Backward snow depth reconstruction at high spatial resolution based on time‐lapse photography

We report a methodology for reconstructing the daily snow depth distribution at high spatial resolution in a small Pyrenean catchment using time‐lapse photographs and snow depletion rates derived from an on‐site measuring meteorological station. The results were compared with the observed snow depth distribution, determined on a number of separate occasions using a terrestrial laser scanner (TLS). The time‐lapse photographs were projected onto a digital elevation model of the study site, and converted into snow presence/absence information. The melt‐out date (MOD; first occurrence of melt out after peak snow accumulation) was obtained from the projected photograph series. Commencing the backward reconstruction for each grid cell at the MOD, the method uses simulated snow depth depletion rates using a temperature index approach, which are extrapolated to the grid cells of the domain to arrive at the snow distribution of the previous day. Two variants of the reconstruction techniques were applied (1) using a spatially constant degree day factor (DDF) for calculating the daily expected snow depth depletion rate, and (2) allowing a spatially distributed DDF calculated from two consecutive TLS acquisitions compared to the snow depth depletion rate observed at the meteorological station. Validation revealed that both methods performed well (average R² = 0.68; standard RMSE = 0.58), with better results obtained from the spatially distributed approach. Nevertheless, the spatially corrected DDF reconstruction, which requires TLS data, suggests that the constant DDF approach is an efficient, and for most applications sufficiently accurate and easily reproducible method. The results highlight the usefulness of time‐lapse photography for not only determining the snow covered area, but also for estimating the spatial distribution of snow depth. Copyright © 2016 John Wiley & Sons, Ltd.     

Regional variability in dust‐on‐snow processes and impacts in the Upper Colorado River Basin

Dust deposition onto mountain snow cover in the Upper Colorado River Basin frequently occurs in the spring when wind speeds and dust emission peaks on the nearby Colorado Plateau. Dust loading has increased since the intensive settlement in the western USA in the mid 1880s. The effects of dust‐on‐snow have been well studied at Senator Beck Basin Study Area (SBBSA) in the San Juan Mountains, CO, the first high‐altitude area of contact for predominantly southwesterly winds transporting dust from the southern Colorado Plateau. To capture variability in dust transport from the broader Colorado Plateau and dust deposition across a larger area of the Colorado River water sources, an additional study plot was established in 2009 on Grand Mesa, 150 km to the north of SBBSA in west central, CO. Here, we compare the 4‐year (2010–2013) dust source, deposition, and radiative forcing records at Grand Mesa Study Plot (GMSP) and Swamp Angel Study Plot (SASP), SBBSA's subalpine study plot. The study plots have similar site elevations/environments and differ mainly in the amount of dust deposited and ensuing impacts. At SASP, end of year dust concentrations ranged from 0.83 mg g^?1 to 4.80 mg g^?1, and daily mean spring dust radiative forcing ranged from 50–65 W m^?2, advancing melt by 24–49 days. At GMSP, which received 1.0 mg g^?1 less dust per season on average, spring radiative forcings of 32–50 W m^?2 advanced melt by 15–30 days. Remote sensing imagery showed that observed dust events were frequently associated with dust emission from the southern Colorado Plateau. Dust from these sources generally passed south of GMSP, and back trajectory footprints modelled for observed dust events were commonly more westerly and northerly for GMSP relative to SASP. These factors suggest that although the southern Colorado Plateau contains important dust sources, dust contributions from other dust sources contribute to dust loading in this region, and likely account for the majority of dust loading at GMSP. Copyright © 2015 John Wiley & Sons, Ltd.     

Integrating airborne and multi‐temporal long‐range terrestrial laser scanning with total station measurements for mapping and monitoring a compound slow moving rock slide

A slow moving compound rock slide located in the northern Apennines of Italy was mapped and monitored through the integration of Airborne Laser Scanning (ALS), multi‐temporal long‐range Terrestrial Laser Scanning (TLS), and Automated Total Station (ATS) measurements. Landslide features were mapped using a High Resolution Digital Terrain Model (HR‐DTM) obtained by merging ALS and TLS data in an Iterative Closest Point (ICP) procedure. Slope movements in the order of centimeters to a few decimeters were quantified with Differential TLS (D‐TLS) based on a Surface Matching approach and supported by ATS data to define stable reference surfaces. The integrated approach allowed mapping of the composite geomorphic features of the rock slide under examination, revealing its complex dynamic nature and further proving that laser scanning is a versatile and widely applicable tool for slope process analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Spatio‐temporal controls of snowmelt and runoff generation during rain‐on‐snow events in a mid‐latitude mountain catchment

