ecosystems are diverse (e.g. Carlisle et al., 2011). The composition of species in riverine ecosystems often changes following the commissioning of dams with large storage capacities that regulate high- and low-flow extremes (e.g., Poff et al., 2007; Mims and Olden, 2013). Prescribing operating rules that sustain pre-dam ecosystems has become an increasingly recognized challenge, especially when flow manipulation benefits off-stream human interests (e.g., Cardwell et al., 1996; Suen and Eheart, 2006; Poff et al., 2009). Short streamflow records make it more difficult to determine whether ecosystem changes are due to dam impacts or natural variability (e.g. Kennard et al., 2010; Nikghalb et al., 2016). Moreover, there are few guidelines for incorporating uncertainty stemming from short streamflow records into these tradeoffs. Streamflow has been identified as the primary driver in riverine ecosystems (Power et al., 1995; Walker et al, 1995) since it influences ecological conditions through changes in velocity, depth, temperature, water quality and substrate (e.g. Poff et al. 1997; Jager, 2014; McManamay et al., 2015). Indeed, many interconnections between streamflow and habitat conditions are indirect, which can moderate any apparent correlation between hydrologic alteration and ecological responses (e.g. Jager, 2014; McManamay, 2015). Yet, the availability of streamflow data relative to other proximate indicators of ecological degradation has generated tremendous interest in characterizing ecological responses to flow alteration, including reviews by Poff and Zimmerman (2010) and Webb et al. (2013). Flow-based approaches to managing environmental flows can also be implemented in data-poor regions where hydrologic and ecological monitoring can be more challenging (McKay, 2015; Lamouroux, 2015; Eriyagama et al., 2016). Institutions representing ecological interests, such as The Nature Conservancy, have recently promoted expert-elicited flow-ecology relationships in stakeholder negotiations (e.g., Kendy et al., 2012; Steinschneider et al., 2015). In this paper, we introduce a tool suited for assessing impacts to
following test determines the likelihood of a violation for at least one of these two ecologically critical AFDC quantiles as follows: No threshold violations At least one threshold violation We then compute the probability of hypothesis testing errors for K independent AFDC quantiles: Type II errors are conditional upon the type I errors selected for each AFDC quantile hypothesis test, and vice versa, since a value of one uniquely determines the other. Future work may consider the impact of cross-correlations among individual hypothesis test results when determining the overall field significance (Douglas et al., 2000). Informing dam operation decisions with hypothesis test results In this section, we introduce our Bayesian decision-tree framework, which accounts for both type I and II errors associated with hypothesis tests regarding the exceedance of percent deviation thresholds when evaluating potential hydropower and ecological consequence of reservoir operation decisions. We also contrast this approach with common deterministic and probabilistic decision-making methods. 3.1 Approaches for incorporating Type I and II errors in decisions In our post-hoc, or observed, power analysis, we determine the power 1 - corresponding to a given α, estimated effect size , and sample sizes m and n. We show the importance of carefully choosing among numerous methods for incorporating hypothesis test results into decisions. First, we apply null hypothesis significance testing (NHST), a common practice for
Oommen, T., Baise, L.G., Vogel, R.M. 2011. Sampling bias and class imbalance in maximum likelihood logistic regression. Math. Geosci., 43 (1), 99-120. Pearsall, S.H., McCrodden, B.J., Townsend, P.A. 2005. Adaptive management of flows in the Lower Roanoke River, North Carolina, USA. Environ. Manage., 35(4), 353-367. F.J., Barquín, J., Álvarez, C. 2016. Assessing hydrologic alteration: Evaluation of different alternatives according to data availability. Ecol. Ind., 60, 470-482. Perkin, J.S., Knorp, N.E., Boersig, T.C., Gebhard, A.E., Hix, L.A., Johnson, T.C. 2016. Life history theory predicts long-term fish assemblage response to stream impoundment. Can J. Fish Aquat. Sci., 3 Poff, N.L., Zimmerman, J.K.H. 2010. Ecological responses to altered flow regimes: a literature review to inform the science and management of environmental Freshwater Biol., 55, 194-205. Poff, N.L. and many others. 2010. The ecological limits of hydrologic alteration (ELOHA): a new framework for developing regional environmental flow standards. Freshwater Biol., 55, 147-170. Poff, N.L. 2009. Managing for variability to sustain freshwater ecosystems. J. Water Res. Plann. Manage., 135, 1-4. Poff, N.L., Olden, J.D., Merritt, D.M., Pepin, D.M. 2007. Homogenization of regional river dynamics by dams and global biodiversity implications. Proc. Nat. Acad. Sci., 104(14), Poff, N.L., Allan, J.D., Bain, M.B., Karr, J.R., Prestegaard, K.L., Richter, B.D., Sparks, R.E., Stromberg, J.C. 1997. The natural flow regime: a paradigm for river conservation and restoration.
