Flood Frequency Analysis Methods Research Articles

Modelling non-stationary flood frequency in England and Wales using physical covariates

Abstract Non-stationary methods of flood frequency analysis are widespread in research but rarely implemented by practitioners. One reason may be that research papers on non-stationary statistical models tend to focus on model fitting rather than extracting the sort of results needed by designers and decision makers. It can be difficult to extract useful results from non-stationary models that include stochastic covariates for which the value in any future year is unknown. We explore the motivation for including such covariates, whether on their own or in addition to a covariate based on time. We set out a method for expressing the results of non-stationary models as an integrated flow estimate, which removes the dependence on the covariates. This can be defined either for a particular year or over a longer period of time. The methods are illustrated by application to a set of 375 river gauges across England and Wales. We find annual rainfall to be a useful covariate at many gauges, sometimes in conjunction with a time-based covariate. For estimating flood frequency in future conditions, we advocate exploring hybrid approaches that combine the best attributes of non-stationary statistical models and simulation models that can represent changes in climate and river catchments.

Alternate pathway for regional flood frequency analysis in data-sparse region

Accurately analyzing flood frequency is crucial for developing effective flood management strategies and designing flood protection infrastructure, but the complex and nonlinear nature of the hydrological system poses significant challenges. The use of advanced statistical techniques, hydrological modeling, and computational tools has facilitated the implementation of several regional flood frequency analysis (RFFA) methods, including machine learning (ML) approaches. However, such regional methods, being statistical and data-intensive with limited hydrologic inferences, can be challenging for regions with limited data. In this study, we evaluated an alternate approach or path for RFFA in two contrasting regions: a data-sparse region in India and a data-dense region in the USA. The alternate approach involves using deep learning (DL)-based model for streamflow prediction, followed by at-site flood frequency analysis to estimate flood quantiles. The proposed alternate approach was compared with the classical RFFA method, which utilized the Random Forest (RF) and eXtreme Gradient Boosting (XGBoost) algorithms to establish the intricate relationship between different flood quantiles and predictor variables related to physio-meteorological conditions. The findings showed that the alternate approach outperformed the classical RFFA method in the data-sparse region of India, reducing the mean absolute error (MAE) and root mean squared error (RMSE) by approximately 50 %, and achieving a higher coefficient of determination (R2 = 0.85 to 0.96). In the data-dense region, the classical and alternate approaches produced comparable results. However, the alternate approach has the benefit of flexibility and offers a complete time series of daily flow at the ungauged watersheds, enabling the estimation of other flow attributes or magnitudes for any return period without needing a separate classical RFFA model. The study demonstrates that the alternate approach can produce reliable flood quantile estimates in regions with limited data, offering a promising solution for managing floods in these areas.

Prediction of Flood Events from the Nekor River Discharge Using the Flood Frequential Analysis Method

This work aims to analyze the yearly most extreme release of the Nekor River monitoring station Tamellaht between 1973 and 2011 and to predict possible future events using the Flood Frequency Analysis Method (FFA). We use the four most estimated distributions that are accessible for prediction of hydrological risk: the three Log Normal, LogPerson Type III, Weibull and GAMMA distributions, and conclude that the Weibull distribution is the suitable statistical model that describe well into our data series, even though the other distributions show data adjustment. Given the Weibull dispersion, the upsides of 580.3 m3/s, 1339 m3/s and 2146.7 m3/s are for the time of return of 10, 50 and 100 years, individually, still high relying upon the semi-dry environment that wins around this region. In fact, the period of extreme returns of the 10th period which can cause dangerous flooding especially considering the mountainous characteristics of the region. The magnitude of the floods is greater because the return period is greater, which explains the semi-arid climate of this region. In addition, a simple statistical description shows that the maximum flow trend has declined over the years, reflecting a possible impact of climate change phenomena.

