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Assessment of Lagrangian particle dispersion model “LAPMOD” through short range field tracer test in complex terrain
Journal of Environmental Radioactivity 205–206 (2019) 34–41
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Assessment of Lagrangian particle dispersion model “LAPMOD” through short range field tracer test in complex terrain
T
Amin ul Haq∗, Qaisar Nadeem, Amjad Farooq, Naseem Irfan, Masroor Ahmad, Muhammad Rizwan Ali Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, Islamabad, Pakistan
ARTICLE INFO
ABSTRACT
Keywords: Atmospheric pollutant dispersion modeling Field tracer test in complex terrain Lagrangian particle models LAPMOD
In this paper the mesoscale application of the 3D Lagrangian particle dispersion model LAPMOD has been assessed for a field tracer test performed in a short-range complex terrain. The meteorological input was provided through the diagnostic model CALMET, the meteorological pre-processor of the CALPUFF model. The CALMET/LAPMOD coupled system was used to simulate the hourly averaged ground level concentration at 47 discrete receptors. The LAPMOD model has a general tendency to slightly underestimate the hourly averaged ground-level concentrations. A Q-Q plot shows that the predicted concentration distribution has a good comparison with observed one. The Robust Highest Concentration (RHC) indicates that the LAPMOD model slightly underestimates the simulated peak concentration in short-term release conditions. The Fractional Bias (FB), Normalized Mean Squared Error (NMSE), Factor of Two (FAC2), Factor of Four (FAC4) and Factor of Exceedance (FOEX) statistical indices were calculated. The predicted results by LAPMOD are generally in good agreement with observed ones and the model is justified for the use in complex terrain for short-term near-field applications.
1. Introduction The Lagrangian particle dispersion (Monte Carlo or random walk) technique is widely used for modeling of hazardous air pollutants transport over complex terrain. The advancement of computational resources in terms of speed and performance as well as big data processing and storage has made possible the use of Lagrangian Particle Dispersion Models (LPDMs) for real time applications. This technique is capable of incorporating turbulent, non-homogeneous real time wind flow and consequently the pollutant dispersion over complex terrain (Basit et al., 2008). LPDMs are typically used for long-range applications which require a large number of particles to be released and hence have greater computational space and cost. However the computational cost is independent of output grid resolution, which makes them favorable for short-range applications as compared to high-resolution gridded computations (Leelőssy et al., 2014). LPDMs are based on releasing a large number of independent “fictitious” particles, each representing a fraction of the total released mass (Daly and Zannetti, 2007). The motion of Lagrangian particles is driven by the wind field which is divided into mean (deterministic) and turbulent (stochastic) components. The turbulent component describes the fluctuation in
∗
wind field due to atmospheric turbulence. The mean wind component is derived from a prognostic or diagnostic meteorological model and causes the advection of plume. The turbulent component is simulated using nonlinear Langevin stochastic differential equation and determines the horizontal and vertical mixing through diffusion (Leelőssy et al., 2017). Lagrangian particle models consider spatial and temporal variations in wind fields; therefore these models give better outputs than steady state Gaussian plume model for near sources as well as long range transport (greater than 10 Km). Lagrangian stochastic models are currently used to simulate atmospheric transport and dispersion of air pollutants on scales ranging from meters to hundreds of kilometers (Thomson and Wilson, 2012). Lagrangian stochastic models do not depend upon the computational grid. Therefore these models provide high resolution simulation constrained by the number of particles released in domain and non-availability of meteorological fields at high resolution. The conceptual simplicity and ability to incorporate high temporal and spatial variations in the meteorological field are among the key advantages of using Lagrangian particle dispersion model over complex terrain (Rao, 1999). In the past two decades, Computational Fluid Dynamics (CFD) tools have been extensively used as an emergent
Corresponding author. DNE, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, Islamabad, Pakistan. E-mail address: [email protected] (A.u. Haq).
https://doi.org/10.1016/j.jenvrad.2019.04.015 Received 12 March 2019; Received in revised form 24 April 2019; Accepted 29 April 2019 Available online 13 May 2019 0265-931X/ © 2019 Published by Elsevier Ltd.
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simulation technique for atmospheric dispersion modeling in urban complex terrain. CFD can simulate small scale changes in fluid properties like velocity and concentration along flow streamlines therefore it is very effective in presence of obstacles and resolving sub-grid scale complex terrain features (Labovský and Jelemenský, 2013). However, it is computationally more expensive than the Gaussian puff and Lagrangian particle models. Similarly, it is challenging to simulate several physical processes such as boundary layer stratification, buoyancy and chemical transformation etc. in the CDF model, while they can be easily applied in the operational models. One of the available LPDMs is LAPMOD, which is a 3D non-steady state Lagrangian particle dispersion model. LAPMOD can simulate the dispersion of inert and radioactive gases and aerosols over complex terrain. LAPMOD is currently an open source and freely available model. Development of basic formulations for LAPMOD and inclusion of different modules from time to time in order to incorporate different chemical and physical processes has been discussed in detail by R. Bellasio et al. (2017). The LAPMOD code, pre-processors and postprocessor are available at Enviroware's website (https://www. enviroware.com/lapmod). The model has the capability to simulate both dry and wet depositions, radioactive decay and also has a module for dispersion of odor. A source attribution tool was developed for LAPMOD by Bonafè et al. (2016) to assess the origin of air pollutants at receptor locations. The LAPMOD modeling system has multiple options for meteorological data input. An important feature of this model is that it can be interfaced with the diagnostic model CALMET (Scire et al., 2000), which is a meteorological pre-processor of the CALPUFF dispersion model. LAPMOD has its own meteorological pre-processor LAPMET, which takes input from AERMET (U.S. EPA, 2018a, 2018b) (AERMOD meteorological pre-processor). The AERMET generates the surface and upper air meteorological profile at single grid point. Therefore, the LAPMET produce meteorological fields which are horizontally homogenous but vary the in the vertical direction. LAPMET is used for simple applications over flat homogenous terrain or where dense meteorological data is not available. CALMET is preferred when 3D meteorological fields are required to simulate the non-homogenous conditions such as in complex terrain. A brief symbolic description of various