Magnitude Of Debris Flows Research Articles

Climate change impacts on mass movements — Case studies from the European Alps

This paper addresses the current knowledge on climate change impacts on mass movement activity in mountain environments by illustrating characteristic cases of debris flows, rock slope failures and landslides from the French, Italian, and Swiss Alps. It is expected that events are likely to occur less frequently during summer, whereas the anticipated increase of rainfall in spring and fall could likely alter debris-flow activity during the shoulder seasons (March, April, November, and December). The magnitude of debris flows could become larger due to larger amounts of sediment delivered to the channels and as a result of the predicted increase in heavy precipitation events. At the same time, however, debris-flow volumes in high-mountain areas will depend chiefly on the stability and/or movement rates of permafrost bodies, and destabilized rock glaciers could lead to debris flows without historic precedents in the future. The frequency of rock slope failures is likely to increase, as excessively warm air temperatures, glacier shrinkage, as well as permafrost warming and thawing will affect and reduce rock slope stability in the direction that adversely affects rock slope stability. Changes in landslide activity in the French and Western Italian Alps will likely depend on differences in elevation. Above 1500m asl, the projected decrease in snow season duration in future winters and springs will likely affect the frequency, number and seasonality of landslide reactivations. In Piemonte, for instance, 21st century landslides have been demonstrated to occur more frequently in early spring and to be triggered by moderate rainfalls, but also to occur in smaller numbers. On the contrary, and in line with recent observations, events in autumn, characterized by a large spatial density of landslide occurrences might become more scarce in the Piemonte region.

Possible impacts of climate change on debris-flow activity in the Swiss Alps

This study uses a long dataset of past debris flows from eight high-elevation catchments in the Swiss Alps for which triggering conditions since AD 1864 have been reconstructed. The torrents under investigation have unlimited sediment supply and the triggering of debris flows is thus mainly controlled by climatic factors. Based on point-based downscaled climate scenarios for meteorological stations located next to the catchments and for the periods 2001–2050 and 2051–2100, we study the evolution of temperature and rainfall above specific thresholds (10, 20, 30, 40 and 50 mm) and durations (1, 2 or 3 days). We conclude that the drier conditions in future summers and the wetting of springs, falls and early winters are likely to have significant impacts on the behavior of debris flows. Based on the current understanding of debris-flow systems and their reaction to rainfall inputs, one might expect only slight changes in the overall frequency of events by the mid-21st century, but possibly an increase in the overall magnitude of debris flows due to larger volumes of sediment delivered to the channels and an increase in extreme precipitation events. In the second half of the 21st century, the number of days with conditions favorable for the release of debris flows will likely decrease, especially in summer. The anticipated increase of rainfall during the shoulder seasons (March, April, November, December) is not expected to compensate for the decrease in future heavy summer rainfall over 2 or 3 days.

Characteristics, causes and mitigation of catastrophic debris flow hazard on 21 July 2011 at the Longda Watershed of Songpan County, China

