On Rayleigh Optical Depth Calculations

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "On Rayleigh Optical Depth Calculations"

Transcription

1 1854 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 On Rayleigh Optical Depth Calculation BARRY A. BODHAINE NOAA/Climate Monitoring and Diagnotic Laboratory, Boulder, Colorado NORMAN B. WOOD Cooperative Intitute for Reearch in Environmental Science, NOAA/Climate Monitoring and Diagnotic Laboratory, Boulder, Colorado ELLSWORTH G. DUTTON NOAA/Climate Monitoring and Diagnotic Laboratory, Boulder, Colorado JAMES R. SLUSSER Natural Reource Ecology Laboratory, Colorado State Univerity, Fort Collin, Colorado 1 January 1999 and 3 May 1999 ABSTRACT Many different technique are ued for the calculation of Rayleigh optical depth in the atmophere. In ome cae difference among thee technique can be important, epecially in the UV region of the pectrum and under clean atmopheric condition. The author recommend that the calculation of Rayleigh optical depth be approached by going back to the firt principle of Rayleigh cattering theory rather than the variety of curvefitting technique currently in ue. A urvey of the literature wa conducted in order to determine the latet value of the phyical contant neceary and to review the method available for the calculation of Rayleigh optical depth. The recommended approach require the accurate calculation of the refractive index of air baed on the latet publihed meaurement. Calculation etimating Rayleigh optical depth hould be done a accurately a poible becaue the inaccuracie that arie can equal or even exceed other quantitie being etimated, uch a aerool optical depth, particularly in the UV region of the pectrum. All of the calculation are imple enough to be done eaily in a preadheet. 1. Introduction Modern Rayleigh cattering calculation have traditionally been made by tarting with thoe preented by Penndorf (1957). In Penndorf paper, the refractive index of air wa calculated uing the equation of Edlén (1953): (n 1) , (1) where n i the refractive index of air and i the wavelength of light in micrometer. Thi equation i for tandard air, which i defined a dry air at 760 mm Hg ( mb), 15C (88.15 K), and containing 300 Correponding author addre: Barry A. Bodhaine, NOAA/ CMDL, R/E/CG1, 35 Broadway, Boulder, CO ppm CO. It i an empirical relationhip derived by fitting the bet available experimental data and i dependent on the compoition of air, particularly CO and water vapor. Next, Penndorf (1957) calculated the Rayleigh cattering coefficient for tandard air uing the claic equation that i preented in many textbook (e.g., van de Hult 1957; McCartney 1976): 3 4 (n 1) 6 3, () 4 N (n ) 6 7 where i the cattering cro ection per molecule; N i molecular denity; the term (6 3)/(6 7) i called the depolarization term, F(air), or the King factor; and i the depolarization factor or depolarization ratio, which decribe the effect of molecular aniotropy. The F(air) term i the leat known for purpoe of Rayleigh cattering calculation and i reponible for the mot uncertainty. The depolarization term doe not depend on temperature and preure, but doe depend on the ga mixture. Alo, N depend on temperature and pre American Meteorological Society

2 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1855 ure, but doe not depend on the ga mixture. The reulting value of, the cattering cro ection per molecule of the ga, calculated from Eq. (), i independent of temperature and preure, but doe depend on the compoition of the ga. Note that N depend on Avogadro number and the molar volume contant, and i expreed a molecule per cubic centimeter, and that value for n and N mut be expreed at the ame temperature and preure. However, ince ( n 1)/ ( n ) i proportional to N, the reulting expreion for i independent of temperature and preure (Mc- Cartney 1976; Bucholtz 1995). Note that the uual approximation n 3 wa not included in Eq. () in the interet of keeping all calculation a accurate a poible. Reult of uch calculation were preented by Penndorf (1957) in hi Table III. It i thi table of value that ha been ued by many worker in the field to etimate Rayleigh optical depth, uually by ome curve-fitting routine over a particular wavelength range of interet. Soon after Penndorf paper wa publihed, Edlén (1966) preented a new formula for etimating the refractive index of tandard air: (n 1) , (3) although the maximum deviation of n from the 1953 formula wa given a only Edlén (1953, 1966) alo dicued the variation of refractive index with temperature and preure, and alo with varying concentration of CO and water vapor. In light of the Edlén (1966) reviion, Owen (1967) preented an indepth treatment of the indexe of refraction of dry CO - free air, pure CO, and pure water vapor, and provided expreion for dependence on temperature, preure, and compoition. However, Owen (1967) main interet wa in temperature and preure variation, and hi analyi doe not ignificantly impact our preent work becaue our calculation are performed at the temperature and preure of tandard air. Peck and Reeder (197) further refined the currently available data for the refractive index of air and uggeted the formula (n 1) (4) for the mot accuracy over a wide range of wavelength. Equation (4) i pecified for tandard air but at the beginning of their paper, Peck and Reeder (197) pecify tandard air a having 330 ppm CO. Alo, they repeat Edlén (1966) formula, which had clearly defined tandard air a having 300 ppm CO, but tate that it applie to air having 330 ppm CO. Here we will ue the equation of Peck and Reeder (197) and aume that it hold for tandard air having 300 ppm CO. Poible error in the depolarization term were conidered by Hoyt (1977), Fröhlich and Shaw (1980), and Young (1980, 1981). The correction propoed by Young (1981) had been accepted for modern Rayleigh cattering calculation in atmopheric application. In brief, Young (1981) uggeted that the value F(air) (6 3)/(6 7) be ued rather than the value ued by Penndorf (1957). Thi effect alone reduced Rayleigh cattering value by 1.%; however, it cannot be applied over the entire pectrum becaue F(air) i dependent on wavelength. Furthermore, ince the depolarization ha been meaured for the contituent of air (at leat in a relative ene), it i poible in principle to etimate the depolarization of air a a function of compoition. Bate (1984) and Bucholtz (1995) dicued the depolarization in detail. It appear that currently the bet etimate for (6 3)/(6 7) ue the equation given by Bate (1984) for the depolarization of N,O, Ar, and CO a a function of wavelength. It i therefore poible to calculate the depolarization of air a a function of CO concentration. Bate (1984) gave a formula for the depolarization of N a a function of wavelength a 1 4 F(N ) , (5) and for the depolarization of O a 1 F(O ) (6) Furthermore, Bate (1984) recommended that F(air) be calculated uing Eq. (5) and (6), auming that F(Ar) 1.00, F(CO ) 1.15, and ignoring the other contituent of air.. Optical depth A quantity of fundamental importance in atmopheric tudie i the optical depth (or optical thickne). Thi quantity ha been dicued by numerou author (e.g., Dutton et al. 1994; Stephen 1994) and i derived from the exponential law of attenuation variouly known a Bouguer law, Lambert law, or Beer law. For purpoe of illutration only, Bouguer law may be imply written a I() I 0 () exp[()/co], (7) where I 0 () i the extraterretrial flux at wavelength, I() i the flux reaching the ground, i the olar zenith angle, and () i the optical depth. Clear-ky meaurement of I() a a function of, and plotted a lni() veru ec, hould yield a traight line with lope () and intercept I 0 (extrapolated back to ec 0). An excellent example, along with a dicuion of thi proce, i hown by Stephen (1994) in hi Fig

