15. POSTHS and POSTHT

User Guide MAIN MENU



The heavy gas dispersion models HEGADAS-S and HEGADAS-T (steady state and transient version respectively), are among the more complex HGSYSTEM models. In order to help the user to interpret the HEGADAS (-S and -T) results, in HGSYSTEM version 1.0 (NOV90), two 'interactive' post-processors were available, called HSPOST and HTPOST.

These two post-process utilities have been completely revised for HGSYSTEM version 3.0 and they are now called POSTHS and POSTHT respectively. POSTHS and POSTHT now can be run in 'batch' mode, that is they can be used as all other main HGSYSTEM modules, and they read their input data from an input file having the same structure as all other HGSYSTEM input files.

Data from HEGADAS (-S and -T) is communicated to POSTHS and POSTHT using a so-called 'model data file'. These data files have a file name with extension HSM and HTM respectively. The first part of the model data file name is the user-specified case name. This name should be used when calling POSTHS and POSTHT.

The first part of this Chapter describes input parameters for POSTHS which processes HEGADAS-S results. The second half deals with POSTHT, the HEGADAS-T post-processor.

POSTHS

General introduction

POSTHS is a utility for post-processing the model data files produced by HEGADAS-S, creating output files for submission to suitable user-selected plotting packages.

Range of applications and limitations

The post-processor can handle any HEGADAS-S model data file having a DOS filename 'casename.HSM', where 'casename' is the user-supplied name of the problem.

As well as being able to create all output previously produced by HSPOST (the post-processor available in HGSYSTEM 1.0), additional functionality is available, iso-concentration contour plots now being an option.

Guidance for use

When first used to post-process the HEGADAS-S output for a new case, it is strongly recommended that most of the data for each input block is not specified by the user, but allowed to take default values. Such usage has the advantage of requiring little if any data analysis by the user, enabling automatic running of the post-processor and the rapid production of an initial set of useful output files. Further refinement of the input data can then be made in a meaningful manner and the exact output requirements finalised for the current case.

This does not of course apply where the user is interested in exact values, such as when producing iso-concentration plots at lower and upper flammability limits, where it would obviously make sense to specify the required values in the contour input block immediately.

Whether values are specified by the user or the defaults taken, within the program most values will be adjusted if necessary to take account of the actual data in the input model file. This particularly applies to ranges of downwind x-values and contour values which are not allowed outside the ranges computed by HEGADAS-S.

Note that restraint should be shown when specifying long downwind x-ranges with small step-sizes. The resulting output files can be very large indeed for steady-state simulations terminating several kilometres downwind and a step-size such as 1 meter.
In such cases it is recommended that the user looks at the full x-range using a large step-size, or looks in detail at a section of the x-range using a small step-size. Such usage also avoids the danger of exceeding size limitations in the user's preferred plotting package.

A standard report file 'casename.PSR' containing a summary of the input from HEGADAS-S, is always produced. If the user-requested output files contain little or no (useful) data because of parameters being specified out of the relevant range, reference to the 'casename.PSR' file should enable the user to alter the required parameter values so as to obtain useful results.

POSTHS INPUT FILE PARAMETERS

A description of all the input parameters that can occur in a POSTHS input file will be given.

The POSTHS input file has the DOS filename 'casename.PSI', where 'casename' is the user-supplied name of the problem and must match that used for the original HEGADAS-S run which produced the model data file 'casename.HSM'.

When creating an input file the user should ensure that each specified output file has a unique filename, and that existing files having such names are deleted or renamed before POSTHS is run as POSTHS assumes that files with the specified names do not yet exist. An error will occur if the file does exist.

In the following, actual keywords are given in capitals and in bold. The descriptions of less important parameters or parameters that need not normally be set by the user, are given in a smaller font.

All parameters, except TITLE, occur in blocks preceded by a specific block keyword. For POSTHS these block keywords are: GRAPH2, CONCBOX, CONTOUR, PARMSX, CONCXYZ and ERRORFUN.

