Procedure

Penland and Sardeshmukh (1995) provide strong evidence that Tropical Indo-Pacific sea surface temperature anomalies (SSTAs) are governed by stable linear dynamics forced with spatially coherent white noise. Indeed, SSTA forecasts using their empirical technique do quite well. Their success suggests that a similar application to the low-frequency atmosphere could prove useful.

Our experiment uses 30 years (1969-70 to 1998-99) of wintertime streamfunction and diabatic heating to construct a linear inverse model of the atmosphere's low-frequency circulation. The streamfunction is measured at 750 and 250 hPa and is restricted to the Northern Hemisphere. The diabatic heating field is integrated from surface to tropopause and is taken from 30S-30N. Both fields are dynamically consistent, that is the large-scale mass and vorticity budgets are satisfied, as determined from the generalized baroclinic chi problem (Sardeshmukh 1993). Also, each variable has the first 3 harmonics of its seasonal cycle removed, is filtered with a 7 day running mean, and is projected onto its leading EOFs.

We have used a jack-knifing procedure to estimate a linear dynamical operator in order to test the validity of our model. In this procedure we sub-sample our data record by removing one of the available years, construct the dynamical operator from the remaining data, and then generate forecasts in the independent year.

Comparison with MRF

So how well does the linear inverse model do? The local anomaly correlations of linear inverse model forecasts compare quite favorably to MRF ensemble mean forecasts at week 2 for DJF 1996-97 and 1997-98. Additionally, the spatial correlation of linear inverse model forecasts is at least as good as the MRF in these two years.

Spatial correlations for all winters

RMS Error for all winters

The root-mean-squared error of linear inverse model forecasts from all years is also available for streamfunction (week 2, week 3) and tropical heating (week 2, week 3).

References

Penland, C., and P. D. Sardeshmukh 1995: The optimal growth of sea surface temperature anomalies. J. Climate, 8, 1999-2023.

Sardeshmukh, P.D. 1993: The baroclinic chi problem and its application to the diagnosis of atmospheric heating rates. J. Atmos. Sci., 50, 1099-1112.