PMF is a multivariate factor analysis tool that decomposes a matrix of speciated sample data into two matrices: factor contributions G and factor profiles F. These factor profiles need to be interpreted by the user to identify the source types that may be contributing to the sample using measured source profile information, and emissions or discharge inventories.
The method is reviewed briefly here and described in greater detail elsewhere Paatero and Tapper, ; Paatero, Jump to main content. Contact Us. Large positive scaled residuals may indicate that PMF is not fitting the species or the species is present in an infrequent source.
The screen also displays the samples with scaled residuals that are greater than a user- specified value Figure 14, 3. The default value is 3. The residuals can be displayed as "Dates by Species" or "Species by Dates" by choosing the appropriate option above the table.
When a species is selected in the list on the left Figure 14, 1 , the table on the right Figure 14, 3 automatically scrolls to that species. Species that do not have a strong correlation between observed and predicted values should be evaluated by the user to determine whether they should be down-weighted or excluded from the model. These numbers are calculated using the observed and predicted concentrations to indicate how well each species is fit by the model. The table also indicates whether the residuals are normally distributed, as determined by a Kolmogorov-Smirnoff test.
If not all statistics are visible, the user can use the scroll bars at the bottom and side of the table to display additional statistics. A blue one-to-one line is provided on this plot for reference a perfect fit would line up exactly on this line , and the regression line is shown as a dotted red line. The status bar on this screen Figure 15 displays the date, x-value, y-value, and regression equation between predicted and observed data as data points are moused-over Figure 15, 3.
Weak 0 Strong 0. Two graphs are shown for each factor, one displaying the factor profile and the other displaying the contribution per sample of each factor Figure The profile graph, displayed on top Figure 17, 1 , shows the concentration of each species apportioned to the factor as a pale blue bar and the percent of each species apportioned to the factor as a red box. The concentration bar corresponds to the left y-axis, which is a logarithmic scale.
The percent of species corresponds to the right y-axis. The bottom graph shows the contribution of each factor to the total mass by sample Figure 17, 2. This graph is normalized so that the average of all contributions for each factor is 1. The status bar on this screen Figure 17, red box displays the date and contributions of data points as they are moused-over on the Factor Contributions plot.
Beginning in the bottom left corner, each run can be chosen by toggling to and clicking on the appropriate run number. The user can quickly compare runs to assess the stability of the solution or determine what, if any, individual species or factors are varying between runs.
Users can switch between the factors resolved by PMF by using the pull-down menu second from the left. Factor 1 is currently selected. The user can create a stacked plot of the profiles or time series by first selecting either the factor profile plot or the factor concentration plot, right-clicking on the mouse to view the menu, and selecting "Stacked Graphs.
If this option is selected, the GUI multiplies the contributions by the mass of the total variable in that factor. The status bar displays the date, factor contribution, total variable selected, and the species factor as they are moused-over on the Factor Contributions plot Figure 18, red box.
Factor 1 has high concentrations of sulfate and ammonium ions and it represents secondary sulfate formation from the combustion of coal in power plants. The identification of factors from PMF requires review of measured species relationships. Some sources may be easily identified; an industrial source, for example, may be dominated by peaks in zinc concentrations.
Other sources may be more difficult to identify. These days might have had unique source impacts and should be investigated further. Factor Fingerprints The concentration in percent of each species contributing to each factor is displayed as a stacked bar chart in the Factor Fingerprints screen Figure This plot can be used to verify factor names and determine the distribution of the factors for individual species.
The plot only displays the currently selected run. Example of the Factor Fingerpints screen. G-Space Plot The G-Space Plot screen Figure 21 shows scatter plots of one factor versus another factor, which can be used to assess rotational abiguity as well as the relationship between source contributions.
A more stable solution will have many samples with zero contributions on both axes, which provide greater stability in the PMF solution to less rotational ambiguity. A solution or combination of sources may also have no points on or near the axes, which results in greater rotational ambiguity. The user selects one factor for the y-axis and one factor for the x- axis from lists on the left of the screen.
