GNSS Zenith Wet Delay and PWV Explained

What a navigation satellite can reveal about water vapour

GNSS precipitable water vapour is a striking example of a scientific observation with an indirect path to its final meaning. A ground receiver listens to radio signals from navigation satellites, such as those in GPS and other global constellations. The atmosphere slows and bends those signals relative to an ideal vacuum path. Precise processing estimates the additional signal path delay. After separating a comparatively predictable hydrostatic component from a more variable wet component, the remaining delay can be converted to a water-vapour column estimate. A receiver does not scoop vapour from the air or measure rainfall directly.

The essential terms are zenith total delay, zenith hydrostatic delay and zenith wet delay, usually shortened to ZTD, ZHD and ZWD. They are often expressed as metres or millimetres of equivalent signal path. In the standard decomposition ZTD equals ZHD plus ZWD, and therefore ZWD equals ZTD minus ZHD. That subtraction is the bridge between a positioning-related signal correction and a meteorological measurement. It is also where errors in station pressure and atmospheric modelling can masquerade as errors in humidity.

Precipitable water vapour, PWV, describes the liquid-water depth that would result if vapour in the vertical atmospheric column were condensed and collected over the column footprint. Integrated water vapour, IWV, refers to mass per horizontal area, usually kilograms per square metre. Their numerical values are approximately equal when PWV is given in millimetres of water because one kilogram spread over one square metre forms one millimetre of liquid water at the conventional water-density approximation. Neither quantity says that the atmosphere will actually release that amount of rain.

Translate the delay without confusing metres and millimetres

Start by documenting the site, antenna position, retrieval time, satellite geometry, processing method and whether a product contains zenith total delay or merely a slant-path value. A zenith delay is referenced to a vertical direction. A signal from a satellite low over the horizon traverses a longer slanted atmospheric path; converting multiple slant observations to a representative zenith quantity requires mapping functions or equivalent atmospheric models. You cannot treat a large slant delay as if it were directly the column’s zenith delay.

Suppose an illustrative analysis reports ZTD of 2.430 m and estimated ZHD of 2.260 m. Subtracting gives ZWD of 0.170 m, or 170 mm of signal-path delay. That 170 mm is not 170 mm of precipitable water. A separate conversion factor, conventionally written Π, maps zenith wet delay to precipitable water. For an assumed illustrative dimensionless factor of 0.155, PWV equals 0.155 times 170 mm, which is 26.35 mm. The multiplication must be shown so the quantities cannot be confused.

A useful reading exercise asks what happens if someone reports 26.35 metres instead of 26.35 millimetres. They have introduced a thousandfold unit error, not a slight change of meteorological interpretation. It is better to write the calculation with units at every step: 2.430 m minus 2.260 m equals 0.170 m; 0.170 m multiplied by 0.155 equals 0.02635 m, or 26.35 mm. In a scientific report a plausible-looking output with the wrong unit can be more dangerous than an obviously impossible number.

Why the hydrostatic component occupies most of the delay

Much of the lower atmosphere’s refractivity arises from gases associated with the bulk atmospheric mass. The hydrostatic delay responds strongly to surface pressure and is often near a couple of metres at low-elevation stations, depending on conditions and altitude. The wet delay is frequently a smaller residual and depends on vapour distribution and temperature. This imbalance matters because the sought moisture signal is calculated after subtracting two larger numbers. A small mistake in the hydrostatic estimate can therefore be important for the remaining wet component.

Pressure-based ZHD formulas may contain latitude and height corrections, and pressure must refer to the appropriate station location rather than an unrelated reduced sea-level pressure. Surface weather reports often present mean-sea-level pressure for comparison across geography. The GNSS antenna may stand hundreds of metres above sea level. Substituting the sea-level-reduced value as though it were local station pressure creates a systematic error in ZHD and hence ZWD. The fix is not to apply a random moisture correction; it is to use an appropriate station-pressure estimate and document its reference level.

At ordinary conditions an error of 1 hPa in local pressure changes a simple hydrostatic delay estimate by roughly 2.3 mm, with exact sensitivity depending on the model and location. With Π set to 0.155, this can correspond to about 0.35 mm of inferred PWV error, before considering other dependencies. This numerical sensitivity is not a universal uncertainty claim. It illustrates the direction and scale of error propagation through a subtraction. Readers should ask whether a reported pressure came from a nearby station, an instrument at the antenna, or a reanalysis field.

