Long period Fourier amplitude spectra of strong motion acceleration

The empirical equations for scaling Fourier amplitude spectra in the frequency band from ~0·1 to 25 Hz can be extrapolated to describe the long period strong motion amplitudes. The results of this extrapolation can agree with (1) the seismological and field estimates of permanent ground displacement (near field), and with (2) the independent estimates of seismic moment and the observed frequencies of far field Fourier spectrum amplitudes.     

Duration of earthquake fault motion in California

Duration of high frequency (5–25 Hz) radiation of energy from earthquake sources in California is consistent with the estimates of fault length and with dislocation velocity estimates of 2–3 km/sec. This duration can be described by an exponential function of magnitude for 2·5 < M < 7·5. It is related to the times it takes the dislocation to spread over the fault width (1/f₂), and the fault length (～ 1/f₁), and to reach its ultimate amplitude (T₀). The results in this paper can be used to estimate the range of amplitudes and the duration of long period pulses of strong ground motion near faults, as these long period pulses can be related to the properties of high-frequency radiation from the source. Such pulses must be considered in the analyses of yielding structures, when the average peak acceleration of the pulse exceeds the yield resistance seismic coefficient of the structure.     

Relationship between soil moisture of near surface and multiple depths of the root zone under heterogeneous land uses and varying hydroclimatic conditions

This paper presents an assessment of the relationship between near-surface soil moisture (SM) and SM at other depths in the root zone under three different land uses: irrigated corn, rainfed corn and grass. This research addresses the question whether or not near-surface SM can be used reliably to predict plant available root zone SM and SM at other depths. For this study, a realistic soil-water energy balance process model is applied to three locations in Nebraska representing an east-to-west hydroclimatic gradient in the Great Plains. The applications were completed from 1982 through to 1999 at a daily time scale. The simulated SM climatologies are developed for the root zone as a whole and for the five layers of the soil profile to a depth of 1·2 m. Over all, the relationship between near-surface SM (0–2·5 cm) and plant available root zone SM is not strong. This applies to all land uses and for all locations. For example, r estimates range from 0·02 to 0·33 for this relationship. Results for near-surface SM and SM of several depths suggest improvement in r estimates. For example, these estimates range from − 0·19 to 0·69 for all land uses and locations. It was clear that r estimates are the highest (0·49–0·69) between near-surface and the second layer (2·5–30·5 cm) of the root zone. The strength of this type of relationship rapidly declines for deeper depths. Cross-correlation estimates also suggest that at various time-lags the strength of the relationship between near-surface SM and plant available SM is not strong. The strength of the relationship between SM modulation of the near surface and second layer over various time-lags slightly improves over no lags. The results suggest that use of near-surface SM for estimating SM at 2·5–30 cm is most promising. Copyright © 2007 John Wiley & Sons, Ltd.     

A supplementary approach for estimating reaeration rate coefficients

Different commonly used predictive equations for the reaeration rate coefficient (K₂) have been evaluated using 231 data sets obtained from the literature and 576 data sets measured at different reaches of the River Kali in western Uttar Pradesh, India. The data sets include stream/channel velocity, bed slope, flow depth, cross‐sectional area and reaeration rate coefficient (K₂), obtained from the literature and generated during the field survey of River Kali, and were used to test the applicability of the predictive equations. The K₂ values computed from the predictive equations have been compared with the corresponding K₂ values measured in streams/channels. The performance of the predictive equations has been evaluated using different error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and coefficient of determination (r²). The results show that the reaeration rate equation developed by Parkhurst and Pomeroy yielded the best agreement, with the values of SE, NME, MME and r² as 33·387, 4·62, 3·58 and 0·95, respectively, for literature data sets (case 1) and 37·567, 3·57, 2·6 and 0·95, respectively, for all the data sets (literature data sets and River Kali data sets) (case 2). Further, to minimize error estimates and improve correlation between measured and computed reaeration rate coefficients, supplementary predictive equations have been developed based on Froude number criteria and a least‐squares algorithm. The supplementary predictive equations have been verified using different error estimates and by comparing measured and computed reaeration rate coefficients for data sets not used in the development of the equations. Copyright © 2003 John Wiley & Sons, Ltd.     