3 1856 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 An important point i that (), the total optical depth, may be compoed of everal component given by () R () a () g (), (8) where R () i the Rayleigh optical depth, a () i aerool optical depth, and g () i the optical depth due to aborption by gae uch a O 3,NO, and H O. In principle it i poible to meaure () and then derive aerool optical depth by ubtracting etimate of R () and g (). In practice, however, arriving at reaonable etimate of thee quantitie can be difficult, particularly during fairly clean atmopheric condition uch a thoe found at Mauna Loa, Hawaii. At thi point it hould be apparent that in order to iolate the individual component of optical depth it i neceary to provide accurate etimate of Rayleigh optical depth. Rayleigh optical depth i relatively eay to calculate once the cattering cro ection per molecule ha been determined for a given wavelength and compoition becaue it depend only on the atmopheric preure at the ite. That i, it i neceary to calculate only the total number of molecule per unit area in the column above the ite, and thi depend only on the preure, a hown in the formula PA R(), (9) mg a where P i the preure, A i Avogadro number, m a i the mean molecular weight of the air, and g i the acceleration of gravity. Note that m a depend on the compoition of the air, wherea A and g are contant of nature. Although g may be conidered a contant of nature, it doe vary ignificantly with height and location on the earth urface and may be calculated according to the formula (Lit 1968) g (cm ) g 0 ( co)z ( co)z ( co)z 3, (10) where i the latitude, z i the height above ea level in meter, and g 0 i the ea level acceleration of gravity given by g ( co co ). (11) 3. Approximation for Rayleigh optical depth Many author have imply taken Rayleigh cattering cro-ection data from Penndorf (1957) over a particular wavelength interval of interet and applied a curvefitting routine to approximate the data for their own purpoe. Some, but not all, of thee author have applied Young (1981) correction. Teillet (1990) compared the formulation of everal author and found ignificant difference among them. It i not the purpoe of thi paper to urvey all of the approximation in ue by variou author nor i it to compare accuracie of the variou method; however, a few example will erve to illutrate ome of the difficultie. The implet approach, taken by many author, i to fit an equation of the form () A B, (1) where A and B are contant to be determined from a power-law fit and the equation i normalized to mb preure. An example wa given by Dutton et al. (1994), who performed uch a fit over the viible range and provided the equation p 4.05 () , (13) R p 0 where p i the ite preure, p 0 i mb, and i in micrometer. Clearly, one problem with thi approximation i that it cannot be extrapolated to other part of the pectrum, particularly the UV, where the powerlaw exponent i ignificantly different. To account for the fact that the exponent change, ome author (e.g., Fröhlich and Shaw 1980; Nicolet 1984) ued equation of the form molecule (BCD 1) R() A, (14) cm where the term molecule cm i calculated from the urface preure, a explained above. Thi equation i likely to be more accurate over a greater range of the pectrum. A lightly different approach wa taken by Hanen and Travi (1974), who uggeted the equation R () ( ), (15) where R () i normalized to mb. A a final example Stephen (1994) uggeted the equation R () (4.150.) (0.1188z z e ), (16) where the expreion i given in term of altitude (km) above ea level uing the tandard atmophere. The point here i that all of thee equation were ueful for the particular author over a limited wavelength range and at limited accuracy. Comparing thee variou equation how ignificant difference, epecially in the UV (Teillet 1990). More importantly, the difference among thee equation can be ignificantly greater than typical aerool optical depth found in the atmophere. In the cae of clean condition at Mauna Loa, it i poible for aerool optical depth to be calculated a negative value becaue of thee error.

4 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1857 TABLE 1. Contituent and mean molecular weight of dry air. Ga % volume Molecular wt % vol mol wt N O Ar Ne He Kr H Xe CO Mean molecular weight with zero CO Mean molecular weight with 360 ppm CO gm mol gm mol 1 4. Suggeted method to calculate Rayleigh optical depth of air Here we ugget a method for calculation of Rayleigh optical depth that goe back to firt principle a uggeted by Penndorf (1957) rather than uing curve-fitting technique, although it i true that the refractive index of air i till derived from a curve fit to experimental data. We ugget uing all of the latet value of the phyical contant of nature, and we ugget including the variability in refractive index, and alo the mean molecular weight of air, due to CO even though thee effect are in the range of 0.1% 0.01%. It hould be noted that aerool optical depth are often a low a 0.01 at Mauna Loa. Since Rayleigh optical depth i of the order of 1 at 300 nm, it i een that a 0.1% error in Rayleigh optical depth tranlate into a 10% error in aerool optical depth. Furthermore, it imply make ene to perform the calculation a accurately a poible. We hould note that the effect of high concentration of water vapor on the refractive index of air may be of the ame order a CO (Edlén 1953, 1966). However, for practical atmopheric ituation the total water vapor in the vertical column i mall and doe not ignificantly affect the above calculation. Furthermore, the water vapor in the atmophere i uually confined to a thin layer near the urface, which ignificantly complicate the calculation, wherea CO i generally well mixed throughout the atmophere. To facilitate the following Rayleigh optical depth calculation, the latet value of Avogadro number ( molecule mol 1 ), and molar volume at K and mb (.4141 L mol 1 ) were taken from Cohen and Taylor (1995). In order to calculate the mean molecular weight of dry air with variou concentration of CO, the percent by volume of the contituent gae in air were taken from Seinfeld and Pandi (1998), and the molecular weight of thoe gae were taken from the Handbook of Phyic and Chemitry (CRC 1997). Thee reult are hown in Table 1. The mean molecular weight (m a ) for dry air were calculated from the formula (%Vol MolWt) ma. (17) (%Vol) Note that the error ariing from the fact that (%Vol) i not exactly 100 i negligible. Auming a imple linear relationhip between m a and CO concentration, m a may be etimated from the equation m a (CO ) gm mol 1, where CO concentration i expreed a part per volume (ue for 360 ppm). We recommend tarting with Peck and Reeder (197) formula for the refractive index of dry air with 300 ppm CO concentration: (n300 1) , (18) and caling for the deired CO concentration uing the formula (n 1) CO (CO ), (19) (n 1) 300 where the CO concentration i expreed a part per volume (Edlén 1966). Thu the refractive index for dry air with zero ppm CO i (n0 1) , (0) and the refractive index for dry air with 360 ppm CO i (n360 1) , (1) where it mut be emphaized that Eq. (18) (1) are given for K and mb, and in unit of micrometer. We recommend that the cattering cro ection (cm molecule 1 ) of air be calculated from the equation 3 4 (n 1) 6 3, () 4 N (n ) 6 7 where n i the refractive index of air at the deired CO concentration, i expreed in unit of centimeter, N molecule cm 3 at K and mb, and the depolarization ratio i calculated a follow. Uing the value for depolarization of the gae O,N, Ar, and CO provided by Bate (1984), we recommend that the depolarization of dry air be calculated uing Eq. (5) (6) and the following equation to take into account the compoition of air:

5 1858 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME F(N ) 0.946F(O ) CCO 1.15 F(air, CO ), (3) C CO where C CO i the concentration of CO expreed in part per volume by percent (e.g., ue for 360 ppm). The reult of Eq. (3) for tandard air (300 ppm CO ) are hown in Fig. 1. Note that the value of N in Eq. () wa calculated from Avogadro number and the molar volume, and then caled to K according to the formula 3 N (molecule cm ) molecule mol K L mol K 1L. (4) 1000 cm 3 Finally, we recommend that the Rayleigh optical depth be calculated from the formula PA R(), (5) mg a where P i the urface preure of the meaurement ite (dyn cm ), A i Avogadro number, and m a i the mean molecular weight of dry air calculated from the formula m a (CO ) , a in Eq. (17). The value for g need to be repreentative of the maweighted column of air molecule above the ite, and hould be calculated from Eq. (10) (11), modified by uing a value of z c determined from the U.S. Standard Atmophere, a provided by Lit (1968). To determine z c we ued Lit (1968, p. 67) table of the denity of air a a function of altitude and calculated a maweighted mean above each altitude value, uing an average altitude and average denity for each layer lited in the table. Next a leat quare traight line wa paed through the reulting z c value up to m, giving the following equation: z c z , (6) where z i the altitude of the oberving ite and z c i the effective ma-weighted altitude of the column. For example, an altitude of z 0 m yield an effective maweighted column altitude of z c m to ue in the calculation of g. The reulting value or R hould be conidered the bet currently available value for the mot accurate etimate of optical depth. 5. Optical depth of the contituent of air A a enitivity tudy, the contribution of CO to the Rayleigh optical depth of air may be etimated a a function of wavelength by uing the above formula expreed for CO. Owen (1967) give the refractive index of CO at 15C and mb a 8 (nco 1) , (7) where i expreed in unit of micrometer a before. Next the cattering cro ection of a CO molecule can be calculated from Eq. (), where N molecule cm 3 at K and mb a before, and the King factor F(CO ) taken to be 1.15, a uggeted by Bate (1984). Finally (CO, ) can be calculated uing Eq. (5), where m (the molecular weight of CO ), and multiplying by (for a CO concentration of 360 ppm) to etimate the number of CO molecule. Note that (H O, ) for 44 kg m column water vapor wa calculated in a imilar manner uing the refractive index of H O given by Harvey et al. (1998) and a depolarization ratio of 0.17 for H O given by Marhall and Smith (1990). The reult of thee calculation are hown in Table, where the change of optical depth (H O) i given for the cae where dry air molecule are replaced by H O molecule for 44 kg m column water vapor. Thu for a Rayleigh optical depth of 1.4 for air at 300 nm, a CO con- TABLE. Optical depth of the contituent of air (tandard preure mb and altitude 0 m). FIG. 1. Depolarization factor for dry air with 300 ppm CO. (nm) (N O Ar) (CO ) (H O) (H O)

6 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1859 centration of 360 ppm would contribute an optical depth about Some example calculation Uing the above equation we now preent example calculation to how new value for the cattering cro ection (a a function of wavelength) of dry air containing 360 ppm CO, imilar to the preentation of Penndorf (1957) and Bucholtz (1995). In addition we preent new value for Rayleigh optical depth for dry air containing 360 ppm CO at ea level, mb, and a latitude of 45; and at Mauna Loa Obervatory (MLO) (altitude 3400 m, preure 680 mb, and a latitude of ). The reult of thee calculation are hown in Table 3. For thoe reader who wih to ue curve-fitting technique, we have invetigated everal different equation imilar to thoe ued by other author, a dicued earlier in thi paper. We found that the accuracie of thoe equation were not ufficient for our purpoe, and therefore we looked for a more accurate approach. We find that the equation a b c y (8) 1 d e give excellent accuracy. Thi five-parameter equation fall in the cla of ratio of polynomial commonly ued in curve-fitting application. It give an excellent FIG.. Percent error for Eq. (9) fit to the cattering cro-ection data in Table 3. fit in thi cae becaue the general form of the data being fit by the equation i alo a ratio of polynomial. For the cattering cro-ection data in Table 3 the bet-fit equation i 8 (10 cm ) (9) Equation (9) i accurate to better than 0.01% over the nm range, and till better than 0.05% out to 1000 nm when fitting the cattering cro-ection data in Table 3. In fact, thi equation i accurate to better than 0.00% over the range nm (ee Fig. ). Bet fit for the other two example provided in Table 3 are R(ea level, 45N) and (30) R(MLO, 3.4 km, 680 mb) (31) It hould be noted that only the leading coefficient in Eq. (30) (31) are different from thoe in Eq. (9). Thee numerical value repreent the value of the PA/ m a g term (molecule in the column) given in Eq. (5) for the two cae (taking into account the 10 8 factor that wa removed from the cattering cro ection data to facilitate curve fitting calculation). 7. Concluion We have preented the latet value of the phyical contant neceary for the calculation of Rayleigh optical depth. For the mot accurate calculation of thi quantity it i recommended that uer go directly to firt principle and that Peck and Reeder (197) formula be ued to etimate the refractive index of tandard air. Next, we recommend that Penndorf (1957) method be ued to calculate the cattering cro ection per molecule of air, taking into account the concentration of CO. In mot cae the effect of water vapor may be neglected. The recommendation of Bate (1984) were ued for the depolarization of air a a function of wavelength. Next the Rayleigh optical depth hould be calculated uing the atmopheric preure at the ite of interet. Note the importance of taking into account variation of g. We do not necearily recommend the ue of curve-fitting technique to generate an equation for etimating Rayleigh optical depth becaue the inaccuracie that arie can equal or even exceed other quantitie being etimated, uch a aerool optical depth. Furthermore, all of the above calculation are imple enough to be done in a preadheet if deired, or can eaily be programmed in virtually any computer language. However, for thoe who wih to ue a imple

7 1860 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 TABLE 3. Scattering cro ection (per molecule) and Rayleigh optical depth ( R ) for dry air containing 360 ppm CO. Rayleigh optical depth are given for a location at ea level, mb, 45 latitude, and at MLO at altitude 3400 m, preure 680 mb, and latitude WV (m) (cm ) E E E E E6 8.55E6 7.68E E E E E E E E E E E E E E6.989E6.7589E6.6011E6.4546E6.3183E6.1915E6.0733E E E E E E E E E E E E E E E E E E E7 8.31E E E E E E E E E E E E E E E E E7 R (ea level, 45N).7137E00.488E00.766E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E01.941E E E E01.461E E01.111E01.116E E E E E E E E E E E E E E E E E E E E E0 R (MLO, 680 mb) King factor 1.864E E E E E E E E E E E E E E E E E E E E E E E E E E E01.843E E E01.443E01.30E E E E E E E E E E E E E E E E E E E E0 9.64E E E E E E E E E E E WV (m) (cm ) E E E E E E E E E E7.9583E7.8618E7.7691E7.680E7.5948E7.518E7.4341E7.3584E7.856E7.157E7.1484E7.0836E7.013E E E E E E E E E E E E7 1.48E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E8 TABLE 3. (Continued ) R (ea level, 45N) E E E E E E0 7.91E E E E E E E E E E E E E E E E E0 4.07E E E E E E E E E E E E0.9898E0.9089E0.8308E0.755E0.68E0.6116E0.5433E0.477E0.413E0.3514E0.914E0.334E0.177E0.18E0.0701E0.0190E E E E E E E0 1.70E E E E E E E E0 R (MLO, 680 mb) King factor E E E E E E E E E E E E E E E E E E E E E E0.975E0.8406E0.7569E0.676E0.5985E0.536E0.4514E0.3818E0.3146E0.498E0.187E0.168E0.0685E0.01E E E E E E E E E E0 1.54E E E E E E E E E E E E E E E E E E E E