internal and externally attachable modules and subroutines to LAPMOD along with pre-processors and post processor is summarized in Fig. 1. The plume rise calculation is fundamental in atmospheric dispersion modeling. The plume rise is determined by buoyancy flux and momentum flux. Buoyancy flux is calculated from temperature difference between released gas and atmosphere, exit velocity of the gas and the stack diameter. The momentum flux is proportional to the exit velocity and the stack diameter. Different algorithms have been developed to calculate the plume rise in the atmospheric dispersion modeling. They can be categorized into analytical, semi-empirical and numerical algorithms. In the LAPMOD model, plume rise can be estimated using two different numerical algorithms proposed by Janicke (Janicke and Janicke, 2001) (JJ) and Webster et al. (Webster and Thomson, 2002) (WT). The numerical algorithms solve the differential equations for conservation of mass, energy and momentum representing emissions from the stack to calculate the plume rise (Bellasio et al., 2018). The numerical algorithms do not consider constant input variable (e.g., wind speed, temperature) in contrary to analytical or semi-empirical algorithms. The JJ algorithm also solves equation for mass conservation of water and is more suitable for wet plumes. When the wind speed is higher than the gas exit velocity, the ground level concentration close to the stack will increase due to stack wake effect. In such case the model considers the stack tip downwash using Briggs (Hanna et al., 1982) algorithm. Partial plume penetration in case of an elevated inversion is simulated using Manins algorithm (Manins, 1979). LAPMOD can consider multiple point, line, area and volume sources with varying emission rates (from 1 s to 1 h) for different air pollutants. Normally the ‘box counting technique’ is used in a LPDM to calculate the
concentration at any receptor position. In this methodology, the concentration is estimated by counting the number of particles enclosed in a ‘box’ centered at the receptor and then dividing the total mass of those particles by the box volume. For this method, a large number of particles are needed which may result in a large computational time and cost. An alternative method for estimating concentrations in a typical LPDM is the ‘kernel density estimator’. In this method, the mass of particle is assumed to be spread in space following some density distribution. This density distribution having center of mass at particle position is called density kernel. The kernel density estimator for concentration calculations require less number of particles and supports grid free computations and hence results in an economy of computational time. Using the kernel density estimator the concentration (c ) at position x i is given by (De Haan, 1999)
c (X ) =
1 nh
n
K
X
i=1
xi h
(1)
Where n is number of particle of equal mass, K is the kernel function representing the spatial distribution of mass associated with each particle and h is the smoothing parameter called bandwidth of kernel. LAPMOD incorporates different types of formulations for the calculation of K (kernel function) for example Gaussian kernel, uniform kernel and parabolic kernel (Bellasio et al., 2017). Implementation of different kernels in Lagrangian particle models and estimation of the bandwidth has been investigated in literature (De Haan, 1999; Monforti et al., 2006; Vitali et al., 2006). Only a few studies have been conducted so far to validate the LAPMOD modeling system against experimental datasets. The performance of the model was evaluated by Bellasio et al. (2017) against Kincaid datasets (Olesen, 2005) for short-term and long-term release of SF6 and SO2 respectively. Overall, the model shows good results and its ability to be used for regulatory purposes may be justified, when compared to Kincaid dataset. Recently the incorporation of two plumerise algorithms in LAPMOD and its impact on concentration has been studied by Bellasio et al. (2018) using the Indianapolis (Olesen, 2005) and Kincaid tracer field datasets. The purpose of this present study is to further investigate the application of LAPMOD over highly complex terrain for regulatory and operational purposes and its validation through short range tracer field experiment dataset. 2. Methodology 2.1. Field tracer test The field tracer test was conducted in a rural hilly area east of Islamabad (33.72⁰ N, 73.38⁰ E) on 21st April 2018. Fig. 2 depicts the topography of the site, receptors positions and source location during the tracer test. The highest sampling point is at 3707 feet while the source elevation above mean sea level is 2533 feet. As shown in Fig. 3, most of the receptors are at a height greater than source elevation, therefore representing highly complex terrain. Some of the receptors were located in a deep valley away from the source. Due to the uneven ground level and forest land, discrete receptors were selected on the basis of prevailing wind direction forecasted from a high-resolution WRF model. The 47 discrete receptors were deployed within 16 square kilometers of area in a radius of 8 km from the source location. The wind field typically is highly transitional during day time, therefore a suitable time for release was selected when the wind direction was from the southwest. The average wind speed at the source was 2.48 m/s during the experiment. During the test, a passive tracer gas sulfur hexafluoride (SF6) was released continuously at an average rate of 8 g/s for two hours (0700UTC to 0900UTC) from a height of 75 ft above ground level. Three samples were collected at each receptor in order to have hourly averaged concentrations for comparison with model 35
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Fig. 1. Data flow chart of LAPMOD modeling system.
predicted values. All samples were collected using two Litre bags through automated air sampling devices. The distance between most adjacent receptors was almost 500 m. Sampling was started with a time delay (calculated from wind speed and distance) to ensure that released gas may arrive and get collected at each sampling point. Highly sensitive Gas Chromatography with Electron Capture Detector (GC-ECD) was used to analyze the samples.
processes of convection and moisture and PBL schemes for turbulent mixing through entire planetary boundary layer (Skamarock et al., 2005). The input parameters for WRF model are given in Table 1. 2.3. Configuration of CALMET The center of the output domain in CALMET was set at the release point (33.71 °N, 73.35 °E). The model output domain was taken as (20 km × 20 km) with grid spacing of 300 m and 11 vertical layers with cell heights (meters) at 0, 20, 40, 80, 160, 320, 640, 1200, 2000, 3000 and 4000. The Shuttle Radar Topography Mission version 2 (SRTM3) dataset (Farr et al., 2007), having global coverage of terrain elevation at 90 m resolution, was used as input to CALMET. Global Land Cover Characterization (GLCC) (U.S. Geological Survey, 2010) is a series of global land cover classification dataset (1-km) and was used as input for land use/land cover (LULC) in CALMET. The gridded surface, upper air and precipitation data was provided by WRF. CALMET was set to calculate the 3D wind field, temperature and micrometeorological variables required by CALPUFF. The 10 m wind fields and wind directions simulated by CALMET are given in Fig. 5.
