Ensemble average: Difference between revisions

Latest revision as of 16:54, 25 April 2012

ensemble average

The value of a meteorological variable found by averaging over many independent descriptions or realizations of that variable.

While this type of average often forms the basis of theories and simulations (numerical or physical models) for turbulence, it is usually impossible to compute in real life because we cannot control the atmosphere in order to reproduce multiple ensemble members. In real life, an ergodic hypothesis is often used, where time or space averages are assumed to be reasonable approximations to ensemble averages.
In numerical weather prediction, the average found by averaging over many different forecasts for the same domain and time period, but starting from slightly different initial conditions or using different numerical models or parameterizations.

This ensemble average is usually more accurate than any single model run because it partially counteracts the sensitive dependence to initial conditions associated with the nonlinear equations that govern the atmosphere.

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-<div class="definition"><div class="short_definition">An average taken over many different flow realizations that have the same [[initial condition|initial]]  and [[boundary conditions]].</div><br/> <div class="paragraph">In the limit of the [[sample]] size going to infinity, the ensemble average approaches the [[ensemble mean|ensemble  mean]] and may be a function of both time and position. When the flow is steady and homogeneous,  the ensemble, space, and time means are equal. <br/>''See'' [[ergodicity]].</div><br/> </div><div class="reference">Hinze, J. O. 1975. Turbulence. 2d ed., McGraw&ndash;Hill, . p. 5. </div><br/>
+#<div class="definition"><div class="short_definition">The value of a meteorological [[variable]] found by averaging over many independent  descriptions or realizations of that variable.</div><br/> <div class="paragraph">While this type of average often forms the basis of theories and simulations (numerical or  physical models) for [[turbulence]], it is usually impossible to compute in real life because we cannot  control the [[atmosphere]] in order to reproduce multiple ensemble members. In real life, an [[ergodic]]  hypothesis is often used, where time or space averages are assumed to be reasonable approximations  to ensemble averages.</div><br/> </div>
+#<div class="definition"><div class="short_definition">In [[numerical weather prediction]], the average found by averaging over many different  forecasts for the same domain and time period, but starting from slightly different [[initial conditions]]  or using different numerical models or parameterizations.</div><br/> <div class="paragraph">This ensemble average is usually more accurate than any single [[model]] run because it partially  counteracts the sensitive dependence to initial conditions associated with the [[nonlinear]] equations  that govern the [[atmosphere]].</div><br/> </div>
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