Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast of West Africa

Abstract

This study uses observed and simulated data to analyze the dynamics LSB rotation along the Guinean Coast of West Africa. A non-hydrostatic fully compressible numerical model is used to simulate LSB circulation. To evaluate the model’s ability to capture the LSB kinematics, the study used a modified model code with ERA-Interim and CFS as forcing data. Comparison of observed and simulated LSB patterns shows that the model reliably captures the LSB circulation in the region. The simulated diurnal evolutions of hodographs and onshore/offshore winds also follow the observations. A dynamical analysis performed by extracting individual forcing terms from the horizontal momentum equations at selected regions within the study area showed that the direction of the wind rotation is a result of a complex interaction between surface and synoptic pressure gradients, advection, and horizontal and vertical diffusions forces. However, hourly analysis of the rotation term suggests that surface gradient seems to dominate over oceanic region, while diffusion terms are more important for land area. This may be attributed to the variation of surface roughness due the landscape and urbanization. Therefore, this reveals the link between urbanization and LSB circulation in coastal region of West Africa, where most important cities are located.

1. Introduction

The theory of land and sea breezes (LSB) is based on the thermal contrasts between the land and water. During the day, the land is warmer than the sea because of heating from the sun. Hence, the warm air over the land rises and expands forming cumulus clouds, while cooler air from the sea surface therefore flows inland to replace the rising warm air. The resulting circulation can move several kilometers inland as onshore wind circulation, called sea breeze. At night, the land cools faster than the nearby ocean and a shallow mesoscale pressure gradient develops, with a higher surface pressure over the land. The resulting circulation is directed from the land to the sea (offshore circulation) near the surface, called land breeze.

Generally, the land breeze (LB) circulation is weaker than the sea breeze (SB) in both velocity and height of development because the heat source for the land breeze is much weaker than the heat source for the sea breeze circulation [1]. LB fronts tend to only affect a small area of the sea, in comparison with the much larger effect of SB.

In West Africa along the Guinea coast, LSB circulation occurs almost throughout the year although in varying strength [2, 3]. During the day, the circulation is driven by strong heating, while at night it is driven by cooling of the landmasses and resulting pressure anomalies. In tropical West African region, Coulibaly et al. [4] showed the winter frequency and the seasonality behaviors of LSB with both clockwise (anti-cyclonic) and anticlockwise (cyclonic) hodograph rotations. Kusuda and Alpert [5] and Haurwitz [6] evaluate the diurnal evolution of SB in the Northern Hemisphere with an influence of the Coriolis force in the sense of rotation, while over Sardinia (mid-latitude), the sense of rotation seems to be influenced by the combination of surface and synoptic pressure gradients and Coriolis and advection forces [7].

LSB is more frequently and prominently observed in tropical regions than in higher latitudes due to strong radiative heating, convection, and weak Coriolis force. It is also influenced by the prevailing large-scale wind and topographic friction. When LSB circulation prevails on land, changes in the temperature structure, humidity, and roughness occur in the air adjacent to the coast and lead to formation of a thermal internal boundary layer (TIBL) [8]. This effectively reduces the mixing height in the coastal regions in the daytime. LSB circulation and TIBL are the two important phenomena that influence the pollution plume direction and diffusion in coastal regions. Many factors such as topography, synoptic flow, and latitude are shown to influence the evolution and characteristics of the SB.

With the growing computational power and resulting improved modeling capabilities, numerical simulations of LSB circulation have gained attention since the 1960s. Much of the earlier numerical work was performed using two-dimensional hydrostatic models with coarse grid spacing (≈10 km). While these contributed greatly to our understanding of the mechanics and structure of the LSB circulation, they nevertheless remained highly idealized. Due to the large size of the model horizontal grid (>1 km), it is difficult to differentiate between hydrostatic and non-hydrostatic simulations [9]. While non-hydrostatic effects may weaken the mature nature of LSB, hydrostatic influence tends to overestimate LSB intensity [10]. Therefore, to adequately simulate LSB circulation and its associated features such as planetary boundary-layer (PBL) influence, it is decided to use three-dimensional models, even though two-dimensional models may be adequate for many idealized simulations [7].

Many theoretical and numerical modeling studies have been reported on the overall dynamics of the LSB circulations [7, 11, 12, 13, 14, 15, 16]. Also, there have been observational and modeling studies of LSB characteristics over different regions [4, 7, 15, 16, 17, 18, 19, 20, 21, 22].