2.2. WRF model configuration The meso-scale prognostic model WRF was interfaced with the diagnostic model CALMET, a meteorological pre-processor of CALPUFF, to generate meteorological input for LAPMOD. To resolve the smallscale topographical features in complex terrain, WRF was configured with a grid resolution of 1 km. Four nested domains d01, d02, d03 and d04 are shown in Fig. 4 having grid resolutions of 27 km, 9 km, 3 km and 1 km respectively and 35 vertical sigma levels were defined. The domains d01, d02, d03 and d04 had (49 × 49), (61 × 61), (76 × 76) and (121 × 121) grid cells respectively. The model was initialized with 6 hourly (1° × 1°) resolution National Center for Environmental Prediction (NCEP) FNL dataset (NCEP, 2000). The simulation was initiated at 0000UTC on 20th April 2018 and was integrated for a period of 48 h. WRF model has different physics schemes for simulation atmospheric processes in planetary boundary layer (PBL). The WRF physics schemes include microphysics, short and long wave radiation, cumulus physics, PBL, surface layer (SL) and land surface. All schemes are responsible for parameterization of different atmospheric processes. Microphysics scheme is responsible for vapor, cloud and precipitation processes, radiation schemes for downward and upward radiation fluxes causing earth heating and cooling, cumulus for sub-grid scale
2.4. LAPMOD model The LAPMOD model was configured for calculation of the hourlyaveraged ground-level concentrations of SF6 gas. The particle positions were recorded during the simulation in order to plot the plume trajectory. Dry and wet deposition was not considered and SF6 was assumed to be chemically inert. The model was given input from the high grid resolution (300 m) data obtained from CALMET in order to accurately simulate the subgrid scale topographical features and wind field 36
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Fig. 2. The receptors and source location at the experiment site.
Fig. 3. Terrain elevation contours for study domain.
37
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Fig. 4. WRF nested domains.
2004; Hanna, 1993, 1988) have discussed calculation of several statistical indices e.g., Fractional Bias (FB), Normalized Mean Square Error (NMSE), Factor of 2 (FAC2), Factor of 4 (FAC4) and Factor of Exceedance (FOEX) for model performance evaluation. FB measures the difference between the simulated and observed mean value. It gives measure of systematic error of the model. Its value ranges between +2 and −2. The value of FB = 0.67 imply a factor of two over-prediction and FB = −0.67 represent under-prediction by a factor of two. NMSE represents the measure of random scatter in the concentration distribution about mean value and represents both systematic and random errors. For an ideal model the FB and the NMSE are equal to zero. Factor of Exceedance (FOEX) quantifies the magnitude of over-prediction or under-prediction of a model. Its value ranges between −50% and +50%. FAC2 represents the fraction of simulated concentration values that are lying within a factor of 2 of measured values through observation (Giaiotti et al., 2018). Let Cp and Co represent model predicted and experimentally measured concentrations respectively and C¯
Table 1 Configuration of WRF model. Name
Description
Dynamics Horizontal resolution Map projection Vertical levels cumulus option Radiation
non hydrostatic D01:27 km, D02:9 km, D03:3 km, D04:1 km Mercator 35 eta levels. Kain-Fritsch (new Eta) scheme for D01and D02 only. RRTM scheme for longwave radiation Dudhia scheme for shortwave radiation Noah Land-Surface Model (no. of soil layers = 4) SL = MM5 Similarity WRF Single-Moment (WSM) 3-class simple ice scheme ACM2
Land-surface process Surface layer scheme Microphysics Boundary layer
pattern in inhomogeneous meteorological conditions over complex terrain. The simulation started at 1200 PST and ended at 1400 PST on 21st April 2018. The hourly output from CALMET was further interpolated to have higher temporal resolution (300s) in order to resolve small variations in the wind field and other meteorological variables. During the simulation, 60 ‘fictitious’ particles per minute were released. The source parameters were selected the same as in the real-time experiment (variable, point, elevated source). The general input parameters were set to defaults as recommended by (Bellasio et al., 2018, 2017).
is the average overall data. The formulas for these statistical tools are given by Equations (2)–(5).
FB
=
Cp
Co
0.5(Cp + Co )
(2)
Cp ) 2 C¯ 0 C¯p
(3)
NMSE =
(C0
N(Cp > Co)
2.5. Statistical analysis for model performance evaluation
FOEX =
In order to evaluate the performance of dispersion model and its suitability for operational and regulatory purposes, statistical tests were performed. Hanna et al. (Chang and Hanna, 2005; Chang and Hanna,
FAC2 = fraction of data with 0.5
38
N
0.5 × 100
(4)
Cp C0
2.0
(5a)
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Fig. 5. (a) Wind field at 10 m (b) Wind rose at the site during experiment.
