Concentration / Utilities / Transfer Coefficient / Cost Function

This menu can be used to solve the Transfer Coefficient Matrix (TCM) for the source term vector given a measured data vector and where the matrix values are the dilution factors for each source-receptor pair. The measured data vector at multiple receptor locations and/or times is required and it must be defined in the DATEM format. The format of this file is discussed more detail in the GeoLocation menu. If a time-varying source solution is required, the Run Daily menu can be used to generate the required dispersion simulations.

Technical details regarding the computational approach used to solve the TCM can be found in "Source term estimation using air concentration measurements and a Lagrangian dispersion model–Experiments with pseudo and real cesium-137 observations from the Fukushima nuclear accident",T. Chai, R. Draxler, A. Stein, Atmospheric Environment, 106, 241-251.

The inverse modeling executable lbfgsb input files:

The inverse modeling executable lbfgsb output files:

where the 000 represents the process ID, which is always zero for user generated applications.

Step 1: defines the binary input files which are the output file from the dispersion simulations configured to produce output at an interval that can be matched to the measured sampling data. Ideally the model simulation emission rate should be set to a unit value. Each simulation should represent a different discrete emission period. For example, a four day event might be divided into 16 distinct 6-hour duration emission periods. Therefore the matrix would consist of 16 sources (columns) and as many rows as there are sampling data. The entry field in step 1 represents the wild card string *entry* that will be matched to the files in the working directory. The file names will be written into a file called INFILE. This file should be edited to remove any unwanted entries.

Step 2: defines the measured data input file which is an ASCII text file in the DATEM format. The first record provides some general information, the second record identifies all the variables that then follow on all subsequent records. There is one data record for each sample collected. All times are given in UTC. This file defines the receptor data vector for the matrix solution. It may be necessary to edit this file to remove sampling data that are not required or edit the simulation that produces the coefficient matrix to insure that each receptor is within the modeling domain.

Step 3: defines the file conversion details from sampling units to the emission units. For instance, the default value of 10+12 converts the emission rate units pg/hr to g/hr if the sampling data are measured in pg/m3 (pico = 10-12). The exponent is +12 rather than -12 because it is applied to the model results in the denominator (Emission=Measured/Model_TCM). The height and species fields are the index numbers to extract from the concentration file if multiple species and levels were defined in the simulation. The half life (in days) is only required when dealing with radioactive pollutants and the measured data need to be decay corrected back to the simulation start time.

Step 4: creates the comma delimited input file called c2array.csv with the dilution factors in a column for each source and where each row represents a specific receptor location. The last column is the measured value for that receptor. The column title represents the start time of the emission in days from the year 1900. This step calls the program c2array which reads each of the measured data values and matches them to the input files to extact the dilution factors from each source to that measured value. This step also creates an output file called c2array.txt which contains the number of rows and columns in the matrix. This information is needed when creating the Parameters_in.dat input file created by Step 5.

Step 5: creates the PARAMETER_IN_000 input file used by the inverse modeling executable lbfgsb. Detailed information is required that may not always be well known and several solution iterations may be required before the optimal input parameters have been properly defined. The default settings almost certainly will have to be changed.

Step 6 runs inverse modeling executable with options defined in Step 5. Different solutions can be tested by sequentially repeating steps 5 and 6. The solution results from SOURCE_OUT_000 are copied to the output file source.txt defined in this step and also displayed by the GUI. The Parameters_in.dat can also be edited manually to set parameters not defined in the GUI. In this case only repeating step 6 is required. A solution may contain negative values as well as extreme positive emission results. Such values are not realistic and are a result of model errors or other uncertainties.

Fukushima Example Inputs assuming emissions output units mBq

PARAMETER_IN_000 detailed description

  1. ================ DIMENSIONS ================
  2. ================ TCM_INPUTS ================
  3. ================ RUN_CONTRL ================
  4. ================ SMOOTH_PNT ================
  5. ================ SMOOTH_P2D ================
  6. ================ MODEL_UNC ================
  7. ================ LBFGS_CTRL ================
  8. ================ BOUNDS_ARR ================
  9. ================ UNCERTANTY ================

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