Heater power becomes a flow estimate only after the other heat pathways are accounted for
A heated stem carries energy upward with moving sap. That makes heat a useful tracer of water movement, but not every watt supplied by the heater leaves in sap. Some heat travels through the stem, some escapes outward, and some changes the temperature of the heated segment. Ignoring those routes can turn warming wood into apparent water flow.
Stem heat-balance methods use this energy account to estimate sap mass flow through a defined stem section. This guide concentrates on that method, rather than the thermal-dissipation and heat-pulse approaches covered in existing sap-flow guides. We then connect section flow with plant water storage and explain why a stem rate is not automatically canopy transpiration.
All powers, temperatures and plant records below are original fictional examples. They explain interpretation, not heater settings or installation procedures. Real measurements require apparatus-specific guidance and an appropriate study design. The useful skill is recognising which terms support the flow estimate and which downstream conclusions need more evidence.
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Choose your reading route
Route 1: Build the heat account · Chapters 1–3
Route 2: Read losses and storage · Chapters 4–5
Route 3: Test weak signals · Chapters 6–8
Route 4: Connect plants and area · Chapters 9–10
Route 5: Transfer and report · Chapters 11–12
Full chapter index · Independent worked case · Questions and practical checks
Chapter index
Build the heat account · Chapters 1–3
Define the heated stem segment and method
Write energy conservation with a declared sign convention
Convert sap heat transport to mass rate
Read losses and storage · Chapters 4–5
Understand axial and radial losses as different routes
Include warming and cooling storage when it matters
Test weak signals · Chapters 6–8
Treat low temperature differences and low flow carefully
Do not equate night with zero flow
Align thermal response and the reporting interval
Connect plants and area · Chapters 9–10
Connect section flow with plant water storage
Scale plants or branches with a defensible sampling design
Transfer and report · Chapters 11–12
Test the changed stem or changing environment
Report an auditable heat-to-water inference
CHAPTER 1 OF 12
1. Define the heated stem segment and method
A stem heat-balance system applies a known heat input to a bounded stem segment and accounts for energy leaving or remaining in that segment. The energy transported by sap is converted into a mass-flow estimate using the associated sap temperature change. The boundary is a stem section, not automatically the whole plant or plot.
This differs from inferring sap flux from a local temperature response using a thermal-dissipation calibration. It also differs from timing a heat pulse through tissue. Those methods share the use of heat but do not share every equation, parameter or spatial interpretation.
Draw the heated section with incoming and outgoing sap, outward heat loss, axial conduction above and below, and changing internal energy. The Dynamax manual presents the method’s physical accounting. The diagram should show several energy routes before a single number is labelled sap flow.
Whole-stem describes the section included in a particular measurement geometry. It does not mean every heat term is known perfectly or that one stem represents every branch. Keep apparatus geometry, the inferred section flow and the later whole-plant or field inference distinct.
CHAPTER 2 OF 12
2. Write energy conservation with a declared sign convention
For a simple teaching balance, let P be heater power, Qax net conductive heat leaving along the stem, Qrad outward heat loss, Qsap energy transported by sap, and dU/dt the rate of energy storage in the heated segment. Then P = Qax + Qrad + Qsap + dU/dt.
Rearranging gives Qsap = P − Qax − Qrad − dU/dt. All terms are powers in watts, with positive outward losses and positive warming storage under this convention. A cooling segment can have negative dU/dt and release previously stored energy.
Take a fictional 0.50 W input, 0.10 W net axial loss, 0.15 W radial loss and 0.05 W storage increase. The remaining sap-transport term is 0.20 W. Assigning all 0.50 W to sap would overstate transported energy by a factor of 2.5 in this exercise.
A balance equation does not independently observe its residual. If one loss is misestimated, the error can appear in Qsap. Report which terms were measured, estimated or neglected. A tidy equality achieved by defining the residual is not proof that every physical component is correct.
CHAPTER 3 OF 12
3. Convert sap heat transport to mass rate
In the simplified model, Qsap = mdot × cp × ΔT, where mdot is sap mass flow in kg/s, cp is specific heat capacity in J/(kg K), and ΔT is the relevant increase in sap temperature across the heated segment in kelvin. Thus mdot = Qsap/(cp ΔT) when the model and measurements support that calculation.
