Back-trajectories are an easy tool for assessing possible source origin of measured tracer species. In an important study on the Chernobyl accident Persson et al. (1987) used this approach to estimate the amount released from the rampaged nuclear power station.

However, back-trajectories suffer from oversimplifications of the transport-diffusion process, by entirely omit diffusion. Moreover, the nature of trajectories are that a single air parcel is followed implying a very short response at the receptor point. By utilizing adjoint equations in a 3D transport-diffusion model several advantages could be achieved, all transport mechanisms are included and the response at receptor points could more properly mimic the sampled time-period of the measurements.

Using adjoint equations for environmental problems was first described by Marchuk (1986, 1994) where some requirements on air quality where the basis for finding the most optimal emission reductions.

The adjoint technique has thereafter become an important basis for data assimilation procedures now dominating in numerical weather prediction systems (Talagrand and Courtier, 1987, Derber, 1991, Ghil and Malanotte-Rizzoli, 1991, Courtier et al., 1993). Data assimilation using adjoint equations has also been tested on atmospheric tracer transport and chemistry (Robertson and Persson, 1993, Pudykiewicz, 1998, Robertson and Langner, 1998, Elbern and Schmidt, 1999, Robertson and Langner, 2000, Konstadinos and Robertson, 2003).

In this project we explore the options of using adjoint modelling in contrast to traditional back-trajectory models. The purpose is here not to perform data assimilation as such but to get more out of observations in terms of possible source regions. Special attention is paid to the impact from the temporal resolution in measured values. To illustrate the possibilities four different events are examined, the Chernobyl accident, the ETEX I exercise, the Algeciras accident and an event with heavy smoke noticed in Scandinavia.

The basis for this work is the MATCH model (Robertson et al., 1999) into which adjoint equations have been implemented.

Figure 1.Weighted influence function from observations in Sweden, 26 April to 1 May 1986, after the Chernobyl accident.

Figure 2.Weighted influence function at the location of Chernobyl for different heights. The source term may be deduced from this type of product.

Duration: 2002-2003

Funded by: Swedish Radiation Protection Agency (SSI)

Responsible at SMHI: Lennart Robertson

Web site:

Report: Final Report (2.3 Mb)

References

Courtier, P., Derber, J., Errico, R., Louis, J-F., and Vukisevic, T. (1993) Important literature on the use of the adjoint, variational methods and the Kalman filter in meteorology. Tellus, 45A, 342-357.

Derber, J.C. (1989) A Variational Continuous Assimilation Technique. Mon. Weath. Rev., 117, pp. 2437-2446.

Elbern, H. and Schmidt, H. (1999) A four-dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling. J. Geophysical Research, Vol. 104, No. D15, pp. 18,583-18,598.

Ghil, M. and Malanotte-Rizzoli, P. (1991) Data assimilation in Meteorology and Oceanography. Adv. in Geophysics, 33, 141-266.

Konstadinos, P. and Robertson, L. (2003) Bayesian updating of atmospheric dispersion after a nuclear accident, Applied Statistics (in press).

Marchuk, G. I. (1986) Mathematical models in environmental problems. Studies In Mathematics and Its Applications, Vol. 16. Springer, Berlin.

Marchuk, G. I. (1994) Adjoint equations and analysis of complex systems, Mathematics and Its Applications, Vol. 295. Kluwer Academic Press, Dordrecht.

Persson, C., Rodhe, H. and De Geer, L. E. (1987) The Chernobyl accident - A meteorological analysis of how radionuclides reached and were deposited in Sweden. Ambio, 16, pp. 20-31.

Pudykiewicz, J. A. (1998) Application of adjoint tracer transport equations for evaluating source parameters. Atm. Envirorn., Vol. 32, No. 17, pp.3039-3050.

Robertson (2004) Extended back-trajectories by means of adjoint equations. Swedish Meteorological and Hydrological Institute, RMK 105, August 2004. (PDF)

Robertson, L. and Langner, J. (1998) Source function estimate by means of variational data assimilation applied to the ETEX-I tracer experiment. Atmos. Environ., 32, 4219-4225.

Robertson, L. and Langner, J. (2000) On the issue of quality control in data assimilation. Air Pollution Modeling and Its Application XIII, edited by S.-E. Gryning and E. Batchvarova, Kluwer Academic/Plenum Publisher, 299-309.

Robertson, L. and Persson, C. (1993) Attempts to apply four dimensional data assimilation of radiological data using the adjoint technique. Rad. Prot. Dos., 50, 333-337.

Robertson, L., Langner, J. and Engart, M. (1999) An Eulerian limited area Atmospheric transport model. J. Appl. Meteor., 38, 190-210.

Talagrand, O. and Courtier, P. (1987) Variational assimilation of meteorelogical observations with the adjoint vorticity equation. Part 1: Theory. Q. J. R. Meteorol. Soc., 113, 1311-1328.