Drag and Bulk Transfer Coefficients Over Water Surfaces in Light Winds

Abstract

The drag coefficient $(C_{D})$, experimentally determined from observed wind speed and surface stress, has been reported to increase in the low wind-speed range ($<$3 m s$^{-1}$) as wind speed becomes smaller. However, until now, the exact causes for its occurrence have not been determined. Here, possible causes for increased $C_{D}$ values in near-calm conditions are examined using high quality datasets selected from three-year continuous measurements obtained from the centre of Lake Kasumigaura, the second largest lake in Japan. Based on our analysis, suggested causes including (i) measurement errors, (ii) lake currents, (iii) capillary waves, (iv) the possibility of a measurement height within the interfacial/transition sublayer, and (v) a possible mismatch in the representative time scale used for mean and covariance averaging, are not considered major factors. The use of vector-averaged, instead of scalar-averaged, wind speeds and the presence of waves only partially explain the increase in $C_{D}$ under light winds. A small increase in turbulent kinetic energy due to buoyant production at low wind speeds is identified as the likely major cause for this increase in $C_{D}$ in the unstable atmosphere dominant over inland water surfaces.

Appendices

Appendix 1: Lake Kasumigaura: Its Topographical and Climatological Characteristics

Figure 7 provides a map of Lake Kasumigaura and the surrounding area. Lake Kasumigaura mainly consists of Nishiura $(172\,\hbox {km}^{2})$, smaller water bodies [(Kitaura $(36\,\hbox {km}^{2})$ and Sotonasakaura $(6\,\hbox {km}^{2})$], and connecting rivers. The outlet of the lake is located approximately 15 km from the Pacific Ocean and is connected to the ocean through the Tone River. Approximately 30 km to the north-west of the lake is Mt. Tsukuba (877 m), the headwater region of the Kasumigaura watershed.

Figure 8 provides a histogram of the temperature difference between the water surface and the atmosphere during the three-year observation period. Unstable conditions clearly dominate in the region. Figure 9 provides two examples of diurnal meteorological variables, and the radiation and energy balance observed on two typical sunny days during summer and winter. Monthly changes for general climatic data as well as radiation and energy balance were reported in Sugita et al. (2014). In general, sunny weather dominates during the winter and summer periods, while spring and autumn are characterized by alternate sunny and cloudy conditions.

Fig. 7

A map showing the topography surrounding Lake Kasumigaura

Fig. 8

Histograms showing the distribution of the temperature difference between the water surface $(T_{s})$ and the atmosphere at $z= 3.72$ m ($T_{a}$)

Fig. 9

Time changes for: a wind speed (U), water temperature $(T_{w})$ at $z=-1.0$ m, water surface temperature $(T_{s})$, and air temperature $(T_{a})$ at $z= 3.72$ m. b The radiation balance, where $S_{u},S_{d},L_{u},L_{d}$, and $R_{n}$ represent upward shortwave radiation, downward shortwave radiation, upward longwave radiation, downward longwave radiation, and net radiation, respectively. c Energy balance for the winter (15 January 2008) and summer (15 August 2008), where the storage term $Q =R_{n}$–$H -L_{e}E$. JST Japan Standard Time

Appendix 2: Koshin Observatory

Fig. 10

A schematic figure showing instrumentation on and around the Koshin Observatory

Fig. 11

A panoramic view from the turbulence sensors at 9.8 m located above the water surface

Figure 10 provides a schematic view of the instruments at the Koshin Observatory that provided the data used in our study. Figure 11 provides a panoramic view from the turbulence sensors located 9.8 m above the water surface.