USING A NETWORK OF SCINTILLOMETERS AND CEILOMETERS FOR VALIDATION OF THE WRF-MESOSCALE MODEL

Size: px
Start display at page:

Download "USING A NETWORK OF SCINTILLOMETERS AND CEILOMETERS FOR VALIDATION OF THE WRF-MESOSCALE MODEL"

Transcription

1 P.1.2 USING A NETWORK OF SCINTILLOMETERS AND CEILOMETERS FOR VALIDATION OF THE WRF-MESOSCALE MODEL G.J. Steeneveld*, O.K. Hrtogensis*, A.F. Moene*, H. Klein Bltink +, nd A.A.M. Holtslg* *Wgeningen University, Wgeningen, The Netherlnds. + Royl Netherlnds Meteorologil Institute, De Bilt, The Netherlnds 1. INTRODUCTION 1 & BACKGROUND Foresting of ner surfe wether, speies trnsport nd dispersion, nd the inversion of greenhouse gs trnsport on the mesosle relies on the performne of the tmospheri oundry lyer (ABL) nd lnd surfe sheme in limited re models (e.g. Denning et l., 2008: Gerig et l., 2008). However, the PBL desription in NWP models still hs diffiulties (Steeneveld et l., 2008), espeilly in the stle ABL (SBL). Nighttime mixing is often overestimted nd the low level jet misrepresented. During dytime the representtion of ABL entrinment ould e improved. All together this results in errors in the diurnl yle of wind speed, diretion nd the thermodynmi vriles (Olivié, et l., 2004; Svensson nd Holtslg, 2007; Teixeir et l., 2008). Hene there is need to ompre mesosle model results with oservtions to understnd the model limittions s well s their strengths. In the study desried in this pper, the PBL shemes implemented in mesosle model WRF re evluted ginst network of in situ oservtions in The Netherlnds. Previous studies lso evluted WRF, ut these were mostly foused on omplex terrin, the synopti sle (Cheng nd Steenurgh, 2005) or ir qulity (Tie, 2007). Usully tmospheri mesosle models re evluted ginst point mesurements. However, then representtion errors our. Surfe fluxes re lulted on grid sle, so they lso should e evluted ginst oserved re verged fluxes. The innovtive spet of this study is the use of network of sintillometers nd eilometers for model evlution. We will ompre oserved surfe fluxes of momentum (u * ), sensile het (H) nd evpotrnspirtion (L v E), nd next lso the profiles of wind speed (U), potentil temperture (θ), nd speifi humidity (q). The seond im is to ompre modelled diurnl yle etween the MRF sheme (Troen nd Mhrt, 1986) nd its improved equivlent YSU (Noh et l., 2003). 2. OBSERVATIONS A sintillometer is n instrument tht onsists of light trnsmitter nd reeiver. The instrument 1 Corresponding uthor ddress: G.J. Steeneveld, Wgeningen Univ., Meteorology nd Air Qulity Group, P.O. ox 47, 6700 AA Wgeningen, The Netherlnds. E-mil: Gert-Jn.Steeneveld@wur.nl reords the integrted effet of the turulent perturtions of the ir s refrtive index (n), nd its struture prmeters (C n 2 ). Monin-Oukhov theory is used to onvert C n 2 to re-verged surfe fluxes of het, using 10 m wind s input. We use 5 optil Lrge Aperture Sintillometers (LAS) whih operte on sle of ~ m in regions of the Netherlnds with different vegettion types (Fig. 1). See Meijninger et l. (2002) for more informtion on the LAS. A eilometer is n instrument tht mesures the ABL height (h) using lser or other light tehniques. Fig. 1 lso indites 6 lotions with opertionl eilometers. In ddition to this network of innovtive instruments, we lso evlute the model ginst Cuw tower oservtions (e.g. Beljrs nd Bosveld, 1997), wind profiler, nd routine mirometeorologil oservtions. sintillometer eilometer Cuw Wgeningen Fig 1: The Netherlnds with sptil overge of sintillometer nd eilometer network. 3. MODEL SETUP & CASE DESCRIPTION We hve seleted two loud free ontrsting dys: 22 April 2007 (DOY 112) with wek winds (~1.5 m/s t 10m), nd 2 My 2007 (DOY 122) with moderte winds (~4.5 ms -1 t 10m) During the first period, The Netherlnds re loted under high with winds from the southest. In the seond period the wind is est-north-estern. The re onsists of minly grsslnd nd is flt nd reltively homogeneous. Also, the re hs lrge wter supply nd thus high soil moisture vilility. For these simultions, the initil nd oundry onditions (every 6 h) were provided y NCAR-FNL. WRF ws run in n re of 1600 x 1600 km with grid size of 54 km. In this domin, we nested 3 domins with grid sping of 18, 9 nd 2 km respetively to minimize model 1

