conservative regrid changes sum by factor of almost 10

[Timothy-W-Hilton]

My conservative regrid is producing a regridded dataset whose sum is lower by a factor of nearly 10. I am sure I am misunderstanding the way that conservative is defined or the input requirements of xesmf.Regridder, but I sure haven't been able to figure out how.

A minimal example, using two grids in the area of Auckland, New Zealand.

import numpy as np
import xarray as xr
import xesmf

destination_grid_dict = {'coords': {'lon': {'dims': ('lon',), 'attrs': {}, 'data': [172.0, 172.01353383458647, 172.02706766917294, 172.0406015037594, 172.05413533834587, 172.06766917293234, 172.0812030075188, 172.09473684210525, 172.10827067669172, 172.12180451127819, 172.13533834586465, 172.14887218045112, 172.1624060150376, 172.17593984962406, 172.18947368421053, 172.203007518797, 172.21654135338346, 172.23007518796993, 172.2436090225564, 172.25714285714287, 172.27067669172934, 172.2842105263158, 172.29774436090224, 172.3112781954887, 172.32481203007518, 172.33834586466165, 172.35187969924812, 172.36541353383458, 172.37894736842105, 172.39248120300752, 172.406015037594, 172.41954887218046, 172.43308270676692, 172.4466165413534, 172.46015037593986, 172.4736842105263, 172.48721804511277, 172.50075187969924, 172.5142857142857, 172.52781954887217, 172.54135338345864, 172.5548872180451, 172.56842105263158, 172.58195488721805, 172.59548872180451, 172.60902255639098, 172.62255639097745, 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#==================================================

source_data_dict = {'coords': {'latitude': {'dims': ('latitude',), 'attrs': {}, 'data': [-37.35138884, -37.34687495, -37.34236106, -37.33784717, -37.333333280000005, -37.32881939000001, -37.32430550000001, -37.31979161000001, -37.31527772000001, -37.31076383000001, -37.306249940000015, -37.30173605000002, -37.29722216000002, -37.29270827000002, -37.28819438000002, -37.28368049000002, -37.279166600000025, -37.274652710000026, -37.27013882000003, -37.26562493000003, -37.26111104000003, -37.25659715000003, -37.252083260000035, -37.247569370000036, -37.24305548000004, -37.23854159000004, -37.23402770000004, -37.22951381000004, -37.224999920000045, -37.220486030000046, -37.21597214000005, -37.21145825000005, -37.20694436000005, -37.20243047000005, -37.197916580000054, -37.193402690000056, -37.18888880000006, -37.18437491000006, -37.17986102000006, -37.17534713000006, -37.170833240000064, -37.166319350000066, -37.16180546000007, -37.15729157000007, -37.15277768000007, -37.14826379000007, 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ds_destination_grid = xr.Dataset.from_dict(destination_grid_dict)
ds_source = xr.Dataset.from_dict(source_data_dict)
ds_source = ds_source.assign(
    vals=(
        ("latitude", "longitude"),
        np.ones((ds_source.latitude.size, ds_source.longitude.size)),
    )
)
regridder = xesmf.Regridder(ds_source, ds_destination_grid, method="conservative")
ds_regridded = regridder(ds_source)

print("ds_source total: {:0.4e}".format(float(ds_source.vals.sum())))
print("ds_regridded total: {:0.4e}".format(float(ds_regridded.vals.sum())))

For me this results in ds_source total: 9.0882e+04 ds_regridded total: 1.0098e+04

I expected ds_regridded.sum() to be very close to 9.0882e+04.

[huard]

conservative regridding preserves the integral over the area: (cell area * cell value).sum()

[Timothy-W-Hilton]

@huard, thanks, that equation is really helpful. I understand what's happening now.

So I understand now that I need the the cell areas to test that my regrid didn't add or subtract mass. As far as I can tell, xESMF calculates the cell areas internally but does not expose them via the user API. I'm now calculating areas like the below, inspired by this and this. Have I missed a more streamlined way to use xESMF or ESMPy to get cell areas?

Did merging the area branch into main ever get considered (implements xesmf.util.cell_area()? That seems like it would be useful (at least to me).

def grid_calc_area(g: xesmf.backend.Grid):
    """calculate grid cell area in metres squared

    calculate grid cell area in metres squared

    Parameters
    ----------
    g : xesmf.backend.Grid
        xesmf grid object specifying the grid. For a regridding problem, can use
        grid_in and grid_out fields of a xesmf.Regridder object.

    Examples
    --------
    FIXME: Add docs.

    """
    M_PER_KM = 1000.0
    REARTH = 6371.0 * M_PER_KM  # mean radius of Earth, in m

    f = esmpy.Field(g)
    f.get_area()
    # esmpy.Field.get_area assumes a unit sphere. The surface area of a sphere
    # is 4*pi*r^2. Therefore to get area on the actual earth in m2 from unit
    # sphere grid cell area, multiply by REARTh^2.
    area = f.data * REARTH**2
    return area

[aulemahal]

Hi @Timothy-W-Hilton. We could indeed give some attention to the area branch, I didn't even know it existed! This could be a nice and easy addition to xESMF.

[Timothy-W-Hilton]

Hi @Timothy-W-Hilton. We could indeed give some attention to the area branch, I didn't even know it existed! This could be a nice and easy addition to xESMF.

Thanks @aulemahal, that sounds great. I wanted to bring it up but also allow room for whatever I don't know e.g. "oh no we argued about that for months three years ago and no one wants to re-open that can of worms". 😝