Coastal Inundation, Overtopping of Swells and Sea-level Rise

This section describes the methods and results for inundation, overtopping of swells and sea-level rise at Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP.

Modeling the wave cycle of the Big Island of Hawai‘i

It is important to keep in mind that the annually recurring maximum wave (swell) heights (Figure 2 or Table 1) represent open ocean, deep-water wave heights that are unaffected by the presence of the other islands. Because seven of the main eight Hawaiian Islands lie to the northwest of the Big Island, significant blockage (i.e., shadowing) and reduction in nearshore wave heights occurs. Therefore adequate modeling of the wave transformation from deep-water to the nearshore, particularly to capture the reduction in wave height due to island blockage, is important. The ultimate goal of the wave transformation model is to find the maximum annually recurring wave heights in the nearshore at the study sites. These wave heights will provide the boundary conditions (initial assumptions of wave heights) for runup modeling. Without island blockage, the maximum annual wave height would occur from the northwest and the north, somewhere between 300° and 60° as found simply from the annual wave heights (Figure 2, Table 1). However, using this information directly would overestimate the annual wave heights near the national park sites. Instead, we use the information of the open annually recurring maximum wave heights found in Figure 2 or Table 1, as the required boundary conditions (starting point) for nearshore wave transformation modeling.

To model the wave transformation from deep-water to nearshore we use the SWAN (Simulating WAves Nearshore) model, which is widely used within the oceanographic and wave forecasting community. Details on the development and validation of the SWAN model are reported in Booij et al. (1999) and Ris et al. (1999).

To find the maximum annually recurring wave height and direction near the study sites we ran 85 model simulations of the wave field for the Big Island (spatial resolution of 1 km), each of which is nested in the model for the main eight Hawaiian Islands (spatial resolution of 3.5 km). Nesting brings open ocean wave height data to the nearshore environment. The 85 simulations were run in 2.5° directional increments for the south to northeast window (clockwise) from 195° to 45° with maximum annual significant wave heights interpolated from values of the wave heights found in Table 1. Four of the 85 simulations representing different annual wave heights from particular directions are shown in Figure 6.

Figure 6. Four of 85 SWAN model simulations each with representative annual maximum significant wave height from a particular direction. Ho is the deep water wave height (m) and Tp is the wave period (s). Case A: South swell, Ho=2.3 m Tp=16 s Dir=200°. Case B: Northwest swell, Ho=4.1 m Tp=14 s Dir=290°. Case C: North swell, Ho=5.8 m Tp=16 s Dir=340°. Case D: Northeast swell, Ho=6 m Tp=16 s Dir=45°.

Figure 6 . Four of 85 SWAN model simulations each with representative annual maximum significant wave height from a particular direction. Ho is the deep water wave height (m) and Tp is the wave period (s). Case A: South swell, Ho=2.3 m Tp=16 s Dir=200°. Case B: Northwest swell, Ho=4.1 m Tp=14 s Dir=290°. Case C: North swell, Ho=5.8 m Tp=16 s Dir=340°. Case D: Northeast swell, Ho=6 m Tp=16 s Dir=45°.

The goal of these 85 different simulations is to find the maximum annually recurring wave height as a function of wave direction at the national park sites. Plotting the annual significant wave height as a function of wave angle for virtual buoys near the national park sites, we find a maximum annual significant height of 3.3 m from about 290° (Figure 7), for both Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP. The similarity between the wave heights for both Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP allow us to treat the recurrence relationships in a uniform manner rather than individually.

Figure 7. The maximum annual significant wave height for the Big Island national park sites as a function of wave direction (Pu‘ukoholā Heiau NHS = red, Kaloko-Honokōhau NHP = blue). The blue and red ‘x’s on the map of the wave field around the Big Island indicate the virtual buoy (model) locations. The maximum wave height case occurs during west northwest swell where the wave direction is about 290o. There is a small secondary peak associated with north wrap when the wave direction approach can fit in the gap between Maui and the Big Island. Also indicated on the figure is the degree of island blockage, which is the difference between the dashed line and the solid blue and red lines.

Figure 7 . The maximum annual significant wave height for the Big Island national park sites as a function of wave direction (Pu‘ukoholā Heiau NHS = red, Kaloko-Honokōhau NHP = blue). The blue and red 'x's on the map of the wave field around the Big Island indicate the virtual buoy (model) locations. The maximum wave height case occurs during west northwest swell where the wave direction is about 290°. There is a small secondary peak associated with north wrap when the wave direction approach can fit in the gap between Maui and the Big Island. Also indicated on the figure is the degree of island blockage, which is the difference between the dashed line and the solid blue and red lines.

