Documenting Monthly Climatological Mean of Wave Parameters in the Northern Bay of Bengal Using 40 years of ECMWF Reanalysis V5 (ERA5) Data

Abstract

This study has tried to fill the existing gaps of information regarding different wave parameters in the northern Bay of Bengal, especially in the maritime area of Bangladesh. For this purpose, monthly climatological mean of wave parameters in spatial perspective in the whole Bay of Bengal (BoB) domain using about 40 years of ERA5 reanalysis data have been investigated throughout this research. Collected data were analyzed by using Python and R scripts. It is revealed that significant height of combined wind waves and swells (SWH) around 2–2.2 m are found in the deep waters of northern BoB during June–August. Higher values of ocean surface stress equivalent 10 m neutral wind speed (WSP) during August, September and October are respectively 7.4 m/s, 6 m/s and 4.6 m/s found in the northern BoB. Higher values of mean wave period (Tm) around 9 s–10 s are found in the northern BoB during January–February, and August–December. June and July are considered as the roughest months of wave climate in the northern BoB. The monthly upward and downward pattern of the wave parameters in the northern BoB are governed by the influences of tropical cyclones and strong wind forcing. Shelf seas and deep sea domains along with the area close to the southeastern coast of Bangladesh exhibit active wave climatology.

Appendices

Appendix

Ocean Wave Equations

According to Bai and Jin (2015), significant wave height (SWH) in time–domain analysis, is denoted by Hs and given by the Eq. 1:

$$Hs=\frac{1}{N/3}{\sum }_{i=1}^{N/3}Hi$$

(1)

where N is the individual wave heights’ number, and Hi is a wave heights’ series ranged from highest to lowest.

According to Bai and Jin (2015), mean wave period is given by Eq. 2 and 3:

$${T}_{o,1}=2\pi \frac{m0}{m1}$$

(2)

$${T}_{o,2}=2\pi \surd \frac{m0}{m2}$$

(3)

where, T_0,1 and T_0,2 are respectively mean crest period and mean–zero up-crossing period, and m₀ is the zero moment, which is the area under the curve of energy density spectrum.

Wave dispersion relation is given by Eq. 4 according to Lamb (1945):

$${\omega }^{2}=gk\;{tanh}\left(kd\right)$$

(4)

where d is the depth of water, tanh is the hyperbolic tangent, and g is the acceleration due to gravity. In case of deep water waves: d ≥ $\frac{\lambda }{2}$, tanh(kd) ≈ 1; for shallow water waves: h ≤ $\frac{\lambda }{20}$, tanh(kd) = kd; and it is given by: $\frac{\lambda }{20}$ ≤ d ≤ $\frac{\lambda }{2}$, tanh(kd) = tanh(kd) in case of waves in the intermediate depths. Wave frequency in radian per second, also known as angular frequency (ω) which is given by Eq. 5:

$$\omega =2\pi f=\frac{2\pi }{T}$$

(5)

where T is the wave period and f is the wave frequency in hertz (Hz).

The wave number (k) according to Stewart (2008) is given by Eq. 6:

$$k=\frac{2\pi }{\lambda }$$

(6)

Phase velocity (c) of wave is given by Eq. 7:

$$c=\frac{\lambda }{T}=\frac{\omega }{k}$$

(7)

Using the dispersion Eq. (4) for the shallow water waves, the final equation is given by Eq. 8:

$${\omega }^{2}=gk\left(kd\right)={gdk}^{2}$$

(8)

Phase velocity or c for the shallow water wave is given by the Eq. 9:

$$c=\surd (gd)$$

(9)

Wave length or λ for the shallow water wave is given by Eq. 10:

$$\lambda =T\surd (gd)$$

(10)

Group velocity or c_g for the shallow water wave is given by the Eq. 11:

$${c}_{g}=c=\surd (gd)$$

(11)

In case of deep water waves:

$${\omega }^{2}=gk$$

(12)

$$c=\frac{gT}{2\pi }$$

(13)

$$\lambda ={gT}^{2}/2\pi$$

(14)

$${c}_{g}=\frac{1}{2}c=\frac{gT}{4\pi }$$

(15)

In case of intermediate depths:

$$C=\frac{gT}{4\pi }\mathrm{tanh}(\frac{2\pi d}{\lambda })$$

(16)

$$\lambda ={gT}^{2}/2\pi tanh (\frac{2\pi d}{\lambda })$$

(17)

$${c}_{g}=\frac{1}{2}(1+\frac{4\pi \frac{d}{\pi }}{\mathrm{sinh}(4\pi \frac{d}{\pi })})$$

(18)

According to Liakatas et al. (2017), the amount of energy carried by a wave of certain frequency is given by the Eq. 19:

$$E=\rho g{({H}_{1/3})}^{2}{H}_{1/3}$$

(19)

where H_1/3 is the SWH, g is the acceleration due to gravity, ρ is the seawater density.

The wave power (P) can be derived from the above Equation [19] and given by Eq. 20:

$$P={({\rho g}^{2}/64\pi )T({H}_{1/3})}^{2}$$

(20)

where T is the mean wave period.