This page was generated from /home/docs/checkouts/readthedocs.org/user_builds/oceanspy/checkouts/latest/docs/Particles.ipynb.

Use Case 2: Particles

In this example we will subsample a dataset stored on SciServer using trajectories of synthetic Lagrangian particles. OceanSpy enables the extraction of properties at any given location, but it does not have functionality to compute Lagrangian trajectories yet. The trajectories used in this notebook have been previously computed using a Matlab-based Lagrangian particle code (Gelderloos et al., 2016). The Lagrangian particle code, along with synthetic oceanographic observational platforms (such as Argo floats, isobaric floats, current profiler, and gliders), will be incorporated into OceanSpy in future releases.

The animation below shows the change in temperature of synthetic particles along their 3D trajectories. Particles have been released in Denmark Strait and tracked backward in time from day 0 to day 180, and tracked forward in time from day 180 to 360. All particles are animated forward in time. Source: https://player.vimeo.com/video/296949375

[1]:

# Display animation
from IPython.display import HTML

# Link
s = "https://player.vimeo.com/video/296949375"

# Options
w = 640
h = 360
f = 0
a = "autoplay; fullscreen"

# Display
HTML(
    f'<iframe src="{s}"'
    'width="640" height="360" frameborder="0" allow="autoplay; fullscreen"'
    "allowfullscreen></iframe>"
)

/home/idies/mambaforge/envs/Oceanography/lib/python3.9/site-packages/IPython/core/display.py:431: UserWarning: Consider using IPython.display.IFrame instead
  warnings.warn("Consider using IPython.display.IFrame instead")

[1]:
The subsampling method used in this notebook resembles Lagrangian floats deployed by observational oceanographers, such as RAFOS floats. RAFOS floats are isobaric and tracked acoustically. They measure water properties and provide accurate trajectories in both the horizontal and vertical dimensions. The following picture shows the deployment of a RAFOS float during the Overturning in the Subpolar North Atlantic Program (OSNAP). Source: www.o-snap.org
RAFOS

Extract

The computational time to extract particle properties depends on the number of particles, the length of their trajectories, the number of variables requested, and, more importantly, how far the particles travel in the domain and therefore, how dispersed the Lagrangian trajectories are. Thus, it is preferable to extract particle properties asynchronously using the Job mode of SciServer compute (see SciServer access for step-by-step instructions). This notebook, when executed in interactive mode, skips the subsampling step. Instead, it loads an OceanDataset previously created executing the same notebook in Job mode.

Set interactive = True to run in Interactive mode, or interactive = False to run in Job mode. Alternatively, you can activate the Job mode by typing interactive = False in the Parameters slot of the SciServer Job submission form.

[2]:

interactive = True  # True: Interactive - False: Job

# Check parameters.txt
try:
    # Use values from parameters.txt
    f = open("parameters.txt", "r")
    for line in f:
        exec(line)
    f.close()
except FileNotFoundError:
    # Keep preset values
    pass

The following cell starts a dask client (see the Dask Client section in the tutorial).

[3]:

# Start Client
from dask.distributed import Client

client = Client()
client

[3]:

Client

Client-ac9f71bc-d8db-11ed-8a48-0242ac110006

Connection method: Cluster object Cluster type: distributed.LocalCluster
Dashboard: http://127.0.0.1:8787/status

Cluster Info

While the following cell set up the environment.

[4]:

import matplotlib.pyplot as plt
import numpy as np

# Additional imports
import xarray as xr
from cartopy.crs import PlateCarree

# Import OceanSpy
import oceanspy as ospy

Here we open the OceanDataset containing the Eulerian fields that we want to sample along the Lagrangian trajectories. Then, for plotting purposes, we mask out the land from the bathymetry (variable Depth) and merge the variable masked_Depth into the OceanDataset.

[5]:

# Open OceanDataset (eulerian fields)
od_eul = ospy.open_oceandataset.from_catalog("EGshelfIIseas2km_ASR_full")

# Mask depth for plotting purposes
Depth = od_eul.dataset["Depth"]
Depth = Depth.where(Depth > 0)
od_eul = od_eul.merge_into_oceandataset(Depth.rename("masked_Depth"))

Opening EGshelfIIseas2km_ASR_full.
High-resolution (~2km) numerical simulation covering the east Greenland shelf (EGshelf),
and the Iceland and Irminger Seas (IIseas) forced by the Arctic System Reanalysis (ASR).
Citation:
 * Almansi et al., 2020 - GRL.
Characteristics:
 * full: Full domain without variables to close budgets.
See also:
 * EGshelfIIseas2km_ASR_crop: Cropped domain with variables to close budgets.

We will analyze about 4,000 synthetic particles released in Denmark Strait at the end of February, and tracked forward in time for 30 days (with 6 hour resolution). The following properties will be extracted: temperature, salinity, ocean depth, and the vertical component of relative vorticity. Note that OceanSpy can extract any property, and variables such as momVort3 that are not in the model cell centers can be subsampled.

[6]:

import os
import subprocess

# Create or download OceanDataset with particle properties
mat_name = "oceanspy_particle_trajectories.mat"  # Used by Job
nc_name = "oceanspy_particle_properties.nc"  # Created by Job
if interactive:
    # Download OceanDataset
    if not os.path.isdir(mat_name):
        import subprocess

        print(f"Downloading [{nc_name}].")
        commands = [
            f"wget -v -O {nc_name} -L "
            "https://livejohnshopkins-my.sharepoint.com/"
            ":u:/g/personal/malmans2_jh_edu/"
            "EWvf_TyoEdpaDKcFacaPLI4B1fLGf9qleW7xbIDlKVPJDw?"
            "download=1"
        ]
        subprocess.call("&&".join(commands), shell=True)
else:
    # Download trajectories
    if not os.path.isdir(mat_name):
        print(f"Downloading [{mat_name}].")
        commands = [
            f"wget -v -O {mat_name} -L "
            "https://livejohnshopkins-my.sharepoint.com/"
            ":u:/g/personal/malmans2_jh_edu/"
            "ETSRG8OcbWpccc7zx_rbzsIBqBl1UATQSwNTjqtk9fLR-Q?"
            "download=1"
        ]
        subprocess.call("&&".join(commands), shell=True)

    # Read trajectories
    import scipy.io as sio

    particle_data = sio.loadmat(mat_name)

    # Get time
    time_origin = np.datetime64("2008-02-29T00:00")
    times = np.asarray(
        [
            time_origin + np.timedelta64(int(dt * 24), "h")
            for dt in particle_data["timee"].squeeze()
        ]
    )

    # Get trajectories
    Xpart = particle_data["f_lons"].transpose()
    Ypart = particle_data["f_lats"].transpose()
    Zpart = particle_data["f_deps"].transpose()

    # Pick variables (velocities and hydrography)
    varList = ["Temp", "S", "momVort3", "Depth"]

    # Extract properties
    od_lag = ospy.subsample.particle_properties(
        od_eul,
        times=times,
        Ypart=Ypart,
        Xpart=Xpart,
        Zpart=Zpart,
        varList=varList,
    )

    # Save in netCDF format
    od_lag.to_netcdf(nc_name)

# Open OceanDataset
od_lag = ospy.open_oceandataset.from_netcdf(nc_name)

Downloading [oceanspy_particle_properties.nc].