2 errors due to lk of horizontl resolution. Moreover, the U.S. Geologil Survey provided the lnd surfe properties for WRF suh s soil moisture vilility, surfe roughness, nd lnd use. D1 D2 D3 Fig. 2: Model onfigurtion for WRF. WRF ws run with 3 different ABL shemes. First, we use the so-lled MRF sheme (Troen nd Mhrt, 1986; Hong nd Pn, 1996) whih utilizes presried ui eddy diffusivity profile with height, with the mgnitude depending on the hrteristi veloity sle t the surfe lyer. This sheme llows for non-lol het trnsport during the dy. This extension is needed to represent trnsport y lrge eddies on the sle of the ABL itself, insted of lol trnsport. A wellknown drwk of this widely used sheme is exessive dytime ABL top entrinment, nd overestimtion of the turulent trnsport t night (e.g. Vil et l., 2002; Steeneveld et l., 2008). The 2 nd sheme is n extension MRF, (so lled YSU). The extensions onsist of ) inlusion of presried entrinment rte t the ABL top, ) non-lol trnsport of momentum, nd ) Prndtl numer (K M /K H ) depending on height (see lso Noh et l., 2003). As suh, we will evlute whether these modifitions irumvent the defiienies in the MRF sheme. Finlly the 3 rd sheme is 1.5 order losure sheme (MYJ) nd uses prognosti eqution for the turulent kineti energy (see Stull, 1988; Steeneveld et l., 2008). Then the eddy diffusivity is determined y multiplition of the turulent kineti energy nd length sle. The NOAH lnd surfe sheme hs een used (e.g. Ek et l, 2002). For ompleteness, we utilize the Kin- Fritsh umulus onvetion sheme, the RRTM sheme for long wve rdition, the Dudhi sheme for shortwve rdition, nd the WSM 3- lss simple ie mirophysis sheme. In the surfe lyer we use Monin-Oukhov theory s in Jnji (2000). 4. RESULTS ) Clm onditions: DOY 112 The modeled nd oserved H, L v E nd u * for Wgeningen re shown in Fig. 3: ll shemes overestimte dytime H y ~60 Wm -2, while t night ll shemes overestimte the mgnitude of H. However, the sintilometer flux H s is lrger ompred to the eddy ovrine flux H e, nd loser to the model forest. Note tht H e for Cuw is lso shown for omprison. L v E is forested orretly for the full diurnl yle, nd is lso onsistent with eddy ovrine results. Unfortuntely, ll shemes predit u * ftor 2 lrger thn oserved during the dy. At night u * vnishes, while WRF keeps u * t lest 0.14 ms -1. This might our due to the model s reltively lrge roughness length (0.15 m), s dvised for Cuw (Beljrs nd Holtslg, 1991). The surfe skin temperture (T s ) is orretly forested during the dy, ut overestimted t night. This is due to the ft tht inoming longwve rdition in MRF nd YSU is overestimted y 5-10 Wm -2. Finlly, h is well represented y the eilometer (t lest for one lgorithm). Note tht the modeled h ws lulted from the modeled wind nd temperture profile, using Troen nd Mhrt (1986). 2

3 d e Fig.3: Modeled nd oserved time series of sensile (), ltent het flux (), frition veloity (), surfe skin temperture (d), nd ABL height (e).+ Cuw EC flux, = Wgeningen EC flux, Wgeningen sintillometer flux. Fig. 4 shows the modeled profiles of θ, q, nd U. For the dytime ll ABL shemes overestimte the ABL temperture, lthough the ner surfe temperture grees with the oservtions. Speifi humidity is overestimted ompred to the rdio sounding, espeilly for MYJ. Fig.4: Modeled profiles of potentil temperture, humidity, wind speed for DOY ,00 UTC. O = De Bilt sounding, X= Cuw tower. YSU seems to detrin moisture ompred to MRF. YSU seems to produe muh more well mixed U profile ompred to MRF, whih results in out 0.5 ms -1 wind speed differene. However, U is 1 ms -1 too high ompred with tower oservtions nd more ompred to the sounding whih we my onsider suspiious lose to the surfe. 3

4 At night (DOY 112, 00 UTC) the MYJ sheme reprodues the inversion orretly, while MRF nd YSU underestimte the surfe inversion strength, while lso the free tmospheri strtifition is underestimted. All shemes simulte q quite well lose to the surfe. For wind speed onsiderle differenes re seen. MYJ represent the low level jet in very lose greement with tower oservtions. YSU forests the LLJ muh etter thn MRF. This is due to YSU s lrger ner surfe wind speed t dytime, whih results in lrger mplitude of the intertil osilltion t night. ) Windy onditions: DOY 122 Next we evlute the model performne for DOY 122. The forested sensile het flux is pproximtely similr for ll shemes, nd grees well with H s. Note tht the dytime H s is muh lrger thn H e in this se. It is lso worth noting the ler pek of modeled nd simulted H fter the trnsition (Fig. 6). Fig.5: Modeled potentil temperture ), humidity (), wind speed () for DOY , 12UTC. 4