The factor that turns wet delay into precipitable water

The conversion from ZWD to PWV is commonly written PWV equals Π times ZWD. The dimensionless factor Π depends on atmospheric refractivity constants and a temperature-weighting quantity called the mean atmospheric temperature, often written Tm. The mean is not simply the arithmetic average of the thermometer at ground level and the temperature of a high cloud. It represents an integrated weighting associated with water-vapour and temperature profiles. It may be estimated from a numerical weather analysis, radiosonde profile or validated empirical relationship.

To see why this matters, hold a hypothetical ZWD constant at 170 mm while changing Π from 0.150 to 0.160. The resulting PWV spans 25.5 to 27.2 mm. The range of 1.7 mm arises entirely from the assumed conversion factor, not from a different receiver observation. Whether this range is appropriate for a real site requires independent evaluation of Tm and atmospheric state. Do not adopt this demonstration as a generic error bar; it is a sensitivity exercise showing how a conversion model affects the inferred moisture.

The original GNSS meteorology work by Bevis and colleagues established the use of signal-delay estimates for atmospheric integrated water-vapour remote sensing, while operational and research data products now report tropospheric delays and associated moisture retrievals. The link from radio propagation to vapour amount is physically grounded, but not self-validating. A responsible translation identifies which atmospheric model supplied Π and whether the product includes a quality flag, uncertainty estimate or a method-specific correction.

A full worked example that keeps the variables separated

Imagine an invented station at which a calibrated analysis gives ZTD = 2.445 m, a pressure-informed ZHD = 2.265 m and a temperature-informed factor Π = 0.151. First subtract the delays to obtain ZWD = 0.180 m. Next multiply 0.180 m by 0.151 to obtain PWV = 0.02718 m, or 27.18 mm of liquid-equivalent column water. Finally express IWV as approximately 27.18 kg m−2 under the usual liquid-water density convention. All figures are teaching inputs, not field observations from a named station.

The order of operations matters. If a reader multiplies the total delay 2.445 m by 0.151 without subtracting ZHD, the result is 369.2 mm, an enormously misleading water-vapour value. If they subtract 2.265 from 2.445 but forget to convert the units, they may write 0.180 mm instead of 0.180 m. If they treat Π as a fixed universal constant, they may overlook atmospheric thermal variations. Showing each stage is a better error-prevention mechanism than asking the reader to memorise the final number.

To independently check the calculation, reconstruct ZTD from the parts: 2.265 m plus 0.180 m equals 2.445 m, matching the supplied total. Dividing 27.18 mm by 0.151 returns 180 mm, matching the wet delay. A transparent unit trace and reverse check are especially useful when the analysis appears in another software package, spreadsheet or translated-language report. Strong communication preserves the identity and units of every variable so that later reviewers can discover a mistake without reconstructing the whole model.

What the receiver really measures before the meteorological retrieval

GNSS receivers record signals from multiple satellites and solve a positioning and timing problem that includes orbital geometry, clocks, atmospheric propagation and other effects. The tropospheric correction is estimated alongside parameters needed for the navigation solution. Depending on the processing strategy, the final delay can be entangled with receiver coordinates, antenna height, satellite orbit and clock solutions and other model assumptions. Therefore, a suspicious jump in a derived PWV series does not automatically prove that water vapour abruptly surged above the station.

Multipath arises when signals bounce from buildings, wet surfaces, structures or other surroundings before reaching the antenna. Low-elevation satellites can suffer larger atmospheric modelling errors, signal obstruction and multipath. Processing choices such as an elevation cutoff and mapping-function model affect the estimated delay. A station relocation, antenna replacement or change of processing software can introduce an apparent discontinuity in a long-term series. Anyone analysing climate-scale trends must first investigate such non-meteorological changes.

The distinction between the observable and derived parameter matters when teaching translation. A concise statement is that the GNSS processing estimates how the atmosphere affected radio-signal travel, after accounting for the navigation geometry, and a meteorological conversion relates part of that delay to vapour mass. Calling it a direct satellite measurement of humidity is a shortcut that hides too much; calling it purely theoretical ignores the real instrument signal. Both errors can be avoided with one short explanation of the physical chain.

