Weibull Statistics for Upper Ocean Currents with the Fokker-Planck Equation

Upper oceans typically exhibit of a surface mixed layer with a thickness of a few to several hundred meters. This mixed layer is a key component in studies of climate, biological productivity and marine pollution. It is the link between the atmosphere and the deep ocean and directly affects the air-sea exchange of heat, momentum and gases. Vertically averaged horizontal currents across the mixed layer are driven by the residual between the Ekman transport and surface wind stress, and damped by the Rayleigh friction. A set of stochastic differential equations are derived for the two components of the current vector (u, v). The joint probability distribution function of (u, v) satisfies the Fokker-Planck equation (Chu, 2008, 2009), with the Weibull distribution as the solution for the current speed. To prove it, the PDF of the upper (0-50 m) tropical Pacific current speeds (w) was calculated from hourly ADCP data (1990-2007) at six stations for the Tropical Atmosphere Ocean project. In fact, it satisfies the two-parameter Weibull distribution reasonably well with different characteristics between El Nino and La Nina events: In the western Pacific, the PDF of w has a larger peakedness during the La Nina events than during the El Nino events; and vice versa in the eastern Pacific. However, the PDF of w for the lower layer (100-200 m) does not fit the Weibull distribution so well as the upper layer. This is due to the different stochastic differential equations between upper and lower layers in the tropical Pacific. For the upper layer, the stochastic differential equations, established on the base of the Ekman dynamics, have analytical solution, i.e., the Rayleigh distribution (simplest form of the Weibull distribution), for constant eddy viscosity K. Knowledge on PDF of w during the El Nino and La Nina events will improve the ensemble horizontal flux calculation, which contributes to the climate studies. Besides, the Weibull distribution is also identified from the near-real time ocean surface currents derived from satellite altimeter (JASON-1, GFO, ENVISAT) and scatterometer (QSCAT) data on 1o 1o resolution for world oceans (60o S to 60o N) as "Ocean Surface Current Analyses - Real Time (OSCAR)". Such a PDF has little seasonal and interannual variations. Knowledge on PDF of w will improve the ensemble horizontal flux calculation, which contributes to the climate studies. References Chu, P. C., 2008: Probability distribution function of the upper equatorial Pacific current speeds. Geophysical Research Letters, 35,doi:10.1029/2008GL033669 Chu, P. C., 2009: Statistical Characteristics of the Global Surface Current Speeds Obtained from Satellite Altimeter and Scatterometer Data. IEEE Journal of Selected Topics in Earth Observations and Remote Sensing,2(1),27-32.