Chang and Hanna (2005) have defined the criterion for a ‘good’ model as: 1. The fraction of predicted values within a factor of two of observed values should be above 50% (FAC2 > 50%) 2. Bias should be within ± 30% of the mean i.e., |FB| < 0.3 3. NMSE < 1.5 In scatter plot the paired (in time or space) observed and predicted concentrations are plotted against each other which qualitatively give measure of under-prediction or over-prediction. The under or overprediction of the model can be examined visually using scatter plot. If the atmospheric dispersion model is intended to be used for operational purposes, then its compliance to air quality regulations is determined. For this purpose the highest short-term concentrations are studied for potential Exceedance from threshold values irrespective of time and location (Chang and Hanna, 2005). The Q-Q plot gives a measure of how closely the predicted concentration distribution is following the observed one especially for high concentration values. The Q-Q plot is created by first sorting the predicted and observed concentrations by rank and then plotting the quantiles against each other. In Q-Q plot the predicted and observed concentrations are no longer paired in time or space (U.S. EPA, 2003). Another statistical measure is the Robust Higher Concentration (RHC) which shows the model's ability to predict the highest concentrations which are of concern for regulatory purposes. The RHC is calculated as:
RHC = X (N ) + [X¯
X (N )] × ln
3N
1 2
Fig. 6. Fractional difference of predicted and observed hourly averaged SF6 concentration at sampling points (receptor 1 is closest to the source).
Fractional Difference =
Cp
Co (6)
Co
The pattern of fractional difference plot shows that the model has a tendency to slightly underestimate the concentrations. The fractional difference is small at most of the receptors indicating good performance of LAPMOD in simulating ground-level concentration over complex terrain. At receptors close to the source, the model predicted higher
(5b)
Where X (N ) is the Nth largest value, X¯ represents the average of N-1 largest values in dataset, N is the number of highest concentration values in dataset exceeding a predefined limit (Cox and Tikvart, 1990).
Table 2 Statistical index for LAPMOD.
3. Results and discussions Fig. 6 shows the fractional difference plot between predicted and observed hourly averaged ground level concentration. The fractional difference was calculated to compare the predicted (Cp ) and observed (Co ) concentration at each receptor location. 39
Statistical index
Value
Fractional Bias NMSE FAC2 FAC4 FOEX RHC
−0.15 0.30 74.46% 97.87% −3.19 0.97
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shown in Fig. 8, at concentrations ranging from 150 ppt to 300 ppt, the Q-Q plot becomes parallel to x = y line which indicates that model performs better and shows unbiased results at these concentrations. At lower and higher concentrations part of frequency distribution, the model under-predicts within a factor of 2. A theoretical perfect model should ideally reproduce the temporal and spatial distribution of the observed concentrations, in this way it will automatically reproduce the cumulative distribution of the observations. The opposite is not always true. For example, considering the time trend at a fixed point, observations and predictions might have the same maximum value, but predicted at different times. Or, considering a specific time, the map obtained from observations and the one obtained from predictions might show the same maximum value, but at different points. The objective of dispersion models used for regulatory purposes is to simulate accurately the concentration distribution obtained from observation specifically at high end concentration rather than the spatial or temporal distribution of concentration (Venkatram et al., 2001). From regulatory point of view this is a plus point for LAPMOD that it is depicting close to real values of peak concentrations.
Fig. 7. Scatter plot of observed versus predicted concentrations. Solid blue lines indicate FAC2 while dotted lines indicate FAC4 region. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
4. Conclusions The performance of the Lagrangian particle dispersion model LAPMOD was assessed through a short-range field tracer experiment performed over a complex terrain. The model was interfaced with CALMET, a meteorological pre-processor of the CALPUFF model. Highresolution meteorological and geographical input enabled the model to accurately resolve subgrid scale terrain features and simulate particle trajectories. The model was able to accurately simulate the hourly averaged ground level concentrations. LAPMOD has general tendency to slightly underestimate concentrations over complex terrain, especially for receptors located in a deep valley. The statistical analysis shows that the model fulfills the criterion for a ‘good’ dispersion model. The FB (0.15), NMSE (0.3) and FAC2 (74.46%) show that LAPMOD has the capability to be used for simulation of ground level concentrations in near-field complex terrain. The Q-Q plot reflected a close compliance the predicted and observed concentrations. The model also predicted the high-end concentrations (RHC = 0.97) with a slight under-prediction, but still within acceptable range. References
Fig. 8. The Q-Q plot of predicted versus observed concentrations.
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research-notes.dmu.dk. Rao, K.S., 1999. Lagrangian stochastic modeling of dispersion in the stable boundary layer. Boundary-Layer Meteorol. 90, 541–549. https://doi.org/10.1023/ A:1001704928864. Scire, J.S., Robe, F.R., Fernau, M.E., Yamartino, R.J., 2000. A user ’s guide for the CALMET meteorological model (Version 5). Renew. Sustain. Energy Rev. 1–332. Skamarock, W.C., Klemp, J.B., Dudhi, J., Gill, D.O., Barker, D.M., Duda, M.G., Huang, X.Y., Wang, W., Powers, J.G., 2005. A description of the advanced research WRF version 2 NCAR technical note. Natl. Cent. Atmos. Res. 113. https://doi.org/10.5065/ D6DZ069T. Thomson, D.J., Wilson, J.D., 2012. History of Lagrangian stochastic models for turbulent dispersion. Geophys. Monogr. Ser. 200, 19–36. https://doi.org/10.1029/ 2012GM001238. U.S. EPA, 2018a. User's Guide for the AERMOD Meteorological Preprocessor (AERMET). EPA-454/B-18-002. U.S. EPA, 2018b. User's Guide for the AMS/EPA Regulatory Model (AERMOD). pp. 1–137 EPA-454/B-EPA-454/B-18-001. U.S. EPA, 2003. AERMOD: Latest Features and Evaluation Results. U.S. Environmental Protection Agency; Office of Air Quality Planning and Standards, Research Triangle Park, NC EPA-454/R-03-003. U.S. Geological Survey, 2010. Global land cover characterization program. https://doi. org/http://www.src.com/datasets/GLCC_Info_Page.html. Venkatram, A., Brode, R.W., Cimorelli, A., Lee, R., Paine, R., Perry, S., Peters, W., Weil, J., W, R., 2001. A complex terrain dispersion model for regulatory applications. Atmos. Environ. 35 (24), 4211–4221. https://doi.org/10.1016/S1352-2310(01)00186-8. Vitali, L., Monforti, F., Bellasio, R., Bianconi, R., Sachero, V., Mosca, S., Zanini, G., 2006. Validation of a Lagrangian dispersion model implementing different kernel methods for density reconstruction. Atmos. Environ. 40, 8020–8033. https://doi.org/10. 1016/j.atmosenv.2006.06.056. Webster, H.N., Thomson, D.J., 2002. Validation of a Lagrangian Model Plume Rise Scheme Using the Kincaid Data Set. Atmospheric Environment. https://doi.org/10. 1016/S1352-2310(02)00559-9.