Coastal locations may receive large swell, or lie in the shadow of nearby islands and thus have reduced exposure to seasonal waves. The most important result from the directional annual wave height modeling is to characterize the island blockage and find the direction of maximum swell impact for the study sites. This occurs for the very westerly segment, 282°-305° of the North Pacific swell window shown in Figure 2. Knowing the swell window that results in the largest wave heights close to the national park sites, we can return to an extreme value analysis on the open-ocean buoy data (similar to the approach outlined in Vitousek & Fletcher 2008) to determine the relationship between the open swell deep-water wave height and the return period for the 282°-305° window (Figure 8).

Figure 8. The relationship between the open-swell significant wave height and the return period determined from Generalized Extreme Value Analysis (GEV) for the 282o-305o window.

Figure 8 . The relationship between the open-swell significant wave height and the return period determined from Generalized Extreme Value Analysis (GEV) for the 282°-305° window.

Again, this analysis is relevant to deep-water open-ocean wave heights and thus it is necessary to transform these wave heights into nearshore wave heights near the national park sites using the SWAN model (model settings in Appendix A). The output from this model will give the relationship between significant wave height and return period; however this model will also include the effects of island blockage. The effective island blockage, or reduction in wave height, from this particular window (282°-305°) is about 20%. For more northerly directions, the reduction can increase to around 75% (Figure 7). The relevant relationship for the maximum recurring wave heights at the national park sites is given in Figure 9.

Figure 9. The relationship between the significant wave height and the return period at Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP (green) determined from Generalized Extreme Value Analysis (GEV) for the 282o-305o window used as a boundary condition for a wave transformation model from deep water to the national park sites. The x’s are the individual cases modeled. The GEV model is compared with the recurrence relationship for open ocean swell given in Figure 8 (blue). The difference between the blue line and the green line is the effect of island blockage.

Figure 9 . The relationship between the significant wave height and the return period at Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP (green) determined from Generalized Extreme Value Analysis (GEV) for the 282°-305° window used as a boundary condition for a wave transformation model from deep water to the national park sites. The x's are the individual cases modeled. The GEV model is compared with the recurrence relationship for open ocean swell given in Figure 8 (blue). The difference between the blue line and the green line is the effect of island blockage.

The maximum recurring wave heights are then translated to maximum recurring runup elevations at the national park sites using empirical equations following the approach of Vitousek et al. (2008). These empirical equations are best-fit relationships determined from field observations of wave height and runup, and are widely used in engineering computation for lack of a more robust physical or process-based approach. Our approach uses a recently developed equation for the 2% exceedance runup derived from 10 datasets primarily from the continental US, which we refer to as the Stockdon equation (Stockdon et al. 2006):

,

which similarly gives runup as a function of beach slope (foreshore slope), deep-water wave height(), and deep-water wavelength(). We use the Stockdon formula because it is complete: it formulates runup as the sum of setup, and swash , due to both incident and infragravity energy. Wave setup is the increase in nearshore sea level due to the presence of waves, and it can be as large as 10-20% of the significant wave height. Swash is the wave action on the dry beach itself; it is composed of an incident part (at frequencies very close to that of the offshore waves) and an infragravity part (at frequencies much lower than the offshore waves).

The infragravity component can be as large as 10-20% of the significant wave height, while depending on the beach slope and breaking conditions the incident swash component can range from nothing (on fringing reefs or beaches with intense breaking) to larger than the offshore wave heights (on steep beaches with little or no breaking). Using the Stockdon equation, we find the following relationship between the maximum runup elevations and return period at the national park sites (Figure 10). The results for the wave and runup characteristics that exert the greatest influence on Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP are summarized in Table 3.

Figure 10. The relationship between the runup elevation and the return period at Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP (red) determined from the Stockdon equation.  The runup relationship is compared with the recurrence relationship for open ocean swell (blue) given in Figure 8 and for local swell (green) given in Figure 9. As is typical, the runup elevations are much smaller than the wave heights as there is significant energy dissipation due to breaking.

