Multireservoir system optimization in the Han River basin using multi‐objective genetic algorithms

In this study, NSGA‐II is applied to multireservoir system optimization. Here, a four‐dimensional multireservoir system in the Han River basin was formulated. Two objective functions and three cases having different constraint conditions are used to achieve nondominated solutions. NSGA‐II effectively determines these solutions without being subject to any user‐defined penalty function, as it is applied to a multireservoir system optimization having a number of constraints (here, 246), multi‐objectives, and infeasible initial solutions. Most research by multi‐objective genetic algorithms only reveals a trade‐off in the objective function space present, and thus the decision maker must reanalyse this trade‐off relationship in order to obtain information on the decision variable. Contrastingly, this study suggests a method for identifying the best solutions among the nondominated ones by analysing the relation between objective function values and decision variables. Our conclusions demonstrated that NSGA‐II performs well in multireservoir system optimization having multi‐objectives. Copyright © 2005 John Wiley & Sons, Ltd.     

Automatic calibration of HEC‐HMS using single‐objective and multi‐objective PSO algorithms

This study presents single‐objective and multi‐objective particle swarm optimization (PSO) algorithms for automatic calibration of Hydrologic Engineering Center‐ Hydrologic Modeling Systems rainfall‐runoff model of Tamar Sub‐basin of Gorganroud River Basin in north of Iran. Three flood events were used for calibration and one for verification. Four performance criteria (objective functions) were considered in multi‐objective calibration where different combinations of objective functions were examined. For comparison purposes, a fuzzy set‐based approach was used to determine the best compromise solutions from the Pareto fronts obtained by multi‐objective PSO. The candidate parameter sets determined from different single‐objective and multi‐objective calibration scenarios were tested against the fourth event in the verification stage, where the initial abstraction parameters were recalibrated. A step‐by‐step screening procedure was used in this stage while evaluating and comparing the candidate parameter sets, which resulted in a few promising sets that performed well with respect to at least three of four performance criteria. The promising sets were all from the multi‐objective calibration scenarios which revealed the outperformance of the multi‐objective calibration on the single‐objective one. However, the results indicated that an increase of the number of objective functions did not necessarily lead to a better performance as the results of bi‐objective function calibration with a proper combination of objective functions performed as satisfactorily as those of triple‐objective function calibration. This is important because handling multi‐objective optimization with an increased number of objective functions is challenging especially from a computational point of view. Copyright © 2012 John Wiley & Sons, Ltd.     

Semi‐active multi‐step predictive control of structures using MR dampers

A semi‐active multi‐step predictive control (SAMPC) system with magnetorheological (MR) dampers is developed to reduce the seismic responses of structures. This system can predict the next multi‐step responses of structure according to the current state and has a function of self‐compensation for time delay that occurred in real application. To study the performance of the proposed control algorithm for addressing time delay and reducing the seismic responses, a numerical example of an 11‐story structure with MR dampers is presented. Comparison with the uncontrolled structure indicates that both the peak and the norm values of structural responses are all clearly reduced when the predictive length l?10 and the delayed time step d?20 are selected, and the SAMPC strategy can guarantee the stability of the controlled structure and reduce the effects of time delay on controlled responses to a certain extent. A performance comparison is also made between the SAMPC strategy and the passive‐off and passive‐on methods; results indicate that this SAMPC system is more effective than the two passive methods in reducing structural responses subjected to earthquakes. Copyright © 2008 John Wiley & Sons, Ltd.     

A new version of the USLE‐MM for predicting bare plot soil loss at the Sparacia (South Italy) experimental site

Improving empirical prediction of plot soil erosion at the event temporal scale has both scientific and practical importance. In this investigation, 492 runoff and soil loss data from plots of different lengths, λ (11 ≤ λ ≤ 44 m), and steepness, s (14.9 ≤ s ≤ 26.0%), established at the Sparacia experimental station, in Sicily, South Italy, were used to derive a new version of Universal Soil Loss Equation (USLE)‐MM model, by only assuming a value of one for the topographic length, L, and steepness, S, factors for λ = 22 m and s = 9%, respectively. An erosivity index equal to (Q_REI₃₀)^b1, Q_R and EI₃₀ being the runoff coefficient and the event rainfall erosivity index, respectively, with b₁ > 1 was found to be an appropriate choice for the Sparacia area. The specifically developed functions for L and S did not differ appreciably from other, more widely accepted relationships (maximum differences by a factor of 1.22 for L and 1.09 for S). The new version of the USLE‐MM performed particularly well for highly erosive events, because predicted soil loss differed by not more than a factor of 1.19 from the measured soil loss for measured values of more than 100 Mg ha^?1. The choice of the relationships to predict topographic effects on plot soil loss should not represent a point of particular concern in the application of the USLE‐MM in other environments. However, tests of the empirical approach should be carried out in other experimental areas in an attempt to develop analytical tools, usable at the event temporal scale, reasonably simple and of wide validity. Copyright © 2015 John Wiley & Sons, Ltd.     

