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Keywords:

  • Great Lakes;
  • climate risk

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information

[1] Climate change is believed to pose potential risks to the stakeholders of the Great Lakes due to changes in lake levels. This paper presents a model of stakeholder-defined risk as a function of climate change. It describes the development of a statistical model that links water resources system performance and climate changes developed for the Great Lakes of North America. The function is used in a process that links bottom-up water system vulnerability assessment to top-down climate change information. Vulnerabilities are defined based on input from stakeholders and resource experts and are used to determine system performance thresholds. These thresholds are used to measure performance over a wide range of climate changes mined from a large (55,590 year) stochastic data set. The performance and climate conditions are used to create a climate response function, a statistical model to predict lake performance based on climate statistics. This function facilitates exploration and analysis of performance over a wide range of climate conditions. It can also be used to estimate risk associated with change in climate mean and variability resulting from climate change. Problematic changes in climate can be identified and the probability of those conditions estimated using climate projections or other sources of climate information. The function can also be used to evaluate the robustness of a regulation plan and to compare performance of alternate plans. This paper demonstrates the utility of the climate response function as applied within the context of the International Upper Great Lakes Study.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information

[2] The International Upper Great Lakes Study (IUGLS) was launched in 2005 to assess the performance of the operations plan that regulates outflows from Lake Superior, which represents the only hydraulic control on levels in the Great Lakes above Niagara Falls (thus levels on Lakes Superior, Michigan, Huron, and Erie). An important question in this assessment is the potential impact of climate change on the Upper Great Lakes system. The Great Lakes hold approximately 20% of the world's fresh water and are significant economically, environmentally, and socially to a large region of the United States and Canada. Considered as a system, the Great Lakes system represents the largest managed water resources system in the world. The IUGLS capitalized on the best available hydroclimatological science to inform the assessment of climate change impacts. However, a methodology for linking the science, and particularly the uncertain projections of future climate from a variety of sources, with decisions that were based on stakeholder concerns was lacking. Dessai and Hulme [2004] contrasted top-down and bottom-up approaches to inform climate adaptation policy, suggesting that methods that utilize both approaches may be needed. Brown et al. [2011] described a “bottom up meets top down” approach to climate risk assessment and outlined how this approach could be applied to the analysis of Lake Superior outflow regulation alternatives. This study presents the model used to estimate stakeholder-defined impacts as a function of possible changes in climate. A parametric statistical method is used to assess climate change related impact in terms relevant to stakeholders. The process involves correlating climate to hazards and identifying the climate conditions that lead to adverse system impacts. A related study considers the probabilities of climate conditions and how different sources of climate information such as historical climate, paleo reconstructed climate, general circulation model (GCM) climate projections, and expert opinion can be used to estimate climate probabilities and climate related risk.

[3] Previous studies of the impact of climate change on the Great Lakes have used scenario based approaches to assess potential climate change impact by predicting the system response to specific climate conditions [Angel and Kunkel, 2010; Bruce, 1984; Chao, 1999; Cohen, 1986; Croley, 1990; de Loë and Kreutzwiser, 2000; Hartmann, 1990; Lofgren et al., 2002; Mortsch et al., 2000; Sanderson, 1987]. These top-down methods used projections of future conditions and impacts to provide estimates of potential climate change induced impacts from downscaled general circulation model (GCM) projections. These early studies developed methodologies for generating climate change scenarios and impact assessments.

[4] There are a number of limitations to such top-down approaches. Top-down analysis uses GCM projections with high uncertainty and unknown accuracy to project system response and behavior. As Lempert et al. [2010] stated, the “predict-then-act” top-down approach can run into problems in the analysis and development of long term policy due to conditions of deep uncertainty. Increasing spatial and temporal precision of GCM output can easily be misunderstood for increasing accuracy, resulting in overconfidence in the understanding of the future and an underestimation of the irreducible uncertainty [Dessai et al., 2009]. Unlike a deterministic forecast, the skill of a climate projection cannot be tested in comparison to observations. Wilby and Dessai [2010] noted the cascading uncertainty inherent in using GCM projections to support adaptation decisions. To overcome the issue of uncertain model accuracy, studies by Räisänen and Palmer [2001], Tebaldi and Knutti [2007], Angel and Kunkel [2010], and others have considered ensembles of GCM projections. Yet there is no accepted methodology for evaluating relative quality of GCMs in terms of predictive skill or credibility [Angel and Kunkel, 2010]. Even GCM ensembles that include extreme predictions may not capture the true range of climate uncertainty [Stainforth et al., 2007]. Additionally, as Hirsh [2011] points out, the GCM projections may not be answering the questions relevant to water resources decision making. While GCMs may provide credible information about average annual changes, their ability to estimate variability, seasonality, and major storms, and other factors more relevant to water systems is much less reliable. Barsugli et al. [2009] assessed aspects of GCM projections and rated estimates of hydrologic variability as low to moderate. Or, as Hirsh [2011] states, “we have the most confidence in statements about the least important aspects of hydrology (the central tendency), and the least confidence in the most important aspects (extreme events).”

[5] An alternative approach, presented here, starts with the physical system and determines the system conditions that constitute hazards or failure as defined from stakeholder input. The process then identifies the climate conditions that cause those hazards. The hydrological system is modeled with the Coordinated Great Lakes Regulation and Routing Model (CGLRRM) as described by Clites and Quinn [2003]. The CGLRRM uses monthly net basin supply (NBS) values and applies water conservation, routing, and regulation release rules to determine Great Lakes water levels and flow rates in the interconnecting channels. The NBS for each lake is the net water flux due to direct precipitation, runoff, and evaporation. NBS does not include interlake transfers or diversions, which are typically modeled separately. The uncertainties associated with the CGLRRM and estimates of monthly NBS values have been discussed in the context of the IUGLS [Neff et al., 2005]. The CGLRRM has been calibrated, evaluated, and tested with historic data and synthetically generated data to obtain a coherent understanding of system response to a variety of inputs. This understanding of the system response can be combined with input from stakeholder groups that identify the conditions that concern the stakeholders the most. This “hazard discovery” process identifies the climate conditions that result in the most problematic system states. The climate conditions and hazards are linked using a “climate response function,” a model based on the statistical relationship between the climate conditions and hazards. Using this process, one obtains an understanding of which climate conditions pose the most severe hazards in terms relevant to the concerned stakeholder groups. The process is termed “decision scaling” [Brown et al., 2011]. Prudhomme et al. [2010] described a related “scenario neutral approach.”

