Flood Frequency Analysis Along Bagmati River Basin in Khagaria District, Bihar Using Gumbel’s Method and Log Pearson Type lll Distribution

Climate change has remarkably intensified the occurrence of floods around the globe. Flooding causes loss of life and property. Flood frequency analysis (FFA) is an important investigation and plays a key role in flood‐related studies. Geographically, the study area is confined in the lower Brahmaputra floodplains, flat slope, and rivers are braided in nature. Because of Heavy rainfall, major rivers in the area carry huge influxes of surged water during the summer period. Hence, disastrous flooding can be seen every year in the study region. The present study aims to model flood frequency using the hydrological data to understand the effects within the area. FFA approaches like Gumbel, Log Pearson type 3 (LP‐3), and Log‐Normal (LN) were used, and comparative analyses were done using water level data for the Manas, Aie, and Brahmaputra Rivers. Moreover, remote sensing and the geographic information system (GIS) environment were used to generate FFA‐based flood predictive inundation map at 5, 10, 50, 100, and 200 years of return periods. Here, Gumbel's distribution has found the best fit for all the rivers among the three. The distribution reveals that at a 200‐year return period, the highest water level would be increased by 1.45, 2.41, and 4 m for the Manas, Aie, and Brahmaputra Rivers, respectively. The study shows that almost 493.54 and 673.72 km2 of areas are expected to be submerged at 5 and 200‐year return periods according to Gumbel's distribution; LP‐3 distribution predicted 493.01 and 555.66 km2, and the log‐normal distribution method predicted 432.51 and 555.74 km2 of flood‐sensitive areas at 5 and 200‐year return periods, respectively. The FFA highlighted spatio‐temporal effects on the expansion of submerged areas. We hope that the findings of the present study will aid in the different flood hazard management strategies for future endeavors.

With global climate change and human activities, environmental uncertainties are increasing, and extreme flood events are occurring more frequently. The reliability of traditional hydrological frequency analysis theories, based on the assumption of stationarity, is being increasingly questioned. This study aims to develop a non‐stationary flood frequency analysis model using the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) framework, with time and climate indices as covariates. The model calculation and frequency analysis are conducted using 2000 years of climate indices reconstructed by the Paleo Hydrodynamics Data Assimilation product (PHYDA). Design floods for different return periods are then quantified based on the reconstructed data. The results show that the nonstationary model established with climate indices as covariates can accurately identify the trend of first decreasing and then increasing flood series at the FP and ZJG stations in the Daqing River Basin, achieving the best model performance. Moreover, using the PHYDA‐reconstructed climate indices from the past 2000 years to extrapolate floods and calculate design floods provides higher safety for certain return periods than observed series. However, under longer return periods, the design values are smaller than those of the existing observed series. Overall, the nonstationary model proposed in this study can serve as a tool for flood frequency analysis under climate change. Additionally, incorporating the climate indices from the past 2000 years into nonstationary flood frequency analysis provides design results that can offer valuable references for regional water infrastructure design.

Design flood estimation is an essential step in many water engineering design tasks such as the planning and design of infrastructure to reduce flood damage. Flood frequency analysis (FFA) is widely used in estimating design floods when the at-site flood data length is adequate. One of the problems in FFA with an annual maxima (AM) modeling approach is deciding how to handle smaller discharge values (outliers) in the selected AM flood series at a given station. The objective of this paper is to explore how the practice of censoring (which involves adjusting for smaller discharge values in FFA) affects flood quantile estimates in FFA. In this regard, two commonly used probability distributions, log-Pearson type 3 (LP3) and generalized extreme value distribution (GEV), are used. The multiple Grubbs and Beck (MGB) test is used to identify low-flow outliers in the selected AM flood series at 582 Australian stream gauging stations. It is found that censoring is required for 71% of the selected stations in using the MGB test with the LP3 distribution. The differences in flood quantile estimates between LP3 (with MGB test and censoring) and GEV distribution (without censoring) increase as the return period reduces. A modest correlation is found (for South Australian catchments) between censoring and the selected catchment characteristics (correlation coefficient: 0.43), with statistically significant associations for the mean annual rainfall and catchment shape factor. The findings of this study will be useful to practicing hydrologists in Australia and other countries to estimate design floods using AM flood data by FFA. Moreover, it may assist in updating Australian Rainfall and Runoff (national guide).