Short‐term discharge and suspended sediment fluctuations in the proglacial Skeldal River,north‐east Greenland

The summer discharge pattern of the Skeldal River, which drains a 560 km² partly glacierized catchment in north‐east Greenland, is dominated by diurnal oscillations reflecting variations in the melt rate of snow and ice in the basin. Superimposed on this diurnal pattern are numerous short‐lived discharge fluctuations of irregular periodicity and magnitude. The larger fluctuations are described and attributed to both rainfall events and periodic collapse of the glacier margin damming flow from beneath the Skelbrae glacier. Other minor fluctuations are less readily explained but are associated with changes in the channelized and distributed reservoirs and possibly temporary blockage of subglacial conduits caused by ice melt with subsequent damming. Fluctuations in suspended sediment concentration (SSC) are normally associated with discharge fluctuations, although examples of ‘transient flushes’ were observed where marked increases in SSC occurred in the absence of corresponding discharge variations. A strong relationship between the event discharge increase and event SSC increase for rainfall‐induced events was established, but no such relationship existed for non‐rainfall‐induced events. There is some evidence for an exhaustion effect in the SSC patterns both at the event time‐scale and as the month proceeds. A mean suspended sediment load of 1765 ± 0·26 t day^?1 was estimated for the study period, which would be equivalent to a suspended sediment yield of 732 ± 4 t km^?2 year^?1. Copyright © 2001 John Wiley & Sons, Ltd.     

Development of fragility functions as a damage classification/prediction method for steel moment‐resisting frames using a wavelet‐based damage sensitive feature

Fragility functions are commonly used in performance‐based earthquake engineering for predicting the damage state of a structure subjected to an earthquake. This process often involves estimating the structural damage as a function of structural response, such as the story drift ratio and the peak floor absolute acceleration. In this paper, a new framework is proposed to develop fragility functions to be used as a damage classification/prediction method for steel structures based on a wavelet‐based damage sensitive feature (DSF). DSFs are often used in structural health monitoring as an indicator of the damage state of the structure, and they are easily estimated from recorded structural responses. The proposed framework for damage classification of steel structures subjected to earthquakes is demonstrated and validated with a set of numerically simulated data for a four‐story steel moment‐resisting frame designed based on current seismic provisions. It is shown that the damage state of the frame is predicted with less variance using the fragility functions derived from the wavelet‐based DSF than it is with fragility functions derived from an alternate acceleration‐based measure, the spectral acceleration at the first mode period of the structure. Therefore, the fragility functions derived from the wavelet‐based DSF can be used as a probabilistic damage classification model in the field of structural health monitoring and an alternative damage prediction model in the field of performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Fourth‐ to third‐order cycles in the Hakobuchi Formation: Shallow‐marine Campanian final deposition of the Yezo Group,Nakagawa area,northern Hokkaido,Japan

The Yezo Group has a wide longitudinal distribution across Hokkaido, northern Japan. It represents a Cretaceous (Early Aptian–Late Maastrichtian) and Late Paleocene forearc basin‐fill along the eastern margin of the paleo‐Asian continent. In the Nakagawa area of northern Hokkaido, the uppermost part of the Yezo Group consists of the Hakobuchi Formation. Along the western margin of the Yezo basin, 24 sedimentary facies (F) represent 6 facies associations (FA), suggesting prevailing storm‐dominated inner shelf to shoreface environments, subordinately associated with shoreface sand ridges, outer shelf, estuary and fluvial environments. The stacking patterns, thickness and facies trends of these associations allow the discrimination of six depositional sequences (DS). Inoceramids Sphenoceramus schmidti and Inoceramus balticus, and the ammonite Metaplacenticeras subtilistriatum, provide late Early to Late Campanian age constraints to this approximately 370‐m thick final stage of deposition and uplift of the Yezo forearc basin. Six shallow‐marine to subordinately non‐marine sandstone‐dominated depositional sequences include four 10 to 110‐m thick upward‐coarsening regressive successions (FS1), occasionally associated with thin, less than 10‐m thick, upward‐fining transgressive successions (FS2). The lower DS1–3, middle DS4–5 and upper DS6 represent three depositional sequential sets (DSS1–3). These eastward prograding and westward retrograding recurring shallow‐marine depositional systems may reflect third‐ and fourth‐order relative sealevel changes, in terms of sequence stratigraphy.     

