Modeling Normal and Extreme Wave Conditions in Callao Bay,

Peru using Reanalysis Data

Rafael Pimentel

, Emanuel Guzman

and Carmela Ramos

Facultad y Escuela de Ingeniería Civil, Universidad Peruana de Ciencias Aplicadas, Av. Prolongación Primavera 2390,

Santiago de Surco, Lima, Peru

Keywords: Numerical Wave Modelling, Callao Bay.

Abstract: Numerical simulations of wave conditions in Callao bay in normal and extreme conditions were carried out

to characterize the wave dynamics in the bay. Bathymetry data from the navigation charts to represent bottom

depth were used. Waves in deep waters from numerical reanalysis were calibrated with satellite data that have

allowed define scenarios of wave propagation to shallow water in normal and extreme conditions. Model

results were compared with in situ wave data obtaining good approximation between modeling and observed

waves. Results indicates that waves coming from Southwest and South-Southwest, which is the most

predominant waves in deep waters, due to the diffraction effects caused by San Lorenzo Island generate two

areas with different wave height conditions, in this way in the area affected by diffraction wave reach height

between 0.5 to 1m, while area unaffected by diffraction effects wave reach heigh between 2 to 5m. Waves

coming from Northwest has more influence in the bay, due to diffraction effects are neglected and in general

terms all the bay increase the wave height around to 2 to 5m.

1 INTRODUCTION

The study and knowledge of waves in coastal areas

are important due to the impacts that can occur in

them, such as coastal flooding and the erosion and

sedimentation processes in coastlines. Some

numerical Simulation Investigations performed

Along the North Coast of the United States projected

an increase in wave height (Erikson et.al, 2015),

which may have an impact on the increase in sea level

on flooded shores (Ruggiero, 2013). Numerical

simulations of coastal flooding carried out in

California and other coastal areas of the USA indicate

that there would be a loss of 150 billion dollars due to

coastal inundation by waves an sea level (Barnard

et.al, 2019), Gainza et.al 2018 applied a numerical

modeling of tidal and wave factors to predict the

advance of the sea in the territory of Gold Coast,

Australia.

The study area is located in central part of Peru in

the Constitutional Province of Callao (Figure 1), and

currently is the third most populated province in Peru

https://orcid.org/0000-0002-4155-3563

https://orcid.org/0000-0001-8381-4509

https://orcid.org/0000-0002-4269-2944

with an annual growth population rate of 1.3%, (INEI,

2018).

Figure 1: Location of the study area.

Likewise, the study area is considered as a tourist

place due to its beaches like Chucuito, and Cantolao

beaches, gastronomy, and architecture like Real Felipe

Castle. Another important aspect is that Callao Port,

Pimentel, R., Guzman, E. and Ramos, C.

Modeling Normal and Extreme Wave Conditions in Callao Bay, Peru using Reanalysis Data.

DOI: 10.5220/0010458901950202

In Proceedings of the 7th International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM 2021), pages 195-202

ISBN: 978-989-758-503-6

195

which is the most important Peruvian port and carries

out industrial trade activities (Guzman et al, 2020).

In some seasons, especially in summer (January

February and March), Callao bay is affected by

irregular or unusual wave dynamics, for example in

2015, the bay was affected by irregular wave events

that affect the coast and alert to population, due to the

probability of flooding (Lainez, 2015). Similar

situation occurred in 2016, in which wave attack was

so aggressive that it could drag large stones to the

squares (Figure 2) (Perú21, 2016).

Figure 2: Flooding due to waves in the Callao bay. Source:

Peru21, 2016.

The last event similar to the events of 2015 and

2016 occurred in January 2011, when there was a rise

in the tide and anomalous waves coming from the

Northwest (Figure 3), causing serious damage to

infrastructures, flooding and again putting in danger

to the population, because the force of the waves was

so great that they knocked down in Plaza Grau

(Figure 4) and dragged a large amount of stones,

likewise, the waves caused damage to a museum that

was below ground level.