8 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1861 WV (m) (cm ) E E E E E E E E E E E E E E E E E E E E E E8 TABLE 3. (Continued ) R (ea level, 45N) 1.416E E E0 1.66E E0 1.08E E E E E E E E E E E E E E E E E03 R (MLO, 680 mb) King factor E E E E E E E E E E E E E E E E E E E E E E equation and are atified with le accuracy, the technique ued to produce Eq. (9) (31) may be of interet. A more accurate etimate of the variou parameter dicued above become available, the equation of interet may eaily be modified. In ome calculation of optical depth it may be deired to take into account the vertical ditribution of the compoition of air, particularly CO. In thi cae a layerby-layer calculation may be done uing the etimated compoition for each layer, and then the total optical depth may be etimated by umming the optical depth for all of the layer. Acknowledgment. We thank Gail Anderon for her helpful comment concerning curve-fitting technique. APPENDIX Summary of Contant Value for the contant of nature that have been ued in thi paper are lited below. Avogadro number molecule mol 1 Molar volume at K and mb.4141 L mol 1 Molecular denity of a ga at K and mb molecule cm 3 Mean molecular weight of dry air (zero CO ) gm mol 1 Mean molecular weight of dry air (360 ppm CO ) gm mol 1 Acceleration of gravity (ea level and 45 latitude) g 0 (45) cm Ma-weighted air column altitude z c z REFERENCES Bate, D. R., 1984: Rayleigh cattering by air. Planet. Space Sci., 3, Bucholtz, A., 1995: Rayleigh-cattering calculation for the terretrial atmophere. Appl. Opt., 34, Cohen, E. R., and B. N. Taylor, 1995: The fundamental phyical contant. Phy. Today, 48, CRC, 1997: Handbook of Chemitry and Phyic. D. R. Lide and H. P. R. Frederike, Ed., CRC Pre, 447 pp. Dutton, E. G., P. Reddy, S. Ryan, and J. J. DeLuii, 1994: Feature and effect of aerool optical depth oberved at Mauna Loa, Hawaii: J. Geophy. Re., 99, Edlén, B., 1953: The diperion of tandard air. J. Opt. Soc. Amer., 43, , 1966: The refractive index of air. Metrologia,, Fröhlich, C., and G. E. Shaw, 1980: New determination of Rayleigh cattering in the terretrial atmophere. Appl. Opt., 19, Hanen, J. E., and L. D. Travi, 1974: Light cattering in planetary atmophere. Space Sci. Rev., 16, Harvey, A. H., J. S. Gallagher, and J. M. H. Levelt Senger, 1998: Revied formulation for the refractive index of water and team a a function of wavelength, temperature and denity. J. Phy. Chem. Ref. Data, 7, Hoyt, D. V., 1977: A redetermination of the Rayleigh optical depth and it application to elected olar radiation problem. J. Appl. Meteor., 16, Lit, R. J., 1968: Smithonian Meteorological Table. Smithonian, 57 pp. Marhall, B. R., and R. C. Smith, 1990: Raman cattering and inwater ocean optical propertie. Appl. Opt., 9, McCartney, E. J., 1976: Optic of the Atmophere. Wiley, 408 pp. Nicolet, M., 1984: On the molecular cattering in the terretrial atmophere: An empirical formula for it calculation in the homophere. Planet. Space Sci., 3, Owen, J. C., 1967: Optical refractive index of air: Dependence on preure, temperature and compoition. Appl. Opt., 6, Peck, E. R., and K. Reeder, 197: Diperion of air. J. Opt. Soc. Amer., 6, Penndorf, R., 1957: Table of the refractive index for tandard air and the Rayleigh cattering coefficient for the pectral region between 0. and 0.0 and their application to atmopheric optic. J. Opt. Soc. Amer., 47, Seinfeld, J. H., and S. N. Pandi, 1998: Atmopheric Chemitry and Phyic, from Air Pollution to Climate Change. Wiley, 136 pp. Stephen, G. L., 1994: Remote Sening of the Lower Atmophere. Oxford Univerity Pre, 53 pp. Teillet, P. M., 1990: Rayleigh optical depth comparion from variou ource. Appl. Opt., 9, van de Hult, H. C., 1957: Light Scattering by Small Particle. Wiley, 470 pp. Young, A. T., 1980: Revied depolarization correction for atmopheric extinction. Appl. Opt., 19, , 1981: On the Rayleigh-cattering optical depth of the atmophere. J. Appl. Meteor., 0,

Unit 11 Using Linear Regression to Describe Relationships

Unit 11 Using Linear Regression to Describe Relationships Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory

More information

Princo 469 NOVA Model Fortin-type mercurial barometer

Princo 469 NOVA Model Fortin-type mercurial barometer E.1 How it work Princo 469 NOVA odel Fortin-type mercurial barometer A barometer i a kind of manometer ued to meaure atmopheric preure. It wa invented by Evangelita Torricelli, and ued by Blaie Pacal to

More information

6. Friction, Experiment and Theory

6. Friction, Experiment and Theory 6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal

More information

Decision Theory and the Normal Distribution

Decision Theory and the Normal Distribution MODULE 3 Deciion Theory and the Normal Ditribution LEARNING OBJECTIVE After completing thi module, tudent will be able to: 1. Undertand how the normal curve can be ued in performing break-even analyi.

More information

A technical guide to 2014 key stage 2 to key stage 4 value added measures

A technical guide to 2014 key stage 2 to key stage 4 value added measures A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool

More information

Report 4668-1b 30.10.2010. Measurement report. Sylomer - field test

Report 4668-1b 30.10.2010. Measurement report. Sylomer - field test Report 4668-1b Meaurement report Sylomer - field tet Report 4668-1b 2(16) Contet 1 Introduction... 3 1.1 Cutomer... 3 1.2 The ite and purpoe of the meaurement... 3 2 Meaurement... 6 2.1 Attenuation of

More information

State-space analysis of control systems: Part I

State-space analysis of control systems: Part I Why a different approach? State-pace analyi of control ytem: Part I Uing a tate-variable approach give u a traightforward way to analyze MIM multiple-input, multiple output ytem. A tate variable model

More information

Heat transfer to or from a fluid flowing through a tube

Heat transfer to or from a fluid flowing through a tube Heat tranfer to or from a fluid flowing through a tube R. Shankar Subramanian A common ituation encountered by the chemical engineer i heat tranfer to fluid flowing through a tube. Thi can occur in heat

More information

Chapter and. FIGURE 9 36 The deviation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreversibilities.

Chapter and. FIGURE 9 36 The deviation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreversibilities. Chapter 9 The thermal efficiency could alo be determined from where h th q out q out h h 789.7 00.9 89. kj>kg Dicuion Under the cold-air-tard aumption (contant pecific heat value at room temperature),

More information

FLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES

FLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES FLUID MECHANICS TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES In thi tutorial you will continue the work on laminar flow and develop Poieuille' equation to the form known a the Carman - Kozeny equation. Thi

More information

Thus far. Inferences When Comparing Two Means. Testing differences between two means or proportions

Thus far. Inferences When Comparing Two Means. Testing differences between two means or proportions Inference When Comparing Two Mean Dr. Tom Ilvento FREC 48 Thu far We have made an inference from a ingle ample mean and proportion to a population, uing The ample mean (or proportion) The ample tandard

More information

1) Assume that the sample is an SRS. The problem state that the subjects were randomly selected.

1) Assume that the sample is an SRS. The problem state that the subjects were randomly selected. 12.1 Homework for t Hypothei Tet 1) Below are the etimate of the daily intake of calcium in milligram for 38 randomly elected women between the age of 18 and 24 year who agreed to participate in a tudy

More information

Queueing systems with scheduled arrivals, i.e., appointment systems, are typical for frontal service systems,

Queueing systems with scheduled arrivals, i.e., appointment systems, are typical for frontal service systems, MANAGEMENT SCIENCE Vol. 54, No. 3, March 28, pp. 565 572 in 25-199 ein 1526-551 8 543 565 inform doi 1.1287/mnc.17.82 28 INFORMS Scheduling Arrival to Queue: A Single-Server Model with No-Show INFORMS

More information

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement

More information

Mixed Method of Model Reduction for Uncertain Systems

Mixed Method of Model Reduction for Uncertain Systems SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol 4 No June Mixed Method of Model Reduction for Uncertain Sytem N Selvaganean Abtract: A mixed method for reducing a higher order uncertain ytem to a table reduced

More information

Harmonic Oscillations / Complex Numbers

Harmonic Oscillations / Complex Numbers Harmonic Ocillation / Complex Number Overview and Motivation: Probably the ingle mot important problem in all of phyic i the imple harmonic ocillator. It can be tudied claically or uantum mechanically,

More information

ESCI 340 Physical Meteorology Cloud Physics Lesson 2 Formation of Cloud Droplets

ESCI 340 Physical Meteorology Cloud Physics Lesson 2 Formation of Cloud Droplets ESCI 40 Phyical Meteorology Cloud Phyic Leon 2 Formation of Cloud Droplet Reference: A Short Coure in Cloud Phyic, Roger and Yau Reading: Roger and Yau, Chapter 6 The objective of thi leon are: 1) Undertand

More information

Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power

Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power Ohm Law Ohmic relationhip V=IR Ohm law tate that current through the conductor i directly proportional to the voltage acro it if temperature and other phyical condition do not change. In many material,

More information

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction. Newton Law Newton firt law: An object will tay at ret or in a tate of uniform motion with contant velocity, in a traight line, unle acted upon by an external force. In other word, the bodie reit any change

More information

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy

More information

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science aachuett Intitute of Technology Department of Electrical Engineering and Computer Science 6.685 Electric achinery Cla Note 10: Induction achine Control and Simulation c 2003 Jame L. Kirtley Jr. 1 Introduction

More information

Quadrilaterals. Learning Objectives. Pre-Activity

Quadrilaterals. Learning Objectives. Pre-Activity Section 3.4 Pre-Activity Preparation Quadrilateral Intereting geometric hape and pattern are all around u when we tart looking for them. Examine a row of fencing or the tiling deign at the wimming pool.

