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What do glaciers tell us about climate variability and climate change? Gerard H. Roe! 2. Much interannual climate variability is well characterized by white noise." • What is the response of a glacier to this natural interannual variability, and how does it affect the interpretation of past and current changes? Fig. 2 A standard test for trend detection is the Student’s t-test:- dynamic model t = Distance (m) 7500 3100 3150 3200 3250 3300 Time (yrs) Accum (myr-1) 3050 o 2 0 -2 3350 3400 3450 3500 4 2 The challenge here is we have to reply on models to know σL. Typical numbers for the Northwest if we consider the last 100 years, (the period of anthropogenic influence on climate): ΔL=200m, ν=7 (based on a 7-yr response time), t=1.85 for 95% significance. 0 -2 3. How does a glacier respond to this forcing?! • A climate that has no persistence is equivalent to white noise – its power spectrum is flat*. Figure 5: A 500 year segment of a 10,000 yr simulation of the glacier response to interannual climate variability. A standard flowline model calibrated to Mt. Baker, WA, was used. The lower panels are white-noise realizations of interannual fluctuations in accumulation and melt-season temperature, and for which a 30-yr running mean is also shown. The upper panel shows the response of the two glacier models. Kilometer-scale, century-scale glacier fluctuations occur in this simulated climate that by construction has no persistence. " te ma " cli cing r fo " ier glac onse" p res Frequency" • Therefore a constant climate with no persistence produces low frequency glacier fluctuations *n.b. there is equal power at all frequencies, but the phases are random so components different frequencies cancel out, leaving no persistence in the time series. Recent retreat trends are stronger, but the shorter record has fewer degrees of freedom, so the conclusion is the same. 5. What are odds of an advance or retreat in a given period of time?! a) 0.9 Glaciers are retreating globally. Surely that’s enough to prove climate change? Almost certainly, yes. But glaciers within a single region are not independent measures since they experience b) Degrees-of-freedom have to be generally similar climate. theoretical distr.carefully calculated. 0.8 0.8 t-stat, 100-yr trends from flowline model 0.7 0.7 1 1 . linear model flowline model 0.9 0.6 0.5 0.4 • Century-scale, kilometer scale glacier fluctuations occur in a constant climate.! 0.5 0.4 0.3 0.2 0.2 • It is the memory intrinsic to the glacier, not the climate that is responsible for these fluctuation.! 0.1 0.1 1000 7. Lessons! 0.6 0.3 0 • Glacier dynamics act as a low-pass filter, damping high frequencies, but admitting low frequencies (illustrated below). This would require the natural glacier variability, σL, to be less than 45m for the trend to be declared significant, or nearly an order of magnitude less than what is modeled in Figure 5. This is very unlikely. Issues: cumulative prob. Figure 3. (a) Annual mean precipitation recorded at Diablo Dam near Mt Baker, over the last seventy-five years, equal to 1.89±0.36(1σ) m yr-1; (b) melt-season (JJAS) temperature at the same site, equal to 16.8±0.78(1σ) oC; these atmospheric variables at this site are statistically uncorrelated and both are indistinguishable from normally-distributed white noise with the same mean and variance. The commonly performed application of a five-year running mean imparts the artificial appearance of multi-year regimes. Random realizations of white noise are shown for annual-mean accumulation (panels (c) and (e)); and for melt-season temperature (panels (d) and (f)). Note the general visual similarity of the random realizations and the observations. ΔL ⎛ υ − 2 ⎞ ⎜ ⎟ σL ⎝ 12 ⎠ Where: t is the t-statistic ΔL is the linear trend σL is the standard deviation of natural variability ν is€ degrees of freedom = length of record/ (2 ✕ response time) 8000 -4 3000 3100 3200 3300 3400 3500 3000 3100 3200 3300 3400 3500 Time (yrs) Time (yrs) Spectral power" • Interannual fluctuations in accumulation and ablation are intrinsic to a constant climate. -A constant climate is one in which statistical distributions of atmospheric variables do not change. Glaciers and trend detection 8500 7000 3000 • The vast majority of the climate variance in the instrumental is consistent with random year-to-year fluctuation with little to no persistence (or memory). These fluctuations are integrated in time by the glacier which responds on longer timescales. 