A moving heat pulse can reveal water transport, but the heat velocity is not yet the whole tree’s water use
A brief heat pulse is applied inside a stem. Sensors on opposite sides of the heater record different temperature rises. Their ratio can contain information about the direction and rate of heat transport, including low or reverse flow under suitable conditions. The useful signal is not a miniature photograph of sap moving through every vessel.
The heat-ratio method follows a chain: paired temperature rises, a logarithmic heat-velocity estimate, corrections for geometry and tissue effects, conversion to a water-transport quantity, and spatial integration across conducting wood. This guide keeps those stages separate so that a negative value, a small daily flow or a large whole-tree total can be interpreted without skipping the supporting assumptions.
All records and calculations are original fictional exercises. They are not instructions for inserting probes, applying heat or establishing zero flow in a living tree. Those tasks require trained methods, environmental permission where relevant and current equipment documentation. The learning task is to read supplied thermal and flow records and decide what the evidence actually demonstrates.
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Choose your reading route
Route 1: Read the paired signal · Chapters 1–3
Distinguish the heat-ratio method from other sap-flow techniques
Route 2: Audit thermal and geometry assumptions · Chapters 4–5
Treat thermal diffusivity as a material parameter with uncertainty
Route 3: Follow corrections and scaling · Chapters 6–8
Follow wound and contact effects without assuming they are harmless
Route 4: Test low and reverse flow · Chapters 9–10
Route 5: Transfer and communicate · Chapters 11–12
Transfer between trees, roots and pulse-processing choices carefully
Full chapter index · Independent worked case · Questions and practical checks
Chapter index
Read the paired signal · Chapters 1–3
Distinguish the heat-ratio method from other sap-flow techniques
Use temperature rises rather than absolute probe temperatures
Work through the logarithmic heat-velocity equation
Audit thermal and geometry assumptions · Chapters 4–5
Treat thermal diffusivity as a material parameter with uncertainty
Explain why probe symmetry is a physical assumption
Follow corrections and scaling · Chapters 6–8
Follow wound and contact effects without assuming they are harmless
Convert heat velocity to a defined sap-transport quantity
Integrate across conducting wood rather than one convenient point
Test low and reverse flow · Chapters 9–10
Test low and reverse flow against zero-state uncertainty
Separate stem transport from instantaneous canopy transpiration
Transfer and communicate · Chapters 11–12
Transfer between trees, roots and pulse-processing choices carefully
Report the chain from thermal signal to water account
CHAPTER 1 OF 12
1. Distinguish the heat-ratio method from other sap-flow techniques
Several sap-flow methods use heat, but they do not use one interchangeable measurement equation. Thermal-dissipation probes commonly interpret a temperature difference relative to a zero-flow reference through an empirical calibration. Stem heat-balance methods account for heater power and heat losses. The heat-ratio method interprets a short pulse using paired temperature responses around a heater.
A coefficient belonging to one method cannot be applied to another merely because both instruments report a temperature or a value in centimetres per hour. Begin with the installed method, its geometry and the exact reported quantity. An output labelled “velocity” can still refer to heat propagation rather than directly to water movement.
Burgess and colleagues introduced the improved heat-ratio approach to address low and reverse rates within its tested conditions, including physical and thermal corrections. Its purpose does not mean that every negative result in any installation proves reverse sap flow. The method’s advantages depend on the validity of the observation and correction chain.
The existing general sap-flow overview explains transport, nighttime movement and scaling. The dedicated thermal-dissipation and stem heat-balance guides follow different algorithms. Use those comparisons to choose the relevant evidence chain, not to combine all thermal measurements into one apparently stronger average without examining their distinct assumptions.
CHAPTER 2 OF 12
2. Use temperature rises rather than absolute probe temperatures
Let v₁ and v₂ denote the temperature increases after a pulse at the downstream and upstream sensing positions under a stated orientation. Each rise is post-pulse temperature minus its appropriate pre-pulse baseline. The heat ratio is v₁/v₂, not the ratio of the absolute temperatures in degrees Celsius.
Suppose fictional downstream temperature rises from 22.10 to 22.28 °C and upstream temperature rises from 22.00 to 22.12 °C. The rises are 0.18 and 0.12 K, giving a ratio of 1.50. Dividing 22.28 by 22.12 would produce a number near one that answers the wrong question.
A temperature difference has the same numerical magnitude in kelvin and degrees Celsius. A ratio of compatible temperature rises is dimensionless. The separate absolute baselines may differ because of natural gradients or instrumentation. Their treatment belongs to the validated analysis rather than being erased by assuming both probes began at the same temperature.
