Application of artificial neural networks to modeling the transport and dispersion of tracers in complex terrain

Application of artificial neural networks to modeling the transport and dispersion of tracers in complex terrain

Atmospheric Environment 36 (2002) 561–570 Application of artificial neural networks to modeling the transport and dispersion of tracers in complex ter...

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Atmospheric Environment 36 (2002) 561–570

Application of artificial neural networks to modeling the transport and dispersion of tracers in complex terrain Domagoj Podnar*, Darko Korac$ in, Anna Panorska Desert Research Institute, 2215 Raggio Parkway, Reno, NV 89512, USA Received 29 April 2001; accepted 21 August 2001

Abstract Simulation of the transport and dispersion of chemical tracer in complex terrain has been performed using artificial neural networks (ANN). The ANN method has been applied to relatively high temporal resolution data (hourly averagesFlong time series), and lower-resolution data (daily averagesFshort time series). The meteorological input consisting of surface and upper-air data was selected in such a way that it optimally represents the spatial inhomogeneity of the flow field, atmospheric stability, and synoptic conditions. In both cases, the inclusion of previous tracer concentrations as input has significantly improved the ANN performance. For the daily average case, several isolated single-point sharp peaks that were recorded in the series of daily concentrations were not resolved by the ANN. An improved correlation with measurements (from 0.946 to 0.997) was obtained after simple smoothing of the tracer concentrations. Because the number of data samples was small, a ‘‘leave-one-out’’ method was used. The hourly averages provided more cases and thus more significant input for ANN training; however, it brought more uncertainty into the selection of appropriate inputs because of the transport time due to the separation between the source and receptor. Here, training was performed using the first 85% of cases; the rest was used for testing. The ANN-simulated hourly concentrations agreed well with the measured concentrations and yielded correlation coefficients for the training and testing sets of 0.844 and 0.896, respectively. The sensitivity analysis revealed that previous concentration data contributed to resolving peaks in simulated concentrations while meteorological data provided more information on the temporal characteristics of the simulated tracer concentrations. A rudimentary comparison with traditional statistical methods revealed that the ANN performed better and showed fewer limitations as a tool for tracer modeling, especially for long-term prediction. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Air quality modeling; Tracer concentration; Field program; Simulation; Artificial intelligence

1. Introduction Assessing the transport and dispersion of atmospheric pollutants and tracers in complex terrain is a difficult task from both observational (Whiteman, 1982; Blumen, 1990) and modeling (Pielke, 1984; Kora$cin et al., 2000) points of view. From the modeling perspective, this difficulty is primarily caused by the spatial and temporal inhomogeneity of the atmospheric fields and inaccuracies in the models’ structures and initial and boundary *Corresponding author. fax: +1-775-674-7060. E-mail address: [email protected] (D. Podnar).

conditions. Many field programs (Pielke and Pearce, 1994; Clements and Hoard, 1989; Green, 1999) conducted in complex terrain revealed the importance of local circulations and synoptic forcing on the structure of the atmospheric flow and stability and the associated dispersion processes. In 1992, the US Environmental Protection Agency initiated a field program, measurement of haze and visual effects (MOHAVE), in the southwest United States. The main goal of this program was to estimate the impact of an isolated power plant (Mohave Power Project, MOPP) on visibility degradation in the Grand Canyon as compared to long-range transport from

