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Keywords:

  • paleohydrology;
  • Canadian Prairies;
  • water resource management;
  • applied statistical analysis;
  • drought;
  • dendrochronology

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[1] Multidecadal variability can have profound implications for long-term viability of existing water management practices and design of water conveyance, storage, and treatment infrastructure. However, baseline hydrology for water supply planning and engineering design rarely includes the full range of variability and extremes captured by proxies and models of pre- and postinstrumental climate and hydrology. This paper examines the paleohydrology of the Saskatchewan River Basin (SRB), where Canada's fastest growing economy and population are vulnerable to drought and heavily reliant on runoff from the Rocky Mountains. We take a novel approach to time-series analysis of tree-ring reconstructions of the North and South Saskatchewan Rivers. This study evaluates shifts in water availability, volatility as defined in terms of statistical dispersion, and stability as defined in terms of Shannon entropy, between adjacent 30 year windows—corresponding to the standard climatic normal period, and human generational timescales. Broadly speaking, outcomes reveal that gauge records appear unreliable as a basis for long-term water supply planning and engineering design. For example, (1) two preinstrumental periods of stable water deficits represent sustained droughts that current water use and management could not endure, (2) hydroclimatic relationships between the two subbasins, and with the Pacific Decadal Oscillation, change over the generations, and (3) the most anomalous period of the past millennium, with coinciding high levels of availability, volatility, and stability, was about 1890–1920. This happens precisely when the SRB was transformed from prairie and parkland to agricultural land cover—and the precedents for water allocation and use were established.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[2] Runoff generated in the Rocky Mountains of western Alberta is the water supply for most of the population of the Prairie Provinces, most of Canada's irrigated agriculture, and a resource-based economy that comprises a significant and growing proportion of Canada's GDP [Partners for the Saskatchewan River Basin, 2009]. Increasing demand from growth in population and agricultural productivity has been offset by some effective conservation measures. For example, since August 2006, the Alberta government no longer accepts applications for new allocations of water in the Oldman, Bow, and South Saskatchewan subbasins [Alberta Environment, 2006]. Most of the recent and projected increase in demand for surface water comes from the industrial sector, notably for heavy oil extraction and processing and solutional potash mining [Partners for the Saskatchewan River Basin, 2009]. Operational and planning processes in these industrial sectors generally rely on strict adherence to standard engineering practices, in contrast to the more collective and broader perspective of urban and agricultural communities. For system operations and short-term planning, the raw water supply can be reasonably modeled using short records from the recent past, since the probability of exceeding historical extremes is relatively low for intervals of a decade or less. Considerable scientific evidence indicates, however, that with current and inferred further warming of the atmosphere and oceans, hydroclimatic variables are trending away from normal conditions and exceeding historical magnitudes and frequencies [Kharin et al., 2007; PaiMazumder et al., 2012; Tebaldi et al., 2006]. For a longer planning horizon, as required for the design and implementation of water conveyance, storage, and treatment infrastructure, unprecedented water levels become increasingly likely.

[3] Water resource engineering is based almost exclusively on the analysis of decades of data from water and climate gauges. This approach assumes that instrumental time series, which span at most about 100 years (1) capture the full range of hydrologic variability and extremes and (2) are stationary, that is, that the climate and water fluctuate within a fixed envelope of variability. Research on climate change brings into question these foundational engineering concepts [Milly et al., 2008]. Climate cycles that exceed the length of instrumental records generally are not considered for planning or practical purposes, yet the decadal to multidecadal scale of climate variability can have profound implications for the long-term viability of existing water management practices and structures. A long-term cycle in the hydroclimate of western North America, linked to the Pacific Decadal Oscillation (PDO), is well documented [Fleming and Whitfield, 2010; Whitfield et al., 2010; Lapp et al., 2011; Furtado et al., 2011; St. Jacques et al., 2010]. For example, in western Canada, about 30 years of higher water availability from 1947 to 1977 shifted to 30 years of lower streamflows, including the severe droughts of the 1980s and early 2000s. The next shift in 2007–2008 restored wetter conditions, which, if the past is any indication, should dominate the hydrology of western Canada for roughly the next 25 years, notwithstanding some short-term droughts and the tendency for declining summer water levels in a warming climate. Now seems the time to prepare for the next shift, when large-scale climate patterns should lead to consistently lower water levels during a period of rapidly warming climate. This coincidence of widely inferred natural and human-induced climate variation could profoundly affect water supplies and therefore should be factored into the current design of new water supply, storage and treatment infrastructure, and drought mitigation strategies.

