What this method is for
A greenhouse humidity reading is useful only when its meaning is defined. “Humidity” might mean relative humidity at a stated location, height, time, temperature, and logging condition. It might instead mean a dew-point or vapour-pressure quantity derived from temperature and RH. Those are different measurands. Define the quantity before deciding whether a sensor, a calibration report, or a project decision is suitable.
This article explains how to build and interpret an uncertainty budget for one defined reading. It is a method guide, not a field test, equipment specification, greenhouse acceptance band, or engineering sign-off. The greenhouse humidity sensor selection and calibration guide remains the place for sensor selection and calibration planning. The agriculture applications overview provides the wider application context.
Start with the measurand
Write the measurand in a way that another person could reproduce: for example, relative humidity in %RH at a named crop-zone point, at a stated sensor height, during a stated interval, with the associated air temperature recorded. Add the purpose of the reading: trend observation, a control input, a commissioning comparison, or another decision. A single number without location, time and method cannot show whether it represents the intended crop zone.
Temperature matters because RH is a relative quantity. A temperature change can alter RH even when the amount of water vapour has not changed. If the decision depends on condensation or moisture loading, record the temperature and identify whether dew point or vapour pressure is also required. The ASHRAE psychrometric reference and the NOAA vapour-pressure worksheet provide background for those related quantities; they do not establish a greenhouse acceptance limit.
Express the measurement model
Use a measurement model that makes corrections and uncertainty components visible. A simple illustrative form is:
y = x + C₁ + C₂
Here, x is the observed humidity result, while C₁ and C₂ are recognised corrections. A correction is applied to the result when its direction and basis are justified. The uncertainty attached to that correction remains in the budget. NIST TN 1297 explains how sensitivity coefficients, input uncertainties and covariance terms enter the law of propagation of uncertainty in Appendix A.
The model can be expanded when the instrument, method, environment, or derived quantity requires it. Do not force every influence into the two-correction example. List the influence quantity, its estimate, the standard uncertainty, the sensitivity coefficient, the evaluation basis, and whether it may be correlated with another input.
Separate the sources of uncertainty
Repeatability describes variation under a defined repeatability condition. Its standard uncertainty is an assessed uncertainty of the reported result; it should not be casually labelled the standard deviation of raw readings unless that is genuinely the evaluation method. The condition should identify the instrument, location, interval, operating state, and data treatment.
If the reported result is the mean of n independent readings taken under stable repeatability conditions, the Type A standard uncertainty of that mean can be estimated as s/√n, with s the sample standard deviation. For a single reading, the repeatability contribution is not reduced by √n merely because a separate series was collected. Correlated readings, drift or changing conditions require another justified evaluation. NIST Appendix A explains the independent-observation mean case.
A calibration certificate can contribute a calibration uncertainty. First determine which instrument, result, date, conditions, and uncertainty statement the certificate covers. Then determine whether that calibration contribution applies to the intended field method and environment. A certificate’s expanded uncertainty is not automatically the uncertainty of the entire greenhouse reading. Field method, operator, mounting, airflow, condensation, temperature coupling, drift, spatial gradients, and data handling may add components. The NIST calibration policy material is useful for reading the scope and uncertainty statement of a report. The VIM3 definition of instrumental measurement uncertainty describes instrumental uncertainty as a component and notes that specifications may provide relevant information; it does not turn a specification into a complete field budget.
Display resolution is commonly represented with a rectangular distribution when the available evidence supports that treatment. For a display step of 0.1 percentage point RH, a half-width of 0.05 percentage point RH gives a standard uncertainty of 0.05/√3. Check that this effect has not already been included in the repeatability evaluation. Counting the same contribution twice in an RSS calculation inflates the calculated uncertainty and misrepresents the budget.
