Historical Trends in Florida Temperature and Precipitation

Transcription

1 Historical Trends in Florida Temperature and Precipitation Jayantha Obeysekera (SFWMD) - Presenter Michelle M. Irizarry-Ortiz (SFWMD) Eric Gadzinski (UM) February 24, 2010 UF WI Symposium Gainesville, Florida

2 Main Points Precipitation and temperature statistics at 32 stations in Florida analyzed for trends using nonparametric techniques number of wet days during the dry season POR May precipitation throughout the state POR and especially post May be linked to changes in start of the wet season. Urban heat island effect urban (and drained) areas Tave and number of dog days for wet (warm) season especially post-1950 Decrease in DTR ( Tmin > Tmax) Annual maximum of Tave and Tmin for all seasons in POR and especially post-1950

3 Station Data Data for 32 NWS and COOP stations obtained from the office of the state climatologists located at FSU Longest and most complete daily precipitation and temperature records ( ) Raw data obtained and analyzed for trends

4 Variables Precip Tmax Tmin Tave DTR Statistics used for trend detection Averages (magnitude and Variable duration each Extremes (by season) by season and by month) Precipitation Total precipitation Number of wet days Number of days of extreme values (> 1-in-2). Maximum seasonal value Number of heavy precipitation events (> 1-in-5) of duration Daily temperature (Average, Maximum, Minimum, Temperature Range) Average temperature Number of dog days (> 80F) Annual Temperature Range 2, 3, 5, and 7 days Number of days of extreme values (> 1-in-2). Maximum and minimum seasonal values Number of extreme events (> 1-in-5) of duration 2, 3, 5, and 7 days Seasons: Entire year, Wet Season (MJJ+ASO), Dry Season (NDJ+FMA), NDJ, FMA, MJJ, ASO

5 Stations and Variables

6 Stations and Variables

7 Trend Detection Methods Ordinary Least Squares (Linear Regression) Parametric method Assumes residuals ~ N(0, σ). Required for hypothesis testing of trends. Sensitive to outliers (lower R^2) and influential points (extreme values near beginning and end of dataset that greatly affect the slope of the regression line and may increase R^2). The leverage effect can yield incorrect results. Mann-Kendall Test and Theil-Sen Regression Non-parametric test Resistant to outlier effects, influential data, censored data, non-normal data Assumes data is iid. Key issue: Distinguishing between trend and persistence (autocorrelation) in the timeseries. + serial correlation can overestimate probability of a trend

8 Mann-Kendall Test and Theil-Sen Regression Mann-Kendall Test (Mann, 1945 & Kendall, 1938, 1962, 1975) H 0 : The data x i are a sample of n independent and identically distributed random variables (i.e. no trend (τ = 0)) x j and x k are sequential timeseries values. An exact distribution for S exists and is used in the case when there are no ties (Best and Gipps, 1974). In the case of ties, and for large n a normal approximation is used: For n > 10, Z s ~ N(0,1). H 0 is rejected if p-value associated with Zs is less than chosen significance level α.

9 Mann-Kendall Test and Theil-Sen Regression Theil-Sen Regression (Sen, 1968 & Theil, 1950) For all possible distinct pairs of measurements, (x j, x k ) for t k > t j compute the simple pairwise slope estimate: S ij = (x k - x j )/(t k - t j ) Estimate of the slope is β 1 = median(s ij ) Intercept based on Conover (1980) method is β 0 = median(x) - β 1 *median(t) Methods assume data is iid. Zhang s Pre-Whitening method (2000) was used to pre-whiten the timeseries (remove serial autocorrelation). See Wang and Swail (2001). Seasonal Mann-Kendall test and Theil-Sen regression performed on monthly values. For autocorrelated monthly data, used the Modified Seasonal Mann- Kendall test from Hirsch and Slack (1984). The Seasonal test assumes homogeneity in trends across seasons (months), which was first tested using test by van Belle and Hughes (1984).

