Spatial variability of snowmelt timing from AMSR‐E and SSM/I passive microwave sensors,Pelly River,Yukon Territory,Canada

Spring snow melt run‐off in high latitude and snow‐dominated drainage basins is generally the most significant annual hydrological event. Melt timing, duration, and flow magnitude are highly variable and influence regional climate, geomorphology, and hydrology. Arctic and sub‐arctic regions have sparse long‐term ground observations and these snow‐dominated hydrologic regimes are sensitive to the rapidly warming climate trends that characterize much of the northern latitudes. Passive microwave brightness temperatures are sensitive to changes in the liquid water content of the snow pack and make it possible to detect incipient melt, diurnal melt‐refreeze cycles, and the approximate end of snow cover on the ground over large regions. Special Sensor Microwave Imager (SSM/I) and Advanced Microwave Scanning Radiometer for EOS (AMSR‐E) passive microwave brightness temperatures (T_b) and diurnal amplitude variations (DAV) are used to investigate the spatial variability of snowmelt onset timing (in two stages, ‘DAV onset’ and ‘melt onset’) and duration for a complex sub‐arctic landscape during 2005. The satellites are sensitive to small percentages of liquid water, and therefore represent ‘incipient melt’, a condition somewhat earlier than a traditional definition of a melting snowpack. Incipient melt dates and duration are compared to topography, land cover, and hydrology to investigate the strength and significance of melt timing in heterogeneous landscapes in the Pelly River, a major tributary to the Yukon River. Microwave‐derived melt onset in this region in 2005 occurred from late February to late April. Upland areas melt 1–2 weeks later than lowland areas and have shorter transition periods. Melt timing and duration appear to be influenced by pixel elevation, aspect, and uniformity as well as other factors such as weather and snow mass distribution. The end of the transition season is uniform across sensors and across the basin in spite of a wide variety of pixel characteristics. Copyright © 2007 John Wiley & Sons, Ltd.     

A temperature‐precipitation‐based model of thirty‐year mean snowpack accumulation and melt in Oregon,USA

High‐resolution, spatially extensive climate grids can be useful in regional hydrologic applications. However, in regions where precipitation is dominated by snow, snowmelt models are often used to account for timing and magnitude of water delivery. We developed an empirical, nonlinear model to estimate 30‐year means of monthly snowpack and snowmelt throughout Oregon. Precipitation and temperature for the period 1971–2000, derived from 400‐m resolution PRISM data, and potential evapotranspiration (estimated from temperature and day length) drive the model. The model was calibrated using mean monthly data from 45 SNOTEL sites and accurately estimated snowpack at 25 validation sites: R² = 0·76, Nash‐Sutcliffe Efficiency (NSE) = 0·80. Calibrating it with data from all 70 SNOTEL sites gave somewhat better results (R² = 0·84, NSE = 0·85). We separately applied the model to SNOTEL stations located < 200 and ≥ 200 km from the Oregon coast, since they have different climatic conditions. The model performed equally well for both areas. We used the model to modify moisture surplus (precipitation minus potential evapotranspiration) to account for snowpack accumulation and snowmelt. The resulting values accurately reflect the shape and magnitude of runoff at a snow‐dominated basin, with low winter values and a June peak. Our findings suggest that the model is robust with respect to different climatic conditions, and that it can be used to estimate potential runoff in snow‐dominated basins. The model may allow high‐resolution, regional hydrologic comparisons to be made across basins that are differentially affected by snowpack, and may prove useful for investigating regional hydrologic response to climate change. Published in 2011 by John Wiley & Sons, Ltd.     