Floods are a recurring and devastating hazard in West Africa, with significant socio-economic and environmental impacts. A better understanding of their frequency and magnitude is crucial for effective flood risk mitigation, infrastructure design, and water resource management. The lack of reliable hydrometric datasets has hitherto been a major limitation in flood frequency analysis at the scale of West Africa. We combine insights from historical flood frequency analysis and future climate-driven flood projections to provide a more complete description of flood hazards in West Africa. Using a newly developed African hydrological database, annual maximum flow (AMF) time series from 246 river basins (1975–2018) were analyzed with the Generalized Extreme Value (GEV) and Gumbel distributions. The GEV distribution, paired with the Generalized Maximum Likelihood Estimation (GMLE) method, yielded the best results for quantile estimation, enabling the generation of regional envelope curves for the first time in West Africa. Future flood trends have been assessed from the OS LISFLOOD and the HMF-WA large-scale distributed hydrological models, driven by five bias-corrected CMIP6 climate projections under the SSP2-4.5 and SSP5-8.5 scenarios. Both hydrological models consistently projected increases in flood frequency and magnitude across West Africa, despite their differences in hydrological processes representation and calibration schemes. Flood magnitudes are projected to increase in 94% of stations, with some areas experiencing increases exceeding 45%. Significant trends are already observable in many basins as early as the 1980s, emphasizing the robust climate change signal in this region. This combined approach, integrating historical flood frequency analysis with future climate-driven projections, offers critical regional-scale insights into the evolving flood hazards in West Africa.

More frequent flooding? Changes in flood frequency in Switzerland since 1850

The Kaligandaki River Basin in Nepal is highly vulnerable to flooding due to significant variability in precipitation. This study estimates the Probable Maximum Flood (PMF) from Probable Maximum Precipitation (PMP) utilizing the HEC-HMS hydrological model. The basin was segmented into eight sub-basins, and PMP was determined using the Hershfield method, with values ranging from 368 mm to 816 mm. The HEC-HMS model was calibrated and validated using daily data from 1989 to 2017, demonstrating satisfactory performance across most sub-basins. The simulated PMF values were 4,590 m³/s, 3,640 m³/s, and 45,548 m³/s for the Mayagdhi, Modi, and Kaligandaki basins, respectively. When compared to floods with a 10,000-year return period, the PMF was approximately two to three times greater in magnitude. These findings offer a framework for PMP/PMF estimation in Nepalese rivers, thereby aiding in the design of flood-resilient infrastructure.The Kaligandaki River Basin in Nepal faces significant flood risks due to its highly variable precipitation patterns. This study employs a comprehensive approach to estimate the Probable Maximum Flood (PMF) using the Probable Maximum Precipitation (PMP) and the HEC-HMS hydrological model. By dividing the basin into eight sub-basins and applying the Hershfield method, researchers determined PMP values ranging from 368 mm to 816 mm. The model's calibration and validation process, utilizing daily data spanning nearly three decades (1989-2017), demonstrated satisfactory performance across most sub-basins, lending credibility to the results. The study's findings reveal substantial PMF values for the Mayagdhi, Modi, and Kaligandaki basins, at 4,590 m³/s, 3,640 m³/s, and 45,548 m³/s, respectively. These estimates are particularly noteworthy when compared to floods with a 10,000-year return period, as the PMF values are approximately two to three times greater in magnitude. This significant difference underscores the importance of considering extreme flood scenarios in infrastructure planning and design. By providing a robust framework for PMP/PMF estimation in Nepalese rivers, this research contributes valuable insights for developing flood-resilient infrastructure, potentially mitigating the impact of extreme flooding events on local communities and ecosystems in the Kaligandaki River Basin and similar regions. Keywords: Kaligandaki River Basin, Probable Maximum Flood (PMF), Probable Maximum Precipitation (PMP), HEC-HMS hydrological model, Hershfield method, Flood risk assessment, Hydrological modeling, Extreme precipitation events, Flood frequency analysis, Nepal hydrology, River basin management, Flood-resilient infrastructure, Climate variability, Watershed modeling, Flood mitigation strategies

