Wednesday, February 27, 2013

Precipitation - according to instruments, models and proxies

The paper
Bunde, A., U. Büntgen, J. Ludescher, J. Luterbacher, and H. von Storch:  Is there memory in precipitation?
has been published by  Nature Climate Change 3: 174-175. A fine cooperation of theoretical physicists and climate scientists.

The paper asks if  proxies, which supposedly represent rainfall, really present rainfall or something else, such as integrated rainfall, which is something like soil moisture? In any case, shorter rainfall series derived from instrumental data as well as from millennial simulation show a white noise behavior for yearly data, whereas proxies from tree rings have memory. Of course, both instrumental data may be too short and model data flawed, but it is more plausible that the tree ring data reflect not only precipitation but other factors, and, indeed it is the amount of water available to trees in the solid which matters, not how much is precipitating. -

The paper is available from the copyright-walled nature web-page. Alternatively, we offer here an earlier, and shorter version. The published version is longer, explains more details, but is unchanged in substance.
Obviously, this paper is rather technical, and of little interest for those of our readers, who prefer to argue only politically (which is fine :-)) with little interest in the inner working of science. However, I consider the case an interesting example, how scientific progress is meandering forward in little steps - and that self-critical reflection is still an active element in the daily work of climate scientists. Footnote and references are deleted - but the manuscript with references is available from

"Precipitation variation can affect ecological systems, agricultural yields and human societies among various spatio-temporal scales. Paleoclimatic insight on the persistence of wet and dry conditions is relevant to assess perspectives and drivers of ongoing climate change. Since systematic meteorological measurements are mainly limited to the last century, pre-instrumental evidence of precipitation variability during the past millennium derives from proxy-based reconstructions and outputs from climate model simulations. Here we address, if these sources reflect a consistent picture of past precipitation variability. In fact, they do not.

We compare tree ring-based reconstructions from North America, Central Europe and High Asia with forced model simulations and instrumental measurements. To quantify the temporal rhythm of each precipitation record, we first consider the persistence lengths l that are defined by the numbers of successive years in each record during which precipitation is either below or above the median (dry or wet period). It is known that in uncorrelated data (white noise), the persistent length is distributed exponentially, i.e. its frequency of occurrence decreases exponentially with increasing l. We show that the persistence lengths derived from model simulations and instrumental observations resemble white noise (Fig. 1c,d). In contrast, the length distribution of the reconstructions is quite broad and thus indicative for strong multi-annual and multi-decadal persistence (pink noise) (Fig.1a). Long-term persistent data with Hurst exponents ~0.8-0.9 do indeed reveal similar behaviour (Fig. 1b).

We further quantify average precipitation patterns after wet or dry periods of certain lengths l. Data without persistence mirror temporal insensitivity, whereas systems with memory exhibit more (less) precipitation after wet (dry) periods. The reconstructions indicate a strong dependence on previous climate (Fig. 1 insets), again comparable to long-term persistent data with Hurst exponents ~0.8-0.9,whereas the simulations and observations again reflect white noise behaviour. These essential differences also derive from more advanced mathematical techniques like wavelet and detrended fluctuation analysis, and further appear robust in extreme year statistics (see Supplementary Information for details). The reconstructed extremes cluster in time, while the model and observational extremes occur more randomly distributed.

In light of the above, it appears obvious that there is no consistent picture of past precipitation variability emerging from the main two data sources. The course of millennium-long model simulations of regional precipitation variability is supported by instrumental measurements of the last century, suggesting that the occurrence of dry and wet periods generally follows white noise behaviour. It is likely that tree-ring width chronologies overestimate the true precipitation memory,since tree growth is rather influenced by (red) fluctuations in soil moisture availability than by (white) changes in rainfall. Independent lines of palaeoclimatological evidence, however, provide long-term changes in the Earth’s hydrological cycle, which likely caused prolonged episodes of relative droughtat regional to continental scales.

Fig. 1.
Histogram of persistence lengths of
(a) tree ring-based precipitation reconstruction from Central Europe (396BC-604AC) and (985-1985), Colorado (1000-1988), and High Asia (1000-1998), as well as
(b) synthetic long-term persistent data of comparable length (L=1000) with Hurst exponents of 0.8 and 0.9.
(c) ECHAM6 precipitation output for the three proxy areas considered (885-1885), and
(d) monthly precipitation measurements (Potsdam, Germany,1893-1999), together with generated white noise (green) of the same length. The scales are in years for model and reconstructed data, and in months for the instrumental data. The insets show the difference between the (conditional) average precipitation Pn after n consecutive wet or dry years (resp. months) and the mean precipitation P, in units of the standard deviation of each record.


hvw said...

Thanks, nice paper.

Reminds me of another very recent study: Spectral biases in tree-ring climate proxies by Franke et al. They also find a spectral mismatch between proxy records (not only TRW), on the one hand side and GCMs and reanalysis data on the other hand. Regarding precip they find the same (related?) thing, i.e. a red bias of the proxy reconstructions. But they also find this for temperature. Wonder whether this doesn't point to a more general problem with proxy reconstructions, rather than just the neglect of the persistence of soil moisture?

hvw said...

sorry, broken link to the paper. It is here:

Hans von Storch said...