A network of 30 standalone snow monitoring stations was used to investigate the snow cover distribution, snowmelt dynamics, and runoff generation during two rain‐on‐snow (ROS) events in a 40 km² montane catchment in the Black Forest region of southwestern Germany. A multiple linear regression analysis using elevation, aspect, and land cover as predictors for the snow water equivalent (SWE) distribution within the catchment was applied on an hourly basis for two significant ROS flood events that occurred in December 2012. The available snowmelt water, liquid precipitation, as well as the total retention storage of the snow cover were considered in order to estimate the amount of water potentially available for the runoff generation. The study provides a spatially and temporally distributed picture of how the two observed ROS floods developed in the catchment. It became evident that the retention capacity of the snow cover is a crucial mechanism during ROS. It took several hours before water was released from the snowpack during the first ROS event, while retention storage was exceeded within 1 h from the start of the second event. Elevation was the most important terrain feature. South‐facing terrain contributed more water for runoff than north‐facing slopes, and only slightly more runoff was generated at open compared to forested areas. The results highlight the importance of snowmelt together with liquid precipitation for the generation of flood runoff during ROS and the large temporal and spatial variability of the relevant processes. Copyright © 2015 John Wiley & Sons, Ltd.     

Role of temporal resolution of meteorological inputs for process‐based snow modelling

Accurate snow accumulation and melt simulations are crucial for understanding and predicting hydrological dynamics in mountainous settings. As snow models require temporally varying meteorological inputs, time resolution of these inputs is likely to play an important role on the model accuracy. Because meteorological data at a fine temporal resolution (~1 hr) are generally not available in many snow‐dominated settings, it is important to evaluate the role of meteorological inputs temporal resolution on the performance of process‐based snow models. The objective of this work is to assess the loss in model accuracy with temporal resolution of meteorological inputs, for a range of climatic conditions and topographic elevations. To this end, a process‐based snow model was run using 1‐, 3‐, and 6‐hourly inputs for wet, average, and dry years over Boise River Basin (6,963 km²), which spans rain dominated (≤1,400 m), rain–snow transition (>1,400 and ≤1,900 m), snow dominated below tree line (>1,900 and ≤2,400 m), and above tree line (>2,400 m) elevations. The results show that sensitivity of the model accuracy to the inputs time step generally decreases with increasing elevation from rain dominated to snow dominated above tree line. Using longer than hourly inputs causes substantial underestimation of snow cover area (SCA) and snow water equivalent (SWE) in rain‐dominated and rain–snow transition elevations, due to the precipitation phase mischaracterization. In snow‐dominated elevations, the melt rate is underestimated due to errors in estimation of net snow cover energy input. In addition, the errors in SCA and SWE estimates generally decrease toward years with low snow mass, that is, dry years. The results indicate significant increases in errors in estimates of SCA and SWE as the temporal resolution of meteorological inputs becomes coarser than an hour. However, use of 3‐hourly inputs can provide accurate estimates at snow‐dominated elevations. The study underscores the need to record meteorological variables at an hourly time step for accurate process‐based snow modelling.     

Investigating hydrologic responses to spatio‐temporal characteristics of storms using a Dynamic Moving Storm generator

A synthetic storm generator—Dynamic Moving Storm (DMS)—is developed in this study to represent spatio‐temporal variabilities of rainfall and storm movement in synthetic storms. Using an urban watershed as the testbed, the authors investigate the hydrologic responses to the DMS parameters and their interactions. In order to reveal the complex nature of rainfall–run‐off processes, previously simplified assumptions are relaxed in this study regarding (a) temporal variability of rainfall intensity and (b) time‐invariant flow velocity in channel routing. The results of this study demonstrate the significant contribution of storm moving velocity to the variation of peak discharge based on a global sensitivity analysis. Furthermore, a pairwise sensitivity analysis is conducted to elucidate not only the patterns in individual contributions from parameters to hydrologic responses but also their interactions with storm moving velocity. The intricacies of peak discharges resulting from sensitivity analyses are then dissected into independent hydrologic metrics, that is, run‐off volume and standard deviation of run‐off timings, for deeper insights. It is confirmed that peak discharge is increased when storms travel downstream along the main channel at the speed that corresponds to a temporal superposition of run‐off. Spatial concentration of catchment rainfall is found to be a critical linkage through which characteristics of moving storms affect peak discharges. In addition, altering peak timing of rainfall intensity in conjunction with storm movement results in varied storm core locations in the channel network, which further changes the flow attenuation effects from channel routing. For future directions, the DMS generator will be embedded in a stochastic modelling framework and applied in rainfall/flow frequency analysis.     