[4] To address the implications of multidecadal variability of western Canada's hydroclimate, this paper examines the paleohydrology of the Saskatchewan River Basin (SRB; Figure 1, Table 1), the region of Canada where the economy and population is expanding at its fastest rate, but which is also the most susceptible to drought and water deficits, and heavily reliant on runoff from the Rocky Mountains. We analyze and interpret tree-ring reconstructions of the North and South Saskatchewan Rivers in terms of generational-scale (i.e., from one 30 year period to the next) shifts in surface water availability, volatility, stability over the last millennium, and teleconnections to a dominant large-scale pattern of ocean and atmosphere circulation.

image

Figure 1. Location map illustrating major tributaries and overall watershed boundaries for the North and South Saskatchewan Rivers, and locations of hydrometric stations to which our flow reconstructions correspond. Elevation is denoted by gray shading.

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Table 1. Some Key Basin Characteristics for the South and North Saskatchewan Rivers (SSR and NSR)a
BasinGauge IDArea (km2)Glacier (km2)Q (m3/s)R (mm)σQ (m3/s)
  1. a

    Flow statistics are computed from naturalized historical flow series over 1912–2002; Q is long-term mean streamflow rate, R is average annual basin runoff, and σQ is the standard deviation of Q. Percent of upstream catchment area with glacier cover was determined by GIS analysis.

SRB05AK00166,00016423311163
NSR05DF00128,09636921424047

2. Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[5] We employed dendrochronological reconstructions of annual water-year (October–September) flow volume for the North and South Saskatchewan Rivers (NSR, SSR). These paleoflow records were developed by Axelson et al. [2009] and Sauchyn et al. [2011], and the reader is referred to these publications for full details; a summary is provided here.

[6] The inference of hydroclimate from tree-ring proxies is a common approach to paleohydrology, the study of preinstrumental water levels [Meko and Woodhouse, 2010]. This application of dendrochronology has progressed in recent decades with the modeling and analysis of hydroclimatic variability across networks of moisture-sensitive tree-ring chronologies, as exemplified by the North American Drought Atlas [Cook et al., 2004] and the incremental reconstruction of the flow of the Colorado River using increasingly more tree-ring data [Woodhouse et al., 2006]. Axelson et al. [2009] and Sauchyn et al. [2011] reconstructed the flow of the SSR and NSR, respectively, by first establishing new networks of 14 and 7 moisture-sensitive tree-ring chronologies, in the upper runoff generating regions of the respective river basins, where the montane forest includes open canopy stands of long-lived and moisture-sensitive limber pine (Pinus flexilis) and Douglas fir (Pseudotsuga menziesii). Standard methods in dendrochronology were used to derive standardized tree-ring index chronologies from precise (within 0.001 mm) measurements of annual growth increments. Naturalized weekly streamflow data for the NSR at Edmonton (05DF001) and SSR (05AK001) at Highway 41 (see Figure 1) were provided by Alberta Environment for the period 1912–2002. These naturalized flow data were derived from streamflow records, reservoir data, recorded and estimated irrigation withdrawals, and climate data using the streamflow synthesis and reservoir regulation model. A direct link between the soil water balance and rates of both runoff and tree growth accounts for the consistent statistical relationship between mean annual surface water levels and tree growth at dry sites, where the availability of soil moisture is growth limiting. The principles and methods of streamflow reconstruction from tree rings are well documented [e.g., Loaiciga et al., 1993; Meko and Woodhouse, 2010].

[7] Regression models of mean water-year flow were derived from a pool of potential tree-ring predictors: the residual (prewhitened) index chronologies for the current year and at forward lags of 1 and 2 years. The lagged predictors account for an offset of up to 2 years between climate fluctuations and a differential timing of the response of tree growth and streamflow. The models were optimized according to a set of statistical measures of model quality and predictive capacity. The models accounted for up to ∼50% of the instrumental variance and had significant skill when subjected to cross validation. By nesting a series of reconstructions of varying length (following Meko [1997]), the annual hydrographs of NSR and SSR were extended back to 1063 and 1402, respectively. The reconstructions replicated well the interannual variability in streamflow, although they generally were better at capturing the magnitude of low flows, while underestimating high flows throughout the calibration period. Underestimation of peak flows is a common limitation of tree-ring reconstructions; there is a biological limit to the response of tree growth to excess soil moisture and other factors become growth limiting in wet years [Fritts, 1976].

[8] Respective mean values were removed from the NSR and SSR reconstructions, to form yearly time series of excursions from their long-term (1063–2006 and 1402–2003) average flow volumes. While we place some emphasis on the NSR reconstruction due to its greater length and, thus, broader perspective on water resource fluctuations, both reconstructions (and comparisons between the two) provide important information about hydroclimatic variability and change over very long timescales in the Northern Great Plains.

3. Methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[9] A window of length 2N was run through each annual time series, x(t), t = 1, T, advanced 1 year at a time. At each window position along the data series, various characteristics were compared between the (nonoverlapping, length-N) first and second halves of the data window. The three characteristics investigated, and the corresponding technical methods for change detection, are described below. Note that our work appears to be the first time that most of these methods have been applied to dendrochronologically derived streamflow records, and that analyses (2) and (3) below are in some respects more generally novel, though developed from very well-established concepts in geophysical analysis. All calculations were performed in MATLAB® (version R2012a) scripts written for the purpose, with the exception of memory detection which was performed using a script written in the R language (version 2.14.1).

[10] (1) Central tendency: The medians of the leading and trailing half windows for a given window position were calculated and compared using the Mann-Whitney test. Also known as the Wilcoxon rank-sum test, this method is rank based, robust to outliers, and free of distributional assumptions. The null hypothesis of equal medians between the two N-length subsamples is tested against the alternative hypothesis of unequal medians. Similar approaches for change detection have been employed by Mauget [2003], Fleming and Weber [2012], and many others in the context of historical (instrumental) data records. Prior applications of comparable methods to paleohydrologic data are scarcer but exist [e.g., Gray et al., 2004]. The results speak to changes in overall water supply availability, with obvious water resource management implications.

[11] (2) Dispersion: The variance was calculated over each half window, and statistical dispersions over the leading and trailing data half windows were compared using the Ansari-Bradley test. This test is also nonparametric. The null hypothesis of equal dispersion between the two N-length subsamples is tested against the alternative hypothesis of unequal dispersion. Examination of hydroclimatic records for second-order nonstationarity is uncommon, but can be important for water resource management purposes [e.g., Fleming and Weber, 2012]. The results speak to long-term changes in the year-to-year volatility and unpredictability of water supply availability. Higher variance in annual flow volumes over a certain N-year window, for example, denotes greater year-to-year variation, and thus potentially lower supply reliability and heightened challenges with water resource planning. Higher variance also implies greater difficulty with skillful operational forecasting of seasonal water supply. Periods with lower dispersion measures would suggest the converse. For the purposes of this article, we take high dispersion to indicate high water supply volatility, as distinct from low stability; see (3) immediately below.

[12] (3) Information content: The Shannon entropies, H, of the leading and trailing data half windows were calculated and compared at each window position using a Monte Carlo bootstrap test free of distributional assumptions. Shannon entropy is the information content of a datastream, measured in bits:

  • display math(1)

where the probabilities, p, are frequencies of occurrence for each of k = 1, K states, and log2(p) ≡ 0 if p(xk) = 0. Shannon entropy is interpretable as the average minimum number of binary questions that must be asked and answered to ascertain in which of K discrete states the system, as represented by the variate x, resides. Conceptually, it measures the quantity of information in terms of the degree to which uncertainty about the system is removed by monitoring the signal. Note that information quality is not considered in this metric. For further background, see for example Shannon [1948] and Pierce [1980]. Here, we consider K = 2 distinct states: positive and negative excursions from the long-term mean, i.e., xk=1: x(t) > 0 and xk=2: x(t) < 0. Given this specific state definition, the results speak to the stability of water supply availability; in particular, stability in the directionality of excursions. For such an implementation, the maximum possible value is 1, indicating an equal likelihood of positive and negative excursions over the data half window. In this maximum-information case, the system frequently flips between equiprobable wetter- and drier-than-normal states. Consequently, one needs to monitor the signal to know in which of the possible states the system currently resides, obtaining one binary digit of information (wet or dry, which in principle may be represented as 0 or 1) with each annual measurement. The minimum possible entropy value, on the other hand, is 0. This is the minimum-information case, in which all excursions within the half window are in the same direction. There are therefore no system transitions between wetter- and drier-than-normal states, so that in principle one would not need to monitor the signal to know in which state it currently resides. Note that we take high information content to indicate low water supply stability, which is defined for the purposes of this article as distinct though not necessarily fully independent from high volatility (see (2) above). That is, volatility refers here to the size of year-to-year flow fluctuations over an N-year period, whereas stability refers to the degree to which flows over that period were consistently above or below normal.

[13] As to our knowledge no analytical significance test for differences in Shannon entropy between two samples exists, testing was conducted using numerical resampling methods as per Fleming and Weber [2012]. The length-2N time series lying within a given window position was resampled with replacement, and the absolute value of the entropy difference between the leading and trailing halves of this synthetic time series was calculated. This was repeated 2 × 103 times to form a bootstrapped distribution of sequential entropy change magnitudes. The percentile to which the actual entropy change magnitude observed for that window position would correspond, if it was inserted into the synthetic sampling distribution, in turn permits an estimate of the p value for the test. This is the confidence level at which the null hypothesis of no difference in Shannon entropy between the leading and trailing half windows may be rejected in favor of the two-sided alternative hypothesis of unequal information contents. The entire process is repeated at each window position, just as is done for the significance tests in (1) and (2) above.