The three co-ordinate directions used in all input blocks are:
  x down wind
  y lateral (sideways)
  z vertical (height)


The horizontal and vertical axis parameter type described below may take values in the range 1 to 9, where each value has the following meaning:

1 downwind distance X to pool (m)
2 vol%. (dry) gas fraction CAV at y = z = 0
3 vertical dispersion coefficient SZ (m)
4 crosswind dispersion coefficient SY (m)
5 half-width b of middle part of crosswind concentration profile (m)
6 temperature TMP (C)
7 effective cloud half-width Beff (m)
8 effective cloud height Heff (m)
9 cloud half-width (normal definition) (m)


The TITLE keyword does not occur in a parameter block.

TITLE The title of the current problem to be run with POSTHS.
  At most 50 alphanumeric characters.
  Optional, no default.


The GRAPH2 block, which may occur up to 6 times, specifies the parameters to produce output files containing values to generate graphs relating any two types of data. The first type of data is given by HORAX2 (using the horizontal axis) and the second one by VERAX2 (using the vertical axis).
OUT2 Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
XRANGE2 Range of values for down wind distance x.
  Optional, defaults as given below.
Following the XRANGE2 keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for x (m).
-106 <= #1 <=106.
(default is 0.0)
#2 maximum value for x (m).
-106 <= #2 <=106.
(default 1000.0)
#3 step size for x (m).
10-6 #3 106.
(default 10.0).
HORAX2 Horizontal axis parameter type (-).
  1 <= HORAX2 <= 9.
  Mandatory.
VERAX2 Vertical axis parameter type (-).
  1 <= VERAX2 <= 9.
  Mandatory.


CONCBOX block, which may occur up to 6 times, specifies the parameters to produce 4-column output files containing co-ordinates and concentrations in box-shaped regions (3D). It is also possible to produce similar output files for planes (2D) by fixing one axis range while varying the other two axes, or lines parallel to an axis (1D) by only varying the required axis. Note that these latter two types of output must have range values supplied for the non-varying axes in which the minimum and maximum values are identical and the step-sizes are positive and non-zero.
Filename of the required output file 'filename.ext' (full pathname if required).
OUTB At most 40 alphanumeric characters.
  Mandatory.
XRANGEB Range of values for x.
  Optional, defaults as given below.
  Following the XRANGEB keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for x (m).
-106 <= #1 <=106.
(default 0.0)
#2 maximum value for x (m).
-106<= #2 <= 106.
(default 1000.0)
#3 step size for x (m).
10-6 <= #3 <= 106.
(default 100.0)
YRANGEB Range of values for y.
  Optional, defaults as given below.
  Following the YRANGEB keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for y (m).
-106 <= #1 <= 106.
(default 0.0).
#2 maximum value for y (m).
-106 <= #2 <= 106.
(default 20.0).
#3 step size for y (m).
10-6 <= #3 <=106.
(default 10.0).
  Optional, defaults as given below.
ZRANGEB Range of values for z.
  Following the ZRANGEB keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for z (m).
0.0 <= #1 <= 106.
(default 0.0).
#2 maximum value for z (m).
0.0 <= #2 <= 106.
(default 10.0).
#3 step size for z (m).
10-6 <= #3 <= 106.
(default 5.0).


The CONTOUR block, which may occur up to 6 times, specifies the parameters to produce 2-column output files containing data to generate iso-concentration contour plots.
OUTC Filename of the required output file 'filename.ext' (full pathname if required).
At most 40 alphanumeric characters.
  Mandatory.
RANGEC Range of contour values. Optional, defaults as given below.
Following the RANGEC keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum contour value (%).
10-6 <= #1 <= 100.0.
(default set from actual model file data).
#2 maximum contour value (%).
10-6 <= #2 <= 100.0.
(default set from actual model file data).
Limited to 90% of maximum concentration in the model file for the requested plane.
#3 number of contours (-).
1<= #3<= 6.
(default 6).
XC Constant value x for contour plane yz (m).
  -106 XC 106.
  Optional, no default.
YC Constant value y for contour plane xz (m).
  -106 YC 106.
  Optional, if none of XC, YC or ZC are specified, default is taken to be YC = 0.
ZC Constant value z for contour plane xy (m).
  0.0 ZC 106.
  Optional, no default.


