Mixing Height Derived from the DMI-HIRLAM NWP Model, and Used for ETEX Dispersion Modelling

J.H. Sørensen, A. Rasmussen

Danish Meteorological Institute (DMI), Copenhagen, Denmark

Introduction For atmospheric dispersion modelling it is of great significance to estimate the mixing height well. Mesoscale and long-range diffusion models using output from numerical weather prediction (NWP) models may well use NWP model profiles of wind, temperature and humidity in computation of the mixing height. This is dynamically consistent, and enables calculation of the mixing height for predicted states of the atmosphere. In autumn 1994, the European Tracer Experiment (ETEX) (Nodop et al., 1997) was carried out with the objective to validate atmospheric dispersion models. The Danish Me- teorological Institute (DMI) participates in the model evaluations with the Danish Emer- gency Response Model of the Atmosphere (DERMA) (Sørensen et al., 1997b; Sørensen 1997; Sørensen and Rasmussen, 1995) using NWP model data from the DMI version (Rasmussen and Sørensen, 1997; Sass, 1994) of the High Resolution Limited Area Model (HIRLAM) (Källén et al., 1996) as well as from the global model of the European Cen- tre for Medium-Range Weather Forecast (ECMWF). In DERMA, calculation of mixing heights are performed based on a bulk Richardson number approach. Comparing with tracer gas measurements for the first ETEX experiment, a sensitivity study is performed for DERMA. Using DMI-HIRLAM data, the study shows that optimum values of the critical bulk Richardson number in the range 0.15–0.35 are adequate. These results are in agreement with recent mixing height verification studies against radiosonde data (Sørensen et al., 1997a; Sørensen and Rasmussen, 1997). The fairly large range of adequate critical values is a signature of the robustness of the method. Direct verification results against observed mixing heights from operational radiosondes released under the ETEX plume are presented.

Bulk Richardson Number Method The mixing height is estimated by a bulk Richardson number approach (Sørensen et al., 1997a; Sørensen and Rasmussen, 1997; Vogelezang and Holtslag, 1996). The method is robust and fairly accurate, and it is suited for use in situations where the vertical resolution of temperature and wind is limited as e.g. output from NWP models. The bulk

Richardson number at height z above ground is given by the following expression,

θ θ

gz v s =

Ri B 2 2 : (1)

+ θs u v

The quantities θs and θv are the virtual potential temperature at surface and at height z, respectively, u and v are the horizontal wind components at height z,andg is the gravita- tional acceleration. The top of the ABL is given by the height at which the bulk Richard- son number reaches a critical value. In a recent study involving comparisons with radiosonde data (Sørensen et al., 1997a; Sørensen and Rasmussen, 1997), a critical value of 0.24 was found most appropriate (with a correlation of 68%) for the DMI-HIRLAM model. From this study it furthermore appears that critical values of the bulk Richardson number in the range 0.15–0.35 are adequate for DMI-HIRLAM data.

FIG. 1. Boundary layer height at 0 UTC 0-200 200-400 400-600 600-800 800-1000 1000-1200 1200-1400 1400-1600 1600-1800 1800-2000 2000-2200 2200-2400 2400-2600 2600-2800 2800-3000 on October 25, 1994, calculated from ana- Mixing Height (m) DKV 94102500 200 lysed DMI-HIRLAM data. 600 200 200

1000 200

600 600 60N

1000 1000

1000

600

200 50N 600 1400

200 600 200 600 00 600 10 1400

10W 0 10E 20E

In Fig. 1 an example is shown of a calculation of the mixing height over Europe. The calculation which is valid at 0 UTC on October 25, 1994, is based on analysed DMI- HIRLAM data.

Indirect Verification Against ETEX Tracer Gas Measurements Comparisons are performed of DERMA simulations of the first ETEX experiment with observed concentrations (ETEX data set version: etex1 v1.1.960505). In Fig. 2, DERMA simulations of the first ETEX experiment are shown. The results are obtained by using high-resolution DMI-HIRLAM data. In Fig. 3, global values of normalised mean square error (NMSE), correlation and bias are shown for the DERMA simulations based on analysed DMI-HIRLAM and analysed ECMWF data, respectively. The statistical parameters are shown as functions of the critical value of the bulk Richardson number. From the figures it appears that critical values in the range 0.15–0.35 are adequate for DMI-HIRLAM data while it is 0.30–0.60 for ECMWF data. The difference between the two ranges of critical values owes to differences in vertical resolution and physical parametrisations of the corresponding NWP models. The fairly large range of critical values is in accordance with the above-mentioned verifications against radiosonde data.

FIG. 2. Three-hour average surface concentrations from the DERMA simulation based on analysed

DMI-HIRLAM data. On the sub-ﬁgures, the concentration patterns are shown in units of ngm3 at 24, 48 and 72 hours, respectively, after the start of the ﬁrst release. FIG. 3. Global values of normalised mean square error (NMSE), correlation and bias for DERMA simulations using analysed DMI-HIRLAM data (left column), and analysed ECMWF data (right column). Results are shown as a function of the critical bulk Richardson number.