The design of visco‐acoustic weighted L1‐error frequency–space wavefield extrapolators

Seismic imaging is an important step for imaging the subsurface structures of the Earth. One of the attractive domains for seismic imaging is explicit frequency–space (f – x) prestack depth migration. So far, this domain focused on migrating seismic data in acoustic media, but very little work assumed visco‐acoustic media. In reality, seismic exploration data amplitudes suffer from attenuation. To tackle the problem of attenuation, new operators are required, which compensates for it. We propose the weighted L ₁ ‐error minimisation technique to design visco‐acoustic f – x wavefield extrapolators. The L ₁ ‐error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L ₄ ‐norm and L_∞‐norm extrapolation wavenumber responses. To verify the new compensating designs, prestack depth migration is performed on the challenging Marmousi model dataset. A reference migrated section is obtained using non‐compensating f – x extrapolators on an acoustic dataset. Then, both compensating and non‐compensating extrapolators are applied to a visco‐acoustic dataset, and both migrated sections are then compared. The final images show that the proposed weighted L ₁ ‐error method enhances the resolution and results in practically stable images.     

Passive and active control of three‐dimensional buildings

The majority of the recent research effort on structural control considers two‐dimensional plane structures. However, not all buildings can be modelled as plane structures, thus limiting the capability of the proposed procedures only to regular and symmetrical structures. A new procedure is developed in this paper to analyse three‐dimensional buildings utilizing passive and active control devices. In the building model, the floors are assumed rigid in their own plane resulting in three degrees of freedom at each floor. Two types of active control devices utilizing an active tuned mass damper and an active bracing system are considered. The effect of passive mass dampers and active control force in the equations of motion is incorporated by using the Hamilton's principle. The passive parameters of the dampers as well as the controller gain is then optimized using a genetic based optimizer where the H₂, H_∞ and L₁ norms are taken as the objective functions. Copyright © 2000 John Wiley & Sons, Ltd.     

Addressing uncertainty in reflectivity‐rainfall relations in mountain watersheds during summer convection

The use of precipitation estimates from weather radar reflectivity has become widespread in hydrologic predictions. However, uncertainty remains in the use of the nonlinear reflectivity–rainfall (Z‐R) relation, in particular for mountainous regions where ground validation stations are often lacking, land surface data sets are inaccurate and the spatial variability in many features is high. In this study, we assess the propagation of rainfall errors introduced by different Z‐R relations on distributed hydrologic model performance for four mountain basins in the Colorado Front Range. To do so, we compare spatially integrated and distributed rainfall and runoff metrics at seasonal and event time scales during the warm season when convective storms dominate. Results reveal that the basin simulations are quite sensitive to the uncertainties introduced by the Z‐R relation in terms of streamflow, runoff mechanisms and the water balance components. The propagation of rainfall errors into basin responses follows power law relationships that link streamflow uncertainty to the precipitation errors and streamflow magnitude. Overall, different Z‐R relations preserve the spatial distribution of rainfall relative to a reference case, but not the precipitation magnitude, thus leading to large changes in streamflow amounts and runoff spatial patterns at seasonal and event scales. Furthermore, streamflow errors from the Z‐R relation follow a typical pattern that varies with catchment scale where higher uncertainties exist for intermediate‐sized basins. The relatively high error values introduced by two operational Z‐R relations (WSR‐57 and NEXRAD) in terms of the streamflow response indicate that site‐specific Z‐R relations are desirable in the complex terrain region, particularly in light of other uncertainties in the modelling process, such as model parameter values and initial conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