However, the availability of non-hydrostatic numerical models with less than 1 km resolution has highlighted the complex nature of LSB and its associated nonlinear interactions on several scales [23]. Using numerical methods, Estoque [24] showed the development of a zone of low-level convergence at the leading edge of LSB current as it sets in over land, while Pielke [25] showed the effects of topographical friction on LSB evolution using a 3D numerical model. Therefore, numerical simulations can be considered as computational tools in minimizing the identified knowledge gaps by [7, 15] and assessing the governing factors in LSB dynamics over complex terrain and coastlines. Consequently, this study aims to evaluate the dynamics of LSB circulation over the Guinean Coast of West Africa using a fully compressible non-hydrostatic numerical model for simulating.

Based on the study by Moisseeva and Steyn [7] who used WRF-ARW version 3.4, this study will use WRF-ARW version 3.7.1 to examine the dynamics of LSB circulation over the region. The physics and dynamics of WRF-ARW version 3.7.1 allow the extraction of its dynamical factors related to atmospheric radiation, microphysics, planetary boundary layer and surface layer physics, land surface physics, and cumulus options of the model [16].

In winter period, Coulibaly et al. [4] showed both clockwise and anticlockwise rotations of the wind in coastal West Africa identifying some LSB episodes. This has been a good starting point for which the numerical modeling of the LSB circulation and hodograph rotation in the region has been based (see Figure 1).

Figure 1.

Daily hodograph rotations of SB; a: January 1, 2011, b: May 12, 2011, c: August 30, 2011, d: December 13, 2011, e: December 16, 2014, and f: December 17, 2014. The numbers near dots indicate the hour of the day (LST).

2. Data and methods

2.1 Model description

In this study, numerical simulations of LSB dynamics were performed using Weather Research and Forecasting (WRF) model following the method employed by [7, 16]. While the model offers great operational forecasting capabilities, it is limited in dynamical analysis because the basic dynamical equations are deeply embedded in the solver remaining inaccessible to the model user. To overcome this limitation, this study extracted the individual tendency terms from the momentum equation of the model [16]. Details about the extraction processes are available in my PhD thesis called Coulibaly (2016) published in Lambert Academic Publishing (https://www.lap-publishing.com/extern/listprojects).

Using an observational study, Coulibaly et al. [4] identified some days with favorable atmospheric conditions for the formation of LSB called LSB episodes across the Guinea Coast of West Africa. The monthly occurrence of LSB showed a primary maximum occurrence in December over the study region used to do the numerical simulation.

Based on the model configuration used in the studies by Moisseeva and Steyn [7] and Coulibaly et al. [16], this study configures for all identified LSB episodes the entire study domain. The model was forced using Climate Forecast System (WRF-CFS) and ERA-Interim (WRF-ERA) reanalysis data with 15 km and 3 km as outer and inner domain grid spaces, respectively. In order to avoid the effects of the sub-grid scale on the dynamics of the LSB in WRF model, Steyn et al. [26] used grid sizes of 9 km and 3 km for outer and inner domains, respectively. However, as 9 km is within the grid zone of convection-permitting/non-convection-permitting resolution, grid sizes 15 km and 3 km were used in this study (Figure 2).

Figure 2.

Outer domain for real case simulations for both WRF-CFS and WRF-ERA.

A 3-year period (2013–2016) reanalysis data of Climate Forecast System Reanalysis version 2 (CFSRv2) from the National Centers for Environmental Prediction (NCEP2) and ERA-Interim were used to initialize the model. According to Wang et al. [27], the reanalysis data are a global, high-resolution, coupled atmosphere–ocean-land surface-sea ice system designed to provide the best estimate of the state of these coupled domains. For the identified episodes of LSB, high-resolution pressure-level (0.5 degrees latitude/longitude) and surface and radiative flux (0.3 degree Gaussian grid) 6-hour forecasts were obtained for 0000, 0600, 1200, and 1800 UTC. More details about ERA-Interim and CFSRv2 are available in the studies by Barrisford et al. [28] and Saha [29], respectively.