--2023-04-11 22:44:06--  https://livejohnshopkins-my.sharepoint.com/:u:/g/personal/malmans2_jh_edu/EWvf_TyoEdpaDKcFacaPLI4B1fLGf9qleW7xbIDlKVPJDw?download=1
Resolving livejohnshopkins-my.sharepoint.com (livejohnshopkins-my.sharepoint.com)... 13.107.138.8, 13.107.136.8, 2620:1ec:8f8::8, ...
Connecting to livejohnshopkins-my.sharepoint.com (livejohnshopkins-my.sharepoint.com)|13.107.138.8|:443... connected.
HTTP request sent, awaiting response... 302 Found
Location: /personal/malmans2_jh_edu/Documents/BoxMigration/oceanspy_particle_properties.nc?ga=1 [following]
--2023-04-11 22:44:07--  https://livejohnshopkins-my.sharepoint.com/personal/malmans2_jh_edu/Documents/BoxMigration/oceanspy_particle_properties.nc?ga=1
Reusing existing connection to livejohnshopkins-my.sharepoint.com:443.
HTTP request sent, awaiting response... 200 OK
Length: 45981653 (44M) [application/x-netcdf]
Saving to: ‘oceanspy_particle_properties.nc’

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  9550K .......... .......... .......... .......... .......... 21% 9.80M 40s
  9600K .......... .......... .......... .......... .......... 21% 19.0M 40s
  9650K .......... .......... .......... .......... .......... 21% 24.0M 40s
  9700K .......... .......... .......... .......... .......... 21% 12.1M 39s
  9750K .......... .......... .......... .......... .......... 21% 12.0M 39s
  9800K .......... .......... .......... .......... .......... 21% 18.4M 39s
  9850K .......... .......... .......... .......... .......... 22% 11.8M 39s
  9900K .......... .......... .......... .......... .......... 22% 29.6M 38s
  9950K .......... .......... .......... .......... .......... 22% 12.3M 38s
 10000K .......... .......... .......... .......... .......... 22% 14.8M 38s
 10050K .......... .......... .......... .......... .......... 22% 14.2M 38s
 10100K .......... .......... .......... .......... .......... 22% 23.2M 37s
 10150K .......... .......... .......... .......... .......... 22% 14.4M 37s
 10200K .......... .......... .......... .......... .......... 22% 16.1M 37s
 10250K .......... .......... .......... .......... .......... 22% 2.32M 37s
 10300K .......... .......... .......... .......... .......... 23% 11.0M 37s
 10350K .......... .......... .......... .......... .......... 23% 12.1M 36s
 10400K .......... .......... .......... .......... .......... 23% 12.5M 36s
 10450K .......... .......... .......... .......... .......... 23% 53.3M 36s
 10500K .......... .......... .......... .......... .......... 23% 12.8M 36s
 10550K .......... .......... .......... .......... .......... 23% 11.8M 36s
 10600K .......... .......... .......... .......... .......... 23% 62.3M 35s
 10650K .......... .......... .......... .......... .......... 23% 12.5M 35s
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 10750K .......... .......... .......... .......... .......... 24% 14.9M 35s
 10800K .......... .......... .......... .......... .......... 24% 56.9M 34s
 10850K .......... .......... .......... .......... .......... 24% 12.3M 34s
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 11800K .......... .......... .......... .......... .......... 26% 61.8M 31s
 11850K .......... .......... .......... .......... .......... 26% 13.6M 31s
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 11950K .......... .......... .......... .......... .......... 26% 72.3M 30s
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 12050K .......... .......... .......... .......... .......... 26% 69.5M 30s
 12100K .......... .......... .......... .......... .......... 27% 12.1M 30s
 12150K .......... .......... .......... .......... .......... 27% 71.7M 30s
 12200K .......... .......... .......... .......... .......... 27% 4.00M 30s
 12250K .......... .......... .......... .......... .......... 27% 13.7M 29s
 12300K .......... .......... .......... .......... .......... 27% 70.1M 29s
 12350K .......... .......... .......... .......... .......... 27% 11.4M 29s
 12400K .......... .......... .......... .......... .......... 27% 12.9M 29s
 12450K .......... .......... .......... .......... .......... 27% 16.3M 29s
 12500K .......... .......... .......... .......... .......... 27% 27.6M 29s
 12550K .......... .......... .......... .......... .......... 28% 13.1M 28s
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 12650K .......... .......... .......... .......... .......... 28% 12.2M 28s
 12700K .......... .......... .......... .......... .......... 28% 15.3M 28s
 12750K .......... .......... .......... .......... .......... 28% 30.9M 28s
 12800K .......... .......... .......... .......... .......... 28% 13.1M 28s
 12850K .......... .......... .......... .......... .......... 28% 15.5M 28s
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 13050K .......... .......... .......... .......... .......... 29% 12.5M 27s
 13100K .......... .......... .......... .......... .......... 29% 24.1M 27s
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 13350K .......... .......... .......... .......... .......... 29% 15.0M 26s
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 13450K .......... .......... .......... .......... .......... 30% 17.1M 26s
 13500K .......... .......... .......... .......... .......... 30% 13.8M 26s
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 13600K .......... .......... .......... .......... .......... 30% 36.2M 26s
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 13700K .......... .......... .......... .......... .......... 30% 66.1M 25s
 13750K .......... .......... .......... .......... .......... 30% 13.0M 25s
 13800K .......... .......... .......... .......... .......... 30% 69.1M 25s
 13850K .......... .......... .......... .......... .......... 30% 12.7M 25s
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 14000K .......... .......... .......... .......... .......... 31% 61.5M 25s
 14050K .......... .......... .......... .......... .......... 31% 12.9M 24s
 14100K .......... .......... .......... .......... .......... 31% 75.8M 24s
 14150K .......... .......... .......... .......... .......... 31% 13.0M 24s
 14200K .......... .......... .......... .......... .......... 31% 13.6M 24s
 14250K .......... .......... .......... .......... .......... 31% 55.5M 24s
 14300K .......... .......... .......... .......... .......... 31% 13.4M 24s
 14350K .......... .......... .......... .......... .......... 32% 14.0M 24s
 14400K .......... .......... .......... .......... .......... 32% 56.2M 24s
 14450K .......... .......... .......... .......... .......... 32% 12.0M 23s
 14500K .......... .......... .......... .......... .......... 32% 72.8M 23s
 14550K .......... .......... .......... .......... .......... 32% 14.9M 23s
 14600K .......... .......... .......... .......... .......... 32% 67.2M 23s
 14650K .......... .......... .......... .......... .......... 32% 13.0M 23s
 14700K .......... .......... .......... .......... .......... 32% 14.0M 23s
 14750K .......... .......... .......... .......... .......... 32%  395K 23s
 14800K .......... .......... .......... .......... .......... 33% 64.9M 23s
 14850K .......... .......... .......... .......... .......... 33% 6.23M 23s
 14900K .......... .......... .......... .......... .......... 33%  556K 23s
 14950K .......... .......... .......... .......... .......... 33% 6.43M 23s
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 15150K .......... .......... .......... .......... .......... 33% 3.86M 22s
 15200K .......... .......... .......... .......... .......... 33% 5.78M 22s
 15250K .......... .......... .......... .......... .......... 34% 10.5M 22s
 15300K .......... .......... .......... .......... .......... 34% 6.22M 22s
 15350K .......... .......... .......... .......... .......... 34% 10.6M 22s
 15400K .......... .......... .......... .......... .......... 34% 11.3M 22s
 15450K .......... .......... .......... .......... .......... 34% 6.02M 22s
 15500K .......... .......... .......... .......... .......... 34% 11.5M 22s
 15550K .......... .......... .......... .......... .......... 34% 6.13M 22s
 15600K .......... .......... .......... .......... .......... 34% 12.5M 22s
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 15700K .......... .......... .......... .......... .......... 35% 10.6M 21s
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 15800K .......... .......... .......... .......... .......... 35% 11.6M 21s
 15850K .......... .......... .......... .......... .......... 35% 5.28M 21s
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 15950K .......... .......... .......... .......... .......... 35% 11.1M 21s
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 16200K .......... .......... .......... .......... .......... 36% 11.8M 20s
 16250K .......... .......... .......... .......... .......... 36% 7.98M 20s
 16300K .......... .......... .......... .......... .......... 36% 18.8M 20s
 16350K .......... .......... .......... .......... .......... 36% 11.0M 20s
 16400K .......... .......... .......... .......... .......... 36% 12.4M 20s
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 16500K .......... .......... .......... .......... .......... 36% 11.6M 20s
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 16600K .......... .......... .......... .......... .......... 37% 34.2M 20s
 16650K .......... .......... .......... .......... .......... 37% 7.01M 20s
 16700K .......... .......... .......... .......... .......... 37% 32.7M 20s
 16750K .......... .......... .......... .......... .......... 37% 12.0M 19s
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 16850K .......... .......... .......... .......... .......... 37% 11.6M 19s
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 16950K .......... .......... .......... .......... .......... 37% 39.1M 19s
