Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37A degrees 27.6' N, 122A degrees 15.1' E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (nu=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins's linear,model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper. (C) 2002 Elsevier Science Ltd. All rights reserved.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Distribution of calcifying and silicifying phytoplankton in relation to environmental and biogeochemical parameters during the late stages of the 2005 North East Atlantic Spring Bloom

The late stage of the North East Atlantic (NEA) spring bloom was investigated during June 2005 along a transect section from 45 to 66 degrees N between 15 and 20 degrees W in order to characterize the contribution of siliceous and calcareous phytoplankton groups and describe their distribution in relation to environmental factors. We measured several biogeochemical parameters such as nutrients, surface trace metals, algal pigments, biogenic silica (BSi), particulate inorganic carbon (PIC) or calcium carbonate, particulate organic carbon, nitrogen and phosphorus (POC, PON and POP, respectively), as well as transparent exopolymer particles (TEP). Results were compared with other studies undertaken in this area since the JGOFS NABE program. Characteristics of the spring bloom generally agreed well with the accepted scenario for the development of the autotrophic community. The NEA seasonal diatom bloom was in the late stages when we sampled the area and diatoms were constrained to the northern part of our transect, over the Icelandic Basin (IB) and Icelandic Shelf (IS). Coccolithophores dominated the phytoplankton community, with a large distribution over the Rockall-Hatton Plateau (RHP) and IB. The Porcupine Abyssal Plain (PAP) region at the southern end of our transect was the region with the lowest biomass, as demonstrated by very low Chla concentrations and a community dominated by picophytoplankton. Early depletion of dissolved silicic acid (DSi) and increased stratification of the surface layer most likely triggered the end of the diatom bloom, leading to coccolithophore dominance. The chronic Si deficiency observed in the NEA could be linked to moderate Fe limitation, which increases the efficiency of the Si pump. TEP closely mirrored the distribution of both biogenic silica at depth and prymnesiophytes in the surface layer suggesting the sedimentation of the diatom bloom in the form of aggregates, but the relative contribution of diatoms and coccolithophores to carbon export in this area still needs to be resolved.

Wintertime meso-scale horizontal distribution of large tintinnids in the southern Yellow Sea

Spatial distribution of some large tintinnid species (nominally > 76 mu m) is investigated on samples vertically towed in the southern Yellow Sea in winters of 2001 to 2004. Nine tintinnid species are recorded: Codonellopsis morchella, Stenosemella pacifica, S. steini, Tintinnopsis schotti, T. radix, T. karajacensis, Eutintinnus tenuis, Parafavella sp., Leprotintinnus neriticus, of which C. morchella and T. radix dominated in the warm tongue-shaped zone of the Yellow Sea Warm Current (YSWC), and S. pacifica is the next in abundance. Our study shows that these tintinnids occur repeatedly in certain special distribution patterns.

Seasonal changes in the distribution of dissolved organic nitrogen in coastal and open-ocean waters in the North East Pacific: sources and sinks

The distribution of dissolved organic nitrogen (DON) and nitrate were determined seasonally (winter, spring and summer) during three years along line P, i.e. an E-W transect from the coast of British Columbia, Canada, to Station P (50degreesN, 145degreesW) in the subarctic North East Pacific Ocean. In conjunction, DON measurements were made in the Straits of Juan de Fuca and Georgia within an estuarine system connected to the NE Pacific Ocean. The distribution of DON at the surface showed higher values of 4-17 muM in the Straits relative to values of 4-10 muM encountered along line P, respectively. Along line P, the concentration of DON showed an inshore-offshore gradient at the surface with higher values near the coast. The equation for the conservation of DON showed that horizontal transport of DON (inshore-offshore) was much larger than vertical physical mixing. Horizontal advection of DON-rich waters from the coastal estuarine system to the NE Pacific Ocean was likely the cause of the inshore-offshore gradient in the concentration of DON. Although the concentration of DON was very variable in space and time, it increased from winter to summer, with an average build up of 4.3 muM in the Straits and 0.7 muM in the NE subarctic Pacific. This implied seasonal DON sources of 0.3 mmol N m(-2) d(-1) at Station P and 1.5 mmol N m(-2) d(-1) in the Straits, respectively. These seasonal DON accumulation rates corresponded to about 15-20% of the seasonal nitrate uptake and suggested that there was a small seasonal build up of labile DON at the surface. However, the long residence times of 180-1560 d indicated that the most of the DON pool in surface waters was refractory in two very different productivity regimes of the NE Pacific. (C) 2002 Elsevier Science Ltd. All rights reserved.

