Probability distributions of bed load transport rates: A new derivation and comparison with field data


 Agatha Richard
 1 years ago
 Views:
Transcription
1 WATER RESOURCES RESEARCH, VOL. 46,, doi: /2009wr008488, 2010 Probability distributions of bed load transport rates: A ne derivation and coparison ith field data Jens M. Turoski 1 Received 5 August 2009; revised 16 February 2010; accepted 24 February 2010; published 3 August [1] It has been knon for a long tie that sedient transport rates can vary strongly even if the abient hydraulic conditions reain steady. In this article, a ne approach is described to derive probability distributions of bed load transport rates, starting fro the aiting tie beteen the arrivals of individual sedient particles. The foralis should be valid hen transport is not doinated by bed for otion. Without any assuptions about the distribution of interarrival ties, the approach yields the Birnbau Saunders distribution, a to paraeter distribution previously used in lifetie odeling. Observed dependence of ean transport rates on the sapling tie and ultiscaling are predicted by the distribution. Assuing exponentially and Poisson distributed interarrival ties, the sae approach yields the Poisson and the gaa distributions. Using a high resolution bed load transport data set fro the Pitzbach, Austria, the distribution functions are tested on field data. The gaa distribution best describes the data, ith axiu deviations of 5%. Hoever, the Birnbau Saunders distribution ay be ore useful in certain applications, as it is a general approxiation in the proposed foralis and no debated assuptions are necessary for its derivation. Citation: Turoski, J. M. (2010), Probability distributions of bed load transport rates: A ne derivation and coparison ith field data, Water Resour. Res., 46,, doi: /2009wr Introduction [2] Bed load transport, the ater driven rolling, sliding, or hopping otion of coarse particles in a strea, is an iportant ode of sedient transfer in rivers and a key process in shaping the Earth s surface. Accurate calculation of transport rates is necessary both in engineering applications such as flood hazard itigation and in pure science. Bed load transport rates are knon to fluctuate strongly both in nature [e.g., Goez and Church, 1989; Hassan and Church, 2000] and in the laboratory [e.g., Kuhnle and Southard, 1988; Ancey et al., 2008] even under steady flo conditions. Several different causes for these fluctuations have been identified [Goez et al., 1989; Hoey, 1992], including variations in sedient supply [e.g., Benda and Dunne, 1997], spatially and teporally varying distribution of grain sizes, relative grain arrangeent, and grain sorting processes [e.g., Kirchner et al., 1990; Chen and Stone, 2008], and the passage of bed fors [e.g., Lisle et al., 2001; Recking et al., 2009]. [3] Several odels have been proposed to describe the probability distribution functions of bed load transport rates. Einstein [1937] considered bed load transport as a series of rest periods of rando length, interrupted by short periods of otion of rando distances. He assued that both step lengths and rest ties are exponentially distributed and 1 Eidgeno ssische Forschungsanstalt WSL Birensdorf, Birensdorf, Sitzerland. Copyright 2010 by the Aerican Geophysical Union /10/2009WR derived distribution functions for the aount of sedient transported over a cross section. Hoever, it is difficult to easure the distribution functions of rest periods and transport distances directly in the field or laboratory and any of the assuptions underlying Einstein s [1937] odel have not yet been validated. Guided by laboratory observations, Haaori [1962] developed a distribution function of bed load transport rates for cases hen bed for otion is doinant. In his odel, secondary dunes are responsible for the total transport. These secondary dunes entrain aterial and gro linearly ith distance hile oving up the stoss slope of priary dunes. Thus, the assuptions underlying his distribution are physically restrictive and apply only in liited circustances. More recent stochastic odels of bed load transport often describe the entrainent and deposition of particles in a control volue using Markov birth death odels [e.g., Lisle et al., 1998; Papanicolaou et al., 2002; Ancey et al., 2006, 2008; Turoski, 2009]. These odels typically feature a large nuber of paraeters that need to be calibrated on data but are hard to easure even under controlled laboratory conditions [cf. Ancey et al., 2008]. Thus, it is challenging to test and validate such odels directly. [4] Here I take a different approach. Instead of trying to devise an accurate description of the physics of bed load transport, I consider the distribution of aiting ties beteen particle arrivals (interarrival ties) at a cross section to derive probability distributions for bed load transport rates. Using odern equipent such as light tables [Frey et al., 2003; Zierann et al., 2008] or video caeras [Drake et al., 1988], it should be possible to directly easure this distribution in the laboratory and the field. The 1of10
2 Birnbau Saunders distribution [Birnbau and Saunders, 1968] arises as a general approxiation hen no explicit assuptions about the distribution of aiting ties are ade. By assuing exponentially or Poisson distributed aiting ties, one arrives at the Poisson and Gaa distributions, respectively. The distribution functions are copared to a large field data set fro the Pitzbach, Austria [Rickenann and McArdell,2008;Turoski and Rickenann, 2009]. 2. Distribution Functions of Bed Load Transport Rates 2.1. The Birnbau Saunders Distribution [5] In practice often the sedient flux at a channel cross section is of interest. Particles arrive at varying intervals, and e ant to kno the total sedient volue arriving ithin a certain tie period and its variability. For the derivation of the distribution function, I ake the folloing foral assuptions: [6] 1. The aiting tie beteen the arrivals of individual bed load particles (interarrival tie) at a cross section is a stochastic variable ith an unspecified distribution ith ell defined ean and variance s 2. [7] 2. Within each easureent interval, enough particles arrive such that the central liit theore and the la of large nubers are applicable. [8] Iplicit in these to assuptions is the notion that the particles are actually countable and that individual arrivals are statistically independent. The folloing derivation ay thus not be applicable to environents here transport by bed for otion is doinant. This constraint and the to assuptions are discussed in ore detail in section 4.1. [9] Consider the arrival of individual sedient particles at the easureent cross section under steady conditions. The interarrival tie is described by a rando variable t ith ean and variance s 2. The tie T N at the arrival of the N th particle is then T N ¼ T N 1 þ N : Assuing that there are a large nuber of particles, the central liit theore ay be applied. Hence, the probability density function (pdf) for the total tie T N (ith corresponding stochastic variable t N ) at the arrival of the N th particle is approxiately noral. pdfðt N ðnþþ ð1þ ( ) 1 ð pffiffiffiffiffiffiffiffiffi exp t N NÞ 2 2N 2N 2 : ð2þ Note that the noral distribution in equation (2) is not assued but arises as a general approxiation fro the central liit theore. So far, no assuptions have been ade on the underlying distribution of interarrival ties. The size of particles and thus their ass follo a certain site specific distribution. Since N is large, the la of large nubers applies and the total ass is N, here is the ean ass of a single particle. Hence, the cuulative distribution function cdf(t N )oft N is the cuulative noral distribution F((x )/s) of the rando variable x ith ean and standard deviation s, hich is given by cdfðtþ ¼PT ð N ðþ t N Þ 8 Z 1 t N 2 9 >< ¼ q ffiffiffiffiffiffiffiffiffiffiffi 1 2 exp 2 2 >: 0 t N 1 ¼ F rffiffiffiffi B A : >= >; dt The event {M(t N ) } is equivalent to the event {T N () t N }, here M(t N ) is the rando variable representing the ass at tie t N. The cdf() ofm at given t N is then 0 1 cdf ðþ ¼PMðtÞ ð Þ ¼ 1 PTðÞ ð tþ ¼ F t Brffiffiffiffi A ; here t N has no been replaced by a constant t denoting the easureent interval. The probability density function is 8 pdfðjtþ ¼ dgðþ d ¼ þ t 2 9 >< r ffiffiffiffiffiffiffiffiffi 2 2 exp t >= >: 2 2 >; : ð5þ Reparaeterizing ith b = t/ and g 2 = s 2 /t to get the standard for of the Birnbau Saunders distribution yields ( ) pdfðjtþ ¼ p þ 2 ffiffiffiffiffiffiffiffiffiffiffiffi exp ð Þ : ð6þ The Birnbau Saunders distribution has previously been proposed to odel the ties at failure due to fatigue of aterial under cyclic stresses and belongs to a to paraeter exponential faily [Birnbau and Saunders, 1968]. The foralis of the derivation given above closely follos the one developed by Desond [1985]. [10] Equation (6) can easily be reritten in ters of fluxes (defined as Q s = /t) and the pdf of the bed load transport rate Q s in a given easureent interval t is given by ( ) pdfðq s jtþ ¼ Q s þ 0 ð pffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp Q s 0 Þ 2 2Q s 2 0 Q s 2Q s 0 2 ð3þ ð4þ : ð7þ Here b = / is a scale paraeter, and g 2 = s 2 /t is a shape paraeter as before. The expectation value E(Q s )of equation (7) is given by EQ ð s Þ ¼ 0 1 þ 2 2 ¼ 1 þ t 2 : ð8þ And the variance var(q s ) is given by varðq s Þ¼ þ 52 ¼ t þ t 2 2 : ð9þ 2of10