[6] With an understanding of climate related hazards, one can use the climate response function, driven by various types of climate data, to estimate probabilities of problematic climate conditions based on the climate information source. This allows one to examine system risk by using climate probability conditional on the source of climate information. Starting with climate probabilities based on historic observations, one can establish a climate risk baseline. Then one may use other sources such as paleo reconstructed climate or GCM projected climate to determine how the alternate source of climate information alters estimated climate risk. The historic record provides an estimate of the distribution of key predictive climate variables; GCM output, expert judgment, and other sources of climate information can then be used to generate new estimates of climate variable distributions representing possible future conditions.

[7] The novel contribution of this paper is the development of a model of stakeholder-defined risk, termed a climate response function, which links these risks on the Upper Great Lakes to climate conditions as part of a bottom-up meets top-down climate risk assessment process. The model has a number of potential applications, including identification of climate hazards, estimation of climate risks, and evaluation of lake regulation plans. Climate response surfaces developed from the climate response function clearly show the impact of climate on performance and facilitate understanding of the performance of system options such as regulation plans under different climate regimes. The paper proceeds with a review of regulation of the Great Lakes and previous climate change analyses, the description of the model and results for the upper lakes, followed by a discussion of findings and implications.

2. Background

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information

[8] The International Joint Commission (IJC) was established as a result of the Boundary Waters Treaty of 1909 to oversee the regulation of obstructions and diversions that would impact levels or flows in waters on the international boundary waters between Canada and the United States. The IJC complies with the agreements found in the Boundary Waters Treaty, the Orders of Approval from 1914 and the Supplementary Orders of Approval from 1979. The Treaty and the Orders establish the guidelines for lake regulation allowing the IJC latitude to determine and follow a regulation plan that follows the letter and intent of these documents. Clites and Quinn [2003] describe the history of Great Lake regulation and the prior regulation plans that led to the current regulation plan, plan 1977A, which has been in use since 1990. Plan 1977A essentially seeks to keep Lake Superior and Lake Michigan-Huron at the same relative position with respect to their long term mean water level.

[9] The IJC completed the Lake Ontario-St. Lawrence River (LOSLR) study in 2005 to review regulation of levels and flows in the Lake Ontario–St. Lawrence River system while considering the impact of regulation on all affected interests and then launched the International Upper Great Lakes Study (IUGLS) in 2005. Prior to the IUGLS, previous studies have looked at climate change impacts on the Great Lakes, but the IUGLS has provided the opportunity for a comprehensive review of lake-level impacts, regulation plans, and climate related risk.

2.1. Previous Climate Change Assessments of the Great Lakes

[10] As the scientific community began to recognize rising levels of CO2 and other greenhouse gases, scientists and researchers began to model and explore the potential impacts on climate. Prior to the Intergovernmental Panel on Climate Change (IPCC) First Assessment Report (FAR) in 1990, several researchers began to look at the potential impacts of climate change on the Great Lakes system. Early investigations into the impact of climate change have used a top-down approach to estimate changes [Cohen, 1986; Sanderson, 1987; Hartmann, 1990; Mortsch and Quinn, 1996; Croley, 1990; Chao, 1999; Mortsch et al., 2000; Lofgren et al., 2002; Lofgren et al., 2011]. These studies and their findings are discussed below. These studies used a single or limited number of GCM outputs to estimate the impact on NBS, lake levels, economic interests, and environmental interests. Later studies incorporated increasing numbers of GCM simulations, up to large ensembles of model runs.

[11] The following studies considered the hydrologic impact resulting from one or more downscaled GCM projection. Cohen [1986] used steady state double CO2 scenarios from the GISS and GFDL models to estimate NBS components and extrapolate a 10%–30% reduction in NBS over the Great Lakes. Water level changes were not reported. Sanderson [1987] used a steady state double CO2 scenario and the GISS model to estimate mean lake-level reductions of 0.3 to 0.8 m over the Great Lakes, mean flow reductions up to 20%, a higher incidence of low lake levels, and significant increased costs or losses to commercial shipping and hydropower. Sanderson [1987] did not report changes in NBS. Hartmann [1990] used three doubled CO2 scenarios from the GISS, GFDL, and OSU model centers and a GISS transient case for 1980 to 2060. The steady state models predicted an NBS reduction of 16 to 479 mm on Lake Superior and 210 to 399 mm on Lake Michigan-Huron (expressed as a depth over the lake) and lake water level reductions of 0.46 to 0.47 m on Lake Superior and 0.99 to 2.48 m on Lake Michigan-Huron. For the GISS transient case, Lake Superior had an increased NBS of 17 mm per decade and a decreased water level by 13 mm per decade, while Lake Michigan-Huron had a decreased NBS of 34 mm per decade and a decreased water level by 59 mm per decade. Additionally, the climate model caused the lake regulation plan to fail on Lake Ontario for each scenario and on Lake Superior for the GFDL scenario. Croley [1990] considered three steady state double CO2 cases with the GISS, GFDL, and OSU models and one transient case from 1980–2060 using the GISS model. Croley [1990] reported decreases in NBS of 23% to 51% for steady state scenarios and 27 to 75 mm per decade for the transient cast. Croley [1990] did not report lake levels. Chao [1999] conducted climate change analysis using eight transient scenarios (two each from GFDL, UKMO-Hadley, MPI, and CCC) and two doubled CO2 scenarios (from GFDL and CCC). Chao [1999] did not report NBS changes, but did project water level decreases of 0.2 to 0.9 m on Lake Superior and decreases of 0.3 to 1.8 m on Lake Michigan-Huron. Mortsch and Quinn [1996] used four double CO2 scenarios from the CCC, GISS, GFDL, and OSU centers. They did not report changes in NBS but did project lake level reduction ranges of 0.75 to 11.3 m on Lake Superior and 0.01 to 0.31 m on Lake Michigan-Huron. Mortsch et al. [2000] used the CGCM1 and HadCM2 models with doubled CO2 levels and with transient CO2 increases in the 2021–2040 and 2041–2060 timeframes. While NBS was not reported, lake level reductions of 0.23 to 0.47 m on Lake Superior and 0.99 to 2.48 m on Lake Michigan-Huron were reported. Lofgren et al. [2002] used the CGCM1 and HadCM2 models with doubled CO2 scenarios and 20 year transient scenarios centered on 2030, 2050, and 2070. Lofgren et al. [2002] reported decreased Lake Superior levels by 0.01 to 0.8 m and a change −2.48 to +0.35 m on Lake Michigan-Huron. Lofgren et al. [2011] examined how evapotranspiration (ET) is modeled from GCM projections, a key step in using GCM projections to determine NBS. They found that the standard method, based on an air temperature proxy, overestimated ET, resulting in lower NBS and lake levels. By applying an energy budget approach that satisfies conservation of energy, Lofgren et al. [2011] found more conservative changes in NBS and water levels than previous climate change assessments, in some cases reversing water level predictions from a decrease of 0.19 m to an increase of 0.13 m on Lake Superior or from a decrease of 0.44 m to an increase of 0.41 m on Lake Michigan-Huron.

