An evaporation pan measures its own water loss before it estimates anything else
Two pans lose different amounts of water during the same week. One stands beside irrigated grass; the other receives air crossing a dry open patch. Neither reading automatically tells us how much water a nearby reservoir or crop lost. The instrument, its surroundings and the intended target are three parts of the explanation.
This guide follows evaporation-pan measurements from the water balance to a justified conversion. You will correct a pan record for rain and maintenance, distinguish reference evapotranspiration from lake evaporation, and test whether a coefficient still works after the exposure changes. The numerical examples are fictional and deliberately small enough to check by hand.
Begin with the quantity you need. If your task is converting an already established evaporation depth into reservoir volume, use the connected reservoir-geometry guide. Here the harder question comes earlier: what evaporation depth does this particular exposed pan support?
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Choose your reading route
Route 1: Read the instrument · Chapters 1–3
Route 2: Understand exposure · Chapters 4–5
Route 3: Build a conversion · Chapters 6–8
Route 4: Challenge the estimate · Chapters 9–10
Distinguish trend in the instrument from trend in the target
Route 5: Transfer and report · Chapters 11–12
Full chapter index · Independent worked case · Questions and practical checks
Chapter index
Read the instrument · Chapters 1–3
Name the pan observation and the target separately
Reconstruct evaporation with a signed water balance
Match clocks, areas and maintenance records
Understand exposure · Chapters 4–5
Explain fetch as the history of incoming air
Keep advection and heat storage visible
Build a conversion · Chapters 6–8
Define the coefficient by the target it connects
Use the correct weights when conditions change
Calibrate against a compatible independent reference
Challenge the estimate · Chapters 9–10
Distinguish trend in the instrument from trend in the target
Put uncertainty on the observation and the conversion
Transfer and report · Chapters 11–12
Transfer the method into a changed setting
Write a result that preserves its evidence chain
CHAPTER 1 OF 12
1. Name the pan observation and the target separately
A pan is a small water body with a particular material, geometry and exposure. Its evaporation depth describes water leaving that surface over an interval. A reference crop, an actual field and a deep lake present different surfaces and energy stores. A shared unit of millimetres does not make their losses interchangeable.
Write three labels above a calculation: observed pan evaporation, target quantity and conversion method. For example, a pan total may be used with a supported coefficient to estimate grass-reference evapotranspiration. That is not yet actual water use by a stressed crop, and it is not a measured lake loss. Each additional interpretation needs its own relationship.
Suppose a file contains a value of 40 mm labelled evaporation. Before multiplying by anything, inspect its definition. It might already be a converted estimate. Applying the coefficient again would create a second conversion while preserving plausible units. The error would be semantic rather than a failure of multiplication.
This is why a useful first question is not which coefficient everyone uses. Ask what was observed, what was already calculated and what the result is meant to describe. A short definition can prevent a long model from giving a precise answer to the wrong question.
CHAPTER 2 OF 12
2. Reconstruct evaporation with a signed water balance
For a simple constant-area pan, express every addition and removal as an equivalent depth over the pan. Let Δh be ending level minus starting level, P rain entering, A measured water added and D measured water drained. With no leakage, splash loss or overflow, Δh = P + A − D − Epan. Therefore Epan = P + A − D − Δh.
Our first fictional record begins at 190 mm and ends at 184 mm, so Δh = −6 mm. Rain contributes 4 mm, an observer adds 8 mm and drains nothing. Evaporation is 4 + 8 − 0 − (−6) = 18 mm. The 6 mm level fall alone would substantially understate evaporation because it ignores the added water.
Reverse the level change: the pan rises by 3 mm during a rainy interval, with 12 mm rain and no maintenance. Evaporation is 12 − 3 = 9 mm. Water can evaporate while the pan level rises. A net storage increase says that additions exceeded removals, not that a removal process disappeared.
The Hong Kong Observatory explains this measurement logic and the problem of unrecorded overflow. In our equation, missing overflow is an omitted output. A larger rainfall observation cannot reveal its exact volume after the fact. Preserve an affected interval as uncertain rather than naming every unexplained loss evaporation.