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 17050K .......... .......... .......... .......... .......... 38% 11.8M 19s
 17100K .......... .......... .......... .......... .......... 38% 16.0M 19s
 17150K .......... .......... .......... .......... .......... 38% 12.6M 19s
 17200K .......... .......... .......... .......... .......... 38% 12.8M 19s
 17250K .......... .......... .......... .......... .......... 38% 25.9M 19s
 17300K .......... .......... .......... .......... .......... 38% 14.2M 19s
 17350K .......... .......... .......... .......... .......... 38% 12.3M 18s
 17400K .......... .......... .......... .......... .......... 38% 17.7M 18s
 17450K .......... .......... .......... .......... .......... 38%  308K 19s
 17500K .......... .......... .......... .......... .......... 39% 71.0M 18s
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 17600K .......... .......... .......... .......... .......... 39% 11.7M 18s
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 17700K .......... .......... .......... .......... .......... 39% 6.00M 18s
 17750K .......... .......... .......... .......... .......... 39% 11.3M 18s
 17800K .......... .......... .......... .......... .......... 39% 6.59M 18s
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 17900K .......... .......... .......... .......... .......... 39% 11.7M 18s
 17950K .......... .......... .......... .......... .......... 40% 6.29M 18s
 18000K .......... .......... .......... .......... .......... 40% 11.8M 18s
 18050K .......... .......... .......... .......... .......... 40% 10.9M 18s
 18100K .......... .......... .......... .......... .......... 40% 11.5M 18s
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 18200K .......... .......... .......... .......... .......... 40% 12.5M 17s
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 18300K .......... .......... .......... .......... .......... 40% 12.0M 17s
 18350K .......... .......... .......... .......... .......... 40% 11.2M 17s
 18400K .......... .......... .......... .......... .......... 41% 12.2M 17s
 18450K .......... .......... .......... .......... .......... 41% 11.5M 17s
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 18550K .......... .......... .......... .......... .......... 41% 11.3M 17s
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 18650K .......... .......... .......... .......... .......... 41% 10.8M 17s
 18700K .......... .......... .......... .......... .......... 41% 10.5M 17s
 18750K .......... .......... .......... .......... .......... 41% 11.8M 17s
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 18900K .......... .......... .......... .......... .......... 42% 11.8M 16s
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 19100K .......... .......... .......... .......... .......... 42%  534K 16s
 19150K .......... .......... .......... .......... .......... 42% 66.0M 16s
 19200K .......... .......... .......... .......... .......... 42% 3.08M 16s
 19250K .......... .......... .......... .......... .......... 42% 11.3M 16s
 19300K .......... .......... .......... .......... .......... 43% 12.3M 16s
 19350K .......... .......... .......... .......... .......... 43% 57.0M 16s
 19400K .......... .......... .......... .......... .......... 43% 12.4M 16s
 19450K .......... .......... .......... .......... .......... 43% 10.9M 16s
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 19600K .......... .......... .......... .......... .......... 43% 63.5M 16s
 19650K .......... .......... .......... .......... .......... 43% 12.5M 16s
 19700K .......... .......... .......... .......... .......... 43% 11.7M 16s
 19750K .......... .......... .......... .......... .......... 44% 74.8M 15s
 19800K .......... .......... .......... .......... .......... 44% 13.2M 15s
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 20150K .......... .......... .......... .......... .......... 44% 68.8M 15s
 20200K .......... .......... .......... .......... .......... 45% 13.8M 15s
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 20300K .......... .......... .......... .......... .......... 45% 13.6M 15s
 20350K .......... .......... .......... .......... .......... 45% 15.0M 15s
 20400K .......... .......... .......... .......... .......... 45% 50.6M 15s
 20450K .......... .......... .......... .......... .......... 45% 14.8M 15s
 20500K .......... .......... .......... .......... .......... 45% 51.6M 15s
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 20600K .......... .......... .......... .......... .......... 45% 60.1M 14s
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 20700K .......... .......... .......... .......... .......... 46% 64.3M 14s
 20750K .......... .......... .......... .......... .......... 46% 15.6M 14s
 20800K .......... .......... .......... .......... .......... 46% 13.9M 14s
 20850K .......... .......... .......... .......... .......... 46% 42.2M 14s
 20900K .......... .......... .......... .......... .......... 46% 16.0M 14s
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 22000K .......... .......... .......... .......... .......... 49% 56.5M 13s
 22050K .......... .......... .......... .......... .......... 49% 14.9M 13s
 22100K .......... .......... .......... .......... .......... 49% 59.1M 13s
 22150K .......... .......... .......... .......... .......... 49% 15.2M 13s
 22200K .......... .......... .......... .......... .......... 49% 60.9M 13s
 22250K .......... .......... .......... .......... .......... 49% 15.9M 12s
 22300K .......... .......... .......... .......... .......... 49% 35.9M 12s
 22350K .......... .......... .......... .......... .......... 49% 17.9M 12s
 22400K .......... .......... .......... .......... .......... 49% 42.8M 12s
 22450K .......... .......... .......... .......... .......... 50% 15.3M 12s
 22500K .......... .......... .......... .......... .......... 50% 62.5M 12s
 22550K .......... .......... .......... .......... .......... 50% 46.4M 12s
 22600K .......... .......... .......... .......... .......... 50% 16.9M 12s
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 22700K .......... .......... .......... .......... .......... 50% 58.8M 12s
 22750K .......... .......... .......... .......... .......... 50% 62.0M 12s
 22800K .......... .......... .......... .......... .......... 50% 16.0M 12s
 22850K .......... .......... .......... .......... .......... 50% 46.7M 12s
 22900K .......... .......... .......... .......... .......... 51% 17.0M 12s
 22950K .......... .......... .......... .......... .......... 51% 41.2M 12s
 23000K .......... .......... .......... .......... .......... 51% 16.3M 12s
 23050K .......... .......... .......... .......... .......... 51% 53.2M 12s
 23100K .......... .......... .......... .......... .......... 51% 4.27M 12s
 23150K .......... .......... .......... .......... .......... 51% 71.4M 12s
 23200K .......... .......... .......... .......... .......... 51% 74.3M 12s
 23250K .......... .......... .......... .......... .......... 51% 63.0M 11s
 23300K .......... .......... .......... .......... .......... 51% 82.7M 11s
 23350K .......... .......... .......... .......... .......... 52% 75.6M 11s
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 23700K .......... .......... .......... .......... .......... 52% 84.1M 11s
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 23950K .......... .......... .......... .......... .......... 53% 15.5M 11s
 24000K .......... .......... .......... .......... .......... 53% 69.4M 11s
 24050K .......... .......... .......... .......... .......... 53% 13.7M 11s
 24100K .......... .......... .......... .......... .......... 53% 42.2M 11s
 24150K .......... .......... .......... .......... .......... 53% 69.8M 11s
 24200K .......... .......... .......... .......... .......... 54% 17.5M 11s
 24250K .......... .......... .......... .......... .......... 54% 54.4M 11s
 24300K .......... .......... .......... .......... .......... 54%  126K 11s
 24350K .......... .......... .......... .......... .......... 54% 67.9M 11s
 24400K .......... .......... .......... .......... .......... 54%  932K 11s
 24450K .......... .......... .......... .......... .......... 54% 1.51M 11s
 24500K .......... .......... .......... .......... .......... 54%  201K 11s
 24550K .......... .......... .......... .......... .......... 54% 2.39M 11s
 24600K .......... .......... .......... .......... .......... 54% 2.35M 11s
 24650K .......... .......... .......... .......... .......... 55% 2.02M 11s
 24700K .......... .......... .......... .......... .......... 55% 2.89M 11s
 24750K .......... .......... .......... .......... .......... 55% 3.82M 11s
 24800K .......... .......... .......... .......... .......... 55% 3.78M 11s
 24850K .......... .......... .......... .......... .......... 55% 5.58M 11s
 24900K .......... .......... .......... .......... .......... 55% 5.67M 11s
 24950K .......... .......... .......... .......... .......... 55% 5.66M 11s
 25000K .......... .......... .......... .......... .......... 55% 5.76M 11s
 25050K .......... .......... .......... .......... .......... 55% 6.07M 10s
 25100K .......... .......... .......... .......... .......... 56% 10.2M 10s
 25150K .......... .......... .......... .......... .......... 56% 5.86M 10s
 25200K .......... .......... .......... .......... .......... 56% 11.1M 10s
 25250K .......... .......... .......... .......... .......... 56% 5.86M 10s
 25300K .......... .......... .......... .......... .......... 56% 10.8M 10s
 25350K .......... .......... .......... .......... .......... 56% 5.97M 10s
 25400K .......... .......... .......... .......... .......... 56% 10.9M 10s
 25450K .......... .......... .......... .......... .......... 56% 5.94M 10s
 25500K .......... .......... .......... .......... .......... 56% 11.7M 10s