PARMSX block specifies the parameters to produce a multi-column output file containing the value of each model file variable for a series of x-values.
OUTSX Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
XRANGESX Range of values for x.
  Optional, defaults as given below.
  Following the XRANGESX keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for x (m).
-106 <= #1<= 106.
(default 0.0).
#2 maximum value for x (m).
-106 <= #2 <= 106.
(default 1000.0).
#3 step size for x (m).
10-6 <= #3 <= 106.
(default 10.0).


The CONCXYZ block specifies the parameters to produce a 4-column output file containing the co-ordinates and concentrations at a set of up to 20 specified x, y, z co-ordinate positions.
OUTXYZ Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
XYZ Co-ordinate position which may occur up to 20 times, but which must occur at least once.
  Following the XYZ keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 x-co-ordinate (m).
-106 <= #1<= 106.
No default.
#2 y-co-ordinate (m).
-106 <= #2<= 106.
No default.
#3 z-co-ordinate (m).
0.0 <= #3 <= 106.
No default.


ERRORFUN block applies the finite duration error function correction to the model file input data. Any such correction takes place before the processing of other data blocks and affects the results written to the output files.

DURATION Duration of release (s).
  1 DURATION 3600.
  Optional, must be specified if ERRORFUN block is used..
AVTIMC Averaging time for concentrations (s).
  0 AVTIMC 3600.
  Optional, default is the value used in the corresponding HEGADAS-S run.
  Should not normally be set by the user, value will be read from the model data file 'casename.HSM'. Any value set in POSTHS will override the value used in the corresponding HEGADAS-S run.
  If the user has specified DELTA in the HEGADAS-S DISP input block then AVTIMC in HEGADAS-S has no value and AVTIMC must be specified here.
  AVTIMC is only ised in HEGADAS-S for the finite duration correction.


POSTHT

General introduction

POSTHT is a utility for post-processing the model data files produced by HEGADAS-T, creating output files for submission to suitable user-selected plotting packages.

Range of applications and limitations

The post-processor can handle any HEGADAS-T model file having a DOS filename 'casename.HTM', where 'casename' is the user-supplied name of the problem.

As well as being able to create all output previously produced by HTPOST (the post-processor available in HGSYSTEM 1.0), additional functionality is also available, iso-concentration contour plots being one of several new options.

Guidance for use

When first used to post-process the HEGADAS-T output for a new case, it is strongly recommended that most of the data for each input block is not specified by the user, but allowed to take default values. Such usage has the advantage of requiring little if any data analysis by the user, enabling automatic running of the post-processor and the rapid production of an initial set of useful output files. Further refinement of the input data can then be made in a meaningful manner and the exact output requirements finalised for the current case.

This does not of course apply where the user is interested in exact values, such as when producing iso-concentration plots at lower and upper flammability limits, where it would obviously make sense to specify the required values in the contour input block immediately.

Whether values are specified by the user or the defaults taken, within the program most values will be adjusted if necessary to take account of the actual data in the input model file. This particularly applies to ranges of downwind x-values and contour values which are not allowed outside the ranges computed by HEGADAS.

Note that restraint should be shown when specifying long downwind x-ranges with short step-sizes. The resulting output files can be very large indeed for simulations terminating several kilometres downwind and a step-size such as 1 meter.
In such cases it is recommended that the user looks at the full x-range using a large step-size, or looks in detail at a section of the x-range using a small step-size. Such usage also avoids the danger of exceeding size limitations in the user's preferred plotting package. This is not such a problem for POSTHT as it sometimes is for POSTHS, because of the nature of the output criteria in HEGADAS.