[12] Angel and Kunkel [2010] considered an ensemble of 565 model runs from three greenhouse gas emission scenarios and 23 GCMs. While many previous studies indicated a reduction in lake levels due to climate change, this broad ensemble revealed projections implying both higher and lower mean water levels. The range and uncertainty inherent in their findings was wide, with projections of precipitation ranging from an increase of 20 cm to a decrease of 5 cm annually. They found that the total range of mean lake-level change was –3.0 to +1.5 m, which is a large range compared to the range between the historic maximum and minimum lake level of 1.12 m on Lake Superior and 2.07 m on Lake Michigan-Huron.

[13] While the vast majority of previous climate change impact assessments used a top-down approach that started with GCM output, a few have taken alternate approaches. Notably, McBean and Motiee [2008] eschewed GCM data and conducted statistical trends in meteorological and hydrological data and identified statistically significant increasing trends in many variables, including rising flow rates in all connecting channels. No previous study has attempted to define climate risks in stakeholder terms.

2.2. Bottom-Up Assessment Methods

[14] In contrast to the “top-down” approaches described above, a risk-based, or “bottom-up” approach may be more useful for supporting decision making under climate uncertainty [Brown et al., 2011; Lempert et al., 2004]. In general, these approaches consider the system and hazards to the system based on interactions with stakeholders.

[15] Jones [2001] described a risk-based approach that used GCMs as the scenario generator to identify and manage risks. Johnson and Weaver [2009] described a similar approach to identify climate based risk. However, these approaches still use GCM projections to identify climate hazards and thus have similar limitations as other scenario-based methods. These approaches may be well suited to consider system performance under potential future scenarios to estimate a range of potential future impacts, but may not be as well suited to support decision making under uncertainty due to potential climate change.

[16] Recent studies provide examples of rethinking along this direction of analysis. Prudhomme et al. [2010] presented a scenario-neutral approach to identify hazards and the climate conditions that contribute to those hazards. This was used to develop a climate impact model that used climate conditions to predict fluvial flooding. GCM output was used at the end of the process to inform the bounds of the sensitivity analysis. Wilby and Dessai [2010] followed a similar approach to use a system vulnerability analysis to create adaptation options, and then used climate change scenario information to determine no-regrets or low-regrets adaptation options. Brown et al. [2012] used a surrogate system performance function that predicts water system reliability from climate in the metropolitan Boston water supply system to support decision making under uncertainty.

[17] Brown et al. [2011] described a decision-analytic-based approach for estimating climate risk on the Upper Great Lakes called decision scaling that links a bottom-up process with available top-down projections that can be applied in cases where climate information is uncertain but may be informative. The assessment considers the system of interest and its vulnerability to climate impacts. The vulnerability assessment uses input from concerned stakeholders to identify key impacts or system states with unacceptable performance. The hazard identification process identifies climate conditions that lead to poor system performance and is conducted without consideration of the probability of those climate conditions occurring. The relationship between hazards and climate conditions is quantified in a climate response function. This model is the quantitative link between impacts and climate and can be used with projections of climate from a variety of sources to estimate climate-informed risks (conditional on the source of climate information). Combining the hazards associated with climate with estimates of climate probability allows the assessment of climate-informed risks. This paper describes the development of the climate response function as applied to the Upper Great Lakes. The development of estimates of future potential climate probability is an area of active research. Dessai and Hulme [2004] present arguments for and against assigning probability density functions to future climate conditions. Despite being subjective and conditional, probability density functions for future conditions are relevant for climate decision-making [Dessai and Hulme, 2004]. Brown et al. [2012] discussed considerations on how to incorporate different sources of climate information such as GCM projections, regional climate models (RCMs), paleo climate based models, and even expert opinion, to develop conditional probabilities for future climate states.

3. Method

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information

[18] The methodology described in this paper leads to the creation of a climate response function that relates climate statistics to stakeholder-defined risk. The process starts with understanding what is important to stakeholders in terms of risk and impact. This involves interacting with stakeholder groups and translating their priorities and concerns into model variables, resulting in sector specific variables and thresholds that can be used to evaluate system performance in terms relevant to the stakeholders. The next step is a hazard discovery process involving data mining to identify periods of poor system performance (as defined by the stakeholders) and relevant climate variables that influence system performance. This study utilized a 55,590 year stochastic data set based on historic data for this purpose. This data set provides a wide range of climate conditions to create and assess the statistical relationship between model variables and system performance. After the data mining process, statistical models are proposed and evaluated to select a model that is consistent with the data and can effectively explain or replicate the important relationships within the system. The result is the development of the climate response function to predict Upper Great Lake system performance relevant to stakeholders and that uses measures of climate change as function inputs. The function and how it can be used to understand a complex system and inform decisions is described in more detail below.

