Reply to comment by Jack Lewis et al. on “Forests and floods: A new paradigm sheds light on age‐old controversies”

To the extent that two scientific schools disagree about what is a problem and what a solution, they will inevitably talk through each other when debating the relative merits of their respective paradigms. [Kuhn, 1970, p. 109]. [1] Alila et al. [2009] did not intend to present the frequency paired (FP) method for analyzing altered peak flow frequencies after logging as stated by Lewis et al. [2010]. Such a technique is well established in the wider hydrology [e.g., Howe et al., 1966] and climatology [e.g., Wigley, 1985] communities; and the concepts on which it is based are not new to the forest hydrology community [e.g., Troendle, 1970]. Alila et al. [2009] expose a set of flaws of the most fundamental construct in methods that dominated decades of research in forest hydrology and as a result, cast serious doubts on the current state of science on the relation between forest land use and floods. Alila et al. [2009] illustrate, using philosophical, conceptual, physical and empirical arguments, how our prevalent scientific perception of the forests and floods relation is shaped by an invalid experimental design and irrelevant research hypotheses that focus on a change in magnitude between preharvesting and postharvesting floods when paired by equal meteorology or storm input. This type of chronological event pairing (CP) leads to incorrect changes in flood magnitude because it fails to account for the physical reality of changes in frequency of peak flows caused by harvesting, and further reaffirms decades of irrelevant research outcomes through the use of inappropriate statistical methods referred to as the analysis of variance and covariance (ANOVA and ANCOVA). Since many paired watershed studies published earlier did not have a sufficient record length to apply a frequency paired analysis, their outcomes may have been a manifestation of the “expediency” of the moment rather than a substantiation of “scientific facts” [Yevjevich, 1968, p. 1174]. [2] Lewis et al. [2010] choose to remain vague by neither fully denying nor admitting to the fundamental flaws in CP-based analyses but insist that CP can be modified to account for a change in frequency. Lewis et al. [2010] avoid the main question at hand by raising secondary questions of interpretive nature, the answers to which can only serve to further articulate (and not correct or invalidate) our FP method: How do we adjust observed peak flows for hydrologic recovery? How do we correct for the loss of variability caused by a calibration equation? How do we estimate uncertainty in a flood frequency relation? How do we increase statistical power to predict the effects on larger floods? These questions are important but must be considered as a part of a new era of research in forest hydrology guided by the new paradigm of pairing events by equal frequency. Since scientists can only be guided by one paradigm at a time, we contend that the main and real question at hand that we must confront head on remains; which of the two paradigms should guide the future science of forests and floods, CP or FP? The answer may lie in Francis Bacon's maxim: “Truth emerges more readily from error than from confusion.” [3] In this response, we explain why continuing the use of CP-based methods for evaluating the relation between forests and floods will reinforce the misconception, confusion and misinformation that are prevalent in the science literature, as opposed to increasing our understanding of land cover influences on hydrologic response. In our reply, we classified the major discussion points raised by Lewis et al. [2010] under the following six general headings. [4] Lewis et al. [2010] state that “we agree that analyses of changes in flood frequency are useful for evaluating the effects of watershed disturbance” (paragraph 1) and “…attention to flood frequencies is merited and may shed light on the issue” (paragraph 29). Let there be no confusion that flood frequency distributions are not just a “useful” dimension that simply “merits attention”; they absolutely must be included in any evaluation of the relation between forests and floods. If the inextricably linked frequency and magnitude of a flood are not simultaneously invoked, as conducted in the convenient but irrelevant CP-based analysis of variance and covariance, not only we end up with the incorrect change in magnitude but equally important we obscure the most critical facets of the relation between forests and floods, namely, (1) small changes in the magnitude of floods can translate into larger changes in their return periods and (2) the larger the flood, the more dramatic the change in its return period. This is a direct consequence of the highly nonlinear and inverse relation between the magnitude and frequency of floods, which can only be represented by the flood frequency distribution and not a regression fit of any level of complexity. [5] These arguments are easy to demonstrate. Under a stable climate, a flood event may be assumed to occur when, say, a peak flow magnitude, Q, falls above some critical threshold, QT. The probability of occurrence, P, of such a flood is given by the area under the tail of the frequency distribution when Q is larger than QT. This area also defines the return period