Another statistical perspective to detect trends on French annual daily precipitation maxima
Authors: Paquet Emmanuel 
Published: March 2022

&lt;p&gt;Detecting and quantifying trends on intense precipitation is an important topic to assess the impact of climate change on intense rainfall events which can be already observed the last decades. The simpler approach is to deal with annual maxima, and to use a standard statistical test, like Mann-Kendall Test, for trend detection. However, the power of this test is limited by the ratio between the (possible) slope of the trend and the variance of the sample (Wang et al., 2020).&lt;/p&gt;&lt;p&gt;The approach proposed here aims at detecting trends on annual daily precipitation maxima using a non-parametric test performed on the mean of annual maxima over a 35 year moving window. This generates samples with smaller variance in which long-term trends can better be detected. The WAVK test (Wang et al., 2008; Lyubchich et al., 2013), adapted to serial correlation and to detection of non-monotonic trends, is used here. For stations where the no-trend hypothesis is significantly rejected, a trend is computed using a GISTEMP reanalyzed surface temperature (GISTEMP Team, 2021) averaged over France as explanatory variable.&lt;/p&gt;&lt;p&gt;Tests are computed on a dataset of 600 daily rainfall series located in the south-east half of France, with records starting from 1950. It shows that for more than two-third of the tested stations, the no-trend hypothesis can be rejected (p value&lt;0.05). The significant increases of the averaged annual maxima are concentrated around the Mediterranean coast and along the Rh&amp;#244;ne valley. The median slope (% of change / degree of air temperature) of significant trends is 7%/&amp;#176;K, close to the Clausius-Clapeyron relationship, although locally higher (20%/&amp;#176;K and above). This analysis is also performed on some extremes quantiles estimated by locally fitting a Multi-Exponential Weather Pattern Distribution (Garavaglia et al., 2010) to the 35 year sub-samples, showing similar trends and spatial patterns.&lt;/p&gt;&lt;p&gt;Some perspectives are also drawn to perform a seasonal analysis of these trends, to introduce other variables for the trend model, like weather pattern frequency as a clue of the type of circulation bringing intense events, in order use the trend models identified here to compute future estimations of averaged annual maxima thanks to climate projections.&lt;/p&gt;&lt;p&gt;References:&lt;/p&gt;&lt;p&gt;Garavaglia, F., Gailhard, J., Paquet, E., Lang, M., Gar&amp;#231;on, R., &amp; Bernardara, P. (2010). Introducing a rainfall compound distribution model based on weather patterns sub-sampling. Hydrology and Earth System Sciences, 14(6).&lt;/p&gt;&lt;p&gt;GISTEMP Team, 2021: GISS Surface Temperature Analysis (GISTEMP), version 4. NASA Goddard Institute for Space Studies. Dataset accessed 2021-09-01 at https://data.giss.nasa.gov/gistemp/.&lt;/p&gt;&lt;p&gt;Lyubchich, V., Gel, Y. R., &amp; El&amp;#8208;Shaarawi, A. (2013). On detecting non&amp;#8208;monotonic trends in environmental time series: A fusion of local regression and bootstrap. Environmetrics, 24(4).&lt;/p&gt;&lt;p&gt;Wang, L., Akritas, M. G., &amp; Van Keilegom, I. (2008). An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models. Journal of Nonparametric Statistics, 20(5).&lt;/p&gt;&lt;p&gt;Wang, F., Shao, W., Yu, H., Kan, G., He, X., Zhang, D., ... &amp; Wang, G. (2020). Re-evaluation of the power of the mann-kendall test for detecting monotonic trends in hydrometeorological time series. Frontiers in Earth Science, 8, 14.&lt;/p&gt;