03 · Two variables, two questions¶

Context¶

PRISM minimum and maximum temperature share one coordinate system, so we can ask related questions without juggling separate grids.

Question¶

Where was maximum temperature unusual on the coldest regional day, and how did the day-to-night temperature range change through January?

Analysis story¶

We validate the physical relationship between variables, then answer a spatial and a temporal question with two readable pipes.

Data used in this lesson¶

Every value comes from the PRISM Group at Oregon State University's AN91d daily 4 km climate product. This repository carries a small Boulder-region extract for 1–30 January 2024 so the lesson runs offline without replacing observations with generated values. The data validation page records source URLs, terms, checksums, bounds, units, and acceptance tests.

Prepare · Validate the shared dataset¶

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from pathlib import Path

import xarray as xr

# Find the repository from either a root-level documentation build or a kernel
# started beside this notebook, then open the checksum-controlled PRISM extract.
data_path = next(
    candidate / "tests" / "fixtures" / "real_data" / "prism_boulder_january_2024.nc"
    for candidate in (Path.cwd(), *Path.cwd().parents)
    if (candidate / "tests" / "fixtures" / "real_data" / "prism_boulder_january_2024.nc").exists()
)
prism = xr.open_dataset(data_path, engine="scipy").load()

# These assertions are part of the teaching contract: official source,
# canonical cube dimensions, complete daily time, and declared Celsius units.
assert prism.attrs["source"] == "PRISM Group, Oregon State University"
assert prism.attrs["is_synthetic"] == 0
assert prism.sizes == {"time": 30, "y": 24, "x": 24}
assert prism["tmax"].attrs["units"] == "degC"

import numpy as np

# Minimum temperature cannot exceed maximum temperature, and the derived range
# must be exactly traceable to those two observed PRISM variables.
assert bool((prism["tmin"] <= prism["tmax"]).all())
np.testing.assert_allclose(
    prism["diurnal_range"], prism["tmax"] - prism["tmin"], rtol=0, atol=1e-5
)
coldest_day = prism["tmax"].mean(("y", "x")).argmin("time")
from pathlib import Path

import xarray as xr

# Find the repository from either a root-level documentation build or a kernel
# started beside this notebook, then open the checksum-controlled PRISM extract.
data_path = next(
    candidate / "tests" / "fixtures" / "real_data" / "prism_boulder_january_2024.nc"
    for candidate in (Path.cwd(), *Path.cwd().parents)
    if (candidate / "tests" / "fixtures" / "real_data" / "prism_boulder_january_2024.nc").exists()
)
prism = xr.open_dataset(data_path, engine="scipy").load()

# These assertions are part of the teaching contract: official source,
# canonical cube dimensions, complete daily time, and declared Celsius units.
assert prism.attrs["source"] == "PRISM Group, Oregon State University"
assert prism.attrs["is_synthetic"] == 0
assert prism.sizes == {"time": 30, "y": 24, "x": 24}
assert prism["tmax"].attrs["units"] == "degC"

import numpy as np

# Minimum temperature cannot exceed maximum temperature, and the derived range
# must be exactly traceable to those two observed PRISM variables.
assert bool((prism["tmin"] <= prism["tmax"]).all())
np.testing.assert_allclose(
    prism["diurnal_range"], prism["tmax"] - prism["tmin"], rtol=0, atol=1e-5
)
coldest_day = prism["tmax"].mean(("y", "x")).argmin("time")

Pipes · Express each analysis as one sentence¶

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from cubedynamics import pipe, verbs as v

maximum_temperature_anomaly = (
    pipe(prism["tmax"])
    | v.anomaly(dim="time")
).unwrap()

regional_diurnal_range = (
    pipe(prism["diurnal_range"])
    | v.mean(dim=("y", "x"))
).unwrap()
from cubedynamics import pipe, verbs as v

maximum_temperature_anomaly = (
    pipe(prism["tmax"])
    | v.anomaly(dim="time")
).unwrap()

regional_diurnal_range = (
    pipe(prism["diurnal_range"])
    | v.mean(dim=("y", "x"))
).unwrap()

Figure · Put the spatial and temporal answers together¶

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import matplotlib.pyplot as plt

fig, axes = plt.subplots(1, 2, figsize=(10, 3.8), constrained_layout=True)
maximum_temperature_anomaly.isel(time=coldest_day).plot(
    ax=axes[0], cmap="RdBu_r", center=0, cbar_kwargs={"label": "Anomaly (°C)"}
)
date = str(prism.time.isel(time=coldest_day).values)[:10]
axes[0].set_title(f"Maximum-temperature anomaly · {date}")
regional_diurnal_range.plot(ax=axes[1], marker="o", color="#775a3a")
axes[1].set_title("Boulder-region diurnal temperature range")
axes[1].set_ylabel("Daily range (°C)")
plt.show()
import matplotlib.pyplot as plt

fig, axes = plt.subplots(1, 2, figsize=(10, 3.8), constrained_layout=True)
maximum_temperature_anomaly.isel(time=coldest_day).plot(
    ax=axes[0], cmap="RdBu_r", center=0, cbar_kwargs={"label": "Anomaly (°C)"}
)
date = str(prism.time.isel(time=coldest_day).values)[:10]
axes[0].set_title(f"Maximum-temperature anomaly · {date}")
regional_diurnal_range.plot(ax=axes[1], marker="o", color="#775a3a")
axes[1].set_title("Boulder-region diurnal temperature range")
axes[1].set_ylabel("Daily range (°C)")
plt.show()

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What the figure tells us¶

The coldest regional day was not equally unusual everywhere, while the day-to-night range followed a separate trajectory.

Try the next variation¶

Pipe tmin through the same anomaly verb and compare its spatial pattern.

Data used¶

Field	Frozen analysis input
Provider	PRISM Group, Oregon State University
Product	AN91d daily 4 km time series
Dates	2024-01-01 to 2024-01-30
Fixture	`tests/fixtures/real_data/prism_boulder_january_2024.nc`
Provenance record	`tests/fixtures/real_data/prism_boulder_january_2024.provenance.json`

The PRISM source reference describes current catalog support; the fixture record above identifies the observations used here. Data validation documents checksums and acceptance checks. The analytical baseline and thresholds belong to this story, not the provider.

Reproduce¶

Clone the repository, then run these commands from its root:

python -m pip install -e ".[vignettes]"
python scripts/run_vignettes.py docs/vignettes/cube_from_dataset.ipynb

No network is needed after installation. Open the downloaded notebook in Jupyter and run all cells to see the same figures. The website executes these cells during its strict build. Environment setup and the vignette contract explain the workflow.