Figure 10 . The relationship between the runup elevation and the return period at Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP (red) determined from the Stockdon equation.   The runup relationship is compared with the recurrence relationship for open ocean swell (blue) given in Figure 8 and for local swell (green) given in Figure 9 . As is typical, the runup elevations are much smaller than the wave heights as there is significant energy dissipation due to breaking.

Table 3 . Wave and runup summary of Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP.

Return period
[years]

Open
Wave heights [m]

Local
Wave heights [m]

Stockdon
Runup [m]

1

4.1

3.3

1.7

5

5.6

4.5

2.1

10

6.1

4.9

2.2

25

6.9

5.4

2.4

50

7.4

5.8

2.5

The Stockdon runup values (Table 3) may help explain the formation of perched beaches at Kaloko-Honokōhau NHP. Approximately 60% of the beaches at Kaloko-Honokōhau NHP are perched beaches (Hapke et al. 2005). The origins of perched beaches are not well understood, but are thought to be controlled by wave runup during large wave events and the elevation of the slope of the underlying rock platform (Hapke et al. 2005, Richmond et al. 2008). The perched beach behind Kaloko Point is at an elevation ranging from 1 to 3 m and is well within the Stockdon runup values.

The runup predicted by the Stockdon equation may not be the best way of predicting the runup at these particular locations. The equation was developed from datasets of mildly sloping barred beaches without fringing reefs, which are significantly different from many beaches in Hawai‘i. Both Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP have reefs (see Appendix B) that cause waves to break offshore, which will significantly reduce the incident swell energy, incident swash magnitude and overall runup compared to the predictions from the Stockdon equation.

To make better predictions of the runup we make simulations of nearshore wave fields using SWAN. The important features of the nearshore simulations we are looking for are the nearshore wave height, wavelength and wave setup. SWAN can accurately predict these features, although it cannot predict runup. To improve our predictions of runup we use the setup predicted from SWAN and add it to the incident swash component of the Stockdon equation with the nearshore wave heights in place of the deep-water wave heights, and include an infragravity term that comes from the offshore wave height rather than the nearshore wave height. Our modified equation for the 2% runup looks like the following:

where is the foreshore slope, which is given by LIDAR topography and bathymetry data,  is the nearshore significant wave height,  is the offshore (deep-water) significant wave height, and is the nearshore wave length.

The nearshore significant wave height and wavelength for different return periods are modeled using SWAN and forced with deep-water boundary conditions determined from the analysis in Figure 9 and are summarized in Table 4.

Table 4 . Boundary conditions of nearshore wave simulations using SWAN. Tr is the return period, Hs is the significant wave height, Tp is the wave period and Dir is direction.

Case

Tr [yrs]

Hs [m]

Tp [s]

Dir [o]

A

1

3.3

14

285

B

5

4.5

14.5

285

C

10

4.9

15

285

D

25

5.4

15.5

285

E

50

5.8

16

285

The modeling results from the five different cases are shown in the following figures. The wave (height, length, and setup) fields for Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP are shown in Appendix B.

Based on the results of the nearshore wave height, wavelength, and wave setup fields we can determine the regions that are protected from exposure to large offshore wave heights. These protected regions naturally happen to be the reef fronted areas. At Pu‘ukoholā Heiau NHS there is a significant offshore reef providing a barrier to the entire park. Kaloko-Honokōhau NHP has reef fronting the majority of the park, but it is not significant. Only the beach fronting the ‘Aimakapā Fishpond has a significant offshore reef (Gibbs et al. 2006). It is clear from the nearshore wave field that the reef structure and bathymetry (shown in Appendix B) offshore of Pu‘ukoholā Heiau NHS is very efficient at dissipating wave energy. The offshore reef structure at Pu‘ukoholā Heiau NHS, classified as “spur and groove”, is clearly identified from the characteristic fingers or “spurs” of corals extending offshore separated by pockets or “grooves” of sand (Cochran et al. 2006). The spur and groove structure at Pu‘ukoholā Heiau NHS is a function of the underlying lava flow with very little accreted reef. In addition to being a very rough hydraulic structure the spurs and grooves cause localized divergence and convergence, which directly or due to the breaking (respectively) lead to energy dissipation. The reef at Kaloko-Honokōhau NHP is much flatter and has less structure than Pu‘ukoholā Heiau NHS, which results in a much smoother wave field, less dissipation and larger wave heights nearshore. Because there is so much dissipation, and thus wave height and setup variability at Pu‘ukoholā Heiau NHS, we must consider the regions of the park separately in our runup and overtopping hazard analysis. At Kaloko-Honokōhau NHP we must consider the beach fronting the ‘Aimakapā Fishpond separately, in contrast to the rest of the shoreline, which we expect to be exposed to runup levels consistent with those computed from the deep-water wave heights (Table 3, Figure 10). Summaries of the wave fields and total runup at Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP are given in Table 5 and Table 6.

