On this web page, we will gradually release some recently-developed software tools for Markov chain geostatistics (i.e., MCRF simulation and transiogram modeling). We will also edit and release some old computer programs and executables that were developed by Dr. Weidong Li some years ago (during 2004 to 2014). Those old Fortran computer programs are the foundations for later development of software tools using different computer languages.
1. TGRAM (Download the package)
TGRAM is a free software tool with graphical interfaces for estimating experimental transiograms from point sample data (in shapefile format) and performing transiogram joint model-fitting to obtain a whole set of transiogram models for simulation of categorical fields. The linear interpolation joint-fitting method and the mathematical model joint-fitting method were implemented in the current version. It was developed using C# computer language by Dr. Jia Yu, who visited UCONN for one year during 2016 to 2017, based on previous simple Fortran computer programs for transiogram modeling (need to work with Microsoft Excel functions and manual operations) developed by Dr. Weidong Li. Please note that the current version is just an initial version which has limited functions and flexibility. Updated version release with revisions and new functions is expected. To understand the transiogram and the two joint-fitting methods, please read the reference articles attached with the software (in the "References" folder after the software is installed). If you have any problem or feedback about the TGRAM software, please contact Dr. Yu (yujiashnu@126.com). If you use this tool in your research, we politely suggest you cite "Yu et al., 2018. A framework of experimental transiogram modelling for Markov chain geostatistical simulation of landscape categories. Computers, Environment and Urban Systems, https://doi.org/10.1016/j.compenvurbsys.2018.07.007". Note that Yu released the soure code on a permanent website provided in the article. (May 2018).
2. Omni-directional experimental transiogram estimation (Download the executable, Fortran source code, and example data)
This simple Fortran computer program was developed in 2005, for estimating omni-directional experimental transiograms from point sample data for landscape (e.g., soil classes) category simulation in horizontal two dimensions. The computer program asks users to input a value called "Tolerance width" at the run time. The tolerance width here means the number of pixel lengths between two nearest lag values of an experimental transiogram. Users can load the experimental transiogram data into a Microsoft Excel file and make figures to check whether the estimated experimental transiograms are in good shape. Usually, users need to try several times (with different tolerance-width values) to find a suitable tolerance width so that the estimated experimental transiograms do not have strong fluctuations while keeping major rational features. As to how to estimate TPM (transition probability matrix) and transiograms uni-directionally, bi-directionally, and multi-directionally from real data, that should be easy to users by adapting our released codes. (July 2018).
3. Linear interpolation of experimental transiograms (Download the executable, Fortran source code, and example data)
This simple Fortran computer program was developed in 2005, for joint modeling of experimental transiograms through linear interpolation. It is a fast joint modeling method. The transiogram models obtained by this way can be used in MCRF simulation. However, this method should be used with caution. It is proper to use only when experimental transiograms are estimated reliably, that is, estimated from sufficient sample data with a proper tolerance width, so that their shapes are stable - capturing the main features but not having over-fluctuations or even a series of zeros and ones. If the number of classes is small, the sample data are insufficient, and/or some classes are extremely minor (so related experimental transiograms are unreliable), it is suggested to use the mathematical model joint modeling method. See Li and Zhang (2010, Linear interpolation and joint model fitting of experimental transiograms for Markov chain simulation of categorical spatial variables. IJGIS, 24(6): 821-839) for more explanation. (Aug. 2018).
4. Idealized transiograms from TPM (Download the executable, Fortran source code, and example data)
This simple Fortran computer program developed in 2004 computes idealized transiograms from a TPM (transition probability matrix). Users have to estimate their TPM by themselves, which is easy to do. See Li (2007, Transiograms for characterizing spatial variability of soil classes. SSSAJ, 71(3): 881-893) or Li et al. (2012, Modeling experimental cross transiograms of neighboring landscape categories with the gamma distribution. IJGIS, 26(4): 599-620) for explanations about idealized transiograms from TPM. From idealized transiograms, one can find both the auto/cross correlation ranges of classes (i.e., states) under the idealized situation (stationary Markovian) and the occurrence proportions (i.e., transiogram sills, equilibrium probabilities) of classes. This clearly means that using TPMs is equivalent to using idealized transiograms but the latter can explicitly convey much more valuable information. By computing idealized transiograms from a TPM, one also can find whether an improper/wrong TPM (or 1-D Markov chain) was used in a research. Therefore, idealized transiograms have some unique values. (Sept. 2018).