3 The standard deviation std(q s ) is equal to the square root of var(q s ). More inforation on the properties of the distribution can be found in the ork of Johnson et al. [1995]. As ould be expected, the expectation value E(Q s ) approaches the constant value / as t goes to infinity. This gives a constraint on the iniu length of the easureent interval t: it needs to be uch larger than s 2 /2 2 to obtain a reliable estiate of transport rates hich is independent of the length of the easureent interval and thus coparable for different streas or for the sae strea at different discharges [cf. Singh et al., 2009]. [11] The Birnbau Saunders distribution as derived ithout assuptions about the probability distribution of interarrival ties. I ill no outline to additional derivations, assuing interarrival ties, hich are distributed according to the exponential distribution and a continuous for of the Poisson distribution. It is not y ai here to argue that either of these distributions is the correct one, although at least the exponential distribution has been predicted fro certain physically based stochastic transport theories [e.g., Ancey et al., 2008]. Rather, I ant to sho (1) ho physically based results can be incorporated into the fraeork developed above and (2) ho such assuptions can yield various plausible probability distributions for bed load transport rates Exaple 1: Exponentially Distributed Interarrival Ties [12] Let the interarrival ties be exponentially distributed ith a pdf of the folloing for: pdfðþ ¼ 1 exp : ð10þ The tie at the N th arrival is then distributed according to the gaa distribution pdfðt N ðnþþ ¼ 1 N t N 1 N GðNÞ exp t N : ð11þ The gaa function G(x) is defined by GðxÞ ¼ Z 1 0 z x 1 e z dz: ð12þ Folloing the reaining steps of the derivation as given above one obtains the cuulative distribution function (cdf) of asses G ; t cdfðþ ¼ G : ð13þ Here the upper incoplete gaa function G(x, y) is defined by Gðx; yþ ¼ Z 1 y z x 1 e z dz: ð14þ Equation (13) is a continuous for of the Poisson distribution ith the folloing pdf: exp t t = : pdfðþ ¼ G ð15þ Here the usual factorial is replaced by the gaa function (equation (12)), hich is a continuous interpolation of the factorial function. This generalizes the Poisson distribution to apply for continuous variables. In the reainder of the article henever a Poisson distribution is entioned, I generally refer to a continuous version analogous to equation (15) Exaple 2: Interarrival Ties Distributed After a Continuous Version of the Poisson Distribution [13] Alternatively, let the interarrival ties be distributed after a continuous for of the Poisson distribution ith a pdf analogous to equation (15) pdfðþ ¼ 1 expf 1g 1 = : ð16þ G = Here the expected nuber of occurrences is equal to one, because the interarrival tie t as noralized by the ean. Note that this noralization of t ith is necessary to keep the equation diensionally consistent. Of course, the ter 1 = evaluates to one; I left it in to ake the connection to equations (15) and (17) ore explicit. The tie at the N th arrival is also based on a continuous Poisson distribution pdfðt N ðnþþ ¼ 1 expf Ng N t N= : ð17þ G tn Folloing through the reaining steps of the derivation, the asses are then distributed according to the cdf 1 G t ; cdfðþ ¼ : ð18þ G t = Equation (18) gives the cdf for the gaa distribution, and the corresponding pdf is pdfðþ ¼ 1 t t = 1 n exp o : ð19þ G t = The Birnbau Saunders distribution (equation (7)) is an approxiation for both the continuous Poisson distribution (equation (15)) and the gaa distribution (equation (19)), hich orks ell for large transport rates. 3. Testing the Distributions: The Pitzbach Sedient Transport Observations 3.1. Field Site: Pitzbach, Austria [14] The Pitzbach is a sall glacially fed strea in southestern Austria near the village of Ist on the southern side of the Inn valley (Tyrol). It is a gravel bed river ith a 3of10
4 Figure 1. Scheatic plan of the eir and ater intake at the Pitzbach. The ater flos through a Tyrolean eir ith a grid size of 15 c and is led into the sedient settling basin on the orographic left. There, several load cells are used to onitor the deposited volues every 15 in. If a threshold eight is exceeded, the basin is autoatically flushed and the sedient is reinserted into the channel donstrea of the eir. edian grain size of 3 4 c on the bed surface and an average channel bed slope of 9%. At an elevation of 1811 asl the Tyrolean Water Copany (TIWAG) aintains a ater intake in the strea for a hydro poer plant (Figure 1). Approxiately 60% of the total drainage area of 26.8 k 2 is covered by glaciers. As a result, ost bed load is transported throughout the suer onths, hen discharge varies ith the daily cyclicity typical for glaciated catchents. At the ater intake, the ater flos over a Tyrolean ear consisting of a etal grid ith a bar spacing of 15 c into a sedient settling basin. For the suers 1994 and 1995, the basin as equipped ith five load cells and a pressure sensor, hich ere used to easure the aount of accuulated sedient every 15 in. When a threshold eight as exceeded, the sedient in the basin as autoatically flushed out and reinserted into the channel donstrea of the eir. Since discharge is largely elt ater driven, it generally varies sloly over tie and the assuption that discharge is constant ithin a easureent interval can be ade. More inforation on the strea, the instruents and the easureent capaign can be found in the orks of Hofer [1987], Rickenann and McArdell [2008], and Turoski and Rickenann [2009]. For the survey period ore than 10,600 easureents ith nonzero bed load transport rates are available (Figure 2). The instruents reliably pick up a signal hen the deposited volue exceeds Saller volues are often issed and are thus underrepresented in the easureents. At a given discharge, easured transport rates scatter over up to four orders of agnitude around the ean. Nonlinear regression as often used to analyze bed load transport easureents neglects this diension and thus is inadequate to provide a full description of the data. described by the Birnbau Saunders distribution in all cases; hoever, for sall transport rates there are systeatic differences: at very sall and ediu transport rates equation (7) underpredicts the occurrence probability, for sall rates it overpredicts it. [16] At the Pitzbach, both the expected value E(Q s ) and the standard deviation std(q s ) are onotonically increasing functions of discharge, ell described by either an exponential or a poer function (Figures 2 and 4). Hoever, the good fit featured by the exponential function ay be isleading, as for lo transport rates, an iportant fraction of the data ay be cut off due the easureent threshold of the instruents, hich often iss sall deposited values (Figure 2). [17] For discharge classes ith a large nuber of data points (>80) the coefficient of variation cva(q s ) = std(q s )/ E(Q s ) is approxiately constant ith an average value of 1.2. Siilarly, Willis and Bolton [1979] observed cva(q s ) 1.6 for experiental sedient transport data of sand, and Kuhnle and Willis [1998] reported approxiately equal ean and standard deviation at a given shear stress (hich is 3.2. The Pitzbach Data and the Birnbau Saunders Distribution [15] The Pitzbach easureents ere classified into logarithically distributed bins in discharge, and equation (7) as fitted to the data ithin each bin using axiu likelihood estiation (Figure 3). Such a ethod is preferable to nonlinear regression as coonly used to analyze bed load transport data, since it explicitly acknoledges the spread of transport rates at a given discharge and allos the investigation of statistics other than the ean. For the Pitzbach data, the tail behavior at large transport rates is ell Figure 2. Bed load volue accuulated in 15 in periods as function of discharge. Volues saller than are often issed by the instruents and are thus underrepresented. Exponential and poer la fits ere done on binned eans (black circles), instead of on the hole set. Fit values are given in the caption of Figure 4. 4of10
5 Figure 3 5of10