where denotes the efficiency of hydropower production, which is assumed to be 80 percent at all times, is the turbine outflow on each day (m3/s), and indicates the net head (m) on each day. The coefficients of 24 and 9.807 represent the number of hours in a day and the rate of gravitational acceleration at the Earth’s surface (m/s2), respectively. Tables Decision Making Approach High flows (Q5) Low flows (Q95) Overall alteration Deterministic Alteration. Exceeds the 30% decrease threshold, an adverse ecological impact will occur if operations are not changed. Alteration. Exceeds the 50% increase threshold, an adverse ecological impact will if operations are not changed. Alteration. Thresholds at both sites are exceeded, an adverse ecological impact will occur if operations are not changed. Null hypothesis significance testing (p < 0.05) No alteration. = 0.09. Alteration insignificant, no significant risk of an adverse ecological impact. No alteration. = 0.10, Alteration insignificant, no significant risk of an adverse ecological impact. No alteration. = 0.18, Alteration insignificant, no significant risk of an adverse ecological impact. Fixing the type I error probability at 0.20, using decision tree Hydropower and ecological regret probabilities are similar. Even though is much higher than 0.05, (0.38) indicates a high likelihood that test will not recommend changing the reservoir operating rule when necessary. Hydropower and ecological regret probabilities are similar. Even though is much higher than 0.05, (0.26) indicates a high likelihood that test will not recommend changing the reservoir operating rule when necessary. Substantial regret probabilities, decision depends on relative hydropower and ecological values. While the hydropower and ecological regret probabilities are 0.44 and 0.46, respectively, the greater potential ecological consequences of HPFOI make
changing to HPROR worthwhile. Optimal and (minimizing total regret) The hydropower regret dominates because hydropower losses are less important than ecosystem losses. is much higher (> 0.99) than (< 0.01). The lower consequence of hydropower regrets makes a higher much more tolerable. The hydropower regret dominates because hydropower losses are less important than ecosystem losses. is much higher (> 0.99) than (< 0.01). The lower consequence of hydropower regrets makes a higher much more tolerable. The hydropower regret dominates because hydropower losses are much less important than ecosystem losses. Since is very high for both high and low flows, it is also very high for overall alteration. Similarly, since is very low for both flows, it is very low for overall alteration. 1: Management implications of different decision-making approaches. Figures Figure 1: Pre- and post-dam annual flow duration curves from the stylized example in Sec 5. Decision Rule Unknown Truth Alteration not threshold No Alteration, NA Alteration above threshold Alteration, A Keep reservoir operation rules (Conclude No Alteration) CNA P(CNA|NA) Under-protection error (Type II error) P(CNA|A) Change reservoir operation Over-protection (Type I error) P(CA|A)
P(NA) P(A) Decision Rule No protection implemented P(CNA) P(NA|CNA) Ecosystem regret probability P(A|CNA) Protection Implemented P(CA) Hydropower regret probability P(NA|CA) P(A|CA) Figure 7: Regret probabilities for decision analysis in Figure 6 on a non-informative prior probability (0.5) of alteration. Figure 8: Relationship between hypothesis test error probabilities and decision regret probabilities (contours) Figure 9: Inflows and outflows of hypothetical reservoir Figure 10: Tradeoffs between type I and II errors and regret probabilities for high- and low-flow alteration, Threshold Set 2. Figure 11: Optimal regret combinations when (a) a one-percent decrease in hydropower is weighted equally to a 1% increase in the likelihood of adverse ecological impacts, and (b) hydropower and ecological regret probabilities are weighted equally.