A Multi‐Element Ion‐Pair Extraction for Trace Metals Determination in Environmental Samples

A multi‐element ion‐pair extraction method was described for the preconcentration of Cd(II), Co(II), Cr(III), Cu(II), Fe(III), Mn(II), Ni(II), Pb(II), and Zn(II) ions in environmental samples prior to their determinations by flame atomic absorption spectrometry (FAAS). As an ion‐pair ligand 2‐(4‐methoxybenzoyl)‐N′‐benzylidene‐3‐(4‐methoxyphenyl)‐3‐oxo‐N‐phenyl‐propono hydrazide (MBMP) was used. Some analytical parameters such as pH of sample solution, amount of MBMP, shaking time, sample volume, and type of counter ion were investigated to establish optimum experimental conditions. No interferences due to major components and some metal ions of the samples were observed. The detection limits of the proposed method were found in the range of 0.33–0.9 µg L^?1 for the analyte ions. Recoveries were found to be higher than 95% and the relative standard deviation (RSD) was less than 4%. The accuracy of the procedure was estimated by analyzing the two certified reference materials, LGC6019 river water and RTC‐CRM044 soil. The developed method was applied to several matrices such as water, hair, and food samples.     

Climate‐invariant area–slope relations in channel heads initiated by surface runoff

We use a dataset of 38 field‐mapped channel heads from a semi‐arid environment in western Colorado to examine relationships between contributing drainage area (A) and local hillslope gradient (θ) in relation to dominant process of initiation (surface runoff versus subsurface flow). Channel heads resulting primarily from subsurface flow have significantly greater values of A, longer basin lengths, and shallower local gradients than channel heads resulting primarily from surface runoff. We also compare the data from western Colorado to six analogous datasets from more humid regions in other portions of the United States and in southeast Australia. Comparison of the confidence intervals for the exponent values of A–θ regression lines reveals that the confidence intervals for the exponent of western Colorado channel heads with both surface and subsurface flow overlap with the confidence intervals for the exponent of all other datasets. This suggests that A–θ relationships do not differ significantly between diverse geographic locations. Copyright © 2017 John Wiley & Sons, Ltd.     

Effects of Short‐term and Long‐term Aluminium Stress on Photosynthesis,Respiration, and Reproductive Capacity in a Unicellular Green Flagellate (Euglena gracilis)

Effects of short‐term (1 h exposure) and long‐term (7 d exposure) aluminium stress on photosynthesis and reproductive capacity have been studied in Euglena gracilis strain Z. Following concentrations of Al_tot (added as AlCl₃) were tested: 0.5 mg L^‐1, 1.0 mg L^‐1, 1.5 mg L^‐1, 2.5 mg L^‐1, 5.0 mg L^‐1, 7.5 mg L^‐1, 10.0 mg L^‐1, and 15.0 mg L^‐1 Al, respectively. Growth rates at different aluminium concentrations did not show significant differences, except at 15.0 mg L^‐1Al. Initial respiration was higher in long‐term than in the short‐term experiments. It is supposed that an energy‐dependent mechanism of excretion of aluminium ions has been active in the stressed cells. Consequently, the cells of E. gracilis after long‐term exposure to aluminium are believed to be more acclimatised to the aluminium stress. Photosynthetic efficiency (PE) has been negatively affected by aluminium in all experiments performed. Differences between control algae and those treated with aluminium were significant in all cases. PE in long‐term experiments was in general significantly higher at all concentrations of aluminium studied, compared to the short‐term experiments. The aluminium concentrations tested led only to a general decrease in PE while the level of decrease was not especially concentration‐dependent. In general, aluminium tolerance of E. gracilis can be estimated as low, especially by short‐term exposure. However, good acclimatisation capacity of this green flagellate to aluminium doses by long‐term exposure can be supposed.     