A scatter plot of these factors will be shown on the right of the screen. The plot in Figure 21 is an example of a non-optimal rotation of a factor, which has an upper edge that is not aligned with the axis in the G-Space plot red line added for reference. The G-Space plots are also useful for understanding the relationship between the factor source contributions and the pattern in Figure 21 shows not relationship between regional secondary sulfate and local steel production.
Example of the G-Space Plot screen with a red line indicating an edge. The top graph is a pie chart which displays the distribution of each species among the factors resolved by PMF Figure 22, 1. The species of interest is selected in the table on the left of the screen; the categorization of that species is also displayed for reference.
The pie chart for the selected species is on the right side of the screen. If the user has specified a total variable, the distribution of this variable across the factors will be of particular importance. The user may also want to examine the distribution of key source tracer species across factors. The bottom graph shows the contribution of all the factors to the total mass by sample Figure 22, 2.
The dotted orange lines denote January 1 of each year. The graph is normalized so that the average of all the contributions for each factor is 1, to allow for a comparison of the temporal pattern of source contributions. Run 12 Help Figure Example of the Factor Contributions screen. Output Files After the base runs are completed, the GUI creates output files that contain all of the data used for the on-screen display of the results.
The output files are saved to the directory specified in the "Output Folder" box in the Data Files screen, using the prefix specified in the "Output File Prefix" box. Contributions are sorted by run number. Normalized contributions are shown first, followed by contributions in mass units if a total variable is specified. Profiles are sorted by run number. Profiles in mass units are written first, followed by profiles in percent of species and concentration fraction of species total if a total mass variable is specified.
This output file only appears if the user selects "Excel Workbook" as the output file type. After the base runs are completed, the "Factor Names" box located in the lower left portion of the Base Model Runs screen will be populated Figure 23, red box.
Each row in the matrix will be labeled by run number, in ascending order, and each column will be labeled by factor number, in ascending order. The table is then populated with the factor name associated with each column header.
The factor names are used to indicate specific solutions in the tools for assessing model results. Users can input their own factor names, which will replace the defaults in the Factor Names table and be saved in the configuration file. The user can also set a unique factor name for all the base runs by inputting the name in one cell and then pressing the "Apply to All Runs" button; update factors names in the profile and contribution files by pressing the "Update Diag Files" button; or reload the default factor names into the Factor Names table by pressing "Reset to Defaults.
In this case, the GUI will generate a pop-up warning to remind the user to verify that previous factor names are appropriate. Short descriptions of the error estimation methods available in PMF are shown in Figure 24 along with the example base factor concentration blue and upper error limits for the three methods. Random errors are estimated with the BS method described in this section.
Correlation R-Va! Example of the Base Model Runs screen with default base model run factor names. Displacement DISP intervals include effects of rotational ambiguity. They do not include effects of random errors in the data. For modeling errors, if the user misspecifies the data uncertainty, DISP intervals are directly impacted.
Bootstrap BS intervals include effects from random errors and partially include effects of rotational ambiguity. For modeling errors, if the user misspecifies the data uncertertainty, BS results are still generally robust. Comparison of upper error estimates for zinc source.
For the solution chosen by the user, each value in the factor profile is first adjusted up and down and then all other values are computed to achieve the associated PMF convergence to a Q-minimum. It is important to note that the newly computed minimum Q-value modified may be different from the Q-value associated with the unadjusted solution base. Note: DISP intervals include effects of rotational ambiguity.
For modeling errors, if user misspecifies the uncertainty of the concentration data, DISP intervals are directly impacted.
Hence intervals for dcwnweighted or "weak" species are likely too long. Example of the Base Model Displacement Summary screen. If factor swaps occur for the smallest dQmax, it indicates that there is significant rotational ambiguity and that the solution is not sufficiently robust to be used. To improve the solution, the number of factors could be reduced, marginal species could be excluded, or unusual events in time series plots could be excluded.
