Non-stationary Flood Frequency Analysis Research Articles

A systematic review of climate change science relevant to Australian design flood estimation

Abstract. In response to flood risk, design flood estimation is a cornerstone of planning, infrastructure design, setting of insurance premiums, and emergency response planning. Under stationary assumptions, flood guidance and the methods used in design flood estimation are firmly established in practice and mature in their theoretical foundations, but under climate change, guidance is still in its infancy. Human-caused climate change is influencing factors that contribute to flood risk such as rainfall extremes and soil moisture, and there is a need for updated flood guidance. However, a barrier to updating flood guidance is the translation of the science into practical application. For example, most science pertaining to historical changes to flood risk focuses on examining trends in annual maximum flood events or the application of non-stationary flood frequency analysis. Although this science is valuable, in practice, design flood estimation focuses on exceedance probabilities much rarer than annual maximum events, such as the 1 % annual exceedance probability event or even rarer, using rainfall-based procedures, at locations where there are few to no observations of streamflow. Here, we perform a systematic review to summarize the state-of-the-art understanding of the impact of climate change on design flood estimation in the Australian context, while also drawing on international literature. In addition, a meta-analysis, whereby results from multiple studies are combined, is conducted for extreme rainfall to provide quantitative estimates of possible future changes. This information is described in the context of contemporary design flood estimation practice to facilitate the inclusion of climate science into design flood estimation practice.

A practice-oriented framework for stationary and nonstationary flood frequency analysis

In flood frequency analysis (FFA), choices of distribution and methods can hinder the reproducibility of results. Besides, changes in climate, land use/cover, and water management can induce nonstationarity. Frameworks to select between stationary FFA (S-FFA) and nonstationary FFA (NS-FFA) are lacking, and NS-FFA tools are limited. Therefore, this paper introduces a systematic and software-supported framework enabling repeatable workflows for both S-FFA and NS-FFA. The framework has three modules to a) process flood series for exploratory data analysis (EDA) and NS-FFA model determination (if needed), b) select the S-FFA or NS-FFA approach underpinned by the EDA, and c) perform FFA including model determination, parameter estimation, uncertainty quantification, and model performance assessment. The framework incorporates various distributions, methods, and metrics, and recent advancements in NS-FFA for model determination and uncertainty quantification and allows for the modeller's intervention while ensuring reproducibility. The software is freely available to the public.

Non-Stationary Modeling of Annual Flood Peak Heights of Mahanadi River Basin with the q-Generalized Extreme Value Distribution

In recent years, due to climate change, catastrophic events are increased largely in India. Hence researchers are forced to consider non-stationary flood frequency analysis as an improved method. In this paper, non-stationarity of annual daily maximum flood heights were studied at 12 sites of Mahanadi River Basin (MRB) by analyzing the flood frequency of a stationary model and 4 non-stationary models using time dependent q-GEV model by considering trend as a linear function of its location and scale parameters. The q-GEV distribution is utilized in this study because of its flexibility and accuracy than GEV distribution in modeling extreme flood heights. The results found that there is strong evidence of a linear trend existence for both the location and scale parameters at the Kesinga site; for the location parameter at Pathardi and Simga sites; for the scale parameter at Dharmajagarh, Kotni and Seorinarayan, and no linear trend exists for both location and scale parameters at Alipingal, Bomnidhi, Manendragarh, Mohana, Rajim and Sundargarh, there may be exists other form of trend at these sites. The findings also indicate that nonstationarity is present in the MRB due to climate change, which help to water practitioner for taking precautions against adverse effect of extreme floods.

Mitigating infectious disease risks through non-stationary flood frequency analysis: a case study in Malaysia based on natural disaster reduction strategy.