Although Callao Bay has many coastal

structures such as protection walls and breakwaters of

1.3 km long to prevent the waves from exceeding and

reaching the population, these were not enough to

stop the advance of the waves. Therefore, analyzing

the conditions of normal and extreme waves is of

great importance, since depending on the

characteristics of the waves, it could flood the coastal

strip and damage nearby infrastructures and even

against the life of those who live in the area.

Figure 3: Aggressive waves coming from the northwest.

Source: The photograph was taken by the authors in

January 8, 2021.

Figure 4: Collapse of the walls of Plaza Grau and stones

washed away by the waves. Source: The photograph was

taken by the authors in January 24, 2021.

2 METHODOLOGY

2.1 Data Used

To make numerical simulation oceanographic data

were used from global databases and in situ data.

Bathymetric data were used from available

navigation charts for Callao Bay, sea level data

available from University Hawaii Sea Level Center

(UHSLC) (Cadwell et al, 2015) has been used, which

collects the sea level data from tide-gauge stations in

the world and for our case, data from Callao station

recorded from 1970 to 2019 was used. In the case of

waves in deep waters, the wave reanalysis data from

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the NOAA (National Oceanic Atmospheric

Administration) from 1979 to 2019 with 3 hours of

temporal resolution. These data were complemented

with satellite data for a point located on 78°W and

12.5°S. Data has also been collected in shallow

waters off the Callao bay at a depth of 10m (Figure

5), to validate the results obtained in the numerical

wave modeling.

Figure 5: Location of wave data collection in shallow water.

2.2 Wave Climate in Deep Waters

Wave reanalysis data in deep waters have been

compared with the satellite data to calibrate numerical

reanalysis. The uncalibrated reanalysis data shows

good trend and correlation between the wave height

of the model and the satellite (Figure 6 and 7)

obtaining acceptable statistical indicators between the

data of the uncalibrated model and satellite. (Table 1).

When model was calibrated, the indicators regarding

the data observed by the satellite improve

significantly (Table 1).

Figure 6: Time series of wave height comparison between

Waves reanalysis and Satellite data at location 78°W,

12.5°S.

Figure 7: Waves satellite data and wave reanalysis

dispersion at point 78°W, 12.5°S.

Table 1: Wave model calibration.

Indices

Uncalibrated

model

Calibrated

model

BIAS 0.4732 0.1732

RMSE 0.5423 0.3164

SI 0.2934 0.1712

IOA 0.7268 0.907

With the calibrated deep water model, the general

characteristics in deep water are established, and

wave height (Figure 8) and wave period (Figure 9),

observing that there is a predominant swell from the

southwest with wave height between 2 to 3m,

reaching maximum heights of 4m (Figure 8) and

predominant periods of 12 to 14s, with maximum

periods of 22s (Figure 9).

Figure 8: wave height rose in deep waters (78°W, 12.5°S).

Modeling Normal and Extreme Wave Conditions in Callao Bay, Peru using Reanalysis Data

197

Figure 9: wave period rose in deep waters (78°W, 12.5°S).

After calibrating the model in deep waters, a table

has been prepared with the main cases of wave

propagation (Table 2), where the average, 90

percentile and maximum are shown in each wave

direction.

Table 2: Mean regime cases for each wave direction in deep

waters.

Case

Dir

(m)

(s)

Case

Dir

(m)

(s)

SSE

2.9 7.7 13

WSW

2 14.6

2 3.7 8.7 14 2.4 16.5

3 4.9 9.9 15 3.8 20.2

2.5 10 16

1.9 15.2

5 3.3 13.2 17 2.4 16.7

6 4.9 20 18 3.4 20.3

SSW

2.4 13.9 19

WNW

1.9 16.3

8 3.3 13.2 20 2.4 18.7

9 5.3 23.2 21 3.3 21.9

2.2 14.4 22

1.9 17.6

11 2.9 16.9 23 2.3 20.2

12 4.8 23.5 24 2.8 24.9

The extreme regimes consist in establish the most

unusual wave cases that have occurred in deep water

close to study area (Kim & Suh, 2018). The

LogNormal and Gumbell criteria will be used (Frihy

et al, 2010) to calculate wave height over 10, 30 and

50-year return period (Figure 10 and Table 3). Table

3 shows in general terms that wave coming from SW

and SSW have the greatest heights comparing with

other directions.