Understanding subgrid variability of snow depth at 1‐km scale using Lidar measurements

It is well known that snow plays an important role in land surface energy balance; however, modelling the subgrid variability of snow is still a challenge in large‐scale hydrological and land surface models. High‐resolution snow depth data and statistical methods can reveal some characteristics of the subgrid variability of snow depth, which can be useful in developing models for representing such subgrid variability. In this study, snow depth was measured by airborne Lidar at 0.5‐m resolution over two mountainous areas in south‐western Wyoming, Snowy Range and Laramie Range. To characterize subgrid snow depth spatial distribution, measured snow depth data of these two areas were meshed into 284 grids of 1‐km × 1‐km. Also, nine representative grids of 1‐km × 1‐km were selected for detailed analyses on the geostatistical structure and probability density function of snow depth. It was verified that land cover is one of the important factors controlling spatial variability of snow depth at the 1‐km scale. Probability density functions of snow depth tend to be Gaussian distributions in the forest areas. However, they are eventually skewed as non‐Gaussian distribution, largely due to the no‐snow areas effect, mainly caused by snow redistribution and snow melt. Our findings show the characteristics of subgrid variability of snow depth and clarify the potential factors that need to be considered in modelling subgrid variability of snow depth.     

Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment,part 2: development of a sub‐grid‐scale treatment

This paper develops and tests a sub‐grid‐scale wetting and drying correction for use with two‐dimensional diffusion‐wave models of urban flood inundation. The method recognizes explicitly that representations of sub‐grid‐scale topography using roughness parameters will provide an inadequate representation of the effects of structural elements on the floodplain (e.g. buildings, walls), as such elements not only act as momentum sinks, but also have mass blockage effects. The latter may dominate, especially in structurally complex urban areas. The approach developed uses high‐resolution topographic data to develop explicit parameterization of sub‐grid‐scale topographic variability to represent both the volume of a grid cell that can be occupied by the flow and the effect of that variability upon the timing and direction of the lateral fluxes. This approach is found to give significantly better prediction of fluvial flood inundation in urban areas than traditional calibration of sub‐grid‐scale effects using Manning's n. In particular, it simultaneously reduces the need to use exceptionally high values of n to represent the effects of using a coarser mesh process representation and increases the sensitivity of model predictions to variation in n. Copyright © 2005 John Wiley & Sons, Ltd.     

Spatial and temporal variability of groundwater dynamics in a sub‐Mediterranean mountain catchment

The temporal and spatial dynamics of groundwater was investigated in a small catchment in the Spanish Pyrenees, which was extensively used for agriculture in the past. Analysis of the water table fluctuations at five locations over a 6‐year period demonstrated that the groundwater dynamics had a marked seasonal cycle involving a wetting‐up period that commenced with the first autumn rainfall events, a saturation period during winter and spring and a drying‐down period from the end of spring until the end of the summer. The length of the saturation period showed great interannual variability, which was mainly influenced by the rainfall and evapotranspiration characteristics. There was marked spatial variability in the water table, especially during the wetting‐up period, which could be related to differences in slope and drainage area, geomorphology, soil properties and local topography. Areas contributing to runoff generation were identified within the catchment by field mapping of moisture conditions. Areas contributing to infiltration excess runoff were correlated with former cultivated fields affected by severe sheetwash erosion. Areas contributing to saturation excess runoff were characterized by a marked spatial dynamics associated with catchment wetness conditions. The saturation spatial pattern, which was partially related to the topographic index, was very patchy throughout the catchment, suggesting the influence of other factors associated with past agricultural activities, including changes in local topography and soil properties. The relationship between water table levels and stream flow was weak, especially during the wetting‐up period, suggesting little connection between ground water and the hydrological response, at least at some locations. The results suggest that in drier and human‐disturbed environments, such as sub‐Mediterranean mountains, saturation patterns cannot be represented only by the general topography of the catchment. They also suggest that groundwater storage and runoff is not a succession of steady‐state flow conditions, as assumed in most hydrological models. Copyright © 2013 John Wiley & Sons, Ltd.     