Artificial Intelligence-Based Regional Flood Frequency Analysis Methods: A Scoping Review

Flood is one of the most destructive natural disasters, causing significant economic damage and loss of lives. Numerous methods have been introduced to estimate design floods, which include linear and non-linear techniques. Since flood generation is a non-linear process, the use of linear techniques has inherent weaknesses. To overcome these, artificial intelligence (AI)-based non-linear regional flood frequency analysis (RFFA) techniques have been introduced over the last two decades. There are limited articles available in the literature discussing the relative merits/demerits of these AI-based RFFA techniques. To fill this knowledge gap, a scoping review on the AI-based RFFA techniques is presented. Based on the Scopus database, more than 1000 articles were initially selected, which were then screened manually to select the most relevant articles. The accuracy and efficiency of the selected RFFA techniques based on a set of evaluation statistics were compared. Furthermore, the relationships among countries and researchers focusing on AI-based RFFA techniques are illustrated. In terms of performance, artificial neural networks (ANN) are found to be the best performing techniques among all the selected AI-based RFFA techniques. It is also found that Australia, Canada, and Iran have published the highest number of articles in this research field, followed by Turkey, the United Arab Emirates (UAE), India, and China. Future research should be directed towards identification of the impacts of data quantity and quality, model uncertainty and climate change on the AI-based RFFA techniques.

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.

Assessment of Peak Flow Scaling and Its Effect on Flood Quantile Estimation in the United Kingdom

AbstractRegional flood frequency analysis (RFFA) methods are essential tools to assess flood hazard and plan interventions for its mitigation. They are used to estimate flood quantiles when the at‐site record of streamflow data is not available or limited. One commonly used RFFA method is the index flood method (IFM), which assumes that peak floods satisfy the simple scaling hypothesis.In this work we present an integrated approach to assess the spatial scaling behavior of floods in the United Kingdom (UK) for 540 catchments, where the IFM is currently used operationally. This assessment employs product moments, probability weighted moments, and quantile analysis, and is applied to two different types of “hydrologically homogeneous” UK regions: geographical regions as defined in the Flood Studies Report (NERC, 1975) and pooling‐groups as defined in the updated Flood Estimation Handbook (FEH; Institute of Hydrology, 1999). To understand which variables play a significant role in the flood‐peak generating mechanism, the assessment approach considers scaling not only of drainage area alone but also of other hydro‐geomorphological variables. Results provided by the different methodologies consistently showed that only part (ranging from 30% to 70%) of the peak flow variability is explained by drainage area alone; this fraction increases (up to 80%–95%) when multiple regression is used. Supported by the peak flow spatial scaling assessment, we compared the proposed approach for peak flow quantile estimation with the current FEH method in ungauged catchments. The quantile regression method based on the pooling‐group outperforms the current FEH‐ungauged method, providing a 14% relative improvement in root mean square error over the entire country.

Analysis of Magnitude and Frequency of Floods in the Damanganga Basin: Western India

Flood Frequency Analysis (FFA) method was introduced by Fuller in 1914 to understand the magnitude and frequency of floods. The present study is carried out using the two most widely accepted probability distributions for FFA in the world namely, Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). The Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) methods were used to select the most suitable probability distribution at sites in the Damanganga Basin. Moreover, discharges were estimated for various return periods using GEVI and LP-III. The recurrence interval of the largest peak flood on record (Qmax) is 107 years (at Nanipalsan) and 146 years (at Ozarkhed) as per LP-III. Flood Frequency Curves (FFC) specifies that LP-III is the best-fitted probability distribution for FFA of the Damanganga Basin. Therefore, estimated discharges and return periods by LP-III probability distribution are more reliable and can be used for designing hydraulic structures.

Risk Factors for 100-Year Flood Events in the Mid-Atlantic Region of the United States.