 25550K .......... .......... .......... .......... .......... 57%  306K 10s
 25600K .......... .......... .......... .......... .......... 57% 10.6M 10s
 25650K .......... .......... .......... .......... .......... 57% 6.47M 10s
 25700K .......... .......... .......... .......... .......... 57% 10.9M 10s
 25750K .......... .......... .......... .......... .......... 57% 10.1M 10s
 25800K .......... .......... .......... .......... .......... 57% 10.9M 10s
 25850K .......... .......... .......... .......... .......... 57% 7.42M 10s
 25900K .......... .......... .......... .......... .......... 57% 7.81M 10s
 25950K .......... .......... .......... .......... .......... 57% 11.4M 10s
 26000K .......... .......... .......... .......... .......... 58% 10.5M 10s
 26050K .......... .......... .......... .......... .......... 58% 9.52M 10s
 26100K .......... .......... .......... .......... .......... 58% 6.46M 10s
 26150K .......... .......... .......... .......... .......... 58% 11.6M 10s
 26200K .......... .......... .......... .......... .......... 58% 10.8M 10s
 26250K .......... .......... .......... .......... .......... 58% 6.24M 10s
 26300K .......... .......... .......... .......... .......... 58% 11.8M 10s
 26350K .......... .......... .......... .......... .......... 58% 10.5M 10s
 26400K .......... .......... .......... .......... .......... 58% 11.0M 9s
 26450K .......... .......... .......... .......... .......... 59% 10.8M 9s
 26500K .......... .......... .......... .......... .......... 59% 5.79M 9s
 26550K .......... .......... .......... .......... .......... 59% 11.3M 9s
 26600K .......... .......... .......... .......... .......... 59% 11.0M 9s
 26650K .......... .......... .......... .......... .......... 59% 5.95M 9s
 26700K .......... .......... .......... .......... .......... 59% 11.1M 9s
 26750K .......... .......... .......... .......... .......... 59% 11.3M 9s
 26800K .......... .......... .......... .......... .......... 59% 11.3M 9s
 26850K .......... .......... .......... .......... .......... 59% 10.9M 9s
 26900K .......... .......... .......... .......... .......... 60% 6.35M 9s
 26950K .......... .......... .......... .......... .......... 60% 5.87M 9s
 27000K .......... .......... .......... .......... .......... 60% 5.88M 9s
 27050K .......... .......... .......... .......... .......... 60% 4.03M 9s
 27100K .......... .......... .......... .......... .......... 60%  216K 9s
 27150K .......... .......... .......... .......... .......... 60% 3.90M 9s
 27200K .......... .......... .......... .......... .......... 60% 3.86M 9s
 27250K .......... .......... .......... .......... .......... 60% 3.80M 9s
 27300K .......... .......... .......... .......... .......... 60% 3.96M 9s
 27350K .......... .......... .......... .......... .......... 61% 5.83M 9s
 27400K .......... .......... .......... .......... .......... 61% 5.70M 9s
 27450K .......... .......... .......... .......... .......... 61% 3.92M 9s
 27500K .......... .......... .......... .......... .......... 61% 5.90M 9s
 27550K .......... .......... .......... .......... .......... 61% 5.83M 9s
 27600K .......... .......... .......... .......... .......... 61% 5.71M 9s
 27650K .......... .......... .......... .......... .......... 61% 10.5M 9s
 27700K .......... .......... .......... .......... .......... 61% 5.98M 9s
 27750K .......... .......... .......... .......... .......... 61% 11.1M 9s
 27800K .......... .......... .......... .......... .......... 62% 5.92M 9s
 27850K .......... .......... .......... .......... .......... 62% 5.91M 9s
 27900K .......... .......... .......... .......... .......... 62% 10.7M 9s
 27950K .......... .......... .......... .......... .......... 62% 10.9M 8s
 28000K .......... .......... .......... .......... .......... 62% 6.21M 8s
 28050K .......... .......... .......... .......... .......... 62% 11.0M 8s
 28100K .......... .......... .......... .......... .......... 62% 12.1M 8s
 28150K .......... .......... .......... .......... .......... 62% 11.2M 8s
 28200K .......... .......... .......... .......... .......... 62% 6.04M 8s
 28250K .......... .......... .......... .......... .......... 63% 10.9M 8s
 28300K .......... .......... .......... .......... .......... 63% 11.3M 8s
 28350K .......... .......... .......... .......... .......... 63% 12.2M 8s
 28400K .......... .......... .......... .......... .......... 63% 6.26M 8s
 28450K .......... .......... .......... .......... .......... 63% 12.0M 8s
 28500K .......... .......... .......... .......... .......... 63% 11.5M 8s
 28550K .......... .......... .......... .......... .......... 63% 11.9M 8s
 28600K .......... .......... .......... .......... .......... 63% 11.0M 8s
 28650K .......... .......... .......... .......... .......... 63% 11.9M 8s
 28700K .......... .......... .......... .......... .......... 64% 11.6M 8s
 28750K .......... .......... .......... .......... .......... 64% 11.8M 8s
 28800K .......... .......... .......... .......... .......... 64% 11.0M 8s
 28850K .......... .......... .......... .......... .......... 64% 11.4M 8s
 28900K .......... .......... .......... .......... .......... 64% 13.1M 8s
 28950K .......... .......... .......... .......... .......... 64% 11.7M 8s
 29000K .......... .......... .......... .......... .......... 64% 11.3M 8s
 29050K .......... .......... .......... .......... .......... 64% 12.5M 8s
 29100K .......... .......... .......... .......... .......... 64% 12.0M 8s
 29150K .......... .......... .......... .......... .......... 65% 11.1M 8s
 29200K .......... .......... .......... .......... .......... 65% 76.5M 8s
 29250K .......... .......... .......... .......... .......... 65% 12.2M 8s
 29300K .......... .......... .......... .......... .......... 65% 11.2M 8s
 29350K .......... .......... .......... .......... .......... 65% 13.0M 7s
 29400K .......... .......... .......... .......... .......... 65% 13.3M 7s
 29450K .......... .......... .......... .......... .......... 65% 9.92M 7s
 29500K .......... .......... .......... .......... .......... 65% 15.0M 7s
 29550K .......... .......... .......... .......... .......... 65% 53.4M 7s
 29600K .......... .......... .......... .......... .......... 66% 11.9M 7s
 29650K .......... .......... .......... .......... .......... 66% 13.3M 7s
 29700K .......... .......... .......... .......... .......... 66% 10.3M 7s
 29750K .......... .......... .......... .......... .......... 66% 13.8M 7s
 29800K .......... .......... .......... .......... .......... 66% 62.2M 7s
 29850K .......... .......... .......... .......... .......... 66% 12.2M 7s
 29900K .......... .......... .......... .......... .......... 66%  392K 7s
 29950K .......... .......... .......... .......... .......... 66% 3.09M 7s
 30000K .......... .......... .......... .......... .......... 66% 5.60M 7s
 30050K .......... .......... .......... .......... .......... 67% 12.3M 7s
 30100K .......... .......... .......... .......... .......... 67% 11.5M 7s
 30150K .......... .......... .......... .......... .......... 67% 12.1M 7s
 30200K .......... .......... .......... .......... .......... 67%  689K 7s
 30250K .......... .......... .......... .......... .......... 67% 5.87M 7s
 30300K .......... .......... .......... .......... .......... 67% 5.92M 7s
 30350K .......... .......... .......... .......... .......... 67% 11.1M 7s
 30400K .......... .......... .......... .......... .......... 67% 5.57M 7s
 30450K .......... .......... .......... .......... .......... 67% 10.7M 7s
 30500K .......... .......... .......... .......... .......... 68% 11.2M 7s
 30550K .......... .......... .......... .......... .......... 68% 10.2M 7s
 30600K .......... .......... .......... .......... .......... 68% 6.54M 7s
 30650K .......... .......... .......... .......... .......... 68% 10.8M 7s
 30700K .......... .......... .......... .......... .......... 68% 10.6M 7s
 30750K .......... .......... .......... .......... .......... 68% 6.17M 7s
 30800K .......... .......... .......... .......... .......... 68% 11.5M 7s
 30850K .......... .......... .......... .......... .......... 68% 10.3M 7s
 30900K .......... .......... .......... .......... .......... 68% 11.6M 7s
 30950K .......... .......... .......... .......... .......... 69% 11.6M 7s
 31000K .......... .......... .......... .......... .......... 69% 10.4M 6s
 31050K .......... .......... .......... .......... .......... 69% 11.7M 6s
 31100K .......... .......... .......... .......... .......... 69% 11.9M 6s
 31150K .......... .......... .......... .......... .......... 69% 11.9M 6s
 31200K .......... .......... .......... .......... .......... 69% 10.9M 6s
 31250K .......... .......... .......... .......... .......... 69% 11.2M 6s
 31300K .......... .......... .......... .......... .......... 69% 11.3M 6s
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 31400K .......... .......... .......... .......... .......... 70% 11.6M 6s
 31450K .......... .......... .......... .......... .......... 70% 11.5M 6s
 31500K .......... .......... .......... .......... .......... 70% 11.8M 6s
 31550K .......... .......... .......... .......... .......... 70% 12.1M 6s
 31600K .......... .......... .......... .......... .......... 70% 11.1M 6s
 31650K .......... .......... .......... .......... .......... 70% 12.1M 6s
 31700K .......... .......... .......... .......... .......... 70% 10.8M 6s
 31750K .......... .......... .......... .......... .......... 70% 14.0M 6s
 31800K .......... .......... .......... .......... .......... 70% 12.0M 6s
 31850K .......... .......... .......... .......... .......... 71% 11.5M 6s
 31900K .......... .......... .......... .......... .......... 71% 40.4M 6s
 31950K .......... .......... .......... .......... .......... 71% 12.8M 6s
