Wave Energy¶

Ocean waves have an estimated 1,400 TWh/yr of technical energy potential across the U.S. EEZ, equivalent to 34% of U.S. electricity generation [@general_kilcher2021_marine]. The U.S. Department of Energy's Hydropower and Hydrokinetic Office (H2O) produced a 42-year, high-resolution hindcast covering all U.S. coastal and offshore waters to map that resource in detail. The data are freely accessible through the Marine Energy Atlas, a Python API, and raw HDF5 files on AWS S3.

What Is a Hindcast?

A hindcast is a numerical model simulation that estimates past wave conditions over a defined area and time period using historical forcing and boundary conditions. It reconstructs how conditions varied over time and space across a much larger area than can be captured by real-world measurements alone. Hindcasts are particularly valuable for marine energy resource characterization because measured data are often very sparse in both time and location; without a hindcast, the available observations may be too limited to fully describe the resource or operating conditions at a site. By providing a spatially and temporally continuous record, hindcasts help fill those gaps and support resource assessment, site screening, engineering design, and evaluation of long-term variability.

Regional Datasets¶

Period: 1979–2020 · 42 annual files
Total archive: ~3.3 TB
Version: v1.0.1

2011–2020 (10 files)

Grid points: 699,904 · ~71.7 GB per year

Variable definitions (9) · 2011–2020

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Peak wave direction (nautical convention)		PDIR	degr
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (9) · 2011–2020

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,928 × 699,904	`float32`
`energy_period`	s	2,928 × 699,904	`float32`
`maximum_energy_direction`	degr	2,928 × 699,904	`float32`
`mean_absolute_period`	s	2,928 × 699,904	`float32`
`mean_wave_direction`	degr	2,928 × 699,904	`float32`
`omni-directional_wave_power`	W/m	2,928 × 699,904	`float32`
`peak_period`	s	2,928 × 699,904	`float32`
`significant_wave_height`	m	2,928 × 699,904	`float32`
`spectral_width`		2,928 × 699,904	`float32`

Metadata (6 fields) · 2011–2020

Field	Type
`water_depth`	`float32`
`latitude`	`float32`
`longitude`	`float32`
`distance_to_shore`	`float32`
`timezone`	`int16`
`jurisdiction`	`str[20]`

1979–2010 (32 files)

Grid points: 699,904 · ~81.9 GB per year

Variable definitions (10) · 1979–2010

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Direction of maximum directionally resolved wave power (nautical convention)	$\theta_{J}$		degr
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`mean_zero-crossing_period`	Mean absolute zero-crossing period	$T_{z}$, $T_{02}$	TM02	s
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (10) · 1979–2010

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,920 × 699,904	`float32`
`energy_period`	s	2,920 × 699,904	`float32`
`maximum_energy_direction`	degr	2,920 × 699,904	`float32`
`mean_absolute_period`	s	2,920 × 699,904	`float32`
`mean_wave_direction`	degr	2,920 × 699,904	`float32`
`mean_zero-crossing_period`	s	2,920 × 699,904	`float32`
`omni-directional_wave_power`	W/m	2,920 × 699,904	`float32`
`peak_period`	s	2,920 × 699,904	`float32`
`significant_wave_height`	m	2,920 × 699,904	`float32`
`spectral_width`		2,920 × 699,904	`float32`

Metadata (6 fields) · 1979–2010

Field	Type
`water_depth`	`float32`
`latitude`	`float32`
`longitude`	`float32`
`distance_to_shore`	`float32`
`timezone`	`int16`
`jurisdiction`	`str[20]`

View West Coast on the Marine Energy Atlas

Period: 1979–2020 · 42 annual files
Total archive: ~12.7 TB
Version: v1.0.1

2011–2020 (10 files)

Grid points: 2,635,135 · ~316.2 GB per year

Variable definitions (11) · 2011–2020

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Direction of maximum directionally resolved wave power (nautical convention)	$\theta_{J}$		deg
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	deg
`mean_zero-crossing_period`	Mean absolute zero-crossing period	$T_{z}$, $T_{02}$	TM02	s
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`peak_period_direction`	Peak wave direction (nautical convention)		PDIR	deg
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (11) · 2011–2020