Anecdotal information indicates that streams in the Mid-Atlantic region of the United States experience more extreme flood events than might be expected. This leads to the question of whether this is an unfounded perception or if these extreme events are actually occurring more than should be expected. If the latter is true, is this due solely to randomness, or alternately to characteristics that make certain watersheds more prone to repeated events that may be defined as 100-year or greater floods? These questions are investigated through analysis of flood events based on standard flood frequency analysis. 100-year streamflow rates for stream gages were estimated using Bulletin 17B flood frequency analysis methods, and the probability of the annual peak flow record for each gage was calculated. These probabilities were compared to a set of synthetic probabilities to evaluate their distribution. This comparison indicates that for the Mid-Atlantic region as a whole, the Bulletin 17B method does not systematically over or underestimate flood frequency. A Random Forest model of probability of actual flood record (PAFR) versus watershed and stream gage characteristics was developed and used to understand if certain characteristics are associated with PAFR. This analysis indicated that unexpected numbers of large flood events in a stream gage period of record can be attributed primarily to randomness, but there is some correlation with watershed and gage characteristics including weighted skew, drainage area, and mean annual peak discharge. The results indicate that watersheds with high values of these characteristics may warrant advanced flood frequency methods.

Non-Stationary Flood Frequency Analysis Using Cubic B-Spline-Based GAMLSS Model

Under changing environments, the most widely used non-stationary flood frequency analysis (NFFA) method is the generalized additive models for location, scale and shape (GAMLSS) model. However, the model structure of the GAMLSS model is relatively complex due to the large number of statistical parameters, and the relationship between statistical parameters and covariates is assumed to be unchanged in future, which may be unreasonable. In recent years, nonparametric methods have received increasing attention in the field of NFFA. Among them, the linear quantile regression (QR-L) model and the non-linear quantile regression model of cubic B-spline (QR-CB) have been introduced into NFFA studies because they do not need to determine statistical parameters and consider the relationship between statistical parameters and covariates. However, these two quantile regression models have difficulties in estimating non-stationary design flood, since the trend of the established model must be extrapolated infinitely to estimate design flood. Besides, the number of available observations becomes scarcer when estimating design values corresponding to higher return periods, leading to unreasonable and inaccurate design values. In this study, we attempt to propose a cubic B-spline-based GAMLSS model (GAMLSS-CB) for NFFA. In the GAMLSS-CB model, the relationship between statistical parameters and covariates is fitted by the cubic B-spline under the GAMLSS model framework. We also compare the performance of different non-stationary models, namely the QR-L, QR-CB, and GAMLSS-CB models. Finally, based on the optimal non-stationary model, the non-stationary design flood values are estimated using the average design life level method (ADLL). The annual maximum flood series of four stations in the Weihe River basin and the Pearl River basin are taken as examples. The results show that the GAMLSS-CB model displays the best model performance compared with the QR-L and QR-CB models. Moreover, it is feasible to estimate design flood values based on the GAMLSS-CB model using the ADLL method, while the estimation of design flood based on the quantile regression model requires further studies.

Flood Frequency Analysis for Burhi Gandak River Basin

The study is aimed at finding the best distribution to match the steam flow and calculation of magnitude and frequency of flow. In the current study, we have used several statistical distributions to find the best fit distribution for stream flow and used flood frequency analysis techniques to find the magnitude and frequency of stream flow and non-exceedance probability of peak discharge. The study has been performed at Sikandarpur and Rosera gauging sites of BurhiGandak River. Historical (50 years) maximum annual peak discharge data of each station are used for statistical analysis for estimating maximum peak discharge in 5, 10, 25, 50, 100 year return period. In this study, Lognormal distribution, Galton distribution, Gamma distribution, Log Pearson Type III distribution, Gumbell distribution, Generalised extreme values distribution have been considered to describe the annual maximum stream flow. Flood frequency analysis methods were used for estimating the magnitude of the extreme flow events and their associated return periods. For both Sikandarpur and Rosera stations, Log Pearson type III distributions showed the lowest value of K–S and Chi-square test statistic. The annual probable peak discharge for 5, 10, 25, 50, and 100 years return period is calculated for each distribution. The most suitable distribution for both the stations is found to be the log-Pearson type III distribution.