SNOW WETNESS ESTIMATES OF VEGETATED TERRAIN FROM SATELLITE PASSIVE MICROWAVE DATA

The Special Sensor Microwave/Imager (SSM/I) radiometer is a useful tool for monitoring snow wetness on a large scale because water content has a significant effect on the microwave emissions at the snowpack surface. To date, SSM/I snow wetness algorithms, based on statistical regression analysis, have been developed only for specific regions. Inadequate ground-based snow wetness measurements and the non-linearity between SSM/I brightness temperatures (T_Bs) and snow wetness over varied vegetation covered terrain has impeded the development of a general model. In this study, we used a previously developed linear relationship between snowpack surface wetness (% by volume) and concurrent air temperature (°C) to estimate the snow wetness at ground weather stations. The snow condition (snow free, dry, wet or refrozen snow) of each SSM/I pixel (a 37 × 29 km area at 37.0 GHz) was determined from ground-measured weather data and the T_B signature. SSM/I T_Bs of wet snow were then linked with the snow wetness estimates as an input/output relationship. A single-hidden-layer back-propagation (backprop) artificial neural network (ANN) was designed to learn the relationships. After training, the snow wetness values estimated by the ANN were compared with those derived by regression models. Results show that the ANN performed better than the existing regression models in estimating snow wetness from SSM/I data over terrain with different amounts of vegetation cover.     

Combining MODIS and AMSR‐E observations to improve MCD43A3 short‐time snow‐covered Albedo estimation

Land surface albedo plays an important role in the radiation budget and global climate models. NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) provide 16‐day albedo product with 500‐m resolution every 8 days (MCD43A3). Some in‐situ albedo measurements were used as the true surface albedo values to validate the MCD43A3 product. As the 16‐day MODIS albedo retrievals do not include snow observations when there is ephemeral snow on the ground surface in a 16‐day period, comparisons between MCD43A3 and 16 day averages of field data do not agree well. Another reason is that the MODIS cannot detect the snow when the area is covered by clouds. The Advanced Microwave Scanning Radiometer for EOS (AMSR‐E) data are not affected by weather conditions and are a good supplement for optical remote sensing in cloudy weather. When the surface is covered by ephemeral snow, the AMSR‐E data can be used as the additional information to retrieve the snow albedo. In this study, we developed an improved method by using the MODIS products and the AMSR‐E snow water equivalent (SWE) product to improve the MCD43A3 short‐time snow‐covered albedo estimation. The MODIS daily snow products MOD10A1 and MYD10A1 both provide snow and cloud information from observations. In our study region, we updated the MODIS daily snow product by combining MOD10A1 and MYD10A1. Then, the product was combined with the AMSR‐E SWE product to generate new daily snow‐cover and SWE products at a spatial resolution of 500 m. New SWE datasets were integrated into the Noah Land Surface Model snow model to calculate the albedo above a snow surface, and these values were then utilized to improve the MODIS 16‐day albedo product. After comparison of the results with in‐situ albedo measurements, we found that the new corrected 16‐day albedo can show the albedo changes during the short snowfall season. For example, from January 25 to March 14, 2007 at the BJ site, the albedo retrieved from snow‐free observations does not indicate the albedo changes affected by snow; the improved albedo conforms well to the in‐situ measurements. The correlation coefficient of the original MODIS albedo and the in‐situ albedo is 0.42 during the ephemeral snow season, but the correlation coefficient of the improved MODIS albedo and the in‐situ albedo is 0.64. It is concluded that the new method is capable of capturing the snow information from AMSR‐E SWE to improve the short‐time snow‐covered albedo estimation. Copyright © 2012 John Wiley & Sons, Ltd.     

One‐year‐long runoff forecast by a single snowpack evaluation

A degree‐day‐based model is presented for a 1 year ahead runoff forecast, with 1 day time steps. The input information is a single snowpack evaluation collected at the beginning of the snowmelt season. The snow‐cover dynamics, the key information for long‐term snowmelt forecast, are described by the snow‐line dynamics, i.e. by the movements of the downhill snowpack limit. The snowmelt volume, estimated by the snow‐line dynamics, is the exogenous input of an autoregressive transformation model. The model is calibrated by a least‐squares procedure on the basis of observed daily runoff data and the corresponding measurements of the snowpack volume (one measurement per year). A real‐world case study on the Alto Tunuyan River basin (2380 km², Argentinean Andes) is presented. The 1 year ahead Alto Tunuyan River runoff patterns, computed for both calibration and validation periods, reveal high agreement with observed streamflows. Copyright © 2004 John Wiley & Sons, Ltd.     

