WSN 152 (2021) 1-14 EISSN 2392-2192
Numerical Predictions for Rising Water Levels in
the Oceans
Igor G. Zurbenko1, Amy L. Potrzeba-Macrina2,*
1University at Albany, Department of Epidemiology & Biostatistics, 1 University Place, Rensselaer, NY 12144, USA
2George Mason University, Department of Mathematical Sciences, 4400 University Dr., Fairfax, VA 22030, USA
*E-mail address: amacrina@gmu.edu
ABSTRACT
Global warming is an important and popular subject across global communities and in a wide array of literature. Global weather patterns are becoming more violent with an increase in the number of catastrophic events. The fundamental concepts of climate are strongly related to the natural freezers on planet Earth. Global warming affects Earth’s natural ice freezers. The warming climate in the Arctic and Antarctic regions are causing an increase in the melting of glaciers, which in turn generates a rise in ocean levels. The rising water levels are causing major regional problems in coastal areas and more importantly they are further accelerating global warming and extreme weather effects. This paper examines the long-term warming of the Arctic and Antarctic regions and the long-term rising water levels in the oceans, in addition to making predictions of these trends for the upcoming decades.
Keywords: Global temperature, ocean water levels, Kolmogorov-Zurbenko filters, linear / non-linear extrapolations
1. INTRODUCTION
The topics of climate change and global warming are a widely discussed in mainstream news as well as literature, including Zurbenko and Cyr (2011, 2013), Zurbenko and Luo (2012,
2015), Zurbenko and Potrzeba-Macrina (2019a, 2019b), and Potrzeba-Macrina and Zurbenko (2020), Mackintosh et al. (2017), Beckmann et al. (2019), and Siegert et al. (2019), to name a few. The human contribution to long-term temperature change is discussed by Zurbenko and Potrzeba-Macrina (2019a), who are able to separate the effects of solar influence and human contributions and show that the human contribution has been dramatically increasing over the last half a century.
A major contributor to the energy supply on Earth is solar radiation. Total solar irradiation (TSI) data is available for long periods of time. Zurbenko and Potrzeba-Macrina (2019a) prove that sunspot numbers are proportional to solar radiation and therefore can be used in research in lieu of solar radiation since sunspot numbers have been recorded for long periods of time.
Throughout the last half a century, TSI and sunspot numbers have been on the decline and have reached their lowest point in approximately 100 years. Now, TSI and sunspot numbers are increasing (Potrzeba-Macrina and Zurbenko, 2019). Potrzeba-Macrina and Zurbenko (2020) using sunspot numbers as a substitute for TS in their analysis predict significant increases in global temperatures over the next several decades. The overall total change in global temperature increase is high and positive with some regional differences exist (Zurbenko and Potrzeba-Macrina, 2019b). This change will have considerable effects on the Earth’s climate;
including dry outs, extreme weather anomalies and health effects (Zurbenko and Smith 2017;
Valachovic and Zurbenko 2014).
Picture 1. Photo of shore erosion along the Kauai coastline. (Photo credited to author 1).
Specific humidity levels have been increasing and are the result of both global warming and the increase in the total water coverage on Earth. Zurbenko and Luo (2012, 2015) analyze the anomalies of specific humidity and the atmosphere’s level of water vapor. The increase in ocean water levels is an important factor in the wide increases of specific humidity which is strongly affecting all weather anomalies and further accelerates global warming. Global warming is causing glaciers to melt, and the main geographical areas of this phenomena are the Arctic and Antarctic. This is a topic that has been predominant in recent literature, including Meinshausen et al. (2009), Xie et al. (2010), Faezeh et al. (2013), Mackintosh et al. (2017), Beckmann et al. (2019) and Siegert et al. (2019).
In this paper the authors examine the long-term temperature trends in the Arctic and Antarctic together with the rising ocean water levels. Picture 1 is an author photo that shows a giant tree that survived unharmed for approximately 100 years along the Kauai coast. However, due to a recent storm at high tide it has been washed out. The picture was taken in January 2017 several months before a major hurricane hit that area. During that major hurricane all that area was flooded and closed for sufficient time. The authors make numerical predictions of those long-term temperature trends in the Arctica and Antarctic together with the rising ocean water levels up to 30 years in advance. Those predictions are key factors of global climate changes together with extreme weather anomalies in different parts of the planet. Rising water levels could be very problematic for many coastal regions. Some low-level areas may become uninhabitable. Numerical brackets for those water level predictions are provided in this paper.