Most of the LSB episodes identified by Coulibably et al. 4] occurred in the month of highest monthly occurrence (December). Therefore, the simulations were performed, based on the individual LSB episode in December, over 30 hours from 1800LST of the previous day to 0000LST of the following day, with a 6-hour spin-up. As the study is primarily interested in daytime dynamics, the analysis was performed starting 0900 LST, that is, 9 hours after the beginning of each simulation. RK time-step ∆t was set to 90 seconds, as recommended 6 × ∆x (km) [30]. Since WRF allows for output of instantaneous fields only, the history interval was set to 10 minutes. Wind and dynamical tendency fields were hence output six times each hour and subsequently averaged to produce an estimate of hourly averages. Through the analysis of various production runs, it was determined that 50 vertical eta-levels provided sufficient vertical resolution within the boundary layer, and hence, this configuration was adopted for all runs with the pressure top set up to 5000 Pa. In order to reduce the number of figures, this study will only show the results of two LSB episodes (December 16 and 17, 2014). The details of selected stations are shown in Table 1.

Stations	Longitude (°)	Latitude (°)	Distance from the closest sea (km)	Height above sea level (m)
Oshodi	3.383E	6.50 N	16	32
Mowe	3.458E	6.81 N	48	67
Cotonou	2.38 E	6.35 N	0.6	7

Table 1.

Coastal stations metadata.

2.2 Model evaluation

The evaluation of the model was performed using hourly data of two Automated Weather Stations in Oshodi-Lagos and Mowe in Nigeria from 2014 to 2016 [3] and 1-year (2014) 6-hourly data from Cotonou. In this study, the model evaluation processes used by Crosman and Horel [15] are also applied. Based on the findings of Crosman and Horel [15], this study adds the diurnal wind rose analysis to highlight the strength of LSB over the study region [16]. The study is located in the northern part of the Gulf of Guinea; therefore, offshore winds are taken as northerlies (between 330° and 30°), while onshore winds as southerlies (between 150° and 210°). This can facilitate the plots of wind roses and their associated strength at each identified location over a period of time (Figures 3–5). To plot the hodographs for both observed and modeled data, the u and v wind components at 10 m are considered in polar coordinates. In numerous studies, daily hodographs have been considered as primary criteria to evaluate the model based on the variability of wind data. In order to reduce the number of figures, this study will only show the results of two LSB days (December 16 and 17, 2014) in Figures 3, 4 and 6–9.

Figure 3.

Three-year period (2014–2016) hourly average wind roses at different locations.

Figure 4.

Wind roses at Cotonou, Oshodi, and Mowe for December 16, 2014, as LSB day. The first row shows observation; the second and third rows display wind roses from WRF-CFS and WRF-ERA, respectively.

Figure 5.

Wind frequency distribution at Cotonou, Oshodi, and Mowe for December 16, 2014. The first row displays the observation, while the second and third rows are for WRF-CFS and WRF-ERA, respectively.

Figure 6.

Wind hodographs on December 16, 2014. (a): Cotonou, (b): Oshodi, (c): Mowe. The first row represents observation, while the second and third rows are, respectively, for WRF-CFS and WRF-ERA.

Figure 7.

Wind hodographs on December 17, 2014. (a): Cotonou, (b): Oshodi, (c): Mowe. The first row represents observation, while the second and third rows are, respectively, for WRF-CFS and WRF-ERA.

Figure 8.

Diurnal evolution of onshore/offshore wind at 10 m on December 16, 2014. Blue lines represent the observation, green and red, respectively, for WRF-CFS and WRF-ERA.

Figure 9.

Diurnal evolution of onshore/offshore wind at 10 m on December 17, 2014. Blue lines represent the observation, green and red, respectively, for WRF-CFS and WRF-ERA.

Figures 3 and 4 shows that the West African Monsoon (WAM) prevails on LSB over the region for both observed and simulated wind roses even though there are night/early-morning weak offshore winds (LB) and enhanced daytime onshore winds (SB) in Figure 3 Cotonou has only 6-hourly observational data.

Figure 4 shows that CFSRv2 well captured the observed patterns of dominant WAM, night/early-morning weak LB, and enhanced daytime SB, than Era-Interim. The strength of daytime SB depends mainly on the location because it is enhanced for locations close to the sea (Oshodi) than those far away (Mowe).

Figure 4 shows that both simulated and observed wind strength distributions seem to be in good agreement (see Oshodi and Mowe) even though Cotonou has only 6-hourly observational data.