Debris flow is a common natural hazard in the mountain areas of Western China due to favorable natural conditions, and also exacerbated by mountainous exploitation activities. This paper concentrated on the characteristics, causes and mitigation of a catastrophic mine debris flow hazard at Longda Watershed in Songpan County, Sichuan Province, on 21 July 2011. This debris flow deposited in the front of the No.1 dam, silted the drainage channel for flood and then rushed into tailing sediment reservoir in the main channel and made the No.2 dam breached. The outburst debris flow blocked Fu River, formed dammed lake and generated outburst flood, which delivered heavy metals into the lower reaches of Fu River, polluted the drink water source of the population of over 1 million. The debris flow was characterized with a density of 1.87∼2.15 t/m3 and a clay content of less than 1.63%. The peak velocity and flux at Longda Gully was over 10.0∼10.9 m/s and 429.0∼446.0 m3/s, respectively, and the flux was about 700 m3/s in main channel, equaling to the flux of the probability of 1%. About 330,000m3 solid materials was transported by debris flow and deposited in the drainage tunnel (120,000∼130,000 m3), the front of No.1 dam (100,000 m3) and the mouth of the watershed (100,000∼110,000 m3), respectively. When the peak flux and magnitude of debris flow was more than 462 m3/s and 7,423 m3, respectively, it would block Fu River and produce a hazard chain which was composed of debris flow, dammed lake and outburst flood. Furthermore, the 21 July large-scale debris flow was triggered by rainstorm with an intensity of 21.2 mm/0.5 h and the solid materials of debris flow were provided by landslides, slope deposits, mining wastes and tailing sediments. The property losses were mainly originated from the silting of the drainage tunnel for flash flood but not for debris flow and the irrational location of tailing sediment reservoir. Therefore, the mitigation measures for mine debris flows were presented: (1) The disastrous debris flow watershed should be identified in planning period and prohibited from being taken as the site of mining factories; (2) The mining facilities are constructed at the safe areas or watersheds; (3) Scoria plots, concentrator factory and tailing sediment reservoir are constructed in safe areas where the protection measures be easily made against debris flows; (4) The appropriate system and plan of debris flow mitigation including monitoring, remote monitoring and early-warning and emergency plan is established; (5) The stability of waste dump and tailing sediment reservoir are monitored continuously to prevent mining debris flows.

Phoenix Debris-Flow Hazard Assessment: House Location Matters

Three catchments that debouch into Phoenix housing developments from the Ma Ha Tuak Range, South Mountain show a consistent pattern of declines in the magnitude of debris flows over time. We used a mix of field and geospatial methods to estimate volume, and the varnish microlamination technique to estimate minimum ages of debris deposits. Estimates of debris-flow volumes show a drop of more than two orders of magnitude from latest Pleistocene to 20th century or Little Ice Age. Debris-flow run-out lengths also shortened tremendously, with the most recent events stopping inside incised channels. In contrast, a catchment above houses in the Gila Range, South Mountain, where houses were built very close to the debris-flow source area, reveals an increase in debris-flow magnitude over time. These contrasting findings emphasize the importance of the location of home sites with respect to the debris-flow system in the type of small desert mountain catchments that interface with the sprawling urbanism found in Southwestern USA deserts.

Parameterization of a numerical 2-D debris flow model with entrainment: a case study of the Faucon catchment, Southern French Alps

Abstract. The occurrence of debris flows has been recorded for more than a century in the European Alps, accounting for the risk to settlements and other human infrastructure that have led to death, building damage and traffic disruptions. One of the difficulties in the quantitative hazard assessment of debris flows is estimating the run-out behavior, which includes the run-out distance and the related hazard intensities like the height and velocity of a debris flow. In addition, as observed in the French Alps, the process of entrainment of material during the run-out can be 10–50 times in volume with respect to the initially mobilized mass triggered at the source area. The entrainment process is evidently an important factor that can further determine the magnitude and intensity of debris flows. Research on numerical modeling of debris flow entrainment is still ongoing and involves some difficulties. This is partly due to our lack of knowledge of the actual process of the uptake and incorporation of material and due the effect of entrainment on the final behavior of a debris flow. Therefore, it is important to model the effects of this key erosional process on the formation of run-outs and related intensities. In this study we analyzed a debris flow with high entrainment rates that occurred in 2003 at the Faucon catchment in the Barcelonnette Basin (Southern French Alps). The historic event was back-analyzed using the Voellmy rheology and an entrainment model imbedded in the RAMMS 2-D numerical modeling software. A sensitivity analysis of the rheological and entrainment parameters was carried out and the effects of modeling with entrainment on the debris flow run-out, height and velocity were assessed.