Flood is a widespread climate-related hazard with the potential to occur in almost any geographical location where fluvial processes are active and can occur due to the involvement of multiple factors. Flood frequency analysis (FFA) is considered a valuable hydrologic tool to know the magnitude and frequency of the recurrence of floods. In this research, we have examined the Lower Burhi Dehing River (LBDR) in Assam, India, which frequently experiences severe flooding due to its meandering course induced by heavy monsoon rainfall. Therefore, the present research aims to analyze past flood events and current trends and predict future flood frequencies using Gumbel’s extreme value distribution and Log Pearson Type III Method. In this particular investigation, 25 years of annual maximum peak discharge data from 1972 to 1997 was employed to examine the discharge records of LBDR. This research estimated the return periods of different flood magnitudes, quantifying the likelihood of future floods with varying degrees of severity. In this regard, the return periods are estimated at 2, 5, 10, 20, 50, 100, and 200 years. The study reveals that the largest flood event occurred in 1972, with a discharge of 1134.4 m3/s, and the smallest flood event occurred in 1997, with a discharge of 214.65 m3/s. The 2-year flood is a relatively common event with a 50% probability of occurring in any given year, characterized by a moderate discharge of 1384.90 m3/s and minor impacts of 0.3665. The 5-year flood, occurring with a 20% chance annually, brings a significantly higher water level of 2008.81 m3/s and moderate-to-severe impacts of 1.4999, potentially causing widespread flooding. In the 10-year and 50-year return period, which has a probability of returning 10% and 2% chance annually, the discharge will reach 2421.89 m3/s and 3331.01 m3/s, respectively. The outcome of this research will sustainably guide policymakers and environmental planners to mitigate flood hazards.

Modeling the joint behavior of flood characteristics under climate change is necessary for understanding the potential changes in associated flood risk and hazards. In this study, we assessed the changes in flood duration, peak, and volume between historical and future periods through copula-based flood frequency analysis, employing the Soil and Water Assessment Tool (SWAT) hydrological model for modeling flood risk in a tropical watershed (Govindpur) lying in eastern India. Observed streamflow at the watershed outlet is obtained for the baseline period (1990-2014) for flood analysis. A suitable copula model is selected for bivariate flood frequency analysis while assuming copula parameters vary between baseline and future periods under climate change. In this study, high-resolution (12-km) climate reanalysis dataset from the Indian Monsoon Data Assimilation and Analysis (IMDAA) and future climate projections from general circulation models (BCC-CSM2-MR, MPI-ESM1-2-HR) after downscaling and bias correction, are used for simulating flood events using SWAT. The use of high-resolution climate data for hydrological modeling and flood frequency analysis is a novel aspect of the presented study. Uncertainty in the estimation of joint return periods of flood events under climate change due to climate model selection and assumption of stationarity is also quantified in this study for the near future (2041-2070) period under the shared socio-economic pathway (SSP585) scenario. Among the GCMs used, BCC-CSM2-MR performed relatively better in simulating baseline period streamflow in the study watershed. In this study, the Clayton copula is obtained as the most suitable based on its lowest Akaike information criterion (AIC) value, and joint return periods are then derived with the help of a conditional copula. It is found that flood events are projected to become more severe in the near future; the flood peak value increased by more than 90%, while the duration is projected to decrease. Flood volume may likely double in the future, as per our analysis, suggesting the need for mitigation and precautionary measures to reduce flood risk in the watershed. Based on the analysis, uncertainty in flood return period estimation under changed future climate is to be accounted for extreme event studies, and that can aid in managing and minimizing the flood-associated risks. Keywords: Climate Change, Flood Frequency Analysis, Soil and Water Assessment Tool, Copula, General Circulation Model, Uncertainty Analysis