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,928 × 2,635,135	`float32`
`energy_period`	s	2,928 × 2,635,135	`float32`
`maximum_energy_direction`	deg	2,928 × 2,635,135	`float32`
`mean_absolute_period`	s	2,928 × 2,635,135	`float32`
`mean_wave_direction`	deg	2,928 × 2,635,135	`float32`
`mean_zero-crossing_period`	s	2,928 × 2,635,135	`float32`
`omni-directional_wave_power`	W/m	2,928 × 2,635,135	`float32`
`peak_period`	s	2,928 × 2,635,135	`float32`
`peak_period_direction`	deg	2,928 × 2,635,135	`float32`
`significant_wave_height`	m	2,928 × 2,635,135	`float32`
`spectral_width`		2,928 × 2,635,135	`float32`

1979–2010 (32 files)

Grid points: 2,635,135 · ~308.1 GB per year

Variable definitions (10) · 1979–2010

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Direction of maximum directionally resolved wave power (nautical convention)	$\theta_{J}$		deg
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	deg
`mean_zero-crossing_period`	Mean absolute zero-crossing period	$T_{z}$, $T_{02}$	TM02	s
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (10) · 1979–2010

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,920 × 2,635,135	`float32`
`energy_period`	s	2,920 × 2,635,135	`float32`
`maximum_energy_direction`	deg	2,920 × 2,635,135	`float32`
`mean_absolute_period`	s	2,920 × 2,635,135	`float32`
`mean_wave_direction`	deg	2,920 × 2,635,135	`float32`
`mean_zero-crossing_period`	s	2,920 × 2,635,135	`float32`
`omni-directional_wave_power`	W/m	2,920 × 2,635,135	`float32`
`peak_period`	s	2,920 × 2,635,135	`float32`
`significant_wave_height`	m	2,920 × 2,635,135	`float32`
`spectral_width`		2,920 × 2,635,135	`float32`

Metadata (6 fields) · 1979–2010

Field	Type
`latitude`	`float32`
`longitude`	`float32`
`water_depth`	`float32`
`timezone`	`int16`
`distance`	`float32`
`jurisdiction`	`str[14]`

View Atlantic on the Marine Energy Atlas

Period: 1979–2020 · 42 annual files
Total archive: ~4.4 TB
Version: v1.0.0

2011–2020 (10 files)

Grid points: 1,696,188 · ~189.7 GB per year

Variable definitions (10) · 2011–2020

Variable	Description	IEC Name	SWAN name	Units
`depth`	Water depth		Depth	m
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Peak wave direction (nautical convention)		PDIR	degr
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (10) · 2011–2020

Variable	Units	Dimensions	Type
`depth`	m	2,928 × 1,696,188	`float32`
`directionality_coefficient`		2,928 × 1,696,188	`float32`
`energy_period`	s	2,928 × 1,696,188	`float32`
`maximum_energy_direction`	degr	2,928 × 1,696,188	`float32`
`mean_absolute_period`	s	2,928 × 1,696,188	`float32`
`mean_wave_direction`	degr	2,928 × 1,696,188	`float32`
`omni-directional_wave_power`	W/m	2,928 × 1,696,188	`float32`
`peak_period`	s	2,928 × 1,696,188	`float32`
`significant_wave_height`	m	2,928 × 1,696,188	`float32`
`spectral_width`		2,928 × 1,696,188	`float32`

Metadata (7 fields) · 2011–2020

Field	Type
`latitude`	`float32`
`longitude`	`float32`
`depth`	`float32`
`distance_to_shore`	`float32`
`timezone`	`int16`
`eez`	`str[13]`
`jurisdiction`	`str[14]`

1979–2010 (32 files)

Grid points: 700,414 · ~81.9 GB per year

Variable definitions (10) · 1979–2010

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Fraction of total wave energy travelling in the "direction of maximum wave power" direction	$d$
`energy_period`	Spectral width characterizes the relative spreading of energy in the wave spectrum. Large values indicate a wider spectral peak	$T_{e}$	TM02	s
`maximum_energy`	Maximum directionally resolved wave energy	$J_{\sigma,jdmax}$	jdmax	W/m
`maximum_energy_direction`	The direction from which the most wave energy is travelling	$Jsigma_{Jmax}$		deg
`mean_absolute_period`	Resolved Spectral Moment (m_0/m_1)	$T_{p}$	PER	s
`mean_wave_direction`	Direction Normal to the Wave Crests	$\Sigma$	DIR	deg
`omni-directional_wave_power`	Total wave energy flux from all directions	$J$		W/m
`peak_period`	The period associated with the maximum value of the wave energy spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Calculated as the zeroth spectral moment (i.e., H_m0)	$H_{s}$	HSIGN	m
`spectral_width`	Spectral width characterizes the relative spreading of energy in the wave spectrum. Large values indicate a wider spectral peak	$\epsilon_{0}$

