&lt;b&gt;The influence of nonlinear trends on the power of the trend-free pre-whitening approach

Gabriel Constantino Blain

doi:10.4025/actasciagron.v37i1.18199

Abstract

The Mann-Kendall test has been widely used to detect trends in agro-meteorological as well as hydrological time series. Trend-free pre-whitening (TFPW-MK) is an approach that improves the performance of this test in the presence of serial correlation. The main goal of this study was to evaluate the ability of TFPW-MK to detect nonlinear trends. As a case study, this approach was also applied to 10-day values of precipitation (P), potential evapotranspiration (PE) and the difference between P and PE (P- PE) obtained from the weather station of Ribeirao Preto, State of Sao Paulo, Brazil. The results obtained from Monte Carlo simulations indicate that upward convex trends increase the power of this test, while upward concave trends decrease its power. The results obtained from the location of Ribeirao Preto reveal an increasing pressure on agricultural water management due to growing PE values. Thus, we conclude that the power of the TFPW-MK is affected by the shape of the trend and that the hypothesis of the absence of climate change in the abovementioned location cannot be accepted.

Highlights

The rank-based Mann-Kendall test (MK) has been widely used throughout the world to detect trends in agro-meteorological as well as hydrological time series
We carried out sets of Monte Carlo simulations to (i) evaluate the power of the TFPW-MK to detect nonlinear trends with respect to its power to detect linear trends and (ii) to compare the power of the TFPW-MK to the power of the original MK when both tests are applied to uncorrelated data
According to this last statement and the purpose of this study, we note that the TFPW-MK must be as powerful as the original MK when both tests are applied to uncorrelated data that comprise a true trend (Figures 3 and 4; r = 0); otherwise, the TFPW algorithm may erroneously modify the original data, leading to false results

Summary

Introduction

The rank-based Mann-Kendall test (MK) has been widely used throughout the world to detect trends in agro-meteorological as well as hydrological time series. Agronomy possible signals of climate change in several parts of the globe. As described in Chandler and Scott (2011), the MK ‘has been used extremely widely in environmental studies’. The null hypothesis (H0) of the MK test is that the data are realized values of identically distributed and independent (iid) variables (CHANDLER; SCOTT, 2011). From a strictly statistical point of view, the non-acceptance of H0 implies that the sample data under analysis do not meet this iid assumption. The rejection of such H0 is frequently taken as evidence of the presence of a trend (or climate change) in a given set of sample data (BLAIN, 2012b).

Objectives

Methods

Results

Conclusion