BS data sets are constructed by randomly sampling blocks of observations from the original data set. The block length depends on the data set and is chosen so that each BS data set preserves the underlying serial correlation that may be present in the base data set. Blocks of observations are randomly selected until the BS data set is the same size as the original input data.
If no base factors correlate above the threshold for a given BS factor, that factor is considered "unmapped. There can be instances when multiple BS factors from the same run may be mapped to the same base factor. The user should examine the BS results to determine if the base run blue square is within the interquartile ranges box around the profiles.
Species with their base run value outside of the interquartile range should be interpreted with caution because a small set of observations may have impacted the base run results or the species concentration in the factor could be insignificant. The mapping of BS factors to base factors will ideally be one-to-one. That is, factors from each BS run factor should match exactly one, and only one, base factor.
However, it is likely that the presence or absence of a few critical observations can dramatically impact the BS factor profile. In such instances, the affected BS factors may closely match a particular base factor most of the times and some other base factor the rest of the time.
In addition, specification of too many factors in the base model may also create a phantom factor. The base run with the lowest Q robust is automatically provided; the user can enter another run number.
For example, a block size of three means that each BS block will comprise three samples from the input data set i. The default block size is calculated according to Politis and White , but can be overridden by the user. If the default has been overridden, the user can press the "Suggest" button to restore the default value. It is recommended that BS runs be performed to ensure the robustness of the statistics; for preliminary analysis, 50 BS runs may be performed to quickly gauge the stability of a solution.
A minimum of 20 BS runs are required. The default value is 0. If a large number of factors are unmapped, the user may want to investigate the impact of lowering the R-value. This change should be reported with the final solution. As with the base runs, the user can interrupt the runs by pressing the "Stop" button in the lower right corner of the Base Model Runs screen. No outputs will be saved or overwritten if the run is interrupted.
The first eight lines in this screen contain all the input parameters for bootstrapping, as specified by the user in the Base Model Runs screen. The summary screen also includes several tables that summarize the BS run results.
The first table is a matrix of how many BS factors were matched to each base factor. The next table shows the minimum, maximum, median, and 25th and 75th percentiles of the Q robust values. The rest of the summary is the variability in each factor profile, also given as the mean, standard deviation, 5th percentile, 25th percentile, median, 75th percentile, and 95th percentile, using weighted average percentiles see equation The base run of each profile is included as the first column for reference, as is a column indicating if the base run profile is within the interquartile range of the BS run profiles.
This method estimates the 90th and 95th percentile confidence intervals Cl around the base run profile, reported as percentages. The DDP is calculated by taking the 90th and 95th percentiles of the absolute differences between the base run and the BS runs for each species in each profile and expressing it as a percentage of the base run value.
For this example, the base and boot factors are matched except for three factors with three runs that were mapped to factor 7. The total number of mapped factors may also not add up to the number of BS runs if the boot factor run did not converge. QE-QQ1 I. QE 6. QE 8. Example of the Base Bootstrap Summary screen.
Two graphs are presented: the variability in the percentage of each species Figure 28, 1 and the variability in the concentration of each species Figure 28, 2 , which corresponds to the Variability in Factor Profiles table in the Base Bootstrap Summary screen.
In both box plots, the box Figure 29 shows the interquartile range 25thth percentile of the BS runs. The horizontal green line represents the median BS run and the red crosses represent values outside the interquartile range.
The base run is shown as a blue box for reference. Values outside of the interquartile range are shown as red crosses. At the bottom of this screen, the base run numbers are grayed out and not selectable; however, the base run used for bootstrapping is highlighted in orange. The user can select the factor they want to view by clicking on the factor number across the bottom of the screen. Species with the base run profile value blue box outside interquartile range tan box should be interpreted only after evaluating the two additional error estimation results in PMF.
Example of the Base Bootstrap Box Plots screen. Base run value 25thth Percentile of Bootstrap Median of Bootstrap Values below 25th and above 75th percentiles Figure Diagram of box plot.