Pixel‐scale evaluation of SSM/I sea‐ice algorithms in the marginal ice zone during early fall freeze‐up

Observed reduction in recent sea ice areal extent and thickness has focused attention on the fact that the Arctic marine system appears to be responding to global‐scale climate variability and change. Passive microwave remote‐sensing data are the primary source underpinning these reports, yet problems remain in geophysical inversion of information on ice type and concentration. Uncertainty in sea‐ice concentration (SIC) retrievals is highest in the summer and fall, when water occurs in liquid phase within the snow–sea‐ice system. Of particular scientific interest is the timing and rate of new ice formation due to the control that this form of sea ice has on mass, energy and gas fluxes across the ocean–sea‐ice–atmosphere interface. In this paper we examine the critical fall freeze‐up period using in situ data from a ship‐based and aerial survey programme known as the Canadian Arctic Shelf Exchange study combined with microwave and optical Earth observations data. Results show that: (1) the overall physical conditions observed from aerial survey photography were well matched with coincident moderate‐resolution imaging spectroradiometer data and Radarsat ScanSAR imagery; (2) the shortwave albedo was linearly related to old ice concentration derived from survey photography; (3) the three SSM/I SIC algorithms (NASA Team (NT), NASA Team 2 (NT2), and Bootstrap (BT)) showed considerable discrepancies in pixel‐scale comparison with the Radarsat ScanSAR SICs well calibrated by the aerial survey data. The major causes of the discrepancies are attributed to (1) the inherent inability to detect the new thin ice in the NT and BT algorithms, (2) mismatches of the thin‐ice tie point of the NT2 algorithm, and (3) sub‐pixel ambiguity between the thin ice and the mixture of open water and sea ice. These results suggest the need for finer resolution of passive microwave sensors, such as AMSR‐E, to improve the precision of the SSM/I SIC algorithms in the marginal ice zone during early fall freeze‐up. Copyright © 2006 John Wiley & Sons, Ltd.     

Development of a rain‐on‐snow detection algorithm using passive microwave radiometry

Currently observed climate warming in the Arctic has numerous consequences. Of particular relevance, the precipitation regime is modified where mixed and liquid precipitation can occur during the winter season leading to rain‐on‐snow (ROS) events. This phenomenon is responsible for ice crust formation, which has a significant impact on ecosystems (such as biological, hydrological, ecological and physical processes). The spatially and temporally sporadic nature of ROS events makes the phenomenon difficult to monitor using meteorological observations. This paper focuses on the detection of ROS events using passive microwave (PMW) data from a modified brightness temperature (T_B) gradient approach at 19 and 37 GHz. The approach presented here was developed empirically for observed ROS events with coincident ground‐based PMW measurements in Sherbrooke, Quebec, Canada. It was then tested in Nunavik, Quebec, with the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR‐E). We obtained a detection accuracy of 57, 71 and 89% for ROS detection for three AMSR‐E grid cells with a maximum error of 7% when considering all omissions and commissions with regard to the total number of AMSR‐E passes throughout the winter period. Copyright © 2016 John Wiley & Sons, Ltd.     