CHAPTER 3 OF 12
3. Match clocks, areas and maintenance records
Pan readings, rainfall and maintenance must describe the same interval. A midnight-to-midnight rainfall total cannot be inserted without thought into a pan record read at nine each morning. Rain during the non-overlapping hours can create a false evaporation signal. More decimal places cannot align two different clocks.
Imagine 5 mm rain falls between midnight and the morning reading. A daily spreadsheet assigns it to the following pan interval even though it is already included in the starting level. The erroneous calculation adds the water twice across the boundary between days. Over a longer complete period the timing error might cancel, but the individual daily estimates remain wrong.
Convert a measured addition by the pan surface area, not by the much narrower filling cylinder. In a fictional 1 m² pan, 2 litres is 2 mm. The water may rise much farther inside a narrow measuring vessel before being poured. The measuring vessel helps establish volume; the pan area defines the equivalent depth.
Keep raw observations beside the calculation: reading times, levels, rain, additions, removals and any quality flag. A total can then be reconstructed without guessing which maintenance operation was already included. This is especially helpful when an automated system records a pumping event separately from its water-level series.
CHAPTER 4 OF 12
4. Explain fetch as the history of incoming air
Fetch is the distance over a specified upwind surface before air reaches the measurement. It matters because incoming air has interacted with that surface. Air crossing a wet, vegetated patch need not arrive with the same temperature and humidity as air crossing dry ground. A nearby fence also does not tell the whole story of exposure.
FAO’s pan method distinguishes surroundings, upwind surface and wind and humidity conditions when choosing coefficients. Treat these as part of the instrument context rather than decorative site descriptions. A pan placed within a green patch can still receive different air as wind direction changes across a mixed landscape.
For a classroom map, place a pan between irrigated grass to the west and a dry yard to the east. A westerly and an easterly day have different upwind histories even if their mean wind speeds match. The exercise is not a formula for either day. It shows why a direction-free site label can omit the relevant difference.
Record a plan of the surroundings, distances and changes in land cover. An apparently continuous pan series may cross a change from grass to bare ground or from open exposure to growing trees. A break in exposure can affect comparability even when the same pan and ruler remain in use.
CHAPTER 5 OF 12
5. Keep advection and heat storage visible
Advection is transport by moving air or water. For the pan question, incoming air can carry heat and moisture from elsewhere. A pan’s energy supply is therefore not always captured by imagining sunlight falling vertically onto its water surface. Its sides and stored heat also distinguish it from a crop or a large water body.
Use a bounded teaching analogy: a small cup and a large bowl can both contain water, but the relative importance of their sides and their temperature response differ. The analogy does not calculate evaporation. It helps explain why matching air temperature alone is insufficient to guarantee matching evaporation rates.
Suppose two fictional exposures receive the same stated net radiation over an interval, but one additionally receives a supplied 1 MJ/m² of advected energy. If that entire extra amount supported evaporation, using a rounded latent heat of 2.45 MJ/kg would give about 0.41 mm extra water loss. That is a conditional energy conversion, not a measured increment or a universal advection correction.
A deep lake may release energy stored earlier while a shallow pan responds on a different schedule. The connected lake heat-storage article develops that issue. A coefficient that behaves well over a long interval may still fail to reproduce the target’s daily timing. State whether the intended use needs totals, daily estimates or short bursts.
CHAPTER 6 OF 12
6. Define the coefficient by the target it connects
A coefficient is a relationship, not a certificate of accuracy. Write Etarget = K × Epan only after defining Etarget. For grass-reference evapotranspiration, FAO denotes the relationship ETo = Kp × Epan. A coefficient developed for one target should not silently become a coefficient for another.
For an invented ten-day pan total of 60 mm and a supplied grass-reference coefficient of 0.70, estimated ETo is 42 mm over those ten days. The mean is 4.2 mm/day. Neither the 42 mm total nor the coefficient establishes actual crop use without additional crop and water-availability information.
Now consider a separate, independently supported lake conversion of 0.80 for a particular exercise. It would give 48 mm lake evaporation from the same pan total. The two estimates are not contradictory because their targets differ. Calling both corrected evaporation without their target names would hide that distinction.