6 (equation (19)), the distributions due to Haaori [1962] and Carey and Hubbell [1986] are tested, hich ere derived for bed for doinated transport. The Haaori distribution is valid in the range fro zero to four ties the ean transport rate Q and has a pdf of the for The cdf has the for pdfðq s Þ ¼ 1 ln 4Q : ð20þ 4Q Q s cdfðq s Þ ¼ Q s 4Q 1 þ ln 4Q Q s : ð21þ The distribution is top bounded, i.e., transport rates ith values larger than four ties Q are assigned a probability of zero. Carey and Hubbell [1986] generalized the odel and derived the pdf pdfðq s = n 1 Þ ¼ Q1 ax Qs = 1 = n 1 Q ð1 nþq 1 = n ax : ð22þ Here n is a constant, hich is generally saller than one [Goez et al., 1989], and the axiu possible transport rate Q ax is given by Q ax ¼ 2ðn þ 1ÞQ : ð23þ Figure 4. Variation of the best fit ean value and the standard deviation ith discharge for each bin ith at least 15 data points. The coefficient of variation is approxiately constant for all bins ith at least 80 data points. The fit values for the exponential y = A exp(b Q) and the poer la y = aq b arefortheeanvaluein(a)a = /s, B =0.40s/ 3, a = ( 3 /s) 1 b,andb = 3.58, and for the standard deviation in (b) A = /s, B =0.31s/ 3, a = ( 3 /s) 1 b, and b = directly related to discharge at a single location) for bed load transport rates at Goodin Creek. Although this relationship needs to be confired for other streas, the assuption std(q s ) / E(Q s ) ay be a good first approxiation for the standard deviation Coparison to Other Distribution Functions [18] Next, the Pitzbach data is copared to other distributions. In addition to a continuous for of the Poisson distribution (equation (15)) and the gaa distribution The cdf corresponding to the pdf in equation (22) is given by pdfðq s Þ ¼ Q s = Q ð1 n 1 = n n Qs = Q ÞQ ax ð1 nþq 1 = n ax : ð24þ Siilarly to the Haaori distribution, the Carey Hubbell distribution is top bounded at Q ax. In the Pitzbach, axiu transport rates exceed ean transport rates by a factor of four at ost discharges. Thus, the Haaori and Carey Hubbell distributions are clearly of liited value to describe the data. Hoever, in the range for hich they are valid, both odels give a reasonable fit to the data (Figure 5). With a value of n = 0.5, the Carey Hubbell distribution closely traces the data for lo transport rates (belo about the 50 percentile; Figure 5c), hile the Haaori distribution fits ell over the hole range of its validity. [19] Both the continuous Poisson and the gaa distribution give better fits to the data than the Birnbau Saunders distribution for lo transport rates. The gaa distribution gives a good fit for the hole data range, ith axiu deviations of 5%. All three distributions (Birnbau Saunders, continuous version of the Poisson distribution, Figure 3. Cuulative probability distribution and probability density functions (large figures labeled A1, etc.) of the observed loads (open circles, histogra) and the best fit (solid line) using equation (7) for discharges of (a) /s (292 data points), (b) /s (1223 data points), (c) /s (477 data points), and (d) /s (335 data points). The corresponding Shields nuber estiated for the artificial cross section at the easureent site is given on the plot. Sall figures sho (left, 2) percent percent plots and (right, 3) probability ratio plots for the sae discharges. Percent percent plots allo a good optical evaluation of the fit in the loer percentiles, hile ratio plots allo the evaluation of the fits in the right hand tail. 6of10
7 Figure 5. Coparison of the Haaori, Carey Hubbell, Birnbau Saunders, gaa, and Poisson distributions to the Pitzbach data at a discharge of /s (1223 data points). (a) Probability density functions on a seilogarithic plot. (b) Cuulative probability functions. (c) Percent percent plots. This visualization allos an assessent of the goodness of fit for lo and ediu transport rates. (d) Percentileratio plots. This visualization allos the assessent of the goodness of fit in the tail region. The gaa distribution gives the best fit ith axiu deviations of 5%. The Birnbau Saunders distribution provides a reasonable approxiation especially to the right hand tail. gaa) converge onto the right hand tail at high transport rates (Figure 5d). 4. Discussion 4.1. The Birnbau Saunders Distribution [20] The assuptions ade in the derivation of the Birnbau Saunders distribution arrant a discussion of the generality of the function. Since the arguent is purely statistical, the function is independent of the physics of sedient transport and should be idely applicable. Hoever, the applicability is restricted to systes here individual particle arrivals are countable and statistically independent, and the function ay not be applicable in environents here transport is doinated by bed for otion, as in any sand bed streas. In such environents, distribution functions specifically developed for dune otion, such as the Haaori or the Carey Hubbell distributions, ay yield better results (see for exaple the ork of Carey [1985] for field testing of the Haaori distribution in a sand bed river). It ay be possible to adapt the derivation of the Birnbau Saunders distribution by not considering the arrival of individual particles but the arrival of individual bed fors. The final distribution of transport rates ould then have the sae for. Hoever, the assuptions in the derivation set a constraint on the length of the easureent interval needed to ake the distribution applicable to a data set: it needs to be long enough such that the nuber of particles arriving ithin it is large enough such that the central liit theore and the la of large nubers apply. In natural channels discharge can fluctuate quickly and it ay not be easy to find a suitable easureent interval that ensures that hydraulic conditions are approxiately constant hile a sufficient nuber of bed fors arrive. [21] The constraint on the easureent interval iplies that at sall transport rates, i.e., hen only fe particles arrive, the Birnbau Saunders distribution ill necessarily break don. This ay be one of the reasons for the unsatisfactory fit of the function to the Pitzbach data for sall transport rates (cf. Figure 3). The rate of convergence to the noral distribution in the central liit theore can be 7of10
8 quantified ith the Berry Esséen Theore [Berry, 1941; Esséen, 1942], hich states that the axiu difference beteen the real distribution and its noral approxiation scales ith N 1/2. Thus, the approxiation gets better as ore particles are trapped ithin the easureent interval. In general, the error depends on the ean interarrival tie and varies ith discharge. If the underlying distribution is exponential (section 2.2), the construction of a distribution function fro added rando nubers is reasonably approxiated by a noral distribution for N > 100 for the conditions at the Pitzbach. For coparison, assuing that the ean grain size of the aterial deposited in the retention basin at the Pitzbach is close to the 65 percentile of the size distribution of 6 [Rickenann and McArdell, 2008], around 2 illion particles are present in 1 3 of bed load, assuing 50% pore space and 50% fines. A volue of 1 3 is close to the average yield delivered ithin 15 in at a discharge of 8 3 /s (Figure 2). Thus, for ost practical conditions, the rate of convergence to the noral distribution should not be a proble. [22] The assuption of the la of large nubers leads to siilar probles. At the Pitzbach, the ean particle diaeter is around 6 for the aterial deposited in the retention basin. At sall transport rates often large grain sizes are underrepresented in the bed load [Wilcock and McArdell, 1993], and for the Pitzbach there is no inforation available on ho the grain size distribution (and the ean grain size) changes ith discharge and bed load transport rate. An accurate quantification of the rate of convergence is thus not currently possible; hoever, considering the large nuber of arriving particles, the easured ean should be fairly close to the population ean. [23] In addition to these statistical errors, at sall transport rates the instruents are unreliable, hich affects goodness of fit. Often sall volue changes are issed by the equipent and data in this range is underrepresented in the distribution. One can get around these probles by just extending the easureent intervals. Hoever, again it ay be probleatic to find a suitable interval in hich the variation of discharge is slo enough such that the hydraulic conditions can be assued to be constant. [24] In the Birnbau Saunders distribution the ean transport rate decreases ith increasing sapling interval (see equation (8)). Siilarly, both in the field [Bunte and Abt, 2005] and in the laboratory [Singh et al., 2009], it as found that at lo transport rates the estiated ean transport rates decrease as the sapling interval increases, hile at high transport rates the trend reverses. Singh et al. [2009] related this trend reversal to the presence of large bed fors and their doinance in the transport process at high transport rates. As discussed above, the assuptions underlying the Birnbau Saunders distribution are not valid hen transport is doinated by bed for otion, and thus the predictions can be considered to be in line ith observations. The Pitzbach data span 2 years, and during this tie no exceptional flood occurred in the catchent. Sufficient data for the construction of a distribution function is available for discharges up to 10 3 /s, hereby the estiated peak discharge of a 2 year flood is /s. Consequently, the Birnbau Saunders distribution cannot currently be tested under high discharge conditions. Singh et al. [2009] also described ultiscaling of the oents of bed load transport for different sapling intervals, i.e., different oents such as ean and standard deviation are dependent on the sapling interval in different ays. This behavior is predicted by the Birnbau Saunders distribution (cf. equations (8) and (9)) The Pitzbach Data and Coparison With Other Distribution Functions [25] Bed load volues easured at the Pitzbach ithin 15 in periods scatter idely, over