Q and high-frequency strong motion spectra

Empirical scaling equations for Fourier amplitude spectra of strong ground motion are used to describe A₀ and τ in the assumed (high-frequency) shape of strong motion amplitudes: FS(_φ) = A₀e-^πτφ. The res of computed A₀ and τ with other related estimates of spectral amplitudes; (2) smooth decay of strong motion spectral amplitudes up to φ = 25 Hz, without an abrupt low-pass filtering of high frequecies; and (3) good agreement with other estimates of the regionally specific attenuation of high-frequncy seismic waves.As the recorded strong earthquake shaking in the western United States typically samples only the shallow (10 km) and local (100km) characteristics of wave attenuation, the processed strong motion accelerograms can be used as the most direct means of describing the nature of the high-frequency attenuation of the entire strong motion signal for use in earthquake engineering applications. Seismological body wave, Lg and coda wave estimates of Q sample different volumes of the crust surrounding the station, and involve different paths of the waves. These differences must be carefully documented and understood before the results can be used in earthquake engineering characterization of strong motion amplitudes.     

Active microwave remote sensing for soil moisture measurement: a field evaluation using ERS‐2

Active microwave remote sensing observations of backscattering, such as C‐band vertically polarized synthetic aperture radar (SAR) observations from the second European remote sensing (ERS‐2) satellite, have the potential to measure moisture content in a near‐surface layer of soil. However, SAR backscattering observations are highly dependent on topography, soil texture, surface roughness and soil moisture, meaning that soil moisture inversion from single frequency and polarization SAR observations is difficult. In this paper, the potential for measuring near‐surface soil moisture with the ERS‐2 satellite is explored by comparing model estimates of backscattering with ERS‐2 SAR observations. This comparison was made for two ERS‐2 overpasses coincident with near‐surface soil moisture measurements in a 6 ha catchment using 15‐cm time domain reflectometry probes on a 20 m grid. In addition, 1‐cm soil moisture data were obtained from a calibrated soil moisture model. Using state‐of‐the‐art theoretical, semi‐empirical and empirical backscattering models, it was found that using measured soil moisture and roughness data there were root mean square (RMS) errors from 3·5 to 8·5 dB and r² values from 0·00 to 0·25, depending on the backscattering model and degree of filtering. Using model soil moisture in place of measured soil moisture reduced RMS errors slightly (0·5 to 2 dB) but did not improve r² values. Likewise, using the first day of ERS‐2 backscattering and soil moisture data to solve for RMS surface roughness reduced RMS errors in backscattering for the second day to between 0·9 and 2·8 dB, but did not improve r² values. Moreover, RMS differences were as large as 3·7 dB and r² values as low as 0·53 between the various backscattering models, even when using the same data as input. These results suggest that more research is required to improve the agreement between backscattering models, and that ERS‐2 SAR data may be useful for estimating fields‐scale average soil moisture but not variations at the hillslope scale. Copyright © 2004 John Wiley & Sons, Ltd.     

Flow resistance in steep mountain streams

Resistance to flow at low to moderate stream discharge was examined in five small (12–77 km² drainage area) tributaries of Chilliwack River, British Columbia, more than half of which exhibit planar bed morphology. The resulting data set is composed of eight to 12 individual estimates of the total resistance to flow at 61 cross sections located in 13 separate reaches of five tributaries to the main river. This new data set includes 625 individual estimates of resistance to flow at low to moderate river stage. Resistance to flow in these conditions is high, highly variable and strongly dependent on stage. The Darcy–Weisbach resistance factor (ff) varies over six orders of magnitude (0·29–12 700) and Manning's n varies over three orders of magnitude (0·047–7·95). Despite this extreme range, both power equations at the individual cross sections and Keulegan equations for reach‐averaged values describe the hydraulic relations well. Roughness is divided into grain and form (considered as all non‐grain sources) components. Form roughness is the dominant component, accounting for about 90% of the total roughness of the system (i.e., form roughness is on average 8.6 times as great as grain roughness). Of the various quantitative and qualitative form‐roughness indicators observed, only the sorting coefficient (σ = D₈₄/D₅₀) correlates well with form roughness. Copyright © 2008 John Wiley & Sons, Ltd.     