From observational data, the classification of wind strength is followed:

1. 56.5% were between 0.5 and 2.10 ms⁻¹ in both Oshodi and Mowe;

2. 26.1% were between 2.10 and 3.60 ms⁻¹ in Oshodi, while there are only 17.4% in Mowe;

3. more than 8% between 3.6 and 5.7 ms⁻¹ in Mowe; and

4. 17.4% were calmed in both Oshodi and Mowe.

From the simulated wind data, the following is obtained:

1. more than 58% between 0.5 and 2.10 ms⁻¹ in Oshodi and Mowe, while this rate is less than 9% in Cotonou.

2. more than 25% between 2.10 and 3.60 ms⁻¹ in Cotonou and Mowe, which is less than 16% in Oshodi;

3. Era-Interim showed 4.2% of calm winds, and

4. There are no calm winds for CFSRv2.

While both WRF-CFS and WRF-ERA well captured the observed patterns of wind strength distribution, all underestimated calm winds over this study region. Therefore, the WRF model is suitable to evaluate diurnal wind rose behaviors.

Figures 6 and 7 shows that there is agreement between observed and simulated hodographs for selected SB episodes indicating a daily clockwise rotation (see Oshodi and Cotonou locations), even though there is a quite difference in Mowe location where the sense of rotation turns into anticlockwise between 2:00 and 11:00 am on December 16th (Figure 6) and between 9:00 am and 7:00 pm on December 17th, 2014, due to the fact that Mowe is far away from the sea (Figure 7). A clearly onshore-offshore nature of SB circulation with indeterminate sense of rotation can be also seen.

Meanwhile, the existence of daytime clockwise rotation of the theoretical hodographs over the study region, which is one of the important SB characteristics in the northern hemisphere, due to the variation of Coriolis force [5], has been revealed. While the clear diurnal clockwise rotation can be seen in the nearest locations to the sea, the slight anticlockwise rotation appears in the farthest locations. This is consistent with the apparition of the enhanced daytime SB at the closest stations (Figure 3), stippling that the sense of rotation of diurnal winds may be influenced by the distance separating the location to the sea.

As Figures 6–9 shows the agreement in the patterns of daily evolution of observed and simulated winds for closest locations. Again the farthest locations show a slight early morning difference.

Hence, Figures 6–9 show that (for the observed and simulated wind fields):

1. WRF model suitably captured the rotation of LSB in the coastal areas of West Africa.

2. There is a relationship between the sense of rotation of the LSB and the location distance from the sea.

2.3 Analysis of simulation

2.3.1 Horizontal wind rotation

Here, we follow the method of [15, 16] in representing the horizontal momentum equations of WRF in its simplified vector form as follows:

$$\frac{{\partial V}_h}{\partial t}=\frac{{\partial V}_{\mathit{pg}}}{\partial t}+\frac{{\partial V}_{\mathit{adv}}}{\partial t}+\frac{{\partial V}_{\mathit{cor}}}{\partial t}+\frac{{\partial V}_{\mathit{\text{hdif}}}}{\partial t}+\frac{{\partial V}_{\mathit{\text{vdif}}}}{\partial t}$$E1

where V_h is total horizontal velocity vector V = (u,v) and subscripts pg., adv, cor, hdif, and vdif corresponds to forcing due to pressure gradient, advection, Coriolis, horizontal, and vertical diffusion. Taking the 850 mb (hPa) pressure level to be representative of overlying synoptic weather conditions, the pressure gradient term V_pg can be further separated into synoptic (syn) and surface (surf) forcing by assuming that:

$$V_{\mathit{syn}}=V_{\mathit{pg}}\left(850\mathit{mb}\right)$$E2

Therefore, the total wind may be represented as

$$V_{\mathit{pg}}=V_{\mathit{surf}}+V_{\mathit{syn}}$$

So that, the other pressure gradient forcing can be regarded as near ground or surface effects, expressed as follows:

$$V_{\mathit{surf}}=V_{\mathit{pg}}-V_{\mathit{syn}}$$E3

Now, to express the pressure gradient forcing in terms of all its different components, the full WRF horizontal momentum equations, excluding the effects of curvature and acoustic modes, can now be written as follows:

$$\frac{{\partial V}_h}{\partial t}=\frac{{\partial V}_{\mathit{\text{surf}}}}{\partial t}+\frac{{\partial V}_{\mathit{syn}}}{\partial t}+\frac{{\partial V}_{\mathit{adv}}}{\partial t}+\frac{{\partial V}_{\mathit{cor}}}{\partial t}+\frac{{\partial V}_{\mathit{\text{hdif}}}}{\partial t}+\frac{{\partial V}_{\mathit{\text{vdif}}}}{\partial t}$$E4