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southern California and Arizona (Green, 1999). To achieve that goal, a field program was set up to provide a comprehensive experimental data set that can be used for model evaluation and development. The measurements included a dense network of meteorological stations as well as surface and upper-air stations for the measurement of chemical species and artificial tracers released during the experiment. The complexity of the atmospheric and dispersion processes in this area was discussed by Yamada (1992), Enger et al. (1993), Kora$cin and Enger (1994), Enger and Kora$cin (1995), Switzer et al. (1996), Kora$cin et al. (2000), and Yamada (2000). Although complex dispersion models such as some of those mentioned above simulate 3-D atmospheric fields to a certain level of accuracy, they require detailed input conditions and also significant computer effort that is not feasible for wide use in a variety of operational environmental applications now or in the near future. One of the alternatives (or complements) is to use artificial neural networks (ANN) to assess the future impact of emission sources on the environment. The ANN methods have two major advantages: simplicity in use and low computational requirements. In this study, we demonstrate the feasibility of using ANN methods in simulating the transport and dispersion of chemical tracers for both short-term (1 h) and long-term (1 day) averaged time series of input conditions (meteorological parameters and previous tracer concentrations) and output conditions (current simulated tracer concentrations). In addition, one of the objectives is to show the relative importance of meteorological versus previous concentration inputs on the ANNs success in simulating current or future

concentrations. The study also addresses the issue of the appropriate resolution of the input time series on the ANN performance, and compares the ANN method with the multivariate linear regression and Autoregressive Integrated Moving Average (ARIMA) time series (Box et al., 1994) statistical methods.

2. Data To investigate the transport and dispersion of pollutants in the vicinity of the Grand Canyon, orthoperfluorodimethylcyclohexane (o-PDCH) tracer was released during the winter and summer of 1992 from MOPP and measured using the tracer monitoring network setup in the area. The topographic complexity of the study area is shown in Fig. 1. We have investigated the capability of an ANN in simulating two data sets with different temporal resolutionsFhourly and daily averages. A time series with hourly averages provides more cases and thus more significant input for ANN training; however, it brings more uncertainty into the selection of appropriate inputs because of the transport time due to the separation between the source and receptor. Therefore, for this case it is very important to construct the input fields so as to spatially represent the full characteristics of the wind field and associated expected transport. A time series with daily averages provides more practical information and allows for realistic transport time in connecting the source and receptor. The uncertainty in linking 1-h concentration average with meteorology distant by

Fig. 1. Topography of the study area centered at 35.11N, 114.61W.

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Fig. 2. Positions of meteorological and tracer measuring stations for the daily averages case (filled) and hourly averages case (nonfilled) centered at 35.251C, 114.301W. Stations used for both cases are half-filled.

100 km or more in complex terrain is much higher than comparing 24-h average concentrations and 24-h averaged meteorological parameters. Since the emission rate was constant during the period of interest (Green, 1999) it was omitted from the models’ inputs for both daily and hourly averaged cases. The advantage of this condition is that the relationship between meteorology and concentrations is much easier to determine; however, the model does not have the capability to establish the response to emissions changes and therefore in the present selection of input parameters is not applicable to non-constant emission rate situations. Nevertheless, it would be trivial to extend the model inputs to include emission rate for variable emission rate situations.

PrescottFMunicipal (PRCN) stations, and upper-air data from Desert Rock (DRAN), Winslow (INWN), and Miramar NAS (NKXN) stations. Surface data consisted of ambient temperature, relative humidity, wind speed and wind direction. The DRMO station did not report relative humidity, and ambient temperature was not reported at the LOME station. Upper-air data consisted of vertical profiles of ambient temperature, relative humidity, wind speed and wind direction, and was reported at 0400 and 1600 h LST (1200 and 0000 UTC, respectively). The positions of the meteorological and tracer-measuring stations are depicted in Fig. 2. Detailed information on the station positions can be found in Kora$cin et al. (2000). 2.2. Hourly averages data set

2.1. Daily averages data set During the summer period of the MOHAVE experiment, most of the meteorological and daily tracer measurements were made from 5 July 1992 through 3 September 1992. We have selected data collected in August because both meteorological and tracer data were available from a number of stations during that period. Daily tracer concentrations were measured at 6 selected tracer monitoring sites: Baker (BAKE), Dolan Springs (DOSP), Essex (ESSE), Kelso (KELS), Truxton (TRUX), and Yucca (YUCC). Meteorological data consisted of the surface data obtained from the Dagget/ Federal Aviation Administration Airport (DAGN), DRI Mountain (DRMO), Las Vegas McCarran International Airport (LASN), Long Mesa (LOME), and