Variable schema (10) · 1979–2010

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,920 × 700,414	`float32`
`energy_period`	s	2,920 × 700,414	`float32`
`maximum_energy`	W/m	2,920 × 700,414	`float32`
`maximum_energy_direction`	deg	2,920 × 700,414	`float32`
`mean_absolute_period`	s	2,920 × 700,414	`float32`
`mean_wave_direction`	deg	2,920 × 700,414	`float32`
`omni-directional_wave_power`	W/m	2,920 × 700,414	`float32`
`peak_period`	s	2,920 × 700,414	`float32`
`significant_wave_height`	m	2,920 × 700,414	`float32`
`spectral_width`		2,920 × 700,414	`float32`

Metadata (6 fields) · 1979–2010

Field	Type
`latitude`	`float32`
`longitude`	`float32`
`distance_to_shore`	`float32`
`timezone`	`int16`
`jurisdiction`	`str[7]`
`water_depth`	`float32`

View Hawaii on the Marine Energy Atlas

Period: 1979–2020 · 42 annual files
Total archive: ~18.1 TB
Version: v1.0.1

2011–2020 (10 files)

Grid points: 3,894,283 · ~399.1 GB per year

Variable definitions (9) · 2011–2020

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Direction of maximum directionally resolved wave power (nautical convention)	$\theta_{J}$		degr
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (9) · 2011–2020

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,928 × 3,894,283	`float32`
`energy_period`	s	2,928 × 3,894,283	`float32`
`maximum_energy_direction`	degr	2,928 × 3,894,283	`float32`
`mean_absolute_period`	s	2,928 × 3,894,283	`float32`
`mean_wave_direction`	degr	2,928 × 3,894,283	`float32`
`omni-directional_wave_power`	W/m	2,928 × 3,894,283	`float32`
`peak_period`	s	2,928 × 3,894,283	`float32`
`significant_wave_height`	m	2,928 × 3,894,283	`float32`
`spectral_width`		2,928 × 3,894,283	`float32`

Metadata (6 fields) · 2011–2020

Field	Type
`latitude`	`float32`
`longitude`	`float32`
`timezone`	`float32`
`distance`	`float32`
`jurisdiction`	`str[7]`
`water_depth`	`float32`

1979–2010 (32 files)

Grid points: 3,894,283 · ~455.2 GB per year

Variable definitions (10) · 1979–2010

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Direction of maximum directionally resolved wave power (nautical convention)	$\theta_{J}$		degr
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`mean_zero-crossing_period`	Mean absolute zero-crossing period	$T_{z}$, $T_{02}$	TM02	s
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (10) · 1979–2010

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,920 × 3,894,283	`float32`
`energy_period`	s	2,920 × 3,894,283	`float32`
`maximum_energy_direction`	degr	2,920 × 3,894,283	`float32`
`mean_absolute_period`	s	2,920 × 3,894,283	`float32`
`mean_wave_direction`	degr	2,920 × 3,894,283	`float32`
`mean_zero-crossing_period`	s	2,920 × 3,894,283	`float32`
`omni-directional_wave_power`	W/m	2,920 × 3,894,283	`float32`
`peak_period`	s	2,920 × 3,894,283	`float32`
`significant_wave_height`	m	2,920 × 3,894,283	`float32`
`spectral_width`		2,920 × 3,894,283	`float32`

Metadata (6 fields) · 1979–2010

Field	Type
`latitude`	`float32`
`longitude`	`float32`
`timezone`	`float32`
`distance`	`float32`
`jurisdiction`	`str[7]`
`water_depth`	`float32`

View Alaska on the Marine Energy Atlas

Grid points: 461,465
File size: ~47.3 GB per year
Period: 1979–2020 · 42 annual files
Total archive: ~1.9 TB
Version: v1.0.0

Variable definitions (9)

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`maximum_energy_direction`	Direction of maximum directionally resolved wave power (nautical convention)	$\theta_{J}$		degr
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`omni-directional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (9)