[14] We briefly address two technical details as follows. The first regards window length. There is no single statistically optimal value of N in any meaningful sense. Longer windows elucidate longer term shifts with lower resolution, whereas shorter windows identify changes over shorter timeframes at higher resolution. From a water resource management perspective, the optimal window is that which speaks most directly and effectively to key management questions, subject to two technical caveats: it must not be so short that the statistics calculated over it are meaningless (one cannot reliably calculate the variance from a sample size of 3, say), and it should not be so long that there is no ability to track changes over time (for instance, 2N = 800 for a time series of length 1000). We briefly explored sensitivities to window length choice by experimenting with values of N = 20, 30, 40, 70, and 100 for the NSR. The results (not illustrated here in the interest of conciseness) obviously differed in detail between window lengths, although major features tended to persist across window length selections. Here, we ultimately chose to focus on a window half length of 30 years, for four reasons. (1) This window half length coincides with the standard definition of a climate normal, and the statistical change detection results are therefore indicative of hydroclimatic shifts between sequential climatic normal periods. (2) There is precedent for its use in regime detection in paleoclimatic records [e.g., Gray et al., 2004]. (3) N = 30 corresponds reasonably well to many water resource planning and engineering design horizons in general. (4) Also, from a socioeconomic perspective, this generational timescale of potential change in water supply availability, volatility, and stability seems particularly meaningful for the Canadian prairies, e.g., shifts in challenges and opportunities for family farms from one generation to the next.

[15] The second technical detail regards identification of specific change points. While the N-year data half windows being compared in any given test for change are nonoverlapping and thus independent, the 2N-length window is incremented along the time series only 1 year at a time to help ensure that changes are captured. Consequently, the test result for a given window midpoint is not independent of that for the next. Given the relatively long timescale changes being assessed here, this property of the analysis often results in the same general change (e.g., a decadal increase in water supply) being detected multiple times (i.e., at multiple years) in immediate succession. Change detection methods could be adjusted in various ways to avoid this effect, for example by (i) identifying the particular year for which a certain generational-scale change gives the most statistically convincing results or (ii) incrementing the window in steps equal to the half-window length. However, (i) would seem to imply a higher temporal resolution for change-point detection in a centennial-to-millennial paleoclimate record than seems plausible, or perhaps even legitimate insofar as it may be unclear that all physical hydroclimatic shifts are necessarily discrete events that can be meaningfully assigned to specific years. Conversely, (ii) would seem likely to often miss points of maximum change. Neither would seem to provide much additional insight into the general types of questions being addressed in the current study, which centre on identifying overall timeframes and forms of change. By the same token, the likelihood of a statistically significant result by chance can increase with repeated tests, but our interpretations below are conservative and, again, focus on general timeframes and forms of change rather than attempting to precisely identify every potential change point.

4. Results and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[16] Results are illustrated in Figures 2 and 3. We see that generational-scale changes in water supply availability, as detected using the Mann-Whitney test on the medians, are the norm in the Northern Great Plains even in an anthropogenically unaffected and nominally stationary (e.g., preindustrial) climate. As such, one cannot rely on what happened over the last few decades as a clear indication of what one might expect over the next few decades. This outcome has important ramifications for water supply planning and engineering design based on analysis and modeling of historical hydrometric and climate station records. That is, the findings reveal the potentially deep unreliability of gauge records as a basis for long-term water supply planning and engineering design. This reality is of course already well understood within the paleoclimate community, but perhaps not so much elsewhere, and it is interesting to directly reveal it using quantitative methods at restrictive statistical confidence levels in such a long record of prairie hydroclimate.

image

Figure 2. Results of change analyses for the North Saskatchewan River. Thirty-year half window median (availability analysis), variance (volatility analysis), and Shannon entropy (stability analysis) are denoted with black lines and ascribed to the midpoint of the half window. Sequential changes in these quantities between one 30-year half window position and the next (nonoverlapping) 30-year half window position are denoted with gray lines, and associated p values are given in accompanying stem plots; the difference and its significance is ascribed to the first year in the second half window. All windows are moved through the time series one point at a time.

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image

Figure 3. Results of change analyses for the South Saskatchewan River. All notations are as in Figure 2. Time axis is also identical to Figure 1 for ease of comparison, but note that vertical axis dimensions differ in some cases for clarity of presentation.

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[17] Generational-scale changes in water supply volatility, as detected using the Ansari-Bradley test on the dispersion, are also the norm. The implication is that not only is the relatively short-term perspective of human experience and, in general, hydrometric and climatic records potentially misleading with respect to overall water supply availability for the future as noted above, but it likely also provides an inadequately reliable view of the degree to which water supply varies from year to year. Again at restrictive confidence levels, the results reveal that certain periods enjoy much less variable (and thus in general far more predictable) water supply availability than others.