Do not read these illustrative coefficients as recommendations. Real selection depends on instrument, environment, period and supporting evidence. A familiar number copied from a neighbouring report is a hypothesis about transfer. It becomes defensible only when the neighbouring report’s target and exposure are genuinely relevant.
CHAPTER 7 OF 12
7. Use the correct weights when conditions change
If coefficients vary between intervals, accumulate K times pan depth for each interval. The coefficient applicable to a total is weighted by the pan depths, not automatically by the number of days. Averaging first can change the answer when large losses occur under a different exposure.
Take two fictional equal-duration intervals. The first has 20 mm pan evaporation and K = 0.80; the second has 40 mm and K = 0.60. The target total is 16 + 24 = 40 mm. Applying the unweighted mean coefficient, 0.70, to the combined 60 mm gives 42 mm instead.
An equivalent single coefficient is 40/60, approximately 0.667. It reproduces this combined total by construction. It should not be presented as an independently calibrated universal coefficient or used to reconstruct either interval separately. It summarises the particular weighting of these two observations.
Change only the pan depths to 40 and 20 mm. The target becomes 32 + 12 = 44 mm, despite unchanged total pan evaporation and unchanged arithmetic mean coefficient. The relationship between losses and conditions matters. This is the same weighting discipline used in reservoir depth–area calculations, applied one step earlier in the measurement chain.
CHAPTER 8 OF 12
8. Calibrate against a compatible independent reference
Calibration compares the pan-based estimate with evidence for the defined target over matched periods. It does not mean choosing the number that makes an unrelated water-budget residual disappear. A reference calculation, lysimeter observation or other comparison has its own assumptions and uncertainty, which should be identified.
Suppose three fictional training periods have pan totals of 30, 40 and 50 mm and compatible target estimates of 21, 28 and 35 mm. K = 0.70 fits each exactly. This neat dataset demonstrates the model structure. It is not evidence that actual measurements are noiseless or that a constant coefficient always works.
Reserve a different period before tuning. If its pan total is 60 mm and reference target is 33 mm, the old model predicts 42 mm and overestimates by 9 mm. Investigate whether exposure, season, target definition or measurement quality changed. Reporting only the perfect training fit would conceal the failed transfer.
Avoid calibrating and evaluating on the same intervals while calling the exercise independent validation. Keep whole observation periods together and record exclusions. A low error based only on calm dry days does not demonstrate performance during windy weather, maintenance changes or rain-affected intervals.
CHAPTER 9 OF 12
9. Distinguish trend in the instrument from trend in the target
A pan record can be valuable without being a direct time series of every evaporating surface nearby. A trend interpretation needs stable measurement practice and a clear relationship between the pan and the target. Changes in wind, humidity, radiation or surroundings may alter that relationship.
Imagine an unchanged target total of 50 mm in two fictional seasons. Pan totals are 70 and 60 mm because the relationship changes; the corresponding ratios are about 0.714 and 0.833. A fixed coefficient would imply a target decline even though the exercise explicitly holds the target constant. The example establishes possibility, not a diagnosis of a real regional record.
The opposite failure is possible too: a stable pan total can coexist with a changing target if the conversion changes. One observational series alone cannot separate every cause. A useful investigation combines metadata, relevant meteorology and an independent method rather than beginning with a preferred explanation.
Double-mass consistency checks can help identify changes relative to a reference, but they do not automatically identify the physical cause. A slope change may reflect the target, reference or observation process. Follow the linked consistency guide when the task concerns a long record, and keep the pan exposure history attached.
CHAPTER 10 OF 12
10. Put uncertainty on the observation and the conversion
For a simple product, uncertainty comes from both the pan total and K. If they can reasonably be treated as independent with small errors, an approximate variance is K² times the variance of Epan plus Epan² times the variance of K. Dependence adds a covariance term; ignoring it is an assumption, not a property of the multiplication.
For an illustrative 50 mm pan total with standard uncertainty 1 mm, and K = 0.70 with standard uncertainty 0.05, the two contributions are 0.70 mm and 2.50 mm. Their root-sum-square is about 2.60 mm for the 35 mm target estimate. The conversion uncertainty dominates this invented case.
Improving the level reading to halve the pan uncertainty changes the combined value only slightly, to about 2.52 mm. That does not make careful observation unimportant. It shows why the next useful improvement depends on the weak link. Better coefficient evidence may help more than another decimal place in the ruler reading.
