On the Variability of Charleston South Carolina Winds, Atmospheric Temperatures, Water Levels, Waves and Precipitation

Atmospheric winds, air temperatures, water levels, precipitation and oceanic waves in the Charleston South Carolina (SC) coastal zone are evaluated for their intrinsic, internal variability over temporal scales ranging from hours to multi-decades. The purpose of this study was to bring together a plethora of atmospheric and coastal ocean state variable data in a specific locale, to assess temporal variabilities and possible relationships between variables. The ques-tions addressed relate to the concepts of weather and climate. Data comprise the basis of this study. The overall distributions of atmospheric and coastal oceanic state variable variability, including wind speed, direction and kinematic distributions and state variable amplitudes over a variety of time scales are assessed. Annual variability is shown to be highly variable from year to year, making arithmetic means mathematically tractable but physically meaningless. Employing empirical and statistical methodologies, data analyses indicate the same number of intrinsic, internal modes of temporal variability in atmospheric temperatures, coastal wind and coastal water level time series, ranging from hours to days to weeks to seasons, sub-seasons, annual, mul-ti-year, decades, and centennial time scales. This finding demonstrates that the atmosphere and coastal ocean in a southeastern U.S. coastal city are cha-racterized by a set of similar frequency and amplitude modulated phenomena. Kinematic hodograph descriptors of atmospheric winds reveal coherent rotating and rectilinear particle motions. A mathematical statistics-based wind to wave-to-wave algorithm is developed and applied to offshore marine buoy data to create an hour-by-hour forecast capability from 1 to 24 hours; with confidence levels put forward. This affects a different approach to the conventional deterministic model forecasting of waves.


Introduction
The atmospheric weather to sub-seasonal variability in southern climates is very difficult to predict, as southern U.S. states are in highly convective environments most of the year. Interactive couplings of land, ocean and atmospheric boundary layers complicate coastal zone weather forecasting, particularly of winds and precipitation. This is also true of oceanic coastal water levels and wave fields in southern environs [1]. The conventional perspective is that the system is highly chaotic and unpredictable. Extending weather forecasts to seasonal to sub-seasonal forecasts are also seemingly problematic. In this study, we investigate state variable atmospheric and oceanic time series of air temperature, winds and water level data at a specific locale, Charleston South Carolina, to evaluate coherent structures or the lack thereof in the relative atmospheric temperatures and coastal sea level fields. Empirical [2] [3] [4] and statistical [5] [6] methodologies are employed on the data sets, which contain highly nonlinear and non-stationary data. This is a data-based study to reveal what weather-to-climate phenomena are present at a locale in the southeastern USA.

Materials
Data employed in this study are from the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Information (NCEI) archives (https://www.ncei.noaa.gov/).

