Diurnal Tides Data

[Melissa Russian]

Thepurpose of tide analysis is to determine the amplitudeand phase (the so-called tidal harmonic constants) of theindividual cosine waves, each of which represents a tidal constituentidentified by its period in mean solar hours or, alternately, its speedin degrees per mean solar hour (speed = 360/T where T = period). Finding thetidal harmonic constants at a place allows one to predict tides at that place.Tidal constituent amplitudes are usually given in feet or meters, and phase isusually expressed in degrees. Putting these parts together, the partial tidecorresponding to a single tidal constituent is represented by the followingequation,

In addition to overtides, other tides called compoundtides also arise in shallow water. A compound tide (e.g., MS4)results from the shallow-water interaction of its two parent waves (M2and S2). There are many more shallow-water tidal constituents butthe four listed above do a good job of reconstructing the tidal asymmetries andother fine-scaled behavior seen at most locations.

The spring-neap cycle is very apparent at Ras Tanura, a bigoil terminal on the west side of the Persian Gulf. The tidal type there issemidiurnal with two highs and two lows each day. But the Persian Gulf (ArabianGulf to the Saudi Arabs) is a strange place in terms of tidal dynamics. Thetide wave entering the Straits of Hormuz generate two large rotary waves forthe semidiurnal tide and a single large rotary wave for the diurnal tide insidethe Gulf. As you might expect, the amphidromic points for these waves arespaced far apart. To see the consequence of this arrangement on tidal type,look at the next graphic for Safaniya, a coastal town less than two hundredkilometers to the northwest of Ras Tanura.

A quick glance at the residual curve for Safaniya shows thatit is almost identical to the one at Ras Tanura. Thus we see that two tidestations with completely different tidal types can experience the same meteorologicaltide. In fact, the oscillations shown in the green curve coincided with a Shamal,a desert wind that can reach 60 miles per hour and blow for several days,causing periodic water level oscillations in the Northern Persian Gulf basinthat last for many more days, like the ringing of a bell.

Note that the range of the astronomical tide at Safaniya issmaller than that at Ras Tanura while the meteorological tide range is aboutthe same at both stations. This is reflected in the percent of total varianceaccounted for by the tide model, which is only 76 percent (r2 =0.76) at Safaniya as opposed to 90 percent at Ras Tanura. Clearly themeteorological tide has to be taken into account before evaluating the successof the astronomical tide model!

Finally, a place with mixed tides can produce some strangelooking curves as the tide transitions from semidiurnal to mixed to diurnal.The following series of daily tides from Safaniya provide a good example:

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If the Earth were a perfect sphere without large continents, all areas on the planet would experience two equally proportioned high and low tides every lunar day. The large continents on the planet, however, block the westward passage of the tidal bulges as the Earth rotates. Unable to move freely around the globe, these tides establish complex patterns within each ocean basin that often differ greatly from tidal patterns of adjacent ocean basins or other regions of the same ocean basin (Sumich, J.L., 1996).

Some areas, such as the Gulf of Mexico, have only one high and one low tide each day. This is called a diurnal tide. The U.S. West Coast tends to have mixed semidiurnal tides, whereas a semidiurnal pattern is more typical of the East Coast (Sumich, J.L., 1996; Thurman, H.V., 1994; Ross, D.A., 1995).

Semidiurnal tide cycle (upper right). An area has a semidiurnal tidal cycle if it experiences two high and two low tides of approximately equal size every lunar day. Many areas on the eastern coast of North America experience these tidal cycles.

Mixed Semidiurnal tide cycle (lower middle). An area has a mixed semidiurnal tidal cycle if it experiences two high and two low tides of different size every lunar day. Many areas on the western coast of North America experience these tidal cycles.

The mesosphere and lower thermosphere (MLT) is the transition region between the lower atmosphere and the ionosphere/thermosphere. As such, the MLT is pierced by a myriad of waves with different periods and scales. Among them, solar tides are prominent and are essential contributors to the large-scale dynamics and energy budget of the MLT (e.g., Smith 2012).

