Wind energy — hub-height wind resource¶

Wind farm developers need long-term mean wind speed at hub height (typically 80–120 m above ground). ERA5 exposes 100 m wind components directly — enough to compute hub-height wind speed without extrapolation.

Domain context. A turbine's energy yield scales with the cube of wind speed:

$$ P = \tfrac{1}{2}\rho A C_p v^3 $$

where $\rho$ is air density (~1.225 kg/m³), $A$ is rotor swept area, $C_p$ is the power coefficient (max Betz limit 16/27 ≈ 0.593, real turbines reach 0.40–0.45), and $v$ is wind speed. The right metric for siting is the wind power density $WPD = \frac{1}{2}\rho \langle v^3 \rangle$ — note the cube before averaging.

Step 1 — pull a year of monthly 100 m wind components¶

Box: 1° around Cuxhaven, Germany (53°–54°N, 8°–9°E) — North Sea coast, prime onshore wind territory. We need both u and v to reconstruct the speed magnitude $|\mathbf{v}| = \sqrt{u^2 + v^2}$.

In [1]:

from pathlib import Path
from earthlens import EarthLens, AggregationConfig

OUT = Path("data/era5-wind-cuxhaven")
OUT.mkdir(parents=True, exist_ok=True)

earthlens = EarthLens(
    data_source="ecmwf",
    temporal_resolution="monthly",
    start="2022-01-01",
    end="2022-12-01",
    variables={
        "reanalysis-era5-single-levels-monthly-means": [
            "100m-u-component-of-wind",
            "100m-v-component-of-wind",
        ],
    },
    lat_lim=[53.0, 54.0],
    lon_lim=[8.0, 9.0],
    path=str(OUT),
)
earthlens.download(aggregate=AggregationConfig(freq="1MS", op="auto"))

from pathlib import Path from earthlens import EarthLens, AggregationConfig OUT = Path("data/era5-wind-cuxhaven") OUT.mkdir(parents=True, exist_ok=True) earthlens = EarthLens( data_source="ecmwf", temporal_resolution="monthly", start="2022-01-01", end="2022-12-01", variables={ "reanalysis-era5-single-levels-monthly-means": [ "100m-u-component-of-wind", "100m-v-component-of-wind", ], }, lat_lim=[53.0, 54.0], lon_lim=[8.0, 9.0], path=str(OUT), ) earthlens.download(aggregate=AggregationConfig(freq="1MS", op="auto"))

2026-05-10 01:45:45.057 | INFO     | earthlens.ecmwf.backend:download:536 - Download ECMWF reanalysis-era5-single-levels-monthly-means/100m-u-component-of-wind data for period 2022-01-01 00:00:00 till 2022-12-01 00:00:00

2026-05-10 01:45:45.756 | INFO     | earthlens.ecmwf.backend:_api:724 - Requesting reanalysis-era5-single-levels-monthly-means from CDS; this may take several minutes

2026-05-10 01:45:46,310 INFO Request ID is 6ae625ac-75e9-43ae-bb73-4ffba92a81d2

2026-05-10 01:45:46,373 INFO status has been updated to accepted

2026-05-10 01:46:10,256 INFO status has been updated to running

2026-05-10 01:46:21,704 INFO status has been updated to successful

2026-05-10 01:46:22 | INFO | pyramids.base.config | Logging is configured.

2026-05-10 01:46:23.310 | INFO     | earthlens.ecmwf.backend:download:536 - Download ECMWF reanalysis-era5-single-levels-monthly-means/100m-v-component-of-wind data for period 2022-01-01 00:00:00 till 2022-12-01 00:00:00

2026-05-10 01:46:23.311 | INFO     | earthlens.ecmwf.backend:_api:724 - Requesting reanalysis-era5-single-levels-monthly-means from CDS; this may take several minutes

2026-05-10 01:46:23,525 INFO Request ID is 7f49d7a9-8073-473a-9c6b-bb7717a2bf95

2026-05-10 01:46:23 | INFO | ecmwf.datastores.legacy_client | Request ID is 7f49d7a9-8073-473a-9c6b-bb7717a2bf95

2026-05-10 01:46:23,608 INFO status has been updated to accepted

2026-05-10 01:46:23 | INFO | ecmwf.datastores.legacy_client | status has been updated to accepted

2026-05-10 01:46:56,695 INFO status has been updated to successful

2026-05-10 01:46:56 | INFO | ecmwf.datastores.legacy_client | status has been updated to successful

2026-05-10 01:46:56 | INFO | multiurl.base | Downloading https://object-store.os-api.cci2.ecmwf.int:443/cci2-prod-cache-2/2026-05-09/9aaf703c4472b2c344b37c54a297dc0e.nc

2026-05-10 01:46:57.672 | INFO     | earthlens.ecmwf.backend:download:575 - ECMWF download summary: all 2 variables succeeded ([('reanalysis-era5-single-levels-monthly-means', '100m-u-component-of-wind'), ('reanalysis-era5-single-levels-monthly-means', '100m-v-component-of-wind')])

Step 2 — compute monthly mean wind speed¶

Wind components are state variables (instantaneous m/s); auto → mean. The monthly GeoTIFFs carry the time-mean components, from which we get the mean-of-magnitudes (different from the magnitude of the mean — careful!).

