Estimation of Spatial Degrees of Freedom of a Climate Field

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Abstract
This paper analyzes four methods for estimating the spatial degrees of freedom (dof) of a climate field: the χ2 method, the Z method, the S method, and the B method. The results show that the B method provides the most accurate estimate of the dof. The χ2 method, S method, and Z method yield underestimates when the number of realizations of the field is not sufficiently large or the field’s mean and variance vary with respect to spatial location. The dof of the monthly surface temperature field is studied numerically. The B method shows that the dof of the Northern Hemisphere (NH) has an obvious annual cycle, which is around 60 in the winter months and 90 in the summer months. The dof for the Southern Hemisphere (SH) varies between 35 and 50, with large values during its winter months and small ones during its summer months. The dof of the global temperature field demonstrates a similar annual cycle to that of the NH. The dof estimated from the observational data is smaller than that from the GFDL GCM model output of the surface air temperature. In addition, the model output for the SH shows the opposite phase of the seasonal cycle of the dof: large dof in summer and small ones in winter.

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