2.2 Methods

As a first step towards examining the spatial variability of the aforementioned nutrients, seasonal nutrient maps, as well as profiles of nutrients across the Arabian Gulf and the Sea of Oman, are generated. The Redfield ratios are calculated afterwards to determine which nutrient is limiting in each region. Furthermore, the Ekman transport method is utilized to measure the depth of the Ekman layer in the Arabian Gulf and Sea of Oman and identify the regions of curl driven upwellings and coastal upwellings. Coastal upwellings have also been examined based on the SST method. The details are shown below.

The monthly nutrients data (nitrate, phosphate and silicate) have been resampled and interpolated into a grid size of 360 × 180 × 43 (longitude, latitude, depth) for the Arabian Gulf and Sea of Oman domain with latitudes: [22.3738 − 30.5765°N] and longitudes: [47.6979 − 65.0104°E]. In order to analyze seasonal variations in nutrients during summer and winter, the monthly data for December, January, and February were averaged as winter and June, July, and August as summer. Using these averaged data, surface nutrient maps for winter and summer are generated. Similarly, nutrient seasonal profiles have also been extracted but only for five sub-regions, including the northern Arabian Gulf, the center of the Arabian Gulf, the southern Arabian Gulf, the Strait of Hormuz, and the Sea of Oman. The bathymetry of the Arabian Gulf does not exceed 100 m, while that of the Sea of Oman could exceed 3 km. Therefore, in total, 15 locations have been selected in the Arabian Gulf, and 10 in the Strait of Hormuz and Sea of Oman as shown in Fig 1.

In order to determine the limiting nutrients in the Arabian Gulf and the Sea of Oman, the ratios of mean seasonal (i.e. summer and winter) nitrate (NO₃) to phosphate (PO₄) ratios for both surface and depth averaged concentrations are calculated (Table 1). The ratios (N:P) are then compared with the Redfield ratio (16:1), with a lower ratio representing nitrogen limitation and a higher ratio representing phosphorus limitation.

The WOA data are climatological data collected from the periods 1900–2017. The calculation of the average depth waters is based on the average of several depths. Summer (June, July, August); winter (December, January, February).

For the purpose of studying the distribution of nutrients in relation to upwelling, advection and mixing of water, we calculated the monthly Ekman transports to calculate vertical velocities associated with open sea upwelling from the curl of the wind, vertical velocity of coastal upwelling and total vertical velocity in addition to the Ekman depth as shown below.

First, Ekman transport components (U_E, V_E) [m³ s⁻¹ m⁻¹] at each grid point (0.75 degrees) is calculated based on the wind data obtained from ECMWF datasets by applying Eqs 1 and 2:

Where U_E and V_E are the zonal and meridional Ekman transports, ρ_w = 1025 kg m⁻³ is seawater density, f = 2Ωsinθ is the Coriolis parameter where Ω = 7.292 × 10⁻⁵ rad s⁻¹ is the Earth’s angular velocity, and θ indicates the latitude. The wind speed (U₁₀, V₁₀) is automatically computed and converted into wind stress (τ: N m⁻²) with the subscripts x and y indicating zonal (along shore wind stress) (τ_x) and meridional (τ_y) components using Eqs 3 and 4,

where ρ_a = 1.22 kg m⁻³ is the density of air and C_d = 1.3 × 10⁻³ is the drag coefficient (dimensionless).

Considering that Ekman currents decrease exponentially with depth. The thickness of the layer is arbitrary and the velocity at the depth (D_E) [m] that is opposite to velocity at the surface is considered as the Ekman thickness or Ekman depth [41]. The Ekman layer depth is computed by Eq 5.

where φ is the latitude.

The curl-driven upwelling (w_curl) at the base of the Ekman layer is calculated from the divergence of the Ekman transport as shown in Eq 6.

where U_E is the horizontal Ekman transport and ∇ is the horizontal divergence operator. Ekman vertical velocities approach zero at the sea surface (w_surface = 0). Hence,

where τ→ is the vector wind stress and k→ refers to the unit vector in the vertical direction. The wind stress derivatives at each grid point (0.75 degrees) are obtained. Positive wind stress curl produces Ekman suction (upwelling) and negative curl produces Ekman Pumping (downwelling).

Using the offshore Ekman transport associated with the predominant alongshore wind stress (m³ s⁻¹ per meter of coast) calculated above we can determine the vertical velocity of the coastal upwelling (w_coast) [m s⁻¹] as shown in Eq 8,

where R_d = 1 ×10³ km is the Rossby radius of deformation. This average value of R_d is determined by applying Eq 9 to calculate the average R_d acquired at each grid point for the entire region.

Where g is the gravitational acceleration and D is the water depth. The total vertical velocity (w_T) of coastal upwelling and curl-driven upwelling can therefore be obtained by adding the vertical velocity of both processes as shown in Eq 10,

The positive values of w represent upwelling (i.e. upward velocity) and negative values represent downwelling (downward velocity) [41,42].

An additional upwelling index, derived from the difference between the coastal and offshore SST (ΔSST), is used to confirm the upwelling results obtained by the Ekman method. Eq 11 shows the equation used to calculate the resultant SST upwelling index (UI_SST).

Where SST_ocean is that which is 0.5 degrees from the coasts of the Arabian Gulf and 2 degrees from the coasts of the Sea of Oman. Whereas SST_coast is SST observed right along the coast. In the case of a negative UI_SST, the coastal waters are cooler than the open ocean, indicating upwelling, while a positive value showing the opposite, indicating no upwelling.