Study of Boundary Layer Height over West Africa

Monthly means of boundary layer height (BLH) over West Africa are presented based on 36 years (1979-2014) of six-hourly ERA-Interim reanalysis. In this region, we found that there is a link between the West Africa Monsoon (WAM) and the monthly means of BLH in the summer. The trend and empirical orthogonal function (EOF) of BLH are presented, including the mid July variability of BLH with the precipitation. The dominant EOF of BLH accounts for around 42% of the variance with slightly large amplitude in the north while relatively small in the equatorial band. The second EOF which accounts for 16.4%, describes a longitudinal contrast with a zonal gradient. The relationship between BLH and precipitation is found using the canonical correlation analysis (CCA). Significant trends of the first and second pairs of BLH with precipitation are shown. The first and second CCA pair has a correlation of 68% and 60% with 12.2 and 10.8 degrees of freedom respectively. The critical correlation coefficients at the 95% level are 0.21 and 0.65 for the first and second CCA pairs respectively. This first CCA pair mostly determines the arid and semi-arid areas where the rate of explained regional variance is about 78% in the arid area and 73% in the semi-arid area. For the second pair of CCA, the rate of explained regional variance is more than 60% in the Guinea coast and wet equatorial area.


Introduction
The atmospheric boundary layer (ABL) is the part of the troposphere that is di-and provide energy to drive weather and climate. Therefore the Boundary Layer Height (BLH) varies in time and space, ranging from hundreds of meters to a few kilometres. In the climatology literature, it is not more common discussion of mixing height or other measures of planetary boundary layer (PBL) height (Seidel et al., 2012;Santosh et al., 2015). Two factors can explain these reasons.
Firstly, in climate models, the evaluation of PBL height in many schemes was less explicitly prescribed (Kang et al., 2016). Secondary, the climatological study of observational PBL is not fully understood, mainly because of the lack of direct measurements of PBL height, particularly in the Africa region.
West Africa is found to be a unique environment where several factors influence ABL processes during the rainy season (DeLonge & Fuentes, 2012). They also found that strong flows (>10 m/s) associated with the West African Monsoon and sea breezes affect convective boundary-layer development. Farquharson (1939) found that sea to land flows dominate during the rainy season, particularly at night-time. Onshore (sea to land) flows transport moist air, changing the inland moisture budgets and the boundary-layer thermodynamics on a daily basis (Parker et al., 2005;Schrage et al., 2007). However, Saharan Air Layer (SAL) (Dunion & Velden, 2004) also disturbs the diurnal growth patterns of ABL. The level of SAL is between 800 and 500 hPa (Carlson & Prospero, 1972) and is located around 17˚N when the wind moves westward through Sahel towards Atlantic Ocean. A reduction of incoming solar radiation at the surface layers energy exchanges, reduces boundary-layer entrainment rates, and leads to relatively shallower mixed layers (Slingo et al., 2006). Since the work of Flamant et al. (2007), it is known that SAL events affect the ABL in West Africa and as noted by DeLonge and Fuentes (2012) there is a dearth of field observations documenting such impacts. As noted by Seidel et al. (2010), studies of the PBL have been highly localized and of relatively short duration. Hence, these authors explore some issues pertinent to the development of such a climatology, which would have applications for example in interpreting BLH obtained in nontraditional ways, such as from ground-based and space-based lidar measurements of aerosols, from boundary-layer profile observations, from cloud base estimates from ceilometers, and from Global Navigational Satellite System radio occultation Measurements. Seidel et al. (2010)  Campaign where an unprecedented number of soundings were performed over the region (Agusti et al., 2010). We propose to analyze the climatological means of BLH using the Empirical Orthogonal Function (EOF) and how these two parameters are linked to precipitation by means of Canonical Correlation Analysis (CCA). This study is organized as follows: we present data and method used in Section 2, the results are discussed in Section 3 and conclusion is presented in Section 4.
Seven different methods are usually used to estimate BLH from radiosonde (Seidel et al., 2010). Four methods are traditional approaches often encountered in the PBL literature. They include 1) the parcel method, 2) the level of the maximum vertical gradient of potential temperature, 3) the base of an elevated temperature inversion, 4) the top of a surface-based inversion, and by using Global Navigational Satellite System radio occultation data, which can be used to derive vertical profiles of atmospheric 5) refractivity, 6) temperature, and 7) specific humidity. Table 1 summarizes these seven different methods. Figure 1 shows and time, to study the climatology of BLH over West Africa, we will use the reanalysis data. In ECMWF ERA Interim, BLH is defined through Troen and Mahrt parcel lifting method (Troen & Mahrt, 1986), and BLH data from ERA Interim is used in this work even if the values of BLH here are less to 900 m, near to values obtained from the refractivity method.
Before examining the correlation between BLH and the precipitation, we present the climatic zones in West Africa as represented in Figure Maximum vertical gradient of potential temperature (Th) The height corresponding to the maximum of the vertical gradient of the potential temperature Oke (1988); Stull (1988); Sorbjan (1989); Garratt (1992) Specific humidity (Sh) The height corresponding to the minimum of the vertical gradient of the specific humidity Ao et al. (2008) Surface-based inversion (Rh) The height corresponding to the minimum of the relative humidity Sokolovskiy et al. (2006); Basha and Ratnam (2009)