up to four orders of agnitude at a given discharge (Figure 2). It is clear that nonlinear regression ith a poer la, as is often used to analyze field data of sedient transport, is inadequate to describe observations. First, regression alays gives a global optiization and can lead to strong local deviations. Second, the large scatter in the y direction is treated as a easureent error and not as a genuine signal. Herein, a binning procedure as used to analyze the data. This has the advantage that statistics for transport rates at a given discharge can be calculated for each bin, and one can obtain inforation not only on the ean behavior but also on the standard deviation and the shape of the probability distributions. [26] Fro the tested distributions (Birnbau Saunders, continuous Poisson type distribution, gaa, Haaori, Carey Hubbell), the gaa distribution gives the best fit to the Pitzbach data. Both Birnbau Saunders and continuous Poisson distributions provide reasonable fits in the righthand tail, hile the Haaori and Carey Hubbell distributions fit ell for lo transport rates. Fe other data sets exist ith a sufficient size and quality to ake siilar calculations as done here for the Pitzbach. Kuhnle and Willis [1998] tested the exponential, the noral, the gaa, and the Haaori distributions for bed load transport data fro Goodin Creek and likeise found that the gaa distribution gives the best description of the data. Thus, the gaa distribution has been observed to ork ell at to field sites and can be recoended for use in field applications at the current state of knoledge. Hoever, the Birnbau Saunders distribution ay be ore suitable in certain applications, because its derivation is ore general. After all, the gaa distribution as derived fro the assuption of Poisson distributed interarrival ties. The precise for of the distribution of interarrival ties has not been easured in the field and is debated fro a theoretical point of vie. For the Pitzbach data, the tail behavior of sedient transport rates at a given discharge is ell described by the Birnbau Saunders distribution for the upper tentieth percentile, at any discharges the good fit region reaches to the upper thirtieth percentile or further. The upper tentieth percentile corresponds to 60% 70% of the total load transported for a given discharge. The distribution ay therefore provide an adequate approxiation in any instances. [27] The Birnbau Saunders and the gaa distribution decline exponentially in Q s in the liit of large transport rates. Hence, large events occur ore coonly as ould be expected hen using a noral distribution. Environental paraeters often sho a poer la tail (heavy tail), for exaple landslide sizes or strea discharge [e.g., Stark and Hovius, 2001; Lague et al., 2005], and it is soe 8of10
9 ties assued that sedient transport rates likeise are heavy tailed. On the contrary, in the Pitzbach bed load transport rates sho an exponential rather than a poer la tail. Large events are thus not as doinant for the total transport rate as is observed for any other environental processes. Note, hoever, that this is only true for transport rates at a given discharge. The long ter sedient budget of a catchent ay be ore dependent on the distribution of flood sizes (often heavy tailed) than on the properties of the distributions considered herein. 5. Conclusions [28] Bed load transport rates are knon to fluctuate strongly even under steady hydraulic conditions. Here, I have shon a ne ay of deriving probability distributions of bed load transport rates by considering the aiting ties beteen the arrivals of individual particles (interarrival ties). The assuptions underlying the derivation should ake the distributions applicable for bed load transport not doinated by bed for otion. Without any further assuptions about the distribution of interarrival ties, the foralis yields the Birnbau Saunders distribution as a general approxiation. A continuous version of the Poisson distribution and the gaa distribution can be derived if the interarrival ties are assued to be exponentially or Poisson distributed, respectively. The approach circuvents the need for calibration of several paraeters that are hard to observe directly, as is often necessary in odern stochastic theories of sedient transport. In fact, ith odern equipent such as light tables and video based observation [Drake et al., 1988; Frey et al., 2003; Zierann et al., 2008], it should be possible to directly easure the distribution of interarrival ties in the field or the laboratory. [29] Together ith the previously proposed Haaori and Carey Hubbell distributions [Haaori, 1962; Carey and Hubbell, 1986], the derived functions ere tested on a large data set fro the Pitzbach, Austria. Out of the tested distributions, the gaa distribution perfors best, ith axial deviations fro the data of around 5%. The Birnbau Saunders distribution provides a reasonable approxiation especially in the right hand tail. The Poisson distribution fits ell over the hole range of the data. The Haaori and Carey Hubbell distributions give reasonable fits especially for lo transport rates. The gaa distribution has previously been found to also describe the Goodin Creek data ell [Kuhnle and Willis, 1998]. At the current state of knoledge, the gaa distribution can thus be recoended for use in field applications. Hoever, the Birnbau Saunders distribution is a reasonable approxiation, hich has been derived ithout aking any debated physical assuptions. Thus, its use ay be advantageous in certain applications. Notation Variables M Stochastic variable of ass, kg Total ass of N particles, kg Average ass of a particle, kg N Nuber of particles n Carey Hubbell exponent Q Mean bed load ass flux, kg/s Q ax Maxiu bed load ass flux in the Carey Hubbell distribution, kg/s Q s Bed load ass flux, kg/s T Stochastic variable of aiting tie, s T N Tie until the arrival of the Nth particle, s t Length of easureent interval, s t N Stochastic variable of the tie until the arrival of the Nth particle, s x, y, z Variables, used variously b, b Scale factor in the Birnbau Saunders distribution, kg (unpried), kg/s (pried) g Shape factor in the Birnbau Saunders distribution Mean aiting tie beteen individual particle arrivals, s s Standard deviation of aiting ties beteen individual particle arrivals, s Functions cdf(x) Cuulative distribution function of x cva(x) Coefficient of variation of x E(x) Expectation values of x pdf(x) Probability density function of x std(x) Standard deviation of x var(x) Variance of x G(x), G(x, y) Coplete and upper incoplete Gaa function F((x )/s) Cuulative noral distribution of x ith ean and standard deviation s [30] Acknoledgents. Many people have coented on the ideas presented herein and have helped to shape the in discussions. I thank especially D. Rickenann, A. Badoux, J.W. Kirchner, B.W. McArdell, M. Nitsche, D. Lague, and M. Stähli for support, encourageent, stiulating discussions, and coents on earlier versions of the anuscript. TIWAG supported the easureent capaign at the Pitzbach and ade the data available. A. Recking, C. Ancey, and an anonyous revieer coented on an earlier version of the anuscript. References Ancey, C., T. Böh, M. Jodeau, and P. Frey (2006), Statistical description of sedient transport experients, Phys. Rev. E, 74, , doi: /physreve Ancey, C., A. C. Davison, T. Böh, M. Jodeau, and P. Frey (2008), Entrainent and otion of coarse particles in a shallo ater strea don a steep slope, J. Fluid Mech., 595, , doi: / S Benda, L., and T. Dunne (1997), Stochastic forcing of sedient routing and storage in channel netorks, Water Resour. Res., 33(12), , doi: /97wr Berry, A. C. (1941), The accuracy of the Gaussian approxiation to the su of independent variates, Trans. A. Math. Soc., 49, Birnbau, Z. W., and S. C. Saunders (1968), A probabilistic interpretation of Miner s rule, SIAM J. Appl. Math., 16(3), Bunte, K., and S. R. Abt (2005), Effect of sapling tie on easured gravel bed load transport rates in a coarse bedded strea, Water Resour. Res., 41, W11405, doi: /2004wr Carey, W. P. (1985), Variability in easured bed load transport rates, Water Resour. Bull., 21, Carey, W. P., and D. W. Hubbell (1986), Probability distributions for bed load transport, in Proceedings of the 4th Federal Inter Agency Sedient Conference, US Geological Survey, vol. 2, Chen, L., and M. C. Stone (2008), Influence of bed aterial size heterogeneity on bed load transport uncertainty, Water Resour. Res., 44, W01405, doi: /2006wr Desond, A. (1985), Stochastic odels of failure in rando environents, Can. J. Stat., 13(2), Drake, T. G., R. L. Shreve, W. E. Dietrich, P. J. Whiting, and L. B. Leopold (1988), Bed load transport of fine gravel observed by otion picture photography, J. Fluid Mech., 192, of10