2. DATA SOURCES
The analyses in this paper use temperature data that was downloaded in April and May 2020 from the National Climatic Data Center (NCDC). For several stations in Greenland and Antarctica “Global Summaries of the Month” datasets were downloaded from https://www.ncdc.noaa.gov/cdo-web/datasets. Global temperature at 927 locations was obtained from NCDC was the Global Historical Climatology Network Monthly Version 3 (NCDC_NOAA_GHCNM_TempAVG_QCA v3) dataset.
Additionally, the authors analyze mean lower low water (MLLW) data from Wilmington, North Carolina (station ID 8658120) from the National Oceanic and Atmospheric Association’s (NOAA) Tides and Currents information (www.tidesandcurrents.noaa.gov). NOAA defines MLLW data as the average of the lower low water heights observed over the National Tidal Datum Epoch. The authors used NOAA’s water level service to download hourly MLLW data from January 1, 1969 0:00 GMT – December 31, 2019 23:00 GMT.
Sunspots numbers data was also retrieved and analyzed. The sunspots numbers data is was downloaded in August 2020 from the Sunspot Index and Long-term Solar Observations (SILSO) website (sidc.be/silson/infosnmtot).
3. KOLMOGOROV-ZURBENKO FILTERS
Data is typically comprised of several different phenomena mixed. Different natural creations are usually located in different spectral ranges. The only way to understand the data with the ability to predict it is to decompose the data by separating the different spectral ranges.
Kolmogorov-Zurbenko (KZ) filters were designed in the spectral domain but process by time domain algorithms that are available in KZA and KZFT packages in R-software (Close Zurbenko Sun 2018; Yang Zurbenko 2012). The KZ filters provide nonparametric outcomes in different scales. The separation of scales provides the opportunity to return accurate results within each scale. The filters provide nearly optimal separation of different spectral ranges (Zurbenko Smith 2017; Yang Zurbenko 2010). The algorithms are extraordinarily simple in the computational sense and easily provide the opportunity to work in space with substantial missing observations (Potrzeba-Macrina and Zurbenko, 2017).
The KZ filter is an iterated moving average that has parameters m (window size) and k (number of iterations) and is denoted KZ(m,k). The Kolmogorov-Zurbenko Fourier Transform (KZFT) is an iterated moving average of the Fourier Transform and is available in the KZFT package of R-software (Yang and Zurbenko, 2012).
Due to high resolution wavelets KZFT can reconstruct a signal that is inherent to natural data (Zurbenko Porter 1998; Neagu Zurbenko 2002; Yang Zurbenko 2010; Potrzeba-Macrina Zurbenko 2017). For signal reconstruction the KZFT filter has three parameters m (window size), k (number of iterations) and f (frequency of the signal) and is denoted by KZFT(m,k,f).
For more information regarding Kolmogorov-Zurbenko filters refer to Yang and Zurbenko (2010).
4. LONG-TERM TEMPERATURE TRENDS IN THE ARCTIC AND ANTARCTIC An essential source of Earth’s climate are the Arctic and Antarctic ice shields. The ice shields provide Earth with a natural freezer that contains millions of cubic kilometers of ice.
The ice shields permanently are growing by precipitations over the ice shields and are melting on the borders of it. The speed of the melting is certain dependent upon temperature conditions along the borders of those areas.
Temperature components are affected by seasonal fluctuations as well as oscillations in solar activity. Solar activities provide an oscillation of an approximate 11-year period (Hathaway 2015; Stephenson Clark 1978). The authors are only interested in the long-term changes above those periods; therefore, they smooth the temperature dataset using the Kolmogorov-Zurbenko filter.
The authors used several monthly minimum temperature data from the NCDC at several locations in Antarctica and one location in Greenland in addition to the average global monthly temperatures at 927 locations. The Antarctica locations include Base Orcadas (-60.333 latitude, -44.733 longitude), Base Esperanza (-63.4 latitude, -56.983 longitude), and Novolazarevskaja (-70.767 latitude, 11.8333 longitude). The Greenland location is Tasiilaq (65.5997 latitude, - 37.6331 longitude). The temperature datasets did include missing values, but the robustness of the KZ filtration handles missing values. Therefore, the authors smoothed the datasets using the KZ filter with KZ(13years, 3) (Figure 1).