Results
From Figure 1, the question arises: are there naturally occurring phenomena which display these 19 internal, intrinsic modes of variability? To review: 1) at the high frequency end of the spectrum, in the atmospheric, the hourly data, from shorter periods of hours to days, reveal the presence of thermals, fronts, squalls, thunderstorms, diurnal variability, mesoscale events, high and low pressure systems, mid-latitude cyclones, tropical cyclones; 2) extending to planetary waves the order of a month; 3) the Madden-Julian Oscillation of ~2 months; 4) on to 3 and 6 month seasons; 5) annual and inter-annual; 6) multi-year g) 10 -12 year ; 7) 21 -23 year Solar Cycles; 8) the 60 -65 year Meridional Circulation Cycle; and 9) the ~140 year Global Thermohaline Cycle. Cycles (1) and (9) affect the North Atlantic Ocean Basin scale wind-fields such as the North Atlantic Oscillation (NAO). Next, we consider kinematical descriptors of the wind-field.
In Figure 2, we see the water level hourly time series and EEMD IMFs for Charleston SC (Top of the Panel is the 73 year hourly time series) ranging from 0 meters (m) to 4 m. It is of note that the tidal range at Charleston is generally less than 2.5 m but one event in 1990 upped the overall range record and we chose not to clip the data point. There are 18 oscillatory EEMD IMF modes and the 19 th gravest mode, the trend.  Mode 19 is the 73-year (record length) trend and shows a water level rise of 0.027 m or 0.365 cm/yr. We note that IMF 10 is the "annual" mode and is relatively stable with +/− amplitudes of less than 15 cm. However, in the annually averaged plot (Figure 3(a)) there is a large jump of 25 cm, which occurs in the 1940's-1950. The question is, where is this jump reflected in Figure 4? The answer is, in the lower frequency, IMFs of 13 -18, all of which are in a quasi-decade long upward swing in amplitude. Figure 3 is the time series of yearly average hourly water levels for Charleston. As seen, one to two year differences of up to 25 cm of annual averages are evident. During the 1920s and the mid-1930s there was an apparent relative low in the North Atlantic Ocean Basin. These decadal to multi-decadal relative drops and rises in the time series display high amplitude, +/−5 cm to +/−20 cm, 1 to 2-year variations. A yearly average, by definition, contains all of the internal EEMD-IMFs of variability for that particular year.  On an hourly basis, water levels at Charleston not only reflect the astronomical tides but the alongshore component of the wind. If one averages the hourly alongshore components of the winds and water levels at Charleston, then the 60-day plot shown in Figure 4 results. Basically when the alongshore component of the wind blows towards the northeast, then water level drops at the coast and when the alongshore component winds blows down the coast to the southwest, water level rises at the coast. There is the caveat of an 8-hour lag in the non-tidal response, as first reported in [5]. If the winds blow with the coast to the left (right) coastal sea level will fall (rise). This is a mechanical response and carries through from hours to days to weeks to months. Figure 5 demonstrates the tight coupling between the alongshore winds and water levels at Charleston. A moving correlation [6] between the two monthly averaged time series over a 62-year period ( Figure 5) shows that the coupling is very tight. Figure 6(a) and Figure 6(b) reveal the axis orientations, the primary directions of particle motions for different bandwidths, the stability of and repeatability of the motions, and the coherency of the horizontally polarized + u (135˚ east of north), + v (45˚ east of north) components of motion of the entire 2003 time series of hourly wind data. In this decomposition, we employ the u, v directions from the harvested NCEI data sets. In 6a the horizontal axis extends from 0.3 cycles/hour to 1.142 (10 −5 ) cy/hr (3 hours to 1 year) and Figure 6(b) extends from 0.04 cy/hr to 1.142 (10 −5 ) cy/hr (25 hours to 1 year) thereby stretching the axis and making it more readable. We added color in Figure 6(a) for visual relief. However, there are caveats in considering a 12-month period decomposition Figure 5. Upper Panel, alongshore wind speeds (positive is towards the northeast, negative is towards the southwest). Middle Panel, water level rises (upwards) and falls (downwards) at Charleston. Lower Panel, is the moving correlation coefficient, locked in at -0.6, between coastal alongshore winds and water levels at Charleston. International Journal of Geosciences   Recall that these bands sit within the broader band of the IO out to 2 days, which occupies some 30% of the total KED of the wind-field at Charleston. Within the CFS, the particle motions during the summer are very coherent and stable, thus repeatable from day to day, are counterclockwise rotating about elongated ellipses nominally aligned approximately perpendicular to the coastline. However, this is not the situation during the winter months of December-February where the CFS displays low stability and low coherence in u, v particle motions. While the CFS exists, it is intermittent, with incoherent unstable motions. In Figure 8(a) and Figure 8  in 1998-99. As is evident, the CFS is very coherent in the alongshore direction and can penetrate great distances both onshore and offshore (not shown). International Journal of Geosciences The IO is weak to non-existent during the winter period in the Charleston wind-field. It is of note that [9] found that winter cold fronts that pass through the southeastern U.S., and as they do, they excite inertial currents in the coastal ocean from the surface downward throughout the entire water column. That study presented observational current meter data collected offshore of Charleston, band-passed the data to focus on the inertial period and found a robust downward propagating IO signal. The study also included the solution to a closed form numerical model that theoretically confirmed the observations. The study determined that fast-moving atmospheric winter cold fronts, moving from west to east or from land to offshore, impulsively force the coastal ocean at the surface, which responds by propagating inertial waves from the surface downward throughout the water column. That study was the first of its kind at that time and was a pioneering effort.
In Figure 9 the hodograph descriptor plots of u, v particle motions of Charleston atmospheric winds during the summer and winter periods are presented for the entire 3-month periods of observations. The axis orientation, stability High Pressure system present in the SE during the late spring, summer and early fall. In Figure 9(b) (right panel), the winter-time meso-synoptic scale particle motions tend to be relatively unstable, non-repeatable, rectilinear, so straight-line back and forth, aligned between 40˚ and 60˚ east of north, so along the coastline.
These are associated with the passages of wintertime low-pressure storm systems accompanied by drops in atmospheric temperatures, so EEMD-IMFs 5, 6.
In Figure 10 can drop significant amounts of rain in short periods of time and thus render the term "mean" in precipitation to be a mathematical artifact and thus physically meaningless, in non-arithmetic terms.
Next we present wind and wave BWO plots (Figure 11(a) and Figure 11(b)) respectively, and their spectral density analogues (Figure 12(a) and Figure   12(b), respectively. This approach was used previously in [10].
The annual distributions of wind speeds and the wave amplitude distributions are in good agreement with each other. However, it is clear that wave amplitudes are not only a reflection of the local generation of waves ("sea") but also carry the arrival of waves which have been generated elsewhere ("swell") and which have propagated into the area of the buoy and thus contribute to the overall wave amplitude measurements. Curiously, the spectral distributions of the wind speeds (Figure 12(a)) and that of the wave amplitudes (Figure 12(b)) appear to be lognormal in the winds versus exponential in the waves. The reasons for this are unknown and this could be a universal finding, as the literature contains no reference to these results and thus these may be original findings. Momentum inputs from atmospheric winds non-linearly transfer into wave momenta and sea and swell likely coalesce non-linearly. and W is wind speed. We plot the forecasted relationships in Figure 13(a). The hourly R 2 "goodness" of the forecast [7] from 1 to 24 hours forward is shown in Figure 13(b). The red dots employ past waves only to predict waves while the blue dots result from winds and prior waves. The forecasts are quite good for about 10 hours ahead and updating them every hour would yield a statistically solid forecast capability. We have tested this transfer function on NDBC buoys in North Atlantic and North Pacific Ocean Basin and Great Lakes waters and it works uniformly well. That implies a reliable data based forecast of wave amplitudes out to 10 hours at all NDBC sites and could be implemented as a NOAA tool. This tool could be of great benefit to the boating and fishing communities.

