Power laws governing hydrology and carbon dynamics in northern peatlands
Introduction
Environmental and ecological variables fluctuate over different time scales. To describe this variability and to understand the underlying mechanisms, we often need to separate “noise” from “signal”. After removing predictable signal components from time series such as secular trends and periodicities, the residual variability “can be considered as inherently unpredictable in a strictly deterministic sense” (Steele, 1985). However, the structure of environmental fluctuation is well described by a phenomenon called “1/f-noise”, and the understanding of this phenomenon would have important consequences for the interpretation of ecological time series and for ecological modelling (Halley, 1996).
Environmental fluctuations arise from various factors that may correlate on different time scales, so the noise cannot be assumed as “white noise” that has no temporal correlation. In a 1/f-noise model, the correlation of fluctuations falls off as a power law. The 1/f-noise was so named because of the shape of its spectral density, which is characterised by power-law spectra of the form: S(f) ∝ 1/fβ, where 0 ≤ β ≤ 2 (β = 0: white noise/flat spectra; β = 1: pink noise; β = 2: brown noise (Brownian motion/random walk)). The 1/f-spectra have been associated with some ecological and geophysical time series (e.g., Mandelbrot and Wallis, 1969, Steele, 1985, Pimm and Redfearn, 1988, Rhodes and Anderson, 1996, Pelletier and Turcotte, 1997, Pelletier, 1998, Keitt and Stanley, 1988). Temporal variation of the physical environment usually has a reddened spectrum, which means that the amplitude of low frequency in a spectral analysis is consistently greater than that of high frequency and variability appears to increase at the longer time scales. In practice, the spectrum yields an approximately straight-line relationship between log variance and log frequency. Comparison of power-spectral structure between environmental and biological time series would help in understanding the causal mechanisms of ecological changes, such as population fluctuation. If both time series show reddened spectra, changing physical processes may have driven populations (climatic school of population regulation) (Sugihara, 1995). In contrast, different biological fluctuation patterns may suggest independent behaviour or self-regulation of dynamics.
Peatlands are important land surface feature of the globe, and understanding feedback mechanisms of their components is crucial in the study of the global carbon cycle. Northern peatlands have accumulated up to 450 Gt of carbon over the last 12,000 years (e.g., Clymo et al., 1998). Their large C pool raises concerns that peatlands may become significant sources for atmospheric C under a changing climate. However, significant uncertainties exist in addressing the environmental controls of C dynamics and peatlands sensitivity to environmental change. The credible assessment of C sink–source relationships would need to consider processes operating over short and long time scales (Yu et al., 2003, Bauer, 2004).
Numerous studies have been carried out in recent years on environmental controls of carbon fluxes in peatland ecosystems. Most of these studies are trying to find correlative relations statistically or visually between CO2/CH4 and environmental measurements (Moore and Knowles, 1989, Moore and Roulet, 1993, Suyker et al., 1997, Lafleur et al., 1997, Lafleur, 1999, Joiner et al., 1999, Carroll and Crill, 1997, Silvola et al., 1996; among others). Here I explore the differences and similarities of temporal variability in physical environment (temperatures, water tables) and biological variables (CO2 fluxes) from four northern peatlands. Spectral analysis was used to derive the scaling exponents of time series and to understand the underlying fundamental dynamics of these systems. The comparison of physical and biological variability would provide some insights into the environmental controls of carbon dynamics over short time scale (1 h to 1 year). I find that many of these time series have scaling exponents of between 0.5 and 1.5. These 1/f-power spectra suggest that variations of these variables correlate with each other through time.
Section snippets
Peatland data
The data sets (Fig. 1) are from peatlands in central Alberta (Wolf Creek fen), central Saskatchewan (BOREAS Southern Study Area (SSA) fen), northern Manitoba (BOREAS NSA fen) and southwest Scotland (Ellergower Moss raised bog). The Wolf Creek site (lat. 53°25′N, long. 116°03′W; elevation 950 m asl) is a treed fen and is one of several peatland sites for peatland drainage and forestry experiments (Hillman, 1997). It is in a subhumid continental climate. The mean annual temperature from nearby
Power spectral analysis
There are several methods in analysing the dynamic behaviours of time series, including power spectral analysis, rescaled-range analysis and autocorrelation analysis (Schepers et al., 1992). It has been found that the power spectral analysis is better than other methods because it yields the least biased results (Schepers et al., 1992, Pelletier and Turcotte, 1997). The power spectral analysis was carried out using the periodogram method in the computer program AnalySeries (Paillard et al., 1996
Power-law behaviour of peatland time series and its interpretation
The results from spectral analysis of peatland time series show power-law behaviour of peatland hydrology and carbon dynamics. They all show that log (frequency) vs. log (power spectra) plots have a non-flat spectrum with scaling exponents of between 0.5 and 1.5. The spectral structure of air temperatures from four data sets has scaling exponents of ∼ 1.5 at high frequency but of ∼ 0.5 at lower frequency (Fig. 3A). It has a breaking point at 24 h, which show a diurnal temperature cycle. The water
Implication for peatland dynamics
A key feature of peatland ecosystems is their long-term accumulation of peat at slow rates over millennia, in addition to their short-term C flux dynamics. As a result, integration and interactions of these diverse processes at various time scales are an important issue in peatland C dynamics studies (e.g., Bauer, 2004). The analysis results from this paper indicate that time scales are important in discussing hydrology and carbon dynamics in northern peatlands. Possible self-regulation of
Acknowledgments
I thank R.S. Clymo, G.R. Hillman, P.M. Lafleur and A.E. Suyker for making the peatland data available; M.J. Apps, I.D. Campbell, G.R. Hillman, E.D. Hogg, P.M. Lafleur, D.T. Price, N.T. Roulet and D.H. Vitt for discussion; and two anonymous reviewers for helpful comments and suggestions. This work was supported by the Climate Change Action Fund of Canada and U.S. National Science Foundation.
References (31)
Ecology, evolution and 1/f-noise
Trends in Ecology & Evolution
(1996)The power spectral density of atmospheric temperature from time scales of 10− 2 to 106 yr
Earth and Planetary Science Letters
(1998)- et al.
Long-range persistence in climatological and hydrological time series: analysis, modeling and application to drought hazard assessment
Journal of Hydrology
(1997) Self-organizing systems across scales
Trends in Ecology & Evolution
(1995)Modelling effects of litter quality and environment on peat accumulation over different time-scales
Journal of Ecology
(2004)- et al.
Carbon balance of a temperate poor fen
Global Biogeochemical Cycles
(1997) Models of peat growth
Suo
(1992)- et al.
Carbon accumulation in peatland
Oikos
(1998) - Environment Canada, 2003. Canadian Climate Normals....
- et al.
Modelling and analysis of peatlands as dynamical systems
Journal of Ecology
(2000)