Spatio‐temporal variability of Great Lakes basin snow cover ablation events

In the Great Lakes basin of North America, annual run‐off is dominated by snowmelt. This snowmelt‐induced run‐off plays an important role within the hydrologic cycle of the basin, influencing soil moisture availability and driving the seasonal cycle of spring and summer lake levels. Despite this, relatively little is understood about the patterns and trends of snow ablation event frequency and magnitude within the Great Lakes basin. This study uses a gridded dataset of Canadian and United States surface snow depth observations to develop a regional climatology of snow ablation events from 1960 to 2009. An ablation event is defined as an interdiurnal snow depth decrease within an individual grid cell. A clear seasonal cycle in ablation event frequency exists within the basin and peak ablation event probability is latitudinally dependent. Most of the basin experiences peak ablation frequency in March, while the northern and southern regions of the basin experience respective peaks in April and February. An investigation into the interannual frequency of ablation events reveals ablation events significantly decrease within the northeastern and northwestern Lake Superior drainage basins and significantly increase within the eastern Lake Huron and Georgian Bay drainage basins. In the eastern Lake Huron and Georgian Bay drainage basins, larger ablation events are occurring more frequently, and a larger impact to the hydrology can be expected. Trends in ablation events are attributed primarily to changes in snowfall and snow depth across the region.     

Statistical probability distribution of snow depth at the model sub‐grid cell spatial scale

Comprehensive snow depth data, collected using georadar and hand probing, were used for statistical analyses of snow depths inside 1 km grid cells. The sub‐grid cell spatial scale was 100 m. Statistical distribution functions were found to have varying parameters, and an attempt was made to connect these statistical parameters to different terrain variables. The results showed that the two parameters mean and standard deviation of snow depth were significantly related to the sub‐grid terrain characteristics. Linear regression models could explain up to 50% of the variation for both of the snowcover parameters mentioned. Copyright © 2004 John Wiley & Sons, Ltd.     

Spatial patterns and temporal stability of soil moisture across a range of scales in a semi‐arid environment

The antecedent soil moisture status of a catchment is an important factor in hydrological modelling. Traditional Hortonian infiltration models assume that the initial moisture content is constant across the whole catchment, despite the fact that even in small catchments antecedent soil moisture exhibits tremendous spatial heterogeneity. Spatial patterns of soil water distribution across three transects (two in a burnt area and one in an unburnt area) in a semi‐arid area were studied. At the transect scale, when the factors affecting soil moisture were limited to topographical position or local topography, spatial patterns showed time stability, but when other factors, such as vegetation, were taken into account, the spatial patterns became time unstable. At the point scale, and in the same areas, topographical position was the main factor controlling time stability. Scale dependence of time stability was studied and local topography and vegetation presence were observed to play an important role for the correlation between consecutive measures depending on the scale. Copyright © 2000 John Wiley & Sons, Ltd.     

Spatial and temporal variability of pore‐water pressures in residual soil slopes in a tropical climate

It is critical to understand and quantify the temporal and spatial variability in hillslope hydrological data in order to advance hillslope hydrological studies, evaluate distributed parameter hydrological models, analyse variability in hydrological response of slopes and design efficient field data sampling networks. The spatial and temporal variability of field‐measured pore‐water pressures in three residual soil slopes in Singapore was investigated using geostatistical methods. Parameters of the semivariograms, namely the range, sill and nugget effect, revealed interesting insights into the spatial structure of the temporal situation of pore‐water pressures in the slopes. While informative, mean estimates have been shown to be inadequate for modelling purposes, indicator semivariograms together with mean prediction by kriging provide a better form of model input. Results also indicate that significant temporal and spatial variability in pore‐water pressures exists in the slope profile and thereby induces variability in hydrological response of the slope. Spatial and temporal variability in pore‐water pressure decreases with increasing soil depth. The variability decreases during wet conditions as the slope approaches near saturation and the variability increases with high matric suction development following rainfall periods. Variability in pore‐water pressures is greatest at shallow depths and near the slope crest and is strongly influenced by the combined action of microclimate, vegetation and soil properties. Copyright © 2002 John Wiley & Sons, Ltd.     

