Ivan Haigh, Matt Eliot and Chari Pattiaratchi Global influences of the 18.61 year lunar nodal cycle and 8.85 year cycle of lunar perigee on coastal flooding Ivan Haigh, Matt Eliot and Chari Pattiaratchi The School of Environmental Systems Engineering and the UWA Oceans Institute The University of Western Australia When extreme sea level events occur along low-lying, highly populated and/or developed coastlines the impacts can be devastating, including: considerable loss of life; billions of dollars worth of damage; and drastic changes to coastal landforms. As a society, we have become increasingly vulnerable to extreme high sea levels due to the rapid growth in coastal populations and the accompanied increased investment in infrastructure at the coastal zone. School of Environmental Systems Engineering

1. Introduction New Orleans, Hurricane Katrina The occurrence of major coastal floods in the last decade (i.e. those arising from hurricanes Katrina, Sidr and Nargis), have dramatically emphasized the damage that extreme sea level events are capable of, particularly when combined with the rise in coastal population. Source: http://newsmediainsider.blogspot.com/2010/08/katrina-survivor-talks-about-escaping.html

1. Introduction Observed Tide = + Mean Sea Level Astronomical Tide Extreme sea levels (exclusive of surface gravity waves) arise as a combination of three factors: mean sea level, tide and surge. Extreme sea levels are most often viewed in the context of storm surges, but the impacts of storm events in many coastal areas are strongly modulated by the tide Surge 3

1. Introduction FREMATLE 18.6 years BROOME 4.4 years Over inter-annual time-scales, variations in high tides arise as a result of the 18.61 year lunar nodal cycle and the 8.85 year cycle of lunar perigee, the latter of which influences sea level as a quasi-4.4 year cycle.

1. Introduction The aim of this study is to examine the contribution of the 18.61 year lunar nodal cycle and 8.85 year cycle of lunar perigee to high tidal levels (coastal flooding) on a global scale; A global assessment of when these tidal modulations occur allows for prediction of periods when enhanced risk of coastal flooding/inundation is likely in different coastal regions. Over inter-annual time-scales, variations in high tides arise as a result of the 18.61 year lunar nodal cycle and the 8.85 year cycle of lunar perigee, the latter of which influences sea level as a quasi-4.4 year cycle.

2. Background: A. 18.61 year lunar nodal cycle Cross-section view: 23.5° - 5° = 18.5° 23.5° 5° 23.5° + 5° = 28.5° 23.5° 5°

2. Background B. 8.85 year cycle of lunar perigee View from above: Quasi-4.4 years cycle (of perigean influence)

2. Background Tidal analysis (Matlab t-tide) performed on a year or two of tide gauge observations; Inter-annual modulations can not be independently determined from a single year of data; Handled using small adjustment factors: f (amplitude); u (angle); The effects of the lunar nodal and perigean modulations on individual tidal constituents are well understood and are routinely allowed for in tidal analyses of sea level data. Constituent f (factor) M2, N2 3.7% K2 28.6% Q1, O1 18.7% K1 11.5%

3. Methodology Egbert and Erofeeva (2002) TPXO 7.2 Global Ocean Tidal Model Best fits the Laplace Tidal Equations and T/P and Jason altimetry data using OTIS (Oregon State University Tidal Inversion Software); 8 primary and 2 long period const. on ¼ deg resolution global grid; Tidal Model Driver (TMD) Matlab toolbox Infers 16 minor const; Modulation corrections based on equilibrium tide expectations. With recent advances in global ocean tidal models, altimetry missions and assimilation methods, accurate maps of the main tidal constituents are now available on a global scale. Using these major constituents, the minor constituents that can be inferred from them and satellite modulation corrections based on equilibrium tide expectations (described above), predictions of the tide, with inter-annual tidal modulations included, can be made for locations around the world. From these tidal predictions the influence of the 18.61 year lunar nodal cycle and 8.85 year cycle of lunar perigee on high tidal levels can be examined on a global scale. This is the basis of the method used in this current study.

3. Methodology Fremantle Broome 8 cm 2 cm 4 cm 26 cm

4. Results: Range 18.6 lunar nodal year 0 – 80 cm

4. Results: Range 4.4 year cycle of lunar perigee 0 – 50 cm

4. Results: Range Form Factor 18.6 year 4.4 year Tidal Range

4. Results: Range as % of tidal range 18.6 lunar nodal year 18.6 lunar nodal year 4.4 year cycle of lunar perigee

4. Results: Dominant 18.6 year cycle dominates FF >~ 0.6 (mixed, diurnal) FF <~ 0.6 (semi-diurnal)

at expense of semi-diurnal maximise semi-diurnal 4. Results: Phase Broome Fremantle 1997 2006 2006 2008 23.5° + 5° 23.5° - 5° maximise diurnal at expense of semi-diurnal maximise semi-diurnal at expense of diurnal

4. Results: Phase 18.6 year cycle 1987, 2006, 2024 1978, 1997, 2015 FF >~ 0.6 (mixed, diurnal) FF <~ 0.6 (semi-diurnal)

5. Conclusions Paper in press: Haigh, I.D., Eliot, M., Pattiaratchi, C., in press. Global influences of the 18.61 year nodal cycle and 8.85 year cycle of lunar perigee on high tidal levels. Journal of Geophysical Research. Future work compare with measured data – GESLA (Hunter, Woodworth) data set:

6. Future Work Measured Model Brest, France Fremantle, Australia San Francisco, USA Balboa, Panama Honolulu, Hawaii

Ivan Haigh, Matt Eliot and Chari Pattiaratchi Any Questions