5 d e Fig.6: Modeled nd oserved time series of sensile (), ltent het flux (), frition veloity (), surfe skin temperture (d), nd ABL height (e).+ Cuw EC flux, = Wgeningen EC flux, Wgeningen sintillometer flux. The simulted L v E is overestimted, lthough it ompres well with the mesured flux t Cuw. WRF strongly overestimtes u *, espeilly for the dy. Also note tht u * from the sintillometer itertion is sustntilly lower thn from eddy ovrine. Predited T s shows ool is t night, ut is orret during the dy. The dytime h is overpredited ompred with the eilometer oservtions. MRF overestimtes h t night, ompred to YSU nd MYJ. The simulted θ is underestimted, espeilly y MYJ (Fig. 7). This is inonsistent with the lrge surfe H. Therefore, the modeled het dvetion or entrinment is misrepresented. At the sme time q is underestimted ner the surfe, nd the wind speed profile is orretly modeled. Fig.7: Modeled potentil temperture ), humidity (), wind speed () for DOY , 12UTC. 5. CONCLUSIONS We hve evluted the model performne of WRF in the oundry lyer ginst network of eilometers nd sintillometers in the Netherlnds. As suh, this is the first pper in whih grid sle model fluxes re ompred with re verged surfe flux oservtions. The MRF, YSU nd MYJ shemes re used. We find tht the WRF-YSU sheme shows improved skill for the dytime wind profiles, nd nighttime low-level jet ompred to MRF. A ommon defiieny of the shemes is n overestimtion of dytime fluxes, 5

6 nd n overestimtion of surfe temperture t night for lm onditions. Aknowledgements The uthors thnk the BSIK-ME2 projet (Climte hnges sptil plnning). REFERENCES Beljrs A.C.M., F.C. Bosveld, 1997: Cuw dt for vlidtion of lnd surfe prmetriztion shemes. J. Climte, 10, Cheng, W.Y.Y., W.J. Steenurgh, 2005: Evlu-tion of surfe sensile wether forests y the WRF nd Et models over the western United Sttes. We. For., 20, Denning, S.A., N. Zhng, C. Yi, M. Brnson, K. Dvis, J. Kleist, P. Bkwin, 2008: Evlution of modeled tmospheri oundry lyer depth t the WLEF tower. Agri. For. Meteor., 148, Ek, M.B., K.E. Mithell, Y. Lin, E. Rogers, P. Grunmnn, V. Koren, G. Gyno, J.D. Trpley, 2003, Implementtion of the Noh lnd surfe model dvnes in the Ntionl Centers for Environmentl Predition opertionl mesosle Et model. J. Geophys. Res., 108 (D22), 8851, doi: /2002jd Gerig, C., S. Körner, J.C. Lin, 2008: Vertil mixing in tmospheri trer trnsport models: error hrteriztion nd propgtion. Atmos. Chem. Phys., 8, Hong, S.Y. nd H.L. Pn, 1996: Nonlol oundry lyer vertil diffusion in Medium-Rnge Forest model. Mon. We. Rev., 124, Jnjić, Z.I., 1994: The step-mountin oordinte model: Further developments of the onvetion, visous sulyer, nd turulene losure shemes. Mon. We. Rev., 122, Meijninger, W.M.L., O.K. Hrtogensis, W. Kohsiek, J.C.B. Hoedjes, R.M. Zuurier, H.A.R. DeBruin, 2002: Determintion of re-verged sensile het fluxes with lrge perture sintillometer over heterogeneous surfe-flevolnd field experiment. Bound.-Lyer Meteor., 105, Mio, J.-F., D. Chen, K. Borne, 2007: Evlution nd omprison of Noh nd Pleim-Xiu Lnd Surfe Models in MM5 using GÖTE2001 dt: sptil nd temporl vritions in ner surfe ir temperture. J. Appl. Meteor. Clim., 46, Noh, Y., W.G. Cheon, S.Y. Hong, S. Rsh, 2003: Improvement of the K-profile model for the plnetry oundry lyer sed on lrge eddy simultion dt. Bound.-Lyer Meteor., 107, Olivié, D.J.L., P.F.J. vn Velthoven, A.C.M. Beljrs, 2004: Evlution of rhived nd off-line dignosed vertil diffusion oeffiients from ERA-40 with 222 Rn simultions. Atmos. Chem. Phys., 4, Steeneveld, G.J., T. Muritsen, E.I.F. de Bruijn, J. Vilà- Gueru de Arellno, G. Svensson, A.A.M. Holtslg, 2008: Evlution of limited re models for the representtion of the diurnl yle nd ontrsting nights in CASES99. J. Appl. Meteor. Clim. 47, Svensson, G., nd A.A.M. Holtslg, 2007: The diurnl yle GABLS seond interomprison projet. GEWEX newsletter, Ferury. Teixeir, J., B. Stevens, C.S. Bretherton, R. Cederwll, J.D. Doyle, J.C. Golz, A.A.M. Holtslg, S.A. Klein, J.K. Lundquist, D.A. Rndll, A.P. Sieesm, nd P.M.M. Sores, 2008 : Prmeteriztion of the Atmospheri Boundry Lyer-A View from Just Aove the Inversion. Bull. Amer. Meteor. So., 89, Tie, X., S, Mdronih, G. Li, Z. Ying, R. Zhng, A.R. Gri, J. Lee-Tylor, nd Y. Liu, 2007: Chrteriztions of hemil oxidnts in Mexio City: A regionl hemil dynmil model (WRF-Chem) study. Atmos. Environ, 41, Vil, J., P. Csso-Torrl, 2007: The rdition nd energy udget in mesosle models: n oservtionl study se. Físi de l Tierr, 19, Zhong, S., H. In, C. Clements, 2007: Impt of turulene, lnd surfe, nd rdition prmeteriztions on simulted oundry lyer pro-perties in ostl environment. J. Geophys. Res., 112, doi: /2006jd