Table 5 . Nearshore wave and runup modeling summaries for Pu‘ukoholā Heiau NHS. Tr is the return period and Hs is the significant wave height.

Pu‘ukoholā Heiau Park

beach slope ~ 1/14

 

 

Case

Tr [years]

Hs [m]

wave length [m]

Setup [m]

Total runup [m]

A

1

2

100

0.24

1.20

B

5

2

100

0.27

1.43

C

10

2

100

0.32

1.55

D

25

2

100

0.35

1.66

E

50

2

100

0.4

1.77

 

 

 

 

 

 

Pelekane Beach

beach slope ~ 1/150

 

 

Case

Tr [years]

Hs [m]

wave length [m]

Setup [m]

Total runup [m]

A

1

1

100

0.28

0.85

B

5

1

100

0.32

1.09

C

10

1

100

0.35

1.19

D

25

1

100

0.4

1.32

E

50

1

100

0.45

1.43

 

 

 

 

 

 

Spencer Beach

beach slope ~ 1/50

 

 

Case

Tr [years]

Hs [m]

wave length [m]

Setup [m]

Total runup [m]

A

1

2

100

0.25

0.91

B

5

2

100

0.3

1.16

C

10

2

100

0.32

1.25

D

25

2

100

0.35

1.36

E

50

2

100

0.4

1.47

Note: The uncertainties of the values reported in these tables come from many sources including buoy error, model error, and empirical equation error. By far the largest source of error is the estimation of runup based on empirical equations, which can be as large as 50%. The best uncertainty estimate for the final runup value would be ± 0.3 - 0.5 m.

Table 6 . Nearshore wave and runup modeling summaries for Kaloko-Honokōhau NHP.

Beach fronting ‘Aimakapā Fishpond

beach slope ~ 1/7

 

 

Case

Tr [years]

Hs [m]

wave length [m]

Setup [m]

Total runup [m]

A

1

1.6

80

0.4

1.61

B

5

1.8

85

0.5

1.97

C

10

2

90

0.55

2.15

D

25

2.2

95

0.6

2.34

E

50

2.5

100

0.65

2.54

Note: The uncertainties of the values reported in these tables come from many sources including buoy error, model error, and empirical equation error. By far the largest source of error is the estimation of runup based on empirical equations, which can be as large as 50%. The best uncertainty estimate for the final runup value would be ± 0.3 - 0.5 m.

Table 7 . Overtopping frequencies and the influence of sea-level rise (SLR) for historic structures and beach profiles at Kaloko-Honokōhau NHP.

Elevation 1 = 1.5 m : Kaloko Seawall and sandy beach north of ‘Aimakapā Fishpond

SLR

Overtop freq.
[hrs/yr] - Present

Overtop freq.
[hrs/yr] - w/ SLR

Increase
[hrs/yr]

Relative Increase
[factor]

0.25

44

155

111

3.5

0.5

44

540

496

12.3

0.75

44

1660

1616

37.7

1

44

3950

3906

89.8

Elevation 2 = 2 m : Sandy beach between ‘Aimakapā Fishpond and ‘Ai‘ōpio Fishtrap

SLR

Overtop freq.
[hrs/yr] - Present

Overtop freq.
[hrs/yr] - w/ SLR

Increase
[hrs/yr]

Relative Increase
[factor]

0.25

3.5

12

8.5

3.4

0.5

3.5

43

39.5

12.3

0.75

3.5

156

152.5

44.6

1

3.5

542

538.5

154.9

Elevation 3 = 2.25 m : Honokōhau Beach fronting ‘Aimakapā Fishpond

SLR

Overtop freq.
[hrs/yr] - Present

Overtop freq.
[hrs/yr] - w/ SLR

Increase
[hrs/yr]

Relative Increase
[factor]

0.25

1

3.5

2.5

3.5

0.5

1

12.126

11.126

12.1

0.75

1

43

42

43.0

1

1

156

155

156.0

Storlazzi & Presto (2005) and Presto et al. (2007) collected oceanographic data (e.g., directional wave data, water depth, current speed, current direction, etc.) at Kaloko-Honokōhau NHP. The largest significant wave height that they measured during their winter deployments was 2.26 m. Our one-year modeled significant wave height calculations range between 1 m and 2 m, which is in agreement with the collected wave data.