Variable	Units	Dimensions	Type
`directionality_coefficient`		2,928 × 461,465	`float32`
`energy_period`	s	2,928 × 461,465	`float32`
`maximum_energy_direction`	degr	2,928 × 461,465	`float32`
`mean_absolute_period`	s	2,928 × 461,465	`float32`
`mean_wave_direction`	degr	2,928 × 461,465	`float32`
`omni-directional_wave_power`	W/m	2,928 × 461,465	`float32`
`peak_period`	s	2,928 × 461,465	`float32`
`significant_wave_height`	m	2,928 × 461,465	`float32`
`spectral_width`		2,928 × 461,465	`float32`

Metadata (6 fields)

Field	Type
`latitude`	`float32`
`longitude`	`float32`
`timezone`	`int16`
`depth`	`float32`
`distance_to_shore`	`float32`
`jurisdiction`	`str[24]`

View CNMI and Guam on the Marine Energy Atlas

Part of the Gulf of America dataset, using the same grid, variables, and archive period.

View Puerto Rico on the Marine Energy Atlas

Grid points: 4,656,637
File size: ~572.8 GB per year
Period: 1979–2020 · 42 annual files
Total archive: ~23.5 TB
Version: v1.0.1

Variable definitions (11)

Variable	Description	IEC Name	SWAN name	Units
`direction_of_maximum_directionally_resolved_wave_power`	Direction of maximum directionally resolved wave power (nautical convention)	$\theta_{J}$		degr
`directionality_coefficient`	Directionality coefficient	$d$
`energy_period`	Energy period	$T_{e}$, $T_{-10}$	TMM10	s
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`mean_zero-crossing_period`	Mean absolute zero-crossing period	$T_{z}$, $T_{02}$	TM02	s
`omnidirectional_wave_power`	Omnidirectional wave power	$J$		W/m
`peak_period`	Relative peak period of the variance density spectrum	$T_{p}$	RTP	s
`peak_wave_direction`	Peak wave direction (nautical convention)		PDIR	degr
`significant_wave_height`	Significant wave height	$H_{m0}$	HSIGN	m
`spectral_width`	Spectral width	$\epsilon_{0}$

Variable schema (11)

Variable	Units	Dimensions	Type
`direction_of_maximum_directionally_resolved_wave_power`	degr	2,928 × 4,656,637	`float32`
`directionality_coefficient`		2,928 × 4,656,637	`float32`
`energy_period`	s	2,928 × 4,656,637	`float32`
`mean_absolute_period`	s	2,928 × 4,656,637	`float32`
`mean_wave_direction`	degr	2,928 × 4,656,637	`float32`
`mean_zero-crossing_period`	s	2,928 × 4,656,637	`float32`
`omnidirectional_wave_power`	W/m	2,928 × 4,656,637	`float32`
`peak_period`	s	2,928 × 4,656,637	`float32`
`peak_wave_direction`	degr	2,928 × 4,656,637	`float32`
`significant_wave_height`	m	2,928 × 4,656,637	`float32`
`spectral_width`		2,928 × 4,656,637	`float32`

Metadata (6 fields)

Field	Type
`latitude`	`float32`
`longitude`	`float32`
`timezone`	`int16`
`depth`	`float32`
`distance_to_shore`	`float32`
`jurisdiction`	`str[19]`

View Gulf of America on the Marine Energy Atlas

Limitations¶

Important Limitations

Hindcast, not measurements. Model output does not replace in-situ buoy observations.
Not design-grade by itself. Class 3 assessments require site-specific measurements and validated local modeling.
Skill varies by region. Validation was performed against NOAA buoys for selected sites; accuracy is generally higher offshore and lower in complex nearshore areas, near domain boundaries, and ice-affected regions (Alaska).

Data Access¶

Wave energy resource characterization data is available in three data products that serve different needs. Start with the Atlas for visual exploration, then move to the API or raw files as your analysis deepens.

Use Case	Data Product	Reference
Explore the resource spatially, compare regions	Marine Energy Atlas	Atlas guide
Download time series for up to ~100 sites	`us-marine-energy-resource-python` or MHKiT `wave.io.hindcast`	Getting Started
Download or slice the full archive	HSDS or AWS S3	HSDS Setup · AWS S3
Look up variable definitions and units	Variable reference	Wave Variables

Start at the Marine Energy Atlas

Marine Energy Atlas: zero setup, browser-only. Best for stakeholders, initial site screening, and non-programmers.
MHKiT: 5-line Python queries for point or multi-site time series. Best for feasibility studies and comparing candidate sites.
HSDS / S3 raw files: direct HDF5 access. Best for bulk extraction, many sites, large regional studies, and reproducible pipelines. Annual files range from ~87 GB (West Coast) to ~600 GB (Gulf of America and Puerto Rico); the full archive is TB-scale.