More information

published in Statistics and Probability Letters, 78, , 2008 Michael Lechner * SIAW

published in Statistics and Probability Letters, 78, , 2008 Michael Lechner * SIAW publihed in Statitic and Probability Letter, 78, 9-95, 28 A NOTE ON ENDOGENOUS CONTROL VARIABLES IN CAUSAL STUDIES Michael Lechner * SIAW Thi verion: March, 27 Date thi verion ha been printed: 8 May 27

More information

Solution of the Heat Equation for transient conduction by LaPlace Transform

Solution of the Heat Equation for transient conduction by LaPlace Transform Solution of the Heat Equation for tranient conduction by LaPlace Tranform Thi notebook ha been written in Mathematica by Mark J. McCready Profeor and Chair of Chemical Engineering Univerity of Notre Dame

More information

Laboratory 3 Diode Characteristics

Laboratory 3 Diode Characteristics Laboratory 3 Diode Characteritic BACKGROUND A diode i a non-linear, two terminal emiconductor device. he two terminal are the anode and the cathode. he circuit ymbol of a diode i depicted in Fig. 3-1.

More information

International Journal of Heat and Mass Transfer

International Journal of Heat and Mass Transfer International Journal of Heat and Ma Tranfer 5 (9) 14 144 Content lit available at ScienceDirect International Journal of Heat and Ma Tranfer journal homepage: www.elevier.com/locate/ijhmt Technical Note

More information

Exposure Metering Relating Subject Lighting to Film Exposure

Exposure Metering Relating Subject Lighting to Film Exposure Expoure Metering Relating Subject Lighting to Film Expoure By Jeff Conrad A photographic expoure meter meaure ubject lighting and indicate camera etting that nominally reult in the bet expoure of the film.

More information

Laboratory Evidence for Surface Nucleation of Solid Polar Stratospheric Cloud Particles

Laboratory Evidence for Surface Nucleation of Solid Polar Stratospheric Cloud Particles 10238 J. Phy. Chem. A 2002, 106, 10238-10246 Laboratory Evidence for Surface Nucleation of Solid Polar Stratopheric Cloud Particle A. Tabazadeh,*, Y. S. Djikaev, P. Hamill, and H. Rei NASA Ame Reearch

More information

Acceleration-Displacement Crash Pulse Optimisation A New Methodology to Optimise Vehicle Response for Multiple Impact Speeds

Acceleration-Displacement Crash Pulse Optimisation A New Methodology to Optimise Vehicle Response for Multiple Impact Speeds Acceleration-Diplacement Crah Pule Optimiation A New Methodology to Optimie Vehicle Repone for Multiple Impact Speed D. Gildfind 1 and D. Ree 2 1 RMIT Univerity, Department of Aeropace Engineering 2 Holden

More information

Turbulent Mixing and Chemical Reaction in Stirred Tanks

Turbulent Mixing and Chemical Reaction in Stirred Tanks Turbulent Mixing and Chemical Reaction in Stirred Tank André Bakker Julian B. Faano Blend time and chemical product ditribution in turbulent agitated veel can be predicted with the aid of Computational

More information

2. PHASE RELATIONSHIPS OF SOILS

2. PHASE RELATIONSHIPS OF SOILS 41 2. PHASE RELATIONSHIPS OF SOILS Becaue oil i particulate in nature a oppoed to more or le olid a i the rock from hich it come, any ample of oil obtained in the field ha more than jut oil particle in

More information

Optical Illusion. Sara Bolouki, Roger Grosse, Honglak Lee, Andrew Ng

Optical Illusion. Sara Bolouki, Roger Grosse, Honglak Lee, Andrew Ng Optical Illuion Sara Bolouki, Roger Groe, Honglak Lee, Andrew Ng. Introduction The goal of thi proect i to explain ome of the illuory phenomena uing pare coding and whitening model. Intead of the pare

More information

2. METHOD DATA COLLECTION

2. METHOD DATA COLLECTION Key to learning in pecific ubject area of engineering education an example from electrical engineering Anna-Karin Cartenen,, and Jonte Bernhard, School of Engineering, Jönköping Univerity, S- Jönköping,

More information

Exercises for Section 6.1

Exercises for Section 6.1 Exercie for Section 6.1 2. The ph of an acid olution ued to etch aluminum varie omewhat from batch to batch. In a ample of 50 batche, the mean ph wa 2.6, with a tandard deviation of 0.3. Let μ repreent

More information

The quartz crystal model and its frequencies 4,000 3,000 2,000. Reactance X [ohms] 1,000 -1,000 -2,000

The quartz crystal model and its frequencies 4,000 3,000 2,000. Reactance X [ohms] 1,000 -1,000 -2,000 TEHNIA NOTE 3 The quartz crytal model and it frequencie. Introduction The region between and i a region of poitive In thi note, we preent ome of the baic electrical propertie of quartz crytal. In particular,

More information

DETERMINATION OF EARTH RESISTIVITY PROFILE IN MULTILAYER SOIL

DETERMINATION OF EARTH RESISTIVITY PROFILE IN MULTILAYER SOIL DETERMINATION OF EARTH RESISTIVITY PROFILE IN MULTILAYER SOIL I.T.Dharmadaa, Prof.J.R.Luca, Dr.L. Udawatta, Eng.W.D.A.S Wijayapala Department of Electrical Engineering, Univerity of Moratuwa, Sri Lanka

More information

Review of Multiple Regression Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 13, 2015

Review of Multiple Regression Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 13, 2015 Review of Multiple Regreion Richard William, Univerity of Notre Dame, http://www3.nd.edu/~rwilliam/ Lat revied January 13, 015 Aumption about prior nowledge. Thi handout attempt to ummarize and yntheize

More information

Lecture Notes for Laplace Transform

Lecture Notes for Laplace Transform Lecture Note for Laplace Tranform Wen Shen April 9 NB! Thee note are ued by myelf. They are provided to tudent a a upplement to the textbook. They can not ubtitute the textbook. Laplace Tranform i ued

More information

MECH 2110 - Statics & Dynamics

MECH 2110 - Statics & Dynamics Chapter D Problem 3 Solution 1/7/8 1:8 PM MECH 11 - Static & Dynamic Chapter D Problem 3 Solution Page 7, Engineering Mechanic - Dynamic, 4th Edition, Meriam and Kraige Given: Particle moving along a traight

More information

STUDY ON THE EFFECT OF COOLING WATER TEMPERATURE RISE ON LOSS FACTOR AND EFFICIENCY OF A CONDENSER FOR A 210 MW THERMAL POWER UNIT

STUDY ON THE EFFECT OF COOLING WATER TEMPERATURE RISE ON LOSS FACTOR AND EFFICIENCY OF A CONDENSER FOR A 210 MW THERMAL POWER UNIT International Journal of Emerging Technology and Advanced Engineering Volume 3, Special Iue 3: ICERTSD 2013, Feb 2013, page 485-489 An ISO 9001:2008 certified Int. Journal, ISSN 2250-2459, available online

More information

Critical issues in wind turbine design (Uncertainties) IEA-meeting Trondheim, Norway June 14-15 2005

Critical issues in wind turbine design (Uncertainties) IEA-meeting Trondheim, Norway June 14-15 2005 Critical iue in wind turbine deign (Uncertaintie) IEA-meeting Trondheim, Norway June 4-5 005 Proect idea: To ignificantly improve deign bai for offhore wind turbine by: Analying all deign proce component

More information

A Comparison Between Square and Hexagonal Sampling Methods for Pipeline Image Processing.