Very small rises can produce unstable ratios because noise becomes large relative to the denominator. A ratio of two near-zero signals is not rescued by its dimensionless units. Preserve the raw rises, response timing and signal-quality information alongside the calculated ratio so that later interpretation can distinguish a real transport feature from a weak thermal observation.
CHAPTER 3 OF 12
3. Work through the logarithmic heat-velocity equation
For the ideal symmetric teaching geometry, write Vh = (κ/x) ln(v₁/v₂), where κ is thermal diffusivity and x the equal distance from the heater to each probe. With κ in cm² s⁻¹ and x in centimetres, Vh is cm s⁻¹; multiplying by 3,600 expresses it in cm h⁻¹. The equation is conditional on the method’s thermal and geometry assumptions.
Take supplied κ = 0.0025 cm² s⁻¹ and x = 0.60 cm. The hourly coefficient is 0.0025/0.60 × 3,600 = 15 cm h⁻¹. With ratio 1.50, Vh = 15 ln 1.50, approximately 6.082 cm h⁻¹. This is a heat-velocity estimate before the further corrections and water-flow conversion.
If the ratio is exactly one in the idealised account, the logarithm is zero. If it is greater than one, Vh is positive under the chosen orientation. If it is less than one, the logarithm is negative. The meaning of that sign requires a documented probe orientation and a credible zero and symmetry treatment.
Do not replace the logarithm with a simple ratio-minus-one calculation except as an explicitly justified small-change approximation. For ratio 1.50, ln 1.50 is about 0.405, not 0.50. A convenient arithmetic shortcut would overstate the result before any biological or spatial interpretation even begins.
CHAPTER 4 OF 12
4. Treat thermal diffusivity as a material parameter with uncertainty
Thermal diffusivity describes how a thermal disturbance spreads through the material. Fresh wood is a composite of structure and water, so a supplied diffusivity is not automatically a universal constant across species, radial positions or changing conditions. The method should state how its material parameters were obtained or adopted.
In the simplified equation, Vh is proportional to κ. A 20% change in the adopted diffusivity produces a 20% change in the calculated heat velocity when the observed ratio and geometry are held fixed. This is a sensitivity of the inference, not a claim that changing wood properties necessarily leaves the ratio unchanged in a real experiment.
A nominal value can be appropriate for a clearly labelled teaching exercise or an explicitly provisional analysis. Absolute flow claims need the uncertainty and support of the adopted value. Using a familiar constant from another study is an assumption to report, not an independent calibration of the present tree.
Keep heat-capacity and density information separate from diffusivity when the processing chain uses them for later conversion to sap velocity. Combining different material assumptions at different stages can create a result that has no coherent calibration basis. A transparent intermediate record makes such inconsistencies easier to detect.
CHAPTER 5 OF 12
5. Explain why probe symmetry is a physical assumption
The simple ratio relationship presumes specified distances and orientation around the heater. If probes are not symmetrically positioned, unequal heating can occur even when water transport is zero. The resulting offset can mimic low positive or negative flow. This is particularly important when the hydrological question concerns nighttime or reverse movement.
Changing x in the denominator alone does not generally correct an asymmetric installation. The unequal distances can alter the two thermal responses in different ways. A correction must belong to a characterised geometry model or validated calibration, not simply to the spacing written on the installation diagram.
The manufacturer’s SFM documentation explicitly treats spacing, alignment and asymmetry corrections. It also distinguishes limited correctable departures from cases requiring a different installation. This guide does not supply an installation tolerance or a universal rescue factor; the relevant evidence and limits must come from the actual method used.
For a supplied hypothetical zero-state test, suppose the ratio consistently remains 1.03. Under the earlier ideal coefficient, this would imply 15 ln 1.03 ≈ 0.443 cm h⁻¹ even at zero transport. A later apparent velocity of 0.3 cm h⁻¹ is then not convincing positive flow unless the offset and its uncertainty have been resolved.
CHAPTER 6 OF 12
6. Follow wound and contact effects without assuming they are harmless
Inserted probes disturb tissue and the local thermal pathway. Wounding can alter the relationship between heat transport in the measured region and transport in intact conducting wood. A wound correction therefore concerns the physical interpretation of the thermal signal, not merely a cosmetic adjustment applied after plotting.