Discussion and Conclusions
We show that atmospheric temperature, wind and sea-level variability at Char- in general and at a specific location <https://public.wmo.int/en> as: 1) "The state of the atmosphere at a given time and location. Weather is driven by a diverse set of naturally occurring phenomena, especially air pressure, temperature, and moisture differences between one place and another, most of which occur in the troposphere"; and 2) "Climate in a narrow sense is usually defined as the "average weather," or more rigorously, as the statistical description in terms of the mean and variability of relevant quantities over a period of time ranging from months to thousands or millions of years. The classical period is 30 years, as defined by the World Meteorological Organization (WMO). These quantities are most often surface variables such as temperature, precipitation, and wind. Climate in a wider sense is the state, including a statistical description, of the climate system". In our decompositions of coastal atmospheric temperatures, winds and precipitation and coastal sea level, we have uncovered hourly to daily to weekly to seasonal to annual to multi-annual to decadal to multi-decadal well-defined internal, intrinsic frequency and amplitude modulated variability. This is an important finding in our opinion.
Using Charleston as a surrogate, we propose that the terms weather, seasonal and sub-seasonal variability, and climate variability, both in the Charleston atmosphere and coastal ocean are all distinctly separate harmonics, with well-defined frequency and amplitude modulated banded peaks across a spectrum of multi-scaled phenomena. Weather resides at the high frequency end of the spectrum and climate is at the low frequency end of the spectrum. Seasonal and sub-seasonal variability are everything in between. The phenomena are distinct but interactively coupled and collectively they run the gamut from what we commonly refer to as weather to climate riding atop record length trends. In final summary, we have addressed and answered Bothe's question [11] of "when does weather become climate". Our answer is that weather and climate are distinct in the overall continuum of weather to climate.