The experience so far in FASTEX has been that the two methods tend to give similar areas of sensitivity, that there is some similarity with the other adjoint methods, but also there is some sensitivity in the shape of the sensitivity to the "final" conditions (i.e., pair 1 and 2 may give rise to different shapes of sensitivity maxima in the same general area).

In cases of strong sensitivity, there is very good agreement with the SVD method.

Questions/Comments? Please contact:

- Zhaoxia Pu (wd20zp@sun1.wwb.noaa.gov)

Eugenia Kalnay (wd23ek@sun1.wwb.noaa.gov)

Tim Marchok (wd20tm@sun1.wwb.noaa.gov)

The SVD of ensemble forecasts (Toth et al, this volume), is very efficient since it does not require additional model integrations. In addition, we plan to test at NCEP another use of the ensemble, based on the backward integration of the linear tangent model or the adjoint, to determine 2-3 days in advance areas that should be targeted for special observations. The procedure is: 1) the ensemble system (Toth et al 1996, Kalnay and Toth 1996) alerts the forecasters about a crucial but uncertain storm development in the next few days. The area of interest can be defined by a smooth mask centered in this area with an appropriate radius (J. Purser, pers. comm). 2) extreme solutions from the ensemble, indicating the range of uncertainty at 2-3 days lead time, can be subtracted from each other, and filtered with the mask. 3) this difference can be used as initial condition for a backward integration in two possible different ways ---- the adjoint model based on the variational method (Rabier et al. 1996; Pu et al 1996, Langland and Rohaly, 1996) and/or a quasi-inverse linear method based on the backward (in time) integration of the tangent linear model ( Pu et al. 1996) ---- to trace back in time the differences to their region of origin.

As a preliminary study, we performed an experiment to test the ability of both the quasi-inverse and adjoint methods to trace forecast differences to the initial time differences using the NCEP global spectral model and its adjoint, with resolution T62 L28. We took a 24-hours forecast difference (at T=24h) between two ensemble members, chose an area with large forecast differences centered at (150W, 45N) and applied a mask with radius 1500km. Then we integrated backwards in time starting from this local difference, using both the adjoint model and the quasi-inverse tangent linear model, to trace back the original difference (T=0h). The results show some interesting conclusions:

1) The quasi-inverse linear method is able to trace the 24-hours forecast differences back to the "original error" at initial time: when we take the resulting initial difference as initial condition and integrate the tangent linear model forward, the 24 hours forecast differences are recovered quite accurately.

2) In order to reduce the possible impact of imbalances due to the localization of the perturbation, we repeated the experiment taking only vorticity differences at the final time (T=24h) and traced it back to the initial time. The results show that not only almost all the initial errors for wind field are recovered (compared with the experiment including the difference of all the variables), but also most of the error centers for temperature are also marked.

3) The adjoint method is based on variational theory: it determines the pattern that minimizes the error energy at the final time. The pattern obtained is a "gradient" or "sensitivity pattern", and can be used to point out the initial error which caused large forecast error. A comparison of the gradient pattern obtained from the adjoint integration with that obtained from a quasi-inverse method, indicates that they are similar and point out to the same areas, but that there adjoint patterns are further away from thermal balance.

This preliminary experiment proves that it is possible to use both methods for marking the initial error areas where observations are most needed. During FASTEX we plan to compare with the results of the SVD method.

Fehlmann, R. and Davies, 1996: Forecast failure and PV Retrodiction, Preprints of 11th Conference on Numerical Weather Prediction, August 19-23, 1996, Norfolk, Virginia, pp 436-438.

Kalnay, E., and Z. Toth, 1996: Ensemble prediction at NCEP . Preprints of 11th Conference on Numerical Weather Prediction, August 19-23, 1996, Norfolk, Virginia, pp19-j20.

Kalnay, E. , Z. Toth, Z.-X. Pu and S. Lord, 1996: Targeting weather observations to locations where they are most needed. Research Activities in Atmospheric and Oceanic Modelling. CAS/JSAC Working Group on Numerical Experimentation, WMO report No. 23. February 1996.

Langland, R. And G. Rohaly, 1996: Analysis error and adjoint sensitivity in prediction of a N.Atlantic frontal cyclone. Preprints of 11th Conference on Numerical Weather Prediction, August 19-23, 1996, Norfolk, Virginia, pp 150-155.

Lord, S. J., 1996: The impact on synoptic-scale forecasts over the United States of dropwindsonde observations taken in the northeast pacific. Preprints of 11th Conference on Numerical Weather Prediction, August 19-23, 1996, Norfolk, Virginia. P 70-71.

Pu, Z.-X., E. Kalnay, J. C. Derber, J.Sela, 1996: Using forecast sensitivity patterns to improve future forecast skill. Q. J. Roy Meteor. Soc (in press)

Pu, Z.-X., E. Kalnay, J. Sela, 1996: Sensitivity of forecast error to initial condition with a quasi-inverse linear method. Mon. Wea. Rev. (accepted)

Rabier, F., E. Klinker, P. Courtier and A. Hollingsworth, 1996: Sensitivity of forecast errors to initial conditions. Q. J. Roy Meteorol. Soc., 122. 121-150.