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL P3.1 Kot Iwmur*, Hiroto Kitgw Jpn Meteorologil Ageny 1. INTRODUCTION Jpn Meteorologil Ageny

More information

Review Topic 14: Relationships between two numerical variables

Review Topic 14: Relationships between two numerical variables Review Topi 14: Reltionships etween two numeril vriles Multiple hoie 1. Whih of the following stterplots est demonstrtes line of est fit? A B C D E 2. The regression line eqution for the following grph

More information

Lecture Notes No. 10

Lecture Notes No. 10 2.6 System Identifition, Estimtion, nd Lerning Leture otes o. Mrh 3, 26 6 Model Struture of Liner ime Invrint Systems 6. Model Struture In representing dynmil system, the first step is to find n pproprite

More information

Project 6: Minigoals Towards Simplifying and Rewriting Expressions

Project 6: Minigoals Towards Simplifying and Rewriting Expressions MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy

More information

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35. 0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.5 0 5 10 15 20 25 30 35 P (GP) Supplementry Figure 1 Compression

More information

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte

More information

1.3 SCALARS AND VECTORS

1.3 SCALARS AND VECTORS Bridge Course Phy I PUC 24 1.3 SCLRS ND VECTORS Introdution: Physis is the study of nturl phenomen. The study of ny nturl phenomenon involves mesurements. For exmple, the distne etween the plnet erth nd

More information

Generalization of 2-Corner Frequency Source Models Used in SMSIM

Generalization of 2-Corner Frequency Source Models Used in SMSIM Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville

More information

ANALYSIS AND MODELLING OF RAINFALL EVENTS

ANALYSIS AND MODELLING OF RAINFALL EVENTS Proeedings of the 14 th Interntionl Conferene on Environmentl Siene nd Tehnology Athens, Greee, 3-5 Septemer 215 ANALYSIS AND MODELLING OF RAINFALL EVENTS IOANNIDIS K., KARAGRIGORIOU A. nd LEKKAS D.F.

More information

Table of Content. c 1 / 5

Table of Content. c 1 / 5 Tehnil Informtion - t nd t Temperture for Controlger 03-2018 en Tble of Content Introdution....................................................................... 2 Definitions for t nd t..............................................................

More information

Novel Fiber-Optical Refractometric Sensor Employing Hemispherically-Shaped Detection Element

Novel Fiber-Optical Refractometric Sensor Employing Hemispherically-Shaped Detection Element Novel Fier-Optil Refrtometri Sensor Employing Hemispherilly-Shped Detetion Element SERGEI KHOTIAINTSEV, VLADIMIR SVIRID Deprtment of Eletril Engineering, Fulty of Engineering Ntionl Autonomous University

More information

Spacetime and the Quantum World Questions Fall 2010

Spacetime and the Quantum World Questions Fall 2010 Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1

More information

Green s Theorem. (2x e y ) da. (2x e y ) dx dy. x 2 xe y. (1 e y ) dy. y=1. = y e y. y=0. = 2 e

Green s Theorem. (2x e y ) da. (2x e y ) dx dy. x 2 xe y. (1 e y ) dy. y=1. = y e y. y=0. = 2 e Green s Theorem. Let be the boundry of the unit squre, y, oriented ounterlokwise, nd let F be the vetor field F, y e y +, 2 y. Find F d r. Solution. Let s write P, y e y + nd Q, y 2 y, so tht F P, Q. Let

More information

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret

More information

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue TITLE: OBJECTIVE: AUTHOR: SPONSORS: Effets of Drought on the Performne of Two Hyrid Bluegrsses, Kentuky Bluegrss nd Tll Fesue Evlute the effets of drought on the visul qulity nd photosynthesis in two hyrid

More information

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities Appendi Prtil dishrges. Reltionship Between Mesured nd Atul Dishrge Quntities A dishrging smple my e simply represented y the euilent iruit in Figure. The pplied lternting oltge V is inresed until the

More information

Validation of AIRS/AMSU - A Water Vapor and Temperature Data With In Situ Aircraft Observations From the Surface to UT/LS From 87 N 67 S

Validation of AIRS/AMSU - A Water Vapor and Temperature Data With In Situ Aircraft Observations From the Surface to UT/LS From 87 N 67 S Sn Jose Stte University From the SeletedWorks of Minghui Dio June 26, 2013 Vlidtion of AIRS/AMSU - A Wter Vpor nd Temperture Dt With In Situ Airrft Oservtions From the Surfe to UT/LS From 87 N 67 S Minghui

More information

P1.1 VERIFICATION OF SURFACE LAYER OZONE FORECASTS IN THE NOAA/EPA AIR QUALITY FORECAST SYSTEM IN DIFFERENT REGIONS UNDER DIFFERENT SYNOPTIC SCENARIOS