Flood frequency analysis

The recurring flooding causes loss of life and damage to buildings and other structures, including bridges, sewerage systems, roadways and canals. It also frequently damages power transmission and sometimes power generation, which then has knock-on effects caused by the loss of power. The present study compares the relative performance of flood frequency methods to estimate design flood, using available data of 18 small catchments in the Mahanadi River basin (India). The primary objective of the referred approach was for design flood estimation at gauge sites; however, the main focus is referred to ungauged catchments by an interpolation method. In this regard, three interpolation methods are used: (1) inverse distance weighing method, (2) ordinary kriging and (3) area weighted method. As per the recent trends, flood frequency analysis methods are used specifically for two data types, i.e., at-site analysis and for regionalizing the available data within the homogeneous region. In this study, an attempt has been made to categorize the interpolation properties, where the first two approaches belong to site analysis and the third one uses the regional analysis. In the first approach, the output results in terms of flood quantiles are interpolated for the intermediate results, which is generally termed as direct interpolation of flood quantile, and the second approach uses the linear interpolating or L-moments in flood estimation. The above one refers to the interpolation of L-moments, while flood index is interpolated in the third approach, which is named as ‘flood index procedure.’ In the study, it was observed that the designed flood quantile results were better by using the flood index approach at lower return periods at 2 and 5 years, and the direct interpolation method gave a better estimation for higher return periods. Further, it was found that the difference in prediction error of direct interpolation of flood quantiles and the flood index procedure is negligible.

Can we still predict the future from the past? Implementing non‐stationary flood frequency analysis in the UK

AbstractThe Environment Agency in England is investing £2.5 billion with the aim of reducing flood risk to at least 300,000 homes by 2020/21. Several of the schemes being considered are on rivers that have experienced an upsurge of flooding over recent years. Decisions on whether to invest and how high to build are usually made on the basis of stationary methods of flood frequency analysis that assume the probability of flood flows is unchanging over time. Following successive severe floods in Cumbria, trend tests and non‐stationary flood frequency analysis techniques have been applied. These allow parameters of the frequency distribution to change over time or with some other covariate. The resulting estimates of flow, for the present day, were up to 55% higher than the stationary estimates at river gauges in north‐west England. The results have been incorporated into the scheme appraisal process. A national analysis indicates that there is evidence of upward trends in peak flows at nearly a quarter of river flow gauges across Great Britain. Many rivers show an abrupt increase in flood flows in the late 1990s. Trends tend to occur in upland areas but they are also seen on some rivers across south‐east England.

An Empirical Formula for Design Flood Estimation of Un-Gauged Catchments in Brahmani Basin, Odisha

Several statistical methods, viz. flood frequency analysis and hydro-meteorological methods (i.e., unit hydrograph approach) are available for estimation of design flood in un-gauged catchments. Till today, the empirical formulae are relevant as the latest methods require adequate field observation and collection of sufficient data. The available formulae such as Dicken’s formula, Ryves formula and Inglis formula are applicable, respectively, to Northern India, Western India and Southern India. But no such empirical formula is available for eastern India, especially for Odisha region, for which designers depend on the established formulae for other regions. This necessitated developing an empirical formula for computation of design flood for this zone. An empirical formula is developed for computation of design flood of un-gauged catchments in Brahmani Basin of Odisha and presented in this paper. Relation between the peak discharges of the unit hydrograph and the design discharges of individual sub-basins is established. Eight sub-basins are considered for this study. The derived formula is validated through upper and lower envelope curves for probable maximum flood for Mahanadi and adjoining river basins, recommended by Central Water Commission. This would provide guideline in planning any future water resources projects in Brahmani basin. The study would form a part of final work of derivation of a general equation applicable to the State/Eastern zone of India.