This process may be viewed as follows: each DISP defines the span of rotationally accessible space. Each BS resample moves this space around, randomly in different directions. Taken together, all the replications of the rotationally accessible space, in random locations, represent both the random uncertainty and the rotational uncertainty.
The limits obtained by displacing a factor element include both rotational ambiguity and variability due to input data uncertainty. Downweighted variables create a special problem in DISP computations.
If such variables are adjusted, the error intervals can be very large based on simulated data evaluations. The error estimates for downweighted species are best estimated from the results obtained from adjusting non-downweighted species. Occasionally, it is seen that displacements cause a significant decrease of Q, typically by tens or by hundreds of units. If the change in Q is greater than 0. Starting from the most plausible solution, it is possible to transform the solution gradually, without significant increase of Q, so that factor identities change.
In the extreme case, factors may change so much that they exchange identities. This is called factor swap. Physically, a solution with swapped factors represents the same physical model as the original solution. However, the presence of factor swaps means that all those intermediate solutions also exist and must be considered as alternative solutions. For a higher dQmax, a larger uncertainty interval or Cl is usually obtained. The larger the interval, the higher the chance that it contains the true unknown value.
All dQmax values should be evaluated to determine whether the solution is well-defined. A large value is not alarming in itself, it only says that there was at least one resample where a deeper minimum appeared.
If swaps are present in the first line for the lowest dQiaax, it indicates the solution is not well constrained, and caution used when interpreting the solution. The BS-DISP results in Figure 30 show that the solution does not have significant rotational ambiguity and the base model and error estimates can be interpreted.
Steps to reduce the number of swaps include reducing the number of factors and adding constraints. This includes both the full-data case and the accepted not rejected resamples; if all bootstrap cases were accepted, this value would be equal to one plus the number of bootstraps the extra one run is an initialization run. If no cases were excluded, k should be equal to the number of bootstraps times the number of factors times the number of species selected for BS-DISP.
Largest decrease of Q. A large value is not necessarily alarming, but it indicates that there was at least one resample where a deeper minimum appeared. Number of cases with drop of Q. Number of cases with swap in best fit. Number of cases with swap in DISP. In the best case, all of the swaps are zero; however, the probability of creating a BS data set that results in a swap is based on the data characteristics i. The profiles and DISP results should be evaluated to determine whether there is a reason for the swaps.
A result with swaps between two factors is more reliable than swaps occurring across many factors. For this example, the swaps are occurring between the crustal factor 4 and steel production factor 6 , which have many common elements. Also, the number of swaps is one for two factors, which indicates some ambiguity between the factors.
The first two blocks of data are the initial run data, with each row representing a species and each column a factor. The last line of each block is always a series of "T's as a placeholder. These four blocks are then repeated for each BS resample.
The summary files contain the species and diagnostics as well as the error estimates by factor for concentrations, percent of species sum, and percent of total variable if one is selected. Figure 31 shows the error estimation summary plot for the three error estimates. Error estimation summary plot. Rotational Tools In general, the non-negativity constraint alone is not sufficient to produce a unique solution. An infinite number of plausible solutions may be generated and cannot be simply disqualified using mathematical algorithms.
Rotating a given solution and evaluating how the rotated results fill the solution space is one approach to reduce the number of solutions. Due to the non-negativity constraints in PMF, a pure rotation i. If no rotation is possible, the solution is unique. Therefore, approximate rotations that allow some increase in the Q-value and prevent any elements in the solution from becoming negative are useful in PMF. For some solutions, the non-negativity constraint is enough to ensure that there is little rotational ambiguity in a solution.
If there are a sufficient number of zero values in the profiles F-matrix and contributions G-matrix of a solution, the solution will not rotate away from the "real" solution. However, in many cases, the non-negativity constraint is not sufficient to prevent rotation away from the "real" solution. To help determine whether an optimal solution has been found, the user should inspect the G-space plots for selected pairs of factors in the original solution.
The current guidance is to select a regional source type such as coal-fired power plants sulfate and plot it against local industrial sources such as steel production Fe. The user can perform up to five Fpeak runs by checking the appropriate number of boxes and entering the desired strength of each Fpeak run.
