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:687, 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, inline_array, chunked_array_type, from_array_kwargs, backend_kwargs, **kwargs)
    675 decoders = _resolve_decoders_kwargs(
    676     decode_cf,
    677     open_backend_dataset_parameters=backend.open_dataset_parameters,
   (...)    683     decode_coords=decode_coords,
    684 )
    686 overwrite_encoded_chunks = kwargs.pop("overwrite_encoded_chunks", None)
--> 687 backend_ds = backend.open_dataset(
    688     filename_or_obj,
    689     drop_variables=drop_variables,
    690     **decoders,
    691     **kwargs,
    692 )
    693 ds = _dataset_from_backend_dataset(
    694     backend_ds,
    695     filename_or_obj,
   (...)    705     **kwargs,
    706 )
    707 return ds

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:1578, 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)
   1576 filename_or_obj = _normalize_path(filename_or_obj)
   1577 if not store:
-> 1578     store = ZarrStore.open_group(
   1579         filename_or_obj,
   1580         group=group,
   1581         mode=mode,
   1582         synchronizer=synchronizer,
   1583         consolidated=consolidated,
   1584         consolidate_on_close=False,
   1585         chunk_store=chunk_store,
   1586         storage_options=storage_options,
   1587         zarr_version=zarr_version,
   1588         use_zarr_fill_value_as_mask=None,
   1589         zarr_format=zarr_format,
   1590         cache_members=cache_members,
   1591     )
   1593 store_entrypoint = StoreBackendEntrypoint()
   1594 with close_on_error(store):

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:664, 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)
    638 @classmethod
    639 def open_group(
    640     cls,
   (...)    657     cache_members: bool = True,
    658 ):
    659     (
    660         zarr_group,
    661         consolidate_on_close,
    662         close_store_on_close,
    663         use_zarr_fill_value_as_mask,
--> 664     ) = _get_open_params(
    665         store=store,
    666         mode=mode,
    667         synchronizer=synchronizer,
    668         group=group,
    669         consolidated=consolidated,
    670         consolidate_on_close=consolidate_on_close,
    671         chunk_store=chunk_store,
    672         storage_options=storage_options,
    673         zarr_version=zarr_version,
    674         use_zarr_fill_value_as_mask=use_zarr_fill_value_as_mask,
    675         zarr_format=zarr_format,
    676     )
    678     return cls(
    679         zarr_group,
    680         mode,
   (...)    689         cache_members=cache_members,
    690     )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:1777, 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)
   1773 group = open_kwargs.pop("path")
   1775 if consolidated:
   1776     # TODO: an option to pass the metadata_key keyword
-> 1777     zarr_root_group = zarr.open_consolidated(store, **open_kwargs)
   1778 elif consolidated is None:
   1779     # same but with more error handling in case no consolidated metadata found
   1780     try:

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/api/synchronous.py:217, in open_consolidated(use_consolidated, *args, **kwargs)
    212 def open_consolidated(*args: Any, use_consolidated: Literal[True] = True, **kwargs: Any) -> Group:
    213     """
    214     Alias for :func:`open_group` with ``use_consolidated=True``.
    215     """
    216     return Group(
--> 217         sync(async_api.open_consolidated(*args, use_consolidated=use_consolidated, **kwargs))
    218     )

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:362, in open_consolidated(use_consolidated, *args, **kwargs)
    357 if use_consolidated is not True:
    358     raise TypeError(
    359         "'use_consolidated' must be 'True' in 'open_consolidated'. Use 'open' with "
    360         "'use_consolidated=False' to bypass consolidated metadata."
    361     )
--> 362 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:825, in open_group(store, mode, cache_attrs, synchronizer, path, chunk_store, storage_options, zarr_version, zarr_format, meta_array, attributes, use_consolidated)
    823 try:
    824     if mode in _READ_MODES:
--> 825         return await AsyncGroup.open(
    826             store_path, zarr_format=zarr_format, use_consolidated=use_consolidated
    827         )
    828 except (KeyError, FileNotFoundError):
    829     pass

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/core/group.py:538, in AsyncGroup.open(cls, store, zarr_format, use_consolidated)
    531         raise FileNotFoundError(store_path)
    532 elif zarr_format is None:
    533     (
    534         zarr_json_bytes,
    535         zgroup_bytes,
    536         zattrs_bytes,
    537         maybe_consolidated_metadata_bytes,
--> 538     ) = await asyncio.gather(
    539         (store_path / ZARR_JSON).get(),
    540         (store_path / ZGROUP_JSON).get(),
    541         (store_path / ZATTRS_JSON).get(),
    542         (store_path / str(consolidated_key)).get(),
    543     )
    544     if zarr_json_bytes is not None and zgroup_bytes is not None:
    545         # warn and favor v3
    546         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:124, in StorePath.get(self, prototype, byte_range)
    122 if prototype is None:
    123     prototype = default_buffer_prototype()
--> 124 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:230, in FsspecStore.get(self, key, prototype, byte_range)
    228 try:
    229     if byte_range is None:
--> 230         value = prototype.buffer.from_bytes(await self.fs._cat_file(path))
    231     elif isinstance(byte_range, RangeByteRequest):
    232         value = prototype.buffer.from_bytes(
    233             await self.fs._cat_file(
    234                 path,
   (...)    237             )
    238         )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/core.py:1115, in GCSFileSystem._cat_file(self, path, start, end, **kwargs)
   1113 else:
   1114     head = {}
-> 1115 headers, out = await self._call("GET", u2, headers=head)
   1116 return out

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/core.py:481, in GCSFileSystem._call(self, method, path, json_out, info_out, *args, **kwargs)
    477 async def _call(
    478     self, method, path, *args, json_out=False, info_out=False, **kwargs
    479 ):
    480     logger.debug(f"{method.upper()}: {path}, {args}, {kwargs.get('headers')}")
--> 481     status, headers, info, contents = await self._request(
    482         method, path, *args, **kwargs
    483     )
    484     if json_out:
    485         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:474, in GCSFileSystem._request(self, method, path, headers, json, data, *args, **kwargs)
    471 info = r.request_info  # for debug only
    472 contents = await r.read()
--> 474 validate_response(status, contents, path, args)
    475 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