponds to the August break observed for the SWVD. The sunshine hours increases from its minimum value in August to its maximum value in December. The result revealed that high values of sunshine hours were observed during the dry season and low values during the raining season which is the reverse case for the SWVD.

Results and Discussion
The regression equations for the developed models are given by the expressions = −30.8 + 1.16 " ) *-+ 0.257 (14) = 24 − 0.015 9 + 13.9 ;; (15) = −94 + 0.133 9 − 2.61 (16) = 5.04 + 14.9 ;; + 0.373 (17) Table 1 presents the rundown of the various statistical tests implemented. Based on the R 2 the model, equation 14 has the highest value with 99.9 % and is judged the best model.  The ranking of the models ( Table 2) was done based on the validation of the models ( Table 1). The total ranks obtained by the different models ranged from 10 to 22. Based on the overall results the model, equation 14 was found the best and most suitable for estimating Surface water vapour density for the study area.   Figure 15 shows that the model (Eqn 14) gives the best fitting with the SWVD as compared to other calculated models and therefore was recommended for estimating SWVD for Owerri, Nigeria.  The results shown in Table 3 showed that the surface water vapour density, mean temperature, relative humidity, cloud cover and sunshine hours data spread out more to the left of their mean value (negatively skewed), while the surface pressure data spread out more to the right of their mean value (positively skewed). The mean temperature, relative humidity and surface pressure data seem to have a quassi-Gaussian distribution. Skewness of exactly zero is quite not likely for real world data [16]. The surface water vapour density, cloud cover and sunshine hours data are more divergent away from the normal distribution. It can be seen from Table 3 that the surface water vapour density data have positive kurtosis which indicates a relatively peaked distribution and possibility of a leptokurtic distribution while the other terms (mean temperature, relative humidity, surface pressure, cloud cover and sunshine hours) data have negative kurtosis which indicates a relatively flat distribution and possibility of platykurtic distribution.

Conclusion
In this present study, the issue of estimating SWVD and its variation with other meteorological parameters during the period of sixteen years (2000 -2015) and daily variation of SWVD in each month for the year 2015 has been addressed using monthly average and daily average meteorological data obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) at 2m height for Owerri (Latitude 5.48°N, Longitude 7.00°E, and 91 m above sea level) Imo state located in the South Eastern, Nigeria. The results of this study revealed that high values of SWVD are recorded during the raining season and low values during the dry season. It was observed that the maximum and minimum average values of SWVD of 21.002gm -3 and 14.653gm -3 were found in the months of June and January during the raining and dry seasons respectively. The highest value of surface water vapour density was observed on 9 th May, 2015 and the lowest on 14 th January, 2015 during the period under investigation. Four simple two variable correlation models were developed and was statistically tested using statistical indices of coefficient of correlation, mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), Nash -Sutcliffe Equation (NSE) and index of agreement (IA) from which the model that relates temperature and relative humidity was found more suitable for estimating surface water vapour density (SWVD) for the location under investigation. The results of the descriptive statistical analysis revealed that the surface water vapour density, mean temperature, relative humidity, cloud cover and sunshine hours data spread out more to the left of their mean value (negatively skewed), while the surface pressure data spread out more to the right of their mean value (positively skewed). The surface water vapour density data have positive kurtosis which designated a relatively peaked distribution and likelihood of a leptokurtic distribution while the mean temperature, relative humidity, surface pressure, cloud cover and sunshine hours data have negative kurtosis which designated a relatively flat distribution and likelihood of platykurtic distribution. This study is vital to hydro meteorologists and other relevant stakeholders and investors that need to know quantitatively the amount of SWVD and other pertinent information regarding SWVD for the location.