While there are no limits on the values that can be entered as Fpeak strengths under "Selected Fpeak Runs" , generally values between -5 and 5 should be explored first. Positive Fpeak values sharpen the F-matrix and smear the G-matrix; negative Fpeak values smear the F-matrix and sharpen the G-matrix. More details on positive and negative Fpeak values can be found in Paatero Fpeak runs begin when the user presses the "Run" button on the Fpeak Model Runs screen.
Base run and BS run results will not be lost when Fpeak is run. After the Fpeak runs are completed, a summary of the Fpeak results, with the same information contained in the Base Model Run Summary table, is shown in the Fpeak Model Run Summary table Figure 32, red box. Fpeak is useful for examining the span of possible rotations, with an end result of more values at or near 0 in either the contributions or profiles, depending on whether a positive or negative Fpeak is used.
In the profile graph, the concentration of species left y-axis is a green bar and the percent of species right y-axis is an orange box. For comparison, the original base run results are also displayed on the profile graph.
The mass of the species left y-axis is a light gray bar and the percent of species right y-axis is a dark gray box. Factor contributions for the base model results are also displayed gray line. The Fpeak values are in the same order as entered on the Fpeak Model Runs screen; the factors are in the same order as those in Base Model Results. In these graphs, users should look for deviations i. Users can select an Fpeak value and factor number by clicking on the desired number at the bottom of the screen.
The status bar displays the date, concentration, total variable selected, and the species factor as they are moused over on the Factor Contributions plot. Fpeak Factor Fingerprints The Fpeak Factor Fingerprints screen shows the concentration in percent of each species contributing to each factor as a stacked bar chart Figure This plot can be used to verify unique factor names and determine the distribution of the factors for individual species.
Users should look for deviations i. The user can select an Fpeak value by clicking on the desired number at the bottom of the screen. Example of the Fpeak Factor Fingerprints screen. The user assigns a factor to the x- and y-axes by selecting the desired factor from the lists on the left of the screen Figure 35, 1. The Fpeak value to display, the base run G-space plot "Show Base" , and the delta in G-space plots between the base run and an Fpeak run "Show Delta" are selected at the bottom of the screen Figure 35, 2.
The user can also select a point in any Fpeak G-space plot by clicking on that point. This feature helps the user identify and track rotations. For example, if a G-Space plot appears rotated, the user can mark the edge points. Using information such as meteorological conditions or emissions information, the user can determine whether these edge points are expected to have low contributions from the source. Biomass Secondary Nitrate Crusta! S Example of the Fpeak Factor Contributions screen.
Several aspects of the solution should be evaluated to understand how Fpeak changes the PMF solution. In a pure rotation, the Q-value would not change because the rotation is simply a linear transformation of the original solution. However, because of the non-negativity constraints of PMF, pure rotations are not usually possible and the rotations induced by Fpeak are approximate rotations, which change the Q-value.
Additionally, profiles and contributions should be examined to determine the impact of the rotation. G-Space plot and delta between the base run contribution and Fpeak run contribution for each contribution point. For example, if a source is known to be inactive for a certain period, there should be no contributions from the factor that represents that source during the inactive time period.
The contributions can be set to zero or pulled to zero and the penalty in Q is provided for moving the contribution from the optimal solution to one based on external knowledge. Another example is if a source profile from a nearby facility has been quantified, the user could constrain the profile in a factor that represents that facility type to match the measured profile.
Applications of using constraints are discussed in greater detail elsewhere Morris et al. Starting with a selected base run, two types of constraints can be performed: 1 "hard pulling," which is imposed without regard to the change in the Q-value e. The Expression Builder has three radio buttons that users can select to define constraints as constant ratio Figure 38 , mass balance Figure 39 , or customized expression Figure If needed, a number can be input into the "Coefficient" text box, which will be used as a coefficient for the species selected.