Site Analysis Example: PacWave South¶

The visualizations below walk through a Class 2 feasibility workflow at a single grid point near the PacWave wave energy test site off Newport, Oregon (44.62°N, 124.28°W), a U.S. DOE-funded open-water test facility on the West Coast.

What this example covers:

Pulling a multi-year site time series with MHKiT
Seasonal and inter-annual variability of key resource parameters
Monthly wave climate summaries
A wave scatter diagram ($H_{m0}$ × $T_e$ joint probability)
Environmental contours for extreme sea-state design inputs (25, 50, and 100-year return periods)

Wave Conditions Time Series¶

The three plots below show 3-hour hindcast time series at PacWave for 2016 to 2020. Each year is drawn as a grey trace and the 5-year mean is shown in color. Variables are plotted separately so seasonal patterns are easy to read.

PacWave significant wave height time series — Significant wave height ($H_{m0}$) at PacWave, Newport OR, 2016 to 2020. The seasonal signal is strong, with the highest and most variable heights occurring November to February.

PacWave energy period time series — Energy period ($T_e$) at PacWave, 2016 to 2020. Long-period swell dominates the winter months; shorter, locally-generated wind seas are more common in summer.

PacWave wave power time series — Omni-directional wave power ($J$) at PacWave, Newport OR, 2016 to 2020. Winter storms drive peak power well above 100 kW/m; summer conditions typically stay below 20 kW/m.

Show Python code

def _to_ref_year(s: pd.Series, year: int) -> pd.Series:
    """Map one calendar year's data onto REF_YEAR for overlay alignment."""
    mask = s.index.year == year
    sub  = s[mask].copy()
    new_idx = sub.index.map(lambda t: t.replace(year=REF_YEAR))
    return pd.Series(sub.values, index=new_idx, name=str(year))


def _multiyear_df(s: pd.Series) -> pd.DataFrame:
    """Return a DataFrame with one column per year, index aligned to REF_YEAR."""
    frames = {yr: _to_ref_year(s, yr) for yr in YEARS}
    return pd.DataFrame(frames)


def _apply_ts_xaxis(ax: plt.Axes, index: pd.DatetimeIndex) -> None:
    """Monthly ticks (Jan to Dec labels only; year suppressed for overlay plots)."""
    ax.xaxis.set_major_locator(mdates.MonthLocator())
    ax.xaxis.set_major_formatter(mdates.DateFormatter("%b"))
    ax.set_xlim(index[0], index[-1])
    ax.margins(x=0)
    ax.set_xlabel("Time [UTC]")

def fig_wave_height_timeseries(Hm0: pd.Series, force: bool = False) -> None:
    out = FIGURES["wave_height_timeseries"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return

    df  = _multiyear_df(Hm0)
    fig, ax = plt.subplots(figsize=FIGSIZE_TS)
    _plot_multiyear(ax, df, COLOR_HM0)
    _apply_ts_xaxis(ax, df.index)
    ax.set_ylabel("$H_{m0}$ [m]")
    ax.set_title(f"{TITLE_PREFIX}Significant Wave Height, $H_{{m0}}$ [m] | {LOCATION_NAME}")
    fig.tight_layout()
    _savefig(fig, out)

def fig_energy_period_timeseries(Te: pd.Series, force: bool = False) -> None:
    out = FIGURES["energy_period_timeseries"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return

    df  = _multiyear_df(Te)
    fig, ax = plt.subplots(figsize=FIGSIZE_TS)
    _plot_multiyear(ax, df, COLOR_TE)
    _apply_ts_xaxis(ax, df.index)
    ax.set_ylabel("$T_e$ [s]")
    ax.set_title(f"{TITLE_PREFIX}Energy Period, $T_e$ [s] | {LOCATION_NAME}")
    fig.tight_layout()
    _savefig(fig, out)

def fig_wave_power_timeseries(J: pd.Series, force: bool = False) -> None:
    out = FIGURES["wave_power_timeseries"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return

    J_kW = J / 1000.0
    df   = _multiyear_df(J_kW)
    fig, ax = plt.subplots(figsize=FIGSIZE_TS)
    _plot_multiyear(ax, df, COLOR_J)
    _apply_ts_xaxis(ax, df.index)
    ax.set_ylabel("$J$ [kW/m]")
    ax.set_title(f"{TITLE_PREFIX}Omni-directional Wave Power, $J$ [kW/m] | {LOCATION_NAME}")
    fig.tight_layout()
    _savefig(fig, out)

Monthly Wave Climate¶

The bar charts below show the monthly mean and inter-annual spread (error bars = ±1 std across years) for each wave parameter at PacWave, capturing the strong Pacific Northwest seasonal signal.