The occurrence of floods has the potential to escalate the transmission of infectious diseases. To enhance our comprehension of the health impacts of flooding and facilitate effective planning for mitigation strategies, it is necessary to explore the flood risk management. The variability present in hydrological records is an important and neglecting non-stationary patterns in flood data can lead to significant biases in estimating flood quantiles. Consequently, adopting a non-stationary flood frequency analysis appears to be a suitable approach to challenge the assumption of independent and identically distributed observations in the sample. This research employed the generalized extreme value (GEV) distribution to examine annual maximum flood series. To estimate non-stationary models in the flood data, several statistical tests, including the TL-moment method was utilized on the data from ten stream-flow stations in Johor, Malaysia, which revealed that two stations, namely Kahang and Lenggor, exhibited non-stationary behaviour in their annual maximum streamflow. Two non-stationary models efficiently described the data series from these two specific stations, the control of which could reduce outbreak of infectious diseases when used for controlling the development measures of the hydraulic structures. Thus, the application of these models may help prevent biased prediction of flood occurrences leading to lower number of cases infected by disease.

Study of Nonstationary Flood Frequency Analysis in Songhua River Basin

This study aimed to determine the influence of time and precipitation as covariates on the flood frequency distribution in the Songhua River tributaries under the nonstationarity assumption and to investigate the possibility of nonstationary models’ application in river management scope demarcation work. Nonstationary flood frequency analysis (NS-FFA) was conducted in three typical basins of the Songhua River (in Northeastern China) based on the generalized additive models for location, scale, and shape (GAMLSS), and stationary flood frequency analysis was used as a comparison. Under the stationarity assumption, the Pearson type Ⅲ (P-Ⅲ) distribution is the main theoretical distribution for the flood extremum at hydrological stations, followed by a lognormal (LN) distribution. Under the nonstationarity assumption, when time is considered a covariate, the optimal theoretical distribution of the flood extremum is mainly LN (with 63.75%), followed by the Weibull distribution (with 18.75%). When precipitation is considered as a covariate, the optimal theoretical distribution of the flood extremum is mainly LN (with 57.5%). We attempted to apply several FFA methods to calculate the design frequency in this study, referring to the work requirements for river management scope demarcation in three typical basins, and came to the following conclusions. From the simulation results of the p = 10% flood at the export stations of typical basins, it can be seen that time-covariate NS-FFA obtained the best simulation results. Two cases of the simulation under the stationarity assumption are positive, which will lead to a high design scale. The time-covariate GAMLSS in NS-FFA has the advantages of higher calculation accuracy and simpler processes. To better balance construction costs and disaster protection requirements, NS-FFA can be used to determine the design scale of water conservation projects; additionally, it can be used to demarcate the scope of river management. The accuracy of GAMLSS for FFA is also influenced by the complexity of the terrain, with basins with relatively simple terrain having higher calculation accuracy.

Using climate information as covariates to improve nonstationary flood frequency analysis in Brazil

ABSTRACT Climatic drivers of floods have been widely used to improve nonstationary flood frequency analysis (FFA). However, the forecast ability of nonstationary FFA with out-of-sample prediction has not been comprehensively evaluated. We use 379 flood records from Brazil to assess the ability of process-informed nonstationary models for out-of-sample FFA using the generalized extreme value (GEV) distribution. Five drivers of floods are used as covariates: annual temperature, El Nino Southern Oscillation, annual rainfall, annual maximum rainfall, and annual maximum soil moisture content. Our results reveal that a nonstationary model is preferable when there is a significant correlation between flood and climate covariates in both the training period and full record. The rainfall-based covariates lead to better out-of-sample nonstationary FFA models. These findings highlight that using climate information as covariates in nonstationary FFA is a promising approach for estimating future floods and, hence, better infrastructure design, risk assessment and disaster preparedness.