P1.1 VERIFICATION OF SURFACE LAYER OZONE FORECASTS IN THE NOAA/EPA AIR QUALITY FORECAST SYSTEM IN DIFFERENT REGIONS UNDER DIFFERENT SYNOPTIC SCENARIOS P1.1 VERIFICATION OF SURFACE LAYER OZONE FORECASTS IN THE NOAA/EPA AIR QUALITY FORECAST SYSTEM IN DIFFERENT REGIONS UNDER DIFFERENT SYNOPTIC SCENARIOS Mrin Tsidulko 1*, Jeff T. McQueen 2, Geoff DiMego

More information

Graph States EPIT Mehdi Mhalla (Calgary, Canada) Simon Perdrix (Grenoble, France)

Graph States EPIT Mehdi Mhalla (Calgary, Canada) Simon Perdrix (Grenoble, France) Grph Sttes EPIT 2005 Mehdi Mhll (Clgry, Cnd) Simon Perdrix (Grenole, Frne) simon.perdrix@img.fr Grph Stte: Introdution A grph-sed representtion of the entnglement of some (lrge) quntum stte. Verties: quits

More information

University of Sioux Falls. MAT204/205 Calculus I/II

University of Sioux Falls. MAT204/205 Calculus I/II University of Sioux Flls MAT204/205 Clulus I/II Conepts ddressed: Clulus Textook: Thoms Clulus, 11 th ed., Weir, Hss, Giordno 1. Use stndrd differentition nd integrtion tehniques. Differentition tehniques

More information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS AGRICULTURAL ENGINEERING VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS Ltvi University of Agriulture E-mil: ilze.pelee@llu.lv Astrt Use of solr energy inreses every

More information

8 THREE PHASE A.C. CIRCUITS

8 THREE PHASE A.C. CIRCUITS 8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),

More information

Lecture 1 - Introduction and Basic Facts about PDEs

Lecture 1 - Introduction and Basic Facts about PDEs * 18.15 - Introdution to PDEs, Fll 004 Prof. Gigliol Stffilni Leture 1 - Introdution nd Bsi Fts bout PDEs The Content of the Course Definition of Prtil Differentil Eqution (PDE) Liner PDEs VVVVVVVVVVVVVVVVVVVV

More information

( ) as a fraction. Determine location of the highest

( ) as a fraction. Determine location of the highest AB/ Clulus Exm Review Sheet Solutions A Prelulus Type prolems A1 A A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f( x) Set funtion equl to Ftor or use qudrti eqution if qudrti Grph to

More information

Iowa Training Systems Trial Snus Hill Winery Madrid, IA

Iowa Training Systems Trial Snus Hill Winery Madrid, IA Iow Trining Systems Tril Snus Hill Winery Mdrid, IA Din R. Cohrn nd Gil R. Nonneke Deprtment of Hortiulture, Iow Stte University Bkground nd Rtionle: Over the lst severl yers, five sttes hve een evluting

More information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem.

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem. 27 Lesson 2: The Pythgoren Theorem nd Similr Tringles A Brief Review of the Pythgoren Theorem. Rell tht n ngle whih mesures 90º is lled right ngle. If one of the ngles of tringle is right ngle, then we

More information

(h+ ) = 0, (3.1) s = s 0, (3.2)

(h+ ) = 0, (3.1) s = s 0, (3.2) Chpter 3 Nozzle Flow Qusistedy idel gs flow in pipes For the lrge vlues of the Reynolds number typilly found in nozzles, the flow is idel. For stedy opertion with negligible body fores the energy nd momentum

More information

P5.25 NUMERICAL SIMULATIONS OF HEAVY RAINFALL DURING THE MESOSCALE ALPINE PROGRAM (MAP)

P5.25 NUMERICAL SIMULATIONS OF HEAVY RAINFALL DURING THE MESOSCALE ALPINE PROGRAM (MAP) P5.25 NUMERICAL SIMULATIONS OF HEAVY RAINFALL DURING THE MESOSCALE ALPINE PROGRAM (MAP) Jmes A. Thurmn, Y.-L Lin*, nd J.J Chrney North Crolin Stte University, Rleigh, North Crolin 1. Introduction To ssess

More information

Cyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics Ò

Cyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics Ò J Appl Eletrohem (009) 39:9 63 DOI 0.007/s0800-009-9797- ORIGINAL PAPER Cyli voltmmetry simultion t miroeletrode rrys with COMSOL Multiphysis Ò Alessndro Lvhi Æ U. Brdi Æ C. Borri Æ S. Cporli Æ A. Fossti

More information

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES PAIR OF LINEAR EQUATIONS IN TWO VARIABLES. Two liner equtions in the sme two vriles re lled pir of liner equtions in two vriles. The most generl form of pir of liner equtions is x + y + 0 x + y + 0 where,,,,,,

More information

Math 32B Discussion Session Week 8 Notes February 28 and March 2, f(b) f(a) = f (t)dt (1)