A new approach of dynamic monitoring of 5‐day snow cover extent and snow depth based on MODIS and AMSR‐E data from Northern Xinjiang region

Taking the Northern Xinjiang region as an example, we develop a snow depth model by using the Advanced Microwave Scanning Radiometer‐Earth Observing System (AMSR‐E) horizontal and vertical polarization brightness temperature difference data of 18 and 36 GHz bands and in situ snow depth measurements from 20 climatic stations during the snow seasons November–March) of 2002–2005. This article proposes a method to produce new 5‐day snow cover and snow depth images, using Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) daily snow cover products and AMSR‐E snow water equivalent and daily brightness temperature products. The results indicate that (1) the brightness temperature difference (Tb_18h–Tb_36h) provides the most accurate and precise prediction of snow depth; (2) the snow, land and overall classification accuracies of the new images are separately 89.2%, 77.7% and 87.2% and are much better than those of AMSR‐E or MODIS products (in all weather conditions) alone; (3) the snow classification accuracy increases as snow depth increases; and (4) snow accuracies for different land cover types vary as 88%, 92.3%, 79.7% and 80.1% for cropland, grassland, shrub, and urban and built‐up, respectively. We conclude that the new 5‐day snow cover–snow depth images can provide both accurate cloud‐free snow cover extent and the snow depth dynamics, which would lay a scientific basis for water management and prevention of snow‐related disasters in this dry and cold pastoral area. After validations of the algorithms over other regions with different snow and climate conditions, this method would also be used for monitoring snow cover and snow depth elsewhere in the world. Copyright © 2011 John Wiley & Sons, Ltd.     

Uncertainty of snow water equivalent retrieved from AMSR‐E brightness temperature in northeast Asia

Accurate estimation of snow water equivalent (SWE) has been significantly recognized to improve management and analyses of water resource in specific regions. Although several studies have focused on developing SWE values based on remotely sensed brightness temperatures obtained by microwave sensor systems, it is known that there are still a number of uncertainties in SWE values retrieved from microwave radiometers. Therefore, further research for improving remotely sensed SWE values including global validation should be conducted in unexplored regions such as Northeast Asia. In this regard, we evaluated SWE through comparison of values produced by the Advanced Microwave Scanning Radiometer Earth Observing System (AMSR‐E) from December 2002 to February 2011 with in situ SWE values converted from snow‐depth observation data from four regions in the South Korea. The results from three areas showed similarities which indicated that the AMSR‐E SWE values were overestimated when compared with in situ SWE values, and their Mean Absolute Errors (MAE) by month were relatively small (1.1 to 6.5 mm). Contrariwise, the AMSR‐E SWE values of one area were significantly underestimated when compared with in situ SWE values and the MAE were much greater (4.9 to 35.2 mm). These results were closely related to AMSR‐E algorithm‐related error sources, which we analyzed with respect to topographic characteristics and snow properties. In particular, we found that snow density data used in the AMSR‐E SWE algorithm should be based on reliable in situ data as the current AMSR‐E SWE algorithm cannot reflect the spatio‐temporal variability of snow density values. Additionally, we derived better results considering saturation effect of AMSR‐E SWE. Despite the demise of AMSR‐E, this study's analysis is significant for providing a baseline for the new sensor and suggests parameters important for obtaining more reliable SWE. Copyright © 2013 John Wiley & Sons, Ltd.     

On the evaluation of snow water equivalent estimates over the terrestrial Arctic drainage basin

Comparisons between snow water equivalent (SWE) and river discharge estimates are important in evaluating the SWE fields and to our understanding of linkages in the freshwater cycle. In this study, we compared SWE drawn from land surface models and remote sensing observations with measured river discharge (Q) across 179 Arctic river basins. Over the period 1988‐2000, basin‐averaged SWE prior to snowmelt explains a relatively small (yet statistically significant) fraction of interannual variability in spring (April–June) Q, as assessed using the coefficient of determination (R²). Averaged across all basins, mean R²s vary from 0·20 to 0·28, with the best agreement noted for SWE drawn from a simulation with the Pan‐Arctic Water Balance Model (PWBM) forced with data from the European Centre for Medium‐Range Weather‐Forecasts (ECMWF) Re‐analysis (ERA‐40). Variability and magnitude in SWE derived from Special Sensor Microwave Imager (SSM/I) data are considerably lower than the variability and magnitude in SWE drawn from the land surface models, and generally poor agreement is noted between SSM/I SWE and spring Q. We find that the SWE versus Q comparisons are no better when alternate temporal integrations–using an estimate of the timing in basin thaw–are used to define pre‐melt SWE and spring Q. Thus, a majority of the variability in spring discharge must arise from factors other than basin snowpack water storage. This study demonstrates how SWE estimated from remote sensing observations, or general circulation models (GCMs), can be evaluated effectively using monthly discharge data or SWE from a hydrological model. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of melt‐freeze‐cycles on the radionuclide transport in homogeneous laboratory snowpack