The values computed for the beach fronting ‘Aimakapā Fishpond ( Table 6) are very similar to the nominal runup values given in Table 3. This similarity is likely the result of the steep slopes on this portion of the beach, which lead to larger runup values.

Overtopping and Inundation Hazard

Based on the runup values for the different portions of both parks we can now create inundation maps showing the landward extent of the runup or the wash of the waves for a given return period. For particular areas of interest including the kuapā (seawall) at Kaloko Fishpond and the beach the ‘Aimakapā Fishpond we will use a different method with estimates of the number hours per year that a structure is overtopped by waves. This method is more informative when the structure is overtopped much more frequently than once per year. The inundation maps based on the total runup levels computed in Table 5 and Table 6 are given in Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, and Figure 16.

Figure 11. Inundation maps of Pu‘ukoholā Heiau NHS and a portion of the Ala Kahakai National Historic Trail under sea-level rise scenarios.

Figure 11 . Inundation maps of Pu‘ukoholā Heiau NHS and a portion of the Ala Kahakai National Historic Trail under sea-level rise scenarios.

Figure 12. Inundation maps of the northern beach at Pelekane Bay, Pu‘ukoholā Heiau NHS under sea-level rise scenarios.

Figure 12 . Inundation maps of the northern beach at Pelekane Bay, Pu‘ukoholā Heiau NHS under sea-level rise scenarios.

Figure 13. Inundation maps of Spencer Beach Park under sea-level rise scenarios.

Figure 13 . Inundation maps of Spencer Beach Park under sea-level rise scenarios.

Figure 14. Inundation maps of portions of Kaloko-Honokōhau NHP under sea-level rise scenarios.

Figure 14 . Inundation maps of portions of Kaloko-Honokōhau NHP under sea-level rise scenarios.

Figure 15. Inundation maps of the Honokōhau Beach fronting the ‘Aimakapā Fishpond under sea-level rise scenarios.

Figure 15 . Inundation maps of the Honokōhau Beach fronting the ‘Aimakapā Fishpond under sea-level rise scenarios.

Figure 16. Inundation maps of Maliu Point at ‘Ai‘ōpio in the southern portion of Kaloko-Honokōhau NHP under sea-level rise scenarios.

Figure 16 . Inundation maps of Maliu Point at ‘Ai‘ōpio in the southern portion of Kaloko-Honokōhau NHP under sea-level rise scenarios.

The inundation contours of the Pu‘ukoholā Heiau NHS shoreline from the beach at Pelekane Bay to the northern portion by Spencer Park are shown in Figure 11. This shoreline should be fairly resilient to large wave attack. It is rocky and steeply sloping and thus reaches a fairly high elevation very quickly. The contours of inundation do not extend very far inland at present sea level or under future sea-level scenarios. The slight impacts in the inundation map for the region in Figure 11 shows inundation of the Ala Kahakai National Historic Trail (NHT). The extent of the flooding of the trail does increase with sea-level rise. Particularly, the southern portions of Ala Kahakai NHT may begin to experience wave spray and overwash under future sea-level conditions of 0.5-1 m and greater. Ala Kahakai NHT at Pelekane appears to experience wave spray and overwash on a yearly basis; there is also clearly erosion and root exposure of the sand seaward of the coastal trail as shown in Figure 17. The erosion of the bank fronting the trail should be isolated to the trail near Pelekane beach. Rocky outcrops with vegetation and small amounts of topsoil above the seasonal wave wash are located in front of majority of the shoreline trail at Pu‘ukoholā Heiau NHS . This section of shoreline should be resistant to erosion and to future effects of sea-level rise.

Figure 17 . The shoreline trail, the Ala Kahakai NHT, at Pelekane Bay experiences erosion and root exposure of the sand seaward of the trail.

Figure 17 . The shoreline trail, the Ala Kahakai NHT, at Pelekane Bay experiences erosion and root exposure of the sand seaward of the trail.