1. A classic challenge in signalto-noise detection! 4. Glaciers undergo ! century-scale, kilometer-scale fluctuations, even in a constant climate.! 9000 • It is common to find very little persistence in instrumental records (see Burke and Roe (2010) for Europe, Huybers and Roe (2009) for the Pacific Northwest, Stouffer et al., 2000, more generally) Figure 1: Major Mount Baker glaciers superposed on a contour map (c.i. = 250 m) Glaciers are shown at their ‘Little Ice Age’ maxima, 1930, and present positions. What is the correct interpretation of the cause of these changes? The climate is warming, and glaciers are retreating because of it, but are glaciers, by themselves, independent evidence of that warming? In other words if we threw away all instrumental data, would the glaciers alone be enough to conclude a climate change was occurring? Department of Earth and Space Sciences, University of Washington" Temp ( C) Glaciers respond to long-term climate changes and also to the yearto-year fluctuations inherent in a constant climate. Differentiating between these factors is critical for the correct interpretation of past glacier fluctuations, and for the correct attribution of current changes. Previous work has established that century-scale, kilometer-scale fluctuations can occur in a constant climate. This study asks two further questions of practical significance: how likely is an excursion of a given magnitude in a given amount of time, and how large a trend in length is statistically significant? A linear model permits analytical answers wherein the dependencies on glacier geometry and climate setting can be clearly understood. The expressions are validated with a dynamic glacier model. The likelihood of glacier excursions is well characterized by extremevalue statistics, though probabilities are acutely sensitive to some poorly-known glacier properties. Conventional statistical tests can be used for establishing the significance of an observed glacier trend. However it is important to determine the independent information in the observations, which can be effectively estimated from the glacier geometry. Finally, the retreat of glaciers around Mt. Baker in Washington State is consistent with, but not independent proof of, the regional climate warming that is established from the instrumental record. Probability of exceeding Abstract! • Only when a glacier advance/retreat significantly exceeds the natural variability can it be said to reflect a climate change 6. Are glaciers good detectors of climate change?! 1200 1400 1600 1800 2000 2200 Maximum - minimum excursion (m) 2400 2600 0 -4 -3 Figure 6: The probability of exceeding a given maximum total excursion (i.e., maximum advance minus maximum retreat), in any 1000 yr period. Crosses shows calculations from the dynamic model output. The curves are calculated from analytical expressions in Vanmarcke (1983). Extreme value statistics (e.g., Vanmarcke, 1983) can be used to predict the likelihood of an excursion in a given period of time. Such formula are very successful in describing the dynamic glacier model. • So for the example shown here (Mt. Baker, Wa), in any 1000yr period in a constant climate, you are: -Very likely (>95%) to see a total excursion of >1.4km -Very unlikely (<5%) to see a total excursion of >2.2km -2 • The interpretation of the cause of past glaciers fluctuations should factor in the potential role of -1 0 1 2 3 4 t-statistic interannual variability.! • Mt. Baker glaciers are not by themselves independent evident of the warming that is established from the instrumental record.! • Glaciers are messy thermometers!! References! Burke, E.E., and G.H. Roe, 2010: The persistence of memory in the climatic forcing of European glaciers. In preparation. Huybers, K.M., and G.H. Roe, 2009: Glacier response to regional patterns of climate variability. J. Climate, 22, 4606-4620. Roe and O'Neal, 2009: The response of glaciers to intrinsic climate variability: observations and models of late-Holocene variations in the Pacific Northwest. J. Glaciol., 55, 839-854. Roe., 2010: What do glaciers tell us about climate variability and climate change? Submitted, available at http://earthweb.ess.washington.edu/roe/GerardWeb/Publications.html. Stouffer, R.J., G. Hegerl and S. Tett, 2000: A comparison of surface air temperature variability in three 1000-yr coupled ocean–atmosphere model integrations. J. Climate, 13(3), 513-537. Vanmarcke, E., 1983: Random Fields: Analysis and Synthesis. The MIT Press, Cambridge, 382 pp.