Adjusting design floods for urbanization across groundwater-dominated watersheds of Long Island, NY

The magnitude and variability of floods have increased for many nontidal streams on Long Island (LI), NY since the mid-20th century. One of the most densely populated regions of the United States, LI has experienced amplified floods in step with increases in impervious land cover, storm, and sanitary sewers that have accompanied urban development. To better understand the drivers of observed flood trends and effects of urbanization, a nonstationary flood frequency analysis is conducted, using historical annual peak flow records from 17 gaged watersheds on LI using conditional moments based on physical covariates from a two-stage sequential robust linear regression procedure. Regression results indicate that urban development and precipitation are significant co-predictors of peak flows for LI watersheds that have undergone rapid development during the available peak flow record. In watersheds with less intense urbanization or that were fully developed before the peak flow record began, precipitation alone was a significant explanatory variable. Long-term baseflow patterns identified using a nonparametric smoother explained some patterns of decreasing peak flows and heteroskedasticity in the peak flow records. Fitting a log-Pearson III distribution with these conditional moments, floods corresponding to a 20% annual exceedance probability (AEP) are up to 80% higher under a nonstationary framework compared with stationary under current watershed conditions, and differ significantly (95% confidence) from stationary estimates for 6 out of 17 watersheds. Larger floods corresponding to 1% AEPs do not differ significantly between nonstationary and stationary estimates at a 95% confidence level. Nonmonotonic trends observed in two watersheds indicate that recent stormwater management practices, such as rerouting stormwater outfalls away from the channel, substantially reduce flood frequency. Reduced nonstationary flood quantile estimates at these two watersheds are 20 to 40% lower than stationary estimates when accounting for changing watershed conditions over time. Across LI, stormwater management and water-table fluctuations have increased peak flow variability, characteristic of a late phase urban adjustment period on LI. Results of this study demonstrate that a nonstationary framework is a necessary step forward toward a regional flood-frequency analysis for LI. This nonstationary framework will allow flood managers to update flood discharge estimates to current conditions that reflect altered relationships between urban cover and climate for more targeted planning of flood control, transportation infrastructure, and management of floodplain ecosystems.

On method of regional non-stationary flood frequency analysis under the influence of large reservoir group and climate change

Global climate change and reservoir regulations can alter the natural flow of rivers. Influenced by these two drivers, flood sequences may no longer satisfy the assumption of stationary, thereby making it difficult to accurately analysis flood frequency and to design water conservancy projects. Therefore, it is of great significance to analyse the non-stationary frequency of flood sequences in a changing environment. In this study, we proposed a method for conducting nonstationary flood frequency analysis caused by cascade reservoirs as well as the low-frequency climate indices. The proposed non-stationary model 2, with the explanatory variables of climate indices and modified reservoir index (MRI), was compared with the traditional stationary model and the widely used non-stationary model 1 with time as the explanatory variable. The study was conducted at six hydrological stations in the main stream and tributaries of the upper reaches of the Yangtze River in China (considered as the Three Gorges Reservoir Area). The results of the generalized additive model for location, scale and shape (GAMLSS) showed that the Akaike information criterion and Bayesian information criterion values of the proposed non-stationary model method 2 are smaller than those of the two comparison models. When the low-frequency South Oscillation Index is high or the Arctic Oscillation and North Pacific Oscillation are low, the stationary model underestimates the design value of flood quantiles compared with the non-stationary model 2. Compared with the non-stationary model 1, the MRI and low-frequency climate indices as the explanatory variables in model 2 can better describe the non-stationary characteristics of flood frequency and amplitude. In addition, the non-stationary model considering external physical factors can provide better prediction of future design flood compared with two traditional models.

Nonstationary Annual Maximum Flood Frequency Analysis Using a Conceptual Hydrologic Model with Time-Varying Parameters

Recent evidence of the impact of watershed underlying conditions on hydrological processes have made the assumption of stationarity widely questioned. In this study, the temporal variations of frequency distributions of the annual maximum flood were investigated by continuous hydrological simulation considering nonstationarity for Weihe River Basin (WRB) in northwestern China. To this end, two nonstationary versions of the GR4J model were introduced, where the production storage capacity parameter was regarded as a function of time and watershed conditions (e.g., reservoir storage and soil-water conservation land area), respectively. Then the models were used to generate long-term runoff series to derive flood frequency distributions, with synthetic rainfall series generated by a stochastic rainfall model as input. The results show a better performance of the nonstationary GR4J model in runoff simulation than the stationary version, especially for the annual maximum flow series, with the corresponding NSE metric increasing from 0.721 to 0.808. The application of the nonstationary flood frequency analysis indicates the presence of significant nonstationarity in the flood quantiles and magnitudes, where the flood quantiles for an annual exceedance probability of 0.01 range from 4187 m3/s to 8335 m3/s for the past decades. This study can serve as a reference for flood risk management in WRB and possibly for other basins undergoing drastic changes caused by intense human activities.