A correction can depend on the method’s characterisation of wound effects and geometry. Do not assume the same factor applies to all species, installation ages or radial positions. If a factor is adopted from a validated method, retain its provenance and the conditions under which it was supported.
As an explicitly fictional processing example, suppose a characterised linear transformation is Vh,c = 1.10Vh − 0.20 cm h⁻¹. For Vh = 2.735 cm h⁻¹, corrected heat velocity is about 2.808 cm h⁻¹. These supplied coefficients illustrate a transformation only; they are not recommended values for any tree or instrument.
The transformation changes both scale and zero. A later revision should therefore trigger reprocessing of the original heat records or retained uncorrected values, not just multiplication of the final daily total by an unexplained percentage. Preserve the stage at which every correction enters so that its effects remain auditable.
CHAPTER 7 OF 12
7. Convert heat velocity to a defined sap-transport quantity
Heat moves through both wood and water. The heat-pulse velocity is therefore not automatically the water velocity through every conduit. Converting it to a sap-related velocity or flux-density quantity requires the method’s material and heat-capacity treatment, with a clear definition of the resulting denominator.
Some outputs describe volume flow per unit sapwood area; others may be reported under different velocity conventions. Before multiplying by an area, establish what that area is supposed to represent. A velocity normalised to conducting tissue cannot be multiplied by total stem area including heartwood without a new and usually unsupported assumption.
Continue the fictional corrected heat velocity of 2.808 cm h⁻¹. If a supplied, independently characterised material conversion factor is 1.50, the resulting sapwood-area flux-density velocity is 4.212 cm h⁻¹ for this exercise. The factor is additional information. It was not measured by the temperature ratio alone.
State the conversion stage even when software performs it automatically. A dashboard value in litres per hour may depend on a sequence of adopted thermal parameters, wound corrections and sapwood areas. Seeing only the final unit does not make the quantity directly observed or independent of those assumptions.
CHAPTER 8 OF 12
8. Integrate across conducting wood rather than one convenient point
Sap transport can vary radially and around the stem. A point or depth-specific estimate therefore does not automatically represent the whole conducting cross-section. Spatial integration needs a defined sapwood domain and a supported way to weight the available observations.
For a fictional two-zone example, outer active sapwood area is 20 cm² with flux density 4.0 cm h⁻¹, and inner active area is 30 cm² with 1.5 cm h⁻¹. The volume flow is 20 × 4.0 + 30 × 1.5 = 125 cm³ h⁻¹, or 0.125 L h⁻¹. Each zone contributes its own area times compatible flux density.
The unweighted mean velocity would be 2.75 cm h⁻¹. Multiplying it by 50 cm² gives 137.5 cm³ h⁻¹, which overweights the faster outer zone in this example. Weighting is a physical area account, not a statistical preference. Circumferential variation creates an additional sampling issue that two radial observations may not resolve.
Sapwood geometry can change with growth or the definition of active conducting tissue. Keep area measurement and timing attached to the flow record. A precise heat ratio cannot compensate for an unsupported conducting area, just as a precise rainfall depth cannot establish volume without a representative catchment area.
CHAPTER 9 OF 12
9. Test low and reverse flow against zero-state uncertainty
The ability to detect low or reverse transport is a reason to use a suitable heat-ratio method, but an observed negative sign remains an inference to test. Natural thermal gradients, asymmetry, weak pulses and processing offsets can also affect a ratio near one.
With the fictional hourly coefficient of 15 cm h⁻¹, ratio 1.01 gives Vh ≈ 0.149 cm h⁻¹. Ratio 0.99 gives approximately −0.151 cm h⁻¹. If differential signal uncertainty readily spans both ratios, the direction is poorly resolved. Reporting a negative number with three decimal places does not establish a biological reversal.
A reciprocal ratio illustrates the sign logic more clearly. Ratio 1.20 gives about +2.735 cm h⁻¹; ratio 1/1.20 gives the same magnitude with a negative sign under the same ideal parameters. Do not use 0.80 as the reciprocal of 1.20: it would imply a different magnitude, about −3.347 cm h⁻¹.
A credible reverse-flow interpretation therefore combines orientation, adequate signal, zero and geometry evidence, method validity and repeatable context. It should also distinguish local reverse movement from a claim about whole-plant water uptake or redistribution. A particular measured stem or root pathway does not automatically identify the complete plant network.
CHAPTER 10 OF 12
10. Separate stem transport from instantaneous canopy transpiration
Water crossing the measured stem section can refill plant stores before it leaves through leaves. Conversely, stored water can support transpiration while stem transport is smaller. The heat-ratio instrument measures a transport inference at its own location; it does not directly measure all vapour leaving the canopy.