When uncertainty is not statistical, use explicit alternatives instead. A supported range of coefficients can give a sensitivity range, but that is not automatically a confidence interval. Label the method, explain what is varied and preserve omitted uncertainty such as missing overflow or an untested change in exposure.
CHAPTER 11 OF 12
11. Transfer the method into a changed setting
Move the fictional pan from an irrigated patch to a dry site while keeping its material and dimensions unchanged. Which parts of the old calculation survive? The signed water balance and unit conversion still apply. The empirical relationship to the reference surface requires fresh checking because the incoming-air history has changed.
Next leave the pan in place but change the target from grass reference to open-water evaporation. The observation remains useful, but the previous coefficient answers a different question. A new target cannot be introduced merely by changing a chart label. Trace the physical and empirical connection again.
Finally keep target and exposure but shorten the reporting interval from ten days to one hour. Thermal storage and timing mismatches may matter more. FAO’s discussion of the pan method cautions about the relevant averaging period; do not interpret a longer-period relationship as proof of hourly fidelity.
A successful transfer explanation identifies what is invariant and what is not. Conservation, dimensions and explicit boundaries travel well. Site-specific coefficients, timing response and calibration scope travel only with supporting evidence. This separation is more useful than memorising one conversion and hoping the new question is identical.
CHAPTER 12 OF 12
12. Write a result that preserves its evidence chain
A concise report might say: the maintained pan lost 60 mm over the stated ten days after rain and additions were reconciled; applying the supplied grass-reference coefficient gave 42 mm estimated ETo; the coefficient’s exposure and time-scale support were reviewed. That statement separates observation, calculation and intended meaning.
Include pan type, location, upwind context, reading times, maintenance and quality flags. State the coefficient source, target surface and validation period. If the result will enter a reservoir budget, identify the separate method converting to lake evaporation and the area representation used for volume.
When a component is unresolved, say which one. An uncertain rain correction differs from an unvalidated coefficient. Combining them into one vague warning prevents the reader from choosing a useful next check. A good limitation helps another person improve the estimate.
For retrieval practice, explain why the pan can rise while evaporation continues, why identical wind speed does not imply identical fetch, and why the mean of two coefficients can misestimate a total. If you can answer those without the worked lines, you have retained the structure rather than just the example numbers.
Independent worked case and evidence checks
Independent case: Mira receives a fictional four-day pan record. The level falls by 7 mm, rain totals 9 mm, measured additions equal 10 mm and measured removals equal 3 mm. No overflow, leakage or other transfer is allowed in this exercise. First reconstruct the pan evaporation before considering any coefficient.
The answer is 9 + 10 − 3 − (−7) = 23 mm. A student who reports 7 mm has treated net level change as gross evaporation. A student who reports 3 mm may have subtracted the fall with the wrong sign. Diagnose the relationship before repeating the arithmetic.
The record contains two equal-length subperiods: pan losses of 8 and 15 mm. Supplied target coefficients are 0.80 and 0.60 because the exercise assigns different supported conditions. The target total is 6.4 + 9.0 = 15.4 mm. The single equivalent coefficient is 15.4/23, approximately 0.670, not the unweighted 0.70.
Change the question: the target estimate is to be applied over a fixed 0.4 km² water surface only after a separate lake-conversion relationship has established that 15.4 mm is appropriate lake evaporation. Under that explicit extra assumption, the volume is 0.0154 × 400,000 = 6,160 m³. Without the lake assumption, multiplying grass-reference ETo by lake area would be unjustified.
Now remove the no-overflow assumption. A note says an unknown amount spilled from the pan during rain. The level-based 23 mm combines evaporation with the omitted spill. The correct response is not to choose a smaller coefficient to compensate. Mark the gross evaporation as unresolved and seek the missing overflow evidence.
For an evidence check, list one observation that addresses each weakness: a matched rain record for timing, a maintenance log for additions, an overflow record for the missing exit and independent target estimates for conversion. None substitutes for all the others. That is the practical lesson of a small pan: the calculation is reliable only when each link answers its own question.