Spatial features of mid-latitude field-line resonances from simultaneous ground-satellite measurements

Three series of simultaneous pulsation measurements (f<0.06 Hz) on the Freja satellite and at the Budkov Observatory have been spectrally processed (FFT) in 6-min intervals of Freja’s transits near the local Budkov field line. Doppler-shifted, weighted spectral-peak frequencies, determined in both transverse magnetic components in the mean field-aligned coordinate system on Freja, allowed the estimation, by comparison with the stable frequency at Budkov, of fundamental frequencies of the local magnetic-field-line resonance ranged from 13 to 17 mHz in two pulsation events analyzed, with K_p=2₊ to 0₊. The ratio of total amplitudes of the spectral-pulsation components on the ground and on Freja at an altitude of \sim1700 km (values <0.7) characterizes the transmissivity of the ionosphere. In the Pc3 frequency range this correlates well with simulation computations using models of the ionosphere under low solar activity.     

Near‐saturated surface soil hydraulic properties under different land uses in the St Denis National Wildlife Area,Saskatchewan, Canada

Surface soil hydraulic properties are key factors controlling the partition of rainfall and snowmelt into runoff and soil water storage, and their knowledge is needed for sound land management. The objective of this study was to evaluate the effects of three land uses (native grass, brome grass and cultivated) on surface soil hydraulic properties under near‐saturated conditions at the St Denis National Wildlife Area, Saskatchewan, Canada. For each land use, water infiltration rates were measured using double‐ring and tension infiltrometers at ?0·3, ?0·7, ?1·5 and ?2·2 kPa pressure heads. Macroporosity and unsaturated hydraulic properties of the surface soil were estimated. Mean field‐saturated hydraulic conductivity (K_fs), unsaturated hydraulic conductivity at ?0·3 kPa pressure head, inverse capillary length scale (α) and water‐conducting macroporosity were compared for different land uses. These parameters of the native grass and brome grass sites were significantly (p < 0·1) higher than that of the cultivated sites. At the ?0·3 kPa pressure head, hydraulic conductivity of grasslands was two to three times greater than that of cultivated lands. Values of α were about two times and values of K_fs about four times greater in grasslands than in cultivated fields. Water‐conducting macroporosity of grasslands and cultivated fields were 0·04% and 0·01% of the total soil volume, respectively. Over 90% of the total water flux at ?0·06 kPa pressure head was transmitted through pores > 1·36 × 10^?4 m in diameter in the three land uses. Land use modified near‐saturated hydraulic properties of surface soil and consequently may alter the water balance of the area by changing the amount of surface runoff and soil water storage. Copyright © 2004 John Wiley & Sons, Ltd.     

Spatio‐temporal distribution of near‐surface and root zone soil moisture at the catchment scale

Soil moisture is highly variable both spatially and temporally. It is widely recognized that improving the knowledge and understanding of soil moisture and the processes underpinning its spatial and temporal distribution is critical. This paper addresses the relationship between near‐surface and root zone soil moisture, the way in which they vary spatially and temporally, and the effect of sampling design for determining catchment scale soil moisture dynamics. In this study, catchment scale near‐surface (0–50 mm) and root zone (0–300 mm) soil moisture were monitored over a four‐week period. Measurements of near‐surface soil moisture were recorded at various resolutions, and near‐surface and root zone soil moisture data were also monitored continuously within a network of recording sensors. Catchment average near‐surface soil moisture derived from detailed spatial measurements and continuous observations at fixed points were found to be significantly correlated (r² = 0·96; P = 0·0063; n = 4). Root zone soil moisture was also found to be highly correlated with catchment average near‐surface, continuously monitored (r² = 0·81; P < 0·0001; n = 26) and with detailed spatial measurements of near‐surface soil moisture (r² = 0·84). The weaker relationship observed between near‐surface and root zone soil moisture is considered to be caused by the different responses to rainfall and the different factors controlling soil moisture for the soil depths of 0–50 mm and 0–300 mm. Aspect is considered to be the main factor influencing the spatial and temporal distribution of near‐surface soil moisture, while topography and soil type are considered important for root zone soil moisture. The ability of a limited number of monitoring stations to provide accurate estimates of catchment scale average soil moisture for both near‐surface and root zone is thus demonstrated, as opposed to high resolution spatial measurements. Similarly, the use of near‐surface soil moisture measurements to obtain a reliable estimate of deeper soil moisture levels at the small catchment scale was demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.     