3.1. Stakeholder-Defined Thresholds

[19] The IUGLS established six technical working groups (TWGs) to address six primary areas of stakeholder concern on the Upper Great Lakes. The 1909 Boundary Waters Treaty and the 1914 Orders of Approval governing the regulation of the Great Lakes specify that water use, commercial navigation, and hydropower are protected interests [Clites and Quinn, 2003]. The Treaty requires the IJC to consider impacts in the three specified areas and encourages the IJC to consider impact on other interests. These additional interests include ecosystems, coastal, recreational boating, and tourism. As part of this analysis, the IUGLS commissioned the six TWGs to determine which changes to the Great Lakes were of greatest concern. In all sectors, lake levels were determined to be the most important measure of sector performance. The hydropower, commercial navigation, and ecosystem TWGs also found that flow rates in the interconnecting channels were relevant indicators of system performance. A similar model can be created to consider exceedance of threshold flow rates, where channel flow rates are relevant to stakeholders.

[20] Each TWG conducted extensive surveying, working groups, public information sessions, and analysis to determine how lake levels related to sector performance. The TWGs used this stakeholder input to develop coping zone thresholds as a state-based method to quantify sector performance. While the TWGs each provided a single set of thresholds per lake, there is some underlying uncertainty in their definition. Coping zone thresholds inherently reflect sensitivity to extreme lake levels, so the threshold values vary spatially within a sector. Also, the thresholds are not fixed in time; they will change with better understanding of the relationship between water levels and performance and with response to adaptation measures that affect this sensitivity. More details about the process each TWG used to determine coping zone thresholds are on the IUGLS technical report site (unpublished data, 2012) available at (www.iugls.org/sup-tech-reports.aspx). Coping zone A is the preferred or acceptable zone where there is little to no environmental or economic negative impact due to lake levels. Coping zone B is the range above and below zone A, where there is a temporary, reversible, and nonsevere negative impact due to the lake levels. Coping zone C is the range above and below zone B where the negative environmental or economic impact is acute, irreversible, or potentially long lasting. The coping zone levels are included in Figure 1 for all lakes and sectors. The method described in this article has been applied to each of the TWG-defined coping zones and on each of the Upper Great Lakes. While each coping zone threshold is represented by a single water-surface elevation level, there is remaining uncertainty associated with the threshold values. The TWGs amassed data from across their respective stakeholder groups to determine a single lake-wide value. Extrapolating the site-specific impact thresholds over an entire Great Lake does not capture the uncertainty and variability in sensitivity to changing water levels within each sector. This source of uncertainty and variability is not included in this analysis. Coping zones are similar to the impact thresholds described by Jones [2001]. Jones [2001] stated that stakeholder-defined thresholds clearly communicate uncertain outcomes in terms that are relevant to stakeholders and decision makers.

image

Figure 1. Coping zone levels for coastal, water use, recreational boating, commercial navigation and ecosystem sectors for Lake Superior, Michigan-Huron, Saint Clair, and Erie. Coping zones correspond to sector impact tolerance. Coping zone A is negligible impact, coping zone B is moderate impact, and coping zone C is severe impact.

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[21] This analysis focuses on the coastal TWG coping zone definitions for Lake Superior and Lake Michigan-Huron in the interest of brevity. While the model and analysis for each stakeholder coping zone and for each Great Lake were provided to the IUGLS, only the model and analysis for the coping coastal coping zone on Lakes Superior and Michigan-Huron are presented here. As seen in Figure 1, the coastal coping zone thresholds are relatively close to the historic average water levels compared to other coping zones. This is an indication that the coastal interests are relatively sensitive to water level extremes. Unlike the LOSLR study where gains by one stakeholder group were offset by losses from another group, stakeholder impacts based on coping zone threshold exceedance did not exhibit tradeoffs between stakeholder groups. There are tradeoffs between impacts on Lake Superior versus Lake Michigan-Huron, which will be discussed further. Additionally, the IUGLS study into the regulation of Lake Superior outflow focused on the impacts on Lakes Superior and Michigan-Huron. A summary of average coastal coping zone levels for Superior and Michigan Huron is included in Table 1. The coastal coping zones were defined based on the historic lake levels from 1918 through 2010. With these thresholds established, the risks associated with climate change could be estimated.

Table 1. Coastal Coping Zone Definitions for Lakes Superior, Michigan, and Huron
LakeZoneElevation (m)Definition
SuperiorHigh C183.70Average (by month) of 1985–1986 water level
High B183.6110% exceedance levels (by month) from 1918 to 2010
Low B183.2290% exceedance levels (by month) from 1918 to 2010
Low C182.89Record low water levels (by month) from 1918 to 2010
Michigan-HuronHigh C177.21Average (by month) of 1985–1986 water level
High B176.9410% exceedance levels (by month) from 1918 to 2010
Low B176.0480% exceedance levels (by month) from 1918 to 2010
Low C175.76Average (by month) of July 1963–June 1965 water levels

3.2. Hazard Discovery

[22] The hazard discovery process was described by Brown et al. [2011] and by Lempert et al. [2010] as a method of exploring the system robustness under a wide range of plausible states without determining the probability of the conditions. Plausible climate states are states that are possible and reasonable through studies of sources of climate data, including but not limited to historical climate records, stochastically generated climate sequences, paleo-based climate sequences, GCM and RCM projections, and expert opinion. Climate states that are inferred from one or more sources of climate information cannot be entirely ruled out. This avoids the modeling pitfall of avoiding certain extreme conditions based on the prejudice that the conditions are unlikely, so they should not be considered. This process facilitates system or policy risk assessment by identifying the conditions under which failure or poor performance occurs. It also allows comparison of the range of successful plan performance in climate space. This analysis may identify “satisficing” alternatives that are robust or have acceptable performance over a wide range of inputs rather than options that are optimal for a small range of inputs. Loucks et al. [2005] described a satisficing approach that establishes minimum performance values for each objective and selects alternatives that meet these criteria over the range of scenarios considered.