Floods are natural disasters that cause extreme economic damage and therefore have a significant impact on society. Understanding the spatial and temporal characteristics exhibited by floods is one of the crucial parts of effective flood management. The Danube River with its basin is an important region in Europe and floods have occurred in the Danube River basin throughout history. Flood frequency analysis (FFA) and seasonality analysis were performed in this study using the annual maximum discharge series data from 86 gauging stations in order to form a comprehensive characterisation of floods in the Danube River basin. The results of the study demonstrate that some noticeable clusters of stations can be identified based on the best-fitting distribution regarding FFA. Furthermore, the best-fitting distributions regarding FFA for the stations in the Danube River basin are generalized extreme values (GEV) and log Pearson type 3 (LP3) distributions as among 86 considered gauging stations, 76 stations have one of these two distributions among their two best fits. Moreover, seasonality analysis demonstrates that large floods in the Danube River basin mainly occur in the spring, and flood seasonality in the basin is highly clustered.

Comment on “A paradigm shift in understanding and quantifying the effects of forest harvesting on floods in snow environments” by Kim C. Green and Younes Alila

The availability of the new generation Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) V06 products facilitates the utility of long-term higher spatial and temporal resolution precipitation data (0.1° × 0.1° and half-hourly) for monitoring and modeling extreme hydrological events in data-sparse watersheds. This study aims to evaluate the utility of IMERG Final run (IMERG-F), Late run (IMERG-L) and Early run (IMERG-E) products, in flood simulations and frequency analyses over the Mishui basin in Southern China during 2000–2017, in comparison with their predecessors, the Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis (TMPA) products (3B42RT and 3B42V7). First, the accuracy of the five satellite precipitation products (SPPs) for daily precipitation and extreme precipitation events estimation was systematically compared by using high-density gauge station observations. Once completed, the modeling capability of the SPPs in daily streamflow simulations and flood event simulations, using a grid-based Xinanjiang model, was assessed. Finally, the flood frequency analysis utility of the SPPs was evaluated. The assessment of the daily precipitation accuracy shows that IMERG-F has the optimum statistical performance, with the highest CC (0.71) and the lowest RMSE (8.7 mm), respectively. In evaluating extreme precipitation events, among the IMERG series, IMERG-E exhibits the most noticeable variation while IMERG-L and IMERG-F display a relatively low variation. The 3B42RT exhibits a severe inaccuracy and the improvement of 3B42V7 over 3B42RT is comparatively limited. Concerning the daily streamflow simulations, IMERG-F demonstrates a superior performance while 3B42V7 tends to seriously underestimate the streamflow. With regards to the simulations of flood events, IMERG-F has performed optimally, with an average DC of 0.83. Among the near-real-time SPPs, IMERG-L outperforms IMERG-E and 3B42RT over most floods, attaining a mean DC of 0.81. Furthermore, IMERG-L performs the best in the flood frequency analyses, where bias is within 15% for return periods ranging from 2–100 years. This study is expected to contribute practical guidance to the new generation of SPPs for extreme precipitation monitoring and flood simulations as well as promoting the hydro-meteorological applications.

Flood quantile estimation using available streamflow records, known as at-site flood frequency analysis (FFA), are widely used in hydrology. The estimated flood quantiles by at-site FFA are used in the planning and design of many water resources management tasks. However, FFA estimates often suffer from high sampling variability, in particular when length of streamflow record is relatively short. This aspect of FFA has not been fully examined for Australian catchments. As the hydrology in Australia suffers from a very high degree of variability, it is likely that the sampling variability in FFA is also very high. This paper presents results from a case study based on three different gauged stations located in New South Wales, Queensland and Victoria using the FLIKE (an extreme value analysis package) software. These stations represent different hydrological regimes (e.g. Victoria is dominated by winter rainfall and Queensland is by summer rainfall). Two widely used probability distribution functions, Generalized Extreme Value (GEV) and Log Pearson type 3 (LP3) distributions are adopted in this case study. We have used updated flood data which have been prepared for Australian Rainfall and Runoff Project 5. The selected streamflow data length ranges from 58 to 102 years. The annual maximum flood data at each of these stations have been sub-divided into three sub-sets: full data set, 50% split and 25% split, which enables to carry out this test with sample sizes in the range of 14 years to 51 years. The study shows that for all the three stations, at-site flood quantile estimates are more affected by the sampling variability in the case of the LP3 (Bayesian) distribution than the GEV (L moments) distribution. Based on the results of this empirical study, it has been found that for 50, 40, 30, 20 and 15 years of annual maximum flood data lengths, the sampling variability estimates are in between -41% to 326% (for LP3 distribution) and -42% to 39% (for GEV distribution) relative to the full data length. The findings of this study have crucial implications in the field of FFA as at-site FFA estimates are generally taken 'accurate' in decision making. Furthermore, in assessing the performances of the regional flood frequency estimation models and calibration of runoff routing model, at-site flood frequency analysis estimates based on about 25 years of data are considered 'robust' and 'accurate', which seems to be not the case. This exercise is being conducted to a greater number of stations by applying boot-strap and Monte Carlo simulation techniques, which will enable to generalize the findings of this study.