A standard report file 'casename.PTR' containing a summary of the input from HEGADAS-T, is always produced. If the user-requested output files contain little or no (useful) data because of parameters being specified out of the relevant range, reference to the 'casename.PTR' file should enable the user to alter the required parameter values so as to obtain useful results.

POSTHT INPUT FILE PARAMETERS

A description of all the input parameters that can occur in a POSTHT input file will be given.

The following information is valid for POSTHT version 2.0.

The POSTHT input file has the DOS filename 'casename.PTI', where 'casename' is the user-supplied name of the problem and must match that used for the original HEGADAS-T run which produced the model data file 'casename.HTM'.

When creating an input file the user should ensure that each specified output file has a unique filename, and that existing files having such names are deleted or renamed before POSTHT is run, as POSTHT assumes that files with the specified names do not yet exist. An error will occur if the file does exist.

In the following, actual keywords are given in capitals and in bold. The descriptions of less important parameters or parameters that need not normally be set by the user, are given in a smaller font.

All parameters, except TITLE, occur in blocks preceded by a specific block keyword. For POSTHT these block keywords are: GRAPHDX, CONCBOX, CONTOUR, PARMSX, CONCXYZ, GRAPHDT, CONCXYZT, DOSAGE, GRAPHMX, ENVCURVE and AVTIMC.

The three co-ordinate directions used in all input blocks are:
  x down wind
  y lateral (sideways)
  z vertical (height)

The dispersion data type described below may take values in the range 1 to 7 where each value has the following meaning:

1 vol% (dry) gas fraction CAV at y = z = 0
2 vertical dispersion coefficient SZ (m)
3 crosswind dispersion coefficient SY (m)
4 half-width b of middle part of crosswind concentration profile (m)
5 effective cloud half-width Beff (m)
6 effective cloud height Heff (m)
7 concentration at y = z = 0 (kg/m3)


The TITLE keyword does not occur in a parameter block.

TITLE The title of the current problem to be run with POSTHT.
  At most 50 alphanumeric characters.
  Optional, no default.




The GRAPHDX block, which may occur up to 6 times, specifies the parameters to produce 2-column output files containing values to generate graphs of dispersion data (indicated by TYPEDX) against x.

OUTDX Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
TIMEDX Required time for output (s).
  0 <= TIMEDX <= 3600.
  (default set to first time in model file data).
TYPEDX Dispersion data type (-).
  1 <= TYPEDX <= 7.
  Mandatory.
XRANGEDX Range of values for x.
  Optional.
  Following the XRANGEDX keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for x (m).
-106 <= #1 <= 106.
(default 0.0).
#2 maximum value for x (m).
-106 <= #2<= 106.
(default 1000.0).
#3 step size for x (m).
10-6 <= #3 <= 106.
(default 10.0).


CONCBOX block, which may occur up to 6 times, specifies the parameters to produce 4-column output files containing co-ordinates and concentrations in box-shaped regions (3D). It is also possible to produce similar output files for planes (2D) by fixing one axis range while varying the other two axes, or lines parallel to an axis (1D) by only varying the required axis. Note that these latter two types of output must have range values supplied for the non-varying axes in which the minimum and maximum values are identical and the step-sizes are positive and non-zero.
Filename of the required output file 'filename.ext' (full pathname if required).
OUTB At most 40 alphanumeric characters.
  Mandatory.
TIMEB Required time for output (s).
  0 <= TIMEB <= 3600.
  (default set to first output time in model file data).
XRANGEB Range of values for x.
  Optional.
  Following the XRANGEB keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for x (m).
-106 <= #1 <= 106.
(default 0.0).
#2 maximum value for x (m).
-106 <= #2 <= 106.
(default 1000.0).
#3 step size for x (m).
10-6 <= #3 <= 106.
(default 100.0).
YRANGEB Range of values for y.
  Optional.
  Following the YRANGEB keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for y (m).
-106 <= #1 <= 106.
(default 0.0).
#2 maximum value for y (m).
-106 <= #2<= 106.
(default 20.0).
#3 step size for y (m).
10-6 <= #3 <= 106.
(default 10.0).
ZRANGEB Range of values for z.
  Optional.
  Following the ZRANGEB keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for z (m).
0.0 <= #1 <= 106.
(default 0.0).
#2 maximum value for z (m).
0.0 <= #2 <= 106.
(default 10.0).
#3 step size for z (m).
10-6 <= #3<= 106.
(default 5.0).