[23] In this application, a large database of synthetically generated climate conditions was created using an existing stochastic data set. This study made use of the historic-based, stochastically developed NBS series developed originally for the Lake Ontario–St Lawrence River study (LOSLR study) by Fagherazzi et al. [2005]. This data series provides 55,590 years of monthly NBS values for each of the Great Lakes. The IUGLS study board recommended use of the NBS series developed for the LOSLR Study for evaluation of regulation plans and lake performance [International Joint Commission, 2005]. The climate conditions represented in the data series span a greater range of plausible climate than the historic record, which allows testing the Great Lakes system and regulation plans over a broader range of climate than would be possible just using the historic record. The coordinated Great Lakes regulation and routing model (CGLRRM), described by Clites and Quinn [2003], was used to relate the stochastic NBS series to the corresponding monthly lake levels and lake outflows.

[24] The stochastic data set contains ample data to explore the relationship between climate and impact as defined by the coping zones. To determine this relationship, the data were parsed into segments that would capture the prevailing climate and resultant impact. This allowed comparison of system performance and climate statistics from each segment. Several data segment lengths were considered and explored. Thirty year analysis segments were selected for two reasons. First, the available GCM projections for this study were provided in 30 year segments, which is a typical time span used in climate change analysis. Thus the selection of a 30 year segment for the development of a climate response function would facilitate the link to GCM projections. In addition, 30 years is a World Meteorological Organization standard time period to specify climate conditions [Arguez and Vose, 2011].

[25] Once the data set was parsed into 30 year segments, coping zone occurrences and climate statistics were calculated for each segment. Analysis showed that three predictor variables explained a majority of the variation in the coping zone B and C occurrences. The three variables were the mean, standard deviation, and serial correlation of the annual NBS. The mean and standard deviation were normalized to a percent change from the historic mean and standard deviation. Figure 2 shows the coastal coping zone C occurrences on Lake Superior as a function of the percent change mean annual NBS and the percent change annual NBS standard deviation. In this figure, upper zone C occurrences are shown as red circles and lower zone C occurrences are blue diamonds with the size of the circle or diamond proportional to the number of occurrences.

image

Figure 2. Scatter histogram of 30 year realizations from the stochastic data set, plotted by percent change mean and standard deviation of the annual net basin supply. Each dot represents a 30 year segment from the stochastic data set. The size of the red circles and blue diamonds are proportional to the number of coastal coping zone C (severe impact) occurrences.

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[26] Figure 2 provides important information regarding the relationship between prevailing climate conditions and the impacts as defined by stakeholders. These figures demonstrate the increase in upper zone C occurrence when the system is wetter and more variable, or when the percent change mean NBS and the percent change annual NBS standard deviation increase. Increases in mean NBS imply that there is more water in the system and a greater chance of upper zone C occurrence. The lower zone C occurrences increase as the percent change mean NBS decreases and the percent change annual NBS standard deviation increases. These results are intuitively consistent with the physical system and demonstrate where significant impacts begin to accumulate.

[27] The hazard discovery process highlighted important features of the Great Lakes response to climate changes. While increases or decreases in the mean NBS increased the prevalence of upper and lower coping zone C occurrences respectively, Lake Michigan-Huron was much more sensitive to change, especially with regard to reduced NBS. Note that this sensitivity is also partially a function of the regulation of flows between Superior and Michigan-Huron according to the current regulation plan 77A.

3.3. Climate Response Function

[28] The hazard discovery process identified climate variables that were most strongly related to impacts as measured by zone occurrences. The next step in the process is the formalizing of this relationship in the form of a climate response function, a statistical model that links climate with system performance. Many models were proposed and assessed before the current model was selected. The objective was a parsimonious model that was computationally efficient to enable the use of a variety of climate information sources to estimate risk. To evaluate alternatives to the current regulation plan, the model had to be parameterized for each regulation plan. This section will describe model output, input, the deterministic and stochastic model components, and model parameterization. The climate response function uses three model inputs. This paper includes a brief section that analyzes adding a fourth model input. This paper does not describe the alternate models that were rejected during the modeling process.

3.3.1. Model Output—Coping Zone Occurrences

[29] The climate response function determines the expected fraction of months in each coping zone for a given set of climate inputs. This means that the model outputs are fractional values between 0 and 1, inclusive, and are not independent since the five coping zone occurrence fractions must sum to 1. The format of the predictand limits the type of stochastic model components that can be used. For instance, a normal stochastic model component is not appropriate because the normal distribution is supported over an infinite domain while the predictands are not. The model can be used to provide an estimate of the expected value of coping zone occurrence or can be used to estimate a probability distribution for each coping zone.

3.3.2. Model Input—Climate Measurement

[30] The parametric statistical model uses three climate statistics as predictors: the mean, standard deviation, and the serial correlation of the annual NBS. The mean and the standard deviation of the annual NBS were normalized based on the historic NBS series mean and standard deviation. The percent change mean and standard deviation are centered on or near 0 and effectively unbounded. The serial correlation is bounded between −1 and 1. The three predictors used in the model are defined below:

  • display math
  • display math
  • display math
  • display math
  • display math

where NBSi is the average annual NBS for the ith year, m is 30 years in each analysis segment, the bar indicates an average value, X1 is the percent change mean annual NBS from the historical mean, the asterisk indicates percent change in the variable, the “hist” subscript indicates the historical value based on an NBS record from 1900 to 2006, SNBS is the standard deviation of annual NBS values, X2 is the percent change in standard deviation of NBS from the historical standard deviation, and X3 is the serial or auto correlation within the annual NBS values with a 1 year lag. In section 3.3.5 the inclusion of a fourth input parameter, the starting water level for the time segment under analysis, is discussed.