The modeling of peak flood discharges and flood frequency analysis at various sites on a river is essential for planning, design, and management of hydraulic structures. The first and the foremost aim of this study is to choose the best-fit flood model among Log Pearson type 3 (LP3), Generalized Extreme Value (GEV), and Gumble (EV1) for each of the eight sites on the Jhelum River and for the same purpose goodness-of-fit tests like Anderson–Darling (A–D) and Kolmogorov–Smirnow (K–S) and distribution graphs (P–P plot and Probability difference graph) were used. The parameters of these models were determined by L-moments. The outcomes of the study reveal that the LP3 model is best-fit for Khanabal, Sangam, Awantipora, Padshahi Bagh, Ram Munshi Bagh, and Asham, and GEV is the best fit for Sopore, and Baramullah sites. Furthermore, peak discharges for 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year return periods were estimated and the analysis depicts that the discharge rate determined by distribution models at a return period of 5 years or more would surpass the safe carrying capacity (990.85 cumecs) of the Jhelum river. The study further shows that there exists a high positive correlation (R2 = 0.99) between observed and predicted peak discharges of LP3 and GEV models. Thus, indicating LP3 and GEV as best-fit models for modeling and flood frequency analysis of annual peak discharges on the Jhelum River.

Flood frequency estimates are widely used in water resources engineering for the design of drainage structures such as culverts and bridges. These estimates are also essential for effective floodplain management. The discharge values used in flood frequency analysis are frequently obtained using stage-discharge rating curves. Consequently, errors inherent in stage measurements and stage-discharge rating curves adversely affect both river discharge and flood frequency estimates. These errors are especially significant for high-magnitude river discharge estimates produced by catastrophic flood events that are accompanied by unsteady flow conditions, heavy sediment loads, and debris. This study uses a Monte-Carlosimulation-based approach to evaluate the impact of these errors on design flood estimates. A log-Pearson type 3 distribution is used to obtain the necessary flood frequency estimates. The results are analyzed for several return periods that are commonly used in water resources engineering. The study’s findings show that for flood frequency analysis results to be useful for floodplain management and engineering design analysis, it is important that they explicitly account for discharge measurement errors.