Duration of strong ground motion in terms of earthquake magnitude,epicentral distance,site conditions and site geometry

The physical bases and empirical equations for modelling the duration of strong earthquake ground motion in terms of the earthquake magnitude, the epicentral distance and the geological and local soil site conditions are investigated. At 12 narrow frequency bands, the duration of a function of motion f(t), where f(t) is acceleration, velocity or displacement, is defined as the sum of time intervals during which the integral S f² (τ) dτ gains a significant portion of its final value. All the records are band-pass filtered through 12 narrow filters and the duration of strong ground motion is studied separately in these frequency bands. It is shown that the duration of strong motion can be modelled as a sum of the source duration, the prolongation due to propagation effects and the prolongation due to the presence of the sediments and local soils. It is shown how the influence of the magnitude on the duration of strong ground motion becomes progressively stronger, in going from low to moderate frequencies, and that the duration is longer for ‘soft’ than for ‘hard’ propagation paths, at low and at moderate frequencies. At high frequencies, the nature of the broadening of the strong motion portion of the record with increasing distance is different, and is most likely related to the diffraction and scattering of the short waves by the velocity inhomogeneities along the wave path. It is also shown that the geological and local soil conditions should both be included in the model. The duration can be prolonged by 3–5 sec at a site on a deep sedimentary layer at frequencies near 0.5 Hz, and by as much as 5–6 sec by the presence of soft soil underneath the station, at a frequency of about 1 Hz. An empirical equation for a probabilistic estimate of the discrepancies of the predictions by our models relative to the observed data (distribution function of the residuals) is presented.     

Registration of weak ULF/ELF oscillations of the surface electric field strength

Measurements of the atmospheric electric field strength made by an electrostatic fluxmeter with a unique threshold sensitivity for such devices (6 × 10^–2–10^–3 V m^–1 Hz^–1/2 in the 10^–3–25 Hz frequency range) and wide dynamic (120 dB) and spectral (0–25 Hz) ranges, are presented. The device parameters make it possible to observe the electric component of global electromagnetic Schumann resonances and long-period fluctuations in the atmospheric electric field strength.     

Separation of Source, Propagation and Site Effects from S Waves¶of Local Earthquakes in Bursa Region, Northwestern Turkey

—?We have used micro-earthquake recordings (M= 1.8–4.1) of local events in the distance range of 5–60?km in order to quantify the attenuation and site effects in the vicinity of the Bursa city, Marmara region, Turkey. The data set consists of 120 three-component recorded accelograms from 69 earthquakes, recorded at six stations. Each station is deployed on different geologic units, such as massive limestone, slope deposit and Quaternary young sediments, in the framework of the Marmara Poly-Project.¶In this study a nonparametric inversion method was applied to acceleration records from the Bursa region to estimate source, site and path effects using a two-step inversion. At the first step, we determined attenuation functions by analyzing the distance dependence of the spectral amplitudes and retrieved values of Q _s (f) = 46.59f ^0.67. At the second step, the corrected S-waves spectral records for the attenuation function, including the geometrical spreading effect, were inverted to separate source and site response for 21 different frequencies selected between 0.5 and ～25?Hz. The near-surface attenuation, κ value, was also estimated by using the model proposed by Anderson and Hough (1984) at each site. We observed that κ₀ is smaller for stations located on rock site (I?dιr, SIGD, κ₀～0.004) compared to the one that is located on Neogene sediment (Çukurca, SCKR, κ₀～0.018).¶Site amplifications from inversion showed that the station located within the Bursa basin, Çukurca (SCKR), is the most important site with about 4.0 amplification value at 1.8?Hz. Demirta? (SDEM) amplifies the spectral amplitudes about 3.0 times at 2.0?Hz, SHMK about 3.5 times between 2.5 and 3.5?Hz and SHMT nearly reaching 3.5 times between 1.5 and 4.0?Hz. However, stations located on the Uluda? Mountain Massif (SKAY and SIGD), which correspond to a deep limestone geological unit, have the smallest amplification, that values between 0.6 and 1.4.     