Linear, nonlinear, parametric and nonparametric regression models for nonstationary flood frequency analysis

In recent years, nonstationary flood frequency analysis (NFFA) has become an active area of research. It is crucial for water resources management and hydrologic engineering design to cope with the changing environment. Finding suitable and effective models could help perform better flood frequency analysis and make reliable estimates under the nonstationary environment. This study assesses different modelling techniques for nonstationary flood frequency analysis, including linear, nonlinear, parametric and nonparametric models using an extensive data set of 161 catchments across the UK. It identifies that rejection rates are generally higher for precipitation-informed NFFA models than time-varying NFFA models. For both time-varying and precipitation-informed NFFA, rejection rates for linear and cubic polynomial models are the highest. The models with the fewest rejections are fractional polynomial models followed by cubic spline models. Because of the flexibility, parsimony, and user-friendly features, fractional polynomial models could be a potential alternative for modelling the nonstationary behaviour of flood series. To investigate whether the seasonal flood variation and catchment characteristics influence the goodness-of-fit, a quantified seasonality index was calculated to illustrate the degree of seasonal variation of flooding for each catchment. It was found that the southeast of the UK has more significant seasonal flood variation than the northwest, and most of the catchments with high seasonality indexes are close to the Scotland and England border. Nevertheless, the correlation analysis shows insufficient evidence to conclude that catchment characteristics and seasonal flood variation impact the goodness-of-fit of the NFFA models.

The decomposition-based nonstationary flood frequency analysis

• The performance-based NS-FFA is challenged theoretically and practically. • A new decomposition procedure for the decomposition-based NS-FFA is proposed. • The proposed decomposition procedure preserves the stationary component. • The proposed decomposition-based NS-FFA captures the nonstationary process better. • This approach overcomes the previous issues of the NS-FFA and performs competitively. The nonstationary flood frequency analysis (NS-FFA) is conducted when the assumption of stationarity in hydrologic extremes is violated. The commonly used approach is the performance-based NS-FFA, which jointly determines the distribution and the nonstationary structure based upon the model performance. However, this approach is challenged from both theoretical and practical perspectives. An alternative is the herein named decomposition-based NS-FFA, which determines the two NS-FFA model components separately and explicitly uses the available knowledge of the nonstationarity. However, it has been barely implemented in practice. This paper proposed a novel decomposition procedure that strictly follows the theoretical decomposition of nonstationary stochastic processes to advance the decomposition-based NS-FFA. The proposed decomposition procedure was compared with a previously reported method in both an analytical deduction and a simulation study. The proposed decomposition-based NS-FFA was further compared to the performance-based NS-FFA using both synthetic and real datasets from North America, which exhibit different patterns of nonstationarity. The Particle Filter was adopted for uncertainty quantification and parameter estimation. The results revealed that the proposed decomposition-based approach was advantageous in preserving the moments of underlying stochastic component, particularly the higher-order moment (i.e., skewness). In addition, the comparison of the two NS-FFA approaches demonstrated the superiority of the proposed decomposition-based approach in capturing the underlying (known) nonstationary stochastic process and being competitive with the performance-based approach from the performance perspective in real applications. The results from the simulation study and the real application also revealed several caveats of the performance-based approach, including the potential overfitting and equifinality problems as well as the selection of distinct models when adopting different performance metrics. In addition, differing from the performance-based approach, the decomposition-based NS-FFA avoided/alleviated the ergodicity violation. All these results demonstrated the advancements of the proposed decomposition-based NS-FFA and advocated its application in the NS-FFA.