A Comparison Between Square and Hexagonal Sampling Methods for Pipeline Image Processing. A Comparion Between Square and Hexagonal Sampling Method for Pipeline Image Proceing. Richard C. Staunton and Neil Storey The Univerity of Warwick, Coventry, UK, CV4 7AL. ABSTRACT The majority of machine

More information

Analyzing Myopic Approaches for Multi-Agent Communication

Analyzing Myopic Approaches for Multi-Agent Communication Analyzing Myopic Approache for Multi-Agent Communication Raphen Becker Victor Leer Univerity of Maachuett, Amhert Department of Computer Science {raphen, leer, hlomo}@c.uma.edu Shlomo Zilbertein Abtract

More information

Physical Properties of Soils and Compaction

Physical Properties of Soils and Compaction Soil Mechanic Phyical Propertie of Soil and Compaction page 1 Content of thi chapter : CHAPITRE 2. PHYSICAL PROPERTIES OF SOILS AND COMPACTION...1 2.1 UNITS...1 2.2 BASIC DEFINITIONS AND TERMINOLOGY...2

More information

CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY

CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY Annale Univeritati Apuleni Serie Oeconomica, 2(2), 200 CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY Sidonia Otilia Cernea Mihaela Jaradat 2 Mohammad

More information

Chapter 8 Transients & RLC

Chapter 8 Transients & RLC Chapter 8 Tranient & C Chapter 8 Tranient & C... 8. Introduction... 8.3 Tranient... 8.3. Firt Order Tranient... 8.3. Circuit... 3 8.3.3 C Circuit... 4 8.9 C Sytem epone... 5 8.9. C Equation... 5 8.9. Sytem

More information

Chapter 32. OPTICAL IMAGES 32.1 Mirrors

Chapter 32. OPTICAL IMAGES 32.1 Mirrors Chapter 32 OPTICAL IMAGES 32.1 Mirror The point P i called the image or the virtual image of P (light doe not emanate from it) The left-right reveral in the mirror i alo called the depth inverion (the

More information

322 CHAPTER 11 Motion and Momentum Telegraph Colour Library/FPG/Getty Images

322 CHAPTER 11 Motion and Momentum Telegraph Colour Library/FPG/Getty Images Standard 7.7.4: Ue ymbolic equation to how how the quantity of omething change over time or in repone to change in other quantitie. Alo cover: 7.2.6, 7.2.7 (Detailed tandard begin on page IN8.) What i

More information

REDUCTION OF TOTAL SUPPLY CHAIN CYCLE TIME IN INTERNAL BUSINESS PROCESS OF REAMER USING DOE AND TAGUCHI METHODOLOGY. Abstract. 1.

REDUCTION OF TOTAL SUPPLY CHAIN CYCLE TIME IN INTERNAL BUSINESS PROCESS OF REAMER USING DOE AND TAGUCHI METHODOLOGY. Abstract. 1. International Journal of Advanced Technology & Engineering Reearch (IJATER) REDUCTION OF TOTAL SUPPLY CHAIN CYCLE TIME IN INTERNAL BUSINESS PROCESS OF REAMER USING DOE AND Abtract TAGUCHI METHODOLOGY Mr.

More information

Plasma oscillations in high-electron-mobility transistors with recessed gate

Plasma oscillations in high-electron-mobility transistors with recessed gate JOURNAL OF APPLIED PHYSICS 99, 084507 2006 Plama ocillation in high-electron-mobility tranitor with receed gate V. Ryzhii a and A. Satou Computer Solid State Phyic Laboratory, Univerity of Aizu, Aizu-Wakamatu

More information

A model for the relationship between tropical precipitation and column water vapor

A model for the relationship between tropical precipitation and column water vapor Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L16804, doi:10.1029/2009gl039667, 2009 A model for the relationhip between tropical precipitation and column water vapor Caroline J. Muller,

More information

Processor Cooling. Report for the practical course Chemieingenieurwesen I WS06/07. Zürich, January 16,

Processor Cooling. Report for the practical course Chemieingenieurwesen I WS06/07. Zürich, January 16, Proceor Cooling Report for the practical coure Chemieingenieurween I WS06/07 Zürich, January 16, 2007 Student: Francico Joé Guerra Millán fguerram@tudent.ethz.ch Andrea Michel michela@tudent.ethz.ch Aitant:

More information

1 Safe Drivers versus Reckless Drunk Drivers

1 Safe Drivers versus Reckless Drunk Drivers ECON 301: General Equilibrium IV (Externalitie) 1 Intermediate Microeconomic II, ECON 301 General Equilibrium IV: Externalitie In our dicuion thu far, we have implicitly aumed that all good can be traded

More information

8.3 Yield Criteria in Three Dimensional Plasticity

8.3 Yield Criteria in Three Dimensional Plasticity Section 8. 8. ield Criteria in Three Dimenional Platicity The quetion now arie: a material yield at a tre level in a uniaxial tenion tet, but when doe it yield when ubjected to a complex three-dimenional

More information

DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS

DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS Chritopher V. Kopek Department of Computer Science Wake Foret Univerity Winton-Salem, NC, 2709 Email: kopekcv@gmail.com

More information

FEDERATION OF ARAB SCIENTIFIC RESEARCH COUNCILS

FEDERATION OF ARAB SCIENTIFIC RESEARCH COUNCILS Aignment Report RP/98-983/5/0./03 Etablihment of cientific and technological information ervice for economic and ocial development FOR INTERNAL UE NOT FOR GENERAL DITRIBUTION FEDERATION OF ARAB CIENTIFIC

More information

LARGE HOUSING IN NEW ZEALAND: ARE BEDROOM AND ROOM STANDARDS STILL GOOD DEFINITIONS OF NEW ZEALAND HOUSE SIZE?

LARGE HOUSING IN NEW ZEALAND: ARE BEDROOM AND ROOM STANDARDS STILL GOOD DEFINITIONS OF NEW ZEALAND HOUSE SIZE? The 9th Autralaian Houing Reearcher Conference 17-19 February 2016, The Univerity of Auckland LARGE HOUSING IN NEW ZEALAND: ARE BEDROOM AND ROOM STANDARDS STILL GOOD DEFINITIONS OF NEW ZEALAND HOUSE SIZE?