The temperature in Figure 1 displays an average for four high latitude locations an annual increase of approximately 0.3℃ over the past 20 years. Linear extensions of temperature curves in those areas to 2050 provides a further increase in temperature within the range approximately 3℃ − 9℃ (Figure 2). The melting of the ice shields in these areas is inevitable, which will cause an increase of average water levels in the oceans and further increase precipitations.
Figure 1. A comparison of the long-term temperature components from locations in the Arctic and Antarctic. The three Antarctica locations are along the border of the Antarctic ice shield.
The longer fragments are from locations close to South America on the peninsula extension of Antarctica whereas the shortest fragment is from a location on the coast of Antarctica south of Africa.
Figure 2. The long-term temperature component in Antarctica (Base Orcadas) with upper and lower limit predicts through the year 2050.
The melting process can also accelerate itself. Recently the last fully intact ice shelf in the Canadian artic lost more than 40% of its area in just two days at the end of July 2020.
Together with the global temperature rise this will create dangerous weather effects and flooding. Some areas will be affected by torrential rains and floods. Nevertheless, some areas like the southwestern United States and Australia will experience dry out periods (Zurbenko and Smith, 2017).
5. RISING OCEAN LEVELS
Ocean water levels are very important in daily human life. Water levels are precisely measured in many locations. Oceanic tides are very important everywhere along shorelines and have different schedules and amplitudes at different locations. The main periodicities of the tides are 12.5 and 25 hours. These periodicities are caused by lunar gravity and precisely described in literature (Zurbenko and Potrzeba 2009, 2013; Griffiths and Peltier 2013; Marchuk and Kagan 1984).
The authors are interested in the longer periodicities of ocean tides. There are light fluctuations of an 11-year periodicity in water levels that is caused by solar activity oscillations (Figure 3). The 11-year fluctuations typically were in the range of 0.3 feet, but over the last decades the range of those fluctuations increases to 0.4 feet.
Figure 3. The smoothed scaled component KZ(2yrs,3)-KZ(11yrs,3) to select the 11-year scale oscillation in water levels at Wilmington, North Carolina.
The authors are interested in longest scales that are possible within available measurements. Since the scales are practically identical in all locations of measurements the authors selected the mean lower low water (MLLW) data from Wilmington, North Carolina, Hawaii, and Alaska, as well as mean sea level data collected at Victor Harbor, Australia. Figure 4 provides long-term increases in water levels at different regions around the globe.
They are consistently providing an increase of long-term water levels of up to ¼ of a foot in the last 20 years.
Figure 4. The change in the long-term component, KZ(11yr, 3) of water levels at four locations from January 1995 to December 2014.
Linear prediction of ocean levels through the year 2050 provide another increase in water levels of about 1 foot whereas the parabolic approximation of the long-term component of available MLLW data provides further increase of about 3 feet (Figure 5).
Global warming is causing melting ice, which int turn causes more water evaporation, which causes the greenhouse effect.
Thus, an accelerating effect in melting ice and rising water levels is easily possible. The authors regard these approximations as lower and upper bounds for the prediction of increase in ocean water levels over the next several decades.
An increase of 1 foot may cause serious problems in coastal areas, but an increase of up to 3 feet could be catastrophic for many global regions. Any increase provides an increase in water vapor levels within the atmosphere and multiple problematic extreme weather phenomena, such as torrential rains, hurricanes, and tornados (Zurbenko and Potrzeba 2013;
Zurbenko and Potrzeba-Macrina, 2019a; Zurbenko and Smith 2017; Zurbenko and Sun 2014, 2015, 2016).
Figure 5. Smoothed MLLW KZ(10 yr, 2) with upper and lower limit predictions through the year 2050.
6. 11-YEAR OSCILLATION DUE TO SOLAR ACTIVITIES
Solar activity has a strong influence on global temperatures (Potrzeba-Macrina and Zurbenko 2020, Zurbenko and Potrzeba-Macrina 2019b). Global temperatures affect the speed at which glaciers are melting and water levels are increasing in the oceans. The Sun has a standard periodicity of approximately 11 years that is perfectly visible in Figure 6.
Removal of short-term fluctuations of less than one year leave no doubt of 11-year fluctuations in water levels. The authors reproduce the 11-year component by the filter KZ(2years,3) – KZ(11years,3), by removing the short-term noisy fluctutations by KZ(2years,3) and after that removing the long-term component KZ(11years,3) from the graph displayed in Figure 3. There is a strong correlation between sunspot numbers 11-year periodic component (Figure 7) and the same scaled component of the water levels at four different locations (Figure 4). The authors call this an 11-year tide due to solar activity.