Radionuclides released to the environment and deposited with or onto snow can be stored over long time periods if ambient temperature stays low, particularly in glaciated areas or high alpine sites. The radionuclides will be accumulated in the snowpack during the winter unless meltwater runoff at the snow base occurs. They will be released to surface waters within short time during snowmelt in spring. In two experiments under controlled melting conditions of snow in the laboratory, radionuclide migration and runoff during melt‐freeze‐cycles were examined. The distribution of Cs‐134 and Sr‐85 tracers in homogeneous snow columns and their fractionation and potential preferential elution in the first meltwater portions were determined. Transport was associated with the percolation of meltwater at ambient temperatures above 0 °C after the snowpack became ripe. Mean migration velocities in the pack were examined for both nuclides to about 0.5 cm hr^?1 after one diurnal melt‐freeze‐cycle at ambient temperatures of ?2 to 4 °C. Meltwater fluxes were calculated with a median of 1.68 cm hr^?1. Highly contaminated portions of meltwater with concentration factors between 5 and 10 against initial bulk concentrations in the snowpack were released as ionic pulse with the first meltwater. Neither for caesium nor strontium preferential elution was observed. After recurrent simulated day‐night‐cycles (?2 to 4 °C), 80% of both radionuclides was released with the first 20% of snowmelt within 4 days. 50% of Cs‐134 and Sr‐85 were already set free after 24 hr. Snowmelt contained highest specific activities when the melt rate was lowest during the freeze‐cycles due to concentration processes in remaining liquids, enhanced by the melt‐freeze‐cycling. This implies for natural snowpack after significant radionuclide releases, that long‐time accumulation of radionuclides in the snow during frost periods, followed by an onset of steady meltwater runoff at low melt rates, will cause the most pronounced removal of the contaminants from the snow cover. This scenario represents the worst case of impact on water quality and radiation exposure in aquatic environments.     

A modelling framework to simulate field‐scale nitrate response and transport during snowmelt: The WINTRA model

Modelling nutrient transport during snowmelt in cold regions remains a major scientific challenge. A key limitation of existing nutrient models for application in cold regions is the inadequate representation of snowmelt, including hydrological and biogeochemical processes. This brief period can account for more than 80% of the total annual surface runoff in the Canadian Prairies and Northern Canada and processes such as atmospheric deposition, overwinter redistribution of snow, ion exclusion from snow crystals, frozen soils, and snow‐covered area depletion during melt influence the distribution and release of snow and soil nutrients, thus affecting the timing and magnitude of snowmelt runoff nutrient concentrations. Research in cold regions suggests that nitrate (NO₃) runoff at the field‐scale can be divided into 5 phases during snowmelt. In the first phase, water and ions originating from ion‐rich snow layers travel and diffuse through the snowpack. This process causes ion concentrations in runoff to gradually increase. The second phase occurs when this snow ion meltwater front has reached the bottom of the snowpack and forms runoff to the edge‐of‐the‐field. During the third and fourth phases, the main source of NO₃ transitions from the snowpack to the soil. Finally, the fifth and last phase occurs when the snow has completely melted, and the thawing soil becomes the main source of NO₃ to the stream. In this research, a process‐based model was developed to simulate hourly export based on this 5‐phase approach. Results from an application in the Red River Basin of southern Manitoba, Canada, shows that the model can adequately capture the dynamics and rapid changes of NO₃ concentrations during this period at relevant temporal resolutions. This is a significant achievement to advance the current nutrient modelling paradigm in cold climates, which is generally limited to satisfactory results at monthly or annual resolutions. The approach can inform catchment‐scale nutrient models to improve simulation of this critical snowmelt period.     