Experimental study on the aseismic capacity of a wooden house using shaking table

The aseismic capacity of a typical Korean wooden house built using traditional construction methods is quantitatively estimated. Tenon joints were used in wooden frames. Two 1:4 scale models were tested for rock and soil foundation conditions. Scaled real earthquake time histories were input for the tests. The natural frequency and modal damping ratio of the wooden house in the elastic range were 1·66 Hz and 7 per cent, respectively. The Peak Ground Acceleration (PGA) at the collapse of the house at the soil site was 0·25g, whereas PGA for moderate damage at the rock site was 0·6g. A significant reduction in acceleration response and increase in displacement response was observed for rock and soil foundation conditions, respectively. The wooden house studied is much more vulnerable at soil sites than at rock sites due to the rich low-frequency contents of the input motion and the flexible characteristics of the wooden house. Non-linear dynamic analyses using the modified Double-Target model were compared with test results. The modified Double-Target model appropriately simulates the non-linear inelastic behaviour of a wooden house with tenon joints. Copyright © 1999 John Wiley & Sons, Ltd.     

Heterogeneous characteristics of streambed saturated hydraulic conductivity of the Touchet River,south eastern Washington,USA

Traditionally a streambed is treated as a layer of uniform thickness and low saturated hydraulic conductivity (K) in surface‐ and ground‐water studies. Recent findings have shown a high level of spatial heterogeneity within a streambed and such heterogeneity directly affects surface‐ and ground‐water exchange and can have ecological implications for biogeochemical transformations, nutrient cycling, organic matter decomposition, and reproduction of gravel spawning fish. In this study a detailed field investigation of K was conducted in two selected sites in Touchet River, a typical salmon spawning stream in arid south eastern Washington, USA. In‐stream slug tests were conducted to determine K following the Bouwer and Rice method. For the upper and lower sites, each 50 m long and 9 m wide and roughly 20 m apart, a sampling grid of 5 m longitudinally and 3 m transversely was used. The slug tests were performed for each horizontal coordinate at 0·3–0·45, 0·6–0·75, 0·9–1·05 and 1·2–1·35 m depth intervals unless a shallower impenetrable obstruction was encountered. Additionally, water levels were measured to obtain vertical hydraulic gradient (VHG) between each two adjacent depth intervals. Results indicated that K ranged over three orders of magnitude at both the upper and lower sites and differed between the two sites. At the upper site, K did not differ significantly among different depth intervals based on nonparametric statistical tests for mean, median, and empirical cumulative distribution, but the spatial pattern of K varied among different depth intervals. At the lower site, K for the 0·3–0·45 m depth interval differed statistically from those at other depth intervals, and no similar spatial pattern was found among different depth intervals. Zones of upward and downward water flow based on VHG also varied among different depth intervals, reflecting the complexities of the water flow regime. Detailed characterization of the streambed as attempted in this study should be helpful in providing information on spatial variations of streambed hydraulic properties as well as surface‐ and ground‐water interaction. Copyright © 2009 John Wiley & Sons, Ltd.     

Identification of robust hyperspectral indices on forest leaf water content using PROSPECT simulated dataset and field reflectance measurements

In this study, we aim at finding efficient and robust hyperspectral indices for estimating forest leaf water content parameters (equivalent water thickness, EWT and fuel moisture content, FMC), which are useful for the understanding of terrestrial ecosystem functioning and evaluating fire risk. The most efficient hyperspectral indices have been identified (both on the context of index types and wavelength domains) using both a simulated dataset generated from the calibrated leaf reflectance model, PROSPECT, and datasets of field measured reflectance. Results indicate that high precision can be obtained using the type of vegetation index of two wavelength bands based on reflectance derivatives to estimate both parameters, with overall R² and RMSE of 0·60 ～ 0·75 and 0·0009 ～ 0·0012 g cm^?2 for EWT, 0·63 ～ 0·87 and 0·12 ～ 0·20 g g^?1 for FMC, respectively. The best indices identified in this study for vegetation water status in temperate deciduous forests were dSR (1510, 1560) for EWT and dSR (2110, 2260) for FMC, with widths of wavebands (Δλ) be variable up to 50 nm for both dSR indices. Despite the obvious discrepancies found in fit when applying the identified indices to different datasets, the indices identified in this study are applicable to various species (Dataset III), various phenological stages, different sites (Dataset I) and various leaf anatomies (Dataset II), and therefore suitable for an all inclusive wide range of application especially in temperate deciduous forests. Copyright © 2011 John Wiley & Sons, Ltd.     