Reconstruction of a major storm event from its geomorphic signature: The Ladakh floods, 6 August 2010

Extreme precipitation events in arid mountain regions determine flood, debris flow, and landslide hazards, and are principal drivers of geomorphic change. Increased frequency of intense precipitation in many regions of the world over the past few decades increases the importance of documenting and understanding such events when they occur. We use the geomorphic record to reconstruct the distribution and magnitude of river discharge from a devastating convective storm event in the interior of the western Himalaya. We use this record to estimate the rates, magnitudes, and distribution of precipitation and magnitude of debris flows generated by the same event. The storm occurred on 6 August 2010 over the Ladakh Range in the northwest Indian Himalaya, killing ~600 people and devastating more than 60 villages. It triggered numerous debris flows and significantly widened the lower reaches of the main tributary valleys. We demonstrate that rainfall was concentrated in a 6-km-wide, range-parallel band centered 4.5 km up from the range front, and that within this band precipitation intensity was ~30 times that above it. At least 75 mm of rain fell in 30 min during the heaviest part of the storm, which is at least 1.5 times the highest 24 h maximum for the previous 100 yr. The results demonstrate that the geomorphic record can be used to constrain the intensity of rainfall without meteorological stations, and also record its distribution better than could be achieved with normal densities of instrumentation.

Destruction of vegetation due to geo-hazards and its environmental impacts in the Wenchuan earthquake areas

Geo-hazards induced by earthquakes have caused ecosystem degradation and vegetation destruction. Little, however, is known about the consequences of geo-hazards due to a lack of research data. We have undertaken a study in the Wenchuan earthquake-affected area of China in order to identify and characterize vegetation destruction and its consequent environmental impact. The Wenchuan earthquake on 12th May, 2008 induced numerous geo-hazards (including rock avalanches, landslides, landslide-dammed lakes and debris flows) that caused vegetation destruction up to 1249.5km2, of which shrub comprised the largest proportional area with 338.559km2. The vegetation coverage decreased by 4.76% in 9 severely damaged cities and counties and by 12.37% in the Subao river, Beichuan county. Rock avalanches and landslides were the most common destructive types, resulting in 98.73% of all types of geo-hazards, whereas debris flows and landslide-dammed lakes accounted for 1.27%. Vegetation destruction was distributed along both sides of rivers causing erosion, formation of debris flows and landslides. Hydrologic progress was changed and hydrological adjusting function diminished due to vegetation deterioration resulting in bare rock (infiltration reduced, runoff increased and flow concentration expedited) and deposit region (infiltration increased and runoff reduced) in catchment. Soil erosion was intensified causing increased sediment transportation of rivers, decreased storage capacities of reservoirs downstream, a significantly increased area that has suffered severe erosion and aggravated magnitude and damage capability of debris flows and landslides. Ecosystem function declined and vegetation restoration and reconstruction was difficult due to co-degradation of vegetation-soil system in the earthquake-affected areas. Finally, we summarized the challenges faced in the future for vegetation restoration and reconstruction.

Probability distribution of measured debris-flow velocity in Jiangjia Gully, Yunnan Province, China

Debris flow moves in the form of surge waves and consists of dozens or even hundreds of surges that are separated in time and space and have a variety of appearances, as exemplified in Jiangjia Gully, China. Observations there indicate that the deposit is made up by superposition of successive surges and deposit of a single surge is in effect a "frozen" surge. Then the study of debris flow is reduced to the study of surge sequence, which leads to a probabilistic picture of debris flow. This study attempts to find the probability distribution of velocity of surge using a huge data set of Jiangjia Gully. Statistics of the data shows that the velocity satisfies the Weibull distribution, which is believed to be universally valid because the distribution parameters vary little between events, with the shape parameter being well related to the average of velocity. It follows that the same distribution applies also to other quantities of debris flow, such as the flow depth and the discharge. Therefore, the distribution can be used to assess the magnitude and overflow range of a potential debris flow, as well as to the parameter calculation for engineering design.

