Variability of Atmospheric Forecast Error Sensitivity 1996-2000

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Introduction: The Navy Operational Global Atmospheric Prediction System (NOGAPS) operational 2-day Northern Hemisphere extratropical forecast error sensitivity to changes in the initial conditions has been calculated by NRL on a daily basis since October 1996.¹ This 4-year archive of daily adjoint sensitivity calculations provides an opportunity to diagnose the locations where, on average, initial-condition errors have had the largest impact on the forecast errors. The fortuitous occurrence of large variations in the El Niño cycle during this period allows us to examine interannual variations as well as interseasonal variations in predictability.

We use the adjoint of the NOGAPS forecast model to diagnose the sensitivity of the forecast error to changes in the initial conditions in a mathematically rigorous way. The adjoint integration that produces the forecast sensitivity does not contain moist physics, although it does contain a simplified representation of boundary layer physics and vertical diffusion.² The sensitivity calculation is based on the dry total energy of the forecast error between 30°N to 90°N and from the surface to approximately 150 hPa. The operational data assimilation system used throughout this period has been a multivariate optimum interpolation scheme. The same version of the forecast and adjoint model was used for the entire 4-year period.

Interannual Variability: We use time-longitude diagrams to concisely illustrate zonal and temporal variations in forecast error and sensitivity. Because the fastest growing perturbations are dominated by potential energy at initial time and kinetic energy at final time, forecast errors are shown in terms of the wind field, while sensitivity is shown in terms of the temperature field. The left-hand panel in Fig. 6 is a time-longitude diagram of the monthlymean vertically averaged root-mean-square (RMS) wind errors, latitudinally averaged from 30°N to 60°N. A strong seasonal cycle is apparent as well as significant zonal variations during winter. In the wintertime, local forecast error maxima correspond roughly to the longitudinal locations of the North Pacific and North Atlantic storm tracks. Note that winter 1997/98 has smaller peak error values over the North Pacific than the other winters.

The right-hand panel in Fig. 6 is a time-longitude diagram of the vertically averaged RMS temperature fields corresponding to the forecast error sensitivity. In general, the interseasonal and interannual variability of the sensitivity is similar to that of the forecast error, although the sensitivity maxima occur upstream (westward) of the forecast error maxima. This is consistent with the fact that, on average, forecast errors propagate eastward with time. The relatively low values of sensitivity during the El Niño winter of 1997/98 over the North Pacific is evidence that this particular winter was intrinsically more predictable than the other winters. This result is consistent with the fact that the Eady index of baroclinic instability, which is a measure of the potential energy available for conversion to perturbation energy, was also lower during this winter relative to the other winters.

Key Analysis Errors: The adjoint sensitivity of the forecast errors also allows us to diagnose "key" analysis errors (i.e., the components of the analysis errors that grow rapidly and dominate the forecast errors). Figure 7 shows vertical cross sections corresponding to the forecast error and sensitivity fields shown in Fig. 6 for a typical winter month (January 1999). The forecast errors tend to be largest near the jet stream in the upper troposphere, but are most sensitive to upstream changes in the middle-lower troposphere. These results are consistent with our previous findings, which show that rapidly growing perturbations tend to originate in the lower atmosphere, but propagate upward and eastward rapidly as they evolve. These results highlight the necessity of accurate analyses of the lower-tropospheric atmo- spheric structure over the central North Pacific for accurate forecasts over the eastern North Pacific and North America.

Summary: The results presented here highlight the prominence of wintertime forecast errors and initial condition sensitivity over the North Pacific, a region of vigorous baroclinic activity and relatively few observations. These results confirm the importance of accurate analyses in the middle to lower troposphere. The 4-year time series also provides evidence of significant interannual variability in predictability, indicating that the El Niño winter of 1997/98 appears to have been an anomalously predictable period.

Acknowledgments: Computer resources were provided by the DOD High Performance Computing Program at the NAVO MSRC.

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