Sea Surface Altimetry Data Analysis - Physical Oceanography Cookbook

For this example we will use gridded sea-surface altimetry data from The Copernicus Marine Environment. This is a widely used dataset in physical oceanography and climate.

The dataset has been extracted from Copernicus and stored in google cloud storage in xarray-zarr format. It is catalogues in the Pangeo Cloud Catalog at https://catalog.pangeo.io/browse/master/ocean/sea_surface_height/

import numpy as np
import xarray as xr
import matplotlib.pyplot as plt
import hvplot.xarray
plt.rcParams['figure.figsize'] = (15,10)
%matplotlib inline

Initialize Dataset¶

Here we load the dataset from the zarr store. Note that this very large dataset initializes nearly instantly, and we can see the full list of variables and coordinates, including metadata for each variable.

from intake import open_catalog
cat = open_catalog("https://raw.githubusercontent.com/pangeo-data/pangeo-datastore/master/intake-catalogs/ocean.yaml")
ds  = cat["sea_surface_height"].to_dask()
ds

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[2], line 3
      1 from intake import open_catalog
      2 cat = open_catalog("https://raw.githubusercontent.com/pangeo-data/pangeo-datastore/master/intake-catalogs/ocean.yaml")
----> 3 ds  = cat["sea_surface_height"].to_dask()
      4 ds

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/intake_xarray/base.py:8, in IntakeXarraySourceAdapter.to_dask(self)
      6 def to_dask(self):
      7     if "chunks" not in self.reader.kwargs:
----> 8         return self.reader(chunks={}).read()
      9     else:
     10         return self.reader.read()

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/intake/readers/readers.py:121, in BaseReader.read(self, *args, **kwargs)
    119 kw.update(kwargs)
    120 args = kw.pop("args", ()) or args
--> 121 return self._read(*args, **kw)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/intake/readers/readers.py:1327, in XArrayDatasetReader._read(self, data, open_local, **kw)
   1325         f = fsspec.open(data.url, **(data.storage_options or {})).open()
   1326         return open_dataset(f, **kw)
-> 1327 return open_dataset(data.url, **kw)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/xarray/backends/api.py:607, in open_dataset(filename_or_obj, engine, chunks, cache, decode_cf, mask_and_scale, decode_times, decode_timedelta, use_cftime, concat_characters, decode_coords, drop_variables, create_default_indexes, inline_array, chunked_array_type, from_array_kwargs, backend_kwargs, **kwargs)
    595 decoders = _resolve_decoders_kwargs(
    596     decode_cf,
    597     open_backend_dataset_parameters=backend.open_dataset_parameters,
   (...)    603     decode_coords=decode_coords,
    604 )
    606 overwrite_encoded_chunks = kwargs.pop("overwrite_encoded_chunks", None)
--> 607 backend_ds = backend.open_dataset(
    608     filename_or_obj,
    609     drop_variables=drop_variables,
    610     **decoders,
    611     **kwargs,
    612 )
    613 ds = _dataset_from_backend_dataset(
    614     backend_ds,
    615     filename_or_obj,
   (...)    626     **kwargs,
    627 )
    628 return ds

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/xarray/backends/zarr.py:1683, in ZarrBackendEntrypoint.open_dataset(self, filename_or_obj, mask_and_scale, decode_times, concat_characters, decode_coords, drop_variables, use_cftime, decode_timedelta, group, mode, synchronizer, consolidated, chunk_store, storage_options, zarr_version, zarr_format, store, engine, use_zarr_fill_value_as_mask, cache_members)
   1681 filename_or_obj = _normalize_path(filename_or_obj)
   1682 if not store:
-> 1683     store = ZarrStore.open_group(
   1684         filename_or_obj,
   1685         group=group,
   1686         mode=mode,
   1687         synchronizer=synchronizer,
   1688         consolidated=consolidated,
   1689         consolidate_on_close=False,
   1690         chunk_store=chunk_store,
   1691         storage_options=storage_options,
   1692         zarr_version=zarr_version,
   1693         use_zarr_fill_value_as_mask=None,
   1694         zarr_format=zarr_format,
   1695         cache_members=cache_members,
   1696     )
   1698 store_entrypoint = StoreBackendEntrypoint()
   1699 with close_on_error(store):

