Dfsu - 2D interpolation

Interpolate dfsu data to a grid, save as dfs2 and geotiff. Interpolate dfsu data to another mesh.

import mikeio

ds = mikeio.read("../../data/wind_north_sea.dfsu", items="Wind speed")
ds

<mikeio.Dataset>
dims: (time:6, element:958)
time: 2017-10-27 00:00:00 - 2017-10-27 05:00:00 (6 records)
geometry: Dfsu2D (958 elements, 570 nodes)
items:
  0:  Wind speed <Wind speed> (meter per sec)

da = ds.Wind_speed
da.plot();

Interpolate to grid

Get an overset grid covering the domain
Then interpolate all data to the new grid and plot.
The interpolated data is then saved to a dfs2 file.

g = da.geometry.get_overset_grid(dx=0.1)
g

<mikeio.Grid2D>
x: [-1.563, -1.463, ..., 8.837] (nx=105, dx=0.1)
y: [49.9, 50, ..., 55.3] (ny=55, dy=0.1)
projection: LONG/LAT

da_grid = da.interp_like(g)
da_grid

<mikeio.DataArray>
name: Wind speed
dims: (time:6, y:55, x:105)
time: 2017-10-27 00:00:00 - 2017-10-27 05:00:00 (6 records)
geometry: Grid2D (ny=55, nx=105)

da_grid.plot();

Save to dfs2 file

da_grid.to_dfs("wind_north_sea_interpolated.dfs2")

Save to NetCDF

xr_da = da_grid.to_xarray()
xr_da.to_netcdf("wind_north_sea_interpolated.nc")

Save to GeoTiff

Note

This section requires the rasterio package.

import numpy as np
import rasterio
from rasterio.transform import from_origin
# Dcoumentation https://rasterio.readthedocs.io/en/latest/index.html

with rasterio.open(
     fp='wind.tif',
     mode='w',
     driver='GTiff',
     height=g.ny,
     width=g.nx,
     count=1,
     dtype=da.dtype,
     crs='+proj=latlong', # adjust accordingly for projected coordinate systems
     transform=from_origin(g.bbox.left, g.bbox.top, g.dx, g.dy)
     ) as dst:
        dst.write(np.flipud(da_grid[0].to_numpy()), 1) # first time_step

Interpolate to other mesh

Interpolate the data from this coarse mesh onto a finer resolution mesh

msh = mikeio.Mesh("../../data/north_sea_2.mesh")
msh

<Mesh>
number of nodes: 1296
number of elements: 2259
projection: LONG/LAT

dsi = da.interp_like(msh)
dsi

<mikeio.DataArray>
name: Wind speed
dims: (time:6, element:2259)
time: 2017-10-27 00:00:00 - 2017-10-27 05:00:00 (6 records)
geometry: Dfsu2D (2259 elements, 1296 nodes)

da[0].plot(figsize=(9,7), show_mesh=True);

dsi[0].plot(figsize=(9,7), show_mesh=True);

Note: 3 of the new elements are outside the original mesh and data are therefore NaN by default

nan_elements = np.where(np.isnan(dsi[0].to_numpy()))[0]
nan_elements

array([ 249,  451, 1546])

da.geometry.contains(msh.element_coordinates[nan_elements,:2])

array([False, False, False])

We can force extrapolation to avoid the NaN values

dat_interp = da.interp_like(msh, extrapolate=True)

n_nan_elements = np.sum(np.isnan(dat_interp.values))
n_nan_elements

np.int64(0)

Interpolate scatter data to mesh

We want to interpolate scatter data onto an existing mesh and create a new dfsu with the interpolated data.

This uses lower level private utility methods not part of the public API.

Interpolating from scatter data will soon be possible in a simpler way.

from mikeio.spatial._utils import dist_in_meters
from mikeio._interpolation import get_idw_interpolant

dfs = mikeio.open("../../data/wind_north_sea.dfsu")

dfs.geometry.plot.mesh();

# scatter data: x,y,value for 4 points
scatter= np.array([[1,50,1], [4, 52, 3], [8, 55, 2], [-1, 55, 1.5]])
scatter

array([[ 1. , 50. ,  1. ],
       [ 4. , 52. ,  3. ],
       [ 8. , 55. ,  2. ],
       [-1. , 55. ,  1.5]])

Let’s first try the approx for a single element:

calc distance to all interpolation points
calc IDW interpolatant weights
Interpolate

dist = dist_in_meters(scatter[:,:2], dfs.geometry.element_coordinates[0,:2])
dist

array([4.00139539, 3.18881018, 6.58769411, 2.69722991])

w = get_idw_interpolant(dist, p=2)
w

array([0.19438779, 0.30607974, 0.07171749, 0.42781498])

np.dot(scatter[:,2], w) # interpolated value in element 0

np.float64(1.8977844597276883)

Let’s do the same for all points in the mesh and plot in the end

dati = np.zeros((1, dfs.geometry.n_elements))
for j in range(dfs.geometry.n_elements):
    dist = dist_in_meters(scatter[:, :2], dfs.geometry.element_coordinates[j, :2])
    w = get_idw_interpolant(dist, p=2)
    dati[0, j] = np.dot(scatter[:, 2], w)

da = mikeio.DataArray(data=dati, geometry=dfs.geometry, time=dfs.start_time)
da

<mikeio.DataArray>
name: NoName
dims: (time:1, element:958)
time: 2017-10-27 00:00:00 (time-invariant)
geometry: Dfsu2D (958 elements, 570 nodes)

da.plot(title="Interpolated scatter data");

da.to_dfs("interpolated_scatter.dfsu")

Clean up

import os

os.remove("wind_north_sea_interpolated.dfs2")
os.remove("wind_north_sea_interpolated.nc")
os.remove("wind.tif")
os.remove("interpolated_scatter.dfsu")