Solar tides have periods of 24, 12, 8 h and other sub-harmonics of a solar day. They are mainly excited by the latent heat release and the absorption of near-infrared radiation by the water vapor in the troposphere and the absorption of UV radiation by the ozone in the stratosphere (e.g., Forbes 1995; Hagan and Forbes 2003). Tides can be further classified into migrating and non-migrating. Migrating tides are sun-synchronous, that is, they propagate westward following the apparent movement of the Sun. Non-migrating tides are not sun-synchronous; they can be eastward- or westward-propagating or stationary. These non-migrating tidal components have different sources, such as longitudinal variation in the diurnal heating and non-linear interactions between planetary waves and migrating tides (e.g., Hagan 1996). A typical notation is [period][direction of phase propagation][wavenumber]; for instance, DW1 refers to the diurnal (24-h) tide, westward-propagating with wavenumber \(k=1\). As the tides propagate vertically towards the upper atmosphere, they may be modulated by, e.g., planetary waves (e.g., Laštovička 2006). On the other hand, lunar tides (waves with periods of 12.42 h) have also been reported at low latitudes with relatively weak but significant amplitudes (e.g., Sandford and Mitchell 2007).

This paper is structured as follows. The used data sets are described in "Dataset" Section. The methodology implemented to post-process the data sets is presented in "Methods" Section. In "Results" Section, the observed and simulated results are presented, which are later discussed in "Discussion" Section. Finally, the concluding remarks are given in "Concluding Remarks" Section.

The observational data set used in this work comprises zonal and meridional winds with resolutions of 1-h, and 2-km between October 2019 and January 2023. These winds were estimated every 30 min and 1 km (sampling) between 80 and 100 km of altitude, using the homogeneous method (e.g., Conte et al. 2021). They were estimated from measurements made by the multistatic meteor radar SIMONe (Spread-spectrum Interferometric Multistatic meteor radar Observing Network) deployed around the Jicamarca Radio Observatory (11.95\(^\circ\)S, 76.87\(^\circ\)W SIMONe Jicamarca) (Chau et al. 2021). This system has a horizontal coverage of approximately 400 km in diameter.

The least squares method allows for the selection and fitting of specific harmonic components. Furthermore, this method has the advantage of not being affected by data gaps, i.e., the time series is not required to be equally spaced.

The least squares method described in the previous section was implemented with bins of 21 days shifted by 1 day at each given altitude. This was done to both the observed and simulated data, with the purpose of estimating the mean wind and the total amplitudes of the tides with periods 8, 12, 12.42, and 24 h as well as the Q2DW with a period of 48 h. The size of the fitting window was selected equal to 21 days to separate the contributions from the 12-h solar tide and the lunar tide of period 12.42 h. In this way, any contamination of the 12-h solar tide by the 12.42-h lunar tide is reduced significantly (Chau et al. 2015).

Regarding the mean meridional wind, it is mainly northward-directed from November to January for altitudes between 80 and 100 km. For the rest of the months, this wind component is southward-directed, except above 92 km from July to October, where it blows northward.

The Q2DW reaches maximum intensity during the local summer months (mainly in January). The meridional component reaches a second intensity peak from March 15 until April 15 between 86 and 96 km. These two peaks show higher inter-annual amplitude variability (10 m/s) above 90 km.

For the meridional 12-h tide, there are signatures between February and November, mainly above 85 km. The main peak occurs from April 15 to May 10 between 85 and 100 km. This peak coincides with that of the 24-h tide (mentioned above). For the zonal 12-h tide, signatures are observed from October until January and in June, mainly above 90 km, with one maximum in October between 95 and 100 km and another one in January between 90 and 100 km. At these maxima, the zonal component is twice the meridional one. Inter-annual amplitude variability is found above 93 km for both the zonal (5 m/s) and meridional (6 m/s) components.

The observations show that the Q2DW has its maximum in January, while the model shows maxima during the local summer months (January), but also during the local winter months (beginning of June and July).

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