possible issue with _cell_area_from_latitude function?

[uturuncoglu]

I am wondering if following line of code is correct or not,

weatherbenchX/weatherbenchX/weighting.py

Line 86 in 9c54b9b

# Normalized cell area: integral from lower to upper of cos(latitude).

in my case it is creating very large weights on poles. If I change them from sin to cos it is disappearing and weights seems fine. Any idea?

[raspstephan]

Can you share the latitude array you have as input?

[uturuncoglu]

I know that poles are singularity points and maybe it is expected (check for -90 and 90, the code gives value around 720) but here is the code:

# from https://github.com/google-research/weatherbench2/blob/021c0b33d9dd165d1e7aa476fcc985be855fbc7b/weatherbench2/metrics.py#L40
def _latitude_cell_bounds(x: np.ndarray) -> np.ndarray:
  pi_over_2 = np.array([np.pi / 2], dtype=x.dtype)
  return np.concatenate([-pi_over_2, (x[:-1] + x[1:]) / 2, pi_over_2])
    
# From https://github.com/google-research/weatherbench2/blob/021c0b33d9dd165d1e7aa476fcc985be855fbc7b/weatherbench2/metrics.py#L45
def _cell_area_from_latitude(points: np.ndarray) -> np.ndarray:
  """Calculate the area overlap as a function of latitude."""
  bounds = _latitude_cell_bounds(points)
  upper = bounds[1:]
  lower = bounds[:-1]
  # normalized cell area: integral from lower to upper of cos(latitude)
  return np.sin(upper) - np.sin(lower)

# From https://github.com/google-research/weatherbench2/blob/021c0b33d9dd165d1e7aa476fcc985be855fbc7b/weatherbench2/metrics.py#L55
def get_lat_weights(ds: xr.Dataset) -> xr.DataArray:
  """Computes latitude/area weights from latitude coordinate of dataset."""
  weights = _cell_area_from_latitude(np.deg2rad(ds.latitude.data))
  weights /= np.mean(weights)
  weights = ds.latitude.copy(data=weights)
  return weights

# Load era5 dataset
ds_era5 = xr.open_dataset(os.path.join(data_path, f"20210101_era5/era5_35d.nc")).rename({'valid_time': 'time'})

# Calculate weights
weights = get_lat_weights(ds_era5)
for i in range(0, 721):
    print(weights.values[i], ds_era5.latitude.values[I])

Here is the output:

720.9991420739356 90.0
-0.0068633840167481325 89.75
-0.013726637364602726 89.5
-0.020589629377031633 89.25
-0.027452229392585688 89.0
-0.03431430675726011 88.75
-0.041175730827056015 88.5
-0.04803637097022169 88.25
-0.05489609657017437 88.0
-0.06175477702758144 87.75
-0.06861228176300195 87.5
-0.07546848021952826 87.25
-0.08232324186494719 87.0
-0.08917643619450175 86.75
-0.09602793273329249 86.5
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-0.11657093135514099 85.75
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[uturuncoglu]

@raspstephan If this is correct maybe it needs to threat poles specifically and assign 0 weight to those points.

[raspstephan]

but wait, in the example above you are using the WB2 function instead of WBX.
This gives me the correct answer:

from weatherbenchX import weighting
lats = np.linspace(90, -90, 721)
# Note that the latitudes must be increasing.
weighting.cell_area_from_latitude(np.deg2rad(lats[::-1]))

[uturuncoglu]

@raspstephan Thanks for your help. If you check the following routines,

https://github.com/google-research/weatherbench2/blob/021c0b33d9dd165d1e7aa476fcc985be855fbc7b/weatherbench2/metrics.py#L45

and

weatherbenchX/weatherbenchX/weighting.py

Line 81 in c5adf96

def cell_area_from_latitude(points: np.ndarray) -> np.ndarray:

They are same. The only difference is that https://github.com/google-research/weatherbench2/blob/021c0b33d9dd165d1e7aa476fcc985be855fbc7b/weatherbench2/metrics.py#L55C5-L55C20 does some extra work. So, maybe it is large because of it. Does this mean weatherbench2 scores have some king of issue over polar regions?

[langmore]

The fact that your weights are negative tells me things are very wrong. The above code assumes latitude is increasing. So try reversing your latitude, and it should be much better.

[uturuncoglu]

@raspstephan @langmore Thanks to both of you. Reversing latitude is indeed solve the issue. Now, I do not have any issue in the poles. It would be nice to document it in somewhere in the code.

[langmore]

The WB2 code has an _assert_increasing call that your code above is missing. Maybe you need a more recent copy?

def _cell_area_from_latitude(points: np.ndarray) -> np.ndarray:
  """Calculate the area overlap as a function of latitude."""
  bounds = _latitude_cell_bounds(points)
  _assert_increasing(bounds)
  upper = bounds[1:]
  lower = bounds[:-1]
  # normalized cell area: integral from lower to upper of cos(latitude)
  return np.sin(upper) - np.sin(lower)