PacWave monthly Hm0 bar chart — Monthly mean significant wave height ($H_{m0}$) at PacWave, Newport OR, 2016 to 2020. Winter months (Nov to Feb) average 2 to 3 m; summer months (Jun to Aug) are consistently calmer at 1 to 1.5 m.

PacWave monthly Te bar chart — Monthly mean energy period ($T_e$) at PacWave, 2016 to 2020. Long-period swell extends the energy period in winter; short-period wind seas suppress it in summer.

PacWave monthly J bar chart — Monthly mean omni-directional wave power ($J$) at PacWave, 2016 to 2020. The seasonal contrast is pronounced, with winter power often exceeding summer levels by 5 to 10x.

Show Python code

def fig_monthly_barchart_hm0(Hm0: pd.Series, force: bool = False) -> None:
    out = FIGURES["monthly_barchart_hm0"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return
    fig, ax = plt.subplots(figsize=FIGSIZE_BAR)
    _monthly_bar(ax, Hm0, COLOR_HM0,
                 ylabel="$H_{m0}$ [m]",
                 title=f"{TITLE_PREFIX}Significant Wave Height, $H_{{m0}}$ [m] | {LOCATION_NAME}")
    fig.tight_layout()
    _savefig(fig, out)


def fig_monthly_barchart_te(Te: pd.Series, force: bool = False) -> None:
    out = FIGURES["monthly_barchart_te"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return
    fig, ax = plt.subplots(figsize=FIGSIZE_BAR)
    _monthly_bar(ax, Te, COLOR_TE,
                 ylabel="$T_e$ [s]",
                 title=f"{TITLE_PREFIX}Energy Period, $T_e$ [s] | {LOCATION_NAME}")
    fig.tight_layout()
    _savefig(fig, out)


def fig_monthly_barchart_j(J: pd.Series, force: bool = False) -> None:
    out = FIGURES["monthly_barchart_j"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return
    J_kW = J / 1000.0
    fig, ax = plt.subplots(figsize=FIGSIZE_BAR)
    _monthly_bar(ax, J_kW, COLOR_J,
                 ylabel="$J$ [kW/m]",
                 title=f"{TITLE_PREFIX}Omni-directional Wave Power, $J$ [kW/m] | {LOCATION_NAME}")
    fig.tight_layout()
    _savefig(fig, out)

Resource Matrix and Environmental Contours¶

The joint probability distribution (JPD) maps how often each $H_{m0}$ and $T_e$ combination occurs, binned at $0.5\,\text{m} \times 1\,\text{s}$. The environmental contours (PCA method) define the extreme sea state envelope at 25, 50, and 100-year return periods, providing design load inputs per IEC 62600-101 [@iec_62600_101].

PacWave joint probability distribution — Joint probability distribution ($H_{m0}$ × $T_e$) at PacWave, Newport OR, 1995 hindcast year. Cells are colored by occurrence (hours/year). The dominant sea states cluster around $H_{m0}$ = 1.5 to 3.5 m and $T_e$ = 8 to 14 s.

PacWave environmental contours — Environmental contours at PacWave, Newport OR (PCA method, 1995 hindcast). Steel-blue points are the observed sea states; curves show the 25, 50, and 100-year return period envelopes. Sea states on or outside a contour exceed that return period.

Show Python code

def fig_scatter_diagram(Hm0: pd.Series, Te: pd.Series, force: bool = False) -> None:
    out = FIGURES["scatter_diagram"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return

    Hm0_edges, Te_edges = _wave_bin_edges(Hm0, Te)

    # Bin using left edges as labels so the matrix index/columns are the bin edges
    H_bins = pd.cut(Hm0, bins=Hm0_edges, labels=Hm0_edges[:-1])
    T_bins = pd.cut(Te,  bins=Te_edges,  labels=Te_edges[:-1])

    matrix = pd.crosstab(H_bins, T_bins).replace(0, np.nan)
    matrix = (matrix / matrix.sum().sum() * 100)   # convert counts to %
    matrix.index   = matrix.index.astype(float)
    matrix.columns = matrix.columns.astype(float)