Moisture in a column does not identify its vertical distribution

Two columns may contain similar amounts of precipitable water but have moisture placed at very different altitudes. In one, the lower kilometre may be very humid while air above is comparatively dry. In another, mid-level moisture may contribute more strongly. Ground-based GNSS PWV typically integrates over the column and cannot independently reveal the precise vertical humidity profile. That limitation does not make the measure unhelpful. It makes it complementary to radiosondes, weather models, lidar or other profiling systems.

Consider two hypothetical soundings with identical IWV of 30 kg m−2. One places much of the vapour near a warm surface; the other spreads moisture more deeply into the middle troposphere. Their cloud and precipitation behaviour can differ because ascent, stability, temperature profiles, winds and forcing also matter. A GNSS column reading alone should not be converted into a prediction that rain is imminent. It can help recognise a moist environment or changing moisture supply when combined with other relevant evidence.

The language ‘water waiting to rain’ is often used in popular explanations of PWV. It risks implying that condensation of the entire column is physically expected. Precipitation efficiency, cloud microphysics, ascent, ventilation and horizontal moisture transport constrain actual rainfall. A location can receive more rainfall than its initial column PWV if moisture is continuously transported into the storm region, or receive no rain despite high PWV if the required lifting and cloud processes do not occur.

Time-series interpretation and the meaning of a moisture increase

Suppose a GNSS product reports PWV values of 22.4, 24.1, 25.8 and 25.6 mm at regular thirty-minute intervals. The observed increase from the first to third values is 3.4 mm over sixty minutes, followed by a slight decrease of 0.2 mm. It is valid to describe this column-moisture change as represented by the retrieval, assuming consistent processing and quality. It is not automatically valid to claim the moisture was transported from a particular sea, that a storm must occur, or that a surface hygrometer would show the same trend.

The time resolution of the underlying GNSS solution and any averaging should be checked. A five-minute output cadence does not prove the retrieval represents an instantaneous five-minute-independent measurement. Sliding windows, smoothing, model constraints and data gaps can spread a rapid event over several records. The user of a product needs to distinguish its timestamp, update frequency, effective smoothing window and latency. These details become important when comparing abrupt changes with radar, lightning or observed rainfall.

For long-term analyses, apparent trends may reflect station changes, atmospheric model upgrades, pressure-sensor changes, satellite constellation expansion or a shift in processing choices. A trend should be tested against the metadata and against independent moisture measurements where possible. Cross-checking is especially important when a few tenths of a millimetre matter. A complete explanation documents the data’s processing history instead of treating every numerical fluctuation as a change in the atmosphere.

Compare GNSS water vapour with a microwave radiometer

A passive ground-based microwave radiometer measures atmospheric emission at selected frequencies and retrieves water-vapour and liquid-water quantities through radiative-transfer models. A GNSS receiver begins instead with propagation delay of navigation signals. The two instruments therefore have different sensitivities and failure mechanisms. Microwave retrievals can be complicated by clouds, rain and instrumental calibration; GNSS processing can be complicated by pressure, radio-signal multipath, coordinates, mapping functions and thermal conversion factors. Agreement is useful, but disagreement is an invitation to diagnose, not automatically proof that one is defective.

Suppose GNSS PWV is 28 mm and a coincident microwave product reports 30 mm. Their raw difference is 2 mm. It is not meaningful to declare a 6.7 percent sensor error without knowing which denominator and reference is chosen. Relative to the microwave figure, the magnitude of the difference is 2 divided by 30, or 6.67 percent. Relative to GNSS it is 7.14 percent. Neither percentage establishes the truth value because both are retrievals. A proper intercomparison includes uncertainty, collocation interval and representativeness.

Even simultaneous instruments may sample somewhat different atmospheric footprints or apply different averaging and quality criteria. A GNSS station’s radio paths span different sky directions, while a radiometer may scan the zenith or selected elevation angles. Rain on an antenna radome and rapidly moving moisture gradients can influence comparability. Before building a bias correction from paired data, review the definitions, units, time windows and instrumental flags, then test the correction on observations not used to fit it.

Pressure, height and coordinate checks that prevent false moisture

One of the most useful diagnostic tables for GNSS PWV lists station latitude, longitude, ellipsoidal or orthometric height, antenna reference point, local meteorological sensor height, pressure-unit convention and the origin of the surface-pressure estimate. A geodetic position is not interchangeable with a weather-observer’s rounded place name. Small coordinate or height mismatches may be inconsequential for a casual weather map but important when processing a precise long-term delay record or building a pressure-height correction.

