6. Are glaciers good detectors of climate change? 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? Glaciers and trend detection A standard test for trend detection is the Student’s t-test:- Where: t is the t-statistic  L is the linear trend  L is the standard deviation of natural variability is degrees of freedom = length of record/ (2 ✕ response time) The challenge here is we have to reply on models to know  L. Typical numbers for the Northwest if we consider the last 100 years, (the period of anthropogenic influence on climate):  L=200m,  based on a 7-yr response time), t=1.85 for 95% significance. This would require the natural glacier variability,  L, 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: Recent retreat trends are stronger, but the shorter record has fewer degrees of freedom, so the conclusion is the same. 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 generally similar climate. Degrees-of-freedom have to be carefully calculated. 5. What are odds of an advance or retreat in a given period of time?. 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*. Glacier dynamics act as a low-pass filter, damping high frequencies, but admitting low frequencies (illustrated below). 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. 7. Lessons Century-scale, kilometer scale glacier fluctuations occur in a constant climate. It is the memory intrinsic to the glacier, not the climate that is responsible for these fluctuation. The interpretation of the cause of past glaciers fluctuations should factor in the potential role of 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, 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, Roe., 2010: What do glaciers tell us about climate variability and climate change? Submitted, available at 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), Vanmarcke, E., 1983: Random Fields: Analysis and Synthesis. The MIT Press, Cambridge, 382 pp. What do glaciers tell us about climate variability and climate change? Gerard H. Roe Department of Earth and Space Sciences, University of Washington 2. Much interannual climate variability is well characterized by white noise. Abstract Glaciers respond to long-term climate changes and also to the year- to-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 extreme- value 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. 1.A classic challenge in signal- to-noise detection 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. What is the response of a glacier to this natural interannual variability, and how does it affect the interpretation of past and current changes? Only when a glacier advance/retreat significantly exceeds the natural variability can it be said to reflect a climate change Fig Glaciers undergo century-scale, kilometer-scale fluctuations, even in a constant climate. 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. 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? 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. 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) 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. Frequency Spectral power climate forcing glacier response 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 yr period in a constant climate, you are: -Very likely (>95%) to see a total excursion of >1.4km -Very unlikely ( 2.2km