5. Basic mathematical models for transiogram modeling (Download the executable, Fortran source code, and example)
This simple Fortran computer program coded some of basic mathematical models that may be used for transiogram modeling, including the gamma-based composite models proposed in Li et al. (2012). Note that some models (e.g., nugget, hole effect, and gamma distribution) were coded only for showing a proportion line and testing them for constructing composite models, respectively. This computer program was used to show, test and fit individual transiogram models. To perform joint model fitting, one has to import all fitted transiogram model data into an Excel file and obtain the (1-Others) model for each transiogram matrix row by using the calculation function of Excel, so that all fitted transiogram models in each matrix row meet the sum-to-unity condition. Because this is tedious, we sugegsted users use the TGRAM software developed by Dr. Jia Yu to perform transiogram joint modeling. See Li (2007, Transiograms for characterizing spatial variability of soil classes. SSSAJ, 71(3): 881-893) or Li et al. (2012, Modeling experimental cross transiograms of neighboring landscape categories with the gamma distribution. IJGIS, 26(4): 599-620) for explanations about these basic models. In addition, to accurately fit an experimental transiogram with a complex shape by math models, one may need to combine multiple basic math models together; because that is more tedious, we suggest that users only need to choose a suitable model to fit the low-lag section of an experimental transiogram that may be needed in conditional simulation. (Sept. 2018).
1. MCSS-Quadrantal-2006 (Download the executable, Fortran source code, and example)
This computer executable is a MCRF sequential class simulation algorithm with quadrantal neighborhood (i.e., one nearest datum per quadrant), developed by Weidong Li using Fortran computer language in spring 2006 (during the 2005-2006 winter period). It can directly work with sample data and parameters within the same folder. No installation is needed. It was used for preparing the article of Li and Zhang (2007, SSSAJ) and in some of our later researches. Because the neighborhood search part is inefficient (it searches the whole study area for nearest data at each location), this algorithm is very time consuming when used for large data sets. One can test using the attached example data to see whether it can generate the exact results as presented in Li and Zhang (2007) [Note that the SIS part in Li and Zhang (2007) was performed using a graphical geostatistical software bought from University of Alberta (Prof. Deutsch's research group) in 2005]. If you use this tool, please cite "Li, W., and C. Zhang, 2007. A random-path Markov chain algorithm for simulating categorical soil variables from random point samples. Soil Science Society of America Journal, 71(3): 656-668". (May 2018)
2. MCSS-Quadrantal-Spiral-2014 (Download the executable, Fortran source code, and example)
This computer executable is a fast MCRF sequential class simulation algorithm with quadrantal neighborhood, moving window and
spiral search, developed by Weidong Li using Fortran computer language during 2011 to 2014 on the basis of the 2006 slow algorithm,
implementing the same random-path MCRF sequential simulation algorithm with a more efficient nearest data search method. It can directly
work with sample data and parameters within the same folder. No installation is needed. Because it used a spiral search algorithm to
search for the nearest datum in each quadrant, it is much more efficient in computation. This efficient MCRF simulation algorithm provided
the basic condition for using the MCRF approach (coMCRF model) to land cover postclassification from remotely sensed imagery. However, the
Fortran computer language is not convenient for directly processing large-size images. If you use this tool, please also cite "Li, W., and
C. Zhang, 2007. A random-path Markov chain algorithm for simulating categorical soil variables from random point samples. Soil Science
Society of America Journal, 71(3): 656-668". (July 2018)
Comments are welcome and may be sent to W. Li (weidong.li@uconn.edu).