Spatio‐temporal variability of dryness/wetness in the Danube River Basin

The present study focuses on the analysis of dryness/wetness conditions in the Danube River catchment area from 1901 to 2013 based on reanalysis data. The spatio‐temporal variability of dryness/wetness conditions is analyzed by means of the Standardized Precipitation Index (SPI) for an accumulation periods of 6 months. To characterize the spatial variability of SPI6 at monthly time scales, an empirical orthogonal function (EOF) analysis was applied. The leading mode of SPI variability captures in‐phase variability of SPI over the entire catchment area of Danube River. The leading mode of dryness/wetness variability was found to be strongly related to the different phases of the Arctic Oscillation. The second and third modes of variability show a more regional character of the dryness/wetness variability over the Danube River catchment area. Based on a composite map analysis, between the time series corresponding to the first three leading modes of dryness/wetness variability and the geopotential height at 850 mb and precipitation totals, it is shown that dryness (wetness) conditions over the Danube catchment area are associated with an anticyclonic (cyclonic) circulation, transport of dry (humid) air towards the Danube catchment area and reduced (enhanced) number of rain days. Copyright © 2015 John Wiley & Sons, Ltd.     

Variability and trends in the annual snow‐cover cycle in Northern Hemisphere land areas, 1972–2000

This study investigated variability and trends in the annual snow‐cover cycle in regions covering high‐latitude and high‐elevation land areas in the Northern Hemisphere. The annual snow‐cover cycle was examined with respect to the week of the last‐observed snow cover in spring (WLS), the week of the first‐observed snow cover in autumn (WFS), and the duration of the snow‐free period (DSF). The analysis used a 29‐year time‐series (1972–2000) of weekly, visible‐band satellite observations of Northern Hemisphere snow cover from NOAA with corrections applied by D. Robinson of Rutgers University Climate Laboratory. Substantial interannual variability was observed in WLS, WFS and DSF (standard deviations of 0·8–1·1, 0·7–0·9 and 1·0–1·4 weeks, respectively), which is related directly to interannual variability in snow‐cover area in the regions and time periods of snow‐cover transition. Over the nearly three‐decade study period, WLS shifted earlier by 3–5 days/decade as determined by linear regression analysis. The observed shifts in the annual snow‐cover cycle underlie a significant trend toward a longer annual snow‐free period. The DSF increased by 5–6 days/decade over the study period, primarily as a result of earlier snow cover disappearance in spring. The observed trends are consistent with reported trends in the timing and length of the active growing season as determined from satellite observations of vegetation greenness and the atmospheric CO₂ record. Copyright © 2002 John Wiley & Sons, Ltd.     

Assessing regional‐scale spatio‐temporal patterns of groundwater–surface water interactions using a coupled SWAT‐MODFLOW model

Interaction between groundwater and surface water in watersheds has significant impacts on water management and water rights, nutrient loading from aquifers to streams, and in‐stream flow requirements for aquatic species. Of particular importance are the spatial patterns of these interactions. This study explores the spatio‐temporal patterns of groundwater discharge to a river system in a semi‐arid region, with methods applied to the Sprague River Watershed (4100 km²) within the Upper Klamath Basin in Oregon, USA. Patterns of groundwater–surface water interaction are explored throughout the watershed during the 1970–2003 time period using a coupled SWAT‐MODFLOW model tested against streamflow, groundwater level and field‐estimated reach‐specific groundwater discharge rates. Daily time steps and coupling are used, with groundwater discharge rates calculated for each model computational point along the stream. Model results also are averaged by month and by year to determine seasonal and decadal trends in groundwater discharge rates. Results show high spatial variability in groundwater discharge, with several locations showing no groundwater/surface water interaction. Average annual groundwater discharge is 20.5 m³/s, with maximum and minimum rates occurring in September–October and March–April, respectively. Annual average rates increase by approximately 0.02 m³/s per year over the 34‐year period, negligible compared with the average annual rate, although 70% of the stream network experiences an increase in groundwater discharge rate between 1970 and 2003. Results can assist with water management, identifying potential locations of heavy nutrient mass loading from the aquifer to streams and ecological assessment and planning focused on locations of high groundwater discharge. Copyright © 2016 John Wiley & Sons, Ltd.     

