OJMS  Vol.7 No.1 , January 2017
Modelling Three-Dimensional Winds on a NW Pacific Region of Mexico Using Boundary-Fitted Grids
ABSTRACT
In this study, the momentum equations describing an atmospheric flow over a NW Pacific region of Mexico are solved numerically. In order to capture the complex flow-topography interactions with detail, a combination of a numerical wind model in full 3D curvilinear coordinates, along with a high resolution boundary-fitted grid is used. Boundary conditions were obtained from ten years (2002-2012) of measured offshore wind data. Prevailing winds from April to September during that period of observations were selected for the simulations. For the cases analyzed, it was found that at the points of the study region (PSS, PSM, PM), wind speed increased about 10% to 20% of its offshore values, while inland they decreased about 86% to 96%. This spatial behavior agreed very well with the observed local winds. A coastal jet (CJ), 35 km long with speeds about 1.5 - 2 m/s, emanating from PSS was found for NNW winds. Modeled winds were also used to compute wind stresses, wind stress curl, and CUI fields. Wind stress values agreed very well to those reported in the literature. High values of wind stress curl, and CUI were found at the lee of the points (PSS, PSM, PM). Indirect estimations of sea surface currents were about 15 - 20 cm/s offshore and 5 - 10 cm/s at the coast.

1. Introduction

Orographic modification of stably stratified air flow past a topographic obstacle has been the subject of numerous investigations. Previous research has focused on many aspects of idealized low-level three-dimensional flow in the vicinity of isolated topography [1] [2] [3] and associated downstream wake dynamics [4] [5] [6] , while studies on realistic topography have been performed in other parts of the world by several authors such as [7] - [12] among others. Regionally, while a great deal of attention has been paid to modeling wind driven ocean currents, the related problem of marine air flow over land has received considerably less attention. Thus, the present contribution repre- sents one of the firsts modelling efforts to study wind effects at high resolution in the region (see Figure 1); moreover, use of boundary-fitted grids captures the complexity of the orography of the study site. The study of flow modification by orography in this region is a challenge for a variety of reasons that include a combination of complex topography, wind variability, and associated boundary-layer processes.

Ensenada city is located on the NW Pacific Coast of Mexico, bordered on the North and East by variable orography, with mountains 1500 m tall, South by Point Banda, PB (a cape, approximately 8 km, long), and West by the Pacific Ocean and a small pair of islands (Islas de Todos Santos, ITS) (Figure 1). The region is an example of a developing urban area located in complex terrain where most of the population is settled along the coast.

The purpose of this investigation is to explore the dynamics of flow past complex topographic obstacles with special emphasis on the formation of lower-boundary jet streams emanating from capes and points such as Point Salsipuedes (PSS), Point San Miguel (PSM), Point Morro (PM) and Point Banda (PB). Particularly, we are interested in the response of winds within the study region to coastal topographic forcing of the marine airflow. With this aim in mind, we conducted a series of numerical experiments using the General Curvilinear Atmospheric Model (GCAM) [13] [14] with 100 m

Figure 1. (a) Baja Penìnsula, (b) a zoom showing the complex orography of the study site; contour elevation (in black) is in meters and the yellow dots mark the sites of wind monitoring stations.

horizontal grid resolution. The experiments were performed for the most persistent winds and the results were compared with available observations. Subsequently, they were used for calculating the wind stress, wind stress curl and other variables of biological interest.

2. Observations

The Institute of Oceanological Research (IIO) from Autonomous University of Baja California (UABC), maintains several meteorological stations in the Ensenada area. The locations of two of them, ITS (island station) and PM (coastal station), are shown in Figure 1. Of interest for this study are the winds from April to September, in which the climate over the region is warm, dry and stable due to the strong subtropical high over the adjacent North Pacific Ocean [15] . During this period, winds blow steadily alongshore from the northwest and the large-scale sinking motion almost completely suppresses precipitation [15] . Monthly averages of available data from 2005-2012 for this month’s period are presented in Table 1. At ITS station, winds come from 287˚ to 330˚;

(a) (b)

Table 1. Monthly wind average and direction at ITS and PM stations for several months from 2005-2012. (a) ITS, (b) PM.

estimated maximum velocity was 3.90 m/s; similar wind velocity estimates have been reported previously [16] [17] [18] [19] [20] . At the coastal PM station, the direction range is modified to 255˚ - 310˚, while maximum wind velocity decreases by approximately 26%. It is worth to mention that farther offshore, the surface wind speeds derived from SSM/I satellite data range from 5 - 6 m/s [21] [22] .