 32000K .......... .......... .......... .......... .......... 71% 11.4M 6s
 32050K .......... .......... .......... .......... .......... 71% 11.8M 6s
 32100K .......... .......... .......... .......... .......... 71% 12.4M 6s
 32150K .......... .......... .......... .......... .......... 71% 61.0M 6s
 32200K .......... .......... .......... .......... .......... 71% 12.3M 6s
 32250K .......... .......... .......... .......... .......... 71% 11.7M 6s
 32300K .......... .......... .......... .......... .......... 72% 12.8M 6s
 32350K .......... .......... .......... .......... .......... 72% 12.8M 6s
 32400K .......... .......... .......... .......... .......... 72% 43.1M 6s
 32450K .......... .......... .......... .......... .......... 72% 12.0M 6s
 32500K .......... .......... .......... .......... .......... 72% 14.5M 6s
 32550K .......... .......... .......... .......... .......... 72% 11.7M 6s
 32600K .......... .......... .......... .......... .......... 72% 56.1M 5s
 32650K .......... .......... .......... .......... .......... 72% 12.5M 5s
 32700K .......... .......... .......... .......... .......... 72% 13.3M 5s
 32750K .......... .......... .......... .......... .......... 73% 12.5M 5s
 32800K .......... .......... .......... .......... .......... 73% 73.6M 5s
 32850K .......... .......... .......... .......... .......... 73% 11.5M 5s
 32900K .......... .......... .......... .......... .......... 73% 12.9M 5s
 32950K .......... .......... .......... .......... .......... 73% 12.0M 5s
 33000K .......... .......... .......... .......... .......... 73% 69.2M 5s
 33050K .......... .......... .......... .......... .......... 73%  138K 5s
 33100K .......... .......... .......... .......... .......... 73%  625K 5s
 33150K .......... .......... .......... .......... .......... 73% 61.7M 5s
 33200K .......... .......... .......... .......... .......... 74% 6.76M 5s
 33250K .......... .......... .......... .......... .......... 74% 10.8M 5s
 33300K .......... .......... .......... .......... .......... 74% 6.10M 5s
 33350K .......... .......... .......... .......... .......... 74% 11.0M 5s
 33400K .......... .......... .......... .......... .......... 74% 2.81M 5s
 33450K .......... .......... .......... .......... .......... 74% 11.0M 5s
 33500K .......... .......... .......... .......... .......... 74% 11.0M 5s
 33550K .......... .......... .......... .......... .......... 74% 6.05M 5s
 33600K .......... .......... .......... .......... .......... 74%  255K 5s
 33650K .......... .......... .......... .......... .......... 75%  106K 5s
 33700K .......... .......... .......... .......... .......... 75% 2.05M 5s
 33750K .......... .......... .......... .......... .......... 75% 1.56M 5s
 33800K .......... .......... .......... .......... .......... 75% 2.07M 5s
 33850K .......... .......... .......... .......... .......... 75% 2.40M 5s
 33900K .......... .......... .......... .......... .......... 75% 4.03M 5s
 33950K .......... .......... .......... .......... .......... 75% 5.94M 5s
 34000K .......... .......... .......... .......... .......... 75% 5.89M 5s
 34050K .......... .......... .......... .......... .......... 75% 5.73M 5s
 34100K .......... .......... .......... .......... .......... 76% 5.65M 5s
 34150K .......... .......... .......... .......... .......... 76% 5.71M 5s
 34200K .......... .......... .......... .......... .......... 76% 10.6M 5s
 34250K .......... .......... .......... .......... .......... 76% 3.95M 5s
 34300K .......... .......... .......... .......... .......... 76% 11.1M 5s
 34350K .......... .......... .......... .......... .......... 76% 5.87M 5s
 34400K .......... .......... .......... .......... .......... 76% 11.3M 5s
 34450K .......... .......... .......... .......... .......... 76% 6.15M 5s
 34500K .......... .......... .......... .......... .......... 76% 11.2M 5s
 34550K .......... .......... .......... .......... .......... 77% 11.4M 5s
 34600K .......... .......... .......... .......... .......... 77%  507K 5s
 34650K .......... .......... .......... .......... .......... 77% 7.05M 5s
 34700K .......... .......... .......... .......... .......... 77%  303K 5s
 34750K .......... .......... .......... .......... .......... 77% 76.8K 5s
 34800K .......... .......... .......... .......... .......... 77% 25.0K 5s
 34850K .......... .......... .......... .......... .......... 77% 20.6K 6s
 34900K .......... .......... .......... .......... .......... 77% 24.9K 7s
 34950K .......... .......... .......... .......... .......... 77% 32.2K 7s
 35000K .......... .......... .......... .......... .......... 78%  342K 7s
 35050K .......... .......... .......... .......... .......... 78% 2.93M 7s
 35100K .......... .......... .......... .......... .......... 78%  710K 7s
 35150K .......... .......... .......... .......... .......... 78% 2.84M 7s
 35200K .......... .......... .......... .......... .......... 78% 3.83M 7s
 35250K .......... .......... .......... .......... .......... 78% 3.83M 7s
 35300K .......... .......... .......... .......... .......... 78% 5.75M 7s
 35350K .......... .......... .......... .......... .......... 78% 3.93M 7s
 35400K .......... .......... .......... .......... .......... 78% 5.78M 7s
 35450K .......... .......... .......... .......... .......... 79% 3.94M 7s
 35500K .......... .......... .......... .......... .......... 79% 5.72M 7s
 35550K .......... .......... .......... .......... .......... 79% 9.21M 7s
 35600K .......... .......... .......... .......... .......... 79% 7.00M 7s
 35650K .......... .......... .......... .......... .......... 79% 6.46M 7s
 35700K .......... .......... .......... .......... .......... 79% 9.02M 6s
 35750K .......... .......... .......... .......... .......... 79% 11.2M 6s
 35800K .......... .......... .......... .......... .......... 79% 7.35M 6s
 35850K .......... .......... .......... .......... .......... 79% 8.65M 6s
 35900K .......... .......... .......... .......... .......... 80% 7.56M 6s
 35950K .......... .......... .......... .......... .......... 80% 12.1M 6s
 36000K .......... .......... .......... .......... .......... 80% 7.29M 6s
 36050K .......... .......... .......... .......... .......... 80% 11.2M 6s
 36100K .......... .......... .......... .......... .......... 80% 11.6M 6s
 36150K .......... .......... .......... .......... .......... 80% 12.4M 6s
 36200K .......... .......... .......... .......... .......... 80% 6.52M 6s
 36250K .......... .......... .......... .......... .......... 80% 11.5M 6s
 36300K .......... .......... .......... .......... .......... 80% 11.6M 6s
 36350K .......... .......... .......... .......... .......... 81% 12.0M 6s
 36400K .......... .......... .......... .......... .......... 81% 12.9M 6s
 36450K .......... .......... .......... .......... .......... 81% 12.3M 6s
 36500K .......... .......... .......... .......... .......... 81% 11.5M 6s
 36550K .......... .......... .......... .......... .......... 81% 12.4M 6s
 36600K .......... .......... .......... .......... .......... 81% 13.2M 6s
 36650K .......... .......... .......... .......... .......... 81% 6.11M 6s
 36700K .......... .......... .......... .......... .......... 81% 11.9M 6s
 36750K .......... .......... .......... .......... .......... 81% 11.9M 6s
 36800K .......... .......... .......... .......... .......... 82% 58.9M 6s
 36850K .......... .......... .......... .......... .......... 82% 12.4M 6s
 36900K .......... .......... .......... .......... .......... 82% 11.5M 5s
 36950K .......... .......... .......... .......... .......... 82% 8.63M 5s
 37000K .......... .......... .......... .......... .......... 82% 11.9M 5s
 37050K .......... .......... .......... .......... .......... 82% 10.5M 5s
 37100K .......... .......... .......... .......... .......... 82% 13.3M 5s
 37150K .......... .......... .......... .......... .......... 82% 11.8M 5s
 37200K .......... .......... .......... .......... .......... 82% 12.2M 5s
 37250K .......... .......... .......... .......... .......... 83% 76.1M 5s
 37300K .......... .......... .......... .......... .......... 83% 11.5M 5s
 37350K .......... .......... .......... .......... .......... 83% 12.5M 5s
 37400K .......... .......... .......... .......... .......... 83% 12.6M 5s
 37450K .......... .......... .......... .......... .......... 83% 3.93M 5s
 37500K .......... .......... .......... .......... .......... 83% 11.1M 5s
 37550K .......... .......... .......... .......... .......... 83% 12.1M 5s
 37600K .......... .......... .......... .......... .......... 83% 13.0M 5s
 37650K .......... .......... .......... .......... .......... 83% 51.0M 5s
 37700K .......... .......... .......... .......... .......... 84% 11.2M 5s
 37750K .......... .......... .......... .......... .......... 84% 13.2M 5s
 37800K .......... .......... .......... .......... .......... 84%  126K 5s
 37850K .......... .......... .......... .......... .......... 84%  497K 5s
 37900K .......... .......... .......... .......... .......... 84% 10.6M 5s
 37950K .......... .......... .......... .......... .......... 84%  519K 5s
 38000K .......... .......... .......... .......... .......... 84%  124K 5s
 38050K .......... .......... .......... .......... .......... 84% 11.6M 5s
 38100K .......... .......... .......... .......... .......... 84%  384K 5s
 38150K .......... .......... .......... .......... .......... 85%  136K 5s
 38200K .......... .......... .......... .......... .......... 85%  124K 5s
 38250K .......... .......... .......... .......... .......... 85% 59.6K 5s
 38300K .......... .......... .......... .......... .......... 85% 5.63M 5s
 38350K .......... .......... .......... .......... .......... 85% 93.8K 5s
 38400K .......... .......... .......... .......... .......... 85%  149K 5s
 38450K .......... .......... .......... .......... .......... 85% 2.90M 5s