3.3.3. Statistical Model Description

[31] At the core of the statistical model is the idea that changes in climate will shift and stretch the shape and range of the level exceedance curves for each lake, impacting the probability of exceeding a given threshold value within a given month. A level exceedance curve plots the cumulative nonexceedance probability versus the lake level. Wetter conditions will shift the curve upward, increasing the probability of exceeding upper zone C thresholds and decreasing the probability of exceeding lower zone C thresholds. Increased variability will tend to vertically stretch the exceedance curve resulting in increases for both upper and lower zone C coping zone probability. The model uses climate statistics to estimate the probability of being above or below a lake-level threshold, which then can be translated into an expected number of months or fraction of time in a given coping zone. The statistical model is composed of a generalized linear model with a logit transformation and a binomial distribution. This is used to predict the number of months above or below a level threshold out of the 30 year analysis window. The binomial distribution is governed by two parameters: n is the total number of time steps (in this case 360 months in the analysis window) and πj is the probability of not exceeding a given lake level for a given month. The subscript j refers to each of the four coping zone thresholds. The inverse logit transformation maps the linear combination of predictor variables from the real number range of [−∞ : ∞] to the probability range of [0 : 1]. An input vector X is multiplied by a vector of regression coefficients β as shown in equations (6) through (8):

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[32] The logit transformation is shown in equation (9) and the inverse logit transformation is shown in equation (10), with a and b serving as dummy variables:

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[33] Using the inverse logit transformation, the probability of nonexceedance is calculated using equation (11). The nonexceedance probability is πj, where j indicates the coping zone threshold being modeled. It is used in the binomial distribution in equation (12), where n is 360 or the number of months in the 30 year analysis window and Yj is the number of months with the water level below the jth coping zone threshold:

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[34] The binomial distribution has a mean or expected value equal to nπ, and the probability of the lake level z being less than or equal to a threshold Zj in a given month is πj. This model effectively treats the outcome for each month as independent. An area of future work is to consider models that do not treat the individual monthly outcomes as independent, but maintains persistence. The current model is adequate to describe the reliability of a given system which is calculated as the fraction of time not in a failure condition, but would be insufficient to predict system resilience as defined by Loucks et al. [2005], which is the conditional probability that if the system is currently in an unsatisfactory state, it will transition to a satisfactory state in the next time step.

[35] The model parameters were determined using a generalized linear regression by minimizing the residual sum of squares to estimate the parameter vector β. The climate statistics and threshold occurrences for each 30 year window comprised the data to fit the parameters.

[36] The estimated nonexceedance probabilities from each 30 year analysis window are calculated using equations (13) through (16), where inline image is the fraction of months that do not exceed the j zone threshold for each coping zone threshold (LC for lower C, LB for lower B, UB for upper B, and UC for upper C) and Nj is the number of months out of n total months in coping zone j:

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[37] The generalized linear regression is repeated for each coping zone threshold producing a parameter vector β for each. Since this analysis is based on the nonexceedance probability, it is fairly straightforward to calculate the proportion or probability of a lower C or an upper C zone. The probability of the lake being in lower C, or P(LC), is shown in equation (17) and for being in upper C in equation (18):

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[38] To be in lower zone B, the lake level z has to be below ZLB and above ZLC. Hence the probability of lower zone B is given by equation (19) and by similarity, the probability of upper zone B is given by equation (20):

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3.3.4. Climate Response Function Results for Lake Superior and Lake Michigan-Huron

[39] This section presents the climate response function results for Lake Superior using the coastal coping zones and regulation plan 77A. For brevity, model evaluation results are shown for Lake Superior only; the results for Lake Michigan Huron are similar. Figure 3 shows the relationship between the actual zone fraction, in black, and the predicted zone fraction, in blue, for upper C, upper B, lower B, and lower C zones on Lake Superior. These graphs show one predictor variable, percent change mean NBS, so the predictand variability based on the NBS standard deviation and serial correlation is not accounted for in the figures.

image

Figure 3. Comparison of observed and modeled expected value of coastal coping zone fractional occurrences for Lake Superior. Figure includes coping zone C (severe impact) and coping zone B (moderate impact) occurrences as a function of mean NBS.

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[40] Figure 4 provides a perspective on the model fit for Lake Superior by showing the percent change mean NBS on the x axis, the zone occurrence fraction on the y axis, and the probability density function value plotted on the z axis. The black dots represent the data points from the historic based stochastic series, while the red curves represent the zone occurrence expected value and the zone occurrence probability density functions. This figure allows the visual comparison of measured and predicted lake performance for upper coping zone B, or moderate impact from high water levels. The figures for lower B, lower C, and upper B coping zones and for Lake Michigan-Huron are similar but not included. The modeled expected value captures the data trends; increasing zone occurrences corresponding with increasing percent change mean NBS for upper C and upper B zones and with decreasing percent change mean NBS for lower B and lower C zones.

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Figure 4. Lake Superior coastal upper zone B (moderate impact). The observed mean NBS and zone fraction values from the stochastic series are plotted with black dots. The modeled expected value curve and probability distribution functions shown for NBS mean percent changes of −15% to 15% are plotted in red.

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[41] The binomial stochastic model component captures two key components of the data distribution. First, the distribution is appropriate for the predictand in that it supports the range from 0 and 1. Additionally, the binomial distribution accounts for the heteroscedasticity of the data, as shown by the increased variance or dispersion of the data with increasing mean value. For the binomial distribution, the mean or expected value is nπ and the standard deviation is (1 − π). When the probability is near 0 or 1, the distribution resembles an exponential distribution with a sharp peak near the domain boundary and a skewed tail. As the probability increases from 0, the peak decreases, the spread increases, and the distribution appears more like a normal probability distribution. In this way, the binomial probability density function correctly models the increasing spread and decreasing skewness with increasing probability that characterizes the observed data set.

