Trends in hydro-climatic time series

1. Trends in hydro-climatic time series Guillaume Lacombe IWMI technical meeting – 25-29 April, IWMI-HQ, Colombo Sri Lanka

2. Introduction • Needs to quantify hydro-meteorological changes • to assess water resources, risks (floods, droughts) • to identify and characterize drivers of changes (land cover changes, storage reservoirs, irrigation, climate variability) North Africa Southeast Asia

3. How to quantify changes ? • Several ways to quantify changes over time • Comparing averages of successive multi-year periods • Advantage of trends: To quantify long-term change while accounting for inter-annual variability

4. How to use trends to distinguish natural variability from man-made climate change ? “I remember that extreme events were less intense before” 16 years Vientiane, rain>40mm/day How long should be a trend so that it reflects climate change ? 52 years

5. The longest available hydro-climatic data-set: Annual minimum water level of Nile River for years 622 to 1284 A.D. (663 observations), measured at the RodaNilometer near Cairo … challenges the 30-year base line proposed by ipcc → A 80-year period with a natural downward trend…

6. “Climate changes irregularly, for unknown reasons, on all timescales” (National Research Council, 1991, p.21) • Irregular changes in time series are better modeled as stochastic fluctuations on many time scales rather than deterministic components (Hurst, 1951; Koutsoyiannis, 2002) • Human-induced increase in GHG concentration is most likely altering climate as evidence by global warming but causal effect with rainfall fluctuations are much more difficult to evidence

7. Despite this difficulty, research efforts to: • improve accuracy of trend detection tests • understanding the meaning of trends very important over recent years because climate change has become a great concern

8. A trend is defined by a slope and a significance level

9. How to calculate the slope of a trend ? • Method of least squares (Excel) • Method of Sen (1968) Sen’s slope well suited for climate time series as low-sensitive to outliers

10. Why do we need to calculate the significance of a trend?

11. True trends or random process ? • Possibility to observe a trend that occurred by chance only. Example: trends produced by the Excel random function

12. Need for tests to assess trend significance Two trends with the same slope, but different statistical significance… Significance = likelihood that the trend does not occur by chance

13. Need for tests to assess trend significance

14. Different types of trend tests…(parametric versus non parametric, bootstrap-based tests) • Parametric tests require data to have specific distribution (i.e. gaussian distribution) • Non-parametric tests: not dependent on assumptions about data distribution. Suitable for hydro-meteorological data Example: the T-test

15. The Mann-Kendall test, designed to detect monotonous trends The most extensively used trend detection test in Hydrometeorology (Mann, 1945, Kendall 1975) Significance of trends tested by comparing standardized S with standard normal variate at desired significance level Advantages: rank-based test, low sensitive to outliers

16. Requirement of most of parametric and non-parametric tests: data have to be independent • Problem of hydro-meteorological data: most of time series are auto-correlated (Hurst, 1951) Hurst phenomenon: long term hydrological persistence : tendency of wet (dry) years to cluster into multi-year wet (dry) periods

17. Why is it a problem ? Positive auto-correlation leads to overestimated trend significance (Cox and Stuart, 1955) Distribution of the MK statistics of 5000 generated AR (1)

18. 2 methods to solve this problem: • 1/ Removal of correlation structure in original time series • Prewhitening (Von Storch, 1995). Problem: removing auto-correlation also removes part of the trend → underestimated trend • Trend-free prewhitening (Yue et al, 2002): remove trend, then remove auto-correlation, and then add trend. Problem: the auto-correlation coefficient was not totally removed ! → overestimated trend • Simultaneous estimation of auto-correlation and trend slope (Hamed, 2009)

19. 2 methods to solve this problem: • 2/ Modification of the test to account for autocorrelation • Assuming AR[1] process (Lettenmaier, 1976) • Assuming scaling behavior (i.e. Hurst phenomenon) (Hamed, 2008) Hurst phenomenon: long term hydrological persistence : tendency of wet (dry) years to cluster into multi-year wet (dry) periods

20. 3 case studies: • Observed rainfall in the Mekong (1953-2004) • RCM-simulated rainfall and temperature in the Mekong (1960-2049) • Observed rainfall in Ghana (1960-2005)

21. Climate variables Possibility to observe contrasted changes that may occur in different weather extremes (light/heavy rainfall) : trends in small variables are not offset by the presence or absence of trends in the variables involving large values.

22. Study area and data 17 stations in central Mekong Basin. Longest rainfall time series in Southeast Asia: 1953-2004 29 variables capturing main climate features that control rainfed agriculture and have impacts on human livelihoods

23. Results: local trends at stations Local significant trends : Increase Decrease Less than 10% of trends significant at 95% confidence level

24. Results: regional trends Station showing significant trends for 5-8 climate variables among the 29 Field significance indicates whether one significant trend emerges from all stations. Regional average Kendall’s statistic (Douglas et al. 2000) None of the variables displays significant trend at the regional scale

25. Comparison of our results with previous studies Difference in length periods is likely to explain part of the opposite results 1961-1998 : Decrease 1953 -2004 : Increase

26. Investigation of trends in projected rainfall and temperature in the Greater Mekong Sub-region : 1960-2049 Rainfall • Analysis of trends in rain & temp. time series from regional climate model Temperature Year Wetter wet season, drier dry season outside Mekong catchment. Temperature follows global warming trend

27. Rainfall trend analyses in Ghana 16 stations in Ghana over period 1960-2005

28. Trend results Apparent inconsistency Significant reduction of light rainfall (<20mm/day) and associated number of rainy day Similar annual rainfall amounts but produced by reduced number of rainy days Longer rainless period during wet season. → Deleterious effects on crops.

29. “Local” versus “regional” significance Variable: length of the longest drought during the wet season

30. Trend attribution (1) • When a trend is detected, how to explain it ? • Result of a random process ? (significance = likelihood to occur by chance alone) • Is there a deterministic cause (if not, not possible to extrapolate the trend) • Climatic time series: GHG concentration increase, El Nino/La Nina, Solar cycles, volcanic eruption • Hydrologic time series: land-cover change, soil permeability change, water table level drawdown, water storage development

31. Trend attribution (2) • To conclude on causal-effect, need to cross check different data and look for consistencies between several phenomenon occurring at same time. • Easy to explain temperature increase with global warming • More difficult to attribute rainfall change to climate change