Math 32B Discussion Session Week 8 Notes February 28 and March 2, f(b) f(a) = f (t)dt (1) Green s Theorem Mth 3B isussion Session Week 8 Notes Februry 8 nd Mrh, 7 Very shortly fter you lerned how to integrte single-vrible funtions, you lerned the Fundmentl Theorem of lulus the wy most integrtion

More information

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL Mhun Peng *, Lin Xie nd Leonrd J. Pietrfes Deprtment of Mrine, Erth nd Atmospheri

More information

2. There are an infinite number of possible triangles, all similar, with three given angles whose sum is 180.

2. There are an infinite number of possible triangles, all similar, with three given angles whose sum is 180. SECTION 8-1 11 CHAPTER 8 Setion 8 1. There re n infinite numer of possile tringles, ll similr, with three given ngles whose sum is 180. 4. If two ngles α nd β of tringle re known, the third ngle n e found

More information

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and Leture 7: iffusion of Ions: Prt : oupled diffusion of tions nd nions s desried y Nernst-Plnk Eqution Tody s topis Continue to understnd the fundmentl kinetis prmeters of diffusion of ions within n eletrilly

More information

Electromagnetism Notes, NYU Spring 2018

Electromagnetism Notes, NYU Spring 2018 Eletromgnetism Notes, NYU Spring 208 April 2, 208 Ation formultion of EM. Free field desription Let us first onsider the free EM field, i.e. in the bsene of ny hrges or urrents. To tret this s mehnil system

More information

Technische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution

Technische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution Tehnishe Universität Münhen Winter term 29/ I7 Prof. J. Esprz / J. Křetínský / M. Luttenerger. Ferur 2 Solution Automt nd Forml Lnguges Homework 2 Due 5..29. Exerise 2. Let A e the following finite utomton:

More information

Section 4.4. Green s Theorem

Section 4.4. Green s Theorem The Clulus of Funtions of Severl Vriles Setion 4.4 Green s Theorem Green s theorem is n exmple from fmily of theorems whih onnet line integrls (nd their higher-dimensionl nlogues) with the definite integrls

More information

Comparing the Pre-image and Image of a Dilation

Comparing the Pre-image and Image of a Dilation hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity

More information

COMPARISON BETWEEN TWO FRICTION MODEL PARAMETER ESTIMATION METHODS APPLIED TO CONTROL VALVES. Rodrigo Alvite Romano and Claudio Garcia

COMPARISON BETWEEN TWO FRICTION MODEL PARAMETER ESTIMATION METHODS APPLIED TO CONTROL VALVES. Rodrigo Alvite Romano and Claudio Garcia 8th Interntionl IFAC Symposium on Dynmis nd Control of Proess Systems Preprints Vol., June 6-8, 007, Cnún, Mexio COMPARISON BETWEEN TWO FRICTION MODEL PARAMETER ESTIMATION METHODS APPLIED TO CONTROL VALVES

More information

Compression of Palindromes and Regularity.

Compression of Palindromes and Regularity. Compression of Plinromes n Regulrity. Kyoko Shikishim-Tsuji Center for Lierl Arts Eution n Reserh Tenri University 1 Introution In [1], property of likstrem t t view of tse is isusse n it is shown tht

More information

Engr354: Digital Logic Circuits

Engr354: Digital Logic Circuits Engr354: Digitl Logi Ciruits Chpter 4: Logi Optimiztion Curtis Nelson Logi Optimiztion In hpter 4 you will lern out: Synthesis of logi funtions; Anlysis of logi iruits; Tehniques for deriving minimum-ost

More information

EXPERIMENTAL AND NUMERICAL ANALYSIS OF SUPERSONIC BLADE PROFILES DEVELOPED FOR HIGHLY LOADED IMPULSE TYPE STEAM TURBINE STAGES

EXPERIMENTAL AND NUMERICAL ANALYSIS OF SUPERSONIC BLADE PROFILES DEVELOPED FOR HIGHLY LOADED IMPULSE TYPE STEAM TURBINE STAGES Pper ID: ETC2017-190 Proeedings of 12th Europen Conferene on Turomhinery Fluid dynmis & Thermodynmis ETC12, April 3-7, 2017; Stokholm, Sweden EXPERIMENTAL AND NUMERICAL ANALYSIS OF SUPERSONIC BLADE PROFILES

More information

Linear Algebra Introduction

Linear Algebra Introduction Introdution Wht is Liner Alger out? Liner Alger is rnh of mthemtis whih emerged yers k nd ws one of the pioneer rnhes of mthemtis Though, initilly it strted with solving of the simple liner eqution x +

More information

Alpha Algorithm: Limitations

Alpha Algorithm: Limitations Proess Mining: Dt Siene in Ation Alph Algorithm: Limittions prof.dr.ir. Wil vn der Alst www.proessmining.org Let L e n event log over T. α(l) is defined s follows. 1. T L = { t T σ L t σ}, 2. T I = { t

More information

1B40 Practical Skills

1B40 Practical Skills B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need

More information

Stable Atmospheric Boundary Layers and Diurnal Cycles

Stable Atmospheric Boundary Layers and Diurnal Cycles Stable Atmospheric Boundary Layers and Diurnal Cycles Introduction and overview of GABLS Bert Holtslag DICE and GABLS4 Workshop, Toulouse, May 20, 2015 Meteorology and Air Quality Department Modeling Atmospheric

More information

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light. 1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the

More information

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es

More information

NON-DETERMINISTIC FSA

NON-DETERMINISTIC FSA Tw o types of non-determinism: NON-DETERMINISTIC FS () Multiple strt-sttes; strt-sttes S Q. The lnguge L(M) ={x:x tkes M from some strt-stte to some finl-stte nd ll of x is proessed}. The string x = is

More information

SECTION A STUDENT MATERIAL. Part 1. What and Why.?