During the MOHAVE experiment, in addition to the daily tracer concentration measurements discussed in the previous sub-section, hourly tracer concentrations were measured from 28 July to 14 August at the Meadview station (MEAD), located 120 km NNW from MOPP. Surface meteorological data selected included ambient temperature, relative humidity, and wind speed and wind direction from the DAGN, LASN, LOME, MEAD, MOPP, and PRCN stations. Temperature was not recorded at LOME station. Upper-air data consisted of wind speed and wind direction at three vertical levels from the MEAD and MOPP wind profilers. Also, Radio Acoustic Sounding System (RASS) measurements of ambient virtual temperature at three levels at MOPP were available. The positions of the meteorological and

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tracer receptor stations for the hourly data set are also depicted in Fig. 2.

network that is used in this study is shown in Fig. 3. In this project, commercial software was used for performing the ANN simulation (see http://www. logicaldesigns. com/#Thinks Web page for the description).

3. Artificial neural network method 3.1. Daily averages data set Artificial Neural Networks are mathematical structures that emulate the structure and behavior of a human brain (Bishop, 1995). They are capable of learning from training samples without knowing any laws or equations. If considered as a ‘‘black box’’, an ANN accepts an input vector and generates a response in the form of an output vector. In the training phase, a learning algorithm is applied to reduce the error between the desired and produced output. In the testing phase, the network is presented with the new input vector and produces (simulates) the output. Among many types of neural networks, we have selected a feed-forward neural network with a back propagation learning algorithm because of its simplicity and widespread use (Bo$znar et al., 1993; Narasimhan et al., 2000). During the ANN setup phase, numerous tests were performed with different combinations of values for learning rate, momentum, and weights decay. It appeared that the ANN performed best when momentum and weights decay was set to zero; small values for momentum did not have any effect on training while larger values prevented good convergence. Therefore, the default learning rate of 0.01 was used and momentum rate and weights decay parameters were set to zero for both daily and hourly average cases. The ANNs used contained hidden layers and bias weights and therefore, provided a large number of weights which minimized the problem of reaching local minima during training. To make sure that local minima were avoided, we first trained a subset of ANNs with seven different, randomly selected sets of initial weights and used the five that gave the best learning results for subsequent training. The topology of the three-layer feed-forward

We have designed the meteorological input for both data sets so that it represents as much as possible the spatial inhomogeneity of the wind field, atmospheric stability, and characteristics of the synoptic field. The ANN’s inputs for the daily average case consisted of ambient temperature, relative humidity, and u and v wind components (since representation of wind direction is of a circular nature, u and v wind components were calculated and used instead of wind speed and direction) from the selected surface and upper-air stations, as well as the previous day’s tracer concentrations at six tracer receptors. Daily averages of the surface meteorological data were obtained by averaging the hourly data originally reported. Five surface stations provided 18 inputs. Three upper-air stations yielded 72 inputs since four meteorological fields were reported twice daily at three selected vertical levels (500, 700, and 850 mb). As in the case of the surface data, u and v components were calculated and used instead of wind direction and speed. The previous day’s tracer concentrations at six tracer monitoring stations were also used as input, providing additional 6 inputs. Thus, the total number of input nodes was 96. Input values were normalized to a 0.1–0.9 range to achieve faster convergence. Output data consisted of the simulated tracer concentrations measured at six monitoring stations. Because some of the measured tracer data exhibited isolated peaks in concentration, concentrations were three-point averaged so that the network could resolve these maxima in more than one point. Since the available number of input sets was small (31), a ‘‘leave-one-out’’ method was selected. In this method,

Fig. 3. Topology of the three-layered feed-forward neural network used in this study.