The inundation contours of the beach at Pelekane Bay are shown in Figure 12. The annual inundation contour at present sea level extends to the base of the tree line of the beach. Several inundation lines at Pelekane Beach can be seen as evidenced by the multiple debris lines on the beach (Figure 18). Under future sea-level scenarios of 0.25-0.5 m, these runup contours will extend further inland under the trees. This runup will lead to significant erosion and tree loss. Eventually, through erosion and sea-level rise above 0.5 m, the beach will be mostly submerged at high tide. Under sea-level rise conditions above 1 m the beach in its present state will be constantly submerged. Additionally, under sea-level conditions of 0.5-1 m the archeological sites at Pelekane will be exposed to wave overwash and spray. Under sea-level conditions exceeding 1 m, the sites may be submerged under high tide.

Figure 18 . The debris lines on Pelekane Beach are evidence of high wave wash.

Figure 18 . The debris lines on Pelekane Beach are evidence of high wave wash.

The inundation contours of Spencer Beach Park are shown in Figure 13. The 5-year return period inundation contour at present sea level extends to the vegetation line and small rock wall backing the beach. Several inundation lines at Spencer Beach can be seen as evidenced by the multiple debris lines on the beach (Figure 19). Under future sea-level scenarios of 0.25-0.5 m, the overwash of the small rock wall will occur for greater than 5-10 yr. return period events. Under sea-level rise conditions above 1 m, the majority of the beach in its present state will be submerged or eroded close to the small rock wall barrier. The barrier itself will be overtopped several times per year during large swell events under this scenario.

Figure 19 . The debris lines on Spencer Beach are evidence of high wave wash.

Figure 19 . The debris lines on Spencer Beach are evidence of high wave wash.

The inundation contours of the Kaloko-Honokōhau NHP shoreline are shown in Figure 14. Kaloko-Honokōhau NHP is flat, low-lying, and exposed to significantly larger open swell than Pu‘ukoholā Heiau NHS, due to the lack of shallow reef fronting a majority of the park. As a result of such characteristics the park will likely be exposed to significant impact from sea-level rise scenarios in the form of increased erosion, deterioration of coastal historic sites and estuary and marsh ecosystem change. Under future sea-level scenarios of 0.25-0.5 m, the overwash of the shoreline trail (a portion of the Ala Kahakai NHT) will increase in frequency. However, the impacts of this increase in overwash frequency should be fairly minimal for the rocky stretch of shoreline between the two fishponds due to the strong dissipation of wave and runup bore energy by basaltic lava outcrops along this portion of shoreline. Only under sea-level scenarios of 0.5 – 1+ m, which submerge many of the once exposed rocky outcrops, do significant impacts occur. Figure 14 shows that the northern portion of the ‘Aimakapā Fishpond wetland will be constantly submerged under 0.5 – 1 m of sea-level rise. Currently there are low-lying areas in the park supporting thick cover of saltwater tolerant species, the alien pickleweed, Batis maritima, and the native Sesuvium portulacastrum, that regularly become partially submerged during spring tides (Figure 20).

Figure 20 . ‘Aimakapā Fishpond wetland on the shoreline at Kaloko-Honokōhau NHP that partially flooded during a spring high tide.

Figure 20 . ‘Aimakapā Fishpond wetland on the shoreline at Kaloko-Honokōhau NHP that partially flooded during a spring high tide.

When such low areas become permanently flooded through island subsidence, ecosystem and habitat changes occur. In Figure 20, a large rocky outcrop extends seaward from the shoreline. This rocky outcrop is now submerged and the vegetated areas that may have once existed are now submerged in shallow water. Several ecosystem and habitat changes such as this will occur with regular island subsidence and under scenarios of 0.5-1 m. For instance, water depth will increase over shallow reef areas, intertidal zones, and coastal wetlands.

Figure 21 . Flooding of low-lying lands vegetated with saltwater tolerant species at Kaloko-Honokōhau NHP.

Figure 21 . Flooding of low-lying lands vegetated with saltwater tolerant species at Kaloko-Honokōhau NHP.

