Rural sustainability under threat in Zimbabwe – Simulation of future land use/cover changes in the Bindura district based on the Markov-cellular automata model

Spatially explicit land use/cover models are indispensable for sustainable rural land use planning, particularly in southern African countries that are experiencing rapid land use/cover changes. Using Zimbabwe as an example, we simulated future land use/cover changes up to 2030 based on a Markov-cellular automata model that integrates Markovian transition probabilities computed from satellite-derived land use/cover maps and a cellular automata spatial filter. A multicriteria evaluation (MCE) procedure was used to generate transition potential maps from biophysical and socioeconomic data. Dynamic adjustments of transition probabilities and transition potential map thresholds were implemented in the Markov-cellular automata model through a multi-objective land allocation (MOLA) procedure. Using the normalised transition probabilities, the Markov-cellular automata model simulated future land use/cover changes (up to 2030) under the 2000 calibration scenario, predicting a continuing downward trend in woodland areas and an upward trend in bareland areas. Future land use/cover simulations indicated that if the current land use/cover trends continue in the study area without holistic sustainable development measures, severe land degradation will ensue.     

A rational explanation of cross-profile morphology for glacial valleys and of glacial valley development

The fact that the cross-profile of the glacial valley could be well approximated by parabolas (Y = aX^b, b = 2.0) is explained by the variation principle, assuming that the glacier erosion works towards minimizing thefriction between ice and bedrock. The variation principle proves that the ideal or fully-developed morphology of the glacial valley should be a catenary, the curve which a chain hanging from two fixed points forms. Maclaurin's series expansion of the catenary equation shows that a parabola is a very good approximation of the catenary; hence, the good approximation of the cross-profile by parabolas. Different catenaries are generated by changing the form ratio (depth/rim width) and are then approximated by Y = aX^b by the method of last-squares. The b values obtained become only fractionally larger than 2.0 with invreasing form ratios of up to 1.0, indicating that b values would range, in practice, between 1.0 and about 2.0 Two types of trend in the relationship between b values and the form ratio were obtained from several glaciers. For one type the b value becomes larger with increasing form ratios, and for the other the opposite. The first type is called the Rocky Mountain model after its source of data and represents overdeepening of the glacial valley development. The second type is caalled the Patagonia-Antarctica model, representing a widening, instead of a deepening, process of development. These differences are attributed to the nature of the glaciers which produced these valleys, i.e. alpine glaciers and continental ice sheets.     

Response to Morgan's comment

We respond to Morgan's comment on our model for cross‐profile morphology for glacial valleys. Copyright © 2005 John Wiley & Sons, Ltd.