Tutorial: Estimate Wind Speed with Extrapolation

Tutorial: Estimate Wind Speed with Extrapolation#

In this tutorial, we will learn how to estimate wind speed using the extrapolation model from the geodata library.

Warning

Performing wind speed estimation using extrapolation requires a dataset with known wind speed values at multiple locations.

Currently, only the weather_data_config slv_flux_hourly from the MERRA2 dataset contains the necessary wind speed data for extrapolation.

Therefore, all of the information below only applies with slv_flux_hourly or cutouts derived from it. Using any other dataset will lead to a ValueError.

Step 1: Import the necessary libraries#

To get started, we need to import the required libraries. We will import the WindExtrapolationModel from the geodata library, as well as any other libraries needed for data handling and visualization.

import geodata
import xarray as xr

from geodata.model.wind import WindExtrapolationModel

Step 2: Load the dataset#

Next, we need to load the dataset that contains the wind speed data. We will use the slv_flux_hourly dataset from the ERA5 dataset.

# Load the dataset
ds = geodata.Dataset(
    module="merra2",
    weather_data_config="slv_flux_hourly",
    years=slice(2010, 2010),
    months=slice(1, 1),
    bounds=[-10, 35, 10, 45] # Optional: specify the bounding box
)

if not ds.prepared:
    ds.get_data()  # Download the data if we don't have it locally

Step 3: Compute extrapolation parameters#

The extrapolation is separated into two steps, first estimating extrapolation parameters using linear regression, and second extrapolating to desired heights). First, we compute the extrapolation parameters. For more information on the model, see below “How the Extrapolation Model Works”.

# Create a model based on the above dataset. The model will be associated with
# the dataset forever. If you wish to use a different dataset, you will need to
# create a new model.

model = WindExtrapolationModel(ds)
model.prepare()

If you have already prepared a cutout with the config slv_flux_hourly, you can also pass that into the model as well. The model treats dataset and cutouts indifferently. Simply replace ds with your cutout variable.

Note

The prepare method computes the necessary parameters for the extrapolation model based on the loaded dataset. Everything will be saved under the models directory under the path GEODATA_ROOT.

Note

It is not necessary to call the prepare method every time you want to perform extrapolation. You only need to call it once after loading the dataset. From that point on, you can load and use the model directly without re-preparing it.

Step 4: Estimate using the extrapolation model#

Now that we have prepared the model, we can perform the extrapolation to estimate wind speed at the desired locations. Suppose we want to estimate the wind speed at a height of 60 above ground during Jaunary of 2006 for the entire region covered by the original dataset, we can do this as follows:

estimated_wind_speed = model.estimate(
    height=60,
    years=slice(2006, 2006),
    months=slice(1, 1),
)

This will return an xarray DataArray containing the estimated wind speed values. Note that you can also select a subset area by passing in xs=slice(start, end) and/or ys=slice(start, end) parameters to the estimate method.

Note

As the underlying MERRA2 dataset already contained wind speed at certain heights, the model also has a feature to return the original wind speed values from the dataset if desired. To do this, simply set the use_real_data parameter to True in the estimate method. You do not need worry about whether the height you queried is available in the dataset; the model will handle that for you. If the height is not available, it will perform extrapolation instead.

How the Extrapolation Model Works#

The model calculates hub height wind speed from MERRA2, extrapolating the variables in MERRA’s tavg1_2d_slv_Nx data collection, which is a set of the time-averaged single-layer diagnostics.

Specifically, the variables we use for extrapolation are: 2-m wind (U2M, V2M, in m/s), 10-m wind (U10M, V10M), 50-m wind (U50M, V50M), and the zero-plane displacement height (DISPH, in meters). Additionally, we also use the wind speed at MERRA2’s lowest model level (ULML, VLML, in m/s), the height of the lowest model level (HLML, in meters), may vary depending on the location. We can obtain the wind speed at any given location and height by computing the norm of the vector sum of the U and V components.

The hub height wind speed can be calculated as

\[\nu = \alpha \ln\left(\frac{H - d}{z}\right)\]
\[z = e^{-\beta/\alpha}\]

where \(\nu\) is the hub height wind speed, \(\alpha\) is the best-fit slope from a linear regression of wind speeds on vertical heights, \(\ln\) is the natural logarithm, \(H\) is the hub height, \(d\) is the zero-plane displacement height, and \(\beta\) is the intercept from the linear regression fit.

Here we estimate \(\alpha\) and \(\beta\) fitting a simple linear regression model to the heights and wind speeds in the data.