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Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad
Assessment of Lagrangian particle dispersion model “LAPMOD” through short range field tracer test in complex terrain
T
Amin ul Haq∗, Qaisar Nadeem, Amjad Farooq, Naseem Irfan, Masroor Ahmad, Muhammad Rizwan Ali Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, Islamabad, Pakistan
ARTICLE INFO
ABSTRACT
Keywords: Atmospheric pollutant dispersion modeling Field tracer test in complex terrain Lagrangian particle models LAPMOD
In this paper the mesoscale application of the 3D Lagrangian particle dispersion model LAPMOD has been assessed for a field tracer test performed in a short-range complex terrain. The meteorological input was provided through the diagnostic model CALMET, the meteorological pre-processor of the CALPUFF model. The CALMET/LAPMOD coupled system was used to simulate the hourly averaged ground level concentration at 47 discrete receptors. The LAPMOD model has a general tendency to slightly underestimate the hourly averaged ground-level concentrations. A Q-Q plot shows that the predicted concentration distribution has a good comparison with observed one. The Robust Highest Concentration (RHC) indicates that the LAPMOD model slightly underestimates the simulated peak concentration in short-term release conditions. The Fractional Bias (FB), Normalized Mean Squared Error (NMSE), Factor of Two (FAC2), Factor of Four (FAC4) and Factor of Exceedance (FOEX) statistical indices were calculated. The predicted results by LAPMOD are generally in good agreement with observed ones and the model is justified for the use in complex terrain for short-term near-field applications.
1. Introduction The Lagrangian particle dispersion (Monte Carlo or random walk) technique is widely used for modeling of hazardous air pollutants transport over complex terrain. The advancement of computational resources in terms of speed and performance as well as big data processing and storage has made possible the use of Lagrangian Particle Dispersion Models (LPDMs) for real time applications. This technique is capable of incorporating turbulent, non-homogeneous real time wind flow and consequently the pollutant dispersion over complex terrain (Basit et al., 2008). LPDMs are typically used for long-range applications which require a large number of particles to be released and hence have greater computational space and cost. However the computational cost is independent of output grid resolution, which makes them favorable for short-range applications as compared to high-resolution gridded computations (Leelőssy et al., 2014). LPDMs are based on releasing a large number of independent “fictitious” particles, each representing a fraction of the total released mass (Daly and Zannetti, 2007). The motion of Lagrangian particles is driven by the wind field which is divided into mean (deterministic) and turbulent (stochastic) components. The turbulent component describes the fluctuation in
∗
wind field due to atmospheric turbulence. The mean wind component is derived from a prognostic or diagnostic meteorological model and causes the advection of plume. The turbulent component is simulated using nonlinear Langevin stochastic differential equation and determines the horizontal and vertical mixing through diffusion (Leelőssy et al., 2017). Lagrangian particle models consider spatial and temporal variations in wind fields; therefore these models give better outputs than steady state Gaussian plume model for near sources as well as long range transport (greater than 10 Km). Lagrangian stochastic models are currently used to simulate atmospheric transport and dispersion of air pollutants on scales ranging from meters to hundreds of kilometers (Thomson and Wilson, 2012). Lagrangian stochastic models do not depend upon the computational grid. Therefore these models provide high resolution simulation constrained by the number of particles released in domain and non-availability of meteorological fields at high resolution. The conceptual simplicity and ability to incorporate high temporal and spatial variations in the meteorological field are among the key advantages of using Lagrangian particle dispersion model over complex terrain (Rao, 1999). In the past two decades, Computational Fluid Dynamics (CFD) tools have been extensively used as an emergent
Corresponding author. DNE, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, Islamabad, Pakistan. E-mail address: [email protected] (A.u. Haq).
https://doi.org/10.1016/j.jenvrad.2019.04.015 Received 12 March 2019; Received in revised form 24 April 2019; Accepted 29 April 2019 Available online 13 May 2019 0265-931X/ © 2019 Published by Elsevier Ltd.