Neumann [31] showed that any changes in horizontal wind direction can be expressed as:

$$\frac{\partial \alpha }{\partial t}=\frac{1}{V_h^2}k.\left(V_h\times \frac{{\partial V}_h}{\partial t}\right)$$E5

Where:

• α represents the angle of wind vector relative to the horizontal axis,

• V_h is the horizontal wind vector,

• k is a vertical unit vector.

Positive values of Eq. (5) represent anticlockwise rotation (ACR), while negative values correspond to clockwise rotation (CR). Using the components of the total wind vector in Eq. (4) to expand the cross product in Eq. (5), it is possible to determine the terms significantly influencing the sense of rotation of LSB.

2.3.2 Hodograph rotation patterns

From Eq. (5), it is possible to create contour maps representing CR and ACR regions for the simulated domain. From bottom to top, the module output has 49 pressure levels.

To take into account surface averages of hodograph rotation, the third model level (∼ 989 hPa) was used representing appropriate surface level (10 m above). To identify the possible invariant features of SB circulation, daytime hourly $\frac{\partial \alpha }{\partial t}$ values were averaged between 0900 and 1700 LST to produce$\frac{{\partial \alpha }_{\mathit{day}}}{\partial t}$. Figure 10 represents the daytime regional patterns of CR ($\frac{{\partial \alpha }_{\mathit{day}}}{\partial t}$ < 0) and ACR ($\frac{{\partial \alpha }_{\mathit{day}}}{\partial t}$> 0) for both WRF-CFS and WRF-ERA.

Figure 10.

Patterns of hodograph rotation for the selected SB day, December 16, 2014. Total $\frac{\partial \alpha }{\partial t}$ values are averaged over daytime (0900–1700 LST) showing the subregions 1 and 2 (red circle and triangle) identified.

Figure 10 shows two different regions with positive rotation tendency (region 1, over water) and negative rotation tendency (region 2, over land) for both WRF-CFS and WRF-ERA. The choice of these regions was based on fact that they represent two different topographies, and one on water is dominated by ACR, while the one on land dominated by CR. Therefore, it is obvious that the circulation of SB is influenced by the topographies of the region.

2.3.3 Individual components of surface wind circulation

Using the components of the total wind vector in Eq. (4) to expand the cross product in Eq. (5), Crosman and Horel [15] and Coulibaly et al. [16] showed that the total rate of rotation can be written in terms of individual forcing as:

$$\frac{{\partial \alpha }_{\mathit{tot}}}{\partial t}=\frac{{\partial \alpha }_{\mathit{\text{surf}}}}{\partial t}+\frac{{\partial \alpha }_{\mathit{syn}}}{\partial t}+\frac{{\partial \alpha }_{\mathit{adv}}}{\partial t}+\frac{{\partial \alpha }_{\mathit{cor}}}{\partial t}+\frac{{\partial \alpha }_{\mathit{\text{hdif}}}}{\partial t}+\frac{{\partial \alpha }_{\mathit{\text{vdif}}}}{\partial t}$$E6

2.3.3.1 Influence of the individual tendency terms

In order to investigate the influence of each component of Eq. (6) over each region in Figure 10, hourly tendency values for the selected grid points were extracted. These values were normalized by the Coriolis parameter to produce non-dimensional values and also spatially averaged among the selected grid points for each hour. Table 2 summarizes the daily evolution of the individual forcing terms for WRF-ERA-Region1, (red circle in Figure 10).

