The self-thinning exponent in overcrowded stands of the mangrove, Kandelia obovata, on Okinawa Island, Japan

Weller??s allometric model assumes that the allometric relationships of mean area occupied by a tree $ \bar{s} $ , i.e., the reciprocal of population density $ \rho $ , $ \bar{s}\left( { = {1 \mathord{\left/ {\vphantom {1 {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right. \kern-0em} {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right) $ , mean tree height $ \bar{H}\left( { = g_{\theta } \cdot \bar{w}^{\theta } } \right) $ , and mean aboveground mass density $ \bar{d}\left( { = g_{\delta } \cdot \bar{w}^{\delta } } \right) $ to mean aboveground mass $ \bar{w} $ hold. Using the model, the self-thinning line $ \left( {\bar{w} = K \cdot \rho^{ - \alpha } } \right) $ of overcrowded Kandelia obovata stands in Okinawa, Japan, was studied over 8?years. Mean tree height increased with increasing $ \bar{w} $ . The values of the allometric constant $ \theta $ and the multiplying factor $ g_{\theta } $ are 0.3857 and 2.157?m?kg^???, respectively. The allometric constant $ \delta $ and the multiplying factor $ g_{\delta } $ are ?0.01673 and 2.685?m^?3?kg^1???, respectively. The $ \delta $ value was not significantly different from zero, showing that $ \bar{d} $ remains constant regardless of any increase in $ \bar{w} $ . The average of $ \bar{d} $ , i.e., biomass density $ \left( {{{\bar{w} \cdot \rho } \mathord{\left/ {\vphantom {{\bar{w} \cdot \rho } {\bar{H}}}} \right. \kern-0em} {\bar{H}}}} \right) $ , was 2.641?±?0.022?kg?m^?3, which was considerably higher than 1.3?C1.5?kg?m^?3 of most terrestrial forests. The self-thinning exponent $ \alpha \left( { = {1 \mathord{\left/ {\vphantom {1 {\varphi = }}} \right. \kern-0em} {\varphi = }}{1 \mathord{\left/ {\vphantom {1 {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right. \kern-0em} {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right) $ and the multiplying factor $ K\left( { = \left( {g_{\theta } \cdot g_{\delta } } \right)^{\alpha } } \right) $ were estimated to be 1.585 and 16.18?kg?m^?2??, respectively. The estimators $ \theta $ and $ \delta $ are dependent on each other. Therefore, the observed value of $ \theta + \delta $ cannot be used for the test of the hypothesis that the expectation of the estimator $ \theta + \delta $ equals 1/3, i.e., $ \alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2} $ , or 1/4, i.e., $ \alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-0em} 3} $ . The $ \varphi $ value was 0.6310, which is the same as the reciprocal of the self-thinning exponent of 1.585, and was not significantly different from 2/3 (t?=?1.860, df?=?191, p?=?0.06429), i.e., $ \alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2} $ . Thus the self-thinning exponent is not significantly different from 3/2 based on the simple geometric model. On the other hand, the self-thinning exponent was significantly different from 3/4 (t?=?6.213, df?=?191, p?=?3.182?×?10^?9), i.e., $ \alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-0em} 3} $ . Therefore, the self-thinning exponent is significantly different from 4/3 based on the metabolic model.     

In-water algorithms for ADEOS/OCTS

In-water algorithms for OCTS standard products were developed using in situ data and installed for operationally processing at NASDA/EOC. This paper describes the in-water algorithms Version 1.0 for chlorophylla concentration, pigment concentration, and attenuation coefficient at a wavelength of 490 nm. The selected OCTS standard algorithms (Ver. 1.0) are as follows:      

Alkenone distribution in surface sediments of the southern Yellow Sea and implications for the {\text{U}}^{{{\text{K}}\prime}}_{{37}} thermometer