Nonstationary flood and low flow frequency analysis in the upper reaches of Huaihe River Basin, China, using climatic variables and reservoir index as covariates

Conventional water infrastructure designs for flood and low flows are usually based on the assumption of stationarity of extreme events. However, recent evidence suggests that the influences of climate variability and human activities have made the hypothesis of stationarity questionable. In this study, we used the generalized additive models for location, scale, and shape (GAMLSS) to construct a nonstationary model in which the parameters of the selected distributions were modelled as a function of climatic variables (i.e., climate indices and precipitation) and/or the reservoir index (RI). The nonstationary models were then used to analyse annual flood and low flow frequency at four hydrological stations in the upper reaches of the Huaihe River Basin, including Dapoling (DPL), Changtaiguan (CTG), Zhuganpu (ZGP), and Xixian (XX) stations. Annual floods were represented by the maximum daily streamflow in each year, and low flows were represented by the 95th quantile of the daily streamflow (Q95) in each year. The change point and trend analysis revealed that the flood series of the ZGP station and the low flow series of the DPL and XX stations exhibited significant downward and upward trends (p < 0.1)), respectively. The low flow series of the ZGP station showed a significant change point in 1980 (p < 0.1). GAMLSS modelling results showed that, in comparison with stationary models, nonstationary models that included precipitation and the Arctic Oscillation climate index as covariates for the gamma distribution location parameter provided a superior description of the flood series at the four stations. Nonstationary models that incorporated precipitation and/or RI as covariates for the Weibull distribution parameters fit the low flow series better than stationary models at all stations. Furthermore, we found that nonstationary models outperformed stationary models in terms of flood frequency analysis, covering all flood observation points and capturing the generally decreasing trend in flood series, as well as a decrease in the scatter of estimated flood value magnitudes. For the low flow frequency analysis, the comparison results showed that the nonstationary and stationary models performed identically for the DPL, CTG, and XX stations, where no significant change point was detected. However, for the ZGP station, where a significant change point was detected, the nonstationary models performed better than the stationary models and could accurately capture the changes in the magnitude of the estimated low flow values before and after the change point. Overall, the proposed nonstationary model can serve as a tool for nonstationary frequency analysis of flood and low flow series under the influence of climate variability and reservoir regulations, thus providing a reference for regional water infrastructure design.

Incorporating nonstationarity in regional flood frequency analysis procedures to account for climate change impact

There now exists clear evidence of the impact of climate change on flooding, creating need for new methodologies for design flood estimation that account for warming induced nonstationarity. Current alternatives for nonstationary flood frequency analysis require the specification of a nonstationary probability model (often with time-varying parameters) that requires sufficient data to be stable. Reliance on the trend in observed data often ignores the dissimilar behaviour of frequent and rare quantiles under a warming climate. This, in turn, results in the direction of change to be consistent across both rare and frequent projected flood quantiles. However, results of multiple recent studies suggest that rarer floods are likely to increase while more frequent floods may decrease in magnitude into the future. In this study, we highlight this limitation of existing nonstationary flood frequency approaches and propose a novel nonstationary regional flood frequency analysis approach that captures the differing behaviour of more frequent and rare flood quantiles under a warming climate. The need for longer flood data to model nonstationarity is accommodated by pooling regional information which makes the projections more precise. Data for 105 Australian catchments are used to validate our proposed approach. Results show the effectiveness of the proposed method in capturing the variation of flood quantiles with varying average recurrence intervals in a changing climate. Finally, a few important statistics of future projections are also presented.