3. Computational Methods

The numerical simulations employ the General Curvilinear Atmospheric Model (GCAM, [13] [14] ). GCAM is a non-hydrostatic, non-linear, curvilinear full 3D primitive variables model that solves the momentum equations using boundary-fitted grids. It utilizes a finite-difference discretization and a semi-implicit time integration scheme to simulate the temporal development of a stratified flow over irregular orography in a rotating system.

The full derivation of the model’s equations can be found in [23] [24] ; here, they are described briefly. The set of perturbed dimensionless equations to be solved is given by [13] ;

(1)

(2)

(3)

where bold letters represent vectors. This way, u = (u, v, w) is the velocity vector; i, j and k are the unit vectors in the x, y, and z coordinates respectively; p is the pressure; ρ is the density of the air and D (=・u) represents the divergence. The dimensionless numbers are the Reynolds number, Re (=UL/AH), the Froude number, F (=U/Nh) and the Ross by number Ro (=U/fL), where U, L and h are typical velocity, length and height scales, respectively, AH is the eddy viscosity coefficient, f (=2Ωsinφ) the coriolis parameter and is the Brünt-Väisälä frequency. As it is noted, in primitive variables, unknowns are (u, ρ, p) as indicated by Equations (1)-(2), while Equation (3) for p substitutes the incompressibility condition・u = 0.

As described in [13] , the set of governing equations is transformed from Cartesian to Curvilinear coordinates (i.e. from physical (x, y, z) domain to computational (ξ, η, ζ) domain and then solved subject to initial and boundary conditions. On solid boundaries u = 0, with no flux of density, (where n is the unit normal vector), while for p, the boundary condition is determined by substituting u = 0 into the transformed momentum Equation (3).

The geometry of the study site is well captured by using a three-dimensional boundary-fitted grid. The domain consists of 446 × 420 × 11 (ξ × η ×ζ) grid points that extends 45 km and 42 km with 100 m horizontal resolution in x and y respectively, and 11 vertical layers covering 3000 m with 10 m minimum mesh size in z. The ground level grid (ζ = 1) along with several vertical grids of the physical domain is shown in Figure 2.

Simulations were performed for four different directions of incident wind: a) 330˚, b) 315˚, c) 300˚ and d) 287˚, with fixed U = 6 m/s [21] [22] ; background stratification was taken as N = 0.01 s1 (which is a typical value for the atmosphere [25] [26] ), and for the

Figure 2. The grid in physical space.

eddy viscosity coefficient we chose the value [6] . The Froude number, based on a 102 m mountain height, was F = 6, while Re = 5.71 × 106. Rotation was not dynamically significant in these simulations as the calculated Ross by number was Ro > 1.

In all the simulations the fluid started impulsively from rest, and several inertial periods were necessary until the fluid adjusted to this impulsive start. Nearly steady solutions, defined by the convergence criterion:, where n is the time step and f represents any one of u, p or ρ, were obtained at dimensionless time, t, between 40 and 60; the dimensionless time increment for the simulations was set to ∆t = 0.001.

For each simulation, an estimate of the surface wind stress was calculated according to the bulk formula [27] :

where τx, τy denote the eastward and northward components of stress, ρa is the surface air density which was considered to have a constant value of 1.22 kg/m3, W10 is the observed wind speed, and U10 and V10 are the eastward and northward components of the wind velocity measured at a height of 10 m. The empirical drag coefficient CD, referenced to the 10m level, was given a constant value of 0.0013 [28] .

Important for biology is the wind stress in relation to upwelling-downwelling generation zones through the Ekman pumping (WE), and the coastal upwelling index (CUI). Wind stress curl, (), derived from wind simulations, was used to calculate WE according to [29] :

where ρw is seawater density (taken as 1024 kg/m3) and f the Coriolis parameter. This, way the effect of wind on ocean circulation and upwelling/downwelling generation can be assessed.