10 Einstein, H. A. (1937), Der Geschiebetrieb als Wahrscheinlichkeitsproble, Mitt. Versuchsanst. Wasserbau Eidg. Tech. Hochsch. Zürich, Rascher, Zürich, Sitzerland. Esséen, C. G. (1942), On the Liapounoff Liit of Error in the theory of probability, Ark. Mat. Astr. Och Fys., 28A(9), Frey, P., C. Ducottet, and J. Jay (2003), Fluctuations of bed load solid discharge and grain size distribution on steep slopes ith iage analysis, Exp. Fluids, 35(6), , doi: /s Goez, B., and M. Church (1989), An assessent of bed load transport forulae for gravel bed rivers, Water Resour. Res., 25(6), Goez, B., R. L. Naff, and D. W. Hubbell (1989), Teporal variations in bed load transport rates associated ith the igration of bed fors, Earth Surf. Processes Landfors, 14, Haaori, A. (1962), A theoretical investigation on the fluctuations of bed load transport, Rep. R4, Delft Hydraulics Laboratory, Delft, Netherlands. Hassan, M. A., and M. Church (2000), Experients on surface structure and partial sedient transport on a gravel bed, Water Resour. Res., 36, , doi: /2000wr Hoey, T. (1992), Teporal variations in bed load transport rates and sedient storage in gravel bed rivers, Prog. Phys. Geog., 16, Hofer, B. (1987), Der Feststofftransport von Hochgebirgsbächen a Beispiel des Pitzbachs, Österreichische Wasserirtschaft, 39, Johnson, N. L., S. Kotz, and N. Balakrishnan (1995), Continuous univariate distributions, 2nd ed., vol. 2, pp , John Wiley, Ne York. Kirchner, J. W., W. E. Dietrich, F. Iseya, and H. Ikeda (1990), The variability of critical shear Stress, friction angle, and grain protrusion in aterorked sedients, Sedientology, 37, Kuhnle, R. A., and J. B. Southard (1988), Bed load transport fluctuations in a gravel bed laboratory channel, Water Resour. Res., 24, Kuhnle, R. A., and J. C. Willis (1998), Statistics of sedient transport in Goodin Creek, J. Hydrol. Eng., 124, Lague, D., N. Hovius, and P. Davy (2005), Discharge, discharge variability, and the bedrock channel profile, J. Geophys. Res., 110, F04006, doi: /2004jf Lisle, I. G., C. W. Rose, W. L. Hogarth, P. B. Hairsine, G. C. Sander, and J. Parlange (1998), Stochastic sedient transport in soil erosion, J. Hydrol., 204, Lisle, T. E., Y. Cui, G. Parker, J. E. Pizzuto, and A. M. Dodd (2001), The doinance of dispersion in the evolution of bed aterial aves in gravel bed rivers, Earth Surf. Processes Landfors, 26, , doi: /esp.300. Papanicolaou, A. N., P. Diplas, N. Evaggelopoulos, and S. Fotopoulos (2002), Stochastic incipient otion criterion of spheres under various bed packing conditions, J. Hydrol. Eng., 128(4), , doi: / (ASCE) (2002)128:4(369). Recking, A., P. Frey, A. Paquier, and P. Belleudy (2009), An experiental investigation of echaniss involved in bed load sheet production and igration, J. Geophys. Res., 114, F03010, doi: /2008jf Rickenann, D., and B. W. McArdell (2008), Calibration of piezoelectric bed load ipact sensors in the Pitzbach ountain strea, Geodin. Acta, 21, 35 52, doi: /ga Singh, A., K. Fienberg, D. J. Jerolack, J. Marr, and E. Foufoula Georgiou (2009), Experiental evidence for statistical scaling and interittency in sedient transport rates, J. Geophys. Res., 114, F01025, doi: / 2007JF Stark, C. P., and N. Hovius (2001), The characterization of landslide size distributions, Geophys. Res. Lett., 28, Turoski, J. M. (2009), Stochastic odeling of the cover effect and bedrock erosion, Water Resour. Res., 45, W03422, doi: / 2008WR Turoski, J. M., and D. Rickenann (2009), Tools and cover effects in bed load transport observations in the Pitzbach, Austria, Earth Surf. Processes Landfors, 34, 26 37, doi: /esp Wilcock, P. R., and B. W. McArdell (1993), Surface based fractional transport rates: Mobilization thresholds and partial transport of a sand gravel sedient, Water Resour. Res., 29(4), Willis, J. C., and G. C. Bolton (1979), Statistical analysis of concentration records, J. Hydrol. Div., 105(1), Zierann, A., M. Church, and M. A. Hassan (2008), Video based gravel transport easureents ith a flue ounted light table, Earth Surf. Processes Landfors, 33, , doi: /esp J. M. Turoski, Eidgenössische Forschungsanstalt WSL Birensdorf, Zürcherstrasse 111, 8903 Birensdorf, Sitzerland. ( 10 of 10
Online Appendix I: A Model of Household Bargaining with Violence. In this appendix I develop a simple model of household bargaining that
Online Appendix I: A Model of Household Bargaining ith Violence In this appendix I develop a siple odel of household bargaining that incorporates violence and shos under hat assuptions an increase in oen
More informationUse of extrapolation to forecast the working capital in the mechanical engineering companies
ECONTECHMOD. AN INTERNATIONAL QUARTERLY JOURNAL 2014. Vol. 1. No. 1. 23 28 Use of extrapolation to forecast the working capital in the echanical engineering copanies A. Cherep, Y. Shvets Departent of finance
More informationThe Virtual Spring Mass System
The Virtual Spring Mass Syste J. S. Freudenberg EECS 6 Ebedded Control Systes Huan Coputer Interaction A force feedbac syste, such as the haptic heel used in the EECS 6 lab, is capable of exhibiting a
More informationPREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW
PREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW ABSTRACT: by Douglas J. Reineann, Ph.D. Assistant Professor of Agricultural Engineering and Graee A. Mein, Ph.D. Visiting Professor
More informationPERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO
Bulletin of the Transilvania University of Braşov Series I: Engineering Sciences Vol. 4 (53) No.  0 PERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO V. CAZACU I. SZÉKELY F. SANDU 3 T. BĂLAN Abstract:
More informationOnline Bagging and Boosting
Abstract Bagging and boosting are two of the ost wellknown enseble learning ethods due to their theoretical perforance guarantees and strong experiental results. However, these algoriths have been used
More information( C) CLASS 10. TEMPERATURE AND ATOMS
CLASS 10. EMPERAURE AND AOMS 10.1. INRODUCION Boyle s understanding of the pressurevolue relationship for gases occurred in the late 1600 s. he relationships between volue and teperature, and between
More informationReliability Constrained Packetsizing for Linear Multihop Wireless Networks
Reliability Constrained acketsizing for inear Multihop Wireless Networks Ning Wen, and Randall A. Berry Departent of Electrical Engineering and Coputer Science Northwestern University, Evanston, Illinois
More informationExtendedHorizon Analysis of Pressure Sensitivities for Leak Detection in Water Distribution Networks: Application to the Barcelona Network
2013 European Control Conference (ECC) July 1719, 2013, Zürich, Switzerland. ExtendedHorizon Analysis of Pressure Sensitivities for Leak Detection in Water Distribution Networks: Application to the Barcelona
More informationThe Mathematics of Pumping Water
The Matheatics of Puping Water AECOM Design Build Civil, Mechanical Engineering INTRODUCTION Please observe the conversion of units in calculations throughout this exeplar. In any puping syste, the role
More informationThis paper studies a rental firm that offers reusable products to price and qualityofservice sensitive
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol., No. 3, Suer 28, pp. 429 447 issn 523464 eissn 5265498 8 3 429 infors doi.287/so.7.8 28 INFORMS INFORMS holds copyright to this article and distributed
More informationEvaluating Inventory Management Performance: a Preliminary DeskSimulation Study Based on IOC Model
Evaluating Inventory Manageent Perforance: a Preliinary DeskSiulation Study Based on IOC Model Flora Bernardel, Roberto Panizzolo, and Davide Martinazzo Abstract The focus of this study is on preliinary
More informationPhysics 211: Lab Oscillations. Simple Harmonic Motion.
Physics 11: Lab Oscillations. Siple Haronic Motion. Reading Assignent: Chapter 15 Introduction: As we learned in class, physical systes will undergo an oscillatory otion, when displaced fro a stable equilibriu.
More informationMachine Learning Applications in Grid Computing
Machine Learning Applications in Grid Coputing George Cybenko, Guofei Jiang and Daniel Bilar Thayer School of Engineering Dartouth College Hanover, NH 03755, USA gvc@dartouth.edu, guofei.jiang@dartouth.edu
More informationAnalyzing Spatiotemporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy
Vol. 9, No. 5 (2016), pp.303312 http://dx.doi.org/10.14257/ijgdc.2016.9.5.26 Analyzing Spatioteporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy Chen Yang, Renjie Zhou
More informationMedia Adaptation Framework in Biofeedback System for Stroke Patient Rehabilitation
Media Adaptation Fraework in Biofeedback Syste for Stroke Patient Rehabilitation Yinpeng Chen, Weiwei Xu, Hari Sundara, Thanassis Rikakis, ShengMin Liu Arts, Media and Engineering Progra Arizona State
More informationarxiv:0805.1434v1 [math.pr] 9 May 2008
Degreedistribution stability of scalefree networs Zhenting Hou, Xiangxing Kong, Dinghua Shi,2, and Guanrong Chen 3 School of Matheatics, Central South University, Changsha 40083, China 2 Departent of
More informationLecture L9  Linear Impulse and Momentum. Collisions
J. Peraire, S. Widnall 16.07 Dynaics Fall 009 Version.0 Lecture L9  Linear Ipulse and Moentu. Collisions In this lecture, we will consider the equations that result fro integrating Newton s second law,
More informationData Streaming Algorithms for Estimating Entropy of Network Traffic
Data Streaing Algoriths for Estiating Entropy of Network Traffic Ashwin Lall University of Rochester Vyas Sekar Carnegie Mellon University Mitsunori Ogihara University of Rochester Jun (Ji) Xu Georgia
More informationInvesting in corporate bonds?
