An essential step for improving climate change models' performance is to evaluate their ability to represent the current climate conditions, especially extreme events. On such background, this study aims at evaluating the performance of the Quantile Delta Mapping (QDM) as a bias correction method for annual maximum daily precipitation series (bmax) generated from downscaled climate change models under tropical–subtropical conditions of Brazil. We selected the QDM due to its ability to correct bias in extreme quantile of wet days. Climate projections obtained from 20 NASA Earth Exchange Daily Downscaled Projections models (NEX‐GDDP) from 1950 to 2005 were subjected to validation processes based on the QDM method. Two climate change scenarios (RCP 4.5 and RCP 8.5 W m⁻²) have also been considered. Several goodness‐of‐fit measures, such as root‐mean‐square‐error (RMSE),SD, percentual bias (pbias), mean absolute error (MAE), Pearson correlation test, modified Willmott test (d_m), have been calculated from the outcomes of the models and their corresponding observed data (obtained from rain gauges). These goodness‐of‐fit measures were calculated before and after applying the QDM method. The QDM was able to correct virtually all biases. More specifically, the QDM successfully adjusted the empirical cumulative distribution of climate change projections, removing the systematic error of raw data. The QDM also presented a suitable performance when applied to future projections (2020–2095). This statement holds for all NEX‐GDDP models, except for the ACCESS1‐0 model in RCP 8.5. In such a scenario, this latter model presented unrealistic rainfall values. Finally, with the improvement resulting from applying the bias correction method QDM, there was an increase in the number of climate projections suitable for end‐users in the study region.

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.

The Mann-Kendall test: the need to consider the interaction between serial correlation and trend - doi: 10.4025/actasciagron.v35i4.16006

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.

Drought is a slow-moving hazard that occurs in virtually all countries of the world. In the light of this, several indices have been developed to improve the detection of drought's onset, as well as quantifying other features of this phenomenon. The Standardized Precipitation Index (SPI) is often used in order to characterize meteorological droughts. In addition, this index is largely used by Brazilian's agricultural institutions. In order to add important information to the drought literature, this review article described a general definition of drought, evaluated it from a statistical point of view, and also described the SPI strengths and limitations. An adaptation of the SPI that aims to develop a probability-based agricultural drought index was also presented. The results obtained herein, associated with several studies carried out throughout the world, demonstrated that the SPI is not an agricultural index. It is just a mathematical approach developed to transforming skewed distributions into the Gaussian form. If this standardization cannot be achieved, the use of this index becomes meaningless. Therefore, a normality test should be used in establishing a temporal lower limit for the SPI computations. It was also verified that for periods in which the probability associated with the zero precipitation value is close to 0.5, the SPI may erroneously indicate the end of an existing drought (or a decrease in its severity) in the presence of a decrease in the actual evapotranspiration values.

The Standardized Precipitation Index was developed as a probability-based index able to monitor rainfall deficit in a standardized or normalized way. Thus, the performance of this drought index is affected by the use of a distribution that does not provide an appropriate fit for the rainfall data. The goal of this study was to evaluate the adjustment of the gamma distribution for the rainfall amounts summed over several time scales (Pelotas, Rio Grande do Sul, Brazil), to assess the goodness-of-fit of alternative distributions to these rainfall series and to evaluate the normality assumption of the Standardized Precipitation Index series calculated from several distributions. Based on the Lilliefors test and on a normality test, it is verified that the gamma distribution is not suitable for calculating this Index in several timescales. The generalized normal distribution presented the best performance among all analysed distributions. It was also concluded that the drought early warning systems and the academic studies should re-evaluate the use of the gamma distribution in the Standardized Precipitation Index calculation algorithm. A computational code that allows calculating this drought index based on the generalized normal distribution has also been provided.