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Validating Climate Models with Spherical Convolutional Wasserstein Distance
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Proposes the spherical convolutional Wasserstein distance (SCWD), a functional sliced Wasserstein distance using Wendland-kernel convolution slices on the sphere, to validate CMIP5/CMIP6 climate models against reanalysis and observations.
Problem
Existing climate model validation metrics (RMSE, correlation, or spatial-mean Wasserstein distance) either ignore distributional differences or discard spatial variability, and sliced Wasserstein methods are defined for vectors or square images, not spherical fields.
Approach
Extends the convolutional sliced Wasserstein distance to functions on the unit sphere by defining a functional sliced WD with radial (chordal-distance) Wendland kernel convolution slicers, then averages local univariate Wasserstein distances over the sphere to get a global, spatially resolved similarity measure.
Key results
- NCEP has lower SCWD to ERA5 than all CMIP6 models for surface temperature, while the GMWD ranks NCEP among median CMIP6 models.
- NorESM2-MM has the lowest CMIP6 SCWD to GPCP for total precipitation by a relatively wide margin.
- Median SCWD of CMIP6 models is lower than CMIP5 for both surface temperature and precipitation, with a more distinct gap for precipitation; the improvement is described as modest.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CMIP6 instead of CMIP5 models | Climate model simulations · Surface temperature to ERA5 | median SCWD | Helped |
| Use CMIP6 instead of CMIP5 models | Climate model simulations · Precipitation to GPCP | median SCWD | Helped |
| Use SCWD with local spatial slices instead of global mean-based WD | Climate model validation · Surface temperature to ERA5 | similarity ranking | Helped |
| Use SCWD with local spatial slices instead of global mean-based WD | Climate model validation · Precipitation to GPCP | similarity ranking | Helped |
| Vary the Wendland kernel range from 1,000 km to 500 km or 2,500 km (ablation) | SCWD model rankings · CMIP6 surface temperature and precipitation | model ranking | No clear effect |
| Increase the Wendland kernel range (ablation) | SCWD model rankings · CMIP6 precipitation | model ranking | Helped |
Surprising findings
- Under the global mean-based WD, NCEP ranks among median CMIP6 models for surface temperature even though its SCWD to ERA5 is lower than all CMIP6 models.
- ERA5 precipitation has a lower SCWD to GPCP than NCEP, and ranks best under SCWD but only average under GMWD.
Limitations
- Metric positivity (identity of indiscernibles) is not proven for the functional sliced WD; only pseudometric properties are established.
- Results depend on the range parameter l, requiring researcher choice of kernel; the kernel must be positive definite for full spatial information.
- Data are gridded with differing resolutions requiring regridding; precipitation reference (GPCP) has some missing data handled by thresholding.
Experimental setup
Datasets: CMIP5 historical outputs CMIP6 historical outputs ERA5 reanalysis NCEP/DOE Reanalysis-2 GPCP daily precipitation
Benchmarks: CMIP5 and CMIP6 historical surface temperature vs ERA5 CMIP5 and CMIP6 total precipitation vs GPCP
Metrics: SCWD (spherical convolutional Wasserstein distance) GMWD model rankings
Baselines: global mean-based Wasserstein distance (GMWD) RMSE NCEP Reanalysis-2 (as reference model)
Builds on: sliced Wasserstein distance convolutional sliced Wasserstein distance generalized sliced Wasserstein distance global mean-based Wasserstein distance
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