Using Physically Based Synthetic Peak Flows to Assess Local and Regional Flood Frequency Analysis Methods

AbstractAlthough prior studies have evaluated the role of sampling errors associated with local and regional methods to estimate peak flow quantiles, the investigation of epistemic errors is more difficult because the underlying properties of the random variable have been prescribed using ad‐hoc characterizations of the regional distributions of peak flows. This study addresses this challenge using representations of regional peak flow distributions derived from a combined framework of stochastic storm transposition, radar rainfall observations, and distributed hydrologic modeling. The authors evaluated four commonly used peak flow quantile estimation methods using synthetic peak flows at 5,000 sites in the Turkey River watershed in Iowa, USA. They first used at‐site flood frequency analysis using the Pearson Type III distribution with L‐moments. The authors then pooled regional information using (1) the index flood method, (2) the quantile regression technique, and (3) the parameter regression. This approach allowed quantification of error components stemming from epistemic assumptions, parameter estimation method, sample size, and, in the regional approaches, the number of pooled sites. The results demonstrate that the inability to capture the spatial variability of the skewness of the peak flows dominates epistemic error for regional methods. We concluded that, in the study basin, this variability could be partially explained by river network structure and the predominant orientation of the watershed. The general approach used in this study is promising in that it brings new tools and sources of data to the study of the old hydrologic problem of flood frequency analysis.

ASSESSMENT OF FAILURE ON DRAINAGE STRUCTURES ALONG THE ETHIOPIAN NATIONAL RAILWAY LINE OF SEBETA-MIESO (CASE STUDY OF AKAKI RIVER CROSSING DRAINAGE STRUCTURE)

A railway drainage system gives vital role for effective, efficient operation of rail track. This study worked on an assessment of railway drainage system problem along the Addis Ababa- Mieso railway line, specifically on Akaki rives crossing. It was done to check adequacy of hydraulic structure provided on Akaki River crossing by undertaking hydrologic and hydraulic analysis.
 Hydrologic modeling of the Akaki catchment area was developed by HEC-GeoHMS program with the help of Arc-GIS and hydrologic analysis was computed by HEC-HMS program. The catchment land use, soil type, rainfall data, Akaki river stream flow data, etc were used to develop hydrological model. SCS unit hydrograph and flood frequency analysis methods were used to estimate instantaneous peak design discharge for 50 and 100 year return period. Model input parameters were calibrated and verified with observed flow data of the river at Akaki gauging station.
 Hydraulic models were developed by HEC-RAS step-backwater to determine water-surface profiles for the bridge. Cross-sectional elevation data, hydraulic-structure geometries, roughness coefficients along with peak-discharge esti¬mated were used as input for the model.
 Finally, adequacy of the bridge was evaluated where the bridge was hydraulically efficient over its design period.

Assessing the performance of regional flood frequency analysis methods in South Africa

In engineering and flood hydrology, the estimation of a design flood associates the magnitude of a flood with a level of exceedance, or return period, for a given site. The use of a regional flood frequency analysis (RFFA) approach improves the accuracy and reliability of estimates of design floods. However, no RFFA method is currently widely used in South Africa, despite a number of RFFA studies having been undertaken in Africa and which include South Africa in their study areas. Hence, the performance of the current RFFA approaches needs to be assessed in order to determine the best approaches to use and to determine if a new RFFA approach needs to be developed for use in South Africa. Through a review of the relevant literature it was found that the Meigh et al. (1997) method, the Mkhandi et al. (2000) method, the Görgens (2007) Joint Peak-Volume (JPV) method and the Haile (2011) method are available for application in a nationwide study. The results of the study show that the Haile method generally performs better than the other RFFA methods; however, it also consistently underestimates design floods. Due to the poor overall performance of the RFFA methods assessed, it is recommended that a new RFFA method be developed for application in design flood practice in South Africa.

Frequency Analysis and Uncertainty Assessment of Annual Maximum Flood Series Using Bayesian MCMC Method

The calculation of flood quantiles and its uncertainty estimation are important subjects of hydraulic engineering planning and water resources management. In this study, the Bayesian theory is used to implement frequency analysis and uncertainty assessment of annual maximum flood series, the Generalized Extreme Value (GEV) distribution is considered as the flood frequency distribution line type, and the Markov chain Monte Carlo (MCMC) method based on Metropolis-Hastings algorithm is used to evaluate the GEV distribution parameters, then the posterior distributions of flood flow quantiles are used to calculate the point estimations and interval estimations of flood design values under different return periods. The results show that the fitting effect of the Bayesian MCMC method is the same as the maximum likelihood estimation (MLE), but the Bayesian MCMC more superior when the uncertainties were considered. Compared with the traditional methods of flood frequency analysis, the proposed Bayesian MCMC method provides not only the design flood estimated values, but also the confidence intervals of the estimated values. In addition, the lengths between upper confidence limits and estimated values are greater than the lower confidence limits and estimated values, this asymmetry is more realistic than the traditional methods such as the delta method, thus improve the reliability of flood frequency analysis.