Formation and characteristics of post-earthquake debris flow: a case study from Wenjia gully in Mianzhu, Sichuan, SW China

During the three flood seasons following the Wenchuan earthquake in 2008, two catastrophic groups of debris flow events occurred in the earthquake-affected area: the 2008-9-24 debris flow events, which had a serious impact on rebuilding; and the 2010-8-13/14 debris flow events, which destroyed much of the progress made in rebuilding. The Wenjia gully is a typical post-earthquake debris flow gully and at least five debris flows have occurred there. As far as the 2010-8-13 debris flow is concerned, the deposits of the Wenjia gully debris flow reached a volume of 3.1 × 106 m3 in volume and hundreds of newly built houses were buried. This study took the Wenjia gully debris flow as an example and discussed the formation and characteristics of post-earthquake debris flow on the basis of field investigations and a remote sensing interpretation. The conclusions drawn from the investigation and analysis were as follows: (1) Post-earthquake debris flows were a joint result of both the earthquake and heavy rainfall. (2) Gully incision and loose material provision are key processes in the initiation and occurrence of debris flows and a cycle can be presented as the following process: runoff—erosion—collapse—engulfment—debris flow—further erosion—further collapse—further engulfment—debris flow enlargement. (3) The amount of rainfall that triggered debris flows from the Wenjia gully was significantly less than the average daily rainfall, while the intraday rainfall threshold decreased by at least 23.3%. (4) The occurrence mechanism of Wenjia gully debris flow was an erosion type and there was a positive relationship between debris flow magnitude and rainfall, which fitted an exponential model. (5) There were five representative characteristics of Wenjia gully debris flow: the long duration of the occurring process; the long distance of deposition chain conversion during the process of damage; magnification in the scale of debris flow; and the high frequency of debris flow events.

Characterization of debris flows by rainstorm condition at a torrent on the Mount Yakedake volcano, Japan

We analyzed rainstorm control on debris-flow magnitude and flow characteristics using the 14 sets of rainstorm and debris-flow data obtained from 1980 to 2005 at the Kamikamihorizawa Creek of Mount Yakedake. With the principal component analysis on five parameters of debris flows: frontal velocity, peak velocity, peak flow depth, peak discharge and total discharge, and with video-record of boulder-dams in motion, and the preceding rainfall intensities, we conclude that the 14 debris flows could be categorized into three groups. The flows in the first group have large hydraulic magnitude and massive and turbulent boulder-dams filled with slurry matrix. The flows in the second group have small hydraulic magnitude and boulder-dams scarcely filled with slurry matrix, and the dam is observed to alternate between stopping and starting. The flows in the third group have small hydraulic magnitude and boulder dams filled with slurry matrix. Analysis of hillslope hydrology and debris-flow data asserted that the antecedent rainfall conditions control not only the hydraulic magnitude of debris flows but also the boulder-dam features. Large rainstorms of high intensity and durations as short as 10 minutes induces fast and large storm runoff to the headwaters and the source reaches of debris flow, while rainstorms with durations as long as 24 h raises water content in the bottom deposits along the debris-flow growth reaches and generates substantial runoff from the tributaries. Classification of the three groups is done based on water availability to debris flows on the source and growth reaches at the occurrence of debris flow.

Prediction of debris-flow danger area by combining hydrological and inundation simulation methods

Debris flows have caused serious human casualties and economic losses in the regions strongly affected by the Ms8.0 Wenchuan earthquake of 2008. Debris flow mitigation and risk assessment is a key issue for reconstruction. The existing methods of inundation simulation are based on historical disasters and have no power of prediction. The rainflood method can not yield detailed flow hydrograph and does not meet the need of inundation simulation. In this paper, the process of water flow was studied by using the Arc-SCS model combined with hydraulic method, and then the debris flow runoff process was calculated using the empirical formula combining the result from Arc-SCS. The peak discharge and runoff duration served as input of inundation simulation. Then, the dangerous area is predicted using kinematic wave method and Manning equation. Taking the debris flow in Huashiban gully in Beichuan County, Sichuan Province, China on 24 Sep. 2008 as example, the peak discharge of water flow and debris flow were calculated as 35.52 m3·s−1 and 215.66 m3·s−, with error of 4.15% compared to the measured values. The simulated area of debris-flow deposition was 161,500 m2, vs. the measured area of 144,097 m2, in error of 81.75%. The simulated maximum depth was 12.3 m, consistent with the real maximum depth between 10 and 15 m according to the field survey. The minor error is mainly due to the flow impact on buildings and variations in cross-section configuration. The present methodology can be applied to predict debris flow magnitude and evaluate its risk in other watersheds inthe earthquake area.