Investing in corporate bonds? This independent guide fro the Australian Securities and Investents Coission (ASIC) can help you look past the return and assess the risks of corporate bonds. If you re thinking
More informationCalculation Method for evaluating Solar Assisted Heat Pump Systems in SAP 2009. 15 July 2013
Calculation Method for evaluating Solar Assisted Heat Pup Systes in SAP 2009 15 July 2013 Page 1 of 17 1 Introduction This docuent describes how Solar Assisted Heat Pup Systes are recognised in the National
More informationLeak detection in open water channels
Proceedings of the 17th World Congress The International Federation of Autoatic Control Seoul, Korea, July 611, 28 Leak detection in open water channels Erik Weyer Georges Bastin Departent of Electrical
More informationOptimal Times to Decrease Extraction Rates During TwoStage Remediation Affected by RateLimited Transport Jose A. Saez, Loyola Marymount University
Optial Ties to Decrease Extraction ates During TwoStage eediation Affected by ateliited Transport Jose A. Saez, Loyola Maryount University Abstract Saez and Haron presented a twostage pup and treat
More informationNote on a generalized wage rigidity result. Abstract
Note on a generalized age rigidity result Ariit Mukheree University of Nottingha Abstract Considering Cournot copetition, this note shos that, if the firs differ in labor productivities, the equilibriu
More informationESTIMATING LIQUIDITY PREMIA IN THE SPANISH GOVERNMENT SECURITIES MARKET
ESTIMATING LIQUIDITY PREMIA IN THE SPANISH GOVERNMENT SECURITIES MARKET Francisco Alonso, Roberto Blanco, Ana del Río and Alicia Sanchis Banco de España Banco de España Servicio de Estudios Docuento de
More informationHW 2. Q v. kt Step 1: Calculate N using one of two equivalent methods. Problem 4.2. a. To Find:
HW 2 Proble 4.2 a. To Find: Nuber of vacancies per cubic eter at a given teperature. b. Given: T 850 degrees C 1123 K Q v 1.08 ev/ato Density of Fe ( ρ ) 7.65 g/cc Fe toic weight of iron ( c. ssuptions:
More informationScaling of Seepage Flow Velocity in Centrifuge Models CUED/DSOILS/TR326 (March 2003) N.I.Thusyanthan 1 & S.P.G.Madabhushi 2
Scaling of Seepage Flow Velocity in Centrifuge Models CUED/DSOILS/TR326 (March 2003) N.I.Thusyanthan 1 & S.P.G.Madabhushi 2 Research Student 1, Senior Lecturer 2, Cabridge University Engineering Departent
More informationThe Velocities of Gas Molecules
he Velocities of Gas Molecules by Flick Colean Departent of Cheistry Wellesley College Wellesley MA 8 Copyright Flick Colean 996 All rights reserved You are welcoe to use this docuent in your own classes
More informationWork, Energy, Conservation of Energy
This test covers Work, echanical energy, kinetic energy, potential energy (gravitational and elastic), Hooke s Law, Conservation of Energy, heat energy, conservative and nonconservative forces, with soe
More informationPure Bending Determination of StressStrain Curves for an Aluminum Alloy
Proceedings of the World Congress on Engineering 0 Vol III WCE 0, July 68, 0, London, U.K. Pure Bending Deterination of StressStrain Curves for an Aluinu Alloy D. TorresFranco, G. UrriolagoitiaSosa,
More informationFuzzy Sets in HR Management
Acta Polytechnica Hungarica Vol. 8, No. 3, 2011 Fuzzy Sets in HR Manageent Blanka Zeková AXIOM SW, s.r.o., 760 01 Zlín, Czech Republic blanka.zekova@sezna.cz Jana Talašová Faculty of Science, Palacký Univerzity,
More informationAn Innovate Dynamic Load Balancing Algorithm Based on Task
An Innovate Dynaic Load Balancing Algorith Based on Task Classification Hongbin Wang,,a, Zhiyi Fang, b, Guannan Qu,*,c, Xiaodan Ren,d College of Coputer Science and Technology, Jilin University, Changchun
More informationQuality evaluation of the modelbased forecasts of implied volatility index
Quality evaluation of the odelbased forecasts of iplied volatility index Katarzyna Łęczycka 1 Abstract Influence of volatility on financial arket forecasts is very high. It appears as a specific factor
More informationExperiment 2 Index of refraction of an unknown liquid  Abbe Refractometer
Experient Index of refraction of an unknown liquid  Abbe Refractoeter Principle: The value n ay be written in the for sin ( δ +θ ) n =. θ sin This relation provides us with one or the standard ethods
More informationA CHAOS MODEL OF SUBHARMONIC OSCILLATIONS IN CURRENT MODE PWM BOOST CONVERTERS
A CHAOS MODEL OF SUBHARMONIC OSCILLATIONS IN CURRENT MODE PWM BOOST CONVERTERS Isaac Zafrany and Sa BenYaakov Departent of Electrical and Coputer Engineering BenGurion University of the Negev P. O. Box
More informationExample: Suppose that we deposit $1000 in a bank account offering 3% interest, compounded monthly. How will our money grow?
Finance 111 Finance We have to work with oney every day. While balancing your checkbook or calculating your onthly expenditures on espresso requires only arithetic, when we start saving, planning for retireent,
More informationInvesting in corporate bonds?
Investing in corporate bonds? This independent guide fro the Australian Securities and Investents Coission (ASIC) can help you look past the return and assess the risks of corporate bonds. If you re thinking
More informationEnergy Proportionality for Disk Storage Using Replication
Energy Proportionality for Disk Storage Using Replication Jinoh Ki and Doron Rote Lawrence Berkeley National Laboratory University of California, Berkeley, CA 94720 {jinohki,d rote}@lbl.gov Abstract Energy
More informationExercise 4 INVESTIGATION OF THE ONEDEGREEOFFREEDOM SYSTEM
Eercise 4 IVESTIGATIO OF THE OEDEGREEOFFREEDOM SYSTEM 1. Ai of the eercise Identification of paraeters of the euation describing a onedegreeof freedo (1 DOF) atheatical odel of the real vibrating
More informationImage restoration for a rectangular poorpixels detector
Iage restoration for a rectangular poorpixels detector Pengcheng Wen 1, Xiangjun Wang 1, Hong Wei 2 1 State Key Laboratory of Precision Measuring Technology and Instruents, Tianjin University, China 2
More informationPricing Asian Options using Monte Carlo Methods
U.U.D.M. Project Report 9:7 Pricing Asian Options using Monte Carlo Methods Hongbin Zhang Exaensarbete i ateatik, 3 hp Handledare och exainator: Johan Tysk Juni 9 Departent of Matheatics Uppsala University
More informationApplying Multiple Neural Networks on Large Scale Data
0 International Conference on Inforation and Electronics Engineering IPCSIT vol6 (0) (0) IACSIT Press, Singapore Applying Multiple Neural Networks on Large Scale Data Kritsanatt Boonkiatpong and Sukree
More informationInsurance Spirals and the Lloyd s Market
Insurance Spirals and the Lloyd s Market Andrew Bain University of Glasgow Abstract This paper presents a odel of reinsurance arket spirals, and applies it to the situation that existed in the Lloyd s
More informationMarkov Models and Their Use for Calculations of Important Traffic Parameters of Contact Center
Markov Models and Their Use for Calculations of Iportant Traffic Paraeters of Contact Center ERIK CHROMY, JAN DIEZKA, MATEJ KAVACKY Institute of Telecounications Slovak University of Technology Bratislava
More informationCRM FACTORS ASSESSMENT USING ANALYTIC HIERARCHY PROCESS
641 CRM FACTORS ASSESSMENT USING ANALYTIC HIERARCHY PROCESS Marketa Zajarosova 1* *Ph.D. VSB  Technical University of Ostrava, THE CZECH REPUBLIC arketa.zajarosova@vsb.cz Abstract Custoer relationship
More informationThe Research of Measuring Approach and Energy Efficiency for Hadoop Periodic Jobs
Send Orders for Reprints to reprints@benthascience.ae 206 The Open Fuels & Energy Science Journal, 2015, 8, 206210 Open Access The Research of Measuring Approach and Energy Efficiency for Hadoop Periodic
More informationADJUSTING FOR QUALITY CHANGE
ADJUSTING FOR QUALITY CHANGE 7 Introduction 7.1 The easureent of changes in the level of consuer prices is coplicated by the appearance and disappearance of new and old goods and services, as well as changes
More informationSearching strategy for multitarget discovery in wireless networks
Searching strategy for ultitarget discovery in wireless networks Zhao Cheng, Wendi B. Heinzelan Departent of Electrical and Coputer Engineering University of Rochester Rochester, NY 467 (585) 75{878,
More informationA shortterm, patternbased model for waterdemand forecasting
39 Q IWA Publishing 2007 Journal of Hydroinforatics 09.1 2007 A shortter, patternbased odel for waterdeand forecasting Stefano Alvisi, Marco Franchini and Alberto Marinelli ABSTRACT The shortter, deandforecasting
More informationKinetic Molecular Theory of Ideal Gases
ecture /. Kinetic olecular Theory of Ideal Gases ast ecture. IG is a purely epirical law  solely the consequence of eperiental obserations Eplains the behaior of gases oer a liited range of conditions.