Determination of snow water equivalent over the eastern part of Turkey using passive microwave data

Information on regional snow water equivalent (SWE) is required for the management of water generated from snowmelt. Modeling of SWE in the mountainous regions of eastern Turkey, one of the major headwaters of Euphrates–Tigris basin, has significant importance in forecasting snowmelt discharge, especially for optimum water usage. An assimilation process to produce daily SWE maps is developed based on Helsinki University of Technology (HUT) model and AMSR‐E passive microwave data. The characteristics of the HUT emission model are analyzed in depth and discussed with respect to the extinction coefficient function. A new extinction coefficient function for the HUT model is proposed to suit models for snow over mountainous areas. Performance of the modified model is checked against the original, other modified cases and ground truth data covering the 2003–2007 winter periods. A new approach to calculate grain size and density is integrated inside the developed data assimilation process. An extensive validation was successfully performed by means of snow data measured at ground stations during the 2008–2010 winter periods. The root mean square error of the data set for snow depth and SWE between January and March of the 2008–2010 periods compared with the respective AMSR‐E footprints indicated that errors for estimated snow depth and predicted SWE values were 16.92 cm and 40.91 mm, respectively, for the 3‐year period. Validation results were less satisfactory for SWE less than 75.0 mm and greater than 150.0 mm. An underestimation for SWE greater than 150 mm could not be resolved owing to the microwave signal saturation that is observed for dense snowpack. Copyright © 2012 John Wiley & Sons, Ltd.     

Development and application of a spatially‐distributed Arctic hydrological and thermal process model (ARHYTHM)

A process‐based, spatially distributed hydrological model was developed to quantitatively simulate the energy and mass transfer processes and their interactions within arctic regions (arctic hydrological and thermal model, ARHYTHM). The model first determines the flow direction in each element, the channel drainage network and the drainage area based upon the digital elevation data. Then it simulates various physical processes: including snow ablation, subsurface flow, overland flow and channel flow routing, soil thawing and evapotranspiration. The kinematic wave method is used for conducting overland flow and channel flow routing. The subsurface flow is simulated using the Darcian approach. The energy balance scheme was the primary approach used in energy‐related process simulations (snowmelt and evapotranspiration), although there are options to model snowmelt by the degree‐day method and evapotranspiration by the Priestley–Taylor equation. This hydrological model simulates the dynamic interactions of each of these processes and can predict spatially distributed snowmelt, soil moisture and evapotranspiration over a watershed at each time step as well as discharge in any specified channel(s). The model was applied to Imnavait watershed (about 2·2 km²) and the Upper Kuparuk River basin (about 146 km²) in northern Alaska. Simulated results of spatially distributed soil moisture content, discharge at gauging stations, snowpack ablations curves and other results yield reasonable agreement, both spatially and temporally, with available data sets such as SAR imagery‐generated soil moisture data and field measurements of snowpack ablation, and discharge data at selected points. The initial timing of simulated discharge does not compare well with the measured data during snowmelt periods mainly because the effect of snow damming on runoff was not considered in the model. Results from the application of this model demonstrate that spatially distributed models have the potential for improving our understanding of hydrology for certain settings. Finally, a critical component that led to the performance of this modelling is the coupling of the mass and energy processes. Copyright © 2000 John Wiley & Sons, Ltd.     