An Overview of Flood Concepts, Challenges, and Future Directions

This review provides a broad overview of the current state of flood research, current challenges, and future directions. Beginning with a discussion of flood-generating mechanisms, the review synthesizes the literature on flood forecasting, multivariate and nonstationary flood frequency analysis, urban flooding, and the remote sensing of floods. Challenges and future flood research directions are outlined and highlight emerging topics where more work is needed to help mitigate flood risks. It is anticipated that the future urban systems will likely have more significant flood risk due to the compounding effects of continued climate change and land-use intensification. The timely prediction of urban floods, quantification of the socioeconomic impacts of flooding, and developing mitigation strategies will continue to be challenging. There is a need to bridge the scales between model capabilities and end-user needs by integrating multiscale models, stakeholder input, and social and citizen science input for flood monitoring, mapping, and dissemination. Although much progress has been made in using remote sensing for flood applications, recent and upcoming Earth Observations provide excellent potential to unlock additional benefits for flood applications. The flood community can benefit from more downscaled, as well as ensemble scenarios that consider climate and land-use changes. Efforts are also needed for data assimilation approaches, especially to ingest local, citizen, and social media data. Also needed are enhanced capabilities to model compound hazards and assess as well as help reduce social vulnerability and impacts. The dynamic and complex interactions between climate, societal change, watershed processes, and human factors often confronted with deep uncertainty highlights the need for transdisciplinary research between science, policymakers, and stakeholders to reduce flood risk and social vulnerability.

Correlation between climate and flood indices in Northwestern Italy at different temporal scales

Abstract The occurrence of river floods is strongly related to specific climatic conditions that favor extreme precipitation events leading to catchment saturation. Although the impact of precipitation and temperature patterns on river flows is a well discussed topic in hydrology, few studies have focused on the relationship between peak discharges and standard Climate Change Indices (ETCCDI) of precipitation and temperature, widely used in climate research. It is of interest to evaluate whether these indices are relevant for characterizing and predicting floods in the Alpine area. In this study, a correlation analysis of the ETCCDI indices annual time series and annual maximum flows is presented for the Piedmont Region, in North-Western Italy. Spearman’s rank correlation is used to determine which ETCCDI indices are temporally correlated with maximum discharges, allowing to hypothesize which climate drivers better explain the interannual variability of floods. Moreover, the influence of climate (decadal) variability on the tendency of annual maximum discharges is examined by spatially correlating temporal trends of climate indices with temporal trends of the discharge series in the last twenty years, calculated using the Theil-Sen slope estimator. Results highlight that, while extreme precipitation indices are highly correlated with extreme discharges at the annual timescale, with different indices that are consistent with catchment size, the decadal tendencies of extreme discharges may be better explained by the decadal tendencies of the total annual precipitation over the study area. This suggests that future projections of the annual precipitation available from climate models simulations, whose reliability is higher compared to precipitation extremes, may be used as covariates for non-stationary flood frequency analysis.

Bivariate Nonstationary Extreme Flood Risk Estimation Using Mixture Distribution and Copula Function for the Longmen Reservoir, North China

Recently, the homogenous flood generating mechanism assumption has become questionable due to changes in the underlying surface. In addition, flood is a multifaced natural phenomenon and should be characterized by both peak discharge and flood volume, especially for flood protection structures. Hence, in this study, data relating to the 55-year reservoir inflow, annual maximum flood peak (AMFP), and annual maximum flood volume (AMFV) for the Longmen Reservoir in North China have been utilized. The 1-day AMFV exhibits a significant correlation with AMFP. The extreme flood peak-volume pairs are then used to detect the heterogeneity and to perform nonstationary flood risk assessment using mixture distribution as the univariate marginal distribution. Moreover, a copula-based bivariate nonstationary flood frequency analysis is developed to investigate environmental effects on the dependence of flood peak and volume. The results indicate that the univariate nonstationary return period is between the joint OR and the AND return periods. The conditional probabilities of 1-day AMFV, when AMFP exceeds a certain threshold, are likely to be high, and the design flood values estimated by joint distribution are larger than the ones in the univariate nonstationary context. This study can provide useful information for engineers and decision-makers to improve reservoir flood control operations.