More information

POSSIBILITIES OF INDIVIDUAL CLAIM RESERVE RISK MODELING

POSSIBILITIES OF INDIVIDUAL CLAIM RESERVE RISK MODELING POSSIBILITIES OF INDIVIDUAL CLAIM RESERVE RISK MODELING Pavel Zimmermann * 1. Introduction A ignificant increae in demand for inurance and financial rik quantification ha occurred recently due to the fact

More information

Estimating V s(30) (or NEHRP Site Classes) from Shallow Velocity Models (Depths 30 m)

Estimating V s(30) (or NEHRP Site Classes) from Shallow Velocity Models (Depths 30 m) Bulletin of the Seimological Society of America, Vol. 94, No. 2, pp. 591 597, April 4 Etimating V () (or NEHRP Site Clae) from Shallow Velocity Model (Depth m) by David M. Boore Abtract The average velocity

More information

Analysis of Mesostructure Unit Cells Comprised of Octet-truss Structures

Analysis of Mesostructure Unit Cells Comprised of Octet-truss Structures Analyi of Meotructure Unit Cell Compried of Octet-tru Structure Scott R. Johnton *, Marque Reed *, Hongqing V. Wang, and David W. Roen * * The George W. Woodruff School of Mechanical Engineering, Georgia

More information

MODIFIED 2D FINITE-DIFFERENCE TIME-DOMAIN TECHNIQUE FOR TUNNEL PATH LOSS PREDICTION. Y. Wu, M. Lin and I.J. Wassell

MODIFIED 2D FINITE-DIFFERENCE TIME-DOMAIN TECHNIQUE FOR TUNNEL PATH LOSS PREDICTION. Y. Wu, M. Lin and I.J. Wassell 2 nd International Conference on Wirele Communication in Underground and Confined Area Augut 25-27, 2008 Val-d Or - Québec - Canada MODIFIED 2D FINITE-DIFFERENCE TIME-DOMAIN TECHNIQUE FOR TUNNEL PATH LOSS

More information

Humidity Fixed Points of Binary Saturated Aqueous Solutions

Humidity Fixed Points of Binary Saturated Aqueous Solutions JOURNAL OF RESEARCH of the National Bureau of Standard-A. Phyic and Chemitry Vol. 81 A, No. 1, January-February 1977 Humidity Fixed Point of Binary Saturated Aqueou Solution Lewi Greenpan Intitute for

More information

Performance of a Browser-Based JavaScript Bandwidth Test

Performance of a Browser-Based JavaScript Bandwidth Test Performance of a Brower-Baed JavaScript Bandwidth Tet David A. Cohen II May 7, 2013 CP SC 491/H495 Abtract An exiting brower-baed bandwidth tet written in JavaScript wa modified for the purpoe of further

More information

Assessing the Discriminatory Power of Credit Scores

Assessing the Discriminatory Power of Credit Scores Aeing the Dicriminatory Power of Credit Score Holger Kraft 1, Gerald Kroiandt 1, Marlene Müller 1,2 1 Fraunhofer Intitut für Techno- und Wirtchaftmathematik (ITWM) Gottlieb-Daimler-Str. 49, 67663 Kaierlautern,

More information

Recall the commutative and associative properties of multiplication. The Commutative Property of Multiplication. If a and b are any integers,

Recall the commutative and associative properties of multiplication. The Commutative Property of Multiplication. If a and b are any integers, 6 MODULE 2. FUNDAMENTALS OF ALGEBRA 2b Order of Operation Simplifying Algebraic Expreion Recall the commutative and aociative propertie of multiplication. The Commutative Property of Multiplication. If

More information

Availability of WDM Multi Ring Networks

Availability of WDM Multi Ring Networks Paper Availability of WDM Multi Ring Network Ivan Rado and Katarina Rado H d.o.o. Motar, Motar, Bonia and Herzegovina Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Univerity

More information

A Life Contingency Approach for Physical Assets: Create Volatility to Create Value

A Life Contingency Approach for Physical Assets: Create Volatility to Create Value A Life Contingency Approach for Phyical Aet: Create Volatility to Create Value homa Emil Wendling 2011 Enterprie Rik Management Sympoium Society of Actuarie March 14-16, 2011 Copyright 2011 by the Society

More information

Brand Equity Net Promoter Scores Versus Mean Scores. Which Presents a Clearer Picture For Action? A Non-Elite Branded University Example.

Brand Equity Net Promoter Scores Versus Mean Scores. Which Presents a Clearer Picture For Action? A Non-Elite Branded University Example. Brand Equity Net Promoter Score Veru Mean Score. Which Preent a Clearer Picture For Action? A Non-Elite Branded Univerity Example Ann Miti, Swinburne Univerity of Technology Patrick Foley, Victoria Univerity

More information

Basic Quantum Mechanics in Coordinate, Momentum and Phase Space

Basic Quantum Mechanics in Coordinate, Momentum and Phase Space Baic Quantum Mechanic in Coorinate, Momentum an Phae Space Frank Rioux Department of Chemitry College of St. Beneict St. Johnʹ Univerity The purpoe of thi paper i to ue calculation on the harmonic ocillator

More information

Engineering Bernoulli Equation

Engineering Bernoulli Equation Engineering Bernoulli Equation R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkon Univerity The Engineering Bernoulli equation can be derived from the principle of conervation

More information

Profitability of Loyalty Programs in the Presence of Uncertainty in Customers Valuations

Profitability of Loyalty Programs in the Presence of Uncertainty in Customers Valuations Proceeding of the 0 Indutrial Engineering Reearch Conference T. Doolen and E. Van Aken, ed. Profitability of Loyalty Program in the Preence of Uncertainty in Cutomer Valuation Amir Gandomi and Saeed Zolfaghari

More information

Introduction to the article Degrees of Freedom.

Introduction to the article Degrees of Freedom. Introduction to the article Degree of Freedom. The article by Walker, H. W. Degree of Freedom. Journal of Educational Pychology. 3(4) (940) 53-69, wa trancribed from the original by Chri Olen, George Wahington

More information

Morningstar Fixed-Income Style Box TM Methodology

Morningstar Fixed-Income Style Box TM Methodology Morningtar Fixed-Income Style Box TM Methodology Morningtar Methodology Paper April 30, 01 01 Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction

More information

SLOPE PROTECTION Revised Oct 98

SLOPE PROTECTION Revised Oct 98 SLOPE PROTECTION Revied Oct 98 1. Replacement or overlayment of the exiting lope protection. 1.1. Replacement of the exiting lope protection. Slope protection on the riveride lope of the flood control

More information

Queueing Models for Multiclass Call Centers with Real-Time Anticipated Delays

Queueing Models for Multiclass Call Centers with Real-Time Anticipated Delays Queueing Model for Multicla Call Center with Real-Time Anticipated Delay Oualid Jouini Yve Dallery Zeynep Akşin Ecole Centrale Pari Koç Univerity Laboratoire Génie Indutriel College of Adminitrative Science

More information

Analyses of Steel Bridge Circular Columns using Fiber Model considering Local Buckling

Analyses of Steel Bridge Circular Columns using Fiber Model considering Local Buckling Civil Engineering Dimenion, Vol. 6, No., March 4, -7 ISSN 4-953 print / ISSN 979-57X online CED 3, 6(), DOI:.9744/CED.6..-7 Analye of Steel Bridge Circular Column uing Fiber Model conidering Local Buckling

More information

DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS. G. Chapman J. Cleese E. Idle

DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS. G. Chapman J. Cleese E. Idle DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS G. Chapman J. Cleee E. Idle ABSTRACT Content matching i a neceary component of any ignature-baed network Intruion Detection

More information

BUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE

BUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE Progre In Electromagnetic Reearch Letter, Vol. 3, 51, 08 BUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE S. H. Zainud-Deen Faculty of Electronic Engineering Menoufia

More information

Method of Moments Estimation in Linear Regression with Errors in both Variables J.W. Gillard and T.C. Iles

Method of Moments Estimation in Linear Regression with Errors in both Variables J.W. Gillard and T.C. Iles Method of Moment Etimation in Linear Regreion with Error in both Variable by J.W. Gillard and T.C. Ile Cardiff Univerity School of Mathematic Technical Paper October 005 Cardiff Univerity School of Mathematic,