Modelling the spatial–temporal variability of spring snowmelt in an arctic catchment

Arctic spring landscapes are usually characterized by a mosaic of coexisting snow‐covered and bare ground patches. This phenomenon has major implications for hydrological processes, including meltwater production and runoff. Furthermore, as indicated by aircraft observations, it affects land‐surface–atmosphere exchanges, leading to a high degree of variability in surface energy terms during melt. The heterogeneity and related differences when certain parts of the landscape become snow free also affects the length of the growing season and the carbon cycle. Small‐scale variability in arctic snowmelt is addressed here by combining a spatially distributed end‐of‐winter snow cover with simulations of variable snowmelt energy balance factors for the small arctic catchment of Trail Valley Creek (63 km²). Throughout the winter, snow in arctic tundra basins is redistributed by frequent blowing snow events. Areas of above‐ or below‐average end‐of‐winter snow water equivalents were determined from land‐cover classifications, topography, land‐cover‐based snow surveys, and distributed surface wind‐field simulations. Topographic influences on major snowmelt energy balance factors (solar radiation and turbulent fluxes of sensible and latent heat) were modelled on a small‐scale (40 m) basis. A spatially variable complete snowmelt energy balance was subsequently computed and applied to the distributed snow cover, allowing the simulation of the progress of melt throughout the basin. The emerging patterns compared very well visually to snow cover observations from satellite images and aerial photographs. Results show the relative importance of variable end‐of‐winter snow cover, spatially distributed melt energy fluxes, and local advection processes for the development of a patchy snow cover. This illustrates that the consideration of these processes is crucial for an accurate determination of snow‐covered areas, as well as the location, timing, and amount of meltwater release from arctic catchments, and should, therefore, be included in hydrological models. Furthermore, the study shows the need for a subgrid parameterization of these factors in the land surface schemes of larger scale climate models. Copyright © 2005 John Wiley & Sons, Ltd.     

The spatio‐temporal variability of annual precipitation and its local impact factors during 1724–2010 in Beijing,China

Rapid population growth and increased economic activity impose an urgent challenge on the sustainability of water resources in Beijing. Understanding the spatial and temporal variability of precipitation is of the upmost importance in order to sustain the region's water resources. Two time series, one long term (1724–2010) from a single meteorological station and a shorter time series (1980–2010) from 20 different meteorological stations within the Beijing area, were analysed using Linear Regression, Moving Average, Mann–Kendall, Rescaled Range and Spatial Interpolation methods. Results from both the long‐ and short‐term meteorological data show a mean annual precipitation rate of 600 mm and 540 mm respectively. Annual precipitation rates have decreased during the 21st century by an estimated 100 mm or 16% in comparison to the 1990s. The 1980–2010 data show an increase in precipitation during the early 1990s followed by a sharp decrease during the subsequent years. The change of annual precipitation with time is more random and diverse in comparison to space. The main local impact factors (terrain, urbanization and elevation) and how they work on the local precipitation especially the spatial diversity are identified qualitatively. Generally speaking, (1) the annual precipitation of the plain area is more than that of the mountainous area (terrain effect), (2) the annual precipitation of the urban area in the plain area is obviously more than that of the surrounding suburb area (urbanization effect) and (3) the annual precipitation of the lower location is approximately more than that of the higher location (elevation effect). Copyright © 2013 John Wiley & Sons, Ltd.     

Traffic‐induced variability in dynamic properties of cable‐stayed bridge

The traffic‐induced variability in the dynamic properties of a cable‐stayed bridge is investigated using ambient vibration measurements. Under a relatively steady wind and temperature environment, the ambient vibration test was conducted on the bridge with normal traffic conditions and totally 24 h acceleration response time histories were recorded. These data are divided into 12 sections with each data section containing 2 h measurements. Thereby the modal variability due to changing traffic loading is investigated through post‐processing of the data in each section in both amplitude and frequency domains. The result indicates that the natural frequencies of the global modes can exhibit as much as 1% variation within a day. The modal amplitudes of each mode as well as the modal deflection at each measurement position vary insignificantly. The damping ratios however are sensitive to the vibration intensity, especially when the deck vibration exceeds a certain level. Copyright © 2002 John Wiley & Sons, Ltd.