Use Qsap = 0.20 W from the previous fictional account, cp = 4,180 J/(kg K) as a water-like teaching value, and ΔT = 2 K. The mass rate is approximately 0.0000239 kg/s, or 0.0861 kg/h. Power divided by energy per kilogram gives kilograms per second.
That rate is not metres per second. Converting a mass rate to a velocity would require an appropriate density and conducting area under a separate interpretation. Do not add a sapwood area multiplier to a whole-section mass-flow output just because another sap-flow method reports flux density.
Nor is 0.0861 kg/h an accumulated daily use. Integrate rates over time using the actual observation intervals. A value held for one hour contributes 0.0861 kg; the same value observed briefly does not establish that it persisted through the whole hour.
CHAPTER 4 OF 12
4. Understand axial and radial losses as different routes
Axial conduction transports heat along the stem material; radial heat loss moves outward from the heated region. They respond to geometry, thermal properties, temperature gradients and the surroundings. Grouping them as one unexplained correction can hide which measurement or assumption needs review.
Suppose the true combined conductive and outward loss in a fictional interval is 0.25 W, but the calculation subtracts only 0.20 W. With storage and ΔT otherwise correct, Qsap is too high by 0.05 W. At cp = 4,180 and ΔT = 2 K, that produces about 0.0215 kg/h excess apparent flow.
If the actual sap-transport term is only 0.05 W, the same loss error can double it. The significance of a fixed absolute heat error therefore depends on the size of the residual being inferred. A percentage accuracy quoted for large flows should not be assumed unchanged near zero.
Contact, insulation and external temperature gradients can affect the measurement chain. Those are hypotheses to investigate with apparatus-specific evidence, not faults that can be diagnosed from one unusual value alone. A lower rate might be real, while a plausible rate can still be compensating for an incorrect loss estimate.
CHAPTER 5 OF 12
5. Include warming and cooling storage when it matters
The heated segment can store energy as its temperature changes. A simple lumped description uses dU/dt = Cseg × dTseg/dt, where Cseg is the segment’s effective heat capacity in J/K. This is a model of the bounded heated system, not merely air temperature near the stem.
For a fictional Cseg = 100 J/K, warming by 0.06 K over 60 seconds stores energy at 0.10 W. If that term is ignored, 0.10 W may be incorrectly assigned to sap transport. With ΔT = 2 K and the supplied cp, the excess is about 0.0431 kg/h.
During cooling, storage can have the opposite sign. A segment releasing 0.10 W can support outward and sap-related energy transfer in addition to current heater input. A steady-state equation used during such a transient can misallocate the released heat.
Grime, Morison and Simmonds specifically examined the storage term, and later research investigated thermal disequilibrium under low flow. The important lesson is not that every interval needs the same numerical correction. Test whether the steady-storage assumption is adequate for the interval, stem and decision being considered.
CHAPTER 6 OF 12
6. Treat low temperature differences and low flow carefully
The division by ΔT makes uncertainty in a small temperature difference consequential. A finite apparent Qsap divided by a nearly zero or unreliable ΔT can produce a very large calculated flow. That number is not automatically a real surge of water.
With Qsap = 0.02 W and cp = 4,180, ΔT = 0.2 K gives about 0.0861 kg/h, while ΔT = 0.1 K gives about 0.172 kg/h. A difference of just 0.1 K doubles the estimate in this constructed comparison. The calculation shows sensitivity, not a recommended operating range.
At the other end, low true sap transport can be a small residual among larger heat terms. The radial and storage uncertainties can then dominate even when ΔT is well resolved. Small denominator and small residual are separate difficulties; inspect both.
Do not automatically set every negative residual or extreme rate to zero and average the remaining positive values. That can create a biased series. Apply a justified quality procedure, preserve affected intervals and distinguish an unavailable estimate from a demonstrated zero flow.
CHAPTER 7 OF 12
7. Do not equate night with zero flow
Some parameter procedures use a zero-flow condition, but nighttime is a clock label rather than proof that sap movement has stopped. Plants can continue transpiring or replenishing internal water stores at night. The appropriate baseline needs evidence for the method and conditions.