 38500K .......... .......... .......... .......... .......... 85% 3.84M 5s
 38550K .......... .......... .......... .......... .......... 85% 3.75M 5s
 38600K .......... .......... .......... .......... .......... 86% 5.79M 5s
 38650K .......... .......... .......... .......... .......... 86% 3.91M 5s
 38700K .......... .......... .......... .......... .......... 86% 11.5M 5s
 38750K .......... .......... .......... .......... .......... 86% 6.18M 5s
 38800K .......... .......... .......... .......... .......... 86% 10.4M 5s
 38850K .......... .......... .......... .......... .......... 86% 11.7M 5s
 38900K .......... .......... .......... .......... .......... 86% 12.5M 4s
 38950K .......... .......... .......... .......... .......... 86% 11.4M 4s
 39000K .......... .......... .......... .......... .......... 86% 13.4M 4s
 39050K .......... .......... .......... .......... .......... 87% 26.5M 4s
 39100K .......... .......... .......... .......... .......... 87% 18.7M 4s
 39150K .......... .......... .......... .......... .......... 87% 12.6M 4s
 39200K .......... .......... .......... .......... .......... 87% 30.5M 4s
 39250K .......... .......... .......... .......... .......... 87% 15.6M 4s
 39300K .......... .......... .......... .......... .......... 87% 41.8M 4s
 39350K .......... .......... .......... .......... .......... 87% 16.7M 4s
 39400K .......... .......... .......... .......... .......... 87% 34.3M 4s
 39450K .......... .......... .......... .......... .......... 87% 16.1M 4s
 39500K .......... .......... .......... .......... .......... 88% 16.4M 4s
 39550K .......... .......... .......... .......... .......... 88% 38.0M 4s
 39600K .......... .......... .......... .......... .......... 88% 16.6M 4s
 39650K .......... .......... .......... .......... .......... 88% 31.5M 4s
 39700K .......... .......... .......... .......... .......... 88% 17.9M 4s
 39750K .......... .......... .......... .......... .......... 88% 38.0M 4s
 39800K .......... .......... .......... .......... .......... 88% 19.6M 4s
 39850K .......... .......... .......... .......... .......... 88% 28.5M 4s
 39900K .......... .......... .......... .......... .......... 88% 18.0M 4s
 39950K .......... .......... .......... .......... .......... 89% 14.1M 4s
 40000K .......... .......... .......... .......... .......... 89% 32.8M 4s
 40050K .......... .......... .......... .......... .......... 89% 17.6M 4s
 40100K .......... .......... .......... .......... .......... 89% 37.7M 3s
 40150K .......... .......... .......... .......... .......... 89% 17.7M 3s
 40200K .......... .......... .......... .......... .......... 89% 42.2M 3s
 40250K .......... .......... .......... .......... .......... 89% 15.2M 3s
 40300K .......... .......... .......... .......... .......... 89% 47.3M 3s
 40350K .......... .......... .......... .......... .......... 89% 16.7M 3s
 40400K .......... .......... .......... .......... .......... 90% 44.9M 3s
 40450K .......... .......... .......... .......... .......... 90% 16.6M 3s
 40500K .......... .......... .......... .......... .......... 90% 35.6M 3s
 40550K .......... .......... .......... .......... .......... 90% 18.5M 3s
 40600K .......... .......... .......... .......... .......... 90% 43.4M 3s
 40650K .......... .......... .......... .......... .......... 90% 8.45M 3s
 40700K .......... .......... .......... .......... .......... 90% 75.7M 3s
 40750K .......... .......... .......... .......... .......... 90% 6.56M 3s
 40800K .......... .......... .......... .......... .......... 90% 77.8M 3s
 40850K .......... .......... .......... .......... .......... 91% 12.8M 3s
 40900K .......... .......... .......... .......... .......... 91% 12.6M 3s
 40950K .......... .......... .......... .......... .......... 91% 76.6M 3s
 41000K .......... .......... .......... .......... .......... 91% 12.0M 3s
 41050K .......... .......... .......... .......... .......... 91% 12.7M 3s
 41100K .......... .......... .......... .......... .......... 91% 12.6M 3s
 41150K .......... .......... .......... .......... .......... 91% 62.8M 3s
 41200K .......... .......... .......... .......... .......... 91% 13.5M 3s
 41250K .......... .......... .......... .......... .......... 91% 61.5M 3s
 41300K .......... .......... .......... .......... .......... 92% 13.5M 3s
 41350K .......... .......... .......... .......... .......... 92% 12.1M 2s
 41400K .......... .......... .......... .......... .......... 92% 70.3M 2s
 41450K .......... .......... .......... .......... .......... 92% 12.1M 2s
 41500K .......... .......... .......... .......... .......... 92% 16.0M 2s
 41550K .......... .......... .......... .......... .......... 92% 4.60M 2s
 41600K .......... .......... .......... .......... .......... 92% 67.4M 2s
 41650K .......... .......... .......... .......... .......... 92% 12.9M 2s
 41700K .......... .......... .......... .......... .......... 92% 12.6M 2s
 41750K .......... .......... .......... .......... .......... 93% 48.8M 2s
 41800K .......... .......... .......... .......... .......... 93% 16.1M 2s
 41850K .......... .......... .......... .......... .......... 93% 49.1M 2s
 41900K .......... .......... .......... .......... .......... 93% 12.6M 2s
 41950K .......... .......... .......... .......... .......... 93% 12.8M 2s
 42000K .......... .......... .......... .......... .......... 93% 63.3M 2s
 42050K .......... .......... .......... .......... .......... 93% 12.9M 2s
 42100K .......... .......... .......... .......... .......... 93% 73.3M 2s
 42150K .......... .......... .......... .......... .......... 93% 13.7M 2s
 42200K .......... .......... .......... .......... .......... 94% 13.2M 2s
 42250K .......... .......... .......... .......... .......... 94% 47.8M 2s
 42300K .......... .......... .......... .......... .......... 94% 12.0M 2s
 42350K .......... .......... .......... .......... .......... 94% 66.3M 2s
 42400K .......... .......... .......... .......... .......... 94% 14.1M 2s
 42450K .......... .......... .......... .......... .......... 94% 67.6M 2s
 42500K .......... .......... .......... .......... .......... 94% 14.5M 2s
 42550K .......... .......... .......... .......... .......... 94% 12.7M 2s
 42600K .......... .......... .......... .......... .......... 94% 65.3M 2s
 42650K .......... .......... .......... .......... .......... 95% 13.0M 2s
 42700K .......... .......... .......... .......... .......... 95% 77.4M 1s
 42750K .......... .......... .......... .......... .......... 95% 13.2M 1s
 42800K .......... .......... .......... .......... .......... 95% 73.2M 1s
 42850K .......... .......... .......... .......... .......... 95% 13.5M 1s
 42900K .......... .......... .......... .......... .......... 95% 12.9M 1s
 42950K .......... .......... .......... .......... .......... 95% 66.7M 1s
 43000K .......... .......... .......... .......... .......... 95% 14.3M 1s
 43050K .......... .......... .......... .......... .......... 95% 56.6M 1s
 43100K .......... .......... .......... .......... .......... 96% 13.5M 1s
 43150K .......... .......... .......... .......... .......... 96% 76.3M 1s
 43200K .......... .......... .......... .......... .......... 96% 12.8M 1s
 43250K .......... .......... .......... .......... .......... 96% 66.5M 1s
 43300K .......... .......... .......... .......... .......... 96% 14.4M 1s
 43350K .......... .......... .......... .......... .......... 96% 69.8M 1s
 43400K .......... .......... .......... .......... .......... 96% 13.9M 1s
 43450K .......... .......... .......... .......... .......... 96% 13.4M 1s
 43500K .......... .......... .......... .......... .......... 96% 56.5M 1s
 43550K .......... .......... .......... .......... .......... 97% 14.5M 1s
 43600K .......... .......... .......... .......... .......... 97% 67.3M 1s
 43650K .......... .......... .......... .......... .......... 97% 13.6M 1s
 43700K .......... .......... .......... .......... .......... 97% 78.9M 1s
 43750K .......... .......... .......... .......... .......... 97% 13.2M 1s
 43800K .......... .......... .......... .......... .......... 97% 68.9M 1s
 43850K .......... .......... .......... .......... .......... 97% 12.9M 1s
 43900K .......... .......... .......... .......... .......... 97% 66.4M 1s
 43950K .......... .......... .......... .......... .......... 97% 14.0M 1s
 44000K .......... .......... .......... .......... .......... 98% 63.3M 1s
 44050K .......... .......... .......... .......... .......... 98% 14.0M 1s
 44100K .......... .......... .......... .......... .......... 98% 65.0M 1s
 44150K .......... .......... .......... .......... .......... 98% 13.6M 0s
 44200K .......... .......... .......... .......... .......... 98% 62.7M 0s
 44250K .......... .......... .......... .......... .......... 98% 14.0M 0s
 44300K .......... .......... .......... .......... .......... 98% 67.0M 0s
 44350K .......... .......... .......... .......... .......... 98% 13.9M 0s
 44400K .......... .......... .......... .......... .......... 98% 54.4M 0s
 44450K .......... .......... .......... .......... .......... 99% 16.1M 0s
 44500K .......... .......... .......... .......... .......... 99% 56.0M 0s
 44550K .......... .......... .......... .......... .......... 99% 14.2M 0s
 44600K .......... .......... .......... .......... .......... 99% 55.1M 0s
 44650K .......... .......... .......... .......... .......... 99% 13.8M 0s
 44700K .......... .......... .......... .......... .......... 99% 64.7M 0s
 44750K .......... .......... .......... .......... .......... 99% 15.9M 0s
 44800K .......... .......... .......... .......... .......... 99% 62.7M 0s
 44850K .......... .......... .......... .......... .......... 99% 73.7M 0s
 44900K ...                                                   100% 7.37T=29s