The \textU^\textK￠₃₇ {\text{U}}^{{{\text{K}}\prime}}_{{37}} index has been widely applied for sea surface temperature (SST) reconstruction in open ocean environments, but has inherently limited applications at smaller, regional scales including some marginal seas where both historical and reconstructed SST records are urgently needed for understanding regional climate evolution. We determined the spatial distribution of alkenone contents in surface sediments from the southern Yellow Sea to assess the regional \textU₃₇^\textK￠ {\text{U}}_{{{37}}}^{{{\text{K'}}}} —SST relationship for paleo-SST reconstructions. C_37:2 and C_37:3 alkenones were detected at all 36 sites covering most of the southern Yellow Sea. Alkenone content ranges from 17 to 1,063 ng/g, with high values (ca. 400 to 1,000 ng/g) at deep water sites and a decreasing trend shoreward. For six samples at shallower depths near the coast and further offshore, the values were too low for statistical evaluation. This spatial pattern of alkenone contents is consistent with existing knowledge on the spatial distribution and productivity of alkenone-producing coccolithophorid species in the region. There is a significant positive relationship ( \textU₃₇^\textK￠ = 0.059\textSST - 0.350 {\text{U}}_{{{37}}}^{{{\text{K'}}}} = 0.059{\text{SST}} - 0.350 , R = 0.912, n = 30) between the \textU₃₇^\textK￠ {\text{U}}_{{{37}}}^{{{\text{K'}}}} values and satellite-derived annual mean SSTs (0 m) for the last 27 years, providing support for the application of a region-specific \textU₃₇^\textK￠ {\text{U}}_{{{37}}}^{{{\text{K'}}}} index as paleothermometer in the southern Yellow Sea. However, the slope of the southern Yellow Sea calibration (0.059) is considerably larger than that of the well-known global core-top calibration (0.033). This implies that global SST trends may not adequately encompass regional SST patterns and/or that environmental factors other than temperature may gain importance in explaining coccolithophore dynamics in marginal seas.     

Mixed layer depth front and subduction of low potential vorticity water under seasonal forcings in an idealized OGCM

The mixed layer depth (MLD) front and subduction under seasonal variability are investigated using an idealized ocean general circulation model (OGCM) with simple seasonal forcings. A sharp MLD front develops and subduction occurs at the front from late winter to early spring. The position of the MLD front agrees with the curve where \({\rm D}T_{\rm s}/{\rm D}t = \partial T_{\rm s} /\partial t + {\user2{u}}_{\rm g} \cdot \nabla T_{\rm s} = 0\) is satisfied (t is time, \({\user2{u}}_{\rm g}\) is the upper-ocean geostrophic velocity, \(T_{\rm s}\) is the sea surface temperature (SST), and \(\nabla\) is the horizontal gradient operator), indicating that thick mixed-layer water is subducted there parallel to the SST contour. This is a generalization of the past result that the MLD front coincides with the curve \({\user2{u}}_{\rm g} \cdot \nabla T_{\rm s} = 0\) when the forcing is steady. Irreversible subduction at the MLD front is limited to about 1 month, where the beginning of the irreversible subduction period agrees with the first coincidence of the MLD front and \({\rm D}T_{\rm s}/{\rm D}t =0\) in late winter, and the end of the period roughly corresponds to the disappearance of the MLD front in early spring. Subduction volume at the MLD front during this period is similar to that during 1 year in the steady-forcing model. Since the cooling of the deep mixed-layer water occurs only in winter and SST can not fully catch up with the seasonally varying reference temperature of restoring, the cooling rate of SST is reduced and the zonal gradient of the SST in the northwestern subtropical gyre is a little altered in the seasonal-forcing case. These effects result in slightly lower densities of subducted water and the eastward shift of the MLD front.     

Nutricline shoaling in the eastern Pacific warm pool during the last two glacial maxima