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/xarray/backends/zarr.py:722, in ZarrStore.open_group(cls, store, mode, synchronizer, group, consolidated, consolidate_on_close, chunk_store, storage_options, append_dim, write_region, safe_chunks, align_chunks, zarr_version, zarr_format, use_zarr_fill_value_as_mask, write_empty, cache_members)
    696 @classmethod
    697 def open_group(
    698     cls,
   (...)    715     cache_members: bool = True,
    716 ):
    717     (
    718         zarr_group,
    719         consolidate_on_close,
    720         close_store_on_close,
    721         use_zarr_fill_value_as_mask,
--> 722     ) = _get_open_params(
    723         store=store,
    724         mode=mode,
    725         synchronizer=synchronizer,
    726         group=group,
    727         consolidated=consolidated,
    728         consolidate_on_close=consolidate_on_close,
    729         chunk_store=chunk_store,
    730         storage_options=storage_options,
    731         zarr_version=zarr_version,
    732         use_zarr_fill_value_as_mask=use_zarr_fill_value_as_mask,
    733         zarr_format=zarr_format,
    734     )
    736     return cls(
    737         zarr_group,
    738         mode,
   (...)    747         cache_members=cache_members,
    748     )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/xarray/backends/zarr.py:1887, in _get_open_params(store, mode, synchronizer, group, consolidated, consolidate_on_close, chunk_store, storage_options, zarr_version, use_zarr_fill_value_as_mask, zarr_format)
   1883 group = open_kwargs.pop("path")
   1885 if consolidated:
   1886     # TODO: an option to pass the metadata_key keyword
-> 1887     zarr_root_group = zarr.open_consolidated(store, **open_kwargs)
   1888 elif consolidated is None:
   1889     # same but with more error handling in case no consolidated metadata found
   1890     try:

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/api/synchronous.py:238, in open_consolidated(use_consolidated, *args, **kwargs)
    233 def open_consolidated(*args: Any, use_consolidated: Literal[True] = True, **kwargs: Any) -> Group:
    234     """
    235     Alias for [`open_group`][zarr.api.synchronous.open_group] with ``use_consolidated=True``.
    236     """
    237     return Group(
--> 238         sync(async_api.open_consolidated(*args, use_consolidated=use_consolidated, **kwargs))
    239     )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/core/sync.py:159, in sync(coro, loop, timeout)
    156 return_result = next(iter(finished)).result()
    158 if isinstance(return_result, BaseException):
--> 159     raise return_result
    160 else:
    161     return return_result

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/core/sync.py:119, in _runner(coro)
    114 """
    115 Await a coroutine and return the result of running it. If awaiting the coroutine raises an
    116 exception, the exception will be returned.
    117 """
    118 try:
--> 119     return await coro
    120 except Exception as ex:
    121     return ex

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/api/asynchronous.py:415, in open_consolidated(use_consolidated, *args, **kwargs)
    410 if use_consolidated is not True:
    411     raise TypeError(
    412         "'use_consolidated' must be 'True' in 'open_consolidated'. Use 'open' with "
    413         "'use_consolidated=False' to bypass consolidated metadata."
    414     )
--> 415 return await open_group(*args, use_consolidated=use_consolidated, **kwargs)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/api/asynchronous.py:866, in open_group(store, mode, cache_attrs, synchronizer, path, chunk_store, storage_options, zarr_version, zarr_format, meta_array, attributes, use_consolidated)
    864 try:
    865     if mode in _READ_MODES:
--> 866         return await AsyncGroup.open(
    867             store_path, zarr_format=zarr_format, use_consolidated=use_consolidated
    868         )
    869 except (KeyError, FileNotFoundError):
    870     pass

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/core/group.py:570, in AsyncGroup.open(cls, store, zarr_format, use_consolidated)
    563         raise FileNotFoundError(store_path)
    564 elif zarr_format is None:
    565     (
    566         zarr_json_bytes,
    567         zgroup_bytes,
    568         zattrs_bytes,
    569         maybe_consolidated_metadata_bytes,
--> 570     ) = await asyncio.gather(
    571         (store_path / ZARR_JSON).get(),
    572         (store_path / ZGROUP_JSON).get(),
    573         (store_path / ZATTRS_JSON).get(),
    574         (store_path / str(consolidated_key)).get(),
    575     )
    576     if zarr_json_bytes is not None and zgroup_bytes is not None:
    577         # warn and favor v3
    578         msg = f"Both zarr.json (Zarr format 3) and .zgroup (Zarr format 2) metadata objects exist at {store_path}. Zarr format 3 will be used."

