The modified Mann-Kendall test: on the performance of three variance correction approaches

Abstract

The Mann-Kendall test has been used to detect climate trends in several parts of the Globe. Three variance correction approaches (MKD, MKDD and MKRD) have been proposed to remove the influence of serial correlation on this trend test. Thus, the main goal of this study was to evaluate the probability of occurrence of types I and II errors associated with these three approaches. The results obtained by means of Monte Carlo simulations and from a case of study allowed us to drawn the following conclusions: All approaches are capable of meeting the adopted significant level when they are applied to trend-free uncorrelated series. The approaches are as powerful as the original MK test when they are applied to uncorrelated series. Regarding serially correlated series it was verified that: (i) the performance of the MKDD and MKRD are comparable; (ii) both approaches may not be able to preserve the adopted significance level and (iii) although the MKD is capable of preserving the adopted significance level, it is less powerful than the MKDD and MKRD. Thus, there is a trade-off between the power of the three approaches and their capability of meeting the nominal significance level. Accordingly, we recommend the use of at least two approaches -MKD and MKDD(MKRD)-to evaluate the presence of trends in a given dataset.Key words: Monte Carlo simulations, serial correlation, climate change. Teste de Mann-Kendall modificado: desempenho de três abordagens da correção da variânciaResumo O teste de Mann-Kendall (MK) vem sendo largamente utilizado para detectar tendências climáticas em diversas partes do globo. Três adaptações têm sido propostas (MKD, MKDD e MKRD) para remover a influência da correlação serial sobre o MK. O objetivo deste trabalho foi avaliar a probabilidade de ocorrência dos erros tipos I e II associada a essas três adaptações. Com base em simulações de Monte Carlo e em um estudo de caso, concluiu-se que as três adaptações são capazes de (i) preservar o nível de significância adotado quando aplicadas à séries livres de tendência e autocorrelações e (ii) apresentam a mesma probabilidade de erro tipo II (power of the test) do MK quando aplicadas a amostras livres de correlação serial. O MKDD e o MKRD apresentam desempenho equivalente, sendo ambos incapazes de preservar o nível de significância adotado quando aplicados a séries autocorrelacionadas. O MKD sempre preserva a significância nominal. Entretanto, a probabilidade de erro tipo II associada a esse último teste tende a ser mais elevada do que as associadas ao MKDD e ao MKRD. Assim, considerando-se que a adoção da adaptação com menor probabilidade de erro tipo I acarreta em aumento da probabilidade de erro tipo II, recomenda-se o uso simultâneo do MKD e do MKDD (MKRD).Palavras-chave: simulações de Monte Carlo, correlação serial, mudança climática.

Climate trends in a non-traditional high quality wine producing region

“…A significant and positive MK result indicates that the Tmin series are systematically moving to a warmer condition. Moreover, according to Blain (2013) and Danneberg (2012), if the outcomes obtained from the original MK and MK-PW test do not significantly differ from each other it may be assumed that there is no significant serial correlation affecting the trend analysis. The results of the trend analyses obtained from the MK and MK-PW did not significantly differ from each other.…”

“…These three temperaturebased indices were selected due to their previous use in studies that address the effect of regional climate conditions on the general wine style (Anderson et al, 2012;Back et al, 2012;2013;Tonietto and Carbonneau, 2004). Also, the use of these three temperature-based indices relies on the fact that the air temperature is one of the most important factors affecting the quality of vinegrapes production (Hall and Jones, 2010).…”

“…Initially proposed by Tonietto and Carbonneau (2004), the HI (Equation 2; Table 1) is largely used in viticulture studies (Anderson et al, 2012;Back 2012;2013;Orlandini et al, 2009). The HI and GDD equations are similar to each other (Anderson et al, 2012) but, the HI gives more emphasis to the effect of the Tmax on the crop development.…”

“…The Mann-Kendall test (MK; Kendall and Stuart, 1967;Mann, 1945) is a non-parametric test widely used to detect trends in meteorological, hydrological and agrometeorological time series (Back et al, 2012;2013;Blain, 2013, among many other). Positive (negative) MK values indicate the presence of increasing (decreasing) trends.…”

“…The TSA is a robust non parametric estimate of the slope of the trend frequently used in (agro/hydro) metorological studies (Back et al, 2012;2013, among many others). All statistical tests were performed at the 5% significant level.…”