[42] The climate response function shows the lake-level sensitivity to changes in climate. On Lake Superior, a 10% decrease in mean NBS causes no change in the expected coping zone C occurrence rate, while a 10% increase in mean NBS causes a 5% increase in coping zone C occurrence. In contrast, on Lake Michigan-Huron, a reduction of 10% in mean NBS causes a 27% increase in coping zone C occurrence while a 10% increase in mean NBS does not increase the coping zone C occurrence rate. This is shown graphically in Figure 5, which clearly shows that Lake Michigan Huron is more sensitive to changes in NBS. Note that the results shown are for regulation plan 1977A. Regulation plan impact on sensitivity is greater on Lake Superior than on Lake Michigan Huron, as discussed in section 3.4.

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Figure 5. Expected coping zone C (severe impact) occurrence on Lake Superior and Lake Michigan-Huron as a function of percent change mean NBS. The mean NBS is varied while the standard deviation and serial correlation are held constant to show the relationship between mean NBS and coping zone C occurrence.

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3.3.5. Sensitivity to Initial Water Level

[43] An additional logical predictor of zone occurrences is the water level of the lakes at the beginning of each 30 year period. For example, if a lake is at a relatively high water level at the beginning of a 30 year segment, it will likely have a greater fraction of months that exceed a high level threshold than a 30 year segment starting at the median water level. The Upper Great Lakes have long residence times, Lake Superior's is 190 years and Lake Michigan-Huron's is 100 years, which contributes to the persistent impact of starting water level. The magnitude of the lake sensitivity to starting lake water level was determined in two ways. First, the CGLRRM was evaluated with four fencepost 30 year NBS sequences and the starting water level at the 5%, median, and 95% exceedance level. The fencepost plans included a change in the mean annual NBS of ±10% and a change in the annual NBS standard deviation of ±20%. Figure 6 shows the impact that starting levels have on the level exceedance curve for these simulations. Note that in each quadrant, the same 30-year NBS sequence was used for each lake level starting value. Figure 6 shows that the upper zone occurrences were more sensitive to initial starting conditions at high percent change annual NBS standard deviations (+20%, shown in the two left plots) and that lower zone occurrences were more sensitive to initial conditions at low percent annual NBS standard deviations (−20%, shown in the two right plots). The initial condition sensitivity did not appear to be impacted by the percent change mean NBS.

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Figure 6. Lake Superior 30-year level exceedance curve sensitivity to initial lake level for four fencepost NBS sequences. The fencepost NBS sequences were selected with ±10% mean and ±20% standard deviation of NBS. The starting levels were the 5%, 50%, and 95% exceedance December lake levels.

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[44] Second, the starting lake level was added as a fourth predictor variable in the climate response function to evaluate model improvement. Model improvement was measured using correlation, a measure of explained variance. Adding the initial lake level to the predictive model improves the model fit, as shown in Figure 7. However, the inclusion of the additional predictor variable is not justified on two counts. First, the model fit is not significantly improved by the inclusion of the added parameter. The correlation between the observed and predicted coping zone occurrences ρ can be interpreted as the percent of variation explained. The inclusion of the fourth parameter only improves the percent of variation explained by 1%–3%. Second, the starting level at some future time period is unknown. The initial lake level for any future time period is uncertain and thus could not be included in estimations of future climate risk.

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Figure 7. Comparison of three- and four-parameter predictive models on Lake Superior coping zone occurrences. The three-parameter model includes the mean, standard deviation, and serial correlation of the annual NBS over a 30 year segment. The four-parameter model adds the starting lake level to the predictive model. The correlation ρ between the observed and predicted value is given for each model.

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3.4. Climate Response Surfaces

[45] The climate response function allows development of powerful new tools to analyze the interaction of climate with a water resources system, resulting in a better understanding of the implications of climate change. One of these powerful, new tools is the climate response surface, which graphically illustrates system performance over a range of conditions in climate space which is shown in the upper quadrants of Figure 8. The hazard discovery process clearly identified climate conditions that lead to adverse lake conditions. The climate response function can be used to predict the impact associated with a given climate condition. The upper quadrants of Figure 8 show the contour lines of equal expected value of coping zone C occurrences. The number of coping zone occurrences has been normalized by the historic rate of coping zone occurrences. The second contour line is located where the expected value of coping zone occurrences is at double the historic rate of coping zone C occurrence. The shaded areas between the contours get progressively darker with increased severity of coping zone C occurrence. This figure clearly shows that the most problematic climate conditions occur in the top right and top left of the graph, corresponding to an increasing standard deviation and an increasing or decreasing mean NBS. The figures show that Lake Superior is more vulnerable to increases in NBS while Lake Michigan-Huron is more vulnerable to decreases in NBS for the coastal coping zones. Also, Lake Michigan-Huron is more sensitive to climate changes as shown by higher increases in unacceptable performance over a similar range of climate change. These findings are consistent with the regions identified in the hazard discovery process and shown in Figure 2.

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Figure 8. Regulation plan performance on Lake Superior and Michigan-Huron. The top graphs show contours of equal expected number of coastal coping zone C occurrences. Each contour n represents n times the historic zone C occurrence rate. The bottom graphs provide a comparison of ten regulation plans. The graphs compare contour lines at twice the historic coping zone C occurrence rate.

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[46] The contours shown in the upper quadrants of Figure 8 are for plan 1977A for the regulation of Lake Superior outflow. The climate response function can be reparameterized based on the coping zone occurrences from alternative regulation plans under consideration during the IUGLS and new hazard contour plots can be developed. To visualize the impact of regulation plans on lake hazards, the contour corresponding to twice the historic coping zone C occurrence has been isolated for ten different regulation plans and is shown in the lower quadrants of Figure 8 for Lake Superior and Lake Michigan-Huron. These figures can be used to identify the plans that perform best over the widest range of climate conditions and identify specific regions of climate space where certain plans are superior to others. These figures also highlight the inherent tradeoffs associated with many water resources problems. Plan 55MR49 offers the best performance on Lake Superior and the worst on Lake Michigan-Huron, while plan P129 has the best performance on Lake Michigan-Huron and the worst on Lake Superior. To gain acceptance with the IUGLS study board and the International Joint Commission, a plan would have to improve performance on one or more lakes without degrading performance on the other lakes. In an accompanying paper, the results displayed in Figure 8 are used to develop robustness indices to assist in regulation plan evaluation and selection (P. Moody and C. Brown, Robustness indicators for evaluation under climate change: application to the Upper Great Lakes, submitted to Water Resources Research, 2012).