Suppose a pressure sensor is 30 m below the antenna and its data are used without a height correction. The pressure difference from this separation may be several hectopascals depending on air density. With a hydrostatic delay sensitivity near 2.3 mm per hPa, that can feed appreciably into ZHD. The purpose of this example is to highlight reference-level consistency, not to prescribe a fixed pressure correction for all sites. Compute the appropriate pressure change from local conditions or a documented atmospheric model.

Verify the timestamp standard as carefully as the vertical datum. A series logged in UTC and a rainfall record labelled in local time can produce a false lead-lag relationship if offsets are ignored. Daylight-saving conventions vary internationally and can create duplicated or missing clock hours in local datasets. For a global learning resource, UTC with an explicit conversion is usually the most portable basis for comparing instruments. A correct statistical correlation attached to wrongly aligned timestamps is not a correct scientific result.

Translate a GNSS-PWV graph into words that a reader can verify

A good explanation begins with the site and retrieval: ‘At the indicated station, a processed GNSS estimate of column PWV rose from one value to another during the specified interval.’ It then explains that the estimate is derived from zenith wet delay after subtracting a pressure-dependent hydrostatic delay. It should describe the change in millimetres, note any visible missing or flagged intervals, and avoid predicting precipitation from PWV alone. A technically honest paragraph often needs fewer adjectives than a dramatic weather update.

When annotating a graph, label the vertical axis PWV in millimetres or IWV in kilograms per square metre, with the relationship explained. A plot of raw ZTD should not be relabelled PWV simply because both vary with atmosphere. State the cadence, window and source processing strategy. If a line is smoothed, show or describe the smoothing method. If there are large isolated spikes, investigate residual quality and station metadata before drawing a line connecting them as if they were trustworthy physical observations.

An especially useful practice is to reproduce one row numerically. Display the supplied ZTD, ZHD and Π, carry out the subtraction and multiplication, and verify the product against the charted value. If the calculation fails, possible causes include use of a different Tm conversion, inconsistent timestamps, hidden precision, unit changes or a mistake in extracting the right series. The exercise makes a reader capable of auditing an unfamiliar dataset rather than simply accepting a polished figure.

Worked diagnostic: the pressure sensor was changed during the afternoon

Suppose a GNSS processing pipeline reports a sudden increase of 0.8 mm in PWV exactly when a station’s pressure input switches to a second sensor. The first explanation to test is not that the atmosphere abruptly acquired moisture. Check the two pressure readings for an offset and determine how that offset changes ZHD. A hydrostatic-delay sensitivity of approximately 2.3 mm per hPa multiplied by an illustrative 2 hPa offset gives a 4.6 mm change in the estimated ZHD. At Π = 0.155, that corresponds to about 0.71 mm in derived PWV, remarkably close to the apparent step.

The direction of the bias matters. If reported station pressure becomes erroneously lower, estimated ZHD decreases, and with unchanged ZTD the residual ZWD increases. The PWV estimate then rises, even without additional vapour. If pressure is overestimated, the reverse happens. The worked values are deliberately simplified, because real pipelines also use latitude, height, atmospheric temperature and other modelling details. The calculation isolates a mechanism that makes a suspicious moisture jump scientifically testable.

The repair is to reconcile sensor heights and pressure calibration, reprocess the affected records with a homogeneous input, and compare the discontinuity with nearby independent observations. Do not apply a permanent arbitrary offset to the PWV series until the reference-level error has been demonstrated. Document the corrected timestamps and preserve the original and corrected data for traceability. A trustworthy dataset should allow reviewers to reconstruct why a value changed.

Worked diagnostic: an apparent rain precursor could be a timing artefact

Consider a rainfall gauge that reports a shower at 14:00 local time and a GNSS column-moisture jump at 06:00 UTC on the same calendar day in a region eight hours ahead of UTC. Those labels could identify the same instant, rather than a GNSS event eight hours earlier. Conversely, a report that mixes an eastern local date with UTC might place observations on different calendar days. A beautifully plotted time lag is no substitute for aligning the time systems before measuring a lead or correlation.

For an independently testable exercise, express both instants as UTC before choosing a comparison window. Convert the 14:00 time at UTC+08 to 06:00 UTC and inspect whether the original series actually align. Then account for data cadence: a half-hourly GNSS estimate at 06:00 may summarize observations from several minutes around that label. A rain gauge’s 14:00 value may be an accumulation over the preceding hour. Temporal support must be harmonised as well as clock labels.