Figure 10: Extreme wave height regime in deep waters

(78°W, 12.5°S).

Table 3: Extreme regime cases obtained in deep waters.

Return

Period

ears

)

Case

Dir

(m)

(s)

Case

Dir

(m)

(s)

10 1

SSE

4.3 8.7 13

WSW

3.2 16.5

30 2 4.7 8.7 14 3.5 16.5

50 3 5.2 8.7 15 3.7 16.5

10 4

4.4 13.2 16

3.0 16.8

30 5 4.9 13.2 17 3.3 16.8

50 6 5.1 13.2 18 3.4 16.8

10 7

SSW

4.9 13.2 19

WNW

2.9 18.7

30 8 5.3 13.2 20 3.2 18.7

50 9 5.5 13.2 21 3.3 18.7

10 10

4.6 16.9 22

2.5 20.2

30 11 5.0 16.9 23 2.7 20.2

50 12 5.1 16.9 24 2.9 20.2

3 SEA LEVEL

Data from UHSLC sea level were grouped in 5

decades to calculated mean sea level (MSL) over each

decade (Table 4) and shows an oscillatory trends of

MSL from 1970 to 2019.

Table 4: Mean sea level in Callao Bay station calculated by

decade.

Decade Mean sea level

1970

–

1979 1097 mm

1980

–

1989 1125 mm

1990

–

1999 1110 mm

2000

–

2009 1071 mm

2010 - 2019 1096 mm

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4 NUMERICAL MODELING

Numerical modeling consists of performing the wave

propagation method from deep waters to several

locations in shallow water of study area to stablish the

climate wave (Yuk, Park & Joh, 2018).

A nested grid to propagate deep water waves were

used (Figure 11), with a coarse grid with 30° rotation

for coarse grid while for shallow water a grid oriented

with x-axis were defined. The main characteristics of

each grid is showed in Table 5.

Figure 11: Wave grid in intermediate and shallow waters.

Table 5: Characteristics of the grids used in numerical wave

modeling.

Grid Deep water Shallow waters

Long 93km 18.3km

Width 113km 21.7km

dx 1158m 77m

1398m 91m

Orientation 30° 0°

The Delft3D-wave model (DELTARES, 2014)

were used to propagate each scenario defined in deep

water to shallow waters. Model was configurated to

propagate waves in stationary mode.

5 RESULTS AND DISCUSSIONS

5.1 Modeling of the Medium Regime

Results of wave modeling of mean regime shows that

waves coming from the south-southeast direction

does not affect La Punta and La Perla districts,

because the maximum wave height reached is less

than 0.5m (Figure 12). For waves coming from

southwest (Figure 13) wave heights in the northern

area of the bay reach 3 to 3.5 m, but in the La Punta

the wave heights are around 1m and in La Perla near

the coast the heights are around 0.5m.

Finally waves coming from northwest are

presented in Figure 14, where the highest wave heights

are 2.5m and are mostly throughout the northern part

of the study area, and the district of La Punta has

nearby waves of heights close to 2 m, but the district of

La Perla has waves less than or equal to 1 m.

Figure 12: Wave modeling for SSE direction. Case 01:

Wave period: 7.7 s, wave height: 4.3 m.

Figure 13: Wave modeling for WSW direction. Case 15:

Wave period: 20.2 s, wave height: 3.8 m.

5.2 Modeling of the Extreme Regime

In general terms, waves coming from Northwest

(Figure 15) shows wave height between 1.5 to 2m in

all the study area, and the northern part of study area

is most affected by waves. Figure 16 shows that wave

coming from Southwest generate two defined wave

areas. The first area correspond to northern part of the

bay, which wave heights reach values between 2 and

5m, and the second area is protected by San Lorenzo

Island which cause the diffraction and wave heights

reached is less than 2m.

