Topological invariance and spatial scaling of surface roughness in two highly eroded zones of Mexico: a comparative study

The Fractal Image Informatics toolbox (Oleschko et al., 2008 a; Torres-Argüelles et al., 2010) was applied to extract, classify and model the topological structure and dynamics of surface roughness in two highly eroded catchments of Mexico. Both areas are affected by gully erosion (Sidorchuk, 2005) and characterized by avalanche-like matter transport. Five contrasting morphological patterns were distinguished across the slope of the bare eroded surface of Faeozem (Queretaro State) while only one (apparently independent on the slope) roughness pattern was documented for Andosol (Michoacan State). We called these patterns ?the roughness clusters? and compared them in terms of metrizability, continuity, compactness, topological connectedness (global and local) and invariance, separability, and degree of ramification (Weyl, 1937). All mentioned topological measurands were correlated with the variance, skewness and kurtosis of the gray-level distribution of digital images. The morphology0 spatial dynamics of roughness clusters was measured and mapped with high precision in terms of fractal descriptors. The Hurst exponent was especially suitable to distinguish between the structure of ?turtle shell? and ?ramification? patterns (sediment producing zone A of the slope); as well as ?honeycomb? (sediment transport zone B) and ?dinosaur steps? and ?corals? (sediment deposition zone C) roughness clusters. Some other structural attributes of studied patterns were also statistically different and correlated with the variance, skewness and kurtosis of gray distribution of multiscale digital images. The scale invariance of classified roughness patterns was documented inside the range of five image resolutions. We conjectured that the geometrization of erosion patterns in terms of roughness clustering might benefit the most semi-quantitative models developed for erosion and sediment yield assessments (de Vente and Poesen, 2005).

Las nuevas medidas agroenergéticas mexicanas: un modelo microeconométrico para la evaluación de su impacto sobre los ecosistemas naturales en los estados de Hidalgo, Querétaro y Tamaulipas (México)

La ley para la Promoción y Desarrollo de Biocombustibles aprobada en México en 2007 permite la producción de bioetanol y biodiesel. Esta producción puede entrar en conflicto con la producción de alimentos y con los ecosistemas naturales y en esta tesis se desarrolla un modelo microeconométrico que puede servir de base para anticiparse a esos conflictos y para diseñar medidas de política agraria orientadas a potenciar la compatibilidad de la producción de biocombustibles con la de alimentos y con la conservación de los ecosistemas naturales. A partir de una muestra de explotaciones de tres Estados de México – Hidalgo, Querétaro y Tamaulipas- y de un modelo logit multinomial mixto, se estima la elasticidad de la superficie destinada a cultivos alimentarios respecto a cambios en los márgenes económicos de los cultivos agroenergéticos. Esa elasticidad resulta ser significativa. Mostramos que su estimación es útil para anticipar cambios en la superficie destinada a los cultivos alimentarios y a los forestales. Se evalúa el impacto de varios escenarios relativos a los márgenes brutos de los cultivos sobre las decisiones de los agricultores y se muestra la utilidad del modelo para detectar tendencias de cambio a largo plazo en la alternativa de cultivos, incluyendo los forestales. ABSTRACT The Law for the Promotion and Development of Biofuels in Mexico adopted in 2007 allows for the production of bioethanol and biodiesel. This production may conflict with food production and natural ecosystems and this thesis develops a microeconometric model that can serve as a basis to anticipate such conflicts and to implement agricultural policy measures designed to enhance the compatibility of biofuels with production food and natural ecosystems conservation. We estimate the elasticity of the area devoted to food crops with respect to changes in economic margins of energy crops, using a sample of farms in three states of Mexico - Hidalgo, Queretaro and Tamaulipas - , and a multinomial mixed logit model. We found that this elasticity is significant. And we show how it can be useful to anticipate changes in area under food crops and forests. The impact of various scenarios about gross margins on farmers' decisions is assessed and it is shown the usefulness of the model to detect trends of long-term change in the crops area, including forests.