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TTim, A Multi-Layer, Transient, Analytic Element Model


TTim is a computer program for the modeling of transient multi-layer flow with analytic elements and consists of a library of Python scripts and FORTRAN extensions. TTim is based on the Laplace-transform analytic element method. The solution is computed analytically in the Laplace domain and converted back to the time domain numerically usig the algorithm of De Hoog, Stokes, and Knight. TTim may be applied to an arbitrary number of aquifers and leaky layers. The head, flow, and leakage between aquifers may be computed semi-analytically at any point in space and time. The design of TTim is object-oriented and has been kept simple and flexible. New analytic elements may be added to the code without making any changes in the existing part of the code. TTim is coded in Python; use is made of FORTRAN extensions to improve performance.

TTim Changes

Version 0.4

Version 0.4 is the new port of TTim to Python 3. The API has changed significantly and some of the API will undergo more changes in future versions. Not all elements that were available in version 0.3 have been ported to version 0.4.


Python versions:

TTim requires Python 3.6 and can be installed from PyPI. The PyPI installation includes compiled versions of the FORTRAN extension for both Windows and MaxOS.


TimML requires NumPy 1.12 (or higher) and matplotlib 2.0 (or higher).

Installation for Python 3.6:

To install TTim, open a command prompt and type:

pip install ttim

To uninstall TTim type:

pip uninstall ttim

Installation for Python 3.7:

There is no installer for Python 3.7. An installer is planned for the summer of 2019. There are two options to run TTim on Python 3.7:

Install a virtual environment for Python 3.6. In a terminal, type

conda create -n py36 python=3.6 anaconda
conda activate py36
pip install ttim

To activate the environment and start a jupyter notebook, type the following in a terminal:

conda activate py36
jupyter notebook

If you have FORTRAN and C compilers installed (for example gfortran), you can go to the directory where TTim is installed and type

f2py -c -m --fcompiler=gfortran bessel bessel.f95
f2py -c -m --fcompiler=gfortran invlap invlap.f90

Testing installation:

import ttim.ttimtest

An example model is imported and two graphs are shown. When this is run from the regular Python prompt (not IPython), the model is created and solved but the figure is probably not shown (depending on your default settings of matplotlib).


  • The manual is available from the docs directory or can be viewed here.
  • Example Notebooks are available from the notebooks directory on github, of from here.


Some of the papers that you may want to cite when using TTim are

  • M. Bakker. 2013. Semi-analytic modeling of transient multi-layer flow with TTim. Hydrogeology Journal, 21: 935Ð943.
  • M .Bakker. 2013. Analytic modeling of transient multi-layer flow. In: Advances in Hydrogeology, edited by P Mishra and K Kuhlman, Springer, Heidelberg, 95-114.
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