or recurrence interval, T in years, which is the inverse of the probability of occurrence P. Shifting the mean of the distribution toward QT causes increases in the area under the tail in a highly nonlinear manner. Figure 1a shows how a 30% change in mean would change roughly a 20 year into a 7 year event, and a 100 year into a 20 year event. The frequencies of larger floods are even more sensitive to changes in the variability around the mean of the frequency distribution. Figure 1b shows how a 10% change in the mean combined with a 20% upward shift in the standard deviation will change a 100 year into a 25 year flood event, which amounts to quadrupling the flood risk. Although highly idealized, these rather “pedagogical” illustrations [Wigley, 2009, p. 67] serve to emphasize the importance of the overlooked frequency distribution conceptual framework in decades of forest hydrology literature. [6] Climatologists have long recognized the significance of a frequency distribution framework, hence the critical aspects of extreme event theory such as return period and risk, for understanding and quantifying the effects of climate change on weather extremes [e.g., Wigley, 1985]. In forest hydrology, however, over 40 years of ANCOVA and ANOVA studies stripped the “risk” out of what was meant to be an evaluation of the relation between forests and flood risk. This created a perception based on the conclusions of irrelevant research which claimed that there is ‘no evidence' that forests affect larger flood events, albeit that those events were ambiguously defined (i.e., ranked by storm input or control watershed peak flows). The time has come for the forest hydrology community to put an end to working in isolation on the topic of forest land use effects on floods. The conclusion that only the frequency paired approach revealed that “all peak flows save the largest event were shifted upward” (AKSH, paragraph 29) reflects the fact that the AKSH procedure itself shifted the peaks used in the FP analysis upward. Figure 7b, showing the unadjusted analysis, is the appropriate figure for comparison to Figure 3a; both reveal a more modest upward shift converging at the two largest events. [8] The quote “all peak flows save the largest event were shifted upward” was truncated and should have been reported as: “all peak flows save the largest event were shifted upward and the largest peak flows on the observed record became more frequent (Figure 3b).” An interpretation of Figure 3a, constructed with or without recovery adjusted peak flows, not only leads to incorrect estimate of a change in magnitude but equally important cannot be used to make inference about changes in frequency of any events, let alone the larger floods, because the CP-based analysis is not designed to reveal changes in event frequency. Figure 3b, however, reveals what Lewis et al. [2010] appear unwilling to admit; that forest harvesting may have increased the frequency of larger events. “Novelty emerges only with difficulty, manifested by resistance, against a background provided by expectation” [Kuhn, 1970, p. 64]. [9] Alila et al. [2009] state that interpretation of the FP analysis displayed in Figure 7b cannot be scientifically defensible because it was constructed using a nonstationary time series. Also, any analysis based on Figure 7 would be invalid because it does not distinguish between the effects of forest harvesting and recovery. These issues cannot be overemphasized and our Figure 7 was included to avoid such highly anticipated misinterpretations. While Figure 7b is admittedly wrong, Figure 3a is “not even wrong” (i.e., its interpretation is irrelevant to whether forest harvesting is affecting floods). We decided to use raw (unadjusted for recovery) data for constructing one of our plots in Figure 3 (i.e., Figure 3a) because it is this convergence of two regression lines that has shaped our prevailing perception: namely forests affect small and medium but not necessarily larger floods. [10] The use of paired watershed data to illustrate the difference between chronological and frequency pairing is not possible without employing a calibration equation to estimate the expected peak flows. The empirical cumulative distribution function (CDF) of these peak flows may have been affected by a loss of variability associated with the use of such equation. As explained in our methods, we corrected for this loss of variability and the outcomes were discussed by Alila et al. [2009, section 4.2]. The calibration equations that we employed at WS1 and WS3 used log-transformed peak flows. Prediction using these regression equations produces a small downward bias in the estimate of the expected discharge. We have not made any adjustment for such downward bias and Lewis et al. [2010, paragraph 12] are correct when they state that “The required bias correction is typically small, but given the sensitivity of upper quantiles to a shift in both mean and variance, the differences reported cannot necessarily be attributed to logging.” [11] Using the proposed bias correction technique, we indeed found the effect to be quite small (in the order of 1–2%) and therefore not substantial enough to change any of our results and conclusions. We find it remarkable that Lewis et al. [2010], on one hand, recognized how changes in mean and variance can have substantial effects on