Imagine a fictional night when 0.02 kg/h enters through the measured stem while leaf loss is 0.005 kg/h. The remaining 0.015 kg/h increases storage above the section under the simplified plant account. A positive stem rate is compatible with small canopy transpiration, not necessarily instrument noise.
If a procedure assumes zero flow and assigns actual sap-carried energy to radial loss, later calculations can inherit that baseline error. The direction and size depend on the procedure. Avoid changing a loss parameter merely until every night becomes zero; that would impose the conclusion being tested.
The existing sap-flow and thermal-dissipation guides explain nighttime movement and zero-flow references in their own contexts. Use them as connected reading, not as a reason to import a different instrument family’s calibration equation into the stem heat-balance model.
CHAPTER 8 OF 12
8. Align thermal response and the reporting interval
Heater response, stem warming, sensor readings and actual sap movement can occur on different time scales. A recorded temperature pattern can include the measurement system’s thermal history. A short lag relative to sunlight therefore does not uniquely describe a plant’s biological response.
For a fictional comparison, current sap transport rises quickly while the heated segment still warms. Neglecting storage can assign part of the transient warming to flow. Later, stored energy can be released as flow changes again. The total over a longer period may appear plausible while the short-time pattern is distorted.
Match the averaging of heat terms and ΔT to the defined calculation. A ratio of interval-average quantities is not generally equal to the average of instantaneous ratios. If Qsap and ΔT vary together, the order of calculation and aggregation can matter.
In a two-part teaching interval, equal durations have Qsap values of 0.1 and 0.3 W and ΔT values of 1 and 3 K. Each yields the same rate, so averaging first happens to work. Change only the second ΔT to 2 K and compare the two procedures. The exercise reveals why any averaging shortcut needs its conditions stated.
CHAPTER 9 OF 12
9. Connect section flow with plant water storage
For a simplified boundary above the measured section, let F be water entering through the stem, T canopy transpiration and ΔW change in stored plant water over an interval. With no other routes, ΔW = F − T. Thus T = F − ΔW.
A fictional stem supplies 0.8 kg during a morning interval while storage above it falls by 0.2 kg. Transpiration is 0.8 − (−0.2) = 1.0 kg. Leaves can lose more than current inflow by using stored water. Later, F may exceed T while stores refill.
This water-storage account differs from the heat storage inside the heated measurement segment. Both use the word storage, but one concerns energy in the instrument boundary and the other water in the plant boundary. Correcting one does not automatically correct the other.
Over a sufficiently complete interval, net plant water-storage change may be small, but it should not be declared zero merely because the interval is one day. The target and supporting evidence determine whether section transport can approximate transpiration at the required time scale.
CHAPTER 10 OF 12
10. Scale plants or branches with a defensible sampling design
One measured branch is not automatically a whole-tree measurement. A stem below the full crown may capture a different boundary from a branch serving one canopy sector. Identify where the sensor lies before expanding its rate.
For an invented stand, small plants occupy a represented group of 80 individuals with mean daily transport 0.5 kg, while 20 larger plants average 2.0 kg. The group total is 80 × 0.5 + 20 × 2.0 = 80 kg/day. Sampling equal numbers in each group and multiplying their unweighted mean by 100 would give 125 kg/day instead.
If the represented land area is 200 m², 80 kg water corresponds to approximately 0.4 mm depth using a water-density conversion. That is a scaled transport estimate under the group assumptions. Calling it total ecosystem evapotranspiration would omit soil evaporation and other relevant exchanges.
Uncertainty in group representation can exceed uncertainty in a precise individual rate. Record plant selection, size classes, positions and exclusions. A larger set of sensors on one unusually vigorous plant does not supply independent information about every unsampled plant in the stand.
CHAPTER 11 OF 12
11. Test the changed stem or changing environment
First change stem size while holding a fictional water mass rate constant. The segment’s thermal storage and conductive routes can change, so an apparatus treatment suitable for the original geometry may not transfer unchanged. Consult the method’s actual supported domain rather than extrapolating a classroom power balance into a new installation.
Next keep geometry but introduce a changing external temperature gradient. The measured thermal pattern may change without the same proportional change in sap flow. Independent tests should separate environmental heating from heat associated with the deliberate source.