4. Results and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information

[47] This analysis discusses how climate conditions can be used to predict risk associated with lake levels on Lake Superior and Lake Michigan-Huron. While the discussion focuses on the coastal coping zones, the same statistical model fitting has been conducted for all coping zones including ecology, commercial navigation, water use, recreational boating, and boat launch coping zones. The model has also been extended to Lake St. Clair and Lake Erie and has been used for ten alternate lake regulation plans. For brevity, the results for the additional zones and lakes are not included in this paper.

[48] The IUGLS goals include assessment of the risk to the lakes associated with climate change and selection of a new regulation plan. Since the results shown in Figure 8 identify climate conditions that increase zone C occurrences beyond an acceptable level, there are several questions that ensue. First, how likely are these climate conditions given the current and potential future climate? Second, are there any plans that perform better overall, in climate conditions that plan 77A does not, or over a wider range of climate conditions? The first question about the likelihood of climate conditions is an area of ongoing research and will be addressed in a future paper. The implications of this question are essential to the understanding of risk associated with climate changes. Conditions with severe consequences but negligible likelihood are low risk. Climate change may alter the distribution of the climate parameters, which may increase the likelihood, and therefore the risk, associated with specific problematic climate conditions.

[49] However, even without the use of climate information to estimate relative probabilities of the identified hazards, much insight is gained from the climate response function. For example, based on the definition of risk prescribed by the coastal TWG stakeholders, it is shown that Lake Michigan-Huron is much more sensitive to small changes in climate. A five percent decrease in the mean NBS yields a doubling of the historical occurrences of problematic lower lake levels. These hazards occur much more frequently on the low side; it takes a mean NBS increase of 15% to double the historic hazard occurrences. These changes to the mean NBS are not only within the range of the historic based stochastic data set, they are within the range of projected NBS values based on GCM projections.

[50] The approach described above is sensitive to the choice of the threshold level. The thresholds represent the lake levels where stakeholder impact increases. These levels are not uniform or static. Dessai and Hulme [2004] discuss adaptation measures and classify them as policy actions taken by governments through legislation, regulation, and other means and actions taken by private decision makers through autonomous, responsive, or instantaneous adaptation actions. Through these private decisions to employ individual adaptation measures, stakeholders and stakeholder groups can widen their coping zone thresholds which would reduce their risk exposure under historic climate variability and potential future climate variability. The climate response function has helped identify the climate conditions that cause the most concern. This work highlights the areas of increasing risk, which can be used to support decision analysis for adaptation measures.

[51] A major advantage of the climate response function is that it allows the use of climate inputs from alternate sources of climate information, such as downscaled GCM projections or paleo analysis. This allows the tailored use of climate information by taking climate statistics for use as predictors in the climate response function. This model can be used with a single climate change projection to generate a point estimate of expected system performance or over a range of climate to generate performance estimates for the entire range. Even more insight may be gained by assigning a probability distribution for each climate variable and allowing the sources of climate information to influence the variable probability distributions. With estimates of climate probability and climate impacts, one can integrate over the range of each climate variable to determine an overall expected value of impact. This expected value of impact will then be a function of the source of climate information through the probability distribution function and a function of the regulation plan through the parameterization of the climate response function. This result can be used to examine how the system performance is related to the source of climate information and the regulation plan. Importantly, when new climate projections become available, the climate response function can be used to quickly estimate the impacts resulting from the climates simulated by those projections.

5. Conclusion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information

[52] Climate change is an issue of grave concern on the Great Lakes. Stakeholders are sensitive to relatively small changes in lake levels. Previous studies of climate change using projections of future climate have shown a wide range of possibilities. In this study the objective was to develop a model of stakeholder-defined risk that could be used to put such climate projections into context. Development of this climate response function is a key component in the “bottom-up meets top-down” process called decision scaling, by linking system performance as defined by stakeholders to climate conditions. The function facilitates the assessment of the vulnerability domain, the region of climate space which results in unsatisfactory system conditions. Using the climate response model, three statistics from a 30 year climate series of net basin supply explains over half of the performance variability in Great Lakes coping zone occurrences. Adding additional inputs, such as initial lake level, could increase the model accuracy, but would reduce the model utility.

[53] The analysis reveals the effect that changes in key climate statistics has on the occurrence of problematic lake levels in the Upper Great Lakes. In doing so, the climate conditions that are problematic are identified. Climate information, including GCM projections or paleo data, can be used to inform decision makers of the possible probabilities associated with these conditions. The climate response function can be used to develop climate response surfaces that show system performance as a function of climate to provide a visual and quantifiable measure of performance and robustness. It can also be used to evaluate alternative regulation plans by assessing the range of climate conditions over which each can provide acceptable performance as measured by lake levels. These applications are being pursued in current work. The model described in this paper was a vital input to the decision making process on lake regulation in the IUGLS.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information

[54] This work was funded through the U.S. Army Corps of Engineers (USACE) and the U.S. Geological Survey (USGS) in support of the International Upper Great Lakes Study (IUGLS). Bill Werick, David Fay, and Wendy Leger provided valuable feedback throughout the development of Climate Response Function. IUGLS study co-chairs Eugene Stakhiv (U.S.) and Ted Yuzyk (Canada) provided guidance and perspective for the research. The manuscript was improved by thoughtful comments from three anonymous reviewers.

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  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Method
  6. 4. Results and Discussion
  7. 5. Conclusion
  8. Acknowledgments
  9. References
  10. Supporting Information
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wrcr13595-sup-0001-t01.txtplain text document1KTab-delimited Table 1.

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