The inundation contours of the Honokōhau Beach fronting the ‘Aimakapā Fishpond shoreline are shown in Figure 15. This beach is the barrier between ocean and the fishpond/wetland, and the protection provided by this barrier is responsible for the existence of the low salinity (~12 PSU) fishpond habitat. Sections of this beach are partially overtopped more than once per year as evidenced by the debris lines shown in Figure 22. Under future sea-level scenarios of 0.25-0.5 m, the overwash of the dune will increase slightly in frequency. The impacts of this increase in overwash frequency should be fairly minimal initially and lead to slightly increased erosion. Under considerable sea-level scenarios (0.5 – 1+ m), the entire beach (barrier) will be fully overtopped several times per year. This could potentially lead to significant erosion and breaching of the sand barrier where the berm is permanently broken and water flows between the pond and ocean. A breaching event may increase salinity levels and lower nutrient levels. Significant increases in salinity of the fishpond may impact breeding habitat for the endangered Hawaiian stilt Himantopus mexicanus knudseni) and Hawaiian coot (Fulica alai) .

Figure 22 . The debris lines on Honokōhau Beach fronting the ‘Aimakapā Fishpond are evidence of high-wave wash and partial overtopping of the dune/sand berm.

Figure 22 . The debris lines on Honokōhau Beach fronting the ‘Aimakapā Fishpond are evidence of high-wave wash and partial overtopping of the dune/sand berm.

The inundation contours of Maliu Point of Kaloko-Honokōhau NHP at the northern side of the Honokōhau Small Boat Harbor entrance are shown in Figure 16. Inundation contours for inside ‘Ai‘ōpio were not done because a data gap in the elevation model resulted in poorly resolved nearshore bathymetry at this location. The Maliu Point region contains many important cultural sites. The base of Pu‘uoina Heiau facing ‘Ai‘ōpio Fishtrap is at sea-level during spring high tide (Figure 23). These portions of Pu‘uoina Heiau however are only exposed to extremely small swell, as it is sheltered by Maliu Point, and northern side of ‘Ai‘ōpio Fishtrap. Regardless of swell exposure, the Heiau, standing approximately 2-3 m in elevation, will be partially submerged under future sea levels. However, lack of swell exposure suggests slight potential deterioration to the structure. Monitoring the Heiau during maximum annual high tide will help determine the rate of deterioration. Monitoring should increase in frequency as sea level rises.

Figure 23 . The base of Pu‘uoina Heiau at sea level during spring tides.

Figure 23 . The base of Pu‘uoina Heiau at sea level during spring tides.

The potential for direct swell exposure comes from the west, although the exposure and impacts also seem to be minimal. Under future sea-level scenarios of 0.25-0.5 m the overwash of the point will increase in extent inland but the overwash will most likely not reach the Heiau as anything but residual spray. Under sea-level scenarios of 0.5 – 1+ m inland extent of the overwash may begin to impact the westward side of the Heiau, although the impacts do not seem severe or frequent enough to undermine the Heiau. Nonetheless, undermining of the Heiau may be possible and should be carefully monitored.

Joint Probability Model of Tide and Runup

A few of the historic sites at Kaloko-Honokōhau NHP are already overtopped several times per year, which makes it unfeasible to assess their overtopping hazard using the analysis performed with inundation maps. Instead we consider and evaluate runup risk in terms of overtopping events with frequencies of several hours per year as opposed to a single event per year. With frequent swell events, tidal fluctuation has a much greater influence on the occurrence of overtopping, and extreme water levels. For Pu‘ukoholā Heiau NHS, the inundation map analysis is sufficient as most of the important coastal features of the park lie outside the 1-year inundation zone.

The idea behind joint probability models is that both tides and runup contribute to the total water level on a beach. Thus combining the individual frequency (or rather probability) distributions for both tides and runup into a joint probability model, will provide a better estimate than either alone. A typical joint probability distribution,, gives the probability that the runup,, is a particular level,, and the tide, , is a particular level,:

A more useful form of the joint probability distribution gives the probability of the sum of runup and tide, . This distribution is achieved through a convolution of the individual probability distribution functions (PDF) of runup and tides.

where the  is the operator that represents convolution. Figure 24 shows how the total water level distribution,, is constructed from individual PDFs of tides, waves and runup.

Figure 24 . Joint probability model of tide and runup: smooth PDFs of tide (part A) and wave height (part B) are constructed from empirical PDFs. The wave height PDF is translated into a runup PDF (part C). The total water level PDF is then constructed as the convolution of the tide and runup PDFs (part D).

Figure 24 . Joint probability model of tide and runup: smooth PDFs of tide (part A) and wave height (part B) are constructed from empirical PDFs. The wave height PDF is translated into a runup PDF (part C). The total water level PDF is then constructed as the convolution of the tide and runup PDFs (part D).