SECTION A STUDENT MATERIAL. Part 1. What and Why.? SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are

More information

Something found at a salad bar

Something found at a salad bar Nme PP Something found t sld r 4.7 Notes RIGHT TRINGLE hs extly one right ngle. To solve right tringle, you n use things like SOH-H-TO nd the Pythgoren Theorem. n OLIQUE TRINGLE hs no right ngles. To solve

More information

Forces on curved surfaces Buoyant force Stability of floating and submerged bodies

Forces on curved surfaces Buoyant force Stability of floating and submerged bodies Stti Surfe ores Stti Surfe ores 8m wter hinge? 4 m ores on plne res ores on urved surfes Buont fore Stbilit of floting nd submerged bodies ores on Plne res Two tpes of problems Horizontl surfes (pressure

More information

On the Scale factor of the Universe and Redshift.

On the Scale factor of the Universe and Redshift. On the Sle ftor of the Universe nd Redshift. J. M. unter. john@grvity.uk.om ABSTRACT It is proposed tht there hs been longstnding misunderstnding of the reltionship between sle ftor of the universe nd

More information

8.3 THE HYPERBOLA OBJECTIVES

8.3 THE HYPERBOLA OBJECTIVES 8.3 THE HYPERBOLA OBJECTIVES 1. Define Hperol. Find the Stndrd Form of the Eqution of Hperol 3. Find the Trnsverse Ais 4. Find the Eentriit of Hperol 5. Find the Asmptotes of Hperol 6. Grph Hperol HPERBOLAS

More information

SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WITH VARIOUS TYPES OF COLUMN BASES

SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WITH VARIOUS TYPES OF COLUMN BASES Advned Steel Constrution Vol., No., pp. 7-88 () 7 SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WIT VARIOUS TYPES OF COLUMN BASES J. ent sio Assoite Professor, Deprtment of Civil nd Environmentl

More information

A study of non-local effects on the Budyko Sellers infrared parametrization using atmospheric general circulation models

A study of non-local effects on the Budyko Sellers infrared parametrization using atmospheric general circulation models Tellus (2005), 57A, 654 661 Copyright C Blkwell Munksgrd, 2005 Printed in Singpore. All rights reserved TELLUS A study of non-lol effets on the Budyko Sellers infrred prmetriztion using tmospheri generl

More information

Thermal energy 2 U Q W. 23 April The First Law of Thermodynamics. Or, if we want to obtain external work: The trick of using steam

Thermal energy 2 U Q W. 23 April The First Law of Thermodynamics. Or, if we want to obtain external work: The trick of using steam April 08 Therml energy Soures of het Trnsport of het How to use het The First Lw of Thermoynmis U W Or, if we wnt to otin externl work: U W 009 vrije Universiteit msterm Close yle stem power plnt The trik

More information

DETERMINING SIGNIFICANT FACTORS AND THEIR EFFECTS ON SOFTWARE ENGINEERING PROCESS QUALITY

DETERMINING SIGNIFICANT FACTORS AND THEIR EFFECTS ON SOFTWARE ENGINEERING PROCESS QUALITY DETERMINING SIGNIFINT FTORS ND THEIR EFFETS ON SOFTWRE ENGINEERING PROESS QULITY R. Rdhrmnn Jeng-Nn Jung Mil to: rdhrmn_r@merer.edu jung_jn@merer.edu Shool of Engineering, Merer Universit, Mon, G 37 US

More information

U Q W The First Law of Thermodynamics. Efficiency. Closed cycle steam power plant. First page of S. Carnot s paper. Sadi Carnot ( )

U Q W The First Law of Thermodynamics. Efficiency. Closed cycle steam power plant. First page of S. Carnot s paper. Sadi Carnot ( ) 0-9-0 he First Lw of hermoynmis Effiieny When severl lterntive proesses involving het n work re ville to hnge system from n initil stte hrterize y given vlues of the mrosopi prmeters (pressure p i, temperture

More information

Learning Partially Observable Markov Models from First Passage Times

Learning Partially Observable Markov Models from First Passage Times Lerning Prtilly Oservle Mrkov s from First Pssge s Jérôme Cllut nd Pierre Dupont Europen Conferene on Mhine Lerning (ECML) 8 Septemer 7 Outline. FPT in models nd sequenes. Prtilly Oservle Mrkov s (POMMs).