10 Block Maxima & Minima Generalized Extreme Value Distribution H 0 : No trend in the location parameter µ (b=0) 2 models fitted: M 0: µ = Constant M 1 :µ(t) = a+bt Significance of trend b evaluated using the Likelihood Ratio Test, which uses the deviance statistic (Coles 2001): D = 2{l 1 (M 1 ) l 0 (M 0 )} D ~ χ 2 (df=1) {z: 1 + ζ (z µ)/σ > 0} µ R (location) ζ R (shape) σ > 0 (scale) H 0 is rejected if p-value associated with D is less than chosen significance level α.

11 Annual Precipitation - POR 3 1 # of Wet Days Dry Season - POR 1 7

12 May Precipitation - POR 10 0 May Precipitation post

13 Max Precip NDJ post

14 Wet Season Tave - POR 4 10 Wet Season Tave post

15 # of Dog Days - POR # of Dog Days post

16 Annual maxima of Tave - POR 1 9 NDJ Maxima of Tave - POR 0 13 MJJ Maxima of Tave - POR 1 10

17 Annual maxima of Tave post NDJ Maxima of Tave post MJJ Maxima of Tave post

18 Annual maxima of Tmin - POR 5 12 Annual maxima of Tmin post

19 Annual maxima of Tmax post

20 Post Post UHI-Tave Ft. Lauderdale +1.8 F Ft. Myers +2.1 F Post Arcadia -0.4 F

21 Post Post UHI-DTR Ft. Lauderdale -3.3 F Ft. Myers -1.5 F Post Arcadia -0.6 F

22 Arcadia -1.9 F Belle Glade +2.6 F

23 Median Deviation of Annual Tave for 32 stations Median Dev of Wet Season Precip for Central FL AMO COOL WARM COOL WARM

24 References Best D.J. and Gipps P.G Algorithm AS 71: The Upper Tail Probabilities of Kendall's Tau Applied Statistics, 23(1): Coles S An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag. ISBN: Conover W.L Practical nonparametric statistics, 2d ed.: New York, John Wiley and Sons, 493 p. Enfield D.B., Mestas-Nuñez A.M., Trimble. P.J The Atlantic multidecadal oscillation and its relationship to rainfall and river flows in the continental U.S.. Geophys. Res. Lett., 28: Hirsch R.M., Slack J. R A Nonparametric test for seasonal data with serial dependence. Water Resour. Res., 20(6): Kendall M.G A new measure of rank correlation. Biometrika, 30:81-93 Kendall M.G Rank Correlation Methods, Charles Griffin and Company: London. Kendall M. G Rank Correlation Methods. Charles Griffin, 196 pp. Kukla G., Karl T.R Nighttime warming and the greenhouse effect. Environ Sci Technol 27(8): Mann H.B Nonparametric tests against trend, Econometrica, 13: Pielke R.A. Sr. et al Unresolved issues with the assessment of multidecadal global land surface temperature trends. J Geophys Res 112:D24S08 Sen P. K Estimates of the Regression Coefficient Based on Kendall s Tau. Journal of the American Statistical Association, 63(324): Theil H A rank-invariant method of linear and polynomial regression analysis, III. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen A, 53: Van Belle G., Hughes J.P Nonparametric tests for trends in water quality. Water Resour. Res., 20(1): Wang X.L. and Swail V.R Changes in extreme wave heights in northern hemisphere oceans and related atmospheric circulation regimes. Journal of Climate, 14: Zhang X., Vincent L.A., Hogg W.D. and Niitsoo A Temperature and Precipitation Trends in Canada during the 20th Century. Atmosphere-Ocean, 38(3):

25 Extra slides

26 Wet Season Tave - POR 4 10 Wet Season Tave post

27 POR POR Ft. Lauderdale +1.4 F Ft. Myers +2.4 F POR Arcadia -1.9 F