SCIENCE · INVESTIGATE AND EXPLAIN

Compare reported and calculated weather humidity

Use recorded temperature and dew point to reconstruct a humidity estimate while retaining the API-reported value separately.

Learning outcome: Calculate RH from the two saturation pressures and interpret agreement without assuming independent measurements.

Starting recap

The liquid-water approximation gives RH = 100es(Td)/es(T). Reported RH is a separate source field whose method is not established by this subset.

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Try

KJFK has T = 18°C and Td = 2°C, a 16°C gap; KSEA has T = 11°C and Td = 8°C, a 3°C gap.

Open the experiment

Predict

Does close agreement between computed and reported RH prove that two independent humidity instruments agreed?

Your prediction and reason

Experiment

Compare each station’s temperature–dew-point gap, calculated RH and reported RH. Then select one station in both controls and explain what the equality checks.

Audit and compare recorded weather observations

Recorded weather observations · frozen source responses · Frozen weather-observations-v1: three deliberately selected NOAA station records dated 25 October 2026, with different observation times and locations. Source values and quality-control codes are retained; missing values stay missing. Calculated humidity is a liquid-water approximation from the reported temperature and dew point, not another observation. No live weather request, pressure-gradient calculation, climate trend or forecast is supplied.

Record A: KJFK · 19:05 UTC Record B: KSEA · 19:10 UTC

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Frozen NOAA source fields and retained missing values
Field	A · KJFK	B · KSEA
Station name	New York, Kennedy International Airport	Seattle, Seattle-Tacoma International Airport
Observation time (UTC)	2026-10-25T19:05:00+00:00	2026-10-25T19:10:00+00:00
Retrieved (UTC)	2026-10-25T19:58:30.501772+00:00	2026-10-25T19:58:31.120219+00:00
Reported station elevation	7 m	137 m
Temperature	18 °C · source QC: V	11 °C · source QC: V
Dew point	2 °C · source QC: V	8 °C · source QC: V
Reported relative humidity	34.25 % · source QC: V	81.75 % · source QC: V
Wind speed	14.832 km/h · source QC: V	9.252 km/h · source QC: V
Wind direction	200 degrees · source QC: V	90 degrees · source QC: V
Wind gust	Not reported (null) · source QC: Z	Not reported (null) · source QC: Z
API barometricPressure	103284.85 Pa · source QC: V	101490.06 Pa · source QC: V
API seaLevelPressure	Not reported (null) · source QC: Z	Not reported (null) · source QC: Z
Precipitation, preceding three hours	Not reported (null) · source QC: Z	Not reported (null) · source QC: Z
Source weather description	Clear	Cloudy
Raw message field	Empty in this response; no raw METAR supplied	Empty in this response; no raw METAR supplied
Specific observation source	KJFK observation record	KSEA observation record

Source QC codes are copied verbatim, not converted into a new quality grade. Decimal places are not an uncertainty interval. Missing gust or precipitation is not evidence of calm wind or zero rain. The API's barometricPressure field is preserved by name: this lesson does not assume it is true station pressure or interchangeable with sea-level pressure or an altimeter setting. No pressure gradient is inferred.

Calculations from reported values, not additional measurements
Quantity	A · KJFK	B · KSEA
Temperature minus dew point	16.00 °C	3.00 °C
Calculated RH = 100 eₛ(Td)/eₛ(T)	34.22%	81.74%
Reported RH	34.25%	81.75%
Wind speed converted by dividing km/h by 3.6	4.120 m/s	2.570 m/s
Signed observation-time difference A − B	-5 minutes; negative means A was observed earlier

The calculated humidity reuses the liquid-water saturation approximation from the humidity investigation. A mismatch can reflect rounding or a different source calculation; agreement is not independent sensor validation. These three records cannot establish a station's usual climate, a causal effect of elevation, a temporal warming trend or the future weather.

Inspect weather dataset provenance

NOAA National Weather Service API; snapshot weather-observations-v1. Three deliberately selected airport station records; not simultaneous, random or a climate sample. Frozen records; no live fetch in the lesson. Exact responses, field units and retrieval times are bundled locally. No source icons or external images are loaded. A later source correction does not silently change saved selections.

NOAA API documentation and open-data terms; NWS humidity calculation reference. The API is a recent-observation service; a historical record link can expire while this frozen teaching snapshot remains available.

