Diurnal variation in the marine wind

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Although wind varies diurnally over land, marine wind usually shows very little diurnal variation except close to the coastline, where sea breezes may be initiated affecting the daytime winds. This article shows that in certain conditions of offshore wind flow, the overland diurnal variation can influence the near surface wind strengths at quite long distances out to sea. The theoretical basis for expecting such variations is discussed, followed by a comparison of onshore and marine wind observations that provide some confirmation of the theory.

Land–sea differences

The diurnal variation of surface wind over land and its cause is well known. Land is a good insulator so that heat-gains due to insolation by day, and radiative losses by night, translate into large temperature changes at the surface. These changes then result in the formation of convective and stable atmospheric boundary layers by day and night, respectively, and these in turn lead to diurnal wind variations. The sea, however, is different. It is partly transparent so that radiative gains and losses occur over a significant depth and turbulent motions within the water conduct heat-changes over a large depth. As a result there are only small temperature changes at the water surface, and only small diurnal wind variations.

The fact that sea-surface temperatures stay fairly constant, however, results in convective heat fluxes in overlying airflows due to advective changes. Such advective effects are very much greater over sea than over land as land-surface temperatures adjust very quickly to any advective changes in the near-surface air temperature.

In certain very specific conditions, the combination of diurnal changes over land together with advective changes over sea can result in diurnal changes in the wind over sea at significant distances from the coastline. Such maritime diurnal changes are the subject of this article.

Diurnal variation over land

To explain such maritime effects, the diurnal variation over land will first be described in detail. By day, the boundary layer is often convective so that only limited wind shear takes place between the top of the boundary layer and the 10-metre level. Turbulence in the surface layer is limited by the presence of the surface itself so that a considerable wind shear exists below the 10-metre level. Because of this, the 10-metre wind speed itself is relatively high.

During the evening, the surface layers become stable over an increasing depth. It is important first to note that very little wind shear is sustainable across a shallow stable layer even if there is a large temperature difference across it. This is because a stable layer can only sustain a maximum wind shear (given by the Richardson number criterion) that is dependent on the depth of the layer as well as the (potential) temperature difference across it. So when the surface starts to cool during the evening, the 10-metre wind decreases only slightly at first, both because the surface inversion has little depth initially and also because the surface layer turbulence is already suppressed by the surface itself so that the stability due to the surface inversion has very little extra effect. With further surface cooling, the surface inversion strengthens, but far more importantly the depth of the inversion starts to increase by diffusion (Figure 1(a)). Diffusion is slow because of the stability. This allows a greater depth of wind shear above the 10-metre level and so the 10-metre wind starts to decrease significantly. After several hours, the inversion depth is great enough for the 10-metre wind to have dropped to a small fraction of its daytime value. At dawn, the surface starts to heat up until, after a couple of hours, the surface layer becomes convective. As the surface temperature continues to rise, the depth of the convective layer increases. More importantly, the temperature gradient in the inversion layer above it rapidly increases and sharpens as the inversion layer depth decreases and the inversion top rises (Figure 1(b)). The shallower inversion layer can no longer support a large wind shear so the 10-metre wind increases again, reaching near its maximum value around noon.

Figure 1.

Illustrative vertical potential temperature profiles during diurnal variations in the overland surface temperature. (a) A series of profiles during evening cooling. (b) A series of profiles during morning warming. The profiles have been generated by a numerical model.

Marine diurnal variation

Now consider the effect of an offshore wind blowing across a sea-surface that has a temperature a few degrees lower than that of the maximum attained over the land it has left. If a time of around noon is considered at first, then a sharp surface inversion is formed immediately the land air flows over the sea (Figure 2(a)) but for the reasons given earlier, this will, of itself, have very little effect on the 10-metre wind. The change in surface roughness, however, will result in an immediate increase in wind speed and this increase is constant by day and night.

Figure 2.

Illustrative vertical potential temperature profiles for an offshore flow with sea temperature 6 degC below the afternoon overland temperature. (a) Afternoon profile 800 metres offshore. (b) Afternoon profile after flow over 40 kilometres of sea. (c) Early morning profile 800 metres offshore. (d) Early morning profile after flow over 40 kilometres of sea. The profiles have been generated by a numerical model.

After a few hours, during which the layers will have moved far out to sea, the surface inversion depth will have increased sufficiently for a significant wind shear to develop above the 10-metre level (Figure 2(b)). As a result, the 10-metre wind will decrease considerably. Because of a partial inertial oscillation that may develop over the smooth sea surface, the 10-metre wind speed will not drop quite as much as it would over land. What has happened here is very similar to the development of the evening stable boundary layer over land, but it is happening by day.

Now, if a time of around midnight is considered, then a fully developed stable layer with a low surface temperature flows out over the sea. Apart from the increase due to roughness length, there is very little initial increase in the 10-metre wind. The sea-surface temperature, however, is usually higher than the nocturnal land temperature and a convective surface layer rapidly develops (Figure 2(c)). As in the case of the morning warming of the overland boundary layer, the upper inversion becomes sharper with an increased temperature gradient and reduced depth (Figure 2(d)). The shallower inversion can no longer support a large wind shear so the 10-metre wind increases, eventually becoming considerably greater than the maritime surface wind after noon. The developments here are very similar to those in the morning boundary layer over land, but it is happening by night.