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/storage/_common.py:168, in StorePath.get(self, prototype, byte_range)
    166 if prototype is None:
    167     prototype = default_buffer_prototype()
--> 168 return await self.store.get(self.path, prototype=prototype, byte_range=byte_range)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/zarr/storage/_fsspec.py:289, in FsspecStore.get(self, key, prototype, byte_range)
    287 try:
    288     if byte_range is None:
--> 289         value = prototype.buffer.from_bytes(await self.fs._cat_file(path))
    290     elif isinstance(byte_range, RangeByteRequest):
    291         value = prototype.buffer.from_bytes(
    292             await self.fs._cat_file(
    293                 path,
   (...)    296             )
    297         )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/gcsfs/core.py:1120, in GCSFileSystem._cat_file(self, path, start, end, **kwargs)
   1118 else:
   1119     head = {}
-> 1120 headers, out = await self._call("GET", u2, headers=head)
   1121 return out

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/gcsfs/core.py:483, in GCSFileSystem._call(self, method, path, json_out, info_out, *args, **kwargs)
    479 async def _call(
    480     self, method, path, *args, json_out=False, info_out=False, **kwargs
    481 ):
    482     logger.debug(f"{method.upper()}: {path}, {args}, {kwargs.get('headers')}")
--> 483     status, headers, info, contents = await self._request(
    484         method, path, *args, **kwargs
    485     )
    486     if json_out:
    487         return json.loads(contents)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/decorator.py:224, in decorate.<locals>.fun(*args, **kw)
    222 if not kwsyntax:
    223     args, kw = fix(args, kw, sig)
--> 224 return await caller(func, *(extras + args), **kw)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/gcsfs/retry.py:135, in retry_request(func, retries, *args, **kwargs)
    133     if retry > 0:
    134         await asyncio.sleep(min(random.random() + 2 ** (retry - 1), 32))
--> 135     return await func(*args, **kwargs)
    136 except (
    137     HttpError,
    138     requests.exceptions.RequestException,
   (...)    141     aiohttp.client_exceptions.ClientError,
    142 ) as e:
    143     if (
    144         isinstance(e, HttpError)
    145         and e.code == 400
    146         and "requester pays" in e.message
    147     ):

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/gcsfs/core.py:476, in GCSFileSystem._request(self, method, path, headers, json, data, *args, **kwargs)
    473 info = r.request_info  # for debug only
    474 contents = await r.read()
--> 476 validate_response(status, contents, path, args)
    477 return status, headers, info, contents

File ~/micromamba/envs/po-cookbook-dev/lib/python3.14/site-packages/gcsfs/retry.py:120, in validate_response(status, content, path, args)
    118     raise requests.exceptions.ProxyError()
    119 elif "invalid" in str(msg):
--> 120     raise ValueError(f"Bad Request: {path}\n{msg}")
    121 elif error and not isinstance(error, str):
    122     raise HttpError(error)

ValueError: Bad Request: https://storage.googleapis.com/download/storage/v1/b/pangeo-cmems-duacs/o/.zattrs?alt=media
User project specified in the request is invalid.

Visually Examine Some of the Data¶

Let’s do a sanity check that the data looks reasonable. Here we use the hvplot interactive plotting library.

ds.sla.hvplot.image('longitude', 'latitude',
                    rasterize=True, dynamic=True, width=800, height=450, 
                    widget_type='scrubber', widget_location='bottom', cmap='RdBu_r')

Create and Connect to Dask Distributed Cluster¶

from dask_gateway import Gateway
from dask.distributed import Client

gateway = Gateway()
cluster = gateway.new_cluster()
cluster.adapt(minimum=1, maximum=20)
cluster

** ☝️ Don’t forget to click the link above to view the scheduler dashboard! **

client = Client(cluster)
client

Timeseries of Global Mean Sea Level¶

Here we make a simple yet fundamental calculation: the rate of increase of global mean sea level over the observational period.

# the number of GB involved in the reduction
ds.sla.nbytes/1e9

# the computationally intensive step
sla_timeseries = ds.sla.mean(dim=('latitude', 'longitude')).load()

sla_timeseries.plot(label='full data')
sla_timeseries.rolling(time=365, center=True).mean().plot(label='rolling annual mean')
plt.ylabel('Sea Level Anomaly [m]')
plt.title('Global Mean Sea Level')
plt.legend()
plt.grid()

In order to understand how the sea level rise is distributed in latitude, we can make a sort of Hovmöller diagram.

sla_hov = ds.sla.mean(dim='longitude').load()

fig, ax = plt.subplots(figsize=(12, 4))
sla_hov.name = 'Sea Level Anomaly [m]'
sla_hov.transpose().plot(vmax=0.2, ax=ax)

We can see that most sea level rise is actually in the Southern Hemisphere.

Sea Level Variability¶

We can examine the natural variability in sea level by looking at its standard deviation in time.

sla_std = ds.sla.std(dim='time').load()
sla_std.name = 'Sea Level Variability [m]'

ax = sla_std.plot()
_ = plt.title('Sea Level Variability')