    # Re-index to the full grid so pcolormesh sees every bin slot
    matrix = matrix.reindex(index=Hm0_edges[:-1], columns=Te_edges[:-1])
    Z = matrix.values   # shape: (n_Hm0_bins, n_Te_bins)

    n_hours = int(len(Hm0) * 3)
    fig, ax = plt.subplots(figsize=FIGSIZE_SQUARE)

    cmap = cmocean.cm.haline
    pcm  = ax.pcolormesh(Te_edges, Hm0_edges, Z, cmap=cmap, vmin=0)

    cbar = fig.colorbar(pcm, ax=ax)
    cbar.set_label("Probability of Occurrence [%]", rotation=270, labelpad=16)

    _apply_matrix_axes(ax, Hm0_edges, Te_edges, grid_color="0.80")
    ax.set_title(f"{TITLE_PREFIX}Joint Probability Distribution [%] | {LOCATION_NAME}")
    fig.tight_layout()
    _savefig(fig, out,
             f"N\u2009=\u2009{n_hours:,} hours  ·  {len(YEARS)} years "
             f"({YEARS[0]}\u2013{YEARS[-1]})")

def fig_environmental_contour(Hm0: pd.Series, Te: pd.Series, force: bool = False) -> None:
    out = FIGURES["environmental_contour"]
    if out.exists() and not force:
        print(f"  skip (exists): {out.name}")
        return

    sea_state_duration = 3 * 3600
    n_hours = int(len(Hm0) * 3)

    # Pre-compute all contours so we can size the axes to contain them fully
    contour_specs = [(25, COLOR_C25, "-"), (50, COLOR_C50, "-"), (100, COLOR_C100, "-")]
    contours = []
    for rp, color, ls in contour_specs:
        c = environmental_contours(
            Hm0.values, Te.values,
            sea_state_duration=sea_state_duration,
            return_period=rp,
            method="PCA",
        )
        contours.append((rp, color, ls, np.array(c["PCA_x1"]), np.array(c["PCA_x2"])))

    # Expand bin edges so the largest contour envelope is fully inside the axes
    Te_max_c  = max(Te_c.max()  for _, _, _, _,     Te_c  in contours)
    Hm0_max_c = max(Hm0_c.max() for _, _, _, Hm0_c, _     in contours)
    Hm0_edges, Te_edges = _wave_bin_edges(
        Hm0, Te,
        Te_max_override=Te_max_c,
        Hm0_max_override=Hm0_max_c,
    )

    fig, ax = plt.subplots(figsize=FIGSIZE_SQUARE)

    # Scatter dots: sns palette[0] with opacity
    ax.scatter(Te.values, Hm0.values, s=2, alpha=0.10, color=COLOR_HM0,
               label=f"Sea states ({YEARS[0]} to {YEARS[-1]})", zorder=1)

    for rp, color, ls, Hm0_c, Te_c in contours:
        # Close the contour without re-sorting (sorting scrambles the closed-loop
        # point order into a zigzag that renders as a filled polygon)
        ax.plot(np.append(Te_c, Te_c[0]), np.append(Hm0_c, Hm0_c[0]),
                color=color, linewidth=2, linestyle=ls,
                label=f"{rp}-yr return (PCA)", zorder=3)

    _apply_matrix_axes(ax, Hm0_edges, Te_edges, grid_color="white")
    ax.set_title(f"{TITLE_PREFIX}Environmental Contours, $H_{{m0}}$ vs $T_e$ | {LOCATION_NAME}")
    leg = ax.legend(fontsize=9)
    leg.get_frame().set_facecolor("white")
    leg.get_frame().set_alpha(1.0)
    fig.tight_layout()
    _savefig(fig, out,
             f"N\u2009=\u2009{n_hours:,} hours  ·  {len(YEARS)} years "
             f"({YEARS[0]}\u2013{YEARS[-1]})")

Resource Characterization (IEC/TS 62600-101)¶

IEC/TS 62600-101 [@iec_62600_101] defines three levels of wave resource assessment, which can be thought of as progressively deeper stages of a development project:

IEC class	What you are doing	Hindcast supports?	Best access path
Class 1: Reconnaissance	Screening regions, comparing broad areas, identifying candidate sites	Yes	Marine Energy Atlas
Class 2: Feasibility	Site time series, seasonal profiles, scatter diagrams, early extreme-value inputs	With caveats	MHKiT or raw H5
Class 3: Design	Device engineering, array layout, certification-grade assessment	Not alone	Site measurements and validated local modeling

Class 1: Reconnaissance¶

The Marine Energy Atlas displays time-averaged wave energy resource parameters (significant wave height, wave power, energy period) across all hindcast domains. Grid cells are color-coded by magnitude and a point-query tool returns summary statistics for any selected location.