Time (hour)	$\frac{{\mathit{\partial \alpha }}_{\mathit{tot}}}{\mathit{\partial t}}$	Surface; gradient	Synoptic; gradient	Advection	Coriolis	Horizontal; diffusion	Vertical; diffusion
09	0.3832836	−2.482071	1.666516	0.1180504	0.1258831	0.429564	0.2070672
10	2.557241	0.7772687	0.429424	0.3793316	0.566098	0.2907483	0.2197096
11	2.935411	1.85723	−0.6445861	1.042618	0.4937116	0.131484	0.235257
12	1.480419	1.073565	−0.4436242	1.007558	−0.1384531	0.2259261	0.2200678
13	1.112699	0.4998687	0.1314001	1.190483	−0.2559998	0.1615198	0.1972847
14	0.8657498	1.085379	−0.4206522	0.5209342	−0.1935283	0.1714763	0.1016577
15	0.2768821	0.3298867	0.1789315	−0.473791	−0.080399	0.2163928	−0.00345805
16	0.02195143	0.5319856	−0.4363321	−0.2797991	0.06992882	0.09765537	−0.1007054
17	0.1945854	0.5197564	−0.1871125	0.1424769	0.1199066	0.08179352	−0.1505437

Table 2.

Daytime evolution of rotation tendency terms by WRF-ERA Region_1.

Table 2 contains the data showing daily occurrence of ACR reaching its maximum around 1100LST before decreasing (Figure 11). This daily occurrence of ACR is leading by both surface pressure gradient and advection in contrast to the synoptic pressure gradient. The contrast between surface and synoptic pressure gradients maybe due to the formation of LSB return flow near 850 hPa level [3]. Due to the combined effects of topographies, pressure, and temperature, the nonzero values of the pressure gradient are justified even though the region is over water. The Coriolis, horizontal, and diffusion terms are rather insignificant in this region because the region is, first of all, close to the equator where Coriolis force is generally weak and the weakness of friction forces over water, which may minimize the effects of both horizontal and diffusion terms (Figure 11).

Figure 11.

Diurnal evolution of components of horizontal wind for WRF-ERA regions (1 and 2), on December 16, 2014. Positive and negative values correspond to ACR and CR, respectively.

Table 3 contains the data showing the daily occurrence of CR reaching its maximum at 1200 LST for WRF-ERA simulations. The sense of rotation is the results of combined effects of horizontal and vertical diffusion terms reinforced by both advection and synoptic pressure gradients. Due to the dynamical features of the land, the surface pressure gradient strongly acts in opposition to all above terms. This opposition is reinforced by a relatively important Coriolis force, which is a noteworthy feature of the dynamics of this region (Figure 12).

Time (hour)	$\frac{{\mathit{\partial \alpha }}_{\mathit{tot}}}{\mathit{\partial t}}$	Surface; gradient	Synoptic; gradient	Advection	Coriolis	Horizontal; diffusion	Vertical; diffusion
09	−0.7839572	0.06672001	0.2442949	−0.1528706	0.8046611	0.1641116	−1.910874
10	−1.222245	0.6371607	0.2133593	−1.073048	1.269202	−0.137919	−2.131
11	−2.819007	4.254928	−1.710708	−2.025437	1.250522	−3.025733	−1.562579
12	−5.095439	1.427554	−0.5770028	−1.813763	0.9864119	−3.143581	−1.975057
13	−2.78958	2.692701	−0.7969017	−0.6335011	1.312145	−2.87843	−2.485593
14	−4.572093	2.805323	−1.379125	−0.7210833	1.167803	−3.460328	−2.984682
15	−4.456161	2.866465	−1.481936	−0.3873717	0.7739218	−2.792548	−3.434692
16	−2.493698	3.756342	−1.390541	−0.4019374	0.8376386	−2.309347	−2.985853
17	−1.481868	2.39475	−0.9565901	−0.8265868	1.086807	−1.480353	−1.699895

Table 3.

Daytime evolution of rotation tendency terms by WRF-ERA over land Region_2.

Figure 12.

Diurnal evolution of components of horizontal wind for WRF-CFS regions (1 and 2), on December 16, 2014. Positive and negative values correspond to ACR and CR, respectively.

Tables 4 and 5 contain the data of the two different regions (Region 1 with ACR and Region 2 with CR) for WRF-CFS simulations. ACR in Region 1 results from the combined actions of horizontal diffusion and surface pressure gradient tendencies in contrast to the synoptic pressure gradient and vertical diffusion terms. The actions of both Coriolis and advection terms are insignificant in this region (Figure 12).

