Perfomance of methods for estimating reference evapotranspiration in the municipalities of Frederico Westphalen and Palmeira das Missoes, State of Rio Grande do Sul, Brazil

The estimation of reference evapotranspiration (ETo), used in water balance, allows to determine soil water content, assisting on irrigation management. The present study aimed to compare simple ETo estimating methods with the Penman-Monteith (FAO), in the folowing time scales: daily, 5, 10, 15 and 30 days and monthly in the counties of Frederico Westphalen and Palmeira das Missoes, in the Rio Grande do Sul state, Brazil. The methods tested had their efficiency improved by increasing the time scale of analysis, keeping the same performance for both locations. The highest and lowest ETo values occurred in December and June, respectively. Most methods underestimated ETo. For any of the time scales Makking and Radiaton FAO24 methods can replace the Penman-Monteith for estimating ETo.

Desempenho de métodos de estimativa da evapotranspiração de referência nas localidades de Frederico Westphalen e Palmeira das Missões, RS

A estimativa da evapotranspiração de referência (ETo), usada no balanço hídrico, possibilita quantificar o armazenamento de água no solo, auxiliando no manejo da irrigação. O objetivo do trabalho foi comparar métodos mais simples de estimativa da evapotranspiração de referência com o método Penman-Monteith (FAO), nas escalas diária e de 5, 10, 15 e 30 dias, e mensal, para os municípios de Frederico Westphalen e Palmeira das Missões, no RS. Os métodos avaliados tenderam a melhorar a eficiência com o aumento da escala temporal de estudo, mantendo o mesmo desempenho para ambas as localidades. Os maiores e menores valores de ETo ocorreram nos meses de dezembro e junho, respectivamente. A maioria dos métodos subestimou os valores de ETo. Em qualquer escala temporal, os métodos de Makking e da Radiação FAO24 podem substituir o modelo de Penman-Monteith.

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

In this work we compared the estimates of the parameters of ARCH models using a complete Bayesian method and an empirical Bayesian method in which we adopted a non-informative prior distribution and informative prior distribution, respectively. We also considered a reparameterization of those models in order to map the space of the parameters into real space. This procedure permits choosing prior normal distributions for the transformed parameters. The posterior summaries were obtained using Monte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebras series from the Brazilian financial market. The results show that the two methods are able to adjust ARCH models with different numbers of parameters. The empirical Bayesian method provided a more parsimonious model to the data and better adjustment than the complete Bayesian method.