The CONTOUR block, which may occur up to 6 times, specifies the parameters to produce 2-column output files containing data to generate iso-concentration contour plots.
OUTC Filename of the required output file 'filename.ext' (full pathname if required).
At most 40 alphanumeric characters.
  Mandatory.
TIMEC Required time for output (s).
  0 <= TIMEC <= 3600.
  (default set to first time in model file data).
RANGEC Range of contour values.
  Optional. Following the RANGEC keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum contour value (%).
10-6 <=#1<= 100.0.
(default set from actual model file data).
#2 maximum contour value (%).
10-6 <=#2<= 100.0.
(default set from actual model file data).
#3 number of contours (-).
1 <= #3 <= 6.
(default 6).
XC Constant value x for contour plane yz (m).
  -106 <=XC <= 106.
  Optional, no default.
YC Constant value y for contour plane xz (m).
  -106 <=YC<= 106.
  Optional.
  If none of XC, YC or ZC are specified, default taken as y=0.
ZC Constant value z for contour plane xy (m).
  0.0 <=ZC <= 106.
  Optional, no default.


PARMSX block specifies the parameters to produce a multi-column output file containing the value of each model data file variable for a series of x-values.
OUTSX Filename of the required output file 'filename.ext' (full pathname if required).
At most 40 alphanumeric characters.
Mandatory.
TIMESX Required time for output (s).
0 <= TIMESX <= 3600.
(default set to first time in model file data).
XRANGESX Range of values for x.
Optional.
Following the XRANGESX keyword, a block of 3 parameters (#1 to #3) must be specified:
#1minimum value for x (m).
-106 <= #1 <= 106.
(default 0.0).
#2maximum value for x (m).
-10
6 <= #2 <=106.
(default 1000.0).
#3 step size for x (m).
10
-6 <= #3 <= 106.
(default 10.0).


CONCXYZ block specifies the parameters to produce a 4-column output file containing the co-ordinates and concentrations at a set of up to 20 specified x, y, z co-ordinate positions.

OUTXYZ Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
TIMEXYZ Required time for output (s).
  0 <=TIMEXYZ <= 3600.
  (default set to first time in model file data).
XYZ Co-ordinate position which may occur up to 20 times, but which must occur at least once.
  Mandatory.
  Following the XYZ keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 x-co-ordinate (m).
-106 <= #1 <= 106.
No default.
#2 y-co-ordinate (m).
-106 <= #2 <= 106.
No default.
#3 z-co-ordinate (m).
0.0 <= #3 <= 106.
No default.


The GRAPHDT block, which may occur up to 6 times, specifies the parameters to produce 2-column output files containing values to generate graphs of dispersion data against time.
OUTDT Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
TRANGEDT Range of values for time.
  Optional.
  Following the TRANGEDT keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for time (s).
0 <= #1 <= 3600.
(default set to first time in model file data).
#2 maximum value for time (s).
0 <= #2 <= 3600.
(default 3600.0).
#3 step size for time (s).
10-6 <= #3<= 3600.
(default 10.0).
TYPEDT Dispersion data type (-).
  1 <=TYPEDT <= 7.
  Mandatory.
XVALDT Value for x (m).
  -106 <=XVALDT<= 106.
  Mandatory.


CONCXYZT block specifies the parameters to produce a 2-column output file containing the concentrations against time at each co-ordinate in a set of up to 20 specified x, y, z co-ordinate positions.