A second independent test examines whether one coefficient can hide opposing errors. Suppose four fictional validation intervals have target estimates of 10, 10, 20 and 20 mm, while pan-based predictions are 12, 12, 18 and 18 mm. Both totals equal 60 mm. The overall volume bias is zero, but the low-target intervals are 20% high and the high-target intervals are 10% low. Perfect total agreement has concealed a condition-dependent error. Report the interval differences as well as the combined sum.
Now assign the first pair to moist upwind exposure and the second pair to dry exposure in this invented design. The pattern suggests a relationship worth investigating, not proof that fetch caused the error. Exposure may coincide with season or measurement quality. A stronger test obtains matched independent comparisons within each relevant exposure and examines whether the pattern persists. Re-labelling all low estimates as dry and all high estimates as moist after seeing the errors would create an explanation by construction rather than a genuine test.
For a practical learning session, ask one reader to reconstruct the raw balance without seeing the coefficient, and another to review the coefficient support without seeing the desired reservoir answer. Compare their conclusions afterwards. This separates an observation audit from a target-model audit. If the balance is wrong, repair its rain, level or maintenance term. If the balance is sound but conversion fails, retain the original pan observation while reconsidering the relationship. Deleting or altering valid raw measurements to improve target agreement would destroy useful evidence.
Finish by choosing the next observation that can change the conclusion. If unknown overflow dominates, another reference coefficient will not recover the missing water. If exposure transfer dominates, a finer level sensor may not resolve it. If the target has changed from grass to lake, even a perfectly maintained pan needs a different supported interpretation. The useful next step is the one aimed at the missing relationship, not automatically the most elaborate instrument or the largest dataset.
Worked comparison
| Fictional interval | Pan depth | Target K | Target depth |
|---|---|---|---|
| First | 20 mm | 0.80 | 16 mm |
| Second | 40 mm | 0.60 | 24 mm |
| Combined | 60 mm | 0.667 equivalent | 40 mm |
Questions and practical checks
Is a pan coefficient always 0.70?
No. The values in this guide illustrate calculations, not field recommendations. A coefficient belongs to a specified pan, target surface, exposure and period. Verify its source and independent performance rather than assuming one familiar value is universal.
Does a rising level mean zero evaporation?
No. Rain or additions can exceed evaporation. Reconstruct the signed balance. The original example has 12 mm rain, a 3 mm rise and 9 mm evaporation, with no other terms.
Can I repair overflow by changing K?
No. Overflow is an omitted water-balance output; K connects a valid pan loss to a target. Adjusting K to hide missing spill mixes instrument accounting with surface conversion.
Can I use this estimate for hourly lake losses?
Not without evidence that the target conversion works at that time scale. Heat storage and timing can differ between a shallow pan and a lake. A longer-period agreement does not establish hourly agreement.
What is the quickest useful check?
Write the target name and signed pan balance, then inspect interval alignment and maintenance. After that, examine the coefficient’s exposure and validation. These checks address different possible errors rather than repeating the final multiplication.
Continue with the connected subjects
Start with quantities and exposure
Evaporation depth, reservoir geometry and water volume
Lake heat storage and the evaporation time window
Check records and alternative explanations
Double-mass curves and changing observation consistency
Budget closure, correlated errors and unresolved fluxes
Compare the observation with another measurement route
Choose the quantity first: these companion studies distinguish water lost from a maintained surface, precipitation accumulated in a vessel, and water condensed or intercepted on a collector. Their readings are connected by water and energy accounts, not interchangeable labels.
Precipitation storage gauges: accumulated catch and maintenance
Dew collectors: cooling, retained water and source attribution
Atmometers: artificial surfaces and reference-crop estimates
Sources and scope
FAO Irrigation and Drainage Paper 56, Chapter 4: pan conversion and exposure
FAO Chapter 1: reference surfaces, evaporation and water-depth units
Hong Kong Observatory: pan water accounting and overflow limits
US Army Corps of Engineers: pan-based evaporation in the monthly-average method
The numerical cases in this guide are original fictional teaching examples, not measurements from a real site. This is an educational explanation, not a field safety instruction, engineering approval or an official certification. For a real project, use qualified practitioners, current product documentation and site-specific evidence. Sources were checked on 30 October 2026.