Then change the target from hourly section flow to daily canopy transpiration. You need time integration and a plant water-storage argument, not merely a different unit label. Change again to field ET and add representative scaling and soil evaporation evidence.
The stable principle through these transfers is conservation with explicit boundaries. Loss parameters, thermal time response, plant storage and sample weights require renewed support. An explanation that names these changed links is more useful than one claiming that a whole-stem method removes all uncertainty.
CHAPTER 12 OF 12
12. Report an auditable heat-to-water inference
A useful report records the measured section, period, applied power, loss terms, storage treatment, ΔT definition and quality criteria. It distinguishes a direct electrical or temperature observation from the derived Qsap and derived mass rate.
Then describe any additional water-system interpretation: branch-to-tree scaling, plant-storage correction, population weighting or conversion to depth. Each should identify its own evidence. The final unit of millimetres can otherwise conceal several different models behind a familiar hydrological quantity.
When a period is outside measurement limits, preserve that status. A nearby weather-based estimate can support a separately labelled reconstruction, but it does not turn an unreliable thermal observation into a measured flow. Keep raw signals and the reason for exclusion available for review.
For independent recall, explain why heater input is not all sap energy, why warming storage can create apparent flow, why night does not establish zero flow and why section transport can differ from transpiration. These four distinctions connect the calculation with the plant rather than treating a sensor output as its own explanation.
Independent worked case and evidence checks
Independent case: Ethan receives a fictional interval with P = 0.60 W, Qax = 0.12 W, Qrad = 0.18 W and warming storage of 0.06 W. The supplied relevant sap temperature increase is 2.0 K and cp is 4,180 J/(kg K). All values describe the same section and interval.
The sap-energy residual is 0.60 − 0.12 − 0.18 − 0.06 = 0.24 W. The rate is 0.24/(4,180 × 2), approximately 0.0000287 kg/s, or 0.1033 kg/h. Neglecting warming storage would give 0.30 W and about 0.1292 kg/h, a 25% overestimate relative to the complete supplied account.
Change the next interval to cooling storage of −0.04 W while holding the other supplied heat terms and ΔT fixed. The residual becomes 0.60 − 0.12 − 0.18 + 0.04 = 0.34 W, giving about 0.1464 kg/h. This changed result follows the declared energy account; it is not evidence that cooling always causes a particular biological flow change.
Now consider a measurement error rather than a physical change. If the first interval’s ΔT is reported as 1.8 K instead of 2.0 K while Qsap remains 0.24 W, calculated flow is about 0.1148 kg/h. A 10% underestimate of the denominator produces about an 11.1% overestimate of the ratio. Ratio errors need not have symmetric percentages.
For time integration, suppose representative rates of 0.10, 0.20 and 0.05 kg/h apply for two, three and one hour respectively. Transport totals 0.20 + 0.60 + 0.05 = 0.85 kg over six hours. The duration-weighted mean is about 0.1417 kg/h. The unweighted mean of the three rates is about 0.1167 kg/h and gives the wrong total if multiplied by six hours.
A separately supplied plant-storage estimate says water above the section decreases by 0.15 kg over those six hours. With no other routes, transpiration is 0.85 − (−0.15) = 1.00 kg. If storage instead increases by 0.15 kg, transpiration is 0.70 kg. The same stem transport can support different leaf-loss totals when plant storage differs.
For a low-signal uncertainty test, let Qsap = 0.05 W have standard uncertainty 0.02 W and ΔT = 1.0 K have standard uncertainty 0.1 K. Ignoring cp uncertainty and dependence for the exercise, relative uncertainty in flow is approximately √(0.40² + 0.10²), or 41%. A precise-looking mass-rate display does not remove the uncertainty in the small residual.
This uncertainty result does not mean the instrument is universally unsuitable. It identifies a weak inference in the stated interval. A different interval with a much larger well-supported residual may have a smaller relative uncertainty. Report quality by the relevant conditions rather than applying one favourable percentage to every hour.
Finish with two diagrams: energy inside the heated segment and water above the measured section. Label thermal storage on the first and plant water storage on the second. Explain which observation would constrain each. Keeping the diagrams separate prevents the most common shortcut: treating one storage correction as though it established both the measurement and the plant’s transpiration.