The coastal upwelling index (CUI; m3/s per 100 m of coast) was estimated by using the outputs from the model using the relation [30] ;

where τa is alongshore wind stress within 100 m of the coastline.

Finally, an estimation of ocean surface current velocity, us, generated by winds is given by the relation; [31] . For example, wind velocities of 10 m/s would generate a surface ocean current of us = 34 cm/s.

4. Results and Discussion

Simulated 10 m winds are presented in Figure 3. The presence of the coast and mountainous topography rising quickly from the ocean induces irregularities of local winds producing zones of >6 m/s velocity (in yellow) at PSS, PSM and PM (Figures 3(a)-(c)). Inland, the wind spatial distribution corresponds closely to the orography; resulting in weak winds with velocities <3 m/s in the lee of the mountains (see also Figure 1(b)). Offshore, wind velocities reach values between 4 - 5 m/s. For 330˚ and 315˚ incoming winds, a 1.5 - 2 m/s a coastal jet, CJ (approximately 35 km long and 3 km width) originates in PSS and enters land between PM and EB (Figure 3(a) & Figure 3(b)); this CJ is reduced in size and limited to a small area around PSS and PSM for 300˚ and 287˚ incoming winds (Figure 3(c) & Figure 3(d)). It is apparent that PSS, PSM and PM terrain features not only act to block or redirect the general flow near the coast; but also they play a key role in the establishment of the CJ.

The structure of the CJ is clearly elucidated through the vorticity field. Figure 4 presents the vertical component, ωz, of the vorticity vector ω = (ωx, ωy, ωz), where ω = × u, corresponding to Figure 3. At the coast, cyclonic vorticity is generated at the major capes of the region such as PSS, PSM and PM, there is also a source of strong anticyclonic vorticity at Point San Miguel (PSM) which probably originates at the canyon connecting Ensenada City and San Antonio village (see Figure 1(b)). Inland, positive and negative vorticity is generated by the complex orography of the region. Once generated, vorticity is advected and diffused leeward.

For winds from 330˚ and 315˚ there is a wake of positive and negative vorticity that extends several kilometers southeast of PSS (Figure 4(a) & Figure 4(b)). The eddies in the EB area are approximately 1.5 km in diameter. It is important to mention that the jet generated by the 330˚ winds enters land at the EB area (Figure 4(a)), while the jet generated by 315˚ incoming winds makes landfall by the Ensenada City area (Figure 4(b)). An incipient wake at the lee of ITS is observed for the 300˚ and 287˚ simulations (Figure 4(c) & Figure 4(d)).

A vertical view of the ωy component of the vorticity along the black vertical lines (1, 2, 3) in Figure 4(a) is presented in Figure 5 (330˚ incoming wind direction). Positive (negative) values represent the seaward (landward) direction, respectively. Over land, positive and negative ωy values are found between 0 - 20 km distances. Over sea, the core of the jet is clearly visible at approximately 19 km (Figure 5(a)), 26 km (Figure 5(b)) and 37 km (Figure 5(c)), vertical influence is of the order of 500 m. The presence of this CJ is important from the point of view of transport of physical properties and

Figure 3. Simulated 10 m wind vectors and contours of wind velocity (m/s) for various incoming wind directions: (a) 330˚; (b) 315˚; (c) 300˚, (d) 287˚. Vectors are suppressed every 20 grid points in both the zonal and meridional direction for clarity.

particles from PSS to the urban zone of the study region.

The computed spatial distribution of wind stress τ (N/m2) and WE (m3/s per 100 m) over the sea portion of the study region is presented in Figure 6. As expected, spatial

Figure 4. Dimensionless vorticity contours corresponding to Figure 4: (a) 330˚; (b) 315˚; (c) 300˚, (d) 287˚. Dotted line in (c) and (d) represents the zero vorticity contours.

stress gradients will induce gradients in the wind stress curl. A spatial inhomogeneity of WE is observed near the coast in response to coastal topographic forcing. Forcing of the marine flow by the curvature of the coastline generates up-welling positive wind stress curl and consequently larger wind stress curl is found in PSS, PSM and PM. Forincoming wind directions 330˚ and 315˚ the influence of WE extends southeast for several kilometers of the generation point (Figure 6(a) & Figure 6(b)). Large WE values are

Figure 5. Contours of vorticity along the black lines (1 - 3) shown in Figure 6(a) for 330˚ winds. (a) line 1; (b) line 2; (c) line 3. Continuous line: positive values; broken line: negative values.

found for 300˚ and 287˚ incoming wind directions (Figure 6(c) & Figure 6(d)).