Combine independent components only when justified
If all sensitivity coefficients are one and the input estimates are independent, or their covariance is justified as negligible, the combined standard uncertainty is the root-sum-square of the component standard uncertainties:
u_c = √(uₓ² + u₁² + u₂² + …)
This is a conditional case, not a universal shortcut. Shared calibration references, a common environment, repeated use of the same data, a common temperature input, or a correction derived from the same observations can create covariance. NIST TN 1297 Section 5 and the propagation appendix show where covariance terms belong. If dependence is material and cannot be evaluated, document the unresolved issue instead of silently using RSS.
A bounded hypothetical example
The following numbers are invented solely to show the arithmetic. They are not a sensor specification, certificate result, greenhouse reading, or acceptance criterion. Suppose a defined measurand has a corrected result of y = 60.0 %RH. Recognised significant corrections have already been applied. For this example only, input estimates are independent, have zero covariance, and have sensitivity coefficients of one.
| Component | Standard uncertainty | Hypothetical basis |
|---|---|---|
| Repeatability, uₓ | 0.30 percentage point RH | Assessed standard uncertainty of the reported result; not raw reading SD |
| Calibration, u_cal | 0.40 percentage point RH | Hypothetical U_cal = 0.80 percentage point RH with k_cal = 2, so 0.80/2 |
| Display resolution, u_res | 0.02887 percentage point RH | Display step 0.1; rectangular half-width 0.05/√3; separate from repeatability in this example |
The combined standard uncertainty is:
u_c = √(0.30² + 0.40² + (0.05/√3)²) ≈ 0.50083 percentage point RH
Selecting k = 2 for this illustration gives:
U = k u_c = 2 × √(0.30² + 0.40² + (0.05/√3)²) ≈ 1.00167 percentage points RH
The illustrative report would therefore be 60.0 %RH ± 1.0 percentage point RH (k = 2; illustrative), with the measurand, assumptions, component basis, and rounding stated beside it. The extra digit in the calculation is retained only to make the arithmetic reproducible; it is not a claim of measurement precision.
Interpret coverage and reporting carefully
An expanded uncertainty is formed by multiplying a combined standard uncertainty by a coverage factor under stated conditions. NIST Section 6 explains that a k = 2 interval is approximately 95% coverage only when the combined distribution is adequately normal and the uncertainty in the combined standard uncertainty is negligible. The factor alone does not establish a probability, confidence statement, or decision rule.
Report the result with the measurand, corrected value, unit, component evaluation, covariance assumption, coverage factor, expanded uncertainty, and relevant conditions. If degrees of freedom, non-normality, correlation, or a decision rule affects the use, record how that issue was handled. NIST Section 7 gives reporting context; the PTB DKD-R 5-8 humidity-calibration guideline is a useful metrology cross-reference. Neither source supplies a greenhouse-specific pass/fail limit.
Do not turn uncertainty into spatial acceptance
Uncertainty describes incomplete knowledge of a defined result. It does not remove real humidity gradients between crop rows, near a vent, beside a heater, or at different heights. Nor does a small uncertainty interval prove that the selected point represents the whole greenhouse. Representativeness requires a separate sampling and placement question. For that work, use the greenhouse humidity monitoring and sensor placement guide and the greenhouse nighttime humidity and dew-point guide. The commissioning checklist and project design data guide help connect a measurement record to operating context; they do not convert this hypothetical budget into a project result.
A practical review sequence
- Define the measurand, point, height, interval, temperature context, and intended decision.
- Record the observed result and every applied correction with its evidence basis.
- Separate repeatability, calibration, resolution, environmental, method, and derived-quantity components.
- State the standard uncertainty and evaluation method for each component; identify Type A or Type B where useful.
- Check for double counting and assess covariance before using RSS.
- Calculate u_c, choose and justify any coverage factor, and report the conditions with the result.
- Compare the reported uncertainty with a separately defined decision rule only when the measurement owner has established that rule.
For the original sensor-selection and calibration task, return to the selection and calibration guide. This standalone method provides a way to prepare and interpret a budget; it does not certify a device, a greenhouse, or a control outcome.