Comparing response of SDF systems to near‐fault and far‐fault earthquake motions in the context of spectral regions

In spite of important differences in structural response to near‐fault and far‐fault ground motions, this paper aims at extending well‐known concepts and results, based on elastic and inelastic response spectra for far‐fault motions, to near‐fault motions. Compared are certain aspects of the response of elastic and inelastic SDF systems to the two types of motions in the context of the acceleration‐, velocity‐, and displacement‐sensitive regions of the response spectrum, leading to the following conclusions. (1) The velocity‐sensitive region for near‐fault motions is much narrower, and the acceleration‐sensitive and displacement‐sensitive regions are much wider, compared to far‐fault motions; the narrower velocity‐sensitive region is shifted to longer periods. (2) Although, for the same ductility factor, near‐fault ground motions impose a larger strength demand than far‐fault motions—both demands expressed as a fraction of their respective elastic demands—the strength reduction factors R_y for the two types of motions are similar over corresponding spectral regions. (3) Similarly, the ratio u_m/u₀ of deformations of inelastic and elastic systems are similar for the two types of motions over corresponding spectral regions. (4) Design equations for R_y (and for u_m/u₀) should explicitly recognize spectral regions so that the same equations apply to various classes of ground motions as long as the appropriate values of T_a, T_b and T_c are used. (5) The Veletsos–Newmark design equations with T_a=0.04 s, T_b=0.35 s, and T_c=0.79 s are equally valid for the fault‐normal component of near‐fault ground motions. Copyright © 2001 John Wiley & Sons, Ltd.     

Estimation of seismic demands on isolators in asymmetric buildings using non‐linear analysis

A procedure based on rigorous non‐linear analysis is presented that estimates the peak deformation among all isolators in an asymmetric building due to strong ground motion. The governing equations are reduced to a form such that the median normalized deformation due to an ensemble of ground motions with given corner period T_d depends primarily on four global parameters of the isolation system: the isolation period T_b, the normalized strength η, the torsional‐to‐lateral frequency ratio Ω_θ, and the normalized stiffness eccentricity e_b/r. The median ratio of the deformations of the asymmetric and corresponding symmetric systems is shown to depend only weakly on T_b, η, and Ω_θ, but increases with e_b/r. The equation developed to estimate the largest ratio among all isolators depends only on the stiffness eccentricity and the distance from the center of mass to the outlying isolator. This equation, multiplied by an earlier equation for the deformation of the corresponding symmetric system, provides a design equation to estimate the deformations of asymmetric systems. This design equation conservatively estimates the peak deformation among all isolators, but is generally within 10% of the ‘exact’ value. Relative to the non‐linear procedure presented, the peak isolator deformation is shown to be significantly underestimated by the U.S. building code procedures. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling snowpack surface temperature in the Canadian Prairies using simplified heat flow models

Three practical schemes for computing the snow surface temperature T_s, i.e. the force–restore method (FRM), the surface conductance method (SCM), and the Kondo and Yamazaki method (KYM), were assessed with respect to T_s retrieved from cloud‐free, NOAA‐AVHRR satellite data for three land‐cover types of the Paddle River basin of central Alberta. In terms of R², the mean T_s, the t‐test and F‐test, the FRM generally simulated more accurate T_s than the SCM and KYM. The bias in simulated T_s is usually within several degrees Celsius of the NOAA‐AVHRR T_s for both the calibration and validation periods, but larger errors are encountered occasionally, especially when T_s is substantially above 0 °C. Results show that the simulated T_s of the FRM is more consistent than that of the SCM, which in turn was more consistent than that of the KYM. This is partly because the FRM considers two aspects of heat conduction into snow, a stationary‐mean diurnal (sinusoidal) temperature variation at the surface coupled to a near steady‐state ground heat flux, whereas the SCM assumes a near steady‐state, simple heat conduction, and other simplifying assumptions, and the KYM does not balance the snowpack heat fluxes by assuming the snowpack having a vertical temperature profile that is linear. Copyright © 2005 John Wiley & Sons, Ltd.     