More information

Original Article: TOWARDS FLUID DYNAMICS EQUATIONS

Original Article: TOWARDS FLUID DYNAMICS EQUATIONS Peer Reviewed, Open Acce, Free Online Journal Publihed monthly : ISSN: 8-8X Iue 4(5); April 15 Original Article: TOWARDS FLUID DYNAMICS EQUATIONS Citation Zaytev M.L., Akkerman V.B., Toward Fluid Dynamic

More information

MATLAB/Simulink Based Modelling of Solar Photovoltaic Cell

MATLAB/Simulink Based Modelling of Solar Photovoltaic Cell MATLAB/Simulink Baed Modelling of Solar Photovoltaic Cell Tarak Salmi *, Mounir Bouzguenda **, Adel Gatli **, Ahmed Mamoudi * *Reearch Unit on Renewable Energie and Electric Vehicle, National Engineering

More information

SHUNT LOUDSPEAKERS FOR MODAL CONTROL IN ROOMS

SHUNT LOUDSPEAKERS FOR MODAL CONTROL IN ROOMS SHUNT LOUDSPEAKERS FOR MODAL CONTROL IN ROOMS Hervé Liek, Romain Boulandet Laboratoire d Electromagnétime et d Acoutique, Ecole Polytechnique Fédérale de Lauanne, Station 11, CH-1015 Lauanne, Switzerland,

More information

Morningstar Fixed Income Style Box TM Methodology

Morningstar Fixed Income Style Box TM Methodology Morningtar Fixed Income Style Box TM Methodology Morningtar Methodology Paper Augut 3, 00 00 Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction

More information

Towards Control-Relevant Forecasting in Supply Chain Management

Towards Control-Relevant Forecasting in Supply Chain Management 25 American Control Conference June 8-1, 25. Portland, OR, USA WeA7.1 Toward Control-Relevant Forecating in Supply Chain Management Jay D. Schwartz, Daniel E. Rivera 1, and Karl G. Kempf Control Sytem

More information

A note on profit maximization and monotonicity for inbound call centers

A note on profit maximization and monotonicity for inbound call centers A note on profit maximization and monotonicity for inbound call center Ger Koole & Aue Pot Department of Mathematic, Vrije Univeriteit Amterdam, The Netherland 23rd December 2005 Abtract We conider an

More information

The geometric resistivity correction factor for several geometrical samples

The geometric resistivity correction factor for several geometrical samples Vol. 36, No. 8 Journal of Semiconductor Augut 05 The geometric reitivity correction factor for everal geometrical ample ; ; Serdar Yilmaz Merin Univerity Science and Art Faculty Phyic Department, Merin,

More information

Redesigning Ratings: Assessing the Discriminatory Power of Credit Scores under Censoring

Redesigning Ratings: Assessing the Discriminatory Power of Credit Scores under Censoring Redeigning Rating: Aeing the Dicriminatory Power of Credit Score under Cenoring Holger Kraft, Gerald Kroiandt, Marlene Müller Fraunhofer Intitut für Techno- und Wirtchaftmathematik (ITWM) Thi verion: June

More information

NUMERICAL SIMULATION OF WATER CIRCULATION IN A CYLINDRICAL HORIZONTAL THERMAL TANK

NUMERICAL SIMULATION OF WATER CIRCULATION IN A CYLINDRICAL HORIZONTAL THERMAL TANK NUMERICAL SIMULATION OF WATER CIRCULATION IN A CYLINDRICAL HORIZONTAL THERMAL TANK D. L. Savicki a, and H. A. Vielmo b, a Federal Univerity of Rio Grande Intitute of Mathematic, Statitic and Phyic Av.

More information

Progress 8 and Attainment 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools

Progress 8 and Attainment 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools Progre 8 and Attainment 8 meaure in 2016, 2017, and 2018 Guide for maintained econdary chool, academie and free chool September 2016 Content Table of figure 4 Summary 5 A ummary of Attainment 8 and Progre

More information

T-test for dependent Samples. Difference Scores. The t Test for Dependent Samples. The t Test for Dependent Samples. s D

T-test for dependent Samples. Difference Scores. The t Test for Dependent Samples. The t Test for Dependent Samples. s D The t Tet for ependent Sample T-tet for dependent Sample (ak.a., Paired ample t-tet, Correlated Group eign, Within- Subject eign, Repeated Meaure,.. Repeated-Meaure eign When you have two et of core from

More information

Chapter 4: Mean-Variance Analysis

Chapter 4: Mean-Variance Analysis Chapter 4: Mean-Variance Analyi Modern portfolio theory identifie two apect of the invetment problem. Firt, an invetor will want to maximize the expected rate of return on the portfolio. Second, an invetor

More information

Candy Phylogeny Lab. Procedure:

Candy Phylogeny Lab. Procedure: Candy Phylogeny Lab Material Candy Bar (2 each) o Baby Ruth o Reee Piece o rhey Cookie and Cream o Snicker Cruncher o Snicker o MM Peanut o MM Plain o rhey o rhey Almond o Skittle Picture of Candy Bar

More information

The Cash Flow Statement: Problems with the Current Rules

The Cash Flow Statement: Problems with the Current Rules A C C O U N T I N G & A U D I T I N G accounting The Cah Flow Statement: Problem with the Current Rule By Neii S. Wei and Jame G.S. Yang In recent year, the tatement of cah flow ha received increaing attention

More information

Although the Office for National

Although the Office for National Economic & Labour Market Review Vol 2 No 5 May 2008 feature Graeme Chamberlin Monitoring the coherence of ONS and Purchaing Manager Index data SUMMARY Thi article outline a methodology for monitoring the

More information

Progress 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools

Progress 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools Progre 8 meaure in 2016, 2017, and 2018 Guide for maintained econdary chool, academie and free chool July 2016 Content Table of figure 4 Summary 5 A ummary of Attainment 8 and Progre 8 5 Expiry or review

More information

Control of Wireless Networks with Flow Level Dynamics under Constant Time Scheduling

Control of Wireless Networks with Flow Level Dynamics under Constant Time Scheduling Control of Wirele Network with Flow Level Dynamic under Contant Time Scheduling Long Le and Ravi R. Mazumdar Department of Electrical and Computer Engineering Univerity of Waterloo,Waterloo, ON, Canada

More information

AMS577. Repeated Measures ANOVA: The Univariate and the Multivariate Analysis Approaches

AMS577. Repeated Measures ANOVA: The Univariate and the Multivariate Analysis Approaches AMS577. Repeated Meaure ANOVA: The Univariate and the Multivariate Analyi Approache 1. One-way Repeated Meaure ANOVA One-way (one-factor) repeated-meaure ANOVA i an extenion of the matched-pair t-tet to

More information

ECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 7: Synchronous Machines and Drives (Textbook Chapter 5)

ECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 7: Synchronous Machines and Drives (Textbook Chapter 5) ECE 30 Energy Converion and Power Electronic Dr. Tim Hogan Chapter 7: ynchronou Machine and Drive (Textbook Chapter 5) Chapter Objective For induction machine, a the rotor approache ynchronou peed, the

More information

of absorption transitions (1, 2) and the mean rate of visits to state or are, respectively, J.=

of absorption transitions (1, 2) and the mean rate of visits to state or are, respectively, J.= Proc. Natl. Acad. Sci. USA Vol. 85, pp. 4577-4581, July 1988 Applied Mathematical Science Number of viit to a tate in a random walk, before aborption, and related topic (kinetic dim/multitate directional

More information

Periodic Symmetric Functions and Addition Related Arithmetic Operations in Single Electron Tunneling Technology

Periodic Symmetric Functions and Addition Related Arithmetic Operations in Single Electron Tunneling Technology Periodic Symmetric Function and Addition Related Arithmetic Operation in Single Electron Tunneling Technology or Meenderinck Sorin otofana omputer Engineering Lab, Delft Univerity of Technology, Delft,

More information