Isoprenoid glycerol dialkyl glycerol tetraethers (GDGTs) and alkenones were analyzed in sediment samples retrieved from Ocean Drilling Program Site 1241 covering the last 150000 years to understand the hydrological evolution of the eastern Pacific warm pool (EPWP). GDGT and alkenone concentrations showed higher values in marine isotope stage (MIS)-2 and MIS-6, which suggests the enhancement of primary production at glacial maxima. $ {\text{TEX}}_{86}^{\text{H}} $ - and $ U_{ 3 7^\prime }^{\text{K}} $ -derived temperature depicted different temperature evolutions. $ U_{ 3 7^\prime }^{\text{K}} $ -derived temperature was marked by small variation during the glacial–interglacial cycles, whereas $ {\text{TEX}}_{86}^{\text{H}} $ -derived temperature showed pronounced glacial–interglacial variation that was similar to Mg/Ca-derived temperature records from nearby cores in the EPWP. Given that enhanced primary production during glacial maxima suggests nutricline shoaling, unchanged $ U_{ 3 7^\prime }^{\text{K}} $ over glacial–interglacial cycles can be interpreted as the shift of alkenone production depth. $ {\text{TEX}}_{86}^{\text{H}} $ seems not to be influenced by glacial–interglacial changes in nutricline depths, recording an integrated temperature in surface and thermocline water. The shallow nutricline in the EPWP during glacial maxima most likely reflected the intense formation of Antarctic intermediate water.     

Sources and transformations of nitrogen in the South China Sea: insights from nitrogen isotopes

To elucidate the sources and transformations of nitrogen in the South China Sea (SCS), the nitrogen isotopic composition of nitrate (\({\updelta }^{ 1 5} {\text{N}}_{{{\text{NO}}_{ 3} }}\)) was measured in seawater samples from the water column of this marginal sea and the adjacent western North Pacific Ocean (WNP). Comparison of the isotopic signatures from these two locations suggests that the main source of nitrogen into the SCS was nitrate that entered from the WNP through the Luzon Strait. Values of \({\updelta }^{ 1 5} {\text{N}}_{{{\text{NO}}_{ 3} }}\) were generally lower in the SCS than in the WNP, and the \({\updelta }^{ 1 5} {\text{N}}_{{{\text{NO}}_{ 3} }}\) maximum observed in the SCS intermediate water was lower than the corresponding WNP maximum. This pattern is attributed to mixing within the SCS in combination with the outflow of SCS intermediate water to the WNP. A mass balance model indicates that atmospherically derived N (a combined input of new nitrogen from marine N₂ fixation and atmospheric deposition) supplied approximately 6% of the particulate nitrogen exported from the euphotic zone to the deep SCS. This supply of isotopically light nitrogen cannot, however, explain the low and downward-decreasing δ¹⁵N that has been previously observed in sinking particles of the deep SCS. We propose that an alternative explanation might be a downward-increasing ratio of isotopically light NH₄ ⁺-N to organic N due to the degradation of organic N within the sinking particles (i.e., relative enrichment of the NH₄ ⁺) and also particle incorporation of excreted ammonium from zooplankton.     

Characterizing air–sea CO2 exchange dynamics during winter in the coastal water off the Hugli-Matla estuarine system in the northern Bay of Bengal, India

The distribution of the fugacity of CO₂ ( $ f_{{{\text{CO}}_{ 2} }} $ ) and air–sea CO₂ exchange were comprehensively investigated in the outer estuary to offshore shallow water region (lying adjacent to the Sundarban mangrove forest) covering an area of ~2,000 km² in the northern Bay of Bengal during the winter. A total of ten sampling surveys were conducted between 1 December, 2011 and 21 February, 2012. Physico-chemical variables like sea surface temperature (SST), salinity, pH, total alkalinity (TAlk), dissolved inorganic carbon (DIC) and in vivo chlorophyll-a along with atmospheric variables were measured in order to study their role in controlling the CO₂ flux. Surface water $ f_{{{\text{CO}}_{ 2} }} $ ranged between 111 and 459 μatm which correlated significantly with the SST (r = 0.71, p < 0.001, n = 62). Neither DIC nor TAlk showed any linear relationship with varying salinity in the estuarine mixing zone, demonstrating the significant presence of non-carbonate alkalinity. An overall net biological control on the surface $ f_{{{\text{CO}}_{ 2} }} $ distribution was established during the study, although no significant correlation was found between chlorophyll-a and $ f_{{{\text{CO}}_{ 2} }} $ (water). The shallow water region studied was mostly under-saturated with CO₂ and acted as a sink for atmospheric CO₂. The difference between surface water and atmospheric $ f_{{{\text{CO}}_{ 2} }} $ ( $ \Updelta f_{{{\text{CO}}_{ 2} }} $ ) ranged from ?274 to 69 μatm, with an average seaward flux of ?10.5 ± 12.6 μmol m^?2 h^?1. The $ \Updelta f_{{{\text{CO}}_{ 2} }} $ and hence the air–sea CO₂ exchange was primarily regulated by the variation in sea surface $ f_{{{\text{CO}}_{ 2} }} $ , since atmospheric $ f_{{{\text{CO}}_{ 2} }} $ varied over a comparatively narrow range of 361.23–399.05 μatm.     

