The color of precipitation Bunde, A., U. Büntgen, J. Ludescher, J. Luterbacher, and H. von Storch Is there memory in precipitation?, Nature climate change 3: , June 2013, 12 IMSC, Jeju. Korea

Motivation The time span of systematic meteorological measurements at the global scale is, mainly restricted to the 20th century. Pre- instrumental information on precipitation variability therefore mainly derives from proxy-based reconstructions and output from climate model simulations, with both lines of independent evidence ideally covering the past millennium. Here we address, if these sources reflect a consistent picture of historical precipitation variability – in fact, they do not. We compare tree ring-based precipitation reconstructions from North America, Central Europe and High Asia with forced millennial simulations and instrumental station measurements from the same geographic areas.

Proxy data Tree ring based precipitation reconstructions from Central Europe [Büntgen et al., 2011], the southern Colorado Plateau [Salzer et al., 2005] and the high mountains of North Pakistan[Treydte, 2006)]. -An April-June reconstruction for Central Europe covering nearly the past 2500 years derived from a total of 7284 precipitation sensitive oak tree- ring width series from Northeast France, Northeast Germany and Southeast Germany. -A October-July reconstruction for North America back to AD 570 derived from three lower forest border tree-ring chronologies from the southern Colorado Plateau, composed of pines and Douglas fir. -An annual reconstruction of annual precipitation back to AD 828 for High Asia derived from four annually resolved oxygen isotope ratio (d180) chronologies from juniper tree-ring cellulose in the Karakorum mountains of northern Pakistan.

Millennial climate simulations Output of an ECHAM 6/CMIP5 -millennium simulations, exposed to estimated external forcing used for the simulation, and extended over the period A.D. To compare with the reconstructions, we selected in the model only those time spans which have been used in the reconstructions. Variations in total solar irradiance imply a change between the Late Maunder Minimum and today of about 0.1. Volcanic forcing according to the reconstructions of atmospheric optical depth due to volcanic aerosols derived from acidity in polar ice cores by Crowley et al. (2008). Vegetation cover was prescribed according to [Pongratz et al., 2009.]. We also used the earlier ECHO-G model. Since these data resulted in the same conclusions as for the ECHAM6-model, no ECHO-G results are shown.

Observational Local data Instrumental daily data in Central Europe (Potsdam, Germany), Colorado (Gunnison) and Central Asia (Irkutsk). For High Asia, daily precipitation data ranging over 100y were not available. For eliminating the short-term persistence due to weather events we averaged the observational data over 1 month. For eliminating the mean seasonal cycle, we subtracted the seasonal means.

Monthly means of precipitation, (a-c) the proxy derived estimates (d-f) the model data, (g-i) the instrumental data. (j-l) the synthetic data

To quantify the temporal rhythm of each precipitation record, we first consider the persistence lengths l that are defined by the number of successive years in each record during which precipitation is either below or above the long-term median (dry or wet period). Colour of precipitation. (a)Histograms of persistence lengths for tree ring-based precipitation reconstructions from Central Europe (396BC-604AC and ), North America ( ), and High Asia ( ). (b)Histograms for the ECHAM6 precipitation output ( ) for the same areas as in (a). (c)Histograms for synthetic long-term persistent data with Hurst exponents 0.8 and 0.9, as well as for white noise (H=0.5), for data of comparable length (L=1000). (d)Histograms of local monthly precipitation measurements (Potsdam, Germany, ), Gunnison, Colorado ( ), and Irkutsk, Central Asia, ). The scales are in years for model and reconstructed data, and in months for the instrumental data.

Histograms of persistence lengths (a)Derived from proxy data (b)From climate model (c)Synthetic long memory series (d)Derived from local data CE=Central Europe

The difference Delta P n between the (conditional) average precipitation P n after n consecutive wet or dry years (resp. months) and the mean precipitation P, in units of the standard deviation of each record, for (e) the reconstructions, (f) the model data, (g) the synthetic data, and (h) the instrumental data. The colour code is the same as in (a-d). Deviations from the mean precipitation after wet and dry periods of specific lengths.

Probability density function P Q (r) of the return intervals between events that exceed the threshold Q. The threshold is characterized by its return period R Q.

Thus, we find … Precipitation records extending cross hundredths of years derived from proxy data exhibit long memory, while Precipitation from local observations extending about 100 years, or so, exhibit short term memory (white) Precipitation from millennial climate model output exhibit also short term memory (white).

Possible explanations Regional and area averaged precipitation have different memories. - Likely not the case, as studies with averaged local observations indicate. 100 years o data in the observed records are too short. – Maybe. Climate model output is unrealistic. – Maybe. Proxy data have archived not precipitation but other quantities, in particular soil moisture. – For me the most plausible explanation.

The color of precipitation Our analysis indicates that precipitation could be WHITE, if we consider the conclusion drawn form local observations and from climate model output reliable PINK, if we believe in the evidence provided by proxy data.

a) DFA2 fluctuation functions G(s)=s for the shuffled paleo data from (top to down) (i) Central Europe (398 BC AD), (ii) Central Europe ( ), (iii) Colorado ( ), (iv) North Pakistan ( ). b) Same as a) but for the corresponding WT2 fluctuation function F(s).