Click the "Clear" buttons to remove the current specifications of the balance equation. The customized equation can be based on either profiles with species as element or contributions with sample as element. The custom equation must follow the same structure as the equations developed by the Expression Builder. For each of the three Expression Builder functions, after the user defines a constraint and presses the "Add to Expressions" button, the corresponding equation in a standardized format will appear in the Expressions table Figure 41, red box.
Since the constraints defined using Expression Builder are "soft pulling," a limit of change in the Q-value must be specified. Users are also allowed to delete the selected constraints or all constraints by pressing the "Remove Selected Expressions" or "Remove All Expressions" buttons at the bottom of the Expressions table. The user can also select multiple data points pressing the CTRL button. Expression Builder - Custom.
Example of expressions on the Constrained Model Runs screen. Selecting constrained species and observations. As discussed in Section 6. If users identify an edge in a G-space plot, constraints can be specified to pull the data points along the edge toward the axis i. The user should examine the points along the edge; if there is any a priori information that would indicate that a value should be zero e.
The strength of each pull is controlled by specifying a limit on the change in the Q-value. If the user wishes to perform a weak pull, a small limit on the change in the Q-value should be allowed. Conversely, if the user wishes to perform a strong pull, a large limit on the change in Q-value should be allowed.
The strength of the pull should be based on a priori information about the pollutant sources that indicate that the contribution for the given sample should be zero. The user can select as many points in as many factors to pull as they wish.
Example of selecting points to pull to the y-axis in the G-space plot. After the Constraint Points are defined in the previous three graphs, the Constraints table will appear on the Rotational Tools, Constraints screen, showing a constraint in each row Figure 44, yellow box. Evaluate all of the plots for all factors to understand the impact of the constraints and determine whether the constraint has provided a more interpretable solution. Typically, species contributions to factors fall into two categories: 1 stiff, in that they will not significantly change or if they are constrained, unreasonable profiles are created; and 2 weak, in that they move easily and are typically not well modeled by PMF.
The understanding of the stiff and weak key tracer species for sources allows for optimization of the solution using measured profile or other information. Weak species should be interpreted as easily moved between sources while stiff species are strongly associated with the factor and should be used in the interpretation of its source. The mass and percentage of species and the time series of factor contributions are presented for both the constrained model run and the selected base run.
The user should look at the deviations in the results between the two model runs and examine the impact of constraints. Example of the Constrained Factor Fingerprints screen. Similar to the Fpeak G-Space Plot screen, the user can select "Show Base" to display the base run G-space plot and select "Show Delta" to display the difference in G-space plots between the constrained model run and the base run.
The top graph is a pie chart, which displays the distribution of each species among the factors resolved by PMF Figure 48, 1. The pie chart for the selected species appears on the right side of the screen.
The bottom graph shows the contribution of all the factors to the total mass by sample Figure 48, 2. The dotted orange reference lines denote January 1 of each year. The graph is normalized so that the average of all the contributions for each factor is 1.
Fpeak Rotation 8. V'' '. Example of the Constrained G-Space Plot screen. Constrained Diagnostics The Constrained Diagnostics screen Figure 49 includes a summary of the constrained model parameters and output for reference e.
Model Data Base Mode! G Example of the Constrained Factor Contributions screen. Constrained BS Runs and Results A constrained model run can be bootstrapped in the same manner as base model runs. After a constrained model run is completed, the user can initiate a BS run for the constrained model in Constrained Model Bootstrapping. The constrained bootstrapping results are displayed in Constrained Bootstrap Box Plots and Constrained Bootstrap Summary in the same format as the Base Run bootstrapping output screens for easy comparison.
All factors and source contribution time series must be evaluated to understand the impact of the constraint s. In addition, the error estimation results need to be evaluated to determine if the constraint has changed the species factor contribution significantly. Example of the Constrained Diagnostics screen. Table 3. Please close all output files. Action Turn off User Access Controls in Microsoft Vista Column headers of concentration and uncertainty files do not match Species names in uncertainty file do not match those in concentration file.