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 statistics, which comprise a direct estimate of the CDF, afford a more powerful measure of frequency-based changes. The variability around a postharvest regression fit of ANCOVA is an artifact of the inappropriate type of event pairing [e.g., Alila et al., 2009, Figure 3a]. Such variability must affect the statistical power of the CP-based methods and impedes the ability to detect a change caused by forest harvesting [e.g., Alila et al., 2009, Figure 3e and paragraph 59]. Our point is that artificiality in the variability is introduced when one forces the treatment and control CP peak discharges to have the same frequency of occurrence; they do not. Furthermore, there may be a case-specific threshold return period beyond which a forest cover does not affect floods, but that threshold flood can only be identified with a frequency-paired approach. In some rain regimes, for instance, the effects of antecedent soil moisture on large floods may decrease with increasing return period [Wood et al., 1990]. In such regimes, however, an open question is where "large" begins or how rare must floods be for antecedent soil moisture to have no effects on floods? [Sturdevant-Rees et al., 2001, p. 2161]. In other regimes, snow accumulation and melt processes can be more important than evapotranspiration, and their effect on flood response can increase with increasing return period [Schnorbus and Alila, 2004, Figure 9; Harr, 1981, p. 297]. [21] Lewis et al. [2010, paragraph 23] state that "Hypothesis tests for CP and FP have entirely different null hypotheses, so direct comparisons of statistical power may not be possible." "CP and FP have entirely different null hypotheses" was the argument we use to build our case against the CP-based paradigm, and we found it remarkable that Lewis et al. [2010] are now using the same argument against our attempt to compare the statistical power of CP and FP methods. [22] Lewis et al. [2010, paragraph 24] state that "FP cannot be easily used to evaluate recovery." Our point is that recovery will occur when the preharvest and postharvest frequency distributions are identical. Therefore, FP should be used to assess recovery in this context; that it cannot be done as easily is irrelevant. [23] Lewis et al. [2010, paragraph 26] argue that CP-based regression analysis "(Figure 3a) does reveal that the frequency of large peaks increased after logging." We categorically disagree because CP-based analysis of covariance was not designed for such purpose. Lewis et al. [2010, paragraph 26] suggested that "[a]dditional calculations could be used to quantify those changes [in frequency]. Frequencies and the conversion of medium peaks to large peaks may indeed deserve more attention, but there is no reason to abandon methods utilizing CP." What Lewis et al. [2010] are suggesting is an indirect and convoluted way of achieving what can be done directly and with elegance under our FP-based paradigm. Hewlett made the same suggestion three decades ago when, facing the challenge of an apparent harvest-induced increase in the "variability" of peak flows collected in Japan, he stated that "…a large increase in the variance of peaks and volumes…..would be worth reanalyzing by more advanced regression techniques…" [Hewlett, 1982, p. 533]. Hewlett and Helvey [1970, p. 779] were aware that the question of forests and floods cannot be settled without invoking the dimension of frequency. Note that Hewlett's last paper on this topic was his 1982 paper quoted above. [24] We recognized that Lewis and coworkers were among the few who invoked the frequency dimension under the CP-based framework [e.g., Lewis et al. 2001, Figure 29]. However, we see no linkages, in terms of physics or statistical theory, between the outcomes of CP and FP analyses. This type of linkage between the outcomes of CP-based methods and the frequency of floods, which does not necessarily preserve the all-important nonlinear and inverse relation between the magnitude and frequency, is not only ambiguous but projects a state of confusion. We need to recognize that since CP-based methods yield the wrong change in magnitude, there is no guarantee that they yield the correct change in frequency, and even if they do, it would be for the wrong reason. [25] Alila et al. [2009] maintained all along that inferences about forest harvesting effects using the analyses of variance and covariance are invalid for flood events smaller and larger than an average peak flow. Lewis et al. [2010] claimed that we have not given any statistical justification for such argument. Our argument against the old paradigm of CP and the analyses of variance and covariance is about "statistical physics" and not pure "statistics" [Koutsoyiannis, 2010, p. 598]. Decades of peer reviewed research on the topic of forest harvesting and floods that used the old paradigm of CP and associated analyses of variance and covariance didn't account for the physical reality of changing flood frequencies and as a consequence stripped the physics from the research question at hand. [26] Lewis et al. [2010] in another "straw man" type of argument implied that we are drawing support for our case against the flawed CP-based methods from a single claim by Harris [1977]. On the contrary, our article drew support for the case against the CP-based methods from decades of literature in several disciplines (hydrology, ecology, climatology, and statistics). Our extensive after-the-fact forest hydrology literature review revealed that a few hinted at the flaws that we exposed in CP-based methods when used to evaluate the relation between forests and floods: Hewlett and Helvey [1970], Harris [1977]; and most importantly Harr [1986, p. 1096], who explicitly referred to the convergence of two regression fits as "irrelevant" to whether or not forest harvesting affects floods. To the best of our knowledge, Harris and Harr have also written little, if anything, on this topic since then. Although we have been "tied up in irrelevancies" [Platt, 1964, p. 347] for decades, it is never too late to act on past cues from the luminaries of Forest Hydrology [Hewlett and Helvey, 1970, p. 779; Berris and Harr, 1987, p. 141]. In light of these past which continue to be the of literature review 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 among we must to in order to and information about causes and flood Forest could be to any of a because our confusion about the processes and their in forests and for and its In in of our FP-based paradigm, Lewis et al. 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