Application of chemical tracers to an estimate of benthic denitrification in the Okhotsk Sea

To estimate benthic denitrification in a marginal sea, we assessed the usefulness of \({\text{N}}_{2}^{*}\) , a new tracer to measure the excess nitrogen gas (N₂) using dissolved N₂ and argon (Ar) with N* in the intermediate layer (26.6–27.4σ _θ ) of the Okhotsk Sea. The examined parameters capable of affecting \({\text{N}}_{2}^{*}\) are denitrification, air injection and rapid cooling. We investigated the relative proportions of these effects on \({\text{N}}_{2}^{*}\) using multiple linear regression analysis. The best model included two examined parameters of denitrification and air injection based on the Akaike information criterion as a measure of the model fit to data. More than 80 % of \({\text{N}}_{2}^{*}\) was derived from the denitrification, followed by air injection. Denitrification over the Okhotsk Sea shelf region was estimated to be 5.6 ± 2.4 μmol kg^?1. The distribution of \({\text{N}}_{2}^{*}\) was correlated with potential temperature (θ) between 26.6 and 27.4σ _θ (r = ?0.55). Therefore, we concluded that \({\text{N}}_{2}^{*}\) and N* can act complementarily as a quasi-conservative tracer of benthic denitrification in the Okhotsk Sea. Our findings suggest that \({\text{N}}_{2}^{*}\) in combination with N* is a useful chemical tracer to estimate benthic denitrification in a marginal sea.     

Problems concerning the Directivity of Tsunami

If knowledge of our theories on the directivity of tsunamis had received worldwide attention, the following operations could have been carried out internationally just after the large earthquake of 19 September 1985 which occurred near Acapulco, Mexico. Having found the great circle, “line S” which is perpendicular to the coast around Acapulco, we could have calculated the angles between line S and line A and between line S and line D, where line A and line D are the great circle connecting Acapulco and Auckland, New Zealand and that connecting Acapulco and Duke of York Island (Chile), respectively. The resultant angles are 30?43′ and 41?49′(>68?48′/2), we could thereafter neglect the eastern half of the offshore energy flux. When we assume that the speed of trans-Pacific tsunami is 400 knots, the probability that the actual tsunami will come earlier than the calculated arrival time proves to be $$\frac{1}{{\sqrt {2\pi } }}\int_{ - {\text{ }}\infty }^{ - {\text{ }}0.689} {e^{ - t^{{2 \mathord{\left/ {\vphantom {2 2}} \right. \kern-\nulldelimiterspace} 2}} } dt = 0.2454} $$ Contact with New Zealand prior to the forecasted arrival time was essential, but the tsunami attention for the Japanese coast was unnecessary. Without such application of our directivity theories, frequent fruitless warnings will be issued for future trans-Pacific tsunamis. Quick improvements in warning procedures are required.     

Wave friction factor rediscovered

The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion (A _wb) at the top of the boundary layer. A _wb, in turn, is normally derived from linear wave theory by \fracU_\textwbT_\textw2p \frac{{{U_{\text{wb}}}{T_{\text{w}}}}}{{2\pi }} , where U _wb is the maximum water particle velocity measured at the top of the boundary layer and T _w is the wave period. However, it is shown here that A _wb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of U _wb, T _w, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549–560, (2010).     

