A Four-Dimensional Analysis Exactly Satisfying Equations Of Motion

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  • 1 Atmospheric and Environmental Research, Inc., Cambridge, MA 02139
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Abstract

For a discretized deterministic model of the atmosphere, a single point in the model's phase space defines a complete trajectory. It is possible to choose a point which minimizes the differences between the model trajectory starting at the chosen point and all data observed during an analysis period (−Tt≤0). In this way data and model dynamics are combined to yield a four-dimensional analysis exactly satisfying the model equations. This analysis is the solution of the model's equations of motion defined by the optimal initial conditions chosen at t=−T. Therefore, provided T is larger than the adjustment time of the model, there should be no need for any initialization at the start of the forecast at t = 0.

This report describes some preliminary experiments which use highly simplified filtered and primitive equation models of an atmosphere with f-plane geometry. These simple models are used because of the substantial computational resources required by the minimization method. It is demonstrated that the method is stable in an assimilation cycle, is able to maintain an accurate estimate of the motion field from temperature observations alone and yields a small analysis error. Unfortunately, forecasts made from the four-dimensional analyses exhibit rapid error growth initially; as a result these forecasts are better than ordinary forecasts only for the first 24 h. Beyond 24 h both types of forecasts have the same skill.

Abstract

For a discretized deterministic model of the atmosphere, a single point in the model's phase space defines a complete trajectory. It is possible to choose a point which minimizes the differences between the model trajectory starting at the chosen point and all data observed during an analysis period (−Tt≤0). In this way data and model dynamics are combined to yield a four-dimensional analysis exactly satisfying the model equations. This analysis is the solution of the model's equations of motion defined by the optimal initial conditions chosen at t=−T. Therefore, provided T is larger than the adjustment time of the model, there should be no need for any initialization at the start of the forecast at t = 0.

This report describes some preliminary experiments which use highly simplified filtered and primitive equation models of an atmosphere with f-plane geometry. These simple models are used because of the substantial computational resources required by the minimization method. It is demonstrated that the method is stable in an assimilation cycle, is able to maintain an accurate estimate of the motion field from temperature observations alone and yields a small analysis error. Unfortunately, forecasts made from the four-dimensional analyses exhibit rapid error growth initially; as a result these forecasts are better than ordinary forecasts only for the first 24 h. Beyond 24 h both types of forecasts have the same skill.

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