Do you wish to continue? If the names are correct, continue. If the columns are in a different order, correct and retry. Number of columns in concentration file is not the same as in uncertainty file Number of species in uncertainty file does not match the number of species in concentration file. Select "OK" and examine input files. The same number of columns, in the same order, should be included in the concentration and uncertainty files. If named ranges are used, check that the ranges are defined correctly.
Blank cells are included in concentration file Empty cells are not permitted in the concentration input file. Please check your data file. Select "OK" and remove blank cells from input file before trying again. Blank cells, zero values, or negative values are included in uncertainty file Null, zero, and negative uncertainty values are not permitted.
Select "OK" and remove inappropriate cells from input file before trying again. Cannot save output files because one is open The process cannot access the file 'file path and name' because it is being used by another process. Close file and select "Retry" or select "Cancel" to change the file path and name. Users can follow the steps outlined in each example to better understand the PMF process and the interaction of the components described in this User Guide.
The examples all follow the flow shown in Figure 50, recommended for all PMF analyses. For some users, the Base Model may be sufficient. However, Fpeak can be used to optimize the solution and Constraints can be used to incorporate information on the source such as composition or emissions. Evaluating the error estimates is a critical component of a PMF analysis.
PMF results evaluation process. This exercise is intended to demonstrate the thought process as well as steps involved in evaluating a small data set with event sampling from multiple sites; it is not intended to be a complete source apportionment analysis.
The PMF input parameters are summarized in Table 4 and all sites were used in the analysis. Table 4. The paper reference is also included on the site tab. All of the species were initially used in the base model run, 3 factors, and 20 runs. A random seed was initially used to evaluate the variability in runs and the following results are based on a seed number of Deep tunnel system. Also, the cadmium concentrations were only at two levels Figure 53 , potentially indicating an issue with using the species.
All of the species have a linear relationship except for cadmium, as shown in Figure Based on these results, cadmium was set to "bad" and the base model was re-run. The stacked graph plot shown in Figure 54, which shows results similar to Bzdusek et al.
Select the new window and right-click for file saving options or use "Copy to Clipboard" to paste the figure into a document. This data set poses some challenges for plotting since the samples were collected from multiple sites on the same day when it is was raining. Rather than on a fixed schedule, the sampling was event-based. The time-series plots have horizontal lines between the sites Figure Information on the site name and sampling time is displayed on the bottom bar after a point is selected on the figure.
The user needs to evaluate whether combining the data in a PMF analysis is justified. The key receptor modeling assumption is the composition of the sources impacting the sites does not change between sites. Base Model Runs 11 Base Mode! The relative magnitude of the source impacts varies across the sampling sites, however, the impacts are variable and multiple sites have both high and low source contributions. Combining the sites seems justified based on the variability between sites. The observed vs.
The time series shows that observed and predicted concentrations are large for a few sampling sites and low for others. The data from the sites with large differences should be evaluated in more detail to determine whether the samples should be combined in the PMF analysis. Time series plots in the Rotational Tools also display the lines between the sites.
The error estimation results are shown in Figure This may be due to PMF not fitting this highly variable source and the BS data sets also might not have captured the variability in the metals.
The number of swaps is low and the results may reflect the relatively small data set with variability introduced by many sampling sites. Base model run number: 5 Number of bootstrap runs: Min. Comparison of error estimation results. The error estimation summary plot provides a summary of the error estimates. Louis Supersite PM2. The exercise is intended to demonstrate the evaluation of base model results and addition of constraints using EPA PMF.
A number of papers have been published on St. Louis particulate matter PM apportionment and Amato and Hopke have recently published an analysis of St. Louis data. The example given here is not a complete analysis; it illustrates how to analyze the data with PMF and the importance of evaluating the model results.
The PMF input parameters are summarized in Table 5. Louis Supersite Figure Version 5. The computer should have at least a 2. No further updates to the PMF Model are planned. PMF 5. The User Guide and a large number of publications provide examples of how to apply the model for air, water, sediment, and other data analyses.
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