[18] Changes in Shannon entropy, as detected using a Monte Carlo procedure, are less common than those in central tendency and statistical dispersion, but do occur. In general, the information content given the K = 2 definition employed here hovers near 1 bit per measurement, i.e., within any given 30-year half window, there is typically a roughly equal chance of encountering above- or below-normal flows. Three fairly conspicuous intervals when this apparently did not occur to quite the same degree were: (i) much of the 14th century, as revealed by the NSR reconstruction (Figure 2) (not sampled by the shorter SSR record); (ii) a period spanning about 1480–1580 in the SSR record (Figure 3), although there is no evidence of this in the NSR record (Figure 2); and (iii) a period spanning the 19th through early 20th centuries, with the effect being most consistent across both the NSR and SSR over about 1870–1920 (Figures 2 and 3). Episode (i) corresponded to a period of anomalously low variance and subtly but consistently below-normal flows (i.e., drought) in the NSR. Although the timing does not seem to match precisely, it is intriguing to speculate whether this event might be related to the widespread drought across the western United States at the end of the 13th century that may have contributed to the collapse of Anasazi civilization [e.g., Gray et al., 2004]. Episode (ii) coincided with a period of anomalously low variance and strongly below-normal flows in the SSR. It may also have corresponded with the 16th century “megadrought” identified [Stahle et al., 2000; Cook et al., 2011] over much of the western United States, and with other identifications of paleodrought in the Canadian prairies [Lapp, 2012]. Finally, episode (iii) coincided with a period of high variance and high flows in both the NSR and SSR. Note that high stability (again, defined here as low entropy) can correspond with high volatility (defined here as high variance) if the absolute value of the overall quantity (as reflected in the mean or median) is sufficiently large that strong year-to-year variations all lie within one side of a zero-anomaly envelope. Episode (iii) also overlaps with the well-known, continental-scale early 20th century North American pluvial period [Cook et al., 2011].

[19] Comparison of Figures 2 and 3 reveals many general similarities between NSR and SSR results, but also some clear differences in detail. The degree and dynamics of coupling between these two major Saskatchewan River subbasins were therefore further investigated by evaluating correlations between NSR and SSR flows, and between each river and a reconstruction of the PDO index by D'Arrigo et al. [2001]. The PDO is defined as the leading mode of an unrotated principal component analysis of North Pacific sea surface temperature. This coherent, repeating pattern of climatic variability is well known to influence streamflows across western Canada, including the Saskatchewan Basin [e.g., Mantua et al., 1997; Whitfield et al., 2010; St. Jacques et al., 2010]. In particular, over the historical record, warm-phase PDO conditions have tended to be associated with warmer and drier conditions in western Canada and lower flows in the SRB. Note that we obtained similar basic outcomes using the considerably longer PDO reconstruction of Macdonald and Case [2005], which provides some assurance that our results are not unduly sensitive to the particular PDO reconstruction used. However, we focus on D'Arrigo et al. [2001] because the Macdonald and Case [2005] PDO index is not fully independent of the NSR reconstruction used here, as both employ the tree-ring chronology from Whirlpool Point. Correlations were evaluated between 30-year segments of each record, incremented 1 year at a time over the period common to all three reconstructions (1700–1979). Spearman rank correlation analysis was used, which makes no distributional assumptions, is robust to outliers, and does not assume linear association.