The correct report says which records are averaged, which are point measurements, and whether their intervals end or begin at the timestamp. Without that clarification, a moisture-rise/rain-onset association could appear persuasive but be built on inconsistent sampling. This issue is not limited to meteorology; the same reasoning applies to translating medical measurements, financial time series and laboratory logs across locations or data providers.

When PWV increases but no precipitation occurs

An atmospheric column can become more humid without producing rain because precipitation requires more than vapour mass. The necessary pathways commonly involve lifting, cooling, condensation, cloud-particle growth and delivery of hydrometeors to the surface. Stable air can retain a large vapour inventory, while a drier environment under sufficiently strong forcing may still produce some precipitation. The amount of column vapour is a state variable, not a direct instruction to the atmosphere to rain.

Imagine two days both showing PWV near 40 mm. On one day a frontal boundary provides organised ascent and deep cloud development. On the other day subsidence suppresses convection and the day remains mostly dry. The identical illustrative column inventory is compatible with different outcomes. A forecasting study should therefore combine PWV with measures of ascent, stability, convergence, moisture transport and cloud observations, then validate its proposed rules against out-of-sample events rather than selecting dramatic anecdotes.

The responsible reader avoids simplistic thresholds such as ‘PWV above X always means flood risk’ unless a calibrated local predictive model explicitly defines and validates such a threshold and its uncertainty. A public warning depends on a larger hazard framework, including rainfall intensity, duration, vulnerability and hydrological response. GNSS column moisture can be useful within that framework without becoming a standalone alarm.

Station-to-station differences require geographical care

Suppose one receiver sits near sea level and another is on elevated terrain. Their PWV values can differ because the atmospheric column above the higher antenna is physically shorter, even when the moisture field below and around the stations has related characteristics. Comparing two stations as though they sampled identical vertical volumes can lead to erroneous conclusions about horizontal gradients. Height, weather patterns and the spatial separation between sites matter along with instrument precision.

A hypothetical coastal site reports 31 mm while a mountain site reports 18 mm. The difference is 13 mm, but it cannot be translated immediately into a 13 mm increase of moisture caused by the coast. The measurements integrate different columns beginning at different elevations. To compare spatial structure, consider the station heights, a common vertical reference and atmospheric profile information. One may also compare time changes at each station rather than assume their absolute magnitudes must coincide.

The network advantage of GNSS is that numerous receivers can supply repeated column-moisture estimates across broad areas. The network limitation is heterogeneity in sensor installations, processing quality and terrain. A gridded map created by spatial interpolation is a modelled field, not an additional measurement at every grid point. Label interpolated cells accordingly and avoid adding fictitious decimal precision when the original stations are sparse.

How to propagate limited numerical uncertainty correctly

Suppose ZTD and ZHD are estimated with independent standard uncertainties of 4 mm and 3 mm for a classroom example. The uncertainty of their difference ZWD under the independence assumption is the square root of 4 squared plus 3 squared, or 5 mm. At fixed Π = 0.155 the corresponding PWV contribution is 0.775 mm. This is a useful way to show unit consistency, but not a complete uncertainty assessment. The two delay estimates may be correlated, and Π itself is uncertain.

If Π has an illustrative uncertainty of 0.004 and ZWD equals 180 mm, the first-order conversion-factor contribution is 180 multiplied by 0.004, or 0.72 mm. If one assumes independence between this term and a separate 0.775 mm term, the quadrature combination is about 1.06 mm. That result depends on the stated assumptions and should not be imposed as an error bar on real GNSS measurements. Multipath, station metadata, time correlation and model biases may dominate in some settings.

The lesson is to distinguish a sensitivity calculation from a validated uncertainty budget. A numerical bound calculated from invented independent errors can illuminate where errors enter, but it does not establish that an operational series meets that bound. Wherever a provider publishes formal quality information, uncertainty should be attributed to that particular product and retrieval process. If uncertainty cannot be estimated confidently, describe the principal potential biases and limit quantitative conclusions accordingly.