Assessment of debris flow magnitude in small catchments of the lombardy alps: the val gola case study

Debris flows are among the most destructive of all water-related disasters. They mainly affect mountain areas in a wide range of morpho- climatic environments. Therefore, accurate pre-diction of their run out distances, magnitudes and velocities plays a role of paramount impor-tance, in order to plan and design appropriate structural and non-structural defence measures. In this context, a number of Authors have de-veloped methods feasible to evaluate the ten-dency of a catchment to generate debris flow, without giving an estimation of the magnitude. Other empirical procedures are based on the analysis of historical series of debris flow, oc-curred in similar environments, to assess the relationship between the catchment character-istics and the maximum movable debris vol-umes. In this paper, and with reference to Val Gola—a small catchment in the North-East Lom- bardy where debris flows frequently occur—a number of methods, belonging to each of the above mentioned categories, have been briefly reviewed and applied in order to evaluate their effectiveness and consistency.

Debris flow hazard modelling on medium scale: Valtellina di Tirano, Italy

Abstract. Debris flow hazard modelling at medium (regional) scale has been subject of various studies in recent years. In this study, hazard zonation was carried out, incorporating information about debris flow initiation probability (spatial and temporal), and the delimitation of the potential runout areas. Debris flow hazard zonation was carried out in the area of the Consortium of Mountain Municipalities of Valtellina di Tirano (Central Alps, Italy). The complexity of the phenomenon, the scale of the study, the variability of local conditioning factors, and the lacking data limited the use of process-based models for the runout zone delimitation. Firstly, a map of hazard initiation probabilities was prepared for the study area, based on the available susceptibility zoning information, and the analysis of two sets of aerial photographs for the temporal probability estimation. Afterwards, the hazard initiation map was used as one of the inputs for an empirical GIS-based model (Flow-R), developed at the University of Lausanne (Switzerland). An estimation of the debris flow magnitude was neglected as the main aim of the analysis was to prepare a debris flow hazard map at medium scale. A digital elevation model, with a 10 m resolution, was used together with landuse, geology and debris flow hazard initiation maps as inputs of the Flow-R model to restrict potential areas within each hazard initiation probability class to locations where debris flows are most likely to initiate. Afterwards, runout areas were calculated using multiple flow direction and energy based algorithms. Maximum probable runout zones were calibrated using documented past events and aerial photographs. Finally, two debris flow hazard maps were prepared. The first simply delimits five hazard zones, while the second incorporates the information about debris flow spreading direction probabilities, showing areas more likely to be affected by future debris flows. Limitations of the modelling arise mainly from the models applied and analysis scale, which are neglecting local controlling factors of debris flow hazard. The presented approach of debris flow hazard analysis, associating automatic detection of the source areas and a simple assessment of the debris flow spreading, provided results for consequent hazard and risk studies. However, for the validation and transferability of the parameters and results to other study areas, more testing is needed.

Probability assessment of river blocking by debris flow associated with the Wenchuan Earthquake

This paper assesses the probability of the main stream in the Dujiangyan–Wenchuan reach of the Minjiang River becoming blocked by debris flows in response to the Wenchuan Earthquake of 12 May 2008, on the basis of analyses of remote sensing data and ground investigations. Background information of debris flow gullies was developed from field investigations and high-resolution remote sensing image interpretation, and was used to estimate the maximum discharge per unit width by means of the revised model of debris flow magnitude according to the situation after the Earthquake. Based on improved discrimination equations of river blocking induced by debris flow, 29 debris flow gullies were evaluated and classified as four probability levels: extreme high, high, moderate and low. The results show that most of the debris flow gullies were at or over moderate hazard level, accounting for 72.4% of the total area. The present results provide a scientific basis for the prevention, elusion and mitigation of debris flow hazards and will contribute to the reconstruction of an earthquake prone area.