[20] Results are illustrated in Figure 4. As expected, although there are in general significant associations between the NSR, SSR, and PDO, these correlations clearly wax and wane in intensity over the generations. These profound nonstationarities in hydroclimatic coupling between adjacent basins, and in large-scale teleconnections, are surprising but plausible in light of other recent findings. Lapp [2012] similarly found that correlations between reconstructions of the PDO and Palmer drought severity index (PDSI) over the Northern Great Plains varied substantially over time. Wavelet analyses of dendrochronologically derived NSR, SSR, and PDSI data sets for the region also suggest substantial time variation in spectral power at the decadal timescales typical of the PDO [Axelson et al., 2009; Sauchyn et al., 2011; Lapp, 2012]. Using both paleoclimatic and instrumental data sets from the southwestern United States, Meko and Woodhouse [2005] and Meko [2010] showed how the degree of hydrologic association between basins can vary over time and how the presence or absence of jointly occurring drought across multiple basins can be related to large-scale circulation patterns as captured by wintertime 500 mb geopotential height anomalies, in particular, the establishment of blocking patterns. Additionally, an emerging body of literature, analyzing historical data sets in western North America and Europe, has revealed the presence/absence of glacial ice as a powerful control on streamflow responses to coherent modes of climatic variability, including the PDO, in some cases decorrelating flow variations between adjacent basins [Neal et al., 2002; Lafrenière and Sharp, 2003; Fleming et al., 2006, 2007; Hodgkins, 2009; Brabets and Walvoord, 2009; Dahlke et al., 2012]. Although percentages of watershed area covered by glacial ice over the historical era are low for the NSRB (1.3%) and SSRB (0.25%), the actual glacier-covered areas are a substantial 369 km2 and 164 km2. Further, both rivers derive much of their runoff from the Rocky Mountains, such that geophysical characteristics at headwater locations likely play an inordinately large role in downstream variability. Thus, differences in ice-covered area between the NSR and SSR might support partial decoupling of flows between them; and changes in ice cover since 1400 might conceivably help to explain changing relationships between the NSR, SSR, and PDO. Finally, also note that even strictly over the historical record, substantial changes in the teleconnection patterns of terrestrial climate variables directly salient to water supply availability in southern Canada have been observed [Gan et al., 2007; Zhao et al., 2012]. Whatever the driving physical mechanism, it is clear that our observations regarding changing degrees of association between two major subbasins of the SRB, and between each of these and a regionally important mode of Pacific climatic variability, are loosely consistent with other work. Considerable further research would be required to identify the correct explanation and assess potential relationships to other circulation patterns, such as the Arctic Oscillation.

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Figure 4. Spearman rank correlation coefficients between North and South Saskatchewan River (NSR, SSR) annual flow volumes and the PDO index over successive 30-year data windows (first panel: black denotes SSR versus NSR, solid light gray denotes SSR versus PDO, dark gray denotes NSR versus PDO), and corresponding significance levels for each comparison (second, third, and fourth panels). Only the time period common to all three reconstructions (1700–1979) is considered in this case.

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[21] Returning to the results in Figures 2 and 3, the period spanning the 19th through early 20th centuries, and perhaps in particular about 1870–1920, was unusual. It is clear from the NSR analyses that this interval contained by far the highest flows, some of the greatest water supply volatility, and some of the highest water supply stability over the last millennium. Much the same can be said for the SSR, although not to the same degree. This interval also appears to be the only period during which shifts in central tendency, dispersion, and information content all clearly appear to mutually coincide: in most cases, on the basis of the data and analyses to date, such shifts generally seem to be somewhat independent. From a socioeconomic perspective, it is interesting that this interval also loosely coincided with the initial widespread settlement of the Canadian prairies. Specifically, these were the three decades when the Canadian prairies were settled by “homesteaders.” Between 1901 and 1911, the populations of Saskatchewan and Alberta rose by 445% and 413%, respectively (www.statcan.gc.ca). The native prairie landscape was converted to agricultural use. In Alberta, the senior water licenses were granted to the irrigation districts; these allocations still account for more than 75% of water consumption in the SSRB.

[22] We performed additional analysis, focussing on the longer NSR record, to explore two points of uncertainty around our results. First, tree-ring reconstruction of annual flow volume at some statistically significant 0 < R2 < 1 over the calibration period implies, but does not guarantee, reproduction of metrics derived from the annual series for either the instrumental or preinstrumental periods. For example, Fleming [2012] found that different reconstructions of the same paleoclimatic time series, generated by different research groups using different data sets and methods, yielded different outcomes with respect to evaluation of power-law spectral scaling behavior, as determined from the full length of each reconstructed series. Clearly, at least some of those reconstructions did not faithfully reproduce the true spectral dynamics. Unfortunately, in our present case, it is impossible to perform a rigorous statistical assessment of the accuracy with which our reconstructed NSR and SSR flow series reproduce central tendency, dispersion, and information content over 30-year half windows. Only three nonoverlapping half windows of instrumental data against which to compare (i.e., three independent samples) are available over the historical (1912–2002) period. Nevertheless, we tentatively explored the question by sliding a 30-year window, incremented 1 year at a time, through the reconstructed NSR flow series over the historical period, generating a time series of median values. The same was done for the naturalized flow record. These two time series were then correlated against each other. The procedure was repeated for the variance and Shannon entropy. This cursory assessment may provide some feeling for how well the reconstructed flows track overall changes in the derived metrics. We obtained correlation coefficients of 0.40, 0.23, and 0.67 for the median, variance, and entropy, respectively. These results are loosely comparable to conventionally determined qualities of fit often found for annual time series of dendrochronologically reconstructed climate and hydrology, and thus seem somewhat encouraging. However, this remains a basic point of uncertainty in paleohydrologic analyses of derived metrics, including but not limited to the current study.