Time (hour)	$\frac{{\mathit{\partial \alpha }}_{\mathit{tot}}}{\mathit{\partial t}}$	Surface; gradient	Synoptic; gradient	Advection	Coriolis	Horizontal; diffusion	Vertical; diffusion
09	0.6366872	1.229313	−0.9747893	−0.1039042	0.438543	0.583059	−0.5355338
10	0.7928402	0.5815904	−0.2575232	0.04461657	0.4180464	0.5713866	−0.5652765
11	1.878465	2.245744	−0.9682401	0.05855043	0.4775602	0.6014003	−0.5365493
12	1.606455	2.10231	−0.762126	0.1646468	0.2456327	0.4714136	−0.6154224
13	1.869271	2.732349	−1.224496	0.3645681	0.1375036	0.47354	−0.6141933
14	0.7143283	1.45007	−1.092533	0.5211268	0.1470429	0.3206365	−0.6320145
15	1.133428	0.7353157	−0.4317437	0.821609	0.214676	0.3336835	−0.5401126
16	1.366479	1.628749	0.03543856	1.095926	−0.1230026	−0.5891124	−0.681519
17	0.6067592	−0.2832675	1.060809	1.03419	−0.2068172	−0.3100053	−0.6881502

Table 4.

Daytime evolution of rotation tendency terms for WRF-CFS over ocean (Region_1).

Time (hour)	$\frac{{\mathit{\partial \alpha }}_{\mathit{tot}}}{\mathit{\partial t}}$	Surface; gradient	Synoptic; gradient	Advection	Coriolis	Horizontal; diffusion	Vertical; diffusion
09	1.290793	1.646445	−1.198673	−0.44654	0.4487459	0.3760073	0.4648078
10	−1.131925	2.804544	−1.30877	−0.8466268	0.245173	−0.482654	−1.543591
11	−3.659746	1.632497	−0.2229338	−1.180996	−0.1330353	−0.5050589	−3.25022
12	−3.409001	−0.02535242	0.516894	−1.068267	−0.229282	0.557843	−3.160837
13	−2.386143	0.001518607	0.9784042	−0.7957155	−0.8215593	0.9847814	−2.733572
14	−1.832128	−0.526906	1.172982	0.04501417	−0.9784316	0.5211309	−2.065917
15	−1.232315	−1.024484	1.710036	0.1978537	−0.8169148	0.09199113	−1.390798
16	−0.5517031	−0.9646802	1.577152	0.09926868	−0.6908129	0.3227653	−0.8953955
17	−0.4564246	−0.864257	1.42138	−0.8347424	−0.07867106	0.5376047	−0.6377391

Table 5.

Daytime evolution of rotation tendency terms for WRF-CFS over land (Region_2).

In Region 2, all of the vertical diffusion, advection, and pressure gradient terms are acting to introduce CR in the afternoon in contrast to the synoptic pressure acting to turn in ACR. The effects of both Coriolis and horizontal diffusion terms are relatively insignificant up to mid-day as a result of the land location where it was expected to have a frictional effect due to the spatial distribution of land use, land cover, and topography, which may induce horizontal diffusion effects [16].

The results further show the significantly influence of the tendency terms such as surface and synoptic pressure gradients, horizontal and vertical diffusions, and advection. Over water (Region 1 for all simulations), the total rotation tendency ($\frac{{\partial \alpha }_{\mathit{tot}}}{\partial t})$ is following the shape of surface pressure tendency ($\frac{{\partial \alpha }_{\mathit{\text{surf}}}}{\partial t})$, while other tendencies are in opposite senses trying to remove themselves. This is consistent with the findings from [16]. This suggests that the evolution of LSB rotation is largely dependent on the topographic and coastal features of the domain, even though these regions are located over water far away from the coast. Since LSB is a mesoscale phenomenon, its scale is not restricted to the immediate coastal region. Hence, the analysis can be performed away from the regions of sharp gradients in topography, roughness, and temperature and still capture the dynamics of the phenomenon [15].

In contrast to the Region 1, Region 2 is showing different scenarios depending on the simulations. While the total tendency term is following the shape of vertical diffusion tendency for WRF-CFS, all tendency terms tend to cancel themselves out being generally in opposite senses for WRF-ERA, which demonstrates that WRF-CFS can suitably simulate the dynamics of LSB circulation than WRF-ERA across the coastal West Africa. Nonetheless, the significant influence of the variation of the surface roughness due to the spatial distribution of land use, land cover, and topography on the evolution of LSB circulation over the region [16] can be seen.