the upper quantiles of a frequency distribution, and are concerned about this small downward bias in the expected discharges, but are still defending the chronological pairing which, as we illustrated, leads to an equivocally incorrect and irrelevant change in magnitude. [12] Our adjustment for recovery of peak flows is also based on chronological pairing; this may introduce uncertainty in our estimated changes in the magnitude and frequency of floods. We have explicitly acknowledged this in section 3.5 of our original article. While it is possible that our recovery adjustment may have affected our results, we think such effects are minimal, in part because of the naturally slow recovery of the cold snow environment at Fool Creek and the even slower recovery of road effects at WS3. Nonetheless, we would like to see the results of an FP analysis on the same data sets, adjusted for recovery using a model that is accepted by the forest hydrology community. [13] Lewis et al. [2010] suggested that a valid analysis of uncertainty would require that potentially overlapping confidence limits be estimated for frequency distributions of both the expected and observed peak flows. The outcomes of statistical hypothesis tests cannot be used to justify a CP-based invalid research hypothesis, which we illustrate to be irrelevant to the forests and floods relations. Our conclusions that the prevalent perception of forests and floods relation is scientifically indefensible will not be invalidated by attempting to impose more stringent statistical tests of significance. Nevertheless, we have used in our original article two nonparametric tests which specifically test whether the two (pretreatment and posttreatment) sample distributions are “far enough apart” that they can be considered to be derived from different populations [Alila et al., 2009, Tables 1 and 2]. [14] Our approach to estimating uncertainty using Monte Carlo simulations and our position on the concept of null hypothesis statistical testing are well documented in our methods. Regardless, since chronological pairing does not lead to estimation of correct changes in magnitude and provides no information on changes in frequency, it is irrelevant whether the two pairing methods provide changes in magnitude that have similarly high type 1 error probabilities. [15] We agree with Lewis et al. [2010] that the lack of statistical power may continue to be a challenge in detecting changes in unusual events and we agree with their suggestion of conducting metastudies to investigate whether analogous changes have repeatedly been measured but declared insignificant in the absence of sufficient statistical power. However, this is outside the scope of our article and should be a recommendation for future research on this topic guided by the FP- and not CP-based paradigm. [16] Lewis et al. [2010, paragraph 19] suggested that “[i]f the available data are uninformative, the reader should avoid conclusions of any kind.” The amount and relevance of information contained in experimental and observational data depends on the appropriateness of the method used to analyze such data. Our FP event analyses revealed how profound the implications of overlooking changes in flood frequency could be in evaluating the relation between forest harvesting and floods. For the first time, Alila et al. [2009] revealed how forest harvesting not only causes a 3 year to become 2 year event, but may also change a 30 year (Fool Creek) and a 40 year (WS3) into a 15 year event. We have acknowledged the uncertainties in the upper tail of flood frequency distributions [Alila et al., 2009, section 4.2] but simultaneously articulated plausible physical explanations for such changing patterns of magnitude and frequency [Alila et al., 2009, paragraphs 28 and 38], which cannot simply be ignored. [17] Blocking is used in chronological pairing and the paired before-after control-impact (BACI) design to create the sort of controlled experiment that will allow for the isolation of the system response of interest. However, the system response of interest in our case is a flood, which has two inextricably linked attributes: magnitude and frequency. Therefore, the frequency distribution is the only framework that allows the control of one of the two attributes in order to calculate the change in the second. This is the only correct method of answering the purely stochastic research hypothesis: What is the change in magnitude (frequency) for an event of a specific frequency (magnitude) of interest? Given a paradigm, interpretation of data is central to the enterprise that explores it…But that interpretive enterprise…can only articulate a paradigm, not correct it. Paradigms are not corrigible by normal science at all. [19] Lewis et al. [2010, paragraph 22] suggested carrying out paradigmatic comparisons using “data sets reflecting the shorter record lengths more typical of those generally available, such as those from WS1 and WS3, and for the 27 year Fool Creek data set” and not just Fool Creek 48 year data. The intriguing differences between the outcomes of the two pairing methods are best illustrated using a long record in a hydroclimate regime with a naturally slow recovery rate. Our analysis of the Fool Creek results at 27 and 48 years indicates that we need longer and not shorter records. Besides, WS1 and WS3 data sets