[23] The second point of uncertainty regards adjustment for autocorrelation. It has been suggested [e.g., Mauget, 2003] that serial dependence may require application of correction procedures to an assessment of the statistical significance of changes between successive median values. In classical statistical terms, the issue is that autocorrelation decreases the effective number of independent samples below the nominal degrees of freedom of the hypothesis test. In an applied hydroclimatology context, the issue is perhaps more usefully or intuitively viewed in terms of the well-known tendency of statistical memory (e.g., autoregressive) processes to generate extended runs of values above or below the mean, which may appear to form hydroclimatic trends or regimes. These regimes are a result of the memory process rather than an underlying structural trend or regime shift, and are therefore often viewed as spurious. The net result is that a given change is more likely to be incorrectly identified as statistically significant than implied by the p value of the test. Scoping calculations using simple linear methods indicate a statistically significant lag-1 serial correlation coefficient for both the NSR and SSR time series, so the question is potentially salient here.

[24] A number of techniques are available to compensate for these effects, but several problems have been identified with such corrections. (i) The observed linear autocorrelation structure of a time series is normally used as the basis for corrections, but it is a basically flawed measure or diagnostic of memory processes in a given data set. The most pressing problem is that genuine first-order nonstationarity, in the absence of any underlying red-noise process whatsoever, commonly generates substantial autocorrelation in a time series. Standard corrections can thus amount to a deliberate corruption of the data, and may render meaningless the outcomes of statistical tests for change [e.g., Fleming and Clarke, 2002; Yue et al., 2002]. (ii) The scientific basis for adjusting statistical tests for serial correlation is context dependent. Elementary statistical considerations must be assessed against the underlying physics of the system under study and the practical questions being asked about it. In particular, it must be appreciated that dynamical memory is not a spurious random effect generating apparent regimes as simple artefacts. Considering streamflow, for instance, short-term linear memory arises from watershed storage (e.g., aquifers, lakes, wetlands) as captured for example using the linear reservoir equation, with direct correspondence to the recession constant [James and Thompson, 1970; Fleming, 2007a]. Similarly, long-term hydrologic persistence may be associated either with a corresponding power-law spectral process in driving climate [e.g., Huybers and Curry, 2006; Newman, 2007], or with the superposition of many different watershed storage mechanisms in upstream sub-basins, and reflecting physical watershed characteristics [Mudelsee, 2007; Szolgayová et al., 2012]. Thus, statistical memory corresponds to specific deterministic physical processes, and the associated apparent hydroclimatic regimes are very real phenomena which will express themselves in no uncertain terms to water resource users. It seems folly to discount the socioeconomic realities, for instance, of a hydroclimatic change simply because it may be statistically characterized by autocorrelation. Put simply, a drought is a drought. (iii) It should be obvious from the foregoing that correcting hydroclimatic change tests for serial dependence is a de facto attempt at signal attribution. This issue is especially important in anthropogenic climate change signal detection analysis using relatively short historical records. In that case, there can be substantial ambiguity between comparatively recent greenhouse effects (an underlying structural trend or shift) and long-term natural variability (finite-duration trends or regimes generated by system memory) [e.g., Koutsoyiannis, 2003]. Adjustments for serial dependence thus act to differentiate between the two process types. In the context of a paleohydrologic record primarily sampling pre-industrial hydroclimatic conditions, however, there are no ambiguities between anthropogenic greenhouse warming effects and natural dynamics. Any large natural change is of interest, irrespective of the source(s), be it deterministic regime switching, internal atmospheric or oceanic circulation modes, physical memory processes, volcanic or solar forcing, and so forth. (iv) At an implementation level, the correct memory model is often ambiguous [e.g., Cohn and Lins, 2005]. In our data sets, for example, in addition to a statistically significant first-order autocorrelation coefficient, we also found statistically significant evidence for power-law scaling of the Fourier spectrum. At the same time, it was unclear that such scaling extended below the critical frequency defined by Fleming [2008], i.e., to the diagnostic low-frequency spectral bands required to uniquely identify long-memory processes. It is therefore unclear whether short- or long-term persistence should be assumed here when making serial dependence adjustments. This nonuniqueness problem appears to be common with hydroclimatic data [Fleming, 2012]. (v) Broadly speaking, nonlinear processes may be more relevant to climate dynamics; and in that case, the distinction between hydroclimatic regimes as a product of red noise, versus hydroclimatic regimes as a product of physical switching between multiple stable states, may be strongly blurred [Fleming, 2009]. In terms of the underlying physics, then, it seems possible that the problem statement motivating corrections for serial dependence may be fundamentally misphrased.