More informationEarnings and Community College Field of Study Choice in Canada
DISCUSSION PAPER SERIES IZA DP No. 1156 Earnings and Counity College Field of Study Choice in Canada Brahi Boudarbat May 2004 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor
More informationSalty Waters. Instructions for the activity 3. Results Worksheet 5. Class Results Sheet 7. Teacher Notes 8. Sample results. 12
1 Salty Waters Alost all of the water on Earth is in the for of a solution containing dissolved salts. In this activity students are invited to easure the salinity of a saple of salt water. While carrying
More informationChapter 5. Principles of Unsteady  State Heat Transfer
Suppleental Material for ransport Process and Separation Process Principles hapter 5 Principles of Unsteady  State Heat ransfer In this chapter, we will study cheical processes where heat transfer is
More information6. Time (or Space) Series Analysis
ATM 55 otes: Tie Series Analysis  Section 6a Page 8 6. Tie (or Space) Series Analysis In this chapter we will consider soe coon aspects of tie series analysis including autocorrelation, statistical prediction,
More informationSoftware Quality Characteristics Tested For Mobile Application Development
Thesis no: MGSE201502 Software Quality Characteristics Tested For Mobile Application Developent Literature Review and Epirical Survey WALEED ANWAR Faculty of Coputing Blekinge Institute of Technology
More informationExperience with WinterKennedy coefficients on hydraulic identical units
IGHEM 014 The 10 th International conference on hydraulic efficiency easureents Itajuba, Brasil Septeber 16 th  18 th, 014 XXXXXX Experience with WinterKennedy coefficients on hydraulic identical units
More informationResearch Article Performance Evaluation of Human Resource Outsourcing in Food Processing Enterprises
Advance Journal of Food Science and Technology 9(2): 964969, 205 ISSN: 20424868; eissn: 20424876 205 Maxwell Scientific Publication Corp. Subitted: August 0, 205 Accepted: Septeber 3, 205 Published:
More informationA magnetic Rotor to convert vacuumenergy into mechanical energy
A agnetic Rotor to convert vacuuenergy into echanical energy Claus W. Turtur, University of Applied Sciences BraunschweigWolfenbüttel Abstract Wolfenbüttel, Mai 21 2008 In previous work it was deonstrated,
More informationA Quantitative Approach to the Performance of Internet Telephony to Ebusiness Sites
A Quantitative Approach to the Performance of Internet Telephony to Ebusiness Sites Prathiusha Chinnusamy TransSolutions Fort Worth, TX 76155, USA Natarajan Gautam Harold and Inge Marcus Department of
More informationGeneral tolerances for Iinearand angular dimensions and geometrical=.tolerances
oa /  UDC 21 753 1 : 21 7 : 21 9 : 744 43 DEUTSCHE NORM April 1991 General tolerances for Iinearand angular diensions and geoetrical= tolerances (not to be used for new destgns) 'j' ;,, DIN 718 Allgeeintoleranzen
More informationPreferencebased Search and Multicriteria Optimization
Fro: AAAI02 Proceedings. Copyright 2002, AAAI (www.aaai.org). All rights reserved. Preferencebased Search and Multicriteria Optiization Ulrich Junker ILOG 1681, route des Dolines F06560 Valbonne ujunker@ilog.fr
More informationThe United States was in the midst of a
A Prier on the Mortgage Market and Mortgage Finance Daniel J. McDonald and Daniel L. Thornton This article is a prier on ortgage finance. It discusses the basics of the ortgage arket and ortgage finance.
More informationManaging Complex Network Operation with Predictive Analytics
Managing Coplex Network Operation with Predictive Analytics Zhenyu Huang, Pak Chung Wong, Patrick Mackey, Yousu Chen, Jian Ma, Kevin Schneider, and Frank L. Greitzer Pacific Northwest National Laboratory
More informationThe Fundamentals of Modal Testing
The Fundaentals of Modal Testing Application Note 2433 Η(ω) = Σ n r=1 φ φ i j / 2 2 2 2 ( ω n  ω ) + (2ξωωn) Preface Modal analysis is defined as the study of the dynaic characteristics of a echanical
More informationExploiting Hardware Heterogeneity within the Same Instance Type of Amazon EC2
Exploiting Hardware Heterogeneity within the Sae Instance Type of Aazon EC2 Zhonghong Ou, Hao Zhuang, Jukka K. Nurinen, Antti YläJääski, Pan Hui Aalto University, Finland; Deutsch Teleko Laboratories,
More informationA Gas Law And Absolute Zero
A Gas Law And Absolute Zero Equipent safety goggles, DataStudio, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution This experient deals with aterials that are very
More informationFactored Models for Probabilistic Modal Logic
Proceedings of the TwentyThird AAAI Conference on Artificial Intelligence (2008 Factored Models for Probabilistic Modal Logic Afsaneh Shirazi and Eyal Air Coputer Science Departent, University of Illinois
More informationProject Evaluation Roadmap. Capital Budgeting Process. Capital Expenditure. Major Cash Flow Components. Cash Flows... COMM2501 Financial Management
COMM501 Financial Manageent Project Evaluation 1 (Capital Budgeting) Project Evaluation Roadap COMM501 Financial Manageent Week 7 Week 7 Project dependencies Net present value ethod Relevant cash flows
More informationAn Integrated Approach for Monitoring Service Level Parameters of SoftwareDefined Networking
International Journal of Future Generation Counication and Networking Vol. 8, No. 6 (15), pp. 1974 http://d.doi.org/1.1457/ijfgcn.15.8.6.19 An Integrated Approach for Monitoring Service Level Paraeters
More informationInternational Journal of Management & Information Systems First Quarter 2012 Volume 16, Number 1
International Journal of Manageent & Inforation Systes First Quarter 2012 Volue 16, Nuber 1 Proposal And Effectiveness Of A Highly Copelling Direct Mail Method  Establishent And Deployent Of PMOSDM Hisatoshi
More informationKeywords: Threedegree of freedom, mathematical model, free vibration, axial motion, simulate.
