mathematics

Goff–Gratch equation

Goff–Gratch equation is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Goff–Gratch equation rather than just read about it. In short: The Goff–Gratch equation is one (arguably the first reliable in history) amongst many experimental correlations proposed to estimate the saturation water vapor pressure at a given temperature. Another similar equation based on more recent data is the Arden Buck equation.

Key takeaways

Goff–Gratch equation belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Goff–Gratch equation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Goff–Gratch equation from memory before moving on to harder problems.

Reference excerpt

The Goff–Gratch equation is one (arguably the first reliable in history) amongst many experimental correlations proposed to estimate the saturation water vapor pressure at a given temperature. Another similar equation based on more recent data is the Arden Buck equation.

Historical note This equation is named after the authors of the original scientific article who described how to calculate the saturation water vapor pressure above a flat free water surface as a function of temperature (Goff and Gratch, 1946). According to the Smithsonian Meteorological Tables, the formula was adopted in Resolution 164 of the Twelfth Conference of Directors of the International Meteorological Organization (Washington, 1947). Goff (1957) later revised his formula, and the latter was recommended for use by the World Meteorological Organization in 1988, with further corrections in 2000. The Guide to Meteorological Instruments and Methods of Observation a.k.a. CIMO-Guide (WMO-No. 8) contains the much simpler Magnus formula (p.197). For temperatures below ‑45 °C for liquid water or ‑65 °C for ice, the CIMO-Guide recommends formulations from Sonntag (1990,1994).

Experimental correlation The original Goff–Gratch (1945) experimental correlation reads as follows:

where:

log refers to the logarithm in base 10 e* is the saturation water vapor pressure (hPa) T is the absolute air temperature in kelvins Tst is the steam-point (i.e. boiling point at 1 atm.) temperature (373.15 K) e*st is e* at the steam-point pressure (1 atm = 1013.25 hPa) Similarly, the correlation for the saturation water vapor pressure over ice is:

where:

log stands for the logarithm in base 10 e*i is the saturation water vapor pressure over ice (hPa) T is the air temperature (K) T0 is the ice-point (triple point) temperature (273.16 K) e*i0 is e* at the ice-point pressure (6.1173 hPa)

See also Vapour pressure of water Antoine equation Arden Buck equation Tetens equation Lee–Kesler method

References

External links Vömel, Holger (2016). "Saturation vapor pressure formulations". Boulder CO: Earth Observing Laboratory, National Center for Atmospheric Research. Murphy, D.M.; Koop, T. (2005). "Review of the vapour pressures of ice and supercooled water for atmospheric applications". Quarterly Journal of the Royal Meteorological Society. 131 (608): 1539–65. Bibcode:2005QJRMS.131.1539M. doi:10.1256/qj.04.94. S2CID 122365938.

Worked examples

Example 1 — a first encounter with Goff–Gratch equation

Start with the simplest possible case. Write down what Goff–Gratch equation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Goff–Gratch equation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Goff–Gratch equation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Goff–Gratch equation

In research: Goff–Gratch equation appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Goff–Gratch equation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Goff–Gratch equation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Atmospheric thermodynamics, so understanding it makes those chapters shorter.
In everyday life: Look for Goff–Gratch equation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Goff–Gratch equation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Goff–Gratch equation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Goff–Gratch equation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Goff–Gratch equation in simple terms?

Why does Goff–Gratch equation matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Goff–Gratch equation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Goff–Gratch equation.