Refractivity (N)
The height corresponding to the minimum of refractivity Smith and Weintraub (1953) Inversion of the temperature in altitude (temp) Basis of altitude inversion of the temperature Bradley et al. (1993) Inversion of the surface temperature Top of the surface temperature inversion Bradley et al. (1993) Journal of Geoscience and Environment Protection

Empirical Orthogonal Function
The where the transpose operation is denoted by the superscript T and each of the M eigenvectors contains one element pertaining to each of the K variables, x k .

Trends
The Mann-Kendall trend test is a non parametric alternative using to investigate the possible trend of a time series.  included in the analysis, if their probability exceeds the 95% significance level.

Canonical Correlation Analysis
Canonical Correlation Analysis (CCA) is a statistical technique which helps to explore the relationship between two multivariate data sets of In this study, we have calculate the CCA of the different parameters by using, instead of the variables x and y, the corresponding EOFs.

The Climatology over West Africa
The distribution of monthly means of BLH (1979-2014) is displayed in Figure 3.  dry and wet region. The ITCZ is strongly perturbed by the convective system over this region Flamant et al. (2007). This evolution of the monsoon, gives by 950 hPa wind, shows that the monsoon arrives in West Africa in April from south to the north before move in the north to the south in September. It is found in these graphs between latitudes 9˚ and 24˚N, the alternation of the south-westerly wind from the Ocean and the Harmattan from Sahara region at the surface. West African monsoon is defined by this alternation where north-easterlies occur constantly farther north, but only south-westerlies occur farther south. This figure also shows that the drought becomes shorter and less complete farther south. Hence, at 12˚N about half year, and at 8˚N it disappears completely at the rainy season (June-September). In this region, the drought results from the arrival of dry surface air issuing from anticyclones formed beyond the Equator in the Southern Hemisphere. The similitude can be made with the "break" of the monsoon in southern India which occurs beyond the Equator. Figure 4 presents monthly means of variations of precipitation in space, ranging from the Equator to 30˚N and covering 20˚W -10˚E during 1979-2014. From these graphs, there is a maximum of precipitation in June over West Africa equatorial coast. This maximum moves much more northward to set around the Sahara area during the months of July and August. In September, there is   (0˚N -15˚N, 10˚E -15˚W). Figure 2 also shows that during the spring/summer, precipitation migrates from the Guinea coast to the Sahel and back again, resulting in two rainy seasons per year in the south and one in the north. The exchange of energy between the ocean and the surface of the continent allow creating and maintaining the lowland flow monsoon of southwest, which advects relatively cool moist air from the Gulf of Guinea into the hot dry continent. over West Africa during the summer 2006. The PC1 time series of the precipitation is in its negative phase from June to the middle of July, and in its positive phase with a little appearance of the negative phase around the lasts days of September. In the PC1, the negative amplitude can be due to the arrival of the monsoon in Sahel zone. Positive amplitude can be linked to the present of the rain in this zone. One notes a high fluctuation of PC2 and PC3 time's series from June to September. One also notes that the PC1 accounts for around 44%, PC2 around 12% and the PC3 more than 7.5% of the total variance. We noted that from PC1 to PC3 represent around 63% of the total variance.  middle of July, from where it was in its positive phase until the last day of September. These components account for 52% of the total variance. The PC2 of BLH was generally in its negative phase in the first half of June and from the second half of August to the end of September; while the PC3 of BLH was in its negative phase in June and August and in its positive phase in July and Septem-Journal of Geoscience and Environment Protection ber. The PC2 and PC3 account respectively for around 12% and more than 6% of the total variance.

