Math/Stat Operation
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MPO Science behind doing it
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Average (x)
- over time (q t)
- over distance (qx)
- over area (qxy) or volume (qxyz) or mass (qxyp)
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Linear effects (terms in
governing equations)
- dT/dt = Q type conservation laws for masses of matter
- divergence theorem ∫ ∫ (∇• F)
dA
=
∮Fn
- Climate heat budget over ocean + atm
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Weighted average
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get mass or area
average from
irregular-grid data (p or lat)
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Deviation from average (anomaly
or perturbation)
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"anomalies" may obey linearized
equations about "base state" (Taylor expansion)
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Average of nonlinearly
transformed
variable
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Nonlinear physics: OLR = σT4,
|U|
=
√u²+v², WD =
atan(u/v), Flux = (wq) |
Average of squared value
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just characterizing
variability as positive definite? sometimes Energy
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Variance (square - mean2) ≡
σ2
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standard deviation σ has units
of
the quantity (variance: units are squared)
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| Average of cube, 4th power, ...
⇒ "moments" |
just statistics? but
distributions can imply processes (future lecture)
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