Wind direction and complex sediment transport response across a beach–dune system

Evidence from a field study on wind flow and sediment transport across a beach–dune system under onshore and offshore conditions (including oblique approach angles) indicates that sediment transport response on the back‐beach and stoss slope of the foredune can be exceedingly complex. The upper‐air flow – measured by a sonic anemometer at the top of a 3·5 m tower located on the dune crest – is similar to regional wind records obtained from a nearby meteorological station, but quite different from the near‐surface flow field measured locally across the beach–dune profile by sonic anemometers positioned 20 cm above the sand surface. Flow–form interaction at macro and micro scales leads to strong modulation of the near‐surface wind vectors, including wind speed reductions (due to surface roughness drag and adverse pressure effects induced by the dune) and wind speed increases (due to flow compression toward the top of the dune) as well as pronounced topographic steering during oblique wind approach angles. A conceptual model is proposed, building on the ideas of Sweet and Kocurek (Sedimentology 37 : 1023–1038, 1990), Walker and Nickling (Earth Surface Processes and Landforms 28 : 111–1124, 2002), and Lynch et al. (Earth Surface Processes and Landforms 33 : 991–1005, 2008, Geomorphology 105 : 139–146, 2010), which shows how near‐surface wind vectors are altered for four regional wind conditions: (a) onshore, detached; (b) onshore‐oblique, attached and deflected; (c) offshore, detached; and (d) offshore‐oblique, attached and deflected. High‐frequency measurements of sediment transport intensity during these different events demonstrate that predictions of sediment flux using standard equations driven by regional wind statistics would by unreliable and misleading. It is recommended that field studies routinely implement experimental designs that treat the near‐surface wind field as comprising true vector quantities (with speed and direction) in order that a more robust linkage between the regional (upper air) wind field and the sediment transport response across the beach–dune profile be established. Copyright © 2012 John Wiley & Sons, Ltd.     

Characteristics of concentrated flow hydraulics for rangeland ecosystems: implications for hydrologic modeling

Concentrated flow is often the dominant source of water erosion following disturbance on rangelands. Because of the lack of studies that explain the hydraulics of concentrated flow on rangelands, cropland‐based equations have typically been used for rangeland hydrology and erosion modeling, leading to less accurate predictions due to different soil and vegetation cover characteristics. This study investigates the hydraulics of concentrated flow using unconfined field experimental data over diverse rangeland landscapes within the Great Basin Region, United States. The results imply that the overall hydraulics of concentrated flow on rangelands differ significantly from those of cropland rills. Concentrated flow hydraulics on rangelands are largely controlled by the amount of cover or bare soil and hillslope angle. New predictive equations for concentrated flow velocity (R² = 0·47), hydraulic friction (R² = 0·52), and width (R² = 0·4) representing a diverse set of rangeland environments were developed. The resulting equations are applicable across a wide span of ecological sites, soils, slopes, and vegetation and ground cover conditions and can be used by physically‐based rangeland hydrology and erosion models to estimate rangeland concentrated flow hydraulic parameters. Published in 2011. This article is a US Government work and is in the public domain in the USA.     

Heat tracing of heterogeneous hyporheic exchange adjacent to in‐stream geomorphic features

There are many field techniques used to quantify rates of hyporheic exchange, which can vary in magnitude and direction spatially over distances of only a few metres, both within and between morphological features. We used in‐stream mini‐piezometers and heat transport modelling of stream and streambed temperatures to quantify the rates and directions of water flux across the streambed interface upstream and downstream of three types of in‐stream geomorphic features: a permanent dam, a beaver dam remnant and a stream meander. We derived hyporheic flux estimates at three different depths at six different sites for a month and then paired those flux rates with measurements of gradient to derive hydraulic conductivity (K) of the streambed sediments. Heat transport modelling provided consistent daily flux estimates that were in agreement directionally with hydraulic gradient measurements and also identified vertical heterogeneities in hydraulic conductivity that led to variable hyporheic exchange. Streambed K varied over an order of magnitude (1·9 × 10^?6 to 5·7 × 10^?5 m/s). Average rates of hyporheic flux ranged from static (q < ±0·02 m/day) to 0·42 m/day. Heat transport modelling results suggest three kinds of flow around the dams and the meander. Copyright © 2010 John Wiley & Sons, Ltd.