Spatial distribution of ciliates, copepod nauplii and eggs, Engraulis japonicus post-larvae and microzooplankton herbivorous activity in the Yellow Sea, China

The abundance of anchovy Engraulis japonicus larvae, >20 mum ciliates, copepod eggs and nauplii, and microzooplankton herbivorous activity were studied in the Yellow Sea in June 2000. Anchovy juveniles and larvae were found in only 6 of the 19 stations sampled. The ciliate communities were dominated by 2 species: Laboea strobila and Strombidium compressum. In the surface waters, the abundance of L. strobila ranged between 0 and 560 ind. l(-1). S. compressum only appeared at Stns 15 to 18 (20 to 3300 ind. l(-1)). L. strobila was found mainly in the top 20 m. The abundance of L. strobila was less than 50 ind, l(-1) in waters deeper than 25 m. S, compressum showed subsurface abundance peaks at the salinity abnormality. Tintinnids occurred occasionally with abundance lower than 100 ind. l(-1), The total ciliate abundance fell in the range of 40 to 3420 ind. l(-1). The ciliate biomass in the surface water and the water column ranged between 0,15 and 6.76 mug C l(-1) and 0.4 and 134.4 mg C m(-2), respectively, In the surface waters, the abundance of copepod eggs and nauplii ranged from 0,3 to 3.1 and 1,1 to 15.6 ind, l(-1), respectively. The average abundance of copepod eggs and nauplii in 4 depth (0, 5, 10 and 20 m) fell in the range of 0.2 to 2.8 and 1.0 to 29.4 ind. l(-1), respectively. As a food item of the E. japonicus post-larvae, the abundance of copepod nauplii and eggs appeared to be low. The abundance peaks of ciliate and E, japonicus post-larvae coincided. Although not found in the gut of E, japonicus post-larvae, aloricate ciliates might be ingested by first-feeding anchovy larvae, preventing initial starvation and prolonging the time to irreversible starvation. On the basis of dilution experiments with positive microzooplankton grazing rates, microzooplankton grazed at rates of 0 to 0.61 d(-1). Grazing pressure of microzooplankton on chlorophyll a standing stock (P-i) and potential chlorophyll a primary production (P-p) were 17 to 46% and 35 to 109% d(-1), respectively.

Seasonal and spatial distribution of matrix-bound phosphine and its relationship with the environment in the Changjiang River Estuary, China

Sediment is commonly considered as a source of phosphine, which is a highly toxic and reactive atmospheric trace gas. This study aims to investigate the seasonal and spatial distribution of matrix-bound phosphine (MBP) and its relationship with the environment in the Changjiang River Estuary. A total of 43 surface sediments were collected in four seasons of 2006, and concentrations of MBP and relative environmental factors were analyzed. MBP ranged from 1.93 to 94.86 ng kg(-1) dry weight (dw) with an average concentration of 17.14 ng kg(-1) dw. The concentrations of MBP in the tipper estuary were, higher than those in the lower estuary, which could be attributed to greater pollutant inputs in the upper estuary. The concentrations of MBP also varied with season, with November > August > May > February. Significant correlations existed between MBP and total phosphorus (TP), organic phosphorus (OP), inorganic phosphorus (W), organic carbon (OC), total nitrogen (TN), the grain size, and redox potential (Eh), suggesting that these sedimentary environmental characteristics played an important role in controlling the MBP levels in the sediments. Notably, there were positive linear relationships between the concentrations of soluble reactive phosphorus (SRP), TP, and chlorophyll a (Chl a) in bottom water and MBP in sediments. These relationships might be very complicated and need further exploration. This work is the first comprehensive study of the seasonal and spatial distribution of MBP in sediments and its relationships with environmental factors in a typical estuary, and will lead to deeper understanding of the phosphorus (P) biogeochemical cycle. (C) 2008 Elsevier Ltd. All rights reserved.

Impact of tidal front on the distribution of bacterioplankton in the southern Yellow Sea, China

Three surveys were carried out in anchovy spawning periods in southern Yellow Sea in May and June 2001, and June 2002. Chlorophyll a (Chl-a) concentration, bacterioplankton abundance, biomass and their variations along the zone of tidal fronts were investigated. The results showed that (1) high Synechococcus abundance distributed more often in frontal area and middle-surface layer of a stratified zone; and (2) the maximal abundance of bacteria occurred in stratified and mixed zone. 2006 Elsevier B.V. All rights reserved.

Meso-scale spatial distribution of large tintinnids in early summer in southern Yellow Sea

The spatial distribution of some large tintinnid species (nominally>76 mu m) was investigated according to samples collected by vertical towing in cruises to the southern Yellow Sea in summer 2000-2002 and 2004. Eight species were identified: Codonellopsis mobilis, Leprotintinnus netritus, Tintinnopsis karajacensis, T. japonica, T. kiaochowensis, T. butschlii, T. radix, and Parafavella sp. With maximum abundance of 158.2 ind/L in June 2004, C mobilis was the dominant species, lasting from May to July 2004. Tintinnid communities were patchy and distributed mainly in shallow waters along the shore.