Direct Verification Against Radiosoundings under ETEX Plume The routine radiosondes which were released under the ETEX plume have been lo- cated. Most radiosoundings correspond to 0 and 12 UTC, only few radiosondes are released at 6 and 18 UTC. By inspection of measured profiles of temperature, humidity and wind corresponding to well-defined boundary layers, a set of observations of mixing heights is obtained. In Fig. 4 observations are compared with model results derived by using the bulk Richardson number approach with a critical value of 0.25 applied to DMI- HIRLAM vertical profiles. The NWP profiles include analysed data as well as forecasts relevant to dispersion simulations of the first tracer gas experiment.

FIG. 4. Comparisons of modelled and observed mixing heights. The model results shown are derived from analysed as well as from 6, 12, 24 and 36 hour forecasts from the DMI-HIRLAM NWP model. From left to right, the number of data points in the scatter plots are 55, 54, 38, 38 and 34, respectively.

At the time the ETEX tracer gas experiments were carried out, the operational DMI- HIRLAM model produced analysed states of the atmosphere corresponding to 0, 6, 12 and 18 UTC. For the 0 and 12 UTC analyses, up to 36-hour forecasts were produced while the forecast length was only 6 hours corresponding to the 6 and 18 UTC analyses. In Fig. 5 statistical parameters are shown as a function of forecast length. The correlation drops from 0.75 to a minimum value of 0.3, and the NMSE increases from 0.08 to

a maximum of 0.35. The bias varies between 0 (analysis) and 100 m.

Conclusions The sensitivity of DERMA to the critical bulk Richardson number is studied by comparing model calculations with tracer gas measurements from the ﬁrst ETEX experiment. FIG. 5. Normalised mean square error (NMSE), correlation and bias calculated from observed mixing heights and model results derived from DMI-HIRLAM using the bulk Richardson number method with a critical value of 0.25. The statistical parameters are shown as functions of forecast length. The number of data points corresponding to analysed results and 6, 12, 18, 24, 30 and 36 hour forecasts are 55, 54, 38, 16, 38, 14 and 34, respectively.

Using DMI-HIRLAM data, optimum values of the critical number in the range 0.15–0.35 are obtained. Direct comparisons are made of modelled and observed mixing heights. The observed mixing heights are obtained from routine radiosoundings within the ETEX tracer gas plume. The corresponding modelled mixing heights are derived from analysed as well as forecast DMI-HIRLAM proﬁles.

References Källén E. (Ed.), 1996: HIRLAM documentation manual, System 2.5. Available from the Swedish Meteo- rological and Hydrological Institute (SMHI). Nodop K. (Ed), 1997: ETEX Symposium on Long-Range Atmospheric Transport, Model Verification and Emergency Response, Proceedings. Vienna, Austria, 13–16 May, 1997, EUR 17346 EN. Rasmussen A. and Sørensen J.H., 1997: Quality Validation of Analyzed and Forecast Vertical Profiles of Wind and Temperature from the DMI-HIRLAM Model in Comparison with Radiosoundings. In: Proceedings of the Sixth Topical Meeting on Emergency Preparedness and Response. San Fransisco, California, April 22–25, 1997, pp. 31–34 (ISBN 0-89448-623-3). Sass B.H., 1994: The DMI Operational HIRLAM Forecasting System, Version 2.3. DMI Technical Report 94–8. Available from DMI. Sørensen J.H., 1997: Sensitivity of DERMA to Boundary-Layer Parameters, and Evidence for Mesoscale Influence on Long-Range Transport. In: ETEX Symposium on Long-Range Atmospheric Transport, Model Verification and Emergency Response, Proceedings. Ed: Nodop K., Vienna, Austria, 13–16 May, 1997, EUR 17346 EN, pp. 207–210. Sørensen J.H. and Rasmussen A., 1995: Calculations Performed by the Danish Meteorological Institute. In: Report of the Nordic Dispersion/Trajectory Model Comparison with the ETEX-1 Fullscale Experiment. Eds: Tveten U. and Mikkelsen T., Risø-R-847(EN), NKS EKO-4(95)1, pp. 16–27. Sørensen J.H. and Rasmussen A., 1997: Method for Calculation of Atmospheric Boundary-Layer Height used in ETEX Dispersion Modeling. In: Proceedings of the Sixth Topical Meeting on Emergency Pre- paredness and Response. San Fransisco, California, April 22–25, 1997, pp. 503–506 (ISBN 0-89448- 623-3). Sørensen J.H., Rasmussen A. and Svensmark H., 1997a: Forecast of Atmospheric Boundary Layer Height Utilised for ETEX Real-time Dispersion Modelling. Accepted for publication in Physics and Chemistry of the Earth. Sørensen J.H., Rasmussen A., Ellermann T. and Lyck E., 1997b: Mesoscale Influence on Long-range Trans- port; Evidence from ETEX Modelling and Observations. Accepted for publication in Atmos. Environ. Vogelezang D.H.P. and Holtslag A.A.M., 1996: Evaluation and model impacts of alternative boundary-layer height formulations. Boundary-Layer Meteorol. 81, 245–269.