[25] As a result, correction for simple serial dependence in a hydroclimatic analysis context seems to be increasingly viewed as problematic and potentially inappropriate [e.g., Déry et al., 2009]. Analogous concerns around adjustment for autocorrelation may also extend to estimates of Shannon entropy [Le and Zidek, 2006], but similar counterarguments again apply in our particular context; see also Fleming [2007b]. Given the foregoing considerations in combination, we chose not to remove or otherwise discount the effects of memory in these data in our primary analyses. As such, our statistical hypothesis tests speak strictly and solely to identification of natural paleohydroclimatic changes, whatever their ultimate sources, against a white-noise background [see also Fleming and Weber, 2012]. Nevertheless, to explore the potential ramifications of that choice, we reperformed the NSR analyses using the commonly used though perhaps extreme [Fleming and Clarke, 2002; Yue et al., 2002] AR(1)-based prewhitening scheme of von Storch [1995]. The prevalence of statistically significant changes in central tendency and information content (although not dispersion) decreased substantially. However, the major conclusions drawn from the primary NSR analyses remained valid: statistically significant shifts in both central tendency and dispersion are the norm, not the exception; significant changes in entropy are less common, but do occur; episode (i), although substantially muted, is still apparent in the median and variance; and episode (iii) not only remains clearly apparent in central tendency, dispersion, and information content, but also remains the most anomalous period of hydroclimate in the NSR over the last millennium.

5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[26] Long high-resolution records of prairie hydroclimate reveal, using time-series analysis at restrictive statistical confidence levels, the limited scope of relatively short instrumental records for long-term water supply planning and engineering design. We apply, perhaps for the first time, well-established concepts in geophysical analysis to tree-ring reconstructions of streamflow. The concept of entropy as applied here to these paleoflow records evaluates the likelihood of positive and negative departures from normal levels, ranging from maximum information, where the hydrologic regime frequently flips between equally probable wetter- and drier-than-normal states, to minimum information, where all excursions are in the same direction. The corresponding notion of water supply stability, i.e., consistently above or below normal, is distinct from volatility, the magnitude of inter-annual fluctuations as captured here by the variance. By applying these concepts and methods to the paleohydrology of the SRB, we were able to identity significant shifts in surface water availability, volatility, and stability between 30-year intervals over the last millennium. We also quantified teleconnections to a dominant large-scale pattern of ocean-atmosphere circulation. Coupling between annual flow in adjacent basins, and with the PDO, was found to be profoundly nonstationary. We identified several precedents and potential physical mechanisms for such waxing and waning of large-scale hydroclimatic correlations.

[27] Generational-scale water supply variability has important implications for conventional water supply planning and engineering design, which is normally based on the analysis and modeling of historical stream gauge and climate station records. Two periods of sustained drought that would very likely exceed the capacity of current water use and management are highlighted by our analysis of pre-instrumental proxy streamflows (episodes (i) and (ii) discussed above). Perhaps the most anomalous episode of the past millennium, however, was a period of consistently high water availability, volatility, and stability (episode (iii), spanning the 19th through early 20th centuries). During the 1890s to1910s, the SRB was transformed from prairie and parkland to agricultural land cover, and the precedents for water allocation and use were established. Given our results, it is conceivable that observations of water resource availability, volatility, and stability during this period may have led to institutional water, industrial, and agricultural policy decisions and practises which may not be consistent with environmental conditions normally (from a longer-term perspective) encountered in the region—an important question given the generally water-stressed setting of the prairies. In particular, water resource availability and stability may be much lower than that assumed during settlement of the Northern Great Plains and the concomitant establishment of institutional controls and governance structures around water resources. This circumstance appears analogous to that around the Colorado River Compact, which was based on early instrumental observations during what paleoclimatic investigations have since revealed to be a period of unusually high flow, leading to water supply overallocation [Stockton and Jacoby, 1976; Meko et al., 1995; Cook et al., 2011]. However, the elevated water supply volatility and stability we found for this period (relative to long-term conditions as captured by paleohydrologic records) do not appear to have been rigorously identified or explored before, in the SRB or elsewhere. An improved understanding of the local, on-the-ground consequences of our results to water supply planning and management will require additional investigation, such as running, e.g., operational water resource management models under nonhistorical conditions consistent with the paleohydrologic record.

[28] Present and future climatic changes potentially associated with human population and economic growth, and attendant deforestation and fossil fuel combustion, may result in additional hydrologic responses [St. Jacques et al., 2010; Lapp, 2012] which may further exacerbate these issues. Conversely, researchers carrying out interpretation of future hydrologic dynamics must bear in mind the changes that can be observed to occur naturally when very long-term proxy data are studied.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[29] Geographic information system (GIS) analysis for glacier-covered area was performed by Judy Kwan and Tommy Diep of the Meteorological Service of Canada. We additionally thank three anonymous reviewers for their constructive comments on an earlier version of the manuscript.

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  5. 3. Methods
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
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