Estimated coastal upwelling index contours (CUI) are shown in Figure 7. Model results indicate that CUI intensifies for wind directions 300˚ and 287˚ (Figure 7(c) & Figure 7(d)) and tends to diminish slightly for the other simulated cases (Figure 7(a) & Figure 7(b)). Maximum CUI values (~30) were found at the major capes of the study site: PSS, PSM, PM and PB for wind from 300˚ and 287˚ (Figure 7(c) & Figure 7(d)). There is no adequate way to compare the present results to previous ones since reported CUI values were obtained with very coarse grids. Besides, the wind stress and the wind stress curl can significantly be affected by the orography as noted in [8] [18] [19] ; for example Pérez-Brunius et al. [32] found CUI = 12 for Point Banda (PB) using different data sources. CUI values in the range −300 to 300, obtained from 1˚ mesh wind and wind stress data, are reported in [33] for Ensenada Bay. It is worth to mention that fish farming sites placed in the region coincide with the zones of maximum CUI and WE found in this study.

Finally, the estimated ocean surface current velocity, us, generated by the simulated winds, is presented in Figure 8. The effect of the spatial variation of winds on the magnitude of the currents is clearly seen. Offshore, values of us are of the order 15 - 20 cm/s. while estimated us values are 5 - 10 cm/s at the coast. These values agree remarkably well to those of 5 - 15 cm/s observed at BTS with HF radars for spring and summer [19]

Figure 6. Wind stress t(N/m2, arrows) and WE (m3/s) (colour) distribution for the simulated cases. (a) 330˚; (b) 315˚; (c) 300˚; (d) 287˚.

[20] . Also, there is an agreement with previous numerical work which used similar winds to force a 2D ocean model of Ensenada Bay [34] .

5. Conclusions

The wind circulation at high resolution over the study site has been characterized for the first time. The GCAM model was able to correctly reproduce the magnitude of the wind speed given by the in-situ observations. It was found that at the points, the wind

Figure 7. CUI (m3/s per 100 m) distribution: (a) 330˚; (b) 315˚; (c) 300˚, (d) 287˚.

speed grows about 10% to 20% of its offshore values; inland, they decrease about 86% and 96%. Estimated wind stress served to identify upwelling/down-welling zones which are important for fisheries farming in the region. Indirect estimates of sea surface currents were about 15 - 20 cm/s offshore and 5 - 10 cm/s at the coast.

Of particular interest is the evolution of a coastal jet (CJ) emanating from PSS and PSM found in this study. This finding is important in relation to microclimate modification and human health as the CJ could transport efficiently air masses of different physical properties as well as particulate matter (such a spore, or toxic agents) from the North to South of the study region.

Figure 8. Estimated ocean surface current velocity, us (cm/s): (a) 330˚; (b) 315˚; (c) 300˚, (d) 287˚.

As the number of local synoptic meteorological stations is small, they provide little information on the spatial structure of the winds over the study region. Studies such as this are an excellent source of information to show the conditions over areas that are not represented by measurements, especially those farther offshore and inland. Finally, these results could be an excellent source of information for identifying zones to place wind energy generation turbines and/or fisheries farming sites.

Acknowledgements

Publication expenses were provided by SEP (Mexico Ministry of Education) through the Program for Professional Teacher Development. S. Larios, A. Mejia and E. Gil from the Physical Oceanography Dept. of the Institute for Oceanological Research (IIO-UABC) provided the meteorological data for this study. Computer time was provided by the Mexico National Oceanographic Data Center. B. Inman kindly revised grammar and style. The manuscript was very thoroughly and constructively reviewed by two anonymous reviewers.

Cite this paper
Torres-Navarrete, C. (2017) Modelling Three-Dimensional Winds on a NW Pacific Region of Mexico Using Boundary-Fitted Grids. Open Journal of Marine Science, 7, 109-123. doi: 10.4236/ojms.2017.71009.
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