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the network is trained on all but one data sample and then tested on the remaining one. To find the most appropriate architecture for the ANN, we randomly selected three cases for each tracer-measuring station and ran ANNs first with no hidden layers and then with one hidden layer. The ANN with no hidden layer could not achieve error convergence for three cases. The average error between the modeled and measured values for all selected cases was 32.4%. When the hidden layer was added, the ANN performed significantly better with only 3.1% average error and without a convergence problem. After sensitivity tests with a different numbers of hidden nodes, we found the optimum number to be 18. After tests with different number of outputs were performed, only one receptor was selected as output at a time because that topology yielded the best training results. This increased the complexity of the simulation and 186 runs were performed. Learning took between a few tens and a few thousand epochs, and the test set was evaluated while training to prevent overfitting.

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all of August 1992. The ANN-simulated concentrations agree well with measured concentrations for a wide range of measured concentrations from 0 to 10 fl l1. The correlation coefficient ranges from 0.946 (KELS) to 0.997 (YUCC). From the scatter plot (Fig. 5) it can be seen that there is some tendency for the ANN simulations to overpredict measurements for relatively small concentrations (less than 0.25 fl l1), while for greater concentrations the level of agreement increases. A possible reason is that there is a larger variety of atmospheric conditions, which lead to low concentrations and fewer conditions favorable to increased concentrations. Such good results come under a few conditions. First, because of the resolution problem, tracer concentrations were smoothed to facilitate the resolving of sharp peaks by the ANN. A simple threepoint average was used for smoothing. Second, the ‘‘leave-one-out’’ method was used because of the small number of data samples. 4.2. Hourly averages data set

3.2. Hourly averages data set The meteorological input for the hourly average case was the ambient temperature, relative humidity, and u and v wind components. Surface stations provided 23 inputs, and wind-profilers and the RASS station yielded 15 inputs, as wind data at three vertical levels (250, 550, and 1350 m AGL) was used along with temperature data at three vertical levels (461, 776, and 1511 m AGL). The previous hour’s tracer concentration at the MEAD tracer monitoring station was also used as an input, providing a total of 39 input nodes. Since some data were missing, 285 samples were selected from the total of 408 samples. The data were normalized to a 0.1–0.9 range but no averaging was performed. In this case, the first 242 cases (85%) were selected as training set and testing was performed on the remaining 43 cases. As with the daily case, tests were performed to find a suitable ANN architecture. An ANN with one hidden layer showed the following improvements over the single layer ANN: maximum test error 9%, average test error 7.5%, and correlation coefficient between the measured and modeled concentrations 2%. After sensitivity tests related to the number of hidden nodes were performed, the number of nodes in the hidden layer was set to 8. Learning took 2525 epochs, and the test set was evaluated while training.

4. Results 4.1. Daily averages data set Fig. 4 shows a comparison of the measured and simulated daily tracer concentrations at six receptors for

The training and testing results are shown in Figs. 6 and 7, respectively. The ANN-simulated concentrations agree well with the measured concentrations and yielded correlation coefficients for the training and testing sets of 0.844 and 0.896, respectively. For the training set, some of the maxima are not fully captured and are underpredicted in most cases. Also, a small lag between the measured and simulated concentrations is visible. In the test set, the ANN was able to simulate all three main maxima as well as reproduce cases with lower values. As with the training set, the results show a slight lag between the modeled and measured values. A scatter plot (Fig. 8) shows underprediction of the highest values of tracer concentration; for lower- and mid-range values the measurements are under and overpredicted almost equally, but follow a zig-zag pattern where subsequent points are on the opposite side of the 1-to-1 line. This zig-zag pattern is a consequence of the lag between measured and simulated values. The probable reasons for the lag are the higher significance of the previous hour tracer concentration over meteorological inputs and the uncertainty in relating a source and receptor at distances up to 300–400 km in complex terrain. The spatial representativeness of the surface stations was chosen to provide sufficient information on spatially inhomogeneous atmospheric fields in the area covering the source and receptors (Green, 1999). In order to assess the importance of meteorological versus previous concentration input we set up two networks with only meteorological parameters and previous concentration as input, respectively. Using meteorological parameters as the only input, the ANNsimulated concentrations yielded a correlation coefficient of 0.566 for training data and 0.495 for test data