of varying length have already been analyzed by three research groups using CP analyses and their outcomes have been summarized and compared to the outcomes of our FP analysis [Alila et al., 2009, paragraphs 49–51]. [20] Lewis et al. [2010, paragraph 23] state that the CDFs are smoother than the CP-based regression analyses because “the data are sorted to create a nondecreasing display.” The “nondecreasing display” is the result of using order statistics as opposed to CP-based estimates. Order which a direct estimate of the a more of The variability around a regression fit of ANCOVA is an of the inappropriate type of event pairing [e.g., Alila et al., 2009, Figure Such variability must affect the statistical power of the CP-based methods and the to a change caused by forest harvesting [e.g., Alila et al., 2009, Figure and paragraph Our is that in the variability is when one the and control CP peak to have the same frequency of they do there may be a return period which a forest cover does not affect floods, but that flood can only be with a In some for the effects of on floods may with increasing return period et al., In such however, an question is or how must floods be for to have no effects on floods? et al., p. In other snow and can be more important than and their effect on flood response can increase with increasing return period and Figure p. Lewis et al. [2010, paragraph 23] state that tests for CP and FP have different null direct comparisons of statistical power may not be and FP have different null was the we use to our case against the CP-based paradigm, and we found it remarkable that Lewis et al. [2010] are using the same against our to the statistical power of CP and FP methods. Lewis et al. [2010, paragraph state that cannot be used to Our is that recovery will occur when the and frequency distributions are Therefore, FP should be used to recovery in this that it cannot be as is Lewis et al. [2010, paragraph that CP-based regression analysis 3a) does reveal that the frequency of peaks increased after logging.” We disagree because CP-based analysis of covariance was not designed for such Lewis et al. [2010, paragraph suggested that could be used to those changes and the of medium peaks to peaks may indeed more but there is no to methods What Lewis et al. [2010] are is an and of what can be and with under our paradigm. made the same suggestion three decades when, the challenge of an increase in the of peak flows in stated that increase in the variance of peaks and be by more regression p. and p. were that the question of forests and floods cannot be without the dimension of frequency. that on this topic was We recognized that Lewis and were the the frequency dimension under the CP-based framework [e.g., Lewis et al. Figure However, we see no in of or statistical between the outcomes of CP and FP This type of between the outcomes of CP-based methods and the frequency of floods, which does not necessarily the nonlinear and inverse relation between the magnitude and frequency, is not only but a state of We need to that since CP-based methods the change in magnitude, there is no that they the correct change in frequency, and even they it would be for the Alila et al. [2009] that about forest harvesting effects using the analyses of variance and covariance are invalid for flood events and larger than an peak Lewis et al. [2010] claimed that we have not given any statistical for such Our against the paradigm of CP and the analyses of variance and covariance is about and not p. of research on the topic of forest harvesting and floods that used the paradigm of CP and associated analyses of variance and covariance account for the physical reality of changing flood frequencies and as a consequence stripped the from the research question at Lewis et al. [2010] in type of that we are for our case against the CP-based methods from a by the our article for the case against the CP-based methods from decades of in and Our forest hydrology revealed that a at the flaws that we in CP-based methods when used to the relation between forests and and and most p. explicitly referred to the convergence of two regression as to whether or not forest harvesting floods. To the best of our and have also on this topic since Although we have been up in p. for it is to on from the of and 1970, p. and p. In light of these which continue to be the of over the outcomes of decades of irrelevant CP-based paired watershed peak flow studies the only of our forests and floods theory which cannot be cannot be by p. have been by the in the and frequency of floods to we must to in order to and information about causes and flood could be to any of a because our confusion about the and their in forests and for and its In in of our paradigm, Lewis et al. [2010] arguments against it are simply We to that CP-based methods are scientifically Although science is in general cumulative and this is one of these on the would not be the of CP-based of the forests and floods relation have our of the rather than and are We must to the that our current perception of forests and flood is We the for of this and by the forest hydrology scientific p. is only a of time it is that the CP-based paradigm has been a convenient We one for on an earlier We and for We are to and for We and for in the of Figure

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