For a compatible simplified plant account, storage change ΔW equals stem inflow F minus canopy transpiration T. If an hour has F = 0.20 kg and storage rises by 0.04 kg, T is 0.16 kg. If storage instead falls by 0.04 kg, the same inflow can support 0.24 kg of transpiration.
Nighttime transport can therefore include recharge as well as transpiration, depending on the system. The fact that a flow minimum occurs at night does not prove zero flow, and the fact that flow persists at night does not uniquely identify its cause. Independent storage, canopy or water-state evidence helps constrain the alternatives.
When comparing with a whole-tree chamber, align the measured tree, interval and pathways. A branch outside the chamber, a stem sensor below a storage compartment, or evaporation from wet foliage can all complicate comparison. A good comparison explains these boundaries rather than forcing one curve to equal the other through arbitrary rescaling.
CHAPTER 11 OF 12
11. Transfer between trees, roots and pulse-processing choices carefully
Changing species can change anatomy and thermal properties. Changing from a stem to a root changes orientation and possibly the question about direction. A previously useful parameter set is not automatically validated for the new material or geometry. The heat-ratio equation’s name does not carry all of its calibration evidence with it.
The timing of the post-pulse observations also belongs to the method. A valid calculation window should be supported by the characterised thermal response. Choosing whichever time gives the expected daily curve can bias the result. If a previous pulse or natural temperature trend affects the response, the raw temperature record is needed to investigate it.
A shorter logging interval does not automatically improve time resolution if successive thermal disturbances are not independent under the chosen protocol. Conversely, a coarse interval may miss brief changes. The appropriate sampling and pulse scheme is a method-specific decision, not a universal setting supplied by this educational example.
For a changed-context exercise, retain the same ratio but double the assumed diffusivity. The calculated heat velocity doubles under the model. Then retain diffusivity but change the observed tissue. The arithmetic can still run while the parameter support fails. Learning to distinguish those two situations is more useful than memorising one factory-like constant.
CHAPTER 12 OF 12
12. Report the chain from thermal signal to water account
A defensible report retains probe orientation and geometry, temperature baselines and rises, ratio window, diffusivity, symmetry treatment, wound correction and material conversion. It identifies the active-area model used for whole-stem scaling and the interval integration used for totals.
Keep raw heat velocity, corrected heat velocity, sapwood-area flux density and total stem flow as distinct variables. A later correction to area should not be confused with a revised thermal signal. This separation allows a reader to identify whether a change in reported tree water use came from new observations or from a reinterpreted conversion.
For a small negative result, report direction uncertainty and the zero-state evidence. For a daily total, state missing intervals and whether modelled values were inserted. Do not turn sensor failure into zero flow or remove genuine negative transport simply because a water-use graph is expected to remain positive.
The gold standard is a reconstructable physical explanation: how the paired rises support heat transport, how the corrections support a sap quantity and how spatial and temporal integration support a wider claim. That explanation preserves the method’s ability to investigate difficult low-flow conditions without giving every signed output more biological meaning than the evidence can support.
Independent worked case and evidence checks
A further fictional stem contains two conducting zones. An outer zone of 30 cm² has a resolved positive flux density of 2 cm h⁻¹, while an inner zone of 20 cm² has a resolved negative flux density of −1 cm h⁻¹. The signed volume contributions are +60 and −20 cm³ h⁻¹. Net transport is +40 cm³ h⁻¹, or 0.040 L h⁻¹.
The positive net does not mean every measured zone moves forward. Gross forward transport is 0.060 L h⁻¹ and the magnitude of reverse transport is 0.020 L h⁻¹ in this constructed account. Adding absolute values gives 0.080 L h⁻¹, which is neither the signed net nor canopy transpiration. The summary must match the hydrological question.
Now let the inner negative estimate fall within its zero-state uncertainty. The net point estimate can still be calculated, but the claim of a resolved reverse pathway becomes weaker. Keep uncertainty and spatial structure in the report rather than hiding them behind one whole-stem total. A negative component is not automatically evidence of a complete hydraulic-redistribution network.
The same distinction applies in time. One hour of +0.10 L followed by one hour of −0.04 L gives net transport +0.06 L, whereas the sum of magnitudes is 0.14 L. Clipping the negative interval would produce a third answer, 0.10 L. Each arithmetic operation can be useful for a defined purpose, but only the signed sum preserves that stated net boundary account.