Statistical Analysis
It is good similitude of the PC1 time series of BLH ( Figure 6) and precipitation from GPCP ( Figure 5). The general configuration of the PC2 times series of BLH is in opposition of phase with its PC1 times series from day 1 (01 June) to day 45 (15 July) and between day 76 (15 August) and day 122 (30 September), and in phase between 15 July and 15 August. They show their positive phase from day 15 (15 June) to day 76 (15 August), and its negative phase in the other days of the period June-September. We have also found that the PC1 (PC2) time series of precipitation and PC1 (PC2) time series of BLH are significantly correlated at the 95% level.

Correlation of BLH with Precipitation
As was noted above, the Canonical Correlation Analysis (CCA) is done in the subspace spanned by the first few EOFs. Hence, we have firstly to analyze the summer CAPE and CIN variability by using EOF analysis and then study the correlation structure of a pair of BLH with precipitation by means of the CCA method. Figure 7 presents the first two CCA pair of BLH and precipitation from GPCP. In this technique, we find that the pair of patterns of BLH and precipitation such that the correlation between two corresponding pattern coefficients is maximized. In Figure 7(a) which presents the first pair of CCA, one notes that the coefficient of correlation decreases and increases northwards. One realizes that the coefficient of correlation of explained regional variance is about 0.7 in the region GIII with a maximum around the point of coordinate (8˚N, 12˚W), and 0.8 in the region GIV. In GI, the coefficient of correlation varies from 0.6 to 0 around 15˚N after where its value becomes negative and increases northwards, with a maximum around (18˚N -23˚N; 12˚E -25˚E).

Conclusion
A BLH was presented in terms of monthly means, seasonal variances, and trends based on 36 years (1979-2014) of six-hourly ERA-Interim reanalysis to characterize and understand the various climate mechanisms that culminate in daily weather over West Africa. The monthly means of BLH show that the influence of the Saharan Air Layer on the BLH and also the impact of monsoon. It was found that the dry region of SAL corresponds to high values of BLH over West Africa from February to October, low values are between Equators to the end of the front of monsoon (around 15˚) during the summer period (June to September). The monthly variation of Inter Topical Convergent Zone (ITCZ) evolves all during the year between dry and wet region over this region was also noted. Largest values BLH variances were developed in the tropics close to the ITCZ, where high temperatures and sufficient moisture are available. The unexpected variability observed in the ABL thermodynamic attributes during AMMA can partly be attributed to the presence of dust layers as noted by DeLonge and Fuentes (2012). Significant trends in BLH occur in the dry Sahara region over West Africa. For a numerical weather prediction system, BLH can be considered as an output variable to highlight problems in the energy and momentum exchange between the surface and the atmosphere (Caporaso et al., 2013).
The first three EOF of BLH and precipitation, during the month from June to September of the year 2006 show that the first EOF of these parameters account respectively for around 42% and 44% of the variance; while the second EOF of these two parameters accounts for more than 16.4% and 12% of the variance respectively. The BLH climatology shows a high correlation of the PC1 time's series of these parameters with precipitation. We have also found that the PC1 (PC2) time series of precipitation and PC1 (PC2) time series of BLH are significantly correlated at the 95% confidence level. All this shows a high correlation between these three parameters.
We also realized that the first CCA show a high dependence of BLH with precipitation especially in the western region of Africa. The link between the different patterns in this southern part is high and would lead to a higher probability of stronger convection combined with the need of forcing to overcome enhanced stable surface conditions. The first CCA pair has a correlation of 68% with 12.2 degrees of freedom and a critical correlation coefficient at the 95% confidence level equals to 0.21. This first CCA pair mostly determines the arid and semi-arid areas where the rate of explained regional variance is about 78% in the arid area and 73% in the semi-arid area. For the second pair of CCA, the correlation coefficient is around 0.65 where there are 10.8 degrees of freedom and the rate of explained regional variance is more than 60% in the Guinea coast and wet equatorial area. So, BLH takes into account the vertical thermodynamic structure of the troposphere in West Africa and could contribute to understanding the evolution of the convection through application of the CCA method. However, as this parameter is more important where the African Easterly Waves (AEW) are very active, it would be necessary to examine the influence of these waves on these parameters over West Africa in summer.
group and is currently funded by a large number of agencies, especially from France, the United Kingdom, the United States, and Africa. It has been the beneficiary of a major financial contribution from the European Community's Sixth Framework Research Programme. (Detailed information on scientific coordination and funding is available online on the AMMA International Web site http://www.amma-international.org). This work was carried out with the scientific, technical and financial support of the Interdisciplinary Research Program on Climate and Urban Environment (PRInCE), in the framework of the project "Douala, sustainable city: sustainable development and enhancement of the Makepe Missoke site", co-financing by FFEM, AFP and CUD.