Thus after the maritime flow has travelled away from the coast for a few hours, the 10-metre wind speed has developed a diurnal cycle that is almost opposite to that of the overland diurnal cycle, with a maximum by night and a minimum by day. In fact, because of the time taken for the vertical temperature profile to become modified as the flow moves offshore, the actual minimum value is during the later afternoon rather than around noon.

The changes in the vertical temperature profile described have been found to occur in a two-dimensional numerical model run (Lapworth, 2005) for the case of offshore flow. They have mostly been verified by a combination of tethered balloon profiling measurements over land and by aircraft measurements over the sea.

Observations

In order to test this theory, observations were used from lightships (Figure 3) moored at distances of about 40 kilometres off the English coastline. These were compared with observations from land stations on the adjacent coastline. Figure 4 shows the land stations and light vessels used. The maximum daytime wind at the land station was used as a reference against which the light-vessel winds on a specific day were plotted. Radiosonde observations show that the maximum daytime wind over land has a fairly linear relation with the geostrophic (600-metre) wind provided the boundary layer becomes convective at some time during the day, which is usually the case.

Figure 3.

Smith's Knoll light vessel in harbour.

Figure 4.

Map showing light vessels and land stations used in this study.

Only days on which the wind flow was directly offshore and of a similar direction at both the land station and the lightship were considered. These were split into two cases: those in which the sea-surface temperature was lower than the maximum daytime overland screen temperature and those in which it was higher. Our earlier discussion predicts that in the latter case there will be little maritime diurnal variation.

Figures 5, 6 and 7 show plots of the averaged diurnal variation in 10-metre wind speed for the three pairs of stations, both for the land sites and the corresponding lightships. The data was taken over a number of years, depending on availability.For the lightships, two curves have been plotted according as to whether the maximum land-screen temperature is higher or lower than the sea-surface temperature. It can be seen that the land sites all show a maximum wind speed around noon, while the lightships show maximum wind speeds overnight and minimum wind speeds during the afternoon when the sea-surface temperatures are lower than the maximum land-screen temperatures. When the sea-surface temperatures are higher than the maximum land-screen temperatures, however, the observable variation in wind speed is much less. The small variation observed in the latter case may be due to the fact that screen temperatures were used overland rather than surface temperatures, which were not available. Note that the length of day at these latitudes varies by about four hours throughout the year which results in a broadening of the peaks in these figures.

Figure 5.

(a) Statistical plot using 18 years of data over the period 1970–1988 of the diurnal variation of 10-metre wind speed Us scaled by the land station maximum wind Us at Smith's Knoll light vessel (516 days). The plot is shown for offshore winds with maximum air temperatures higher than sea temperatures. (b) The same plot as (a) but for the 10-metre wind speed at Gorleston. (c) The same plot as (a) but for maximum air temperatures lower than sea temperatures (148 days).

Figure 6.

(a) Statistical plot using nine years of data over the period 1994–2003 of the diurnal variation of 14-metre wind speed scaled by the land station maximum wind at Greenwich light vessel (68 days). The plot is shown for offshore winds with maximum air temperatures higher than sea temperatures. (b) The same plot as (a) but for the 10-metre wind speed at Herstmonceux. (c) The same plot as (a) but for maximum air temperatures lower than sea temperatures (60 days).

Figure 7.

(a) Statistical plot using 13 years of data over the period 1991–2004 of the diurnal variation of 16-metre wind speed scaled by the land station maximum wind at Channel light vessel (39 days). The plot is shown for offshore winds with maximum air temperatures higher than sea temperatures. (b) The same plot as (a) but for the 10-metre wind speed at Dunkeswell. (c) The same plot as (a) but for maximum air temperatures lower than sea temperatures (59 days).

At all stations the marine diurnal effect might be expected to occur most commonly in summer when both the land–sea temperature difference and the overland temperature range are at their greatest. Smith's Knoll light vessel might be expected to have a fairly low frequency of occurrence as the corresponding overland range is small. It has a relatively high value of 8% of the time, however, fairly evenly distributed throughout the year. This is because the offshore wind direction is often southwesterly, which is the prevailing wind direction for much of the year in Britain, although not in spring when northeasterly winds tend to prevail. For the two light vessels in the English Channel, the most suitable wind direction is much less frequent, although the overland temperature range is greater, so that at the Greenwich light vessel the effect occurs 2% of the time and peaks strongly in summer. At the Channel light vessel there is also a strong summer peak but the effect occurs only 1% of the time, presumably because of the much greater distance from the English coast. For these two stations, however, the overall occurrence frequency will also be affected by the frequency of southerly winds from the French coast. No measurements could be made for winds from this direction as data from a suitable reference land station were not readily available.

Conclusion

There are two points of significance for sailors in these results. If the coastal prevailing wind is offshore and the sea-surface temperature is lower than the overland screen temperature, then lighter winds will probably be found 20–40 kilometres offshore rather than near the coast in the afternoon. Overnight, the lighter winds will be near the coast. The second point is that, in these conditions, there will be wind shear in the surface layer at some distance offshore during the afternoon so that the wind strength and direction may vary significantly over the height of the mast. Such variations will affect the trim of the sails.

Ancillary