Opening dataset from [oceanspy_particle_properties.nc].

2023-04-11 22:44:37 (1.49 MB/s) - ‘oceanspy_particle_properties.nc’ saved [45981653/45981653]

The OceanDataset created by extract_properties has 3 dimensions:

  • particle: Every particle is associated with an ID (integer number).

  • time: All the available snapshots (in this case, from Feb. 29th to Mar. 30th with 6-hour resolution).

  • time_midp: Mid-points of the time dimension. For example, this is the dimension associated with gradients computed along the time axis.

[7]:

print(od_lag.dataset)

<xarray.Dataset>
Dimensions:    (time: 121, particle: 3954, time_midp: 120)
Coordinates:
  * particle   (particle) int64 0 1 2 3 4 5 6 ... 3948 3949 3950 3951 3952 3953
  * time       (time) datetime64[ns] 2008-02-29 ... 2008-03-30
  * time_midp  (time_midp) datetime64[ns] 2008-02-29T03:00:00 ... 2008-03-29T...
Data variables:
    XC         (time, particle) float64 ...
    YC         (time, particle) float64 ...
    Z          (time, particle) float64 ...
    Zl         (time, particle) float64 ...
    Zp1        (time, particle) float64 ...
    Zu         (time, particle) float64 ...
    XG         (time, particle) float64 ...
    YG         (time, particle) float64 ...
    Depth      (time, particle) float64 ...
    Temp       (time, particle) float64 ...
    S          (time, particle) float64 ...
    momVort3   (time, particle) float64 ...
Attributes:
    OceanSpy_grid_coords:  {'time': {'time': -0.5, 'time_midp': None}}

Compute

We can now use ospy.compute functions on the extracted particle properties. For example, here we compute potential density anomalies using temperature and salinity.

[8]:

od_lag = od_lag.compute.potential_density_anomaly()
print(od_lag.dataset["Sigma0"])

Computing potential density anomaly using the following parameters: {'eq_state': 'jmd95'}.
<xarray.DataArray 'Sigma0' (time: 121, particle: 3954)>
array([[28.06448144, 28.06448144, 28.06150693, ..., 27.60797582,
        27.77204289, 27.82874751],
       [28.06722492, 28.06416057, 28.06416057, ..., 27.62017588,
        27.75539891, 27.82740934],
       [28.06796263, 28.06796263, 28.06796263, ..., 27.60038398,
        27.73746555, 27.82305911],
       ...,
       [27.97167365, 27.88427005, 27.81440205, ..., 27.61308105,
        27.61245962, 27.80288992],
       [27.97205047, 27.8742948 , 27.81334513, ..., 27.62929107,
        27.62997148, 27.80246744],
       [27.97295942, 27.86978131, 27.81499219, ..., 27.63008246,
        27.65160468, 27.80403993]])
Coordinates:
  * particle  (particle) int64 0 1 2 3 4 5 6 ... 3948 3949 3950 3951 3952 3953
  * time      (time) datetime64[ns] 2008-02-29 ... 2008-03-30
Attributes:
    units:                kg/m^3
    long_name:            potential density anomaly
    OceanSpy_parameters:  {'eq_state': 'jmd95'}

Here we compute gradients along the time dimension for each variable previously extracted:

[9]:

od_lag = od_lag.compute.gradient()
print(od_lag.dataset)

Computing gradient.
<xarray.Dataset>
Dimensions:          (time: 121, particle: 3954, time_midp: 120)
Coordinates:
  * particle         (particle) int64 0 1 2 3 4 5 ... 3949 3950 3951 3952 3953
  * time             (time) datetime64[ns] 2008-02-29 ... 2008-03-30
  * time_midp        (time_midp) datetime64[ns] 2008-02-29T03:00:00 ... 2008-...
Data variables: (12/26)
    XC               (time, particle) float64 -24.62 -24.62 ... -29.45 -31.48
    YC               (time, particle) float64 65.49 65.49 65.49 ... 67.82 66.79
    Z                (time, particle) float64 -23.5 -23.5 ... -276.5 -351.5
    Zl               (time, particle) float64 -27.0 -27.0 ... -269.0 -344.0
    Zp1              (time, particle) float64 -27.0 -27.0 ... -269.0 -344.0
    Zu               (time, particle) float64 -27.0 -27.0 ... -269.0 -344.0
    ...               ...
    dYG_dtime        (time_midp, particle) float64 -8.841e-07 0.0 ... 0.0 0.0
    dDepth_dtime     (time_midp, particle) float64 4.819e-05 ... -0.000665
    dTemp_dtime      (time_midp, particle) float64 -3.942e-07 ... -1.581e-07
    dS_dtime         (time_midp, particle) float64 1.183e-07 ... 7.341e-08
    dmomVort3_dtime  (time_midp, particle) float64 4.739e-10 ... -7.566e-10
    dSigma0_dtime    (time_midp, particle) float64 1.27e-07 ... 7.28e-08
Attributes:
    OceanSpy_grid_coords:  {'time': {'time': -0.5, 'time_midp': None}}

Mask and Split

Now we focus on particles carried by the dense overflow water, which is defined as water with \(\sigma_{0}\geq\) 27.8 kg m\(^{-3}\).

