**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**).

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 surfacesea ice system designed to provide the best estimate of the state of these coupled

**Figure 2.** *Outer domain for real case simulations for both WRF-CFS and WRF-ERA.*

*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*


**Table 1.**

*Coastal stations metadata.*

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 spinup. 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 Δt was set to 90 seconds, as recommended 6 Δx (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**.

#### **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.*

**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.

*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*

#### **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 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:

**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.*


From the simulated wind data, the following is obtained:


*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*

**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.*

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 onshoreoffshore 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

**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.*

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):


*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*

#### **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.*

#### **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:

$$\frac{\partial V\_h}{\partial t} = \frac{\partial V\_{pg}}{\partial t} + \frac{\partial V\_{adv}}{\partial t} + \frac{\partial V\_{cor}}{\partial t} + \frac{\partial V\_{hdf}}{\partial t} + \frac{\partial V\_{vdf}}{\partial t} \tag{1}$$

where *Vh* 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 *Vpg* can be further separated into synoptic *(syn)* and surface *(surf)* forcing by assuming that:

$$V\_{\rm spn} = V\_{\rm pg}(850mb) \tag{2}$$

Therefore, the total wind may be represented as

#### **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.*

*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*

$$V\_{\text{pp}} = V\_{\text{surf}} + V\_{\text{yn}}$$

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

$$\mathbf{V}\_{\text{surf}} = \mathbf{V}\_{\text{pg}} - \mathbf{V}\_{\text{gm}} \tag{3}$$

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:

$$\frac{\partial V\_h}{\partial t} = \frac{\partial V\_{surf}}{\partial t} + \frac{\partial V\_{syn}}{\partial t} + \frac{\partial V\_{adv}}{\partial t} + \frac{\partial V\_{cor}}{\partial t} + \frac{\partial V\_{hdiff}}{\partial t} + \frac{\partial V\_{vdf}}{\partial t} \tag{4}$$

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

$$\frac{\partial \alpha}{\partial t} = \frac{1}{V\_h^2} k. \left( V\_h \times \frac{\partial V\_h}{\partial t} \right) \tag{5}$$

Where:


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 *<sup>∂</sup><sup>α</sup> <sup>∂</sup><sup>t</sup>* values were averaged between 0900 and 1700 LST to produce*<sup>∂</sup>αday <sup>∂</sup><sup>t</sup>* . **Figure 10** represents the daytime regional patterns of CR (*<sup>∂</sup>αday <sup>∂</sup><sup>t</sup>* <sup>&</sup>lt; 0) and ACR (*<sup>∂</sup>αday <sup>∂</sup><sup>t</sup>* > 0) for both WRF-CFS and WRF-ERA.

**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

#### **Figure 10.**

*Patterns of hodograph rotation for the selected SB day, December 16, 2014. Total <sup>∂</sup><sup>α</sup> <sup>∂</sup><sup>t</sup> values are averaged over daytime (0900–1700 LST) showing the subregions 1 and 2 (red circle and triangle) identified.*

*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*

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:

$$\frac{\partial a\_{\text{tot}}}{\partial t} = \frac{\partial a\_{\text{surf}}}{\partial t} + \frac{\partial a\_{\text{syn}}}{\partial t} + \frac{\partial a\_{\text{adv}}}{\partial t} + \frac{\partial a\_{\text{cor}}}{\partial t} + \frac{\partial a\_{\text{hdf}}}{\partial t} + \frac{\partial a\_{\text{vdf}}}{\partial t} \tag{6}$$

#### *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**).

**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


#### **Table 2.**

*Daytime evolution of rotation tendency terms by WRF-ERA Region\_1.*

**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.*

weakness of friction forces over water, which may minimize the effects of both horizontal and diffusion terms (**Figure 11**).

**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

*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*


#### **Table 3.**

*Daytime evolution of rotation tendency terms by WRF-ERA over land Region\_2.*

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**).

**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**).

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 (*<sup>∂</sup>αtot <sup>∂</sup><sup>t</sup>* Þ is following the shape of surface pressure tendency (*<sup>∂</sup>αsurf <sup>∂</sup><sup>t</sup>* Þ, 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

**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.*

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.

*Numerical Simulation of Land and Sea Breeze (LSB) Circulation along the Guinean Coast… DOI: http://dx.doi.org/10.5772/intechopen.107339*


**Table 4.**

*Daytime evolution of rotation tendency terms for WRF-CFS over ocean (Region\_1).*
