Downscaling of surface moisture flux and precipitation in the Ebro Valley (Spain) using analogues and analogues followed by random forests and multiple linear regression

In this paper, reanalysis fields from the ECMWF have been statistically downscaled to predict from large-scale atmospheric fields, surface moisture flux and daily precipitation at two observatories (Zaragoza and Tortosa, Ebro Valley, Spain) during the 1961-2001 period. Three types of downscaling models have been built: (i) analogues, (ii) analogues followed by random forests and (iii) analogues followed by multiple linear regression. The inputs consist of data (predictor fields) taken from the ERA-40 reanalysis. The predicted fields are precipitation and surface moisture flux as measured at the two observatories. With the aim to reduce the dimensionality of the problem, the ERA-40 fields have been decomposed using empirical orthogonal functions. Available daily data has been divided into two parts: a training period used to find a group of about 300 analogues to build the downscaling model (1961-1996) and a test period (19972001), where models' performance has been assessed using independent data. In the case of surface moisture flux, the models based on analogues followed by random forests do not clearly outperform those built on analogues plus multiple linear regression, while simple averages calculated from the nearest analogues found in the training period, yielded only slightly worse results. In the case of precipitation, the three types of model performed equally. These results suggest that most of the models' downscaling capabilities can be attributed to the analogues-calculation stage.

Catches per unit of effort of bigeye tuna: a new analysis with regression trees and simulated annealing

ENGLISH: We analyzed catches per unit of effort (CPUE) from the Japanese longline fishery for bigeye tuna (Thunnus obesus) in the central and eastern Pacific Ocean (EPO) with regression tree methods. Regression trees have not previously been used to estimate time series of abundance indices fronl CPUE data. The "optimally sized" tree had 139 parameters; year, month, latitude, and longitude interacted to affect bigeye CPUE. The trend in tree-based abundance indices for the EPO was similar to trends estimated from a generalized linear model and fronl an empirical model that combines oceanographic data with information on the distribution of fish relative to environmental conditions. The regression tree was more parsimonious and would be easier to implement than the other two nl0dels, but the tree provided no information about the nlechanisms that caused bigeye CPUEs to vary in time and space. Bigeye CPUEs increased sharply during the mid-1980's and were more variable at the northern and southern edges of the fishing grounds. Both of these results can be explained by changes in actual abundance and changes in catchability. Results from a regression tree that was fitted to a subset of the data indicated that, in the EPO, bigeye are about equally catchable with regular and deep longlines. This is not consistent with observations that bigeye are more abundant at depth and indicates that classification by gear type (regular or deep longline) may not provide a good measure of capture depth. Asimulated annealing algorithm was used to summarize the tree-based results by partitioning the fishing grounds into regions where trends in bigeye CPUE were similar. Simulated annealing can be useful for designing spatial strata in future sampling programs. SPANISH: Analizamos la captura por unidad de esfuerzo (CPUE) de la pesquería palangrera japonesa de atún patudo (Thunnus obesus) en el Océano Pacifico oriental (OPO) y central con métodos de árbol de regresión. Hasta ahora no se han usado árboles de regresión para estimar series de tiempo de índices de abundancia a partir de datos de CPUE. EI árbol de "tamaño optimo" tuvo 139 parámetros; ano, mes, latitud, y longitud interactuaron para afectar la CPUE de patudo. La tendencia en los índices de abundancia basados en árboles para el OPO fue similar a las tendencias estimadas con un modelo lineal generalizado y con un modelo empírico que combina datos oceanográficos con información sobre la distribución de los peces en relación con las condiciones ambientales. EI árbol de regresión fue mas parsimonioso y seria mas fácil de utilizar que los dos otros modelos, pero no proporciono información sobre los mecanismos que causaron que las CPUE de patudo valiaran en el tiempo y en el espacio. Las CPUE de patudo aumentaron notablemente a mediados de los anos 80 y fueron mas variables en los extremos norte y sur de la zona de pesca. Estos dos resultados pueden ser explicados por cambios en la abundancia real y cambios en la capturabilidad. Los resultados de un arbal de regresión ajustado a un subconjunto de los datos indican que, en el OPO, el patudo es igualmente capturable con palangres regulares y profundos. Esto no es consistente con observaciones de que el patudo abunda mas a profundidad e indica que clasificación por tipo de arte (palangre regular 0 profundo) podría no ser una buena medida de la profundidad de captura. Se uso un algoritmo de templado simulado para resumir los resultados basados en el árbol clasificando las zonas de pesca en zonas con tendencias similares en la CPUE de patudo. El templado simulado podría ser útil para diseñar estratos espaciales en programas futuros de muestreo. (PDF contains 45 pages.)

An arithmetical theorem for partially ordered sets

The simplest multiplicative systems in which arithmetical ideas can be defined are semigroups. For such systems irreducible (prime) elements can be introduced and conditions under which the fundamental theorem of arithmetic holds have been investigated (Clifford (3)). After identifying associates, the elements of the semigroup form a partially ordered set with respect to the ordinary division relation. This suggests the possibility of an analogous arithmetical result for abstract partially ordered sets. Although nothing corresponding to product exists in a partially ordered set, there is a notion similar to g.c.d. This is the meet operation, defined as greatest lower bound. Thus irreducible elements, namely those elements not expressible as meets of proper divisors can be introduced. The assumption of the ascending chain condition then implies that each element is representable as a reduced meet of irreducibles. The central problem of this thesis is to determine conditions on the structure of the partially ordered set in order that each element have a unique such representation.

Part I contains preliminary results and introduces the principal tools of the investigation. In the second part, basic properties of the lattice of ideals and the connection between its structure and the irreducible decompositions of elements are developed. The proofs of these results are identical with the corresponding ones for the lattice case (Dilworth (2)). The last part contains those results whose proofs are peculiar to partially ordered sets and also contains the proof of the main theorem.