In [2]:

import numpy as np
import pandas as pd
from pyramids.dataset import Dataset

agg = OUT / "aggregated"
u = np.stack([
    Dataset.read_file(str(p)).read_array()
    for p in sorted(agg.glob("100m_u_component_of_wind_1MS_*.tif"))
])
v = np.stack([
    Dataset.read_file(str(p)).read_array()
    for p in sorted(agg.glob("100m_v_component_of_wind_1MS_*.tif"))
])

speed = np.sqrt(u**2 + v**2)  # (month, lat, lon) — but built from monthly-mean components
site_speed = np.nanmean(speed, axis=(1, 2))

rho = 1.225  # kg/m^3, sea level
wpd = 0.5 * rho * site_speed ** 3  # rough WPD; cubing the *mean* is conservative

months = pd.date_range("2022-01-01", periods=len(u), freq="MS")
df = pd.DataFrame(
    {"|v|_100m [m/s]": site_speed.round(2), "WPD [W/m²]": wpd.round(1)},
    index=months,
)
df

import numpy as np import pandas as pd from pyramids.dataset import Dataset agg = OUT / "aggregated" u = np.stack([ Dataset.read_file(str(p)).read_array() for p in sorted(agg.glob("100m_u_component_of_wind_1MS_*.tif")) ]) v = np.stack([ Dataset.read_file(str(p)).read_array() for p in sorted(agg.glob("100m_v_component_of_wind_1MS_*.tif")) ]) speed = np.sqrt(u**2 + v**2) # (month, lat, lon) — but built from monthly-mean components site_speed = np.nanmean(speed, axis=(1, 2)) rho = 1.225 # kg/m^3, sea level wpd = 0.5 * rho * site_speed ** 3 # rough WPD; cubing the *mean* is conservative months = pd.date_range("2022-01-01", periods=len(u), freq="MS") df = pd.DataFrame( {"|v|_100m [m/s]": site_speed.round(2), "WPD [W/m²]": wpd.round(1)}, index=months, ) df

Out[2]:

	|v|_100m [m/s]	WPD [W/m²]
2022-01-01	6.86	197.300003
2022-02-01	8.56	383.600006
2022-03-01	2.99	16.400000
2022-04-01	1.36	1.500000
2022-05-01	2.90	15.000000
2022-06-01	1.16	1.000000
2022-07-01	3.73	31.700001
2022-08-01	1.17	1.000000
2022-09-01	1.13	0.900000
2022-10-01	5.29	90.500000
2022-11-01	5.35	93.800003
2022-12-01	4.11	42.700001

Step 3 — plot seasonal cycle and wind rose¶

North Sea coastal sites peak in winter (storm season, Nov–Feb) and trough in summer. Mean wind direction is from the west / southwest.

In [3]:

import matplotlib.pyplot as plt

fig, axes = plt.subplots(1, 2, figsize=(11, 4))

axes[0].plot(months, site_speed, marker="o", color="tab:blue")
axes[0].set_ylabel("100 m wind speed [m/s]")
axes[0].set_title("Monthly mean — Cuxhaven 2022")
axes[0].grid(alpha=0.3)

u_mean = np.nanmean(u, axis=(1, 2))
v_mean = np.nanmean(v, axis=(1, 2))
ax2 = axes[1]
ax2.set_xlim(-15, 15)
ax2.set_ylim(-15, 15)
ax2.set_aspect("equal")
ax2.axhline(0, color="gray", lw=0.5)
ax2.axvline(0, color="gray", lw=0.5)
ax2.set_xlabel("u (eastward) [m/s]")
ax2.set_ylabel("v (northward) [m/s]")
ax2.set_title("Monthly mean wind vectors")
for um, vm, m in zip(u_mean, v_mean, months):
    ax2.arrow(0, 0, um, vm, head_width=0.5, alpha=0.6)
    ax2.text(um, vm, m.strftime("%b"), fontsize=8)
ax2.grid(alpha=0.3)

plt.tight_layout()
plt.show()

import matplotlib.pyplot as plt fig, axes = plt.subplots(1, 2, figsize=(11, 4)) axes[0].plot(months, site_speed, marker="o", color="tab:blue") axes[0].set_ylabel("100 m wind speed [m/s]") axes[0].set_title("Monthly mean — Cuxhaven 2022") axes[0].grid(alpha=0.3) u_mean = np.nanmean(u, axis=(1, 2)) v_mean = np.nanmean(v, axis=(1, 2)) ax2 = axes[1] ax2.set_xlim(-15, 15) ax2.set_ylim(-15, 15) ax2.set_aspect("equal") ax2.axhline(0, color="gray", lw=0.5) ax2.axvline(0, color="gray", lw=0.5) ax2.set_xlabel("u (eastward) [m/s]") ax2.set_ylabel("v (northward) [m/s]") ax2.set_title("Monthly mean wind vectors") for um, vm, m in zip(u_mean, v_mean, months): ax2.arrow(0, 0, um, vm, head_width=0.5, alpha=0.6) ax2.text(um, vm, m.strftime("%b"), fontsize=8) ax2.grid(alpha=0.3) plt.tight_layout() plt.show()

Notes¶

• WPD from monthly means is conservative. Real WPD averages $v^3$ over sub-daily samples, capturing the heavy tail of high winds. Computing $\frac{1}{2}\rho \langle v\rangle^3$ from monthly means underestimates by ~20–30% at typical sites. For accurate bankable WPD, use hourly data (temporal_resolution="daily" plus custom slicing) and cube before averaging.
• Hub-height extrapolation. ERA5 also offers 10 m and 100 m components. For 80 m or 120 m hub heights, log-law extrapolation from 10 m and 100 m gives a stability-aware estimate.
• Air density correction. $\rho$ varies with site elevation and temperature. Use surface-pressure and 2m-temperature for an ideal-gas correction in the WPD formula.
• Power curves. Energy yield is the integral of the turbine's power curve weighted by the wind-speed PDF — Weibull-fit the hourly speeds for a proper AEP.