Water exchange and material exchange through a strait due to tidal flow

The process of material transport through a strait due to tidal flow is modeled, and then the differences between various concepts of tidal exchange which have been used hitherto are pointed out using this model. In particular, the exchange of water itself and the exchange of material should be distinguished even in the case where the material of interest is carried by the water,i.e., the material and water move as one body. Further, the physical meaning of “tidal trapping” (Fischeret al., 1979) is discussed by using the model in this paper. The relationship between the exchange ratio for the water itself (r) and the phase lag (δ) of material concentration to the tidal stream in a section of the strait, which is an important factor in tidal trapping, is obtained as follows: $$\delta = \tan ^{ - 1} \left( {\tfrac{1}{r} - 1} \right)$$ Observational results at Lake Hamana (Shizuoka Pref) and at Kabira Cove (Okinawa Pref.) support the validity of the above relationship.     

Role of the beta-effect in the decay of the alongshore baroclinic jet associated with transient coastal upwelling and downwelling: Numerical experiments

A numerical study of the decay of an alongshore baroclinic jet (ABJ) formed by transient wind stress favorable for upwelling and downwelling is carried out. The study is based on the Princeton Ocean Model (POM) applied to a circular stratified basin with a constant depth. In the case of a fully developed upwelling (downwelling), the alongshore jet is subjected to baroclinic instability, and its decay is predominantly accompanied by selective formation of cyclonic (anticyclonic) mesoscale eddies. If the upwelling or downwelling is not fully developed, the necessary condition for the baroclinic instability of the ABJ in a basin with a constant depth is the presence of the β-effect. The β-effect causes separation of the ABJ from the shoreline in the eastern part of the basin and thereby stimulates baroclinic instability. As a result, mesoscale meanders and eddies can be generated in the eastern part of the basin only if the diameter of the basin D is large enough to satisfy the inequality D > $\sqrt {{{R_I f} \mathord{\left/ {\vphantom {{R_I f} \beta }} \right. \kern-0em} \beta }} $ , where R _I is the baroclinic Rossby radius, f is the Coriolis parameter, and β = df/dy.     

Distribution of glycerol dialkyl glycerol tetraethers, alkenones and polyunsaturated fatty acids in suspended particulate organic matter in the East China Sea

We investigated the spatial distribution of glycerol dialkyl glycerol tetraethers (GDGTs), alkenones, and polyunsaturated fatty acids in particulate organic matter collected at four sites along a depth transect from the continental shelf to the Okinawa Trough in the East China Sea during the spring bloom in 2008. The maximum alkenone concentration appeared in the top 25?m at all sites and the $ U_{37}^{{{\text{K}}'}} $ values were consistent with in situ water temperatures in the depth interval, suggesting that the alkenones were produced mainly in surface water. At the slope and shelf sites, GDGTs in the water column showed a concentration maximum at 74?C99?m depth, and the $ {\text{TEX}}_{86}^{\text{H}} $ agreed with in situ water temperatures, suggesting the in situ production of GDGTs in the depth interval. The low-salinity surface water above 20?m depth was characterized by low GDGT concentrations and low $ {\text{TEX}}_{86}^{\text{L}} $ -based temperatures, suggesting either the production of GDGTs in winter season or the lateral advection of GDGTs by an eastward current. At the slope and Okinawa Trough sites, TEX₈₆-based temperatures were nearly constant in the water column deeper than 300?m and corresponded to temperatures at the surface and near-surface waters rather than in situ temperatures. This observation is consistent with a hypothesis that Thaumarchaeota cells produced in surface waters are delivered to deeper water and also indicates that the residence time of suspended GDGTs in the deep-water column is large enough to mix the GDGTs produced in different seasons.     

A quasi-similarity between wind waves and solid surfaces in their roughness characteristics

A formulation for the aerodynamic roughness length of air flow over wind waves $$z_0 = \gamma {\text{ }}u_* /\sigma p$$ which was proposed by Toba (1979) and Toba and Koga (1986) from dimensional considerations with some data analysis, is shown to correspond with a formulation for irregular solid surfaces $$(z_0 /h) = a(h/l)^{1 + \beta } $$ which resulted from work by Woodinget al. (1973) and Kustas and Brutsaert (1986);u _* is the friction velocity,σ _p the spectral peak frequency of wind waves,h the mean height of the solid obstacles,l the mean distance between their crests, andα,Β, andγ are constants. This correspondence is reached by the existence of a statistical 3/2-power law and an effective dispersion relationship for wind waves. Because both approaches of parameterizingz ₀ were arrived at independently, they provide each other mutual reinforcement.     