Sediment loads due to fluvial transport and debris flows during the 2005 flood events in Switzerland

AbstractSevere floods in August 2005 in Switzerland were associated with enormous morphologic changes along the stream channels and with large sediment transport, including many debris flows in the headwater catchments and fluvial bedload transport along the mountain rivers. We compiled data on transported sediment volumes and estimated surface runoff volumes in the streams determined from radar‐based rainfall data and stream gauge measurements lower in the catchments. A quantitative analysis of the data shows that the transported bedload volumes are related to the flood runoff volume and the relevant channel gradient. For channel gradients flatter than about 5%, our data agree with a simplified version of the Meyer‐Peter and Müller equation but two other equations tested tend to under predict bedload volumes. For channel gradients steeper than about 5%, the observed sediment volumes transported by fluvial processes are over predicted by all bedload transport equations tested, though two of them were specifically developed for this slope range, which likely results from non‐accounted energy losses and supply limitation. For events with debris flows as the dominant sediment transfer mechanism, sediment volumes show a large variability for given flood runoff volume and channel gradient. The sediment volumes of the torrent catchments show a similar functional dependence on catchment parameters as for two empirical power law equations for the estimation of a ‘design’ event magnitude of debris flows based on data from Northern Italy but our events are associated with a much smaller coefficient. Finally, the majority of our debris‐flow data is in line with the trend defined by our fluvial transport events, indicating a continuous transition to debris‐flood and debris‐flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.

Frequency and magnitude of debris flows on Cheekye River, British Columbia

Natural hazard and risk assessments are predicated on a detailed understanding of the relationship between frequency and magnitude of the hazardous process under investigation. When information is sought from the deep past (i.e., several thousand years), continuous event records do not exist and the researcher has to rely on proxy data to develop the frequency–magnitude ( F– M) model. Such work is often prohibitively expensive and few well-researched examples for mass movement are available worldwide. The Cheekye fan is a desirable location for land development and has a depth and breadth of previous research unprecedented on any debris-flow fan in Canada. We pursued two principal strains of research to formulate a reliable F– M relationship. The first focuses on stratigraphic analyses combined with radiometric dating and dendrochronology to reconstruct a comprehensive picture of Holocene debris-flow activity. The second approach examines hydrological limitations of rock avalanche evolution into debris flows through either entrainment of saturated sediments or by failure of a landslide-generated dam and upstream impoundment. We thus hypothesize that debris flows from Cheekye River can be separated into two quasi-homogenous populations: those that are typically triggered by relatively small debris avalanches, slumps, or rock falls or simply by progressive bulking of in-stream erodible sediments; and those that are thought to result from transformation of rock avalanches. Our work suggests that debris flows exceeding some 3 million m 3 in volume are unlikely to reach the Cheekye fan as a result of limited water available to fully fluidize a rock avalanche. This analysis has also demonstrated that in order to arrive at reasonable estimates for the frequency and magnitude of debris flows on a complex alluvial fan significant multidisciplinary efforts are required. Without the significant precursor investigations and the additional efforts of this study, life and property may be jeopardized or the design of debris-flow mitigation may be subject to considerable and unquantifiable error.

Distribution of debris flows in Glacier National Park, Montana, U.S.A.