First, we identify all the particles seeded in the overflow. Then, we split these particles into two sets (each one an OceanDataset) using the following criteria:

  1. od_dense: \(\sigma_0\) along the path is always greater than 27.8 kg m\(^{-3}\).

  2. od_mixed: \(\sigma_0\) at the last snapshot is less than 27.8 kg m\(^{-3}\), and at least 50% of the snapshots have \(\sigma_0<\) 27.8 kg m\(^{-3}\).

[10]:

# Overflow mask
DSO_threshold = 27.8  # kg/m^3
mask_DSO = xr.where(od_lag.dataset["Sigma0"] >= DSO_threshold, 1, 0)

# Mask particles always in the overflow
mask_dense = xr.where(mask_DSO.sum("time") == len(od_lag.dataset["time"]), 1, 0)

# Mask mixed particles
mask_mixed = xr.where(
    np.logical_and(
        np.logical_and(mask_DSO.isel(time=0) == 1, mask_DSO.isel(time=-1) == 0),
        mask_DSO.sum("time") <= len(od_lag.dataset["time"]) / 2,
    ),
    1,
    0,
)

# Create OceanDataset
od_dense = ospy.OceanDataset(od_lag.dataset.where(mask_dense, drop=True))
od_mixed = ospy.OceanDataset(od_lag.dataset.where(mask_mixed, drop=True))

Here we plot the trajectories on top of projected maps:

[11]:

ods = [od_dense, od_mixed]
colors = ["fuchsia", "lime"]
titles = [
    r"Particles always denser than 27.8 kg m$^{-3}$.",
    r"Particles ONLY initially denser than 27.8 kg m$^{-3}$",
]
for _, (od_i, col, tit) in enumerate(zip(ods, colors, titles)):
    # Plot Depth
    fig = plt.figure(figsize=(10, 5))
    ax = od_eul.plot.horizontal_section(varName="masked_Depth", cmap="bone_r")
    land_col = (253 / 255, 180 / 255, 108 / 255)
    ax.patch.set_facecolor(land_col)
    ax.set_extent([-40, -19, 63, 68])

    # Plot trajectories
    ax.plot(
        od_i.dataset["XC"],
        od_i.dataset["YC"],
        color=col,
        alpha=0.2,
        linewidth=1,
        transform=PlateCarree(),
    )

    # Plot initial positions
    ax.plot(
        od_i.dataset["XC"].isel(time=0),
        od_i.dataset["YC"].isel(time=0),
        "k.",
        markersize=5,
        transform=PlateCarree(),
    )

    # Title
    _ = ax.set_title(tit)
    plt.show()
_images/Particles_24_0.png
_images/Particles_24_1.png

TS-diagrams

We can use TS-diagrams to investigate the hydrographic properties of the od_dense and od_mixed sets. For example, here we plot each oceandataset color-coded by particle depths separately (subplots a and b), then we plot them together on the same isopycnal contours (subplot c).

[12]:

fig = plt.figure(figsize=(10, 10))

for i, (od_i, col, tit) in enumerate(zip(ods, colors, titles)):
    plt.subplot(int("22" + str(i + 1)))
    ax = od_i.plot.TS_diagram(
        colorName="Z", alpha=0.5, cmap_kwargs={"vmin": -2000, "vmax": 0}
    )
    ax.set_title(chr(ord("a") + i) + ") " + tit)

plt.subplot(212)
Tlim = [
    min([od_i.dataset["Temp"].min().values for od_i in ods]),
    max([od_i.dataset["Temp"].max().values for od_i in ods]),
]
Slim = [
    min([od_i.dataset["S"].min().values for od_i in ods]),
    max([od_i.dataset["S"].max().values for od_i in ods]),
]
for i, (od_i, col, tit) in enumerate(zip(ods, colors, titles)):
    contour_kwargs = {}
    if i == 0:
        contour_kwargs["levels"] = []
    ax = od_i.plot.TS_diagram(
        color=col,
        alpha=0.1,
        Tlim=Tlim,
        Slim=Slim,
        contour_kwargs=contour_kwargs,
    )
tit = "\n".join(
    ["c) "] + [f"{col}: {tit}" for _, (col, tit) in enumerate(zip(colors, titles))]
)
ax.set_title(tit)

plt.tight_layout()

Isopycnals: Computing potential density anomaly using the following parameters: {'eq_state': 'jmd95'}.
Isopycnals: Computing potential density anomaly using the following parameters: {'eq_state': 'jmd95'}.
Isopycnals: Computing potential density anomaly using the following parameters: {'eq_state': 'jmd95'}.
Isopycnals: Computing potential density anomaly using the following parameters: {'eq_state': 'jmd95'}.

/home/idies/mambaforge/envs/Oceanography/lib/python3.9/site-packages/oceanspy/plot.py:306: UserWarning: No contour levels were found within the data range.
  CS = ax.contour(s.values, t.values, dens.values, **contour_kwargs)
_images/Particles_26_2.png

Time series

Now, we select 5 particles that were seeded in the overflow and became less dense along the path using the od_mixed set:

[13]:

nparts = 5
step = np.ceil(len(od_mixed.dataset["particle"]) / 5)
od_5parts = ospy.OceanDataset(
    od_mixed.dataset.isel(particle=slice(None, None, int(step)))
)

Here is a plot of their trajectories:

[14]:

ods = [od_dense, od_mixed]
colors = ["fuchsia", "lime"]
titles = [
    r"Particles always denser than 27.8 kg m$^{-3}$.",
    r"Particles ONLY initially denser than 27.8 kg m$^{-3}$",
]

# Plot Depth
fig = plt.figure(figsize=(10, 5))
ax = od_eul.plot.horizontal_section(varName="masked_Depth", cmap="bone_r")
land_col = (253 / 255, 180 / 255, 108 / 255)
ax.patch.set_facecolor(land_col)
ax.set_extent([-40, -19, 63, 68])

# Plot trajectories
traj = ax.plot(
    od_5parts.dataset["XC"],
    od_5parts.dataset["YC"],
    linewidth=3,
    transform=PlateCarree(),
)

# Plot initial positions
i_pos = ax.plot(
    od_5parts.dataset["XC"].isel(time=0),
    od_5parts.dataset["YC"].isel(time=0),
    "k.",
    markersize=10,
    transform=PlateCarree(),
)
_images/Particles_30_0.png

Now we plot the change in potential density anomaly as a function of time of these five particles (1st plot below), and the potential density anomaly gradient (2nd plot). The rapid decrease in particle density corresponds to intense mixing and entrainment of lighter ambient water as the overflow descends into the Irminger Sea. Notice one particle on the Iceland shelf (in blue) is not part of the overflow and moves north then mixes.

[15]:

varName = "Sigma0"
fig, axes = plt.subplots(2, 1, figsize=(10, 10), sharex=True)
for i, ax in enumerate(axes.flatten()):
    if i == 1:
        varName = f"d{varName}_dtime"
    ax = od_5parts.plot.time_series(varName=varName, ax=ax, linewidth=2)
_images/Particles_32_0.png

The plots above can be easily customized for any of the extracted variables. For example, change varName = 'Sigma0' in the cell above with any of the variables printed below.

[16]:

# Create table
table = {
    var: od_5parts.dataset[var].attrs.pop(
        "long_name", od_5parts.dataset[var].attrs.pop("description", None)
    )
    for var in od_5parts.dataset.variables
    if "time" not in var and "particle" not in var
}
print("\n{:>15}: {}\n".format("varName", "label"))
for name, desc in sorted(table.items()):
    print("{:>15}: {}".format(name, desc))


        varName: label

          Depth: ocean depth
              S: salinity
         Sigma0: potential density anomaly
           Temp: potential_temperature
             XC: longitude
             XG: longitude
             YC: latitude
             YG: latitude
              Z: vertical coordinate of cell center
             Zl: vertical coordinate of upper cell interface
            Zp1: vertical coordinate of cell interface
             Zu: vertical coordinate of lower cell interface
       momVort3: 3rd component (vertical) of Vorticity