The two pieces were written without knowledge of each other, and are thus independent. They both point to a problem with proxies, and with our analysis we do not imply that this would be the only problem, but that assessing the skill of proxies may require more care and concept. Exhibiting a correlation between proxy and target variable may not be enough to qualify for a proxy. Another example is the method, which relates temperature to sea level rise, while the driver is better described by the air sea heat flux (as long as thermal expansion is the major driver) - see von Storch, H., E. Zorita and J.F. González-Rouco, 2008: Relationship between global mean sea-level and global mean temperature and heat flux in a climate simulation of the past millennium, Ocean Dyn. doi 10.1007/s10236-008-0142-9, 10pp.

wflamme said...

Hallo Herr von Storch,

bedeutet ein solches 'Niederschlags-Langzeitgedächtnis' für die Rekonstruktion von Büntgen et al. (2011) nicht, daß über zu enge Konfidenzintervalle hinaus die Rekonstruktion womöglich grundsätzlich vermurkst ist, weil die eher kurze Kalibrierungsperiode durch Memory-Effekte verzerrt worden sein könnte?

Hans von Storch said...

Wflamme - ja, ist schon so - in der Proxy Reihe sind weniger unabhängige Realisierungen als man es in einer Instrumentellen (oder Modellkonstruierten) Reihe erwarten würde, und alle Konfidenzintervalle werden so WEITER; Tests werden konservativer, wenn man Proxy Daten nutzt zur Charakterisierung von Niederschlagseigenschaften (und man die zeitliche Abhängigkeit dabei berücksichtigt); andererseits, wenn man Tests mit Proxy-Daten macht, und die Statistik von instrumentellen Daten zur Konstruktion des statistischen Modells nimmt, wird der Text liberal.
Wie man die Anzahl der unabhängigen Daten in einer langzeitkorrellierten Reihe bestimmt, so daß Tests fair (tatsächliches Risiko für fehlentscheidung = nominelles Risiko) werden, weiß ich nicht. Auch bei kurzzeitkorrellierten Reihen sind die angewandten Methoden ziemlich murksig (wenngleich üblich).

Anonymous said...
This comment has been removed by the author.
Anonymous said...

@Hans von Storchs "Wie man die Anzahl der unabhängigen Daten in einer langzeitkorrellierten Reihe bestimmt, so daß Tests fair (tatsächliches Risiko für fehlentscheidung = nominelles Risiko) werden, weiß ich nicht."

Auch mir ist keine Formel für die effektive Datengröße für statistische Tests bei Langzeitkorrelationen bekannt.

Jedoch könnte hier Subsampling helfen: Bestimmung der Null-Verteilung mit Hilfe von Blockbootstrap-Resampling, bei dem jedoch nur ein einziger Block (mit Anzahl < Datenanzahl) gezogen wird.

Das funktioniert zumindest bei linearer Regression mit ARFIMA(0,d,0)-Rauschen; das Problem ist jedoch die Bestimmung der Subsampling-Länge. Bei dem Regressionsproblem zeigte sich eine Abhängigkeit von d (und n); ich konnte dieses Problem nur durch trial-and-error lösen.

Siehe Mudelsee (2010) Climate Time Series Analysis, Springer, Dordrecht, 474 S. (Abschnitt 4.1.6 darin). []

Manfred Mudelsee

Victor Venema said...

I did work a little on Long Range Dependence, but never on proxy data. So maybe my ideas are somewhat naive. Still just in case.

If I understand it right, if you want to use tree rings as proxy for precipitation, you select trees whose growth are water limited, that is in dry regions. In that case, without much ground water dynamics, I would not expect much correlations from year to year in soil moisture, not much more than in the precipitation itself.

I would expect that the main reason for autocorrelations in general and LRD in proxy data would be in the errors. Precipitation is just one factor determining tree growth. The other factors may well produce strong autocorrelations: pests, damage, adaptation of the tree to its environment (maybe even passed on to its offspring by epigenetics) and the maturity of the tree and changes in its root depth.

Also in the generation of a long proxy time series from single trees and other proxy sources, you will likely easily introduce jumps as the relationship between tree growth and precipitation is a little different for every tree/proxy. In a paper with Henning Rust, we have shown that such jumps (inhomogeneities) in raw instrumental data produce an artificially high Hurst index.

Rust, H.W., O. Mestre, and V.K.C. Venema. Less jumps, less memory: homogenized temperature records and long memory. JGR-Atmospheres, 113, D19110, doi: 10.1029/2008JD009919, 2008.

Anonymous said...

If I understand it right, tree rings are rather a proxy for moisture than precipitation. I would assume that moisture consists both of precipitation and temperature. If temperatures are higher, the soil gets drier.

If right I wouldn't be surprised about autocorrelation. Maybe it's the autocorrelation of temperatures the tree ring proxies are showing.

Best regards

hvw said...

Stefan Brönnimann has written a very accessible description of these issues here (german).

Anonymous said...

Strictly speaking, "tree-ring" is not a climate proxy variable but a climate archive. On a climate archive you may measure climate proxy variables indicating climate variables.

For example, on the "tree-ring" archive, you can measure the proxy variable "ring width" (indicating precipitation and other), the proxy variable "radiocarbon content" (indicating solar activity), or perhaps other variables.

I agree with Victor Venema that it is very interesting to study how the statistical properties of the climate are modified via the archive-proxy combination.