A fictional symmetric heat-ratio record supplies κ = 0.0025 cm² s⁻¹ and x = 0.60 cm. Downstream and upstream temperature rises are 0.144 and 0.120 K. Their ratio is 1.20. The hourly coefficient κ/x × 3,600 is 15 cm h⁻¹, so raw Vh = 15 ln 1.20 ≈ 2.735 cm h⁻¹.
A supplied characterisation gives Vh,c = 1.10Vh − 0.20 cm h⁻¹ and a material conversion factor of 1.50. Corrected heat velocity is approximately 2.808 cm h⁻¹, and the resulting sapwood-area flux-density velocity is about 4.212 cm h⁻¹. Each stage uses additional supplied evidence, not merely a new name for the raw ratio.
If that flux density represents 25 cm² of active conducting area, its volume contribution is approximately 105.3 cm³ h⁻¹, or 0.1053 L h⁻¹. A second zone with area 15 cm² and flux density 2.0 cm h⁻¹ adds 30 cm³ h⁻¹. The two-zone total is about 0.1353 L h⁻¹ under the stated representation.
Changed context one: the apparent zero-state ratio is 1.02 rather than one. Under the ideal raw equation this corresponds to about 0.297 cm h⁻¹. That diagnostic cannot simply be ignored when interpreting a later raw estimate of −0.10 cm h⁻¹. The characterised correction and residual uncertainty determine whether the sign is resolved.
Changed context two: reverse the physical probe orientation but retain the old downstream/upstream labels in the software. The calculated sign can reverse without any biological reversal. Before interpreting a negative trace, verify that the sign convention follows the actual geometry and was preserved through data processing.
For a limited uncertainty calculation, let the ratio be r = 1.20 with independent standard uncertainty σr = 0.02 while κ and x are treated as exact. Because dVh/dr = 15/r, the ratio contribution to σVh is approximately 0.25 cm h⁻¹. It is about 9% of the raw estimate. Diffusivity, geometry and correction uncertainty would increase or otherwise modify the complete account.
Finally compare an hour of stem inflow of 0.135 kg with independently supported plant storage gain of 0.025 kg. The compatible simplified transpiration is 0.110 kg for the hour, not 0.135 kg. The thermal transport calculation can be correct while a claim of equal instantaneous canopy water loss remains incomplete.
Worked comparison
| Stage | Quantity | Main additional evidence |
|---|---|---|
| Paired sensors | Post-pulse temperature rises | Baselines, timing and adequate signal |
| Ideal logarithmic relation | Raw heat-pulse velocity | Diffusivity and symmetric geometry |
| Physical corrections | Corrected thermal transport | Wound, contact and asymmetry characterisation |
| Material conversion | Defined sap-related flux density | Heat capacities, density and unit convention |
| Spatial integration | Stem volume flow | Active sapwood area and representative profiles |
| Plant water account | Canopy transpiration inference | Compatible storage and pathway information |
Questions and practical checks
Should I divide the absolute probe temperatures?
No. The method uses appropriately baselined temperature increases after the heat pulse.
Does a negative value prove reverse flow?
Not alone. Check orientation, signal quality, zero and symmetry evidence, corrections and the method’s limits.
Is heat velocity identical to sap velocity?
Not automatically. A material and method-specific conversion is required before a defined water-transport quantity is inferred.
Can one point be multiplied by total stem area?
Only with a supported representation and compatible denominator. Inactive tissue and radial or circumferential variation matter.
Is nighttime sap flow necessarily nighttime transpiration?
No. Plant storage and other pathways can separate stem transport from canopy loss.
Continue with the connected subjects
Compare the different thermal methods
Sap-flow overview: flux density, nighttime movement and scaling
Thermal-dissipation probes: a different index and zero-flow reference
Stem heat balance: power, stored heat and a separate transport account
Connect transport with canopy exchange and water state
Whole-tree chambers: the canopy vapour boundary
Dendrometers: independent evidence about stem-radius change
Leaf water potential: state rather than a transport rate
Compare a connected evidence chain
Stem psychrometers: local water potential, thermal offsets and hydraulic-gradient interpretation. Keep the measured quantity, represented surface, time interval and additional model assumptions distinct when combining these observations.
Sources and scope
Burgess and colleagues (2001): improved heat-ratio measurement of low and reverse sap flow
ICT International SFM1 manual: heat-ratio theory, asymmetry, corrections and reporting stages
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.