Independent exercises: reconstruct, challenge and repair

Exercise A: a report lists ZTD = 2.400 m, ZHD = 2.210 m and Π = 0.150. Determine ZWD, PWV and IWV. Answer: ZWD = 0.190 m = 190 mm; PWV = 190 mm times 0.150 = 28.5 mm; IWV is approximately 28.5 kg m−2. The checks are 2.210 plus 0.190 equals 2.400 m and 28.5 divided by 0.150 equals 190 mm. An answer of 360 mm from multiplying ZTD by Π skips the hydrostatic subtraction.

Exercise B: keep ZTD fixed but increase the estimated hydrostatic delay by 3 mm. What happens to ZWD and, at Π = 0.150, to PWV? Answer: ZWD decreases by 3 mm, and PWV decreases by 0.45 mm. This direction can be derived by writing ZWD equals ZTD minus ZHD before inserting any numbers. Readers who simply memorise that ‘more pressure means more moisture’ will fail this question, because pressure enters as a correction in the estimated signal delay.

Exercise C: two stations report 30 and 20 mm of PWV. Can one assert that the first has 50 percent more near-surface relative humidity? Answer: no. The ratio of the integrated values is 1.5, but the variables refer to vertical column water and not surface relative humidity. Elevation, temperature and vapour profile differ, and relative humidity itself depends on temperature-dependent saturation. A comparison of those two PWV values cannot recover the near-surface humidity without additional information.

Exercise D: a 5-minute PWV series jumps, but quality flags show several low-elevation satellite observations were rejected and the antenna firmware was upgraded. Is the jump necessarily weather? Answer: no. Compare independent humidity evidence and reprocessing metadata, investigate the effective smoothing window, and inspect whether the discontinuity coincides with the equipment or data-selection change. The right first action is quality diagnosis rather than retroactively constructing a meteorological story.

A reproducible reading workflow from receiver output to paragraph

Step one is to record the source and geometry: GNSS constellation, station identifiers, antenna position, data processing window, time reference and pressure input. Step two is to identify the actual product variable, whether slant delay, estimated ZTD, ZHD, ZWD, PWV or IWV. Step three is to verify the units and carry through a sample calculation. Step four is to inspect quality flags, gaps and metadata changes before interpreting trends. These steps are simple enough to teach, yet specific enough to detect common technical errors.

Step five is independent corroboration. Where available, compare nearby soundings, ground meteorological readings, radiometers and precipitation observations using matched periods and reference heights. Step six is to consider alternative explanations for an unusual pattern: real atmospheric moisture change, pressure-reference error, multipath, changed processing, inadequate temperature modelling or poor temporal alignment. Step seven is to write the result using separate clauses for measured signal, retrieved vapour estimate and any weather interpretation. A paragraph that makes this distinction is more useful than one that merely repeats unexplained acronyms.

When presenting a final figure, preserve the plotted variable, units, interval, data source and definition of missing values. State whether uncertainty is a formal error estimate, a sensitivity experiment or a visual comparison. Supply at least one worked numerical row. Explain why column moisture does not directly give rainfall at a location. The test of success is whether a reader can both understand and reproduce your main conclusion without accepting an unexplained instrument authority.

Frequently asked questions and a final translation test

Is GNSS-PWV the same as rainfall? No. It measures a vapour-column property inferred from radio propagation; rainfall is water reaching the ground through precipitation processes. Is GNSS-PWV a direct humidity sensor? No. The measurement chain uses a GNSS signal-delay analysis, a pressure-based hydrostatic estimate and a temperature-dependent wet-delay conversion. Is the conversion factor always 0.155? No. It depends on atmospheric conditions and the particular processing model. A value used in an example is not a mandated universal constant.

Why does a pressure error change an apparent humidity estimate? Because ZHD is subtracted from ZTD to isolate ZWD. A biased ZHD shifts the residual and therefore the PWV retrieved from it. Can a GNSS receiver report a vertical moisture profile? The ordinary column retrieval does not independently determine detailed vertical distribution. Additional data and methods are necessary. Why compare instruments if they each have uncertainty? Their different physical principles help identify errors that one instrument alone might not reveal.

One final test can be applied to any technical sentence. If a writer says, ‘Satellite delay proves it will rain this evening,’ ask for the missing links: which station delay, which pressure correction, which atmospheric temperature conversion, which time interval, and which forecasting evidence connects column vapour with rain occurrence? If the writer can supply those links, the claim may become useful. If not, the appropriate conclusion is only that a processed signal-delay observation suggests a particular column-vapour estimate within its uncertainties.