ABSTRACT A key step for any modeling study is to compare model-produced estimates with observed/reliable data. The original index of agreement (also known as original Willmott index) has been widely used to measure how well model-produced estimates simulate observed data. However, in its original version such index may lead the user to erroneously select a predicting model. Therefore, this study compared the sensibility of the original index of agreement with its two newer versions (modified and refined) and provided an easy-to-use R-code capable of calculating these three indices. First, the sensibility of the indices was evaluated through Monte Carlo Experiments. These controlled simulations considered different sorts of errors (systematic, random and systematic + random) and errors magnitude. By using the R-code, we also carried out a case of study in which the indices are expected to indicate that th empirical Thornthwaite’s model produces poor estimates of daily reference evapotranspiration in respect to the standard method Penman-Monteith (FAO56). Our findings indicate that the original index of agreement may indeed erroneously select a predicting model performing poorly. Our results also indicate that the newer versions of this index overcome such problem, producing more rigorous evaluations. Although the refined Willmott index presents the broadest range of possible values, it does not inform the user if a predicting model overestimate or underestimate the simulated data, resulting in no extra information regarding those already provided by the modified version. None of the indices represents the error as linear functions of its magnitude in respect to the observed process.

RESUMO Nas últimas décadas, pesquisadores científicos e acadêmicos em todo o mundo têm se preocupado com a avaliação das tendências dos climas regional e global. A avaliação das alterações no clima é uma ferramenta para o planejamento da sociedade, pois permite considerar as possíveis consequências do aumento das temperaturas do ar e de mudanças no regime de precipitação que foram observadas ao redor do mundo. Sob a hipótese da presença de alterações climáticas no Brasil, o objetivo do presente estudo foi identificar a existência de tendências climáticas em 243 séries anuais de temperaturas máxima, mínima e média do ar (T-Máx., T-Mín. e T-Méd.) e precipitação pluviométrica (Prec.) em cidades do Brasil. Foram empregados os testes estatísticos de Mann-Kendall (M-K.) e Pettitt (Pett.) para avaliação de tendências significativas. Para a visualização espacial das tendências observadas, foram elaborados mapas. Os resultados estatísticos mostram que, de todas as cidades estudadas, foram observadas tendências positivas na T-máx. em 35% das séries, negativas em 1% e ausência de tendência em 64%. Para a T-Mín., foram observadas tendências positivas em 30% dos casos, negativas em 8% e ausência de tendência em 63%. Na T-Méd., tendência positiva foi detectada em 35% das cidades analisadas, negativa em 3% e ausência de tendência em 62%. Por fim, na Prec., tendência positiva em 6% dos casos, negativa em 4% e ausência de tendência em 91%. As tendências observadas no presente estudo estão possivelmente relacionadas às atividades antrópicas em cada localidade, como o expansionismo urbano, o desenvolvimento industrial e o adensamento populacional.

ABSTRACT In recent decades, scientific and academic researchers around the world have been concerned with the assessment of regional and global climate trends. The assessment of changes in the climate system is a planning tool for society as it enables the consideration of possible consequences from the increasing air temperature and changes in precipitation that have been observed around the world. Under the hypothesis of climate change presence in Brazil, the aim of this study was to verify the presence of climate trends in 243 annual data from Brazilian cities of maximum, minimum and average air temperatures and rainfall. The Mann-Kendall (M-K.) and the Pettitt (Pett.) tests were applied in order to evaluate the presence of significant trends. Maps were developed for the spatial visualization of the observed trends. The statistical results show that, from all the studied cities, increasing trends in maximum temperature were observed in 35% of the series, decreasing in 1% and no trends were observed in 64%. For the minimum temperature, increasing trends were observed in 30% of the studied series, decreasing in 8% and no trends in 63%. For the average temperature, increasing trends were observed in 35%, decreasing in 3% and no trends in 62%. For rainfall, increasing trends were observed in 6%, decreasing in 4% and no trends in 91%. The observed trends may be related to the anthropic activities like urban expansion, industrial development and the increasing population density in each studied city.

Resumo O objetivo deste trabalho foi identificar tendências climáticas em séries temporais de precipitação pluviométrica acumulada mensal e de temperatura média do ar mensal, nas quatro estações do ano, registradas em 243 localidades distribuídas pelos biomas do Brasil. Os dados foram extraídos do Instituto Nacional de Meteorologia (INMET). Aplicaram-se os testes estatísticos de Mann-Kendall e de Pettitt. Os resultados estatísticos e os mapas de distribuições de tendências sazonais permitem observar que todos os biomas exibiram ausências de tendências significativas em ambas variáveis meteorológicas. A temperatura média foi a variável em que se mostrou o maior número de tendências positivas (72 no outono, 81 no inverno, 80 na primavera e 92 no verão). Tais tendências foram detectadas principalmente durante a década de 1990 e encontram-se nos biomas Amazônia e Cerrado. Tendências negativas foram observadas nos biomas Caatinga e no Cerrado para as estações do outono, inverno e primavera. Para a precipitação, observou-se tendências negativas nas quatro estações do ano, durante as décadas de 1980, 1990 e 2000. Tendências positivas foram observadas na década de 2000 e durante as estações do outono e inverno, especialmente nos biomas Amazônia e Mata Atlântica. Essas tendências podem estar relacionadas aos eventos El Niño e La Niña.

Abstract The aim of this work was to identify climate trends in seasonal time series for precipitation and average air temperature, observed in 243 municipalities distributed over the Brazilian biomes. The data were obtained from National Institute of Meteorology (INMET). The Mann-Kendall and Pettitt tests were applied. The statistical results and the seasonal trend distributions maps allow us to observe that all biomes exhibit non-significant trends in the both meteorological variables. The average temperature was the variable that showed the highest number of positive trends (72 in autumn, 81 in winter, 80 in spring and 92 in summer). Such trends were mostly detected during the decade of 1990 and in the Amazônia and Cerrado biomes. Negative trends were observed in the Caatinga and Cerrado biomes for the seasons of autumn, winter and spring. For the precipitation, negative trends we observed in all the four seasons, during the decades of 1980, 1990 and 2000. Positive trends were observed in the decade of 2000 and during the autumn and winter seasons, especially in the Amazônia and Mata Atlântica biomes. These trends seem to be related to the El Niño and La Niña events.

ABSTRACT The need to use a length of rainfall records of at least 30 years to calculate the Standardized Precipitation Index (SPI) limits its application in several Drought Early Warning Systems of developing countries. Therefore, in order to increase the number of weather stations in which the SPI may be applied, this study quantified the difference among SPI values derived from calibration periods (CP) smaller than 30 years in respect to those computed from the 30-year period of 1985 – 2014 in the State of São Paulo, Brazil (time scales ranging from 1 to 12 months were considered). The correlation, agreement and consistency of SPI values derived from CP ranging from the last 30 to 21 years have been evaluated. The Kolmogorov-Smirnov/Lilliefors test indicated, for all CP, that the 2-parameter gamma distribution may be used to calculate the SPI in the State of São Paulo. The normality test indicated that, even for the period of 1985 – 2014, the normally assumption of the SPI series is not always met. However, it was observed no remarkable difference in the rejection rates of the normality assumption obtained from the different CP. Finally, both absolute mean error and the modified index of agreement indicated a high consistence among SPI values derived from the calibration period of 1991 – 2014 (24 years) in respect to those derived from the 30-year period. Accordingly, it is possible to use weather stations with rainfall records starting in 1991 (or earlier) to calculate, in operational mode, the SPI in the State of São Paulo.