ISSN: 95967 ISO 900:008 Certiied International Journal o Engineering Science and Innovative Technolog (IJESIT) Volue, Issue 4, Jul 0 A ThreeDegree o Freedo Matheatical Model Siulating Free Vibration
More informationModified Latin Hypercube Sampling Monte Carlo (MLHSMC) Estimation for Average Quality Index
Analog Integrated Circuits and Signal Processing, vol. 9, no., April 999. Abstract Modified Latin Hypercube Sapling Monte Carlo (MLHSMC) Estiation for Average Quality Index Mansour Keraat and Richard Kielbasa
More informationABSTRACT KEYWORDS. Comonotonicity, dependence, correlation, concordance, copula, multivariate. 1. INTRODUCTION
MEASURING COMONOTONICITY IN MDIMENSIONAL VECTORS BY INGE KOCH AND ANN DE SCHEPPER ABSTRACT In this contribution, a new easure of coonotonicity for diensional vectors is introduced, with values between
More informationElectric Forces between Charged Plates
CP.1 Goals of this lab Electric Forces between Charged Plates Overview deterine the force between charged parallel plates easure the perittivity of the vacuu (ε 0 ) In this experient you will easure the
More informationReal Time Target Tracking with Binary Sensor Networks and Parallel Computing
Real Tie Target Tracking with Binary Sensor Networks and Parallel Coputing Hong Lin, John Rushing, Sara J. Graves, Steve Tanner, and Evans Criswell Abstract A parallel real tie data fusion and target tracking
More informationCOMPARISON BETWEEN THE NORMAL AND WEIBULL DISTRIBUTIONS FOR ANALYZING THE COMPRESSIVE STRENGTH OF THE CONCRETE
1 COMPARISON BETWEEN THE NORMAL AND WEIBULL DISTRIBUTIONS FOR ANALYZING THE COMPRESSIVE STRENGTH OF THE CONCRETE Jorge Michael Colan 1, Paulo Eduardo Teodoro, Matheus Piazzalunga Neivock 3, Gilson Secco
More informationData Set Generation for Rectangular Placement Problems
Data Set Generation for Rectangular Placeent Probles Christine L. Valenzuela (Muford) Pearl Y. Wang School of Coputer Science & Inforatics Departent of Coputer Science MS 4A5 Cardiff University George
More informationOptimization of a Piezoelectric Crystal Driver Stage using System Simulations
Optiization of a Piezoelectric Crystal Driver Stage using Syste Siulations Jonny Johansson Lulel University of Technology 97 87 Lulel, Sweden Abstract Using SPICE, successful efforts have previously been
More informationA Gas Law And Absolute Zero Lab 11
HB 040605 A Gas Law And Absolute Zero Lab 11 1 A Gas Law And Absolute Zero Lab 11 Equipent safety goggles, SWS, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution
More informationCRITERIUM FOR FUNCTION DEFININING OF FINAL TIME SHARING OF THE BASIC CLARK S FLOW PRECEDENCE DIAGRAMMING (PDM) STRUCTURE
st Logistics International Conference Belgrade, Serbia 830 November 03 CRITERIUM FOR FUNCTION DEFININING OF FINAL TIME SHARING OF THE BASIC CLARK S FLOW PRECEDENCE DIAGRAMMING (PDM STRUCTURE Branko Davidović
More informationAn Approach to Combating Freeriding in PeertoPeer Networks
An Approach to Cobating Freeriding in PeertoPeer Networks Victor Ponce, Jie Wu, and Xiuqi Li Departent of Coputer Science and Engineering Florida Atlantic University Boca Raton, FL 33431 April 7, 2008
More informationEnergy Efficient VM Scheduling for Cloud Data Centers: Exact allocation and migration algorithms
Energy Efficient VM Scheduling for Cloud Data Centers: Exact allocation and igration algoriths Chaia Ghribi, Makhlouf Hadji and Djaal Zeghlache Institut MinesTéléco, Téléco SudParis UMR CNRS 5157 9, Rue
More informationThe Model of Lines for Option Pricing with Jumps
The Model of Lines for Option Pricing with Jups Claudio Albanese, Sebastian Jaiungal and Ditri H Rubisov January 17, 21 Departent of Matheatics, University of Toronto Abstract This article reviews a pricing
More informationEvaluating Software Quality of Vendors using Fuzzy Analytic Hierarchy Process
IMECS 2008 92 March 2008 Hong Kong Evaluating Software Quality of Vendors using Fuzzy Analytic Hierarchy Process Kevin K.F. Yuen* Henry C.W. au Abstract This paper proposes a fuzzy Analytic Hierarchy
More informationDesign, optimization and prototyping of small power transformers
Doctoral School of Energy and Geotechnology January 15 20, 2007. Kuressaare, Estonia Design, optiization and prototyping of sall power transforers Avo Reinap, Rando Pikner, Roan Ionikan, Karl Pärn Tallinn
More informationModeling operational risk data reported above a timevarying threshold
Modeling operational risk data reported above a tievarying threshold Pavel V. Shevchenko CSIRO Matheatical and Inforation Sciences, Sydney, Locked bag 7, North Ryde, NSW, 670, Australia. eail: Pavel.Shevchenko@csiro.au
More informationFactor Model. Arbitrage Pricing Theory. Systematic Versus NonSystematic Risk. Intuitive Argument
Ross [1],[]) presents the aritrage pricing theory. The idea is that the structure of asset returns leads naturally to a odel of risk preia, for otherwise there would exist an opportunity for aritrage profit.
More informationAudio Engineering Society. Convention Paper. Presented at the 119th Convention 2005 October 7 10 New York, New York USA
Audio Engineering Society Convention Paper Presented at the 119th Convention 2005 October 7 10 New York, New York USA This convention paper has been reproduced fro the authors advance anuscript, without
More informationLesson 44: Acceleration, Velocity, and Period in SHM
Lesson 44: Acceleration, Velocity, and Period in SHM Since there is a restoring force acting on objects in SHM it akes sense that the object will accelerate. In Physics 20 you are only required to explain
More informationAn online sulfur monitoring system can improve process balance sheets
Originally appeared in: February 2007, pgs 109116. Used with perission. An online sulfur onitoring syste can iprove process balance sheets A Canadian gas processor used this technology to eet environental
More informationCOMBINING CRASH RECORDER AND PAIRED COMPARISON TECHNIQUE: INJURY RISK FUNCTIONS IN FRONTAL AND REAR IMPACTS WITH SPECIAL REFERENCE TO NECK INJURIES
COMBINING CRASH RECORDER AND AIRED COMARISON TECHNIQUE: INJURY RISK FUNCTIONS IN FRONTAL AND REAR IMACTS WITH SECIAL REFERENCE TO NECK INJURIES Anders Kullgren, Maria Krafft Folksa Research, 66 Stockhol,
More informationREDUCING RISK OF HANDARM VIBRATION INJURY FROM HANDHELD POWER TOOLS INTRODUCTION
Health and Safety Executive Information Document HSE 246/31 REDUCING RISK OF HANDARM VIBRATION INJURY FROM HANDHELD POWER TOOLS INTRODUCTION 1 This document contains internal guidance hich has been made
More informationStandards and Protocols for the Collection and Dissemination of Graduating Student Initial Career Outcomes Information For Undergraduates
National Association of Colleges and Eployers Standards and Protocols for the Collection and Disseination of Graduating Student Initial Career Outcoes Inforation For Undergraduates Developed by the NACE
More informationEUROMAP 46.1. Extrusion Blow Moulding Machines Determination of Machine Related Energy Efficiency Class. Version 1.0, January 2014 13 pages
EUROMAP 46.1 Extrusion Blow Moulding Machines Deterination of Machine Related Energy Efficiency Class Version 1.0, January 2014 13 pages This recoendation was prepared by the Technical Coission of EUROMAP.
More informationOpenGamma Documentation Bond Pricing
OpenGaa Docuentation Bond Pricing Marc Henrard arc@opengaa.co OpenGaa Docuentation n. 5 Version 2.0  May 2013 Abstract The details of the ipleentation of pricing for fixed coupon bonds and floating rate
More informationThe AGA Evaluating Model of Customer Loyalty Based on Ecommerce Environment
6 JOURNAL OF SOFTWARE, VOL. 4, NO. 3, MAY 009 The AGA Evaluating Model of Custoer Loyalty Based on Ecoerce Environent Shaoei Yang Econoics and Manageent Departent, North China Electric Power University,
More informationAirline Yield Management with Overbooking, Cancellations, and NoShows JANAKIRAM SUBRAMANIAN
Airline Yield Manageent with Overbooking, Cancellations, and NoShows JANAKIRAM SUBRAMANIAN Integral Developent Corporation, 301 University Avenue, Suite 200, Palo Alto, California 94301 SHALER STIDHAM
More informationMarkovian inventory policy with application to the paper industry
Coputers and Cheical Engineering 26 (2002) 1399 1413 www.elsevier.co/locate/copcheeng Markovian inventory policy with application to the paper industry K. Karen Yin a, *, Hu Liu a,1, Neil E. Johnson b,2
More informationChapter 13 Simple Harmonic Motion
We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances. Isaac Newton 13.1 Introduction to Periodic Motion Periodic otion is any otion that
More informationAnswer, Key Homework 7 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Hoework 7 David McIntyre 453 Mar 5, 004 This printout should have 4 questions. Multiplechoice questions ay continue on the next colun or page find all choices before aking your selection.
More information