Applying multi‐parameter runoff elasticity to assess water availability in a changing climate: an example from Texas,USA

Adaptation and mitigation efforts related to global trends in climate and water scarcity must often be implemented at the local, single‐catchment scale. A key requirement is understanding the impact of local climate and watershed characteristics coupled with these regional trends. For surface water, determination of multi‐parameter runoff elasticities is a promising tool for achieving such understanding, as explored here for two surface‐water dependent basins in Texas. The first basin is the water supply for Dallas‐Ft. Worth (DFW), and exhibits relatively high precipitation elasticity (proportional change in runoff to change in precipitation) ε_P = 2.64, and temperature elasticity ε_T = ? 0.41. Standard precipitation–temperature elasticity diagrams exhibit unusual concave contours of runoff change, indicating influence of additional parameters, which can be isolated using multi‐parameter approaches. The most influential local parameter in DFW is unexpected reduced runoff fraction in cooler wetter years. Those years exhibit increased summer (JJA) precipitation fraction, but predominant cracking soils in DFW minimize JJA runoff, yielding negative . A comparative basin near Houston shows positive , reflecting the local impact of tropical cyclones and lesser abundance of cracking soils. Both basins exhibit positive elasticity to 1‐year previous precipitation (e.g. DFW ε_{P ? 1} = 1.24), reflecting the influence of soil moisture storage. Only DFW exhibits negative elasticity to 2‐year previous precipitation (ε_{P ? 2} = ? 0.65), reflecting multi‐year influence of vegetation growth and increased evapotranspiration. Using these elasticities, analysis of historical multi‐decadal climate departures for DFW indicates the 80% decrease in runoff during the 1950–1957 drought of record was primarily caused by reduced precipitation. Runoff 56% above‐normal during an unprecedented 1986–1998 wet period was primarily caused by increased precipitation. Since 2000, despite precipitation slightly above normal, runoff has decreased 20%, primarily in response to ～ 1^°C warming. Future precipitation droughts superimposed on this new drier normal are likely to be much more severe than historical experience would indicate. Copyright © 2014 John Wiley & Sons, Ltd.     

Regional variation of recession flow power‐law exponent

Recession flows of a basin provide valuable information about its storage–discharge relationship as during recession periods discharge occurs due to depletion of storage. Storage–discharge analysis is generally performed by plotting ?dQ/dt against Q , where Q is discharge at time t . For most real world catchments, ?dQ/dt versus Q show a power‐law relationship of the type: ?dQ/dt = kQ^α . Because the coefficient k varies across recession events significantly, the exponent α needs to be computed separately for individual recession events. The median α can then be considered as the representative α for the basin. The question that arises here is what are the basin characteristics that influence the value of α ? Studies based on a small number of basins (up to 50 basins) reveal that α has good relationship with several basin characteristics. However, whether such a relationship is universal remains an important question, because a universal relationship would allow prediction of the value of α for any ungauged basin. To test this hypothesis, here, we study data collected from a relatively large number of basins (358 basins) in USA and examine the influence of 35 different physio‐climatic characteristics on α . We divide the basins into 2 groups based on their longitudes and test the relationship between α and basin characteristics separately for the two groups. The results indicate that α is not identically influenced by different basin characteristics for the two datasets. This may suggest that the power‐law exponent α of a region is determined by the way local physio‐climatic forces have shaped the landscape.     

Numerical simulation of groundwater flow patterns using flux as upper boundary

Since the 1960s, most of the studies on groundwater flow systems by analytical and numerical modelling have been based on given‐head upper boundaries. The disadvantage of the given‐head approach is that the recharge into and discharge from a basin vary with changes in hydraulic conductivity and/or basin geometry. Consequently, flow patterns simulated with given‐head boundaries but with different hydraulic conductivities and/or basin geometry may not reflect the effects of these variables. We conducted, therefore, numerical simulations of groundwater flow in theoretical drainage basins using flux as the upper boundary and realistically positioned fluid‐potential sinks while changing the infiltration intensity, hydraulic conductivities, and geometric configuration of the basin. The simulated results demonstrate that these variables are dominant factors controlling the flow pattern in a laterally closed drainage basin. The ratio of infiltration intensity to hydraulic conductivity (R_ic) has been shown to be an integrated pattern‐parameter in a basin with a given geometric configuration and possible fluid‐potential‐sink distribution. Successively, the changes in flow patterns induced by stepwise reductions in R_ic are identical, regardless of whether the reductions are due to a decrease in infiltration intensity or an increase in hydraulic conductivity. The calculated examples show five sequential flow patterns containing (i) only local, (ii) local–intermediate, (iii) local–intermediate–regional, (iv) local–regional, and (v) just regional flow systems. The R_ic was found to determine also whether a particular sink is active or not as a site of discharge. Flux upper boundary is preferable for numerical simulation when discussing the flow patterns affected by a change of infiltration, the hydraulic conductivity, or the geometry of a basin. Copyright © 2012 John Wiley & Sons, Ltd.     