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simulation technique for atmospheric dispersion modeling in urban complex terrain. CFD can simulate small scale changes in fluid properties like velocity and concentration along flow streamlines therefore it is very effective in presence of obstacles and resolving sub-grid scale complex terrain features (Labovský and Jelemenský, 2013). However, it is computationally more expensive than the Gaussian puff and Lagrangian particle models. Similarly, it is challenging to simulate several physical processes such as boundary layer stratification, buoyancy and chemical transformation etc. in the CDF model, while they can be easily applied in the operational models. One of the available LPDMs is LAPMOD, which is a 3D non-steady state Lagrangian particle dispersion model. LAPMOD can simulate the dispersion of inert and radioactive gases and aerosols over complex terrain. LAPMOD is currently an open source and freely available model. Development of basic formulations for LAPMOD and inclusion of different modules from time to time in order to incorporate different chemical and physical processes has been discussed in detail by R. Bellasio et al. (2017). The LAPMOD code, pre-processors and postprocessor are available at Enviroware's website (https://www. enviroware.com/lapmod). The model has the capability to simulate both dry and wet depositions, radioactive decay and also has a module for dispersion of odor. A source attribution tool was developed for LAPMOD by Bonafè et al. (2016) to assess the origin of air pollutants at receptor locations. The LAPMOD modeling system has multiple options for meteorological data input. An important feature of this model is that it can be interfaced with the diagnostic model CALMET (Scire et al., 2000), which is a meteorological pre-processor of the CALPUFF dispersion model. LAPMOD has its own meteorological pre-processor LAPMET, which takes input from AERMET (U.S. EPA, 2018a, 2018b) (AERMOD meteorological pre-processor). The AERMET generates the surface and upper air meteorological profile at single grid point. Therefore, the LAPMET produce meteorological fields which are horizontally homogenous but vary the in the vertical direction. LAPMET is used for simple applications over flat homogenous terrain or where dense meteorological data is not available. CALMET is preferred when 3D meteorological fields are required to simulate the non-homogenous conditions such as in complex terrain. A brief symbolic description of various internal and externally attachable modules and subroutines to LAPMOD along with pre-processors and post processor is summarized in Fig. 1. The plume rise calculation is fundamental in atmospheric dispersion modeling. The plume rise is determined by buoyancy flux and momentum flux. Buoyancy flux is calculated from temperature difference between released gas and atmosphere, exit velocity of the gas and the stack diameter. The momentum flux is proportional to the exit velocity and the stack diameter. Different algorithms have been developed to calculate the plume rise in the atmospheric dispersion modeling. They can be categorized into analytical, semi-empirical and numerical algorithms. In the LAPMOD model, plume rise can be estimated using two different numerical algorithms proposed by Janicke (Janicke and Janicke, 2001) (JJ) and Webster et al. (Webster and Thomson, 2002) (WT). The numerical algorithms solve the differential equations for conservation of mass, energy and momentum representing emissions from the stack to calculate the plume rise (Bellasio et al., 2018). The numerical algorithms do not consider constant input variable (e.g., wind speed, temperature) in contrary to analytical or semi-empirical algorithms. The JJ algorithm also solves equation for mass conservation of water and is more suitable for wet plumes. When the wind speed is higher than the gas exit velocity, the ground level concentration close to the stack will increase due to stack wake effect. In such case the model considers the stack tip downwash using Briggs (Hanna et al., 1982) algorithm. Partial plume penetration in case of an elevated inversion is simulated using Manins algorithm (Manins, 1979). LAPMOD can consider multiple point, line, area and volume sources with varying emission rates (from 1 s to 1 h) for different air pollutants. Normally the ‘box counting technique’ is used in a LPDM to calculate the
concentration at any receptor position. In this methodology, the concentration is estimated by counting the number of particles enclosed in a ‘box’ centered at the receptor and then dividing the total mass of those particles by the box volume. For this method, a large number of particles are needed which may result in a large computational time and cost. An alternative method for estimating concentrations in a typical LPDM is the ‘kernel density estimator’. In this method, the mass of particle is assumed to be spread in space following some density distribution. This density distribution having center of mass at particle position is called density kernel. The kernel density estimator for concentration calculations require less number of particles and supports grid free computations and hence results in an economy of computational time. Using the kernel density estimator the concentration (c ) at position x i is given by (De Haan, 1999)
c (X ) =
1 nh
n
K
X
i=1
xi h
(1)
Where n is number of particle of equal mass, K is the kernel function representing the spatial distribution of mass associated with each particle and h is the smoothing parameter called bandwidth of kernel. LAPMOD incorporates different types of formulations for the calculation of K (kernel function) for example Gaussian kernel, uniform kernel and parabolic kernel (Bellasio et al., 2017). Implementation of different kernels in Lagrangian particle models and estimation of the bandwidth has been investigated in literature (De Haan, 1999; Monforti et al., 2006; Vitali et al., 2006). Only a few studies have been conducted so far to validate the LAPMOD modeling system against experimental datasets. The performance of the model was evaluated by Bellasio et al. (2017) against Kincaid datasets (Olesen, 2005) for short-term and long-term release of SF6 and SO2 respectively. Overall, the model shows good results and its ability to be used for regulatory purposes may be justified, when compared to Kincaid dataset. Recently the incorporation of two plumerise algorithms in LAPMOD and its impact on concentration has been studied by Bellasio et al. (2018) using the Indianapolis (Olesen, 2005) and Kincaid tracer field datasets. The purpose of this present study is to further investigate the application of LAPMOD over highly complex terrain for regulatory and operational purposes and its validation through short range tracer field experiment dataset. 2. Methodology 2.1. Field tracer test The field tracer test was conducted in a rural hilly area east of Islamabad (33.72⁰ N, 73.38⁰ E) on 21st April 2018. Fig. 2 depicts the topography of the site, receptors positions and source location during the tracer test. The highest sampling point is at 3707 feet while the source elevation above mean sea level is 2533 feet. As shown in Fig. 3, most of the receptors are at a height greater than source elevation, therefore representing highly complex terrain. Some of the receptors were located in a deep valley away from the source. Due to the uneven ground level and forest land, discrete receptors were selected on the basis of prevailing wind direction forecasted from a high-resolution WRF model. The 47 discrete receptors were deployed within 16 square kilometers of area in a radius of 8 km from the source location. The wind field typically is highly transitional during day time, therefore a suitable time for release was selected when the wind direction was from the southwest. The average wind speed at the source was 2.48 m/s during the experiment. During the test, a passive tracer gas sulfur hexafluoride (SF6) was released continuously at an average rate of 8 g/s for two hours (0700UTC to 0900UTC) from a height of 75 ft above ground level. Three samples were collected at each receptor in order to have hourly averaged concentrations for comparison with model 35
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Fig. 1. Data flow chart of LAPMOD modeling system.
predicted values. All samples were collected using two Litre bags through automated air sampling devices. The distance between most adjacent receptors was almost 500 m. Sampling was started with a time delay (calculated from wind speed and distance) to ensure that released gas may arrive and get collected at each sampling point. Highly sensitive Gas Chromatography with Electron Capture Detector (GC-ECD) was used to analyze the samples.