Modeling Normal and Extreme Wave Conditions in Callao Bay, Peru using Reanalysis Data

199

Figure 14: Wave modeling for WNW direction. Case 21:

Wave period: 21.9 s, wave height: 3.3 m.

Figure 15: Wave modeling for NW direction. Case 22:

Return Period: 10 years, Wave period: 20.2 s, wave height:

2.5 m.

6 MODEL VALIDATION IN

STUDY AREA

Likewise, Figure 17 shows the comparison of

percentiles of uncalibrated modeled waves, calibrated

model with in situ data. It is observed that

uncalibrated model has the same trends with in situ

date, however model is overestimate 0.20m

approximately, for this reason modeled wave were

calibrated to obtain better index of comparison (

Table

). Consequently, the numerical modeling with

Delft3D program is acceptable for the purposes of

this research.

Figure 16: Wave modeling for SW direction. Case 11:

Return Period: 30 years, Wave period: 16.9 s, wave height:

5 m.

Figure 17: Trend of the percentiles of registered and

modeled wave heights.

Table 6: Wave modelling validation in shallow waters.

Indices

Uncalibrated

Model

Calibrated

Model

BIAS 0.043 0

RMSE 0.053 0.031

SI 0.060 0.035

IOA 0.995 0.998

The events that affected to the bay during January

2021 (Figure 18 and 19) were represented in

numerical modeling as wave from Northwest (Figure

15), in this case ins observed how the wave inside

directly to Callao bay without influence of diffraction

effects from San Lorenzo Island.

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Figure 18: Waves that were presented in Plaza Grau and La

Punta. Source: Martínez, 2021.

Figure 19: Waves that were stopped by the La Arenilla

breakwater. The photograph was taken by the authors in

January 8, 2021.

7 CONCLUSIONS

The numerical modeling presents the possible wave

scenarios in the study area in specific wave situations,

but these scenarios must be validated with data

dispersion criteria. The direction of the waves is an

important variable since it serves as an indicator of

the areas where the waves will be aggressive and

would cause damage to structures and put the

population on alert. Usually, the waves between the

south and southeast directions generate waves less

than 0.5m close to the southern zone of the La Punta

district and the La Perla district. However waves

coming from northwest directions generate waves

with 2m of height close to the north of Callao bay. In

the case of extreme wave events, the lowest wave

height that can occur on the coast has a magnitude of

around 2m, which may vary due to the shape of the

coastline and coastal structures. Likewise, the most

dangerous wave direction is the West-Northwest

since the modeled scenarios show that both in the

medium and extreme regime the wave heights are

significant. In normal conditions the waves coming

from the west southwest can reach heights of around

2m near the coast, but in extreme conditions these

could reach 3m or more. It has been observed that San

Lorenzo Island protect to study area from waves

especially when it is coming from South and South-

west directions.

Finally, the porpoise of this paper was

characterizing the mean and extreme regime of wave

in Callao bay to provide a tools of decision makers to

prevent future events of flooding by waves.

REFERENCES

Erikson, L., Hegermiller, C., Ruggiero, P., & VanOrmondt.

(2015). Projected wave conditions in the Eastern North

Pacific under the influence of two CMIP5 climate

scenarios. Ocean Modelling, 171-185.

doi:http://dx.doi.org/10.1016/j.ocemod.2015.07.004.

Ruggiero, P. (2013). Is the intensifying wave climate of the

US Pacific Northwest increasing flooding and erosion

risk faster than sealevel rise? Journal of Waterway Port

Coastal and Ocean Engineering, 88-97.

doi:10.1061/(Asce)Ww.1943-5460.0000172.

Barnard, P. L., Erikson, L. H., Foxgrover, A. C., Hart, J. A.

F., Limber, P., O’Neill, A. C., … Jones, J. M. (2019).