A change detection algorithm for terrain surface moisture mapping based on multi‐year passive microwave remote sensing (Examples of SSM/I and TMI Channels)

As an indication of the surface polarized emission, a polarization index (PI) of microwave radiance from the terrain surface (half‐space of canopy‐soil land) is derived from the radiative transfer model. This PI separates the radiance effects of the canopy‐soil moisture and interference from surface roughness and atmosphere, and is suitable to describe the change of terrain surface moisture, especially for extreme drought or flood conditions. As an example, the statistics of the monthly average < PI > from 6 years' data of the Defense Meteorological Satellite Program (DMSP) SSM/I observations at the lowest frequency 19·35 GHz channel as available are applied for the demonstration of the surface moisture status over a large and heterogeneous territory such as China. The deviation of the PI data at the same month from the average < PI > , i.e. Δ_nPI(≡(PI? < PI>)/ < PI>), gives prominence to focusing moisture variation of terrain surface, and its anomaly shows possible drought or flood occurrence in extreme conditions. The Δ_nPI mapping is validated by the typical examples of the drought in China's Shanxi area in May 2001 and the flood around China's Yangtze River in August 1998, respectively. Our approach is recommended for lower frequency channels to minimize the influence from vegetation canopy for future applications (such as the channels of the Advanced Microwave Scanning Radiometer [AMSR‐E] launched in May 2002 and microwave imaging radiometer of China's Fengyun satellite series). When the monthly < PI > and the ground truth of average volumetric moisture < m_v > of the region are correctly evaluated, it is tractable to retrieve the soil land surface moisture by using the PI data at the same month and the same region without much knowledge of surface roughness, vegetation canopy and other factors. As an example, the retrieval of m_v is favourably tested by using the Tropical Rainfall Measuring Mission (TRMM) Tropical Microwave Imager (TMI) data. Copyright © 2007 John Wiley & Sons, Ltd.     

A bed‐load transport model for rough turbulent open‐channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation i_bs_b = e_bω, where i_b is the immersed bed‐load transport rate, ω is flow power per unit area, e_b is the efficiency coefficient, and s_b is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s_b and e_b in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation i_b = ω G ^3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to i_b = ω where G approaches 1 in the sheet‐flow regime. That i_b = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i_b is a transport rate that must be multiplied by s_b to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is i_bs_b/ω, which is approximately 0·6 when i_b = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.     

First‐year sea ice spring melt transitions in the Canadian Arctic Archipelago from time‐series synthetic aperture radar data, 1992–2002

This paper synthesizes 10‐years' worth of interannual time‐series space‐borne ERS‐1 and RADARSAT‐1 synthetic aperture radar (SAR) data collected coincident with daily measurement of snow‐covered, land‐fast first‐year sea ice (FYI) geophysical and surface radiation data collected from the Seasonal Sea Ice Monitoring and Modeling Site, Collaborative‐Interdisciplinary Cryospheric Experiment and 1998 North Water Polynya study over the period 1992 to 2002. The objectives are to investigate the seasonal co‐relationship of the SAR time‐series dataset with selected surface mass (bulk snow thickness) and climate state variables (surface temperature and albedo) measured in situ for the purpose of measuring the interannual variability of sea ice spring melt transitions and validating a time‐series SAR methodology for sea ice surface mass and climate state parameter estimation. We begin with a review of the salient processes required for our interpretation of time‐series microwave backscatter from land‐fast FYI. Our results suggest that time‐series SAR data can reliably measure the timing and duration of surface albedo transitions at daily to weekly time‐scales and at a spatial scales that are on the order of hundreds of metres. Snow thickness on FYI immediately prior to melt onset explains a statistically significant portion of the variability in timing of SAR‐detected melt onset to pond onset for SAR time‐series that are made up of more than 25 images. Our results also show that the funicular regime of snowmelt, resolved in time‐series SAR data at a temporal resolution of approximately 2·5 images per week, is not detectable for snow covers less than 25 cm in thickness. Copyright © 2007 John Wiley & Sons, Ltd.