processes of convection and moisture and PBL schemes for turbulent mixing through entire planetary boundary layer (Skamarock et al., 2005). The input parameters for WRF model are given in Table 1. 2.3. Configuration of CALMET The center of the output domain in CALMET was set at the release point (33.71 °N, 73.35 °E). The model output domain was taken as (20 km × 20 km) with grid spacing of 300 m and 11 vertical layers with cell heights (meters) at 0, 20, 40, 80, 160, 320, 640, 1200, 2000, 3000 and 4000. The Shuttle Radar Topography Mission version 2 (SRTM3) dataset (Farr et al., 2007), having global coverage of terrain elevation at 90 m resolution, was used as input to CALMET. Global Land Cover Characterization (GLCC) (U.S. Geological Survey, 2010) is a series of global land cover classification dataset (1-km) and was used as input for land use/land cover (LULC) in CALMET. The gridded surface, upper air and precipitation data was provided by WRF. CALMET was set to calculate the 3D wind field, temperature and micrometeorological variables required by CALPUFF. The 10 m wind fields and wind directions simulated by CALMET are given in Fig. 5.
2.2. WRF model configuration The meso-scale prognostic model WRF was interfaced with the diagnostic model CALMET, a meteorological pre-processor of CALPUFF, to generate meteorological input for LAPMOD. To resolve the smallscale topographical features in complex terrain, WRF was configured with a grid resolution of 1 km. Four nested domains d01, d02, d03 and d04 are shown in Fig. 4 having grid resolutions of 27 km, 9 km, 3 km and 1 km respectively and 35 vertical sigma levels were defined. The domains d01, d02, d03 and d04 had (49 × 49), (61 × 61), (76 × 76) and (121 × 121) grid cells respectively. The model was initialized with 6 hourly (1° × 1°) resolution National Center for Environmental Prediction (NCEP) FNL dataset (NCEP, 2000). The simulation was initiated at 0000UTC on 20th April 2018 and was integrated for a period of 48 h. WRF model has different physics schemes for simulation atmospheric processes in planetary boundary layer (PBL). The WRF physics schemes include microphysics, short and long wave radiation, cumulus physics, PBL, surface layer (SL) and land surface. All schemes are responsible for parameterization of different atmospheric processes. Microphysics scheme is responsible for vapor, cloud and precipitation processes, radiation schemes for downward and upward radiation fluxes causing earth heating and cooling, cumulus for sub-grid scale
2.4. LAPMOD model The LAPMOD model was configured for calculation of the hourlyaveraged ground-level concentrations of SF6 gas. The particle positions were recorded during the simulation in order to plot the plume trajectory. Dry and wet deposition was not considered and SF6 was assumed to be chemically inert. The model was given input from the high grid resolution (300 m) data obtained from CALMET in order to accurately simulate the subgrid scale topographical features and wind field 36
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Fig. 2. The receptors and source location at the experiment site.
Fig. 3. Terrain elevation contours for study domain.
37
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Fig. 4. WRF nested domains.
2004; Hanna, 1993, 1988) have discussed calculation of several statistical indices e.g., Fractional Bias (FB), Normalized Mean Square Error (NMSE), Factor of 2 (FAC2), Factor of 4 (FAC4) and Factor of Exceedance (FOEX) for model performance evaluation. FB measures the difference between the simulated and observed mean value. It gives measure of systematic error of the model. Its value ranges between +2 and −2. The value of FB = 0.67 imply a factor of two over-prediction and FB = −0.67 represent under-prediction by a factor of two. NMSE represents the measure of random scatter in the concentration distribution about mean value and represents both systematic and random errors. For an ideal model the FB and the NMSE are equal to zero. Factor of Exceedance (FOEX) quantifies the magnitude of over-prediction or under-prediction of a model. Its value ranges between −50% and +50%. FAC2 represents the fraction of simulated concentration values that are lying within a factor of 2 of measured values through observation (Giaiotti et al., 2018). Let Cp and Co represent model predicted and experimentally measured concentrations respectively and C¯
Table 1 Configuration of WRF model. Name
Description
Dynamics Horizontal resolution Map projection Vertical levels cumulus option Radiation
non hydrostatic D01:27 km, D02:9 km, D03:3 km, D04:1 km Mercator 35 eta levels. Kain-Fritsch (new Eta) scheme for D01and D02 only. RRTM scheme for longwave radiation Dudhia scheme for shortwave radiation Noah Land-Surface Model (no. of soil layers = 4) SL = MM5 Similarity WRF Single-Moment (WSM) 3-class simple ice scheme ACM2
Land-surface process Surface layer scheme Microphysics Boundary layer
pattern in inhomogeneous meteorological conditions over complex terrain. The simulation started at 1200 PST and ended at 1400 PST on 21st April 2018. The hourly output from CALMET was further interpolated to have higher temporal resolution (300s) in order to resolve small variations in the wind field and other meteorological variables. During the simulation, 60 ‘fictitious’ particles per minute were released. The source parameters were selected the same as in the real-time experiment (variable, point, elevated source). The general input parameters were set to defaults as recommended by (Bellasio et al., 2018, 2017).
is the average overall data. The formulas for these statistical tools are given by Equations (2)–(5).
FB
=
Cp
Co
0.5(Cp + Co )
(2)
Cp ) 2 C¯ 0 C¯p
(3)
NMSE =
(C0
N(Cp > Co)
2.5. Statistical analysis for model performance evaluation
FOEX =
In order to evaluate the performance of dispersion model and its suitability for operational and regulatory purposes, statistical tests were performed. Hanna et al. (Chang and Hanna, 2005; Chang and Hanna,
FAC2 = fraction of data with 0.5
38
N
0.5 × 100
(4)
Cp C0
2.0
(5a)
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Fig. 5. (a) Wind field at 10 m (b) Wind rose at the site during experiment.