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Fig. 4. Comparison of measured (solid), ANN-similated (dashed), and ARIMA-simulated (dotted) daily tracer concentrations at six tracer monitoring stations.

compared to measurements. The reason for the relatively low correlation coefficient is the inability of the network to simulate the sharp increase in concentrations (the last third of the test cases). The network with the previous concentrations as the only input yielded a high correlation coefficient of 0.878 and was able to simulate the three maxima well; on the other hand, it was unable to simulate lower concentrations well and showed a

visible lag between the measured and simulated values. The limitations of the dispersion prediction are caused by the limitations of the available meteorological network in uniquely determining the 3D structure and evolution of winds, thermodynamic stability, and turbulence in complex terrain. Consequently, predictions of dispersion in complex terrain using commonly applied dispersion models generally yield correlation

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coefficients of less than 0.5 when comparing observed and predicted tracer concentrations (e.g., Hanna, 1989).

5. Discussion

Fig. 5. Scatter plot of measured versus ANN (J) and ARIMA (+) simulated tracer concentrations at six monitoring stations for daily averages case.

Since ANNs are relatively new to the area of air dispersion modeling, we include the results of a elementary modeling work using more traditional statistical techniques: time series and multivariate linear regression. The purpose of this section, however, is to develop a preliminary understanding of the differences in performance and applicability between the ANN and classical statistical models. A rigorous comparison of the ANN and statistical methods’ performance is beyond the scope of this paper. The main conclusion of this discussion is that for this particular problem and data the ANN performed better and allowed for long-range predictions that were virtually impossible with time series and linear regression methods. We used two models to fit the hourly tracer data. The first was a time series ARIMA model. Following the

Fig. 6. Measured (solid) versus ANN-modeled (dashed line) hourly tracer concentration at MEAD station for the training set (first 85% of data).

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Fig. 7. Measured (circles) versus ANN (solid line), ANN one-by-one (dashed line), and ARIMA (dotted line) modeled hourly tracer concentration at MEAD station for the testing set (last 15% of data).

ANN approach, we divided the concentration data into two sets: the training and the test set. We first fit the training data set (the first 242 observations) with an ARIMA model. To choose the model, we applied time series fitting techniques to estimate the parameters and order of the ARIMA for the tracer concentration. The only information used for this work was the tracer concentration measured at different times. We did not use any of the meteorological variables in the time series model fitting. After checking the autocorrelation function and Akaike Information Criterion (see Box et al., 1994), we settled on the following ARIMA(6,0,4) model: Xt þ 0:09Xt1 þ 0:19Xt2  0:24Xt3  0:18Xt4  0:45Xt5 þ 0:05Xt6 ¼ et þ 1:13et1 þ 1:21et2 þ 0:84et3 þ 0:45et4 ; where Xt is the concentration at time t and et is a white noise (innovation) process. To examine the fit of this model, we computed one-step forward forecasts of the training data. Results of this phase of modeling correspond to the fit of the ANN to the training data. The mean error and error standard deviation of the onestep ARIMA forecasts were 0.66 and 0.71, respectively.

The second step was to use the ARIMA model to forecast the rest of the observations (test data). ARIMA models, unlike ANNs, are generally not used for longterm prediction; therefore, we use the model for one-step forecasts as if the observations were becoming available one at a time. Each time we had a new data point, we refitted it to the model and forecasted the next concentration. We applied this iterative forecasting to the entire test data set (43 observations). To be able to compare the two methods, we used the same procedure to train and test the ANN one step at a time (referred to in the figures as ANN one-by-one). The results are shown in Figs. 7 and 8. Correlation coefficients between the measured and modeled concentrations for the ARIMA and ANN models were 0.88 and 0.98, respectively, while the average error for ARIMA was 0.95 and for the ANN it was 0.33. Even though the ANN underpredicted high peaks in concentration, it performed better for medium and small values and did not feature a lag relative to measured values. The longterm ANN model yielded a correlation coefficient and average error of 0.896 and 0.96, respectively. As can be seen from the figures and from a comparison of the correlation coefficients and average errors, ARIMA results are more comparable to the long-term ANN

