Compute area-weighted averages

[j08lue]

Global datasets with a lat/lon grid or so can have large variations in cell size.

When calculating averages (zonal statistics) over large areas (across a couple degrees latitude or more), an accurate result would require that

1. Each cell is weighted by the pixel / cell area
2. [much less important!] Cells only partially covered by the query geometry are weighed according to the percent of intersection

As clarified previously, rio-tiler, which we are using, calculates unweighted averages only

https://github.com/cogeotiff/rio-tiler/blob/066878704f841a332a53027b74f7e0a97f10f4b2/rio_tiler/io/rasterio.py#L573-L584

While intersection-weighted averages are complex to compute, simple pixel-area-weighted averages should not be, as pixel areas can be computed from the transform.

Before implementing this functionality, we should make a benchmark (documented in a notebook or so), that shows what difference it makes to have pixel-area weights. Possible cases could be

1. Average over the US (CONUS) for a 1 km resolution grid
2. Average over the North American continent for a 100 km resolution grid

I can also provide sample data for benchmarking, if that helps. There are a bunch of global datasets in https://www.earthdata.nasa.gov/dashboard/data-catalog. Maybe one of the NO2 ones?

To access them, you may need to use the VEDA JupyterHub, though, since the buckets are private.

A relevant GHG dataset to benchmark this against would be CASA-GFED3 Land Carbon Flux, which should be accessible on the VEDA or GHG Center JupyterHub services.

User stories

1. As a user of the zonal statistics function, I would like the results to be accurate no matter what the original projection of the data is, so I can trust the results.
2. As a scientist distributing my large-scale data through TiTiler with the zonal statistics endpoint, I need the results of that calculation to be accurate, such that consumers of that data get correct extracts from my data.
3. As a provider of a zonal statistics service for large-scale data, I need the calculations to be accurate, so I can provide this service with confidence.

Acceptance criteria

• Did a benchmark for the difference area-weighting makes for a few use cases
• Implement weighted averages by pixel area

[j08lue]

What is needed to surface this functionality in the GHG Center backend and use it in the frontend?

When we have a working endpoint, we also need to validate the values we compute.

[j08lue]

Follow-up ticket: https://github.com/NASA-IMPACT/veda-architecture/issues/334