Class 2: Feasibility¶

A Class 2 assessment derives site-specific statistics from the full time series. The hindcast provides all six IEC/TS 62600-101 primary resource parameters:

Significant wave height ($H_{m0}$): mean height of the largest one-third of waves
Energy period ($T_e$): spectral period weighted toward low-frequency components; preferred for wave power calculations
Peak period ($T_p$): period at the dominant spectral peak
Mean zero-crossing period ($T_z$): average zero-crossing period derived from spectral moments
Omni-directional wave power ($J$): total wave energy flux from all directions [W/m]
Directionality coefficient ($d$): fraction of wave power arriving from the dominant direction

Point queries can be made using MHKiT:

from mhkit.wave.io.hindcast.hindcast import request_wpto_point_data

# PacWave site near Newport, OR
lat_lon = (44.624076, -124.280097)

# Fetch one year of significant wave height and energy period
Hm0, meta = request_wpto_point_data("3-hour", "significant_wave_height", lat_lon, [2005])
Te,  meta = request_wpto_point_data("3-hour", "energy_period",            lat_lon, [2005])

MHKiT is ideal for up to ~100 sites. For larger studies, switch to HSDS or S3 bulk access:

from rex import ResourceX

wave_file = '/nrel/US_wave/West_Coast/West_Coast_wave_2005.h5'
with ResourceX(wave_file, hsds=True) as f:
    meta       = f.meta
    time_index = f.time_index
    Hm0        = f['significant_wave_height']
    J          = f['omni-directional_wave_power']

Prerequisites

See Getting Started for HSDS/S3 setup.

Next Steps¶

Access the data: see Getting Started for HSDS/S3 setup and code examples using us-marine-energy-resource-python, MHKiT, and rex.
Explore variables: see Wave Variables for full IEC and SWAN definitions of each output parameter.
Read the references: see References for the publications behind each regional dataset.

Wave Energy¶

Regional Datasets¶

West Coast¶

East Coast¶

Hawaii¶

Alaska¶

Guam and Northern Mariana Islands¶

Puerto Rico¶

Gulf of America¶

Limitations¶

Data Access¶

Site Analysis Example: PacWave South¶

Wave Conditions Time Series¶

Monthly Wave Climate¶

Resource Matrix and Environmental Contours¶

Resource Characterization (IEC/TS 62600-101)¶

Class 1: Reconnaissance¶

Class 2: Feasibility¶

Next Steps¶

Variable	Description	IEC Name	SWAN name	Units
`directionality_coefficient`	Directionality coefficient	\(d\)
`energy_period`	Energy period	\(T_{e}\), \(T_{-10}\)	TMM10	s
`maximum_energy_direction`	Peak wave direction (nautical convention)		PDIR	degr
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`omni-directional_wave_power`	Omnidirectional wave power	\(J\)		W/m
`peak_period`	Relative peak period of the variance density spectrum	\(T_{p}\)	RTP	s
`significant_wave_height`	Significant wave height	\(H_{m0}\)	HSIGN	m
`spectral_width`	Spectral width	\(\epsilon_{0}\)

Variable	Description	IEC Name	SWAN name	Units
`direction_of_maximum_directionally_resolved_wave_power`	Direction of maximum directionally resolved wave power (nautical convention)	\(\theta_{J}\)		degr
`directionality_coefficient`	Directionality coefficient	\(d\)
`energy_period`	Energy period	\(T_{e}\), \(T_{-10}\)	TMM10	s
`mean_absolute_period`	Mean absolute wave period - equivalent to T_m01		PER	s
`mean_wave_direction`	Mean wave direction (nautical convention)		DIR	degr
`mean_zero-crossing_period`	Mean absolute zero-crossing period	\(T_{z}\), \(T_{02}\)	TM02	s
`omnidirectional_wave_power`	Omnidirectional wave power	\(J\)		W/m
`peak_period`	Relative peak period of the variance density spectrum	\(T_{p}\)	RTP	s
`peak_wave_direction`	Peak wave direction (nautical convention)		PDIR	degr
`significant_wave_height`	Significant wave height	\(H_{m0}\)	HSIGN	m
`spectral_width`	Spectral width	\(\epsilon_{0}\)