The HDMR Method
Using the High Dimensional Model Representation
(HDMR) method to generate a reduced model for studying tropospheric
alkane photochemistry*
Section I contains file downloads
along with descriptions of files.
Section II contains procedures for running
the code.
Section I:
Computer codes and associated input data for download: |
| A. |
fullmodel.tar
contains the following code and related input data:
| fullmodel.f |
the original box-model code of the full tropospheric
alkane photochemistry |
| temperature.data |
diurnal temperature profile of the simulation |
| photo.data |
photochemical rate constants |
| rate.data and alrate.data |
other reaction rate constants |
| initial_full.dat |
initial conditions of the input chemical species |
| lsode2.o |
the compiled object of LSODE solver |
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| B. |
dcalmodel.tar
contains the following code and related input data:
| dcal.f |
the code for solving the kinetic equations of reduced
Direct Constrained Approximate Lumping (DCAL) mechanism
of the tropospheric alkane photochemistry |
| temperature.data |
diurnal temperature profile of the simulation |
| photo.data |
photochemical rate constants |
| rate.data and alrate.data |
other reaction rate constants |
| initial_full.dat |
initial conditions of the input chemical species |
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|
| C. |
hdmr.tar contains
the following code and related input data:
| hdmr.f |
the code for generating the tables
of hierachical cut points in the high dimensional input
variable space according to the cut-High Dimensional Model
Representation (cut-HDMR) methodology |
| par_ranges.dat |
dynamic ranges for the input parameters |
| dcal_1st.f |
the dcal model code for generating
the output responses according to the hierarchical input
cut points up to 1st order HDMR expansion |
| dcal_2nd.f |
the dcal model code for generating the output responses
according to the hierarchical input cut points for the
2nd order HDMR expansion |
| hdmrtab.f |
the code for processing the model
outputs generated by dcal_1st.f and dcal_2nd.f with the
cut-HDMR input points to generate the look-up tables of
the HDMR expansion |
| feom1.f |
the code for performing the algebraic manipulation of
the HDMR expansion terms from the 0th order to 1st order
for predicting the kinetic outputs |
| feom2.f |
the code for performing the algebraic
manipulation of the HDMR expansion terms from the 0th
order to 2nd order for predicting the kinetic outputs |
| initial_lumped.dat |
the initial conditions of the lumped input species,
which are produced by multiplying the full initial conditions
(initial_full.dat) with the dcal lumping matrix |
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| D. |
plots.tar contains
the codes for generating diurnal concentration-time profiles
for 4 different inorganic species using GNUPLOT
| o3.gnu |
comparison of O3 profiles for full model, DCAL, and
1st order HDMR outputs |
| no2.gnu |
comparison of NO2 profiles for full model, DCAL, and
1st order HDMR outputs |
| no.gnu |
comparison of NO profiles for full model, DCAL, and
1st order HDMR outputs |
| oh.gnu |
comparison of OH profiles for full model, DCAL, and
1st order HDMR outputs |
|
Section II
Procedures for running the code: |
| A. |
Running the full model
| The initial conditions of the 52 explicit chemical species
are in the file initial_full.dat |
| Compile the code using f77 Fortran compiler: f77 –o
full fullmodel.f lsode2.o |
| Submit the job by typing the executable filename: full |
| The simulation outputs are in the file fullmodel.out,
which includes the diurnal profiles of the 52 explicit
chemical species of the original full mechanism. |
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|
| B. |
Running the dcal model
| The initial conditions are the same as the full model
(initial_full.dat) |
| Compile the code using f77 Fortran compiler: f77 –o
dcal dcal.f lsode2.o |
| Submit the job by typing the executable filename: dcal |
| The simulation outputs are in the file dcal.out, which
includes the diurnal profiles of the 25 species of the
DCAL mechanism (21 explicit inorganic species, methane,
and 3 lumped alkane species). |
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|
| C. |
Running the HDMR code
| Specify the number of input variables, dynamic ranges
of the inputs (in this demonstration case, there are 6
inputs and the ranges are specified in par_ranges.dat) |
| Generate the sampling points in the input variable space
by running the code of hdmr.f (in this demonstration case,
two tables are produced, rhd1.in and rhd2.in, corresponding
to the 1st and 2nd order HDMR expansion terms) |
| Perform the original model runs according to the sampling
input points (in this demonstration case, the dcal_1st.f
and dcal_2nd.f, are used to generate 1st order and 2nd
order HDMR output responses, respectively) |
| Generate the HDMR look-up tables by running the code
of hdmrtab.f (in this demonstration case, the outputs
generated by dcal_1st.f and dcal_2nd.f [rhd1.out and rhd2.out]
are processed by hdmrtab.f to produce the 1st and 2nd
order HDMR look-up tables) |
| Perform the 1st order HDMR-reduced model simulation
by running the code of feom1.f (the required inputs are
the ranges of the inputs and the initial conditions of
input species, which are the files par_ranges.dat and
initial_lumped.dat for this demonstration case). The outputs
are stored in the file dcal-feom1.out. |
| Perform the 2nd order HDMR-reduced model simulation
by running the code of feom2.f (the required inputs are
the ranges of the inputs and the initial conditions of
input species, which are the files of par_ranges.dat and
initial_lumped.dat for this demonstration case). The outputs
are stored in the file of dcal-feom2.out. |
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| D. |
Visualization of the simulation outputs
| The scripts of plotting the diurnal concentration-time
profiles for O3, NO2, NO, and OH are provided in the plot.tar. |
|
Any comments or suggestions, please contact Sheng-Wei
Wang.
*For further details
of the study and HDMR methodology, refer to: Wang S.W., Balakrishnan S. and Georgopoulos P.G. (2005). Fast equivalent operational model of tropospheric alkane photochemistry. American Institute of Chemical Engineers Journal 51(4): 1297-1303 [DOI link]