Dynamic flood modeling essential to assess the coastal

impacts of climate change. Scientific Reports, 9(1), 1–

13. https://doi.org/10.1038/s41598-019-40742-z

Gainza, J., Rueda, A., Camus, P., Tomás, A., Méndez, F. J.,

Sano, M., & Tomlinson, R. (2018). A Meta-Modelling

Approach for Estimating Long-Term Wave Run-Up

and Total Water Level on Beaches. Journal of Coastal

Research, 342(2), 475–489. https://doi.org/10.2112/

jcoastres-d-16-00198.1

INEI (2018) Población del Perú totalizó 31 millones 237

mil 385 personas al 2017.INEI Instituto Nacional de

Estadística e Informática. Recuperado de:

https://www.inei.gob.pe/

Guzman, E., Ramos, C., & Dastgheib, A. (2020). Influence

of the el nino phenomenon on shoreline evolution. Case

study: Callao bay, Peru. Journal of Marine Science and

Engineering, 8(2). https://doi.org/10.3390/jmse8020090

Lainez Yonce, A. (1 de Mayo del 2015) Oleaje: alerta en el

Callao y Costa Verde por inundaciones. Crónica Viva.

Recuperado de: http://www.cronicaviva.com.pe/oleaje-

alerta-en-el-callao-y-costa-verde-por-inundaciones/

Perú 21 (4 de Febrero del 2016) Callao sigue afectado por

fuerte oleaje [Fotos y video]. Perú 21. Recuperado de:

https://peru21.pe/lima/callao-sigue-afectado-fuerte-

oleaje-fotos-video-210087-noticia/?ref=p21r

Modeling Normal and Extreme Wave Conditions in Callao Bay, Peru using Reanalysis Data

201

Caldwell, P. C., M. A. Merrifield, P. R. Thompson (2015),

Sea level measured by tide gauges from global oceans

— the Joint Archive for Sea Level holdings (NCEI

Accession 0019568), Version 5.5, NOAA National

Centers for Environmental Information, Dataset,

doi:10.7289/V5V40S7W.

National Oceanic and Atmospheric Administration (w.d.)

Wavewatch III Hindcast and reanalysis archives.

Environmental Modeling Center NOAA NWS National

Centers FOR Environmental Prediction. Recuperado el

27 de Agosto del 2020. https://polar.ncep.noaa.gov/

waves/hindcasts/

Chen, Y., Xie, D., Zhang, C., & Qian, X. (2013). Estimation

of long-term wave statistics in the East China Sea.

Journal of Coastal Research, 65, 177–182.

https://doi.org/10.2112/si65-031.1

Kim, I. C., & Suh, K. D. (2018). Effect of Sea Level Rise

and Offshore Wave Height Change on Nearshore

Waves and Coastal Structures. Journal of Marine

Science and Application, 17(2), 192–207.

https://doi.org/10.1007/s11804-018-0022-8

Frihy, O. E., Deabes, E. A., & El Gindy, A. A. (2010).

Wave climate and nearshore processes on the

mediterranean coast of Egypt. Journal of Coastal

Research, 26(1), 103–112. https://doi.org/10.2112/08-

1020.1

Yuk, J.-H., Park, J., & Joh, M. (2018). Modelling of Storm-

induced Seawater Flooding in the Suyeong River Area,

South Korea: A Case Study due to the Storm Surge and

Waves during Typhoon Sanba. Journal of Coastal

Research, 85, 746–750. https://doi.org/10.2112/si85-

150.1

DELTARES (2014) Delft3D-WAVE, User Manual. The

Netherlands. Deltares.

Hamza, W., Lusito, L., Ligorio, F., Tomasicchio, G. R., &

D’Alessandro, F. (2018). Wave climate at

shallowwaters along the Abu Dhabi coast. Water

(Switzerland), 10(8), 1–19. https://doi.org/10.3390/

w10080985

Martínez Moreno, Xenia (23 de Enero del 2021) Callao:

Oleaje anómalo se registra en Callao. RPP Noticias.

Recuperado de: https://rpp.pe/peru/callao/callao-

oleaje-anomalo-se-registra-en-la-punta-video-noticia-

1316800?ref=rpp

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