3. Conclusion and discussions

This study examined the dynamics of LSB circulation across the Guinean coast of West Africa. The earlier observational study shows the occurrence of LSB throughout the year with seasonal variability in the region. While LSB circulation formed everywhere along the Guinean coasts, the hodographs exhibited both theoretically expected CR and “anomalous” Counter-Coriolis ACR. Due to the complex, nonlinear nature of LSBs, numerical modeling presented the only possible method by which to understand the underlying dynamics of this mesoscale phenomenon.

A numerical simulation was therefore performed, with ERA-Interim and CFS as forcing data, using the adjusted WRF-ARW model code and subsequently evaluated for accuracy using local observations. The diurnal evolutions of modeled and observed onshore/offshore winds were found to be in good agreement. While WRF model offers great operational forecasting capabilities, effectively no options for dynamical analysis are available. The basic dynamical equations are embedded deeply in the solver and remain inaccessible to the user. This presents a serious limitation to those using WRF to investigate the dynamics driving the LSB circulation, even though the model demonstrates excellent performance and accuracy. In order to overcome this limitation, the model original code was adjusted to allow for the extraction of the individual tendency terms of the horizontal momentum equations [7, 16].

Generally, the terms found to have significant contribution to the total momentum balance of LSB circulation over the domain included pressure gradient (subsequently separated into surface and synoptic components), advection, and horizontal and vertical diffusion. Since the region is close to the equator, Coriolis term generally did not have significant effects on the LSB circulation. The rate of rotation of the total horizontal momentum tendency was plotted for the entire domain. Two regions (for CR and ACR) with one CR and ACR for each of CFS and ERA around the coastline area were selected for term-by-term dynamical analysis. Following [7, 16], the strength of rotation due to each component of the horizontal momentum equations was determined for the selected regions. The direction of rotation was found to be a result of a complex interaction between surface and synoptic pressure gradients, advection, and horizontal and vertical diffusions. However, higher variability as well as unlikely individual term magnitudes suggests that the simulation requires further improvements to be considered conclusive. For more investigations, an idealized simulation should be carried out using a similar domain configuration as that of a real case.

Consequent upon all the above numerical simulations, it can be concluded that:

1. Both observed and simulated hodograph rotations and wind fields for selected LSB days showed good agreement. Therefore, it can be concluded that WRF model is suitable to evaluate the dynamics of LSB rotations in different regions with different topography features. Over ocean, the model performance was quite good for both reanalysis data (CFS and ERA-Interim). But in land side, for CFS re-analysis data, the rotation tendencies seemed to be affected by the presence of steep topography and spatial distribution of land use, cover, which is not clear for ERA-Interim, demonstrating again CFS is better reproducing the LSB dynamics than ERA-Interim. The overall dynamics of the hodograph rotation tendencies were well captured by WRF model.

2. The real case simulations showed complex patterns of LSB rotations across the Guinean Coast of West Africa. The regions over land showed more CR, while regions over ocean seem to be significantly influenced by ACR. This can likely be attributed to the variation of surface roughness due to the spatial distribution of land use, land cover change, and topographies.

3. The sense of rotation seems to be influenced by a complex interaction between pressure gradients, diffusion, and advection terms over regions with different topographies exhibiting different force balance for achieving their sense of rotation. Globally, it is obvious that the balance is not always dominated by the pressure gradient terms in contrast to some earlier studies. The results show different rotation features depending to the locations; thus, when diffusion tendencies are predominantly important over water side, land side seems to be dominated by surface gradient tendencies.

Acknowledgments

This work is supported by the African Institute for Mathematical Sciences, www.nexteinstein.org, with financial support from the Government of Canada, provided through Global Affairs Canada, www.international.gc.ca, and the International Development Research Centre, www.idrc.ca.

This research was carried out through the West African Science Service Centre on Climate Change and Adapted Land Use (WASCAL) initiative supported by the German Federal Ministry of Research and Education.

We acknowledge that the results of this research were achieved using computational resources at the German Climate Computing Center (DKRZ). The ERA-Interim dataset was downloaded from the European Centre for Medium – Range Weather Forecasts (ECMWF) (available online http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/). The CFSv2 dataset was downloaded from the Environmental Modeling Center at NCEP (available online ftp://nomads.ncdc.noaa.gov/modeldata/cfsv2_analysis_flxf).