f_and_c

a FORTRAN90 subroutine is like a C++ void function, and should be declared this way in the C++ code. The qualifier extern should also be used.
a FORTRAN90 subroutine or function expects all its arguments to be passed by reference. This generally means simply that the C++ function must pass scalar variables by reference, not value.
typically, when the FORTRAN90 compiler compiles the FORTRAN90 code, the names of functions and subroutines are stored with an appended underscore. In order for these names to be found by the C++ code, it is necessary that the C++ code declare and invoke the FORTRAN90 functions and subroutines with the underscore explicitly appended to the name.
in many cases, a FORTRAN90 compiler is simply a "front end" to a corresponding C++ compiler, as in the case of the GNU compilers gfortran and g++, or the Intel compilers ifort and icpp. This means that, as long as the corresponding compilers are used to compile the FORTRAN90 and C++ codes, it is probably possible to use either compiler to link and load the object codes; however, the load command may need to specify explicitly certain libraries associated with one of the languages. For instance, if loading using the gcc command, it is necessary to include "-l gfortran" so that the FORTRAN90 I/O libraries, among others, are included in the build.

use bind(C) in F90


gfortran -shared -o math_module.so math_module.f90
g++ hello.cpp -L. -lmath_module -o main
g++ hello.cpp /path/to/math_module.so -o main

install mini-requirements for clm

netCDF-C

sudo apt install libhdf5-dev
wget https://path/to/netcdf-c.source.zip
unzip netCDF.zip
cd netcdf
mkdir build
cd build
cmake ../.
make
sudo make install

netcdf-fortran

wget https://github.com/Unidata/netcdf-fortran/archive/refs/tags/v4.6.1.zip
unzip netcdf-fortran
cd netcdf-fortran
./configure
make check
sudo make install

pnetcdf


git clone https://github.com/Parallel-NetCDF/PnetCDF.git
cd PnetCDF
autoreconf -i

./configure
make
sudo make install

lapack

wget https://github.com/Reference-LAPACK/lapack/archive/refs/tags/v3.12.0.zip
unzip v3.12.0.zip
cd v3.12.0
mkdir build
cd build
cmake ..
make
sudo make install