Microcolonization mechanism of attached bacteria in a natural water-column

A mathematical model of attached bacterial dynamics based on microcolonization was devised using data obtained from a bog. Bacterial samples obtained from any natural water body can be examined by this model with the method of non-linear least squares. The model comprises three bacterial processes; i.e., (1) the attachment rate which was dependent on time after submergence by adsorption onto the substratum surface, and both (2) growth and (3) detachment rate which were dependent on the number of bacterial cells in the microcolony. The population dynamics are expressed as $$\frac{{dC_i }}{{dt}} = - g_i C_i + g_{i - 1} C_{i - 1} - b_i C_i + b_{i + 1} C_{i + 1} + a_i F_i ,$$ where suffixi denotes cell number in each microcolony,C _i is microcolony number on the substratum,F _i is bacterial clump drifting in the water column,a _i , g _i andb _i are the rate coefficients of attachment, growth and detachment. The growth rate was reciprocally proportional to the cell number in the microcolony. The detachment was shown to increase up to a maximum, and then to decrease as the number of bacterial cells increased in each microcolony.     

Wave setup and setdown generated by obliquely incident waves

An analytical theory is developed for the wave setup and setdown induced by obliquely incident waves on an impermeable swell-built beach profile. The wave setup and setdown are found to decrease as wave obliquity increases. The incorporation of wave obliquity in wave setup and setdown formulation offers the physical reality in engineering applications. The general solutions presented in this paper yield the limiting case of normal wave incidence and the result is consistent with the classical theories published. The present theory is primarily applicable to the spilling and plunging breaker across the surf zone, within which wave amplitude is assumed to be linearly related to the local water depth. Experiments were conducted in a large-scale wave basin to compare with theoretical results and especially to investigate the applicability of this assumption to the case of obliquely incident waves. The dimensionless setup versus the distance offshore within the surf zone is found to depend on wave breaking angle and the shape of the beach profile; and it has a non-zero value at the original shoreline position. This implies that the original shoreline will advance landwards, and that the extent of this movement can be related to wave angle at breaking and the beach profile under consideration. The results of the present theory are in good agreement with experimental data and field measurements available.     

Equilibrium beach profile model for perched beaches

A beach profile equilibrium model for perched beaches is presented. The model assumes that wave reflection at the seaward and leeward sides of the breakwater is the most important process that modifies Dean's equilibrium profile model for non-perched beaches. The influence of wave breaking over the submerged structure is also discussed. Several laboratory data sets are used to analyze the merit of the proposed model for describing the equilibrium condition of a perched beach. A good comparison is obtained. Results show that if the ratio between the water depth above the submerged structure, d, and the water depth at the toe of the structure, h_e, is large, d/h_e>0.5, only minor advance of the shoreline is achieved with the construction of a toe structure. A considerable advance is obtained for d/h_e less that 0.1. In these situations, however, resonant effects may result in an inefficient structure. The proposed model is used to provide an estimation for the required sand volume and the associated beach advance for the case of narrow breakwaters.     

The roughness height and drag law over the water surface based on the hypothesis of local equilibrium

A series of measurements of winds and wind-waves were carried out in wind-wave flumes. A data analysis based on the hypothesis of local equilibrium yielded a new empirical formula on the controversial quantity of roughness heightz ₀ over the water surface: , where the nondimensional roughness height is defined bygz ₀/u _* ² and the wave-wind parameterũ byω _p u _*/g, g being the gravitational acceleration,u _* the friction velocity of air,ω _p the peak frequency of wind-wave spectra. The obtained formula is compared with Charnock's (1955) and Toba's (1979) proposals; is constant in the former and inversely proportional toũ in the latter. As in Toba's, this formula immediately leads to a practically important conclusion that the drag coefficientC _d depends not merely on the usual variableU ₁₀ (wind velocity at 10m height over the water surface), but also on the surface state represented by wind-waves. An explicit expression is provided for the drag coefficient incorporating the wave-wind parameter; it covers the range ofC _d calculated from most of the previous drag formulas, by varying the wave-wind parameter.