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Model output statistics

Model output statistics 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 Model output statistics rather than just read about it. In short: In weather forecasting, model output statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities (such as two-meter-above-ground-level air temperature, horizontal visibility, and wind direction, speed and gusts), are related statistically to one or more predictors. The predictors are typically forecasts from a numerical weather prediction (NWP) model, climatic data…

Model output statistics — main illustration
Model output statistics — illustration

Key takeaways

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

Reference excerpt

In weather forecasting, model output statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities (such as two-meter-above-ground-level air temperature, horizontal visibility, and wind direction, speed and gusts), are related statistically to one or more predictors. The predictors are typically forecasts from a numerical weather prediction (NWP) model, climatic data, and, if applicable, recent surface observations. Thus, output from NWP models can be transformed by the MOS technique into sensible weather parameters that are familiar to a layperson.

Background Output directly from the NWP model's lowest layer(s) generally is not used by forecasters because the actual physical processes that occur within the Earth's boundary layer are crudely approximated in the model (i.e., physical parameterizations) along with its relatively coarse horizontal resolution. Because of this lack of fidelity and its imperfect initial state, forecasts of near-surface quantities obtained directly from the model are subject to systematic (bias) and random model errors, which tend to grow with time. In the development of MOS equations, past observations and archived NWP model forecast fields are used with a screening regression to determine the 'best' predictors and their coefficients for a particular predictand and forecast time. By using archived model forecast output along with verifying surface observations, the resulting equations implicitly take into account physical effects and processes which the underlying numerical weather prediction model cannot explicitly resolve, resulting in much better forecasts of sensible weather quantities. In addition to correcting systematic errors, MOS can produce reliable probabilities of weather events from a single model run. In contrast, despite the enormous amount of computing resources devoted to generating them, ensemble model forecasts' relative frequency of events—often used as a proxy for probability—do not exhibit useful reliability. Thus, ensemble NWP model output also requires additional post-processing in order to obtain reliable probabilistic forecasts, using nonhomogeneous Gaussian regression or other methods.

History

United States MOS was conceived and planning for its use began within the U.S. National Weather Service’s (NWS’s) Techniques Development Laboratory (TDL) in 1965 and forecasts first issued from it in 1968. Since then, TDL, now the Meteorological Development Laboratory (MDL), continued to create, refine and update MOS equation sets as additional NWP models were developed and made operational at the National Meteorological Center (NMC) and then the Environmental Modeling Center or EMC. Given its multi-decadal history within the U.S. NWS and its continuous improvement and superior skill over direct NWP model output, MOS guidance is still one of the most valuable forecast tools used by forecasters within the agency.

United States forecast guidance There are eight sets of MOS guidance available from MDL, operational and experimental, covering the span of time from the next hour out to ten days for the United States and most of its territories.

Nested Grid Model MOS was discontinued in 2009. Initially, MOS guidance was developed for airports and other fixed locales where METARs (or similar reports) were routinely issued. Therefore, MOS guidance was and continues to be provided in an alphanumeric 'bulletin' format for these locations. Here is an example of a short-range MOS forecast for Clinton-Sherman Airport, Oklahoma (KCSM) based on the EMC's Global Forecast System model output.

With the availability of private- and government-owned weather mesonets, new objective analysis and interpolation techniques, gridded GFS MOS guidance became available in 2006.

Advantages and disadvantages The advantage of MOS forecast guidance as developed in the United States allowed for

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Model output statistics

Start with the simplest possible case. Write down what Model output statistics 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 Model output statistics 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 Model output statistics 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 Model output statistics

In research
Model output statistics 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 Model output statistics 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
Model output statistics is common in secondary-school and first-year university syllabi. It links to neighbouring topics Climate and weather statistics, Weather forecasting, so understanding it makes those chapters shorter.
In everyday life
Look for Model output statistics 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 Model output statistics in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Model output statistics means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Model output statistics out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Model output statistics in simple terms?

In weather forecasting, model output statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities (such as two-meter-above-ground-level air temperature, horizontal visibility, and wind direction, speed and gusts), are related statistically to one or…

Why does Model output statistics 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 Model output statistics?

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 Model output statistics.

Tags

  • Climate and weather statistics
  • Weather forecasting

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