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/python3.13/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/python3.13/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/python3.13/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/python3.13/site-packages/xarray/backends/api.py:760, 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)
    748 decoders = _resolve_decoders_kwargs(
    749     decode_cf,
    750     open_backend_dataset_parameters=backend.open_dataset_parameters,
   (...)    756     decode_coords=decode_coords,
    757 )
    759 overwrite_encoded_chunks = kwargs.pop("overwrite_encoded_chunks", None)
--> 760 backend_ds = backend.open_dataset(
    761     filename_or_obj,
    762     drop_variables=drop_variables,
    763     **decoders,
    764     **kwargs,
    765 )
    766 ds = _dataset_from_backend_dataset(
    767     backend_ds,
    768     filename_or_obj,
   (...)    779     **kwargs,
    780 )
    781 return ds

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:1654, 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)
   1652 filename_or_obj = _normalize_path(filename_or_obj)
   1653 if not store:
-> 1654     store = ZarrStore.open_group(
   1655         filename_or_obj,
   1656         group=group,
   1657         mode=mode,
   1658         synchronizer=synchronizer,
   1659         consolidated=consolidated,
   1660         consolidate_on_close=False,
   1661         chunk_store=chunk_store,
   1662         storage_options=storage_options,
   1663         zarr_version=zarr_version,
   1664         use_zarr_fill_value_as_mask=None,
   1665         zarr_format=zarr_format,
   1666         cache_members=cache_members,
   1667     )
   1669 store_entrypoint = StoreBackendEntrypoint()
   1670 with close_on_error(store):

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:714, 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)
    688 @classmethod
    689 def open_group(
    690     cls,
   (...)    707     cache_members: bool = True,
    708 ):
    709     (
    710         zarr_group,
    711         consolidate_on_close,
    712         close_store_on_close,
    713         use_zarr_fill_value_as_mask,
--> 714     ) = _get_open_params(
    715         store=store,
    716         mode=mode,
    717         synchronizer=synchronizer,
    718         group=group,
    719         consolidated=consolidated,
    720         consolidate_on_close=consolidate_on_close,
    721         chunk_store=chunk_store,
    722         storage_options=storage_options,
    723         zarr_version=zarr_version,
    724         use_zarr_fill_value_as_mask=use_zarr_fill_value_as_mask,
    725         zarr_format=zarr_format,
    726     )
    728     return cls(
    729         zarr_group,
    730         mode,
   (...)    739         cache_members=cache_members,
    740     )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:1858, 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)
   1854 group = open_kwargs.pop("path")
   1856 if consolidated:
   1857     # TODO: an option to pass the metadata_key keyword
-> 1858     zarr_root_group = zarr.open_consolidated(store, **open_kwargs)
   1859 elif consolidated is None:
   1860     # same but with more error handling in case no consolidated metadata found
   1861     try:

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/api/synchronous.py:231, in open_consolidated(use_consolidated, *args, **kwargs)
    226 def open_consolidated(*args: Any, use_consolidated: Literal[True] = True, **kwargs: Any) -> Group:
    227     """
    228     Alias for :func:`open_group` with ``use_consolidated=True``.
    229     """
    230     return Group(
--> 231         sync(async_api.open_consolidated(*args, use_consolidated=use_consolidated, **kwargs))
    232     )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/core/sync.py:163, in sync(coro, loop, timeout)
    160 return_result = next(iter(finished)).result()
    162 if isinstance(return_result, BaseException):
--> 163     raise return_result
    164 else:
    165     return return_result

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/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/python3.13/site-packages/zarr/api/asynchronous.py:408, in open_consolidated(use_consolidated, *args, **kwargs)
    403 if use_consolidated is not True:
    404     raise TypeError(
    405         "'use_consolidated' must be 'True' in 'open_consolidated'. Use 'open' with "
    406         "'use_consolidated=False' to bypass consolidated metadata."
    407     )
--> 408 return await open_group(*args, use_consolidated=use_consolidated, **kwargs)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/api/asynchronous.py:857, in open_group(store, mode, cache_attrs, synchronizer, path, chunk_store, storage_options, zarr_version, zarr_format, meta_array, attributes, use_consolidated)
    855 try:
    856     if mode in _READ_MODES:
--> 857         return await AsyncGroup.open(
    858             store_path, zarr_format=zarr_format, use_consolidated=use_consolidated
    859         )
    860 except (KeyError, FileNotFoundError):
    861     pass

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/core/group.py:559, in AsyncGroup.open(cls, store, zarr_format, use_consolidated)
    552         raise FileNotFoundError(store_path)
    553 elif zarr_format is None:
    554     (
    555         zarr_json_bytes,
    556         zgroup_bytes,
    557         zattrs_bytes,
    558         maybe_consolidated_metadata_bytes,
--> 559     ) = await asyncio.gather(
    560         (store_path / ZARR_JSON).get(),
    561         (store_path / ZGROUP_JSON).get(),
    562         (store_path / ZATTRS_JSON).get(),
    563         (store_path / str(consolidated_key)).get(),
    564     )
    565     if zarr_json_bytes is not None and zgroup_bytes is not None:
    566         # warn and favor v3
    567         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/python3.13/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/python3.13/site-packages/zarr/storage/_fsspec.py:299, in FsspecStore.get(self, key, prototype, byte_range)
    297 try:
    298     if byte_range is None:
--> 299         value = prototype.buffer.from_bytes(await self.fs._cat_file(path))
    300     elif isinstance(byte_range, RangeByteRequest):
    301         value = prototype.buffer.from_bytes(
    302             await self.fs._cat_file(
    303                 path,
   (...)    306             )
    307         )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/core.py:1119, in GCSFileSystem._cat_file(self, path, start, end, **kwargs)
   1117 else:
   1118     head = {}
-> 1119 headers, out = await self._call("GET", u2, headers=head)
   1120 return out

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/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/python3.13/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/python3.13/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/python3.13/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/python3.13/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')

Introduction

Project Pythia Notebook Template

Example Workflows

Along Track Altimetry Analysis