@article {strzempko_flow_2023,
	title = {The Flow Matrix Offers a Straightforward Alternative to the Problematic Markov Matrix},
	journal = {Land},
	volume = {12},
	year = {2023},
	pages = {1471},
	abstract = {The Flow matrix is a novel method to describe and extrapolate transitions among categories. The Flow matrix extrapolates a constant transition size per unit of time on a time continuum with a maximum of one incident per observation during the extrapolation. The Flow matrix extrapolates linearly until the persistence of a category shrinks to zero. The Flow matrix has concepts and mathematics that are more straightforward than the Markov matrix. However, many scientists apply the Markov matrix by default because popular software packages offer no alternative to the Markov matrix, despite the conceptual and mathematical challenges that the Markov matrix poses. The Markov matrix extrapolates a constant transition proportion per time interval during whole-number multiples of the duration of the calibration time interval. The Markov extrapolation allows at most one incident per observation during each time interval but allows repeated incidents per observation through sequential time intervals. Many Markov extrapolations approach a steady state asymptotically through time as each category size approaches a constant. We use case studies concerning land change to illustrate the characteristics of the Flow and Markov matrices. The Flow and Markov extrapolations both deviate from the reference data during a validation time interval, implying there is no reason to prefer one matrix to the other in terms of correspondence with the processes that we analyzed. The two matrices differ substantially in terms of their underlying concepts and mathematical behaviors. Scientists should consider the ease of use and interpretation for each matrix when extrapolating transitions among categories.},
	keywords = {category, extrapolation, flow, land change, Markov, model},
	issn = {2073-445X},
	doi = {10.3390/land12071471},
	url = {https://www.mdpi.com/2073-445X/12/7/1471},
	author = {Strzempko, Jessica and Pontius, Robert Gilmore}
}
@article {PIE465,
	title = {Intensity Analysis and the Figure of Merit{\textquoteright}s components for assessment of a Cellular Automata {\textendash} Markov simulation model},
	journal = {Ecological Indicators},
	year = {2019},
	note = {PI},
	keywords = {CA-Markov, cellular-automata, figure of merit, intensity analysis, land change, LTER-PIE, Validation},
	doi = {10.1016/j.ecolind.2019.01.057},
	author = {Varga, O.G. and Pontius, R.G., Jr. and Singh, S.K. and Szabo, S.}
}
@article {PIE496,
	title = {Intensity Analysis to communicate land change during three time intervals in two regions of Quanzhou City, China.},
	journal = {GIScience \& Remote Sensing},
	year = {2019},
	note = {PI},
	keywords = {China, GIS, intensity analysis, land change, LTER-PIE, Quanzhou City, regionalization},
	doi = {10.1080/15481603.2019.1658420},
	author = {Quan, B. and Pontius Jr, R.G. and Song H.}
}
@article {PIE451,
	title = {Comparison of Intensity Analysis and the land use dynamic degrees to measure land changes outside versus inside the coastal zone of Longhai, China},
	journal = {Ecological Indicators},
	volume = {89},
	year = {2018},
	note = {PI},
	pages = {336-347},
	keywords = {coastal area, intensity analysis, land change, land use dynamic degree, LTER-PIE, pattern, urbanization},
	doi = {10.1016/j.ecolind.2017.12.057},
	author = {Huang, B. and Huang, J. and Pontius, R.G., Jr. and Tu, Z.}
}
@article {PIE439,
	title = {Methods to summarize change among land categories across time intervals},
	journal = {Journal of Land Use Science},
	volume = {12},
	number = {4},
	year = {2017},
	note = {PI Coastal},
	pages = {218-230},
	keywords = {category, disturbance, flow matrix, GIS, land change, LTER-PIE, time, transition},
	doi = {10.1080/1747423X.2017.1338768},
	author = {Pontius, R.G., Jr. and Krithivasan, R. and Sauls, L. and Yan, Y. and Zhang, Y.}
}
@article {PIE440,
	title = {Rules to write mathematics to clarify metrics such as the land use dynamic degrees},
	journal = {Landscape Ecology},
	volume = {32},
	number = {12},
	year = {2017},
	note = {PI},
	pages = {2249-2260},
	keywords = {annual change percentage, China, CLUDD, disturbance, intensity analysis, land change, LTER-PIE, mathematical notation},
	doi = {10.1007/s10980-017-0584-x},
	author = {Pontius, R.G., Jr. and Huang, J. and Jiang, W. and Khallaghi, S. and Lin, Y. and Liu, J. and Quan, B. and Ye, S.}
}
@mastersthesis {PIE425,
	title = {Analyzing the response of land change models to intractable problems},
	volume = {M.S.},
	year = {2016},
	note = {Grad},
	school = {Clark University},
	type = {mastersthesis},
	keywords = {land change, land change models, LTER-PIE},
	author = {Philbrick, S.}
}
@article {PIE385,
	title = {Behavior-based aggregation of land categories for temporal change analysis},
	journal = {International Journal of Applied Earth Observation and Geoinformation},
	volume = {35},
	year = {2015},
	note = {PI Plum Data},
	pages = {229-238},
	keywords = {disturbance, GIS, land change, LTER-PIE},
	doi = {10.1016/j.jag.2014.09.007},
	author = {Aldwaik, S.Z. and Onsted, J.A. and Pontius, R.G., Jr.}
}
