STATISTICAL EVALUATION OF SIGMA SCHEMES FOR ESTIMATING DISPERSION IN LOW WIND CONDITIONS ANIL KUMAR YADAV and MAITHILI SHARAN Centre for Atmospheric Sciences, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India (First received 5 April 1995 and in final form 25 September 1995) Abstract—-Previously described sigma schemes for the estimation of dispersion parameters in low wind- speed situations are evaluated statistically with the data obtained in a series of diffusion experiments (conducted by U.S. National Oceanic and Atmospheric Administration) under stable and low wind-speed conditions. The qualitative performances of the sigma schemes were intercompared in an earlier study using the same data. Various performance measures for the statistical evaluation of air-quality models are described. The evaluation exercise is carried out, essentially, on seven versions of a K-theory-based model which differed from one another in the choice of dispersion parameters (sigma schemes). The analysis based on selected statistical measures indicated consistency in the qualitative and quantitative performances of the schemes. The performances are evaluated for the peak concentrations as well as for the overall concentra- tion distribution. Those schemes which are based on the approach of dividing the hourly test period into smaller intervals exhibit better performance in predicting the peak as well as the lateral spread. The blocked bootstrap resampling technique was adopted to investigate the statistical significance of the differences in performances of each of the schemes by computing 95% confidence limits on the parameters FB, NMSE and R. Key word index: Statistical analysis, model evaluation, low wind dispersion, sigma schemes. INTRODUCTION The dispersion of a tracer in weak and variable wind conditions (typically U < 2 ms- 1) results in a concen- tration field which generally has non-Gaussian shape (nature) (Yamamoto et al., 1986). As a result, the application of Gaussian models in their primitive form is known to give erroneous results in such atmo- spheric situations. However, for most regulatory pur- poses, Gaussian or modified Gaussian models still find wide usage because of numerous apparent ad- vantages (EPA, 1978; EPRI, 1982; Juda-Rezler, 1989; Zannetti, 1990). One of the most important para- meters in plume dispersion modelling is the plume growth, more commonly referred to as dispersion coefficients ((7). The conventional (standard) methods for the estimation of dispersion coefficients normally lead to overprediction of the concentration peak and underprediction of the plume spread in dealing with low wind-speed situations (Kristensen et al., 1981). Several modifications have been suggested over the years to overcome this problem (Sagendorf and Dick- son, 1974; Zannetti, 1981; Cirillo and Poli, 1992; Sharan et al., 1995). In most of the cases, the solution based on K-theory has been utilized to study various schemes for the estimation of dispersion para- meters in low wind conditions. Sagendorf and Dickson (1974) have used the standard Gaussian plume for- mula, whereas Zannetti (1981) has proposed an algo- rithm for the treatment of low winds using Gaussian puff approach. Cirillo and Poli (1992) have intercom- pared four semiempirical models (out of which three are based on Gaussian approach) under low wind- speed, stable conditions. Sharan et al. (1995) have used a modified analytical solution of K-theory-based ad- vection-diffusion equation including the downwind diffusion term for the comparison of sigma schemes in low wind conditions. They have provided a detailed description of each scheme and intercompared their performances, in a qualitative sense, using concentra- tion data measured in a series of diffusion experiments conducted by U.S. National Oceanic and Atmo- spheric Administration (NOAA) under inversion con- ditions and light winds (Sagendorf and Dickson, 1974). In the last decade or so there has been a great deal of emphasis on assessing/evaluating performance of air-quality models (Weil and Jepsen, 1977; Fox, 1981; Venkatram, 1982; Smith, 1984; Cox and Tikvart, 1990; Hanna et al., 1991). More recently, Weil et al. (1992) have provided an exhaustive review of air-quality model evaluations. Most of the model evaluation exercises essentially deal with opera- tional performance evaluation and model physics 2595