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Fig. 8. Scatter plot of measured versus ANN (J), ANN one-by-one (&), and ARIMA (+) simulated tracer concentrations at MEAD monitoring station for hourly averages case.

prediction, proving the superiority of the ANN method for both short- and long-term predictions. The second model applied to hourly data was a multivariate linear regression of the tracer concentration on all meteorological variables recorded in the experiment. Since the concentration data exhibited quite high volatility suggesting nonlinear behavior, multivariate linear regression performed poorly, as expected. For the daily data set we followed the ANN ‘‘leaveone-out’’ approach and used ARIMA models to estimate the removed observations. Since the data set was short, the time series model performed worse than the ANN, as expected (Figs. 4 and 5). The average errors for the ANN model varied between 0.006 and 0.13, while the average errors for the ARIMA models varied between 0.03 and 0.4.

6. Conclusions Most of the research in the area of using ANNs in air pollution modeling focused on atmospheric pollutants, where atmospheric chemistry plays an important role in the lifecycle of the pollutants and therefore predictions of their concentration. Simulation of tracers simplifies

the modeling process and enables us to separate the roles of meteorological parameters (which are generally available) and previous measured tracer concentrations as the main transport and dispersion driving force (one would include emission rate, but in this study the rate was constant). The ANN method has been applied to relatively lowresolution data (daily averagesFshort time series) and high temporal resolution data (hourly averagesFlong time series). The application of the ANN to daily averages yielded very good agreement between the measured and simulated concentrations; however, the results are somewhat artificial since, due to the small number of samples, the measured concentrations were three-point averaged and the ‘‘leave-one-out’’ method was used. Also, the test set is actually ‘‘an optimizing’’ set of data, because it is used to prevent overtraining during the learning process. The results on the optimizing set are usually slightly better than on a test set that was not used at all during the training process. This is also true for the hourly averages data set. For the reliable test of the method, a database with at least a year of data would be more appropriate. The application of the ANN to hourly averages allowed for a relatively large number of input data

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points, but the averaging interval is much shorter than the usual travel time of tracers between the source and the receptors. This results in the unknown and temporary variable lag in determining cause and effect. However, the inclusion of other data inputs in the area facilitated a representativeness of the overall atmospheric conditions and allowed the ANN to implicitly include complex information on linking a source and a receptor for different weather patterns. It appears that information on the previous spatial structure of the transport and dispersion is essential to a high level of agreement between the ANN-simulated and observed tracer concentrations in this type of complex terrain. The significant improvement in the ANNs success in simulating transport and dispersion using previous tracer concentrations is based on the fact that the final concentration represents all intrinsic information on atmospheric and dispersion processes in complex terrain that are not measurable with standard and even expanded (but still limited) field programs. The ANN method has been compared with the multivariate linear regression and ARIMA time series statistical methods. It should be emphasized that the main advantage of an ANN for this application is its capability to perform very good long-term forecasting and prediction on short data sets. The time series models are generally not applicable for over 40 time steps forward prediction and perform poorly on small data sets. An advantage of statistical models is their inherent capacity for quantification and estimation of confidence bounds for the prediction errors. They are also somewhat faster in implementation than ANN. We believe that the ANN approach was more satisfactory than ARIMA or multivariate linear regression for our study problem. The study results indicate that an ANN can be a valuable and efficient modeling tool in simulating the transport and dispersion of tracers in complex terrain.

Acknowledgements This study was partially supported by the Department of Defense, Office of Naval Research, Marine Meteorology and Atmospheric Effects, Grant N00014-96-11235. We would like to thank Dr. Sushil Louis and Dr. Carl Looney of the University of Nevada at Reno, NV, for their valuable comments and Mr. Travis McCord for technical and editorial assistance.

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