Tetens equation¶

The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12503
Domain group: Natural Sciences
Origin domain: Geology & Earth Sciences
Subdomains: Atmospheric Science, Meteorology → Geology & Earth Sciences

Core Idea¶

Tetens equation is treated here as the recurring natural science, engineering, and health identity summarized by this source-grounded definition: The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice.

The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. It is named after its creator, O. Tetens who was an early German meteorologist.

He published his equation in 1930, and while the publication itself is rather obscure, the equation is widely known among meteorologists and climatologists because of its ease of use and relative accuracy at temperatures within the normal ranges of natural weather conditions. The equation is structurally identical to the August-Roche-Magnus equation, but the coefficients differ. where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa).

For Tetens equation, the abstraction is narrower than the article's general subject matter: a positive case must preserve The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in natural science, engineering, and health, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C.
Constitutive relation — P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right).
Operating condition — where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa).
Recognition evidence — According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C.".
Admissible variation — P = 0.61078 \exp\left(\frac{21.875 T}{T + 265.5}\right).
Characteristic consequence — Murray (1967) provides Tetens' equation for temperatures below 0 °C.
Failure boundary — The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice.

What It Is Not¶

Not the whole field of natural science, engineering, and health. The node requires the specific identity stated by The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice.
Not an over-broad reading. Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C.
Not an over-broad reading. P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right).
Not an over-broad reading. where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa).
Not automatically Saturation Vapor Pressure. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Tetens equation applies literally inside natural science, engineering, and health wherever the source-defined carrier and relation can be established. Its documented habitats include:

Formula. Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C.
Formula. P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right).
Formula. where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa).
Formula. According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C.".
Formula. P = 0.61078 \exp\left(\frac{21.875 T}{T + 265.5}\right).
Formula. Murray (1967) provides Tetens' equation for temperatures below 0 °C.

Outside natural science, engineering, and health, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Measurement or should be marked as analogy.

Clarity¶

A clear use of Tetens equation names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. The strongest recognition evidence in the frozen account is: According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C.". A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Tetens equation compresses multiple natural science, engineering, and health details into a stable diagnostic relation. The source shows both the central mechanism—p = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right).—and the practical consequence—murray (1967) provides Tetens' equation for temperatures below 0 °C. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the natural science, engineering, and health entities to which the claim applies.
State the relation. Use the source-grounded identity: The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice.
Check operation and conditions. where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa).
Demand recognition evidence. According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C.".
Test variation. Change an implementation or setting while preserving p = 0.61078 \exp\left(\frac{21.875 T}{T + 265.5}\right).
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Measurement.

Knowledge Transfer¶

Within the home domain. Knowledge about Tetens equation transfers literally when a new case preserves the same carrier type, relation, and recognition test. Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right).

Beyond the home domain. No canonical parent is asserted for Tetens equation. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice; recognition evidence → According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C."

Applied / In Practice¶

P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right). The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → Formula; invariant → The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice; boundary → the case exits the class when monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C

Structural Tensions¶

T1 — Stable identity versus admissible variation. Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right). The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa). The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C.". The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Tetens equation literally, co-instantiate Measurement, or only resemble it?

T6 — Autonomy versus reduction. P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right). The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Tetens equation distinguish that the broader parent Measurement leaves together?

Terminal boundary synthesis. For Tetens equation, the terminal identity test begins with the definition The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice.. A reviewer must then establish the carrier and operation described by Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. and P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right).. Recognition is constrained by where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa)., while admissible variation is limited by According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C.". and the collapse boundary P = 0.61078 \exp\left(\frac{21.875 T}{T + 265.5}\right).. The source-domain setting in natural science, engineering, and health matters because Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. and P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right). specify where those roles have literal occupants. The strongest negative controls are The node requires the specific identity stated by The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. and Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C.; a case satisfying either exclusion should not be rescued merely because its label or examples look familiar.

Terminal adjudication sequence. First, bind the claimed instance to a concrete carrier and state the criterion by which The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. is recognized. Second, vary implementation, scale, notation, and example while holding P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right). fixed; persistence supports one identity rather than several topic fragments. Third, remove where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa). or trigger P = 0.61078 \exp\left(\frac{21.875 T}{T + 265.5}\right). and verify that the classification fails. Fourth, compare the result with the two negative controls instead of relying on name similarity. Fifth, check scope against Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. and record any qualification supplied by natural science, engineering, and health. Finally, audit the graph claim. The approved unparented placement prevents a weak lexical resemblance from becoming a false ontological claim; a later edge must preserve every constitutive role stated here. This sequence makes the entry rejectable, keeps analogy separate from literal transfer, and exposes which fact would require revision.

Structural–Framed Character¶

Tetens equation is structural-leaning. Its structural side is the repeatable organization summarized by The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. Its framed side is the natural science, engineering, and health vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa). Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Measurement. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. The stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right). It further constrains recognition and variation through: where temperature is in degrees Celsius (°C) and saturation vapor pressure is in kilopascals (kPa). According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C.".

What is domain-bound. natural science, engineering, and health supplies the operative entities, technical vocabulary, warrants, and exceptions that make Tetens equation literal. Its documented scope includes the condition that Monteith and Unsworth (2008) provide Tetens' formula for temperatures above 0 °C. Another bounded application condition is that P = 0.61078 \exp\left(\frac{17.27 T}{T + 237.3}\right). These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—P = 0.61078 \exp\left(\frac{21.875 T}{T + 265.5}\right).—and future graph densification may discover a defensible relation only if it preserves that boundary.

This entry is a kind of Mathematical Relation.

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Tetens equation. The reviewed identity is: The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. The accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Relationships to Other Abstractions¶

Current abstraction Tetens equation Domain-specific

Parents (1) — more general patterns this builds on

Tetens equation is a kind of Mathematical Relation Domain-specific

Tetens equation satisfies the defining boundary of Mathematical Relation: A mathematical relation is a formally specified subset of a Cartesian product, predicate over typed objects, equivalence or order structure, or equation constraining quantities, with arity, domain, parameters, and satisfaction conditions declared.

Hierarchy path (1) — routes to 1 parentless root

Tetens equation → Mathematical Relation

Neighborhood in Abstraction Space¶

Tetens equation sits in a sparse region of the domain-specific corpus (84^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Condensed Matter & Physical Chemistry Models (26 abstractions)

Nearest neighbors

Root-mean-square speed — 0.83
Single Vegetative Obstruction Model — 0.81
Joback method — 0.81
Spectral line ratios — 0.81
Homes's law — 0.81

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Measurement. The parent omits the specialist differentia. Tell: Can the case establish The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice?
Saturation Vapor Pressure. The equilibrium partial pressure of a substance’s vapor over a specified liquid or solid phase at a specified temperature and thermodynamic condition. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Van der Waals Equation. A cubic equilibrium equation of state that corrects the ideal-gas law for finite molecular exclusion and mean-field attraction, producing real-fluid nonideality and a liquid-gas critical point. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Degree of frost. A historical nonstandard temperature expression giving how many Celsius or Fahrenheit degrees the air lies below water’s freezing point. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Tetens equation remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside natural science, engineering, and health lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Measurement?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Tetens_equation (revision 1295512549).
Preserved source candidate: https://books.google.ch/books?id=EhLtk6hkLogC&pg=PA13
Preserved source candidate: https://doi.org/10.1175/1520-0450(1967)006%3C0203:OTCOSV%3E2.0.CO;2

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.