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het

More information

Current and turbulence measurements at the FINO1 offshore wind energy site: analysis using 5-beam ADCPs

Current and turbulence measurements at the FINO1 offshore wind energy site: analysis using 5-beam ADCPs Oen Dynmis (2018) 68:109 130 https://doi.org/10.1007/s10236-017-1109-5 Current nd turulene mesurements t the FINO1 offshore wind energy site: nlysis using 5-em ADCPs Mostf Bkhody-Pskyi 1,2 Ilker Fer 1

More information

5.2 THE EFFECT OF TURBULENCE ON CLOUD MICROSTRUCTURE, PRECIPITATION FORMATION AND THE ORGANISATION OF STRATOCUMULUS AND SHALLOW CUMULUS CONVECTION

5.2 THE EFFECT OF TURBULENCE ON CLOUD MICROSTRUCTURE, PRECIPITATION FORMATION AND THE ORGANISATION OF STRATOCUMULUS AND SHALLOW CUMULUS CONVECTION 5.2 THE EFFECT OF TURBULENCE ON CLOUD MICROSTRUCTURE, PRECIPITATION FORMATION AND THE ORGANISATION OF STRATOCUMULUS AND SHALLOW CUMULUS CONVECTION Charmaine N. Franklin * Centre for Australian Weather

More information

20 b The prime numbers are 2,3,5,7,11,13,17,19.

20 b The prime numbers are 2,3,5,7,11,13,17,19. Topi : Probbility Short nswer tehnology- free The following my be of use in this test:! 0 0 Two rows of Psl s tringle re: ontiner holds irulr piees eh of the sme size. Written on eh is different number,

More information

Arrow s Impossibility Theorem

Arrow s Impossibility Theorem Rep Fun Gme Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Fun Gme Properties Arrow s Theorem Leture Overview 1 Rep 2 Fun Gme 3 Properties

More information

Vapour compression refrigeration system

Vapour compression refrigeration system www.ookspr.om VTU NEWS VTU NOTES QUESTION PAPERS FORUMS RESULTS Vpour ompression refrigertion system Introdution In vpour ompression system, the refrigernts used re mmoni, ron dioxide, freons et. the refrigernts

More information

Arrow s Impossibility Theorem

Arrow s Impossibility Theorem Rep Voting Prdoxes Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Voting Prdoxes Properties Arrow s Theorem Leture Overview 1 Rep

More information

CS 573 Automata Theory and Formal Languages

CS 573 Automata Theory and Formal Languages Non-determinism Automt Theory nd Forml Lnguges Professor Leslie Lnder Leture # 3 Septemer 6, 2 To hieve our gol, we need the onept of Non-deterministi Finite Automton with -moves (NFA) An NFA is tuple

More information

Logarithms LOGARITHMS.

Logarithms LOGARITHMS. Logrithms LOGARITHMS www.mthletis.om.u Logrithms LOGARITHMS Logrithms re nother method to lulte nd work with eponents. Answer these questions, efore working through this unit. I used to think: In the

More information

Computation and Modeling of the Air-Sea Heat and Momentum Fluxes. By Dr. Nasser H. Zaker

Computation and Modeling of the Air-Sea Heat and Momentum Fluxes. By Dr. Nasser H. Zaker Computtion nd Modeling of the Air-e et nd Momentum Fluxes By Dr. Nsser. Zker ICTP June 00 1 Introduction The ocen receives energy through the ir-se interfce by exchnge of momentum nd het. The turbulent

More information

Patch Antennas. Chapter Resonant Cavity Analysis

Patch Antennas. Chapter Resonant Cavity Analysis Chpter 4 Ptch Antenns A ptch ntenn is low-profile ntenn consisting of metl lyer over dielectric sustrte nd ground plne. Typiclly, ptch ntenn is fed y microstrip trnsmission line, ut other feed lines such

More information

Atmospheric Boundary Layers

Atmospheric Boundary Layers Lecture for International Summer School on the Atmospheric Boundary Layer, Les Houches, France, June 17, 2008 Atmospheric Boundary Layers Bert Holtslag Introducing the latest developments in theoretical

More information

Atmospheric Boundary Layers:

Atmospheric Boundary Layers: Atmospheric Boundary Layers: An introduction and model intercomparisons Bert Holtslag Lecture for Summer school on Land-Atmosphere Interactions, Valsavarenche, Valle d'aosta (Italy), 22 June, 2015 Meteorology

More information

Unit-VII: Linear Algebra-I. To show what are the matrices, why they are useful, how they are classified as various types and how they are solved.

Unit-VII: Linear Algebra-I. To show what are the matrices, why they are useful, how they are classified as various types and how they are solved. Unit-VII: Liner lger-i Purpose of lession : To show wht re the mtries, wh the re useful, how the re lssified s vrious tpes nd how the re solved. Introdution: Mtries is powerful tool of modern Mthemtis

More information

H (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a.

H (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a. Chpter Review 89 IGURE ol hord GH of the prol 4. G u v H (, ) (A) Use the distne formul to show tht u. (B) Show tht G nd H lie on the line m, where m ( )/( ). (C) Solve m for nd sustitute in 4, otining

More information

, g. Exercise 1. Generator polynomials of a convolutional code, given in binary form, are g. Solution 1.

, