METHOD FOR CALCULATION OF ATMOSPHERIC BOUNDARY-LAYER HEIGHT USED IN ETEX DISPERSION MODELING

Jens Havskov Sørensen Alix Rasmussen Danish Meteorological Institute (DMI) Danish Meteorological Institute (DMI) Lyngbyvej 100 Lyngbyvej 100 DK-2100 Copenhagen Ø, Denmark DK-2100 Copenhagen Ø, Denmark +4539157432 +4539157431

SUMMARY II. THE BULK RICHARDSON NUMBER METHOD

A method for calculation of the atmospheric boundary The Richardson number is, in general, defined as the ra- layer (ABL) height is studied and verified against radiosonde tio between the buoyant consumption term and the mechan- observations. The method, which is based on a bulk Richard- ical production term in the turbulence kinetic energy (TKE) son number approach, is suitable for use in numerical weather equation.4 Thus the gradient Richardson number is given by prediction (NWP) models where some resolution is possible

within the boundary layer. Based on NWP data from the

g= @ =@ z 

v v ;

Ri = (1) 2

DMI-HIRLAM model, the above method was used for atmo- 2

 @ u=@ z  +@v=@z spheric dispersion modeling during the European Tracer Ex-

periment (ETEX) by the Danish Emergency Response Model

z g

where is the height, the gravitational acceleration, v the

for the Atmosphere (DERMA). In a preliminary model eval- v virtual potential temperature, and u and are the horizon- uation, DERMA performed very well. tal wind components. In order to use a gradient Richardson number method for calculation of the ABL height, involving comparisons of the gradient Richardson number with a criti- I. INTRODUCTION cal value, it is necessary to have available very accurate ver- tical profiles of especially the horizontal wind components. For atmospheric long-range transport modeling it is, in This is due to the denominator in Eq. (1), the square of the general, of utmost significance to estimate the height of the vertical gradient of the horizontal wind vector. This method ABL well.1 Such modeling is involved in emergency response is furthermore sensitive to fine-structures in the ABL. systems for major nuclear or chemical accidents for which The height of the ABL is estimated by a bulk Richardson large amounts of hazardous material are released to the atmo-

number approach. The bulk Richardson number at height z sphere, but also for more conventional air pollution modeling above ground is given by the following expression (e.g., smog and ozone).

We have studied a robust and fairly accurate method for

 

2, 3 gz s

estimating the ABL height. The method is suited for use v

= :

Ri B (2)

2 2

 u + v  in situations where the vertical resolution of temperature and s

wind is limited. This includes output from NWP models.

Use of NWP data for atmospheric dispersion modeling v

The quantities s and are the virtual potential temperature

u v

implies a number of advantages. Of course, the possibil- at the surface and at height z , respectively; and are the g ity of making forecasts of the spread of harmful material in horizontal wind components at height z ;and is the grav- the atmosphere is essential for emergency preparedness sys- itational acceleration. The top of the ABL is given by the

tems. Furthermore, the availability of meteorological data an- height, h, at which the bulk Richardson number reaches a alyzed by NWP models is beneficial for dispersion modeling critical value. In the literature one finds critical values be- because such data also enable calculations over observation- tween, say, 0.2 and 1. In this study an attempt was also made sparse regions such as the oceans. to estimate this critical number. III. DMI-HIRLAM

The HIgh Resolution Limited Area Model (HIRLAM)5 is a primitive-equation NWP model using a grid-point rep- resentation with second-order difference approximations for the spatial derivatives. The horizontal grid is a regular spa- tially staggered latitude/longitude grid (the Arakawa C grid), in a rotated spherical coordinate system. The vertical coor- dinate is a terrain-following hybrid coordinate6.Themete- orological analysis scheme is based on the optimum inter- polation (OI) technique extended to three-dimensional multi- variate interpolation of observed deviations from the forecast first-guess fields. The DMI-HIRLAM model system,7 which is operational at the Danish Meteorological Institute (DMI), is run on two different areas. The boundary fields for the large-area version (G) are obtained from the global model run by the European Center for Medium-Range Weather Forecast (ECMWF). The G version covers Europe, the North Atlantic, Greenland, and parts of USA, Canada and the Arctic Ocean. The small-area Figure 1: In the upper-left figure, a scatter plot compares version (E) covering Europe is nested in the G version, which the observed ABL heights with the calculated values from

provides the boundary values. The horizontal resolution is radiosonde data. In this calculation, a critical value of

 

:42 0:21

0 (46 km) for G and (23 km) for E. The time steps

=0:14

;crit Ri B was used. The remaining three figures are are 4 and 3 minutes for G and E, respectively, and the fore- scatter plots corresponding to ABL heights calculated from cast lengths are 48 and 36 hours, respectively. Both models analyzed, 12- and 24-hour forecast HIRLAM profiles, re- are run with the same vertical resolution (31 hybrid levels). spectively, in comparison with the observed values. A value

The models have nine model levels available for resolving a

=0:24

;crit of Ri B was used in these calculations. typical day-time boundary layer with a height of 1500 m. The DMI-HIRLAM forecasting model system consists of data-assimilation, pre-processing, analysis, initialization, forecast, post-processing, and verification. Both model ver- sions are run with their own six-hour data-assimilation cycle.

square relative error was calculated. This function of the crit-

=0:14

;crit ical value has a minimum at a value of Ri B .The upper-left part of Fig. 1 is a scatter plot comparing the calcu- IV. CALCULATION OF ABL HEIGHT lated heights with the observed values. The same procedure was applied to analyzed HIRLAM The basis of the present study is a set of about one hun- profiles. The resulting root-mean-square relative-error curve dred radio soundings from Copenhagen [World Meteorolog- has a distinct minimum positioned, however, at a slightly

ical Organization (WMO) station number 06181] from Jan-

=0:24

;crit larger value of Ri B . With this value of the crit- uary to August 1994. The soundings used represented bound- ical bulk Richardson number, the method was applied also ary layers with a well-defined top. The observed ABL heights to forecast profiles. In the upper-right part of Fig. 1, a com- were obtained by inspection of the profiles of temperature and parison is made between the ABL heights calculated from wind. The bulk Richardson number method was applied both analyzed HIRLAM data and the observed values. The lower to the radiosonde data and to corresponding profiles from the parts of Fig. 1 show similar comparisons, here based on fore- DMI-HIRLAM model. The latter profiles consisted of an- cast HIRLAM profiles. Table 1 summarizes the statistical alyzed as well as forecast data. The resulting ABL heights evaluation of the method. were compared with the observed values. In Fig. 2, a calculation of the ABL height over Europe The method was applied to the radiosonde data for a at a particular time is shown, illustrating the high degree of range of critical values. For each of these, the root-mean- variation in this field. Table 1: Correlation, relative error, and bias for the bulk Richardson number method applied to radiosonde data as well as analyzed, 12-hour forecast, and 24-hour forecast HIRLAM data.

Radio HIRLAM Soundings AN 12hFC 24hFC Correlation 0.81 0.68 0.62 0.63 Rel. error 0.25 0.29 0.31 0.31 Bias 0.04 -0.10 0.00 0.00

V. DERMA

At DMI we have developed an atmospheric long-range transport model: the Danish Emergency Response Model for the Atmosphere (DERMA).8 DERMA is a three-dimensional atmospheric dispersion model with high resolution, based on Figure 2: Atmospheric boundary-layer height over Europe a multi-level puff parameterization. DERMA utilizes NWP on September 13, 1993, at 0 UTC. The calculation is based data from, e.g., the different versions of DMI-HIRLAM or on the bulk Richardson number method applied to HIRLAM from the global model at the ECMWF. profiles. The advection time step of DERMA is, e.g., 15 minutes, which is a typical turn-over time for the large vertical eddies in the ABL. Thus, one may well assume that the released was carried out in October 1994, and it was repeated in Novem- material is well mixed in the ABL within a few time steps. ber 1994. Before the experiment, about 170 surface-based Correspondingly, an assumption of total mixing is employed. air samplers were set up throughout Europe. These monitors In the model, the released particles are advected by the were in operation the days following the experiment. The air three-dimensional NWP wind. A puff is associated with each samples obtained have been chemically analyzed by the Joint particle adding up the total concentration field. Research Centre (JRC) at Ispra, Italy. In the horizontal, a Gaussian distribution is assumed for During the experiments, real-time calculations of the dif- each puff. In the vertical, the assumption of total mixing is fusion of the gas cloud were performed at 28 institutes from employed for puffs inside the ABL. For puffs above the ABL, Europe, USA, Canada, and Japan. Based upon data from a Gaussian distribution is assumed. 86 air sampling stations, a preliminary evaluation of these The height of the ABL is estimated by the bulk Richard- models have been performed.9 DERMA performed very well son number approach described above. in this evaluation. At the time this paper is being written, the ETEX data set of observations is still confidential. However, during the first VI. ETEX ETEX experiment, the tracer gas was observed with hourly time resolution at the National Environmental Research Insti- Previously, it has been difficult to evaluate atmospheric tute (NERI) at Risø, Denmark, using two measurement tech- long-range transport models. This is due to the fact that no, niques. This recently reported set of observations10 is not or very limited, quality-assured experimental data were avail- included in the official ETEX data set. Apart from the eleven able for atmospheric dispersion over a range of several thou- official tracer-gas observations taken in Denmark during the sand kilometers. With the objective of establishing a database first ETEX experiment, DERMA also shows good agreement of such experimental data, the WMO, the International Atomic with this set of observations, cf. Fig. 3. This is especially so Energy Agency, and the European Union decided to perform when DERMA is based on analyzed DMI-HIRLAM data. In a large-scale atmospheric diffusion experiment in Europe. The this case, the observed double-peak structure at this location experiment, entitled the European Tracer Experiment (ETEX), is reproduced very well. According to DERMA, in combi- model evaluation.

REFERENCES 1. T.J. Sullivan, J.S. Ellis, C.S. Foster, K.T. Foster, R.L. Baskett, J.S. Nasstrom, and W.W. Schalk III, “Atmo- spheric Release Advisory Capability: Real-time Model- ing of Airborne Hazardous Materials,” Bull. Amer. Me- teor. Soc. 74, 2343–2361 (1994). 2. I. Troen and L. Mahrt, “A Simple Model of the Atmo- spheric Boundary Layer; Sensitivity to Surface Evapo- ration,” Boundary-Layer Meteorol. 37, 129–148 (1986). 3. A.A.M. Holzlag and C.H. Moeng, “Eddy Diffusivity and Countergradient Transport in the Convective Atmo- spheric Boundary Layer,” J. Atmos. Sci. 48, 1690–1698 (1991). 4. R.B. Stull, An Introduction to Boundary Layer Meteo- rology, p. 176, Kluwer Academic Publisher, Dordrecht, the Netherlands, (1988). 5. E. K¨all´en (Ed.), “HIRLAM Documentation Manual, System 2.5,” Available from the Swedish Meteorolog- ical and Hydrological Institute (SMHI), (1996).

Figure 3: One-hour average concentrations at Risø, Den- 6. A.J. Simmons and D.M. Burridge, “An Energy and An- mark. The observed data10 and the model data based on gular Momentum Conserving Vertical Finite-Difference analyzed NWP model data are shown with thin and thick Scheme and Hybrid Vertical Coordinates,” Mon. Wea. curves, respectively. The upper figure displays DERMA re- Rev. 109, 758–766 (1981). sults based on ECMWF data, the lower figure DERMA re- 7. B. Hansen Sass, “The DMI Operational HIRLAM Fore- sults based on DMI-HIRLAM data. casting System, Version 2.3,” DMI Technical Report 94–8, (1994). nation with DMI-HIRLAM, the double-peak structure is due 8. J.H. Sørensen and A. Rasmussen, “Calculations Per- to a small horizontal eddy formed at an earlier stage of the formed by the Danish Meteorological Institute,” Report dispersion process. This anti-cyclonic eddy implied the for- of the Nordic Dispersion/Trajectory Model Comparison mation of a toroidal perturbation of the concentration field. with the ETEX-1 Fullscale Experiment, Eds: U. Tveten The double peak is the result of the toroid passing Risø. The and T. Mikkelsen, Risø-R-847(EN), NKS EKO-4(95)1, toroid had a similar effect at five of the official ETEX obser- p. 16–27, (1995). vation sites. 9. W. Klug, G. Graziani, S. Mosca, F. Kroonenberg, G. Archer, K. Nodop, and A. Stingele, “Real Time Long Range Dispersion Model Evaluation, ETEX first exper- VII. CONCLUSIONS iment,” In preparation, (1996). A method for calculating the ABL height, based on a 10. T. Ellermann and E. Lyck, “ETEX-1 Tracer Gas Mea- bulk Richardson number approach, is studied and verified surements at Risø,” Report of the Nordic Disper- against radio soundings. The method is robust and fairly sion/Trajectory Model Comparison with the ETEX-1 accurate, and so it is suited for use in, e.g., long-range at- Fullscale Experiment, Eds: U. Tveten and T. Mikkel- mospheric transport models. As demonstrated, the method sen, Risø-R-847(EN), NKS EKO-4(95)1, p. 11–16, worked well for the DERMA model in the ETEX real-time (1995).