## An evaluation of several methods of atmospheric trajectories

##### Abstract

One of the more important aspects of air pollution at present is the study of acid rain. The processes leading to its formation are basically due to the increasing emissions by man of SO₂ and NOₓ into the atmosphere as well as the increasing concentrations of CO₂ which are regularly found there. After chemical reactions between the pollutants and cloud water or raindrops occur, the by-products, sulfuric, nitric and weak carbonic acid, result. Though the reactions may take from minutes or hours in highly polluted air to weeks or more in slightly polluted air, the build-up of gaseous SO₂ , NOₓ and CO₂ in the atmosphere leading to the acid rain potential can be attributed in part to long-distance transport. To follow this long-distance transport requires the use of trajectories. Many of the trajectory computation schemes reported in the literature may be unreliable in terms of their applicability in following pollutant transport. This case study around Lake Erie attempts to evaluate these techniques by comparing them to an 'estimated' trajectory which is regarded as the best approximation to the actual trajectory. Each trajectory method was classified according to the type of approach used to quantify the winds, i.e., whether the trajectory was a surface, low-level, upper-level or layer- average type as well as the time interval employed in averaging the wind data used to calculate the trajectory. The type of wind data that each trajectory technique used was broken down into either an observed or computed class. The observed wind data class only pertains to trajectory methods that used data measured and reported by the National Weather Service, some other agency or by research measurements. The computed wind data class refers to trajectory methods that applied empirical equations to the observed data, resulting in calculations, such as a layer-average wind, for example. Calculating each trajectory method required the use of wind observations reported at 15-min intervals from 3 Canadian buoys that were geographically centered in Lake Erie and from a stationary Environmental Protection Agency ship (42°00' 00" latitude, 81° 30' 00" longitude) from 0530-1430 LST on the 24 July 1979. This particular date was selected because of personal summer work done at Governors State University in Park Forest South, Illinois with trajectory analysis over Lake Erie. Also for this same time period, wind data were obtained at 1-hr intervals from 6 National Weather Service and 2 Canadian stations around Lake Erie. This data which was then interpolated to every 15-min since the National Weather Service and Canadian stations report only at 1-hr intervals, plus the above buoy and ship data, produced maps of isotach and streamline analyses for appropriate time intervals. This step preceded the actual plotting of each trajectory technique. From these maps, the estimated trajectory which is used as the standard for comparison, was plotted at 15-min intervals. A 'dispersion' trajectory by Boubel, et al. (Fundamentals of Air Pollution, 1973) was then constructed, employing a fan-shaped configuration similar to the Gaussian distribution of an area-source model. It entailed a 1-hr, principal surface trajectory surrounded by 2, 1-hr, extreme surface trajectories which were computed from twice the standard deviation of the variability of the wind directions (2σ). In other words, the resulting extreme surface trajectories encompass an area where 95% of all air parcels must remain if they departed from the origin at time zero. The above trajectory formulates the so-called Boubel Criteria to which each trajectory was compared, to see if at least three-fourths of it fell within the envelope portion. Those methods that did, fulfilled the Boubel Criteria. A total of 9 methods out of the 18 reported in the literature met the criteria and were evaluated in this study. There are several surface, adjusted surface, layer-average and transport trajectories illustrated. A method constructed from trajectories that met the Boubel Criteria was the mean centre trajectory formulated by Ebdon (Statistics in Geography: A Practical Approach, 1977). This statistical approach centered around determining a mean X and Y position per hour (coordinate) of all the trajectories fulfilling the criteria resulting in a mean centre trajectory. Since this trajectory nearly coincided with the estimated and dispersion trajectories, it indicates that the Boubel Criteria approximates real-life conditions. Further evaluation of the methods was conducted by rating each technique according to its average weighted separation distance (kilometers per kilometer) and standard deviation from the estimated trajectory. This process involved determining a weighted separation distance at every hour for each trajectory technique. This was determined by dividing the horizontal separation distance per hour between each trajectory from the estimated trajectory, by the total path length of the individual trajectory from time zero through succeeding 1-hr intervals. The calculation was done for each of the 9, 1-hr intervals. The results were then averaged over the 9-hr period to produce an average weighted separation distance and later, a standard deviation per trajectory. The smaller the average weighted separation distance and standard deviation, the more reliable the trajectory technique is and the better the rating. Each trajectory method was rated either Good, Fair or Poor where Good applied to a low, average weighted separation distance and standard deviation; Fair indicated moderate values and Poor applied to high values. The final results indicated that 4 techniques were rated Good, 3 were Fair and 2 were Poor. One of the better trajectory methods to rely on is the 1-hr, surface trajectory from Governors State University (Forward Trajectories. 1977). Additionally, the 3-hr, adjusted surface trajectory by Peterson (Estimating Low-Level Tetroon Trajectories. 1966) appears to be one of the fairly reliable techniques to apply. However, the 6-hr, layer-average trajectory by Hoecker (Accuracy of Various Techniques for Estimating Boundary-Layer Trajectories, 1977) is 1 of 2 techniques not recommended for application in the atmosphere due to their poor rating. Overall, the better trajectory techniques involve a small time interval which accounts for greater accuracy and reliability, especially when tracking pollutants.