Flood frequency analysis: The Bayesian choice

After an introduction to the traditional flood frequency analysis methods, this article discusses their limits and the risks associated with their thoughtless use: overconfidence in the estimated values of flood quantiles or return periods and systematic underestimation of risks. The article then presents and illustrates the added value of modern Bayesian flood frequency inference procedures that are statistically consistent, numerically accurate, and now computationally affordable. The implementation of such methods shows that estimated flood frequencies, based on observed samples of limited size, are generally affected by large uncertainties. This acknowledgement should be an incentive for increasing the size of the analyzed samples through a more systematic use of historic information as well as regional approaches in flood frequency analyses. It also clearly points out that the margin of errors should be considered when using inference results for design or risk assessment purposes. Several pieces of software are now available to conduct Bayesian flood frequency analyses relatively straightforwardly. There is no remaining obstacle to the implementation of these modern approaches in operational hydrological studies.This article is categorized under: Science of Water > Methods Science of Water > Water Extremes

Uncertainty analysis of designed flood on Bayesian MCMC algorithm: a case study of the Panjiakou Reservoir in China

Estimation of the magnitude of designed flood is a fundamental task crucial for the determination of scale of engineering construction and for the development of flood disaster risk management projects. Due to a high level of uncertainty in observed data, selection of frequency distribution model, and estimation of model parameters, the process of designed flood has uncertainties consequently. A Bayesian flood frequency analysis method is adopted for designed flood estimation with P-III probability distribution as its flood frequency model. In the Bayesian method, the adaptive metropolis Markov Chain Monte Carlo (AM-MCMC) sampling algorithm is employed to estimate posterior distributions of parameters, upon which estimation of expectations and credible intervals of designed floods is obtained. With analyzing the drawback of likelihood function expressed with the product of probability of occurrence of each sample individual, four likelihood functions expressed on residuals are presented, and then based on Bayesian AM-MCMC method, performance of presented likelihood functions is compared with that of the classical likelihood function, with taking peak flow uncertainty analysis of Panjiakou Reservoir as a case study. The results show that expectations of flood peak quantiles estimation with likelihood functions based on residuals between observed/censored and calculated values of flood peaks are almost the same, but there are obvious differences between likelihood function based on occurrence probability of flood sample and those based on residuals with respect to expectation of quantiles estimation and also show that expectation and credible interval of quantiles estimation with Bayesian AM-MCMC method based on the whole likelihood function are more reasonable than those acquired with maximum likelihood function. Finally, some relevant flood frequency analyses issues based on Bayesian AM-MCMC algorithm which need to be further studied are also presented.

Comparison of Flood Frequency Analysis Methods for Ungauged Catchments in France

The objective of flood frequency analysis (FFA) is to associate flood intensity with a probability of exceedance. Many methods are currently employed for this, ranging from statistical distribution fitting to simulation approaches. In many cases the site of interest is actually ungauged, and a regionalisation scheme has to be associated with the FFA method, leading to a multiplication of the number of possible methods available. This paper presents the results of a wide-range comparison of FFA methods from statistical and simulation families associated with different regionalisation schemes based on regression, or spatial or physical proximity. The methods are applied to a set of 1535 French catchments, and a k-fold cross-validation procedure is used to consider the ungauged configuration. The results suggest that FFA from the statistical family largely relies on the regionalisation step, whereas the simulation-based method is more stable regarding regionalisation. This conclusion emphasises the difficulty of the regionalisation process. The results are also contrasted depending on the type of climate: the Mediterranean catchments tend to aggravate the differences between the methods.