An additional averaging check uses the changed pair from Chapter 8. With Qsap of 0.1 and 0.3 W, ΔT of 1 and 2 K, and equal durations, the mean of the calculated rates is (0.1 + 0.15)/(2cp) = 0.125/cp kg/s. Dividing mean power 0.2 W by mean temperature difference 1.5 K gives about 0.1333/cp kg/s instead. Averaging first overestimates this constructed mean by about 6.7%. The discrepancy is arithmetic aggregation, not a discovered biological effect.
For a water-boundary check, place the sensor above a low branch that is outside the measured section’s downstream boundary. Its transpiration is not supplied through that section. Expanding the observed rate to the whole plant without accounting for the branch would omit a pathway. Moving the sensor below the branch changes the represented system even if the same unit of kg/h appears on both graphs. A before-and-after comparison should retain the geometry rather than interpret every rate difference as changed plant demand.
A quality check also separates an unavailable interval from a true biological zero. Suppose ten observed hours total 1.2 kg transport and two hours are missing. Dividing by all twelve and calling the result the measured twelve-hour mean assumes zero for the missing hours. Dividing by ten gives the mean during observed hours only. A twelve-hour reconstruction needs additional evidence or a declared model. Neither convenient denominator can recover water movement during an outage by arithmetic alone.
Finally ask whether validation covers the intended extremes. A comparison that agrees at moderate flow can still fail when the thermal residual is small, the temperature difference is near its limit, the surroundings change rapidly or the measurement section grows. Report those condition classes and any exclusions. An independent reference has its own boundary and uncertainty, so disagreement should initiate a structured comparison rather than an automatic declaration that one sensor is the truth and the other is wrong.
Retain the sequence from observation to interpretation: electrical power and temperatures, the complete heat account, mass flow through the specified section, and any additional plant or field inference. This sequence lets another reader identify which new observation could change a conclusion without discarding every useful part of the record.
Worked comparison
| Fictional heat term | Warming interval | Cooling interval |
|---|---|---|
| Heater input | 0.60 W | 0.60 W |
| Axial loss | 0.12 W | 0.12 W |
| Radial loss | 0.18 W | 0.18 W |
| Storage rate | +0.06 W | −0.04 W |
| Sap-energy residual | 0.24 W | 0.34 W |
Questions and practical checks
Does all heater power measure sap transport?
No. Conductive losses, outward losses and changing internal energy must be accounted for. The sap-carried component is the supported residual of the heat account.
Is whole-stem flow the same as sap flux density?
Not automatically. A whole-section mass rate and a local area-based flux density have different meanings and scaling steps. Read the output definition before multiplying by an area.
Why can warming create apparent flow?
If energy stored in warming tissue is omitted, it can be assigned incorrectly to sap transport. The size and sign depend on the actual transient account.
Can I assume zero flow at night?
Not solely from time of day. Nighttime transpiration and water-storage replenishment can support real movement. Baseline procedures need appropriate independent evidence.
When does section flow equal transpiration?
Only under a compatible plant boundary and adequate treatment of storage and other routes. Over a particular interval, changing plant water stores can make the two quantities differ.
Continue with the connected subjects
Distinguish sap-flow methods and plant quantities
Sap flow, sap flux density and nighttime water movement
Thermal-dissipation probes: a different heat-to-flow method
Dendrometer traces and the interpretation of plant water status
Connect plant transport with wider water loss
Eddy-covariance ET and the wider surface footprint
Reference demand versus actual crop water use
Budget closure and uncertain residual components
Close the soil–plant account carefully
Microlysimeters: isolated soil cores, hydraulic disconnection and exposure age examines the soil-evaporation component alongside a plant account.
Ventilated evaporation chambers: vapour mass balance and boundary disturbance provides another soil-flux route. Neither a chamber reading nor a stem reading automatically represents the full field; align time, area and storage before combining them.
Sources and scope
Dynamax Dynagage manual: stem heat-balance theory and measurement terms
Grime, Morison and Simmonds: including heat storage in stem heat-balance measurements
Original comparison of constant and variable heat inputs in a heat-balance sap-flow gauge
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.