OUTXYZT Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
TRXYZT Range of values for time.
  Optional.
  Following the TRXYZT keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for time (s).
0 <= #1 <= 3600.
(default set to first time in model file data).
#2 maximum value for time (s).
0 <= #2 <= 3600.
(default 3600.0).
#3 step size for time (s).
10-6 <=#3 <=3600.
(default 10.0).
XYZT Co-ordinate position which may occur up to 20 times, but which must occur at least once.
  Mandatory.
  Following the XYZT keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 x-co-ordinate (m).
-106 <=#1 <=106.
No default.
#2 y-co-ordinate (m).
-106 <=#2 <=106.
No default.
#3 z-co-ordinate (m).
0.0 <= #3 <= 106.
No default.



DOSAGE block specifies the parameters to produce a 4-column output file containing the co-ordinates and dosages at a set of up to 20 specified x, y, z co-ordinate positions. For a given position (x,y,z), the dosage at time t is given by the integral, from minus infinity to t, of c(x,y,z,Tau) dTau. In POSTHT the calculated value is given by the integral, from t0 to t, of c(x,y,z,Tau) dTau, where t0 is the first output time. If the dosage calculation is unreliable because x is too far upwind compared to the available data at time t0, a warning is given.

OUTD Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
TIMED Required time for output (s).
  0 <= TIMED <= 3600.
  Mandatory.
XYZD Co-ordinate position which may occur up to 20 times, but which must occur at least once.
  Mandatory.
  Following the XYZD keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 x-co-ordinate (m).
-106 <= #1 <= 106.
No default.
#2 y-co-ordinate (m).
-106 <= #2 <=106.
No default.
#3 z-co-ordinate (m).
0.0 <= #3 <= 106.
No default.



ENVCURVE block specifies the parameters to produce a 3-column output file containing the maximum concentration and its position for a series of output times. The resulting curve is an 'envelope' curve of the concentration profiles per output time.

OUTE Filename of the required output file 'filename.ext' (full pathname if required).
  At most 40 alphanumeric characters.
  Mandatory.
TMINE Minimum time for output (s).
  0 <=TMINE<= 3600.
  Optional (default set to first output time in model file data).
TMAXE Maximum time for output (s).
  0 <= TMAXE <= 3600.
  Optional (default 3600.0).


GRAPHMX block, which may occur up to 6 times, specifies the parameters to produce 2-column output files containing the maximum values of selected types of dispersion data (indicated by TYPEMX) over all times, for a series of x-values.

OUTMX Filename of the required output file 'filename.ext' (full pathname if required).
At most 40 alphanumeric characters.
  Mandatory.
TYPEMX Dispersion data type (-).
  1 <= TYPEMX <= 7.
  Mandatory.
XRANGEMX Range of values for x.
  Optional.
  Following the XRANGEMX keyword, a block of 3 parameters (#1 to #3) must be specified:
#1 minimum value for x (m).
-106 <= #1 <= 106.
(default 0.0).
#2 maximum value for x (m).
-106 <= #2 <= 106.
(default 1000.0).
#3 step size for x (m).
10-6 <= #3 <=106.
(default 10.0).



AVTIMC keyword does not occur in a parameter block. If the keyword is used a time-averaging correction is applied to the model data file input data. Any such correction takes place before the processing of other data blocks and affects the results written to the output files.

AVTIMC Averaging time for concentrations (s).
  0 <= AVTIMC <= 3600.
  Optional, default is the value used in the corresponding HEGADAS-T run.
  Should not normally be set by the user, value will be read from the model data file 'casename.HTM'. Any value set in POSTHT will override the value used in the corresponding HEGADAS-T run.
  If the user has specified DELTA in the HEGADAS-T DISP input block then AVTIMC in HEGADAS-T has no value and AVTIMC must be specified here.
NOTE AVTIMC in POSTHT is (only) used for time-averaging (or time-smoothing) of calculated concentrations c(t) to obtain (average) concentrations cav(t) where cav(t) is 1/AVTIMC multiplied by the integral, from t-AVTIMC/2 to t+AVTIMC/2, of c(Tau) dTAu.


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