Empirical PDFs of the tidal and wave height datasets are constructed individually from the observed data. Smooth probability distributions are fit to the empirical PDFs and used as marginals of joint distributions, Figure 24 (A, B). The wave height dataset is then translated into runup using empirical equations Figure 24(C). Then a numerical convolution is performed on the tide and runup PDFs to give a total water level PDF Figure 24(D). The PDFs shown in Figure 24 can be written in terms of exceedance probability or hours per year an expected overtopping elevation is reached or exceeded. Figure 25 shows the comparison of the exceedance probability models for runup alone and for tide and runup.

Figure 25 . Exceedance curves for runup only, a combination of tide and runup, and for a combination of tide, runup and sea-level rise (SLR). Vertical differences (lines of constant elevation) between curves represent the increase in frequency of one curve vs. the other. Horizontal changes (lines of constant frequency) represent the increase in severity. If a curve is translated on the x-axis, the amount that it is translated represents the scenario of future sea-level rise.

Figure 25 . Exceedance curves for runup only, a combination of tide and runup, and for a combination of tide, runup and sea-level rise (SLR). Vertical differences (lines of constant elevation) between curves represent the increase in frequency of one curve vs. the other. Horizontal changes (lines of constant frequency) represent the increase in severity. If a curve is translated on the x-axis, the amount that it is translated represents the scenario of future sea-level rise.

Figure 25 also shows the exceedance distribution for a combination of tide, runup, and sea-level rise. The key to interpreting this figure, and the influence of tide and sea-level rise on overtopping levels and frequency, is noticing the horizontal and vertical distances between the exceedance curves. For example, in comparing the exceedance curves from the runup only and the combined tide and runup curve, we see that including the tides in the exceedance probability models decreases the frequency of the low overtopping elevations and increases the frequency of the large overtopping elevations. The influence of sea-level rise, which is the equivalent of translating the exceedance distribution horizontally on Figure 25 (vertically in real life), increases the frequency of overtopping at all levels. Figure 26 shows the increase in frequency of overtopping (relative to present sea level) vs. elevation for the sea-level rise scenarios under consideration.

Figure 26 . The increase in frequency of overtopping vs. elevation for the sea-level rise (SLR) scenarios of +0.25, +0.5, +0.75, and +1.0 m. Elevation 1 is at 1.5 m, Elevation 2 is at 2 m, and Elevation  3 is at 2.25 m.

Figure 26 . The increase in frequency of overtopping vs. elevation for the sea-level rise (SLR) scenarios of +0.25, +0.5, +0.75, and +1.0 m. Elevation 1 is at 1.5 m, Elevation 2 is at 2 m, and Elevation 3 is at 2.25 m.

It is clear from Figure 25 and Figure 26 that sea-level rise increases the frequency of overtopping at all levels, however this increase is small for long return-period events. The elevations where the most significant increase in frequency occurs are the peaks of Figure 26. The location, corresponding to elevation, of the peak increases with sea-level rise. An effect of this feature, shown in Figure 26, is that impacts to fixed structures do not increase linearly; they accelerate. If we consider fixed elevations (the dashed lines shown in Figure 26), which correspond to elevations of historic sites at Kaloko-Honokōhau NHP, we can determine the increase in frequency of overtopping at these particular locations (Table 7).

In summary, Kaloko Seawall and the sandy beach north of ‘Aimakapā Fishpond incur the largest risk of overtopping and deterioration from wave impacts. These impacts occur because they are at the lowest elevation and will be inundated each year with increasing duration because of the combined increase of sea-level rise, high tide, and large waves. Presently, Kaloko Seawall is impacted by overwash and wave spray during small to moderate swell and high tides (Figure 27). During large swell and under scenarios of sea-level rise, the wave overwash will become full–wave overtopping where the wave bore will run across the entire length of the seawall and create much greater damage to the seawall. Catastrophic failure and undermining of the seawall may be possible and should be carefully monitored. The sandy beach at Honokōhau Beach (‘Aimakapā Fishpond to ‘Ai‘ōpio Fishtrap) at higher elevation (greater that 2 m elevation) should be relatively resilient against overtopping impacts until sea-level rise scenarios greater than +0.5 m become reality.

Figure 27 . Kaloko Seawall overwash on a moderate south swell at high tide.

Figure 27 . Kaloko Seawall overwash on a moderate south swell at high tide.