Removal of Copper,Nickel and Zinc Ions from Aqueous Solution by Chitosan‐8‐Hydroxyquinoline Beads

In this work, 8‐hydroxyquinoline is used as the active sites in cross‐linked chitosan beads with epichlorohydrin (CT‐8HQ). The CT‐8HQ material was shaped in bead form and used for heavy metal removal from aqueous solution. The study was carried out at pH 5.0 with both batch and column methods and the maximum adsorption capacity of metal ions by the CT‐8HQ was attained in 4 h in the batch experiment. The adsorption capacity order was: Cu²⁺ > Ni²⁺ > Zn²⁺ for both mono‐ and multi‐component systems with batch conditions. From breakthrough curves with column conditions, the adsorption capacity followed the order Cu²⁺ > Zn²⁺ > Ni²⁺ for both mono‐ and multi‐component systems. The CT‐8HQ beads maintained good metal adsorption capacity for all five cycles with absorbent restoration achieved with the use of 1.0 mol L^–1 HCl solution, with 90% regeneration.     

The shape of patterns to come: from initial formation to long‐term evolution

Many studies focus on the emergence and development of rhythmic landscape patterns. In this contribution we explore the different behaviors found as patterns evolve; the trajectories that patterns exhibit as they transit from infinitesimal‐amplitude perturbation to a statistically steady state (or in some cases to continued statistical evolution). The variety of behaviors observed, either through field and laboratory experiments or numerical modeling, can be reduced to four classes: (a) simple stabilization where predictions based on the initial growth of small perturbations corresponds with the characteristics of patterns observed in nature; (b) significant pattern coarsening en route to saturated wavelength, where non‐linear interactions between finite‐amplitude pattern elements change the geometric properties of a pattern as it approaches steady‐state; (c) perpetual coarsening where the wavelength associated with the emerging pattern continues to grow over time and is only limited by physical boundaries or external constrains; (d) slow evolution toward a different attractor, a novel behavior observed in numerical modeling that involves profound temporal changes in pattern characteristics. Within these classes we also observe generalizable non‐linear behaviors: dependence on initial conditions, the emergence of pattern‐scale variables such as pattern defects, and the presence of multiple stable states. Predicting the shape of patterns to come remains a challenge – one that we suggest requires a range of modeling approaches to address both initial instabilities and the emergent properties of evolving patterns, which involve disparate forms of non‐linear interactions. Consideration of generic system behaviors at the pattern scale could enhance future pattern formation studies, facilitating appropriate pairings of analysis approaches and pattern‐evolution modes. Copyright © 2013 John Wiley & Sons, Ltd.     

Application of a multi‐temporal,LiDAR‐derived,digital terrain model in a landslide‐volume estimation

Sediments produced by landslides are crucial in the sediment yield of a catchment, debris flow forecasting, and related hazard assessment. On a regional scale, however, it is difficult and time consuming to measure the volumes of such sediment. This paper uses a LiDAR‐derived digital terrain model (DTM) taken in 2005 and 2010 (at 2 m resolution) to accurately obtain landslide‐induced sediment volumes that resulted from a single catastrophic typhoon event in a heavily forested mountainous area of Taiwan. The landslides induced by Typhoon Morakot are mapped by comparison of 25 cm resolution aerial photographs taken before and after the typhoon in an 83.6 km² study area. Each landslide volume is calculated by subtraction of the 2005 DTM from the 2010 DTM, and the scaling relationship between landslide area and its volume are further regressed. The relationship between volume and area are also determined for all the disturbed areas (V_L = 0.452A_L^1.242) and for the crown areas of the landslides (V_L = 2.510A_L^1.206). The uncertainty in estimated volume caused by use of the LiDAR DTMs is discussed, and the error in absolute volume estimation for landslides with an area >10⁵ m² is within 20%. The volume–area relationship obtained in this study is also validated in 11 small to medium‐sized catchments located outside the study area, and there is good agreement between the calculation from DTMs and the regression formula. By comparison of debris volumes estimated in this study with previous work, it is found that a wider volume variation exists that is directly proportional to the landslide area, especially under a higher scaling exponent. Copyright © 2013 John Wiley & Sons, Ltd.