The spectacular scenery of Glacier National Park is the result of glacial erosion as well as post-glacial mass wasting processes. Debris flow magnitude and frequency have been established through extensive fieldwork across seven separate drainage basins in the eastern portion of the park. This paper summarizes the investigation of the hypotheses that debris flow distribution in the Glacier National Park, east of the Continental Divide is (a) not random; and (b) concentrated adjacent to the Continental Divide. The location of 2317 debris flows were identified and mapped from sixty-three 1-m resolution Digital Orthophoto Quarter Quadrangles and their spatial distribution was then analyzed using ArcView Spatial Analyst GIS software. The GIS analysis showed that the debris flows are not randomly distributed nor are they concentrated directly adjacent to the Divide. While the Continental Divide provides orographic enhancement of precipitation directly adjacent to the Divide, the debris flows are not concentrated there due to a lack of available weathered regolith. The most recent Little Ice Age glaciation removed the debris directly adjacent to the Divide, and without an adequate debris supply, these steep slopes experience few debris flows. Both abundant water and an adequate debris supply are necessary to initiate slope failure, resulting in a clustering of debris flows at the break in slope where valley walls contact talus slopes. A variety of summer storm and antecedent moisture conditions initiate slope failures in the Glacier National Park, with no distinct meteorological threshold. With over two million visitors every year, and millions of dollars of park infrastructure at risk, identifying the hazard of debris flows is essential to future park management plans.

Practical research on quantitative calculation of debris flow magnitude and disaster intensity

Wind scale or earthquake magnitude is easier to remember and to be understood by the community. Although many systems of classifying debris flows are presently available, it is necessary to propose an index as simple as wind scale or earthquake magnitude for measuring debris flows. Based on the principles used in wind scale and earthquake magnitude calculation, this paper presents the concepts of debris flow magnitude and disaster intensity as well as a new numerical calculation method. Debris flow magnitude is a quantitative index describing the scale of a debris flow. The disaster intensity of a debris flow is a quantitative index describing the severity of the damage to society caused by a debris flow. With their explicit definitions and simple concepts, both indices are considered to be important both practically and theoretically.

Magnitude–frequency relations in debris flow

Debris flow occurs frequently in mountainous regions in China. Because of the difficulties involved in predicting and catching live debris flows, an assessment of the potential for debris flow is crucial in hazard mitigation. Magnitude–frequency (MF) relations are of special significance in such assessments. In previous studies, MF relations have been inferred by analyzing environmental factors and historical records and using empirical relations. This paper is concerned with the derivation of MF relations at regional and valley scales, using a large database of statistics. At the regional scale, it is represented by the distribution of the valley area, because the area is often taken to indicate the potential magnitude of debris flow. Statistics from over 5,000 debris flow valleys in various provinces in China show that a power law holds for the distribution, i.e., p(A) ∼ A −n , where p(A) is the percentage of valleys with area A and n varies with region and thus describes regional differences. At the valley scale, a case study focusing on Jiangjia Gully (JJG) was conducted, and the MF relations derived from it were expressed by the distributions of discharge and runoff (i.e., the total volume) of living debris flows observed over the last 40 years. The distributions can be expressed as exponential functions where the exponents vary with the events. These MF relations provide not only a potential quantitative reference for practical purposes but also hint at the intrinsic properties of the debris flow.

Magnitude–frequency relationships of debris flows and debris avalanches in relation to slope relief

Probability of occurrence, hazard intensity and encounter probability are key parameters in the quantitative risk analysis (QRA) of landslides. All are strongly dependent on magnitude of the landslides. As a result, magnitude–frequency analysis should be a part of QRA. Deriving representative magnitude–frequency relationships for debris avalanches and debris flows, however, is difficult. One key problem is illustrated with the example of a unique database from the coastal region of British Columbia, Canada, which was compiled entirely from detailed ground investigations. The magnitude of debris avalanches and debris flows is not an independent statistical quantity, but a function of the scale of a given slope, as characterized by the slope length. Thus, attempting to derive probability and magnitude for a given location or sub-region from a regionally-derived magnitude–frequency curve may lead to incorrect predictions. The same problem is pertinent to the application of the same approach to any type of landslide in which the largest combined dimension of the source volume (including entrainment) is of the same order as the length of the slope. It is recommended that greater emphasis be placed on site-specific geological observations, at the expense of generalized statistics.