Chang and Hanna (2005) have defined the criterion for a ‘good’ model as: 1. The fraction of predicted values within a factor of two of observed values should be above 50% (FAC2 > 50%) 2. Bias should be within ± 30% of the mean i.e., |FB| < 0.3 3. NMSE < 1.5 In scatter plot the paired (in time or space) observed and predicted concentrations are plotted against each other which qualitatively give measure of under-prediction or over-prediction. The under or overprediction of the model can be examined visually using scatter plot. If the atmospheric dispersion model is intended to be used for operational purposes, then its compliance to air quality regulations is determined. For this purpose the highest short-term concentrations are studied for potential Exceedance from threshold values irrespective of time and location (Chang and Hanna, 2005). The Q-Q plot gives a measure of how closely the predicted concentration distribution is following the observed one especially for high concentration values. The Q-Q plot is created by first sorting the predicted and observed concentrations by rank and then plotting the quantiles against each other. In Q-Q plot the predicted and observed concentrations are no longer paired in time or space (U.S. EPA, 2003). Another statistical measure is the Robust Higher Concentration (RHC) which shows the model's ability to predict the highest concentrations which are of concern for regulatory purposes. The RHC is calculated as:
RHC = X (N ) + [X¯
X (N )] × ln
3N
1 2
Fig. 6. Fractional difference of predicted and observed hourly averaged SF6 concentration at sampling points (receptor 1 is closest to the source).
Fractional Difference =
Cp
Co (6)
Co
The pattern of fractional difference plot shows that the model has a tendency to slightly underestimate the concentrations. The fractional difference is small at most of the receptors indicating good performance of LAPMOD in simulating ground-level concentration over complex terrain. At receptors close to the source, the model predicted higher
(5b)
Where X (N ) is the Nth largest value, X¯ represents the average of N-1 largest values in dataset, N is the number of highest concentration values in dataset exceeding a predefined limit (Cox and Tikvart, 1990).
Table 2 Statistical index for LAPMOD.
3. Results and discussions Fig. 6 shows the fractional difference plot between predicted and observed hourly averaged ground level concentration. The fractional difference was calculated to compare the predicted (Cp ) and observed (Co ) concentration at each receptor location. 39
Statistical index
Value
Fractional Bias NMSE FAC2 FAC4 FOEX RHC
−0.15 0.30 74.46% 97.87% −3.19 0.97
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shown in Fig. 8, at concentrations ranging from 150 ppt to 300 ppt, the Q-Q plot becomes parallel to x = y line which indicates that model performs better and shows unbiased results at these concentrations. At lower and higher concentrations part of frequency distribution, the model under-predicts within a factor of 2. A theoretical perfect model should ideally reproduce the temporal and spatial distribution of the observed concentrations, in this way it will automatically reproduce the cumulative distribution of the observations. The opposite is not always true. For example, considering the time trend at a fixed point, observations and predictions might have the same maximum value, but predicted at different times. Or, considering a specific time, the map obtained from observations and the one obtained from predictions might show the same maximum value, but at different points. The objective of dispersion models used for regulatory purposes is to simulate accurately the concentration distribution obtained from observation specifically at high end concentration rather than the spatial or temporal distribution of concentration (Venkatram et al., 2001). From regulatory point of view this is a plus point for LAPMOD that it is depicting close to real values of peak concentrations.
Fig. 7. Scatter plot of observed versus predicted concentrations. Solid blue lines indicate FAC2 while dotted lines indicate FAC4 region. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
4. Conclusions The performance of the Lagrangian particle dispersion model LAPMOD was assessed through a short-range field tracer experiment performed over a complex terrain. The model was interfaced with CALMET, a meteorological pre-processor of the CALPUFF model. Highresolution meteorological and geographical input enabled the model to accurately resolve subgrid scale terrain features and simulate particle trajectories. The model was able to accurately simulate the hourly averaged ground level concentrations. LAPMOD has general tendency to slightly underestimate concentrations over complex terrain, especially for receptors located in a deep valley. The statistical analysis shows that the model fulfills the criterion for a ‘good’ dispersion model. The FB (0.15), NMSE (0.3) and FAC2 (74.46%) show that LAPMOD has the capability to be used for simulation of ground level concentrations in near-field complex terrain. The Q-Q plot reflected a close compliance the predicted and observed concentrations. The model also predicted the high-end concentrations (RHC = 0.97) with a slight under-prediction, but still within acceptable range. References
Fig. 8. The Q-Q plot of predicted versus observed concentrations.
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concentrations. The model under-predicted concentrations at remote receptors located in a valley. The other three indices (FB, NMSE and FAC2) indicate that the model meets the criterion for a ‘good’ model. Table 2 summarizes the statistics for 1 h averaged SF6 concentrations. The negative value of FB (−0.15) indicates that the model under-predicted the measured concentrations by 15%. The NMSE of 0.30 is well below the accepted threshold value which indicated little random scatter in data and hence implies good model performance. The FAC2 (74.46%) and FAC4 (97.87%) show that model was successful in accurately predicting 1-hr averaged ground level concentration at most of the receptor positions. The FOEX value of −3.19 shows that there is an overall slight underestimation by the model. The observed RHC was 428.65 as compared to model predicted RHC value of 417.77. The ratio of these two values is 0.97. The concentration scatter plot in Fig. 7 shows that approximately all the values (97.87%) are within the region of the dotted FAC4 lines while 74.46 per cent of the values are within the solid blue FAC2 lines. In the Q-Q plot shown in Fig. 8, the solid black line represents the exact agreement between measured and modelled concentrations while the solid blue lines give the acceptable FAC4 range. The predicted concentration distribution closely follows the observed one with a slight under-prediction while remaining within the acceptable range. As 40
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