Non-stationary analysis for road drainage design under land-use and climate change scenarios

Frequency analysis has been the most widely used tool worldwide to dimension water-related infrastructures and evaluate flood risks. The concept of stationarity has been a common and practical hypothesis in hydrology for many years. However, in recent decades due to climate change pressure and changes in land use, it has been related to the presence of time-series trends that in hydrology indicate non-stationary effects. In this sense, the need to comprehensively address non-stationary frequency analysis has been identified. This study proposes to incorporate the non-stationary flood frequency analysis into the dimensioning process of road structures with the following objectives: i) evaluate the effect of land use on peak flow in a simulated period of 129 years, ii) evaluate covariates related to land use, and iii) evaluate covariates related to climate change. To this end, road drainage simulation exercises were carried out in three sections of the Ibagué-Cajamarca road located in Colombia. Likewise, the Generalized Additive Models for Location, Scale and Shape was implemented for the non-stationary analysis, and covariates related to climate variability were included, such as El Niño-Southern Oscillation indices (ONI12, ONI3.4, MEI, and SOI), and the Pacific Decadal Oscillation (PDO) index, as well as some related to the evolution of land use such as hydraulic conductivity, soil water storage in the root zone, and infiltration capacity represented in the curve number. The results indicate that the non-stationary analysis improves the prediction of maximum flows, and it is possible to obtain road drainage dimensioning that adjusts to climate and land-use variations.

Comparison of Three-Parameter Distributions in Controlled Catchments for a Stationary and Non-Stationary Data Series

Flood Frequency Analysis (FFA) and the non-stationary FFA approaches are used in flood study, water resource planning, and the design of hydraulic structures. However, there is still a need to develop these methods and to find new procedures that can be used in estimating simple distributions in controlled catchments. The aim of the study is a comparison of three-parameter distributions in controlled catchments for stationary and non-stationary data series and further to develop the procedure of the estimation the simple distributions. Ten rivers from the Czech Republic and Poland were selected because of their existing or planned reservoirs as well as for flood protection reasons. The annual maximum method and the three-parameter Weibull, Log-Normal, Generalized extreme value, and Pearson Type III distributions were used in this study. The analyzed time series are stationary and non-stationary. The methodology used in this study, which makes use of the Maximum Likelihood Estimation, allows one to simplify the analysis whenever there is a series of data that is both stationary and non-stationary. The novelty in our research is the standardization and development of a new procedure for a stationary and non-stationary data series, taking into account to read a specific value of the maximum flow with a given exceedance probability from the lower or upper tail. It determines the optimal choice of the theoretical distribution that can be used, for example in the design of weirs in rural areas (lower quantiles) or in the design of hydrotechnical structures in areas at risk of flooding (upper quantiles).

Non-stationary flood frequency analysis in Australia

Non-stationary flood frequency analysis in Australia

Simulation experiments comparing nonstationary design-flood adjustments based on observed annual peak flows in the conterminous United States

While nonstationary flood frequency analysis (NSFFA) methods have proliferated, few studies have rigorously compared them for modeling changes in both the central tendency and variability of annual peak-flow series, also known as the annual maximum series (AMS), in hydrologically diverse areas. Through Monte Carlo experiments, we appraise five methods for updating estimates of 10- and 100-year floods at gauged sites using synthetic records based on sample moments and change trajectories of observed AMS in the conterminous United States (CONUS). We compare two methods that consider changes in both central tendency and variability - a Gamma generalized linear model estimated with weighted least squares and the Generalized Additive Model for Location, Scale, Shape (GAMLSS) - with a distribution-free approach (quantile regression), and baseline cases assuming stationarity or only changes in central tendency.‘Trend-space’ plots identify realistic AMS changes for which modeling trends in both central tendency and variability were warranted based on fractional root mean squared errors (fRMSE). They also reveal statistical properties of AMS under which NSFFA models perform especially well or poorly. For instance, quantile regression performed especially well (poorly) under strong negative (positive) skewness. Although the nonstationary LP3 distribution accommodates most AMS with trends well, the sensitivity of NSFFA model performance to different sample moments and trends suggests the need for more flexibility in prescribing design-flood adjustments in the CONUS. A follow-up comparison of regional NSFFA models pooling at-site AMS would further illuminate NSFFA guidance, especially for AMS with properties less conducive to NSFFA modeling, such as positive skewness and increasing variability.