A − B temperature difference: 7.00 °C. Observation time difference A − B: -5 minutes.

The station and time both change in a cross-station comparison. A reported null is not zero, dry weather or calm wind. Reported humidity and the calculation from temperature/dew point may share inputs; their agreement is not independent validation.

Observation to attach to a capture

Captures preserve record selections in weather-observations-v1 and replay comparisons of those frozen NOAA reports. Calculations are derived from reported values, not new measurements or live weather updates.

Understand

Keep reported and reconstructed values distinct

Each saved station record supplies air temperature, dew point and relative humidity. The browser also calculates RH from the recorded temperature and dew point using the same liquid-water saturation approximation introduced in the humidity investigation. The calculated and source-reported values remain separate.

Calling one field reported does not establish that it was directly measured by an independent sensor. Its processing method and dependence on other fields are not established by this subset. Close agreement can demonstrate numerical consistency with a formula without proving independent observational confirmation.

Reconstruct the pressure ratio

The approximation is e_s(T) = 6.112 exp(17.67T/(T + 243.5)), with temperature in degrees Celsius and saturation pressure in hPa. Dew point T_d supplies an inferred vapor pressure e_s(T_d). Thus calculated RH is 100e_s(T_d)/e_s(T).

The same factor 6.112 appears in numerator and denominator and cancels. An equivalent expression is 100 exp(17.67T_d/(T_d + 243.5) − 17.67T/(T + 243.5)). Either route should give the same result apart from numerical rounding. The NWS publishes these saturation and humidity relationships; the wet-bulb input procedure in that reference is not part of this record comparison. NWS calculation reference.

For KJFK, T = 18°C and T_d = 2°C. The two saturation pressures are approximately 20.63 and 7.06 hPa, giving calculated RH near 34.22%, compared with the separately reported 34.25%. Write the numerator and denominator labels before dividing so they cannot accidentally be reversed.

Compare all three records

KDEN has T = 13°C and T_d = 3°C, a 10°C separation. KSEA has T = 11°C and T_d = 8°C, a 3°C separation. Their reported RH values are approximately 50.66% and 81.75%, compared with KJFK’s 34.25%. Record each calculated result beside the source value and inspect their difference.

The narrower temperature–dew-point separation at KSEA corresponds to a higher RH in these observations. Do not generalize that into an exact rule that a given Celsius separation always gives the same RH. The saturation function is nonlinear, so the temperatures themselves also matter.

On paper, make a table with five columns: T, T_d, their difference, calculated RH and reported RH. Use a consistent display precision while retaining the underlying source values. Label the RH comparison difference in percentage points rather than degrees Celsius or hPa.

Explain what consistency can and cannot show

If the reported RH was itself derived from these temperatures or a related formulation, agreement would be expected without an independent measurement. The snapshot does not resolve that possibility. It also does not provide a full uncertainty budget for temperature, dew point or RH.

A small difference could reflect formula choice, rounding or other processing, but the difference alone does not identify its cause. A zero difference would likewise not prove that all three source fields are exact. Preserve the provenance question instead of turning an arithmetic check into a calibration certificate.

Select the same station in both controls. Temperature, dew point, timestamps and derived values should agree because both selections refer to the same record. That checks the comparison’s identity behavior, not repeatability across two independent observations.

Separate an observational comparison from an intervention

Changing Record A or B selects different places and times; it does not warm or cool a single parcel while holding moisture fixed. The source temperatures and dew points change together according to what was recorded. A claim that temperature caused the cross-station RH difference would need a suitable design and additional evidence.

These station observations also do not provide a vertical humidity profile or a lifting mechanism. Surface RH alone cannot establish a cloud-base height, rainfall amount or subsequent weather evolution.

Transfer to a known relationship

A hypothetical record has T = T_d = 15°C. What calculated RH follows? If a reported field also says 100%, does this prove two independent measurements agreed?

Check the weather-humidity transfer

The two saturation pressures are equal, so calculated RH is 100%. Agreement with a reported 100% field is consistent with the formula but does not establish independence. The reported value could share inputs or processing; method metadata or additional measurements would be needed to assess that.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Show the saturation-pressure ratio and distinguish a reproducible formula calculation from an independent validation of the observations.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Audit recorded weather observations Next: Limit weather claims to the recorded evidence

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