This tidal wave has less than ½ foot amplitude, but it provides clear evidence of the dependence of water levels on solar activity. This is due to the fingerprint frequency of 11 years known only from the Sun.
The distribution of this wave through different parts of the ocean, according to Figure 4 has a complicated shape due to the restrictions of continents, but everywhere it remains a stable 11-year period. Zurbenko and Potrzeba-Macrina (2019a,b) predict a long rise of solar activity soon. This will certainly affect water levels in the ocean.
Figure 6. Smoothed spectrum of daily points of MLLW KZ(8761 hours, 3) using DZ 20%.
The spectral lines correspond to periodicities of 25.7 years and 10.3 years.
Figure 7. The long-term component of sunspots numbers by KZ(11yr,3) from January 1995 – July 2020.
This together with the overall trend in water levels investigated in the preceding section brings unprecedented water levels in Earth’s oceans.
Figure 7 displays declining long-term solar activity for the past 25 years. Zurbenko and Potrzeba-Macrina (2019a) provide a prediction that the decline is over and a strong increase in solar activity is expected in the at least the next decade and perhaps longer. Similar predictions of increased solar activity are being reported in the news media (such as CNN). This strong increase in solar activity will yield further increases in the water levels of Earth’s oceans in the near future.
7. ANNUAL TIDAL WAVE
Earth orbits the Sun in an elliptical path with a period of 1 year. The authors consider that Earth is mostly a large solid object covered by a comparably “thin layer of ocean waters.” The seasonal differences between the northern and southern hemispheres and their distances to the sun impact the difference in solar gravities within those regions which in turn affects the water.
While those differences are small nevertheless within six-month time, they make an effect.
Looking at the trajectory of Earth around the sun, in our summer Earth reaches the top of its trajectory with its lowest speed. The less speed there is the more the Sun’s gravity is applicable.
The Sun’s gravitation forces accelerate Earth to the opposite side of its trajectory with its highest speed. The water closer to the Sun in the northern hemisphere will be the most vulnerable to being stripped around a solid part of Earth. As a result, the northern hemisphere accumulates more water in the mid-year summer months.
Figure 8. Smoothed spectrum of daily points of MLLW KZ(25 hours, 3) using DZ 20%.
The spectral frequency lines correspond to periodicities of 1 year and ½ year.
Uneven temperature expansions for annual differences also provide some effect on water levels. Those affects will be interrupted by the continents and provide a complicated picture.
Figure 8 leaves no doubt of the presence of annual oscillations in water levels and Figure 9 provides the annual average component for water levels in four different locations. The annual component is determined by removing from a smoothed raw data long-term component together with the 11-year component. Therefore, it is retrieved from the filter KZ(1month,3) – KZ(1year,3). The average annual component provides the highest amplitude close to 1 foot at high latitude and lowest close to the equator (Figure 9). There is a large phase shift between northern and southern hemispheres. In the southern hemisphere high tide occurs close to their summertime.
Figure 9. A comparison of the raw annual component of the mean water levels at four locations.
8. CONCLUSIONS
Water levels in the ocean are affected by multiple reasons, which include wind waves, daily tides, slowly rising average levels, 11-year oscillation of water levels and annual effects.
Separating those complications is the only way to examine their individual effects on water levels. Since they are all in different frequency ranges KZ filters are perfect to use to make the separation. All of them are affected by the solid grounds of the continents. The shape of shorelines may strongly accelerate those scales. It is very well known that the extraordinarily high Fundy Bay tides are strongly accelerated by specific shoreline. Scales longer than 11 years are counted as the long-term component. The filtering of that long-term component from the
temperature data provides an increase in temperatures around the world, which includes Arctic and Antarctic regions. These rising temperatures are causing an acceleration in the melting of glaciers. The melting water is accumulating in the oceans and causes their expansions in low- levels areas and shoreline erosions. It also affects increasing water evaporations which are further accelerating global warming and extreme weather effects. The prediction of increasing solar irradiation over the next few decades will augment those effects. Additionally, some hurricanes are frequently affecting some areas by surf surge. It is well known that damages of surf surge strongly increase during high tide. However, if this happens when total average water levels are higher, the 11-year component is at a peak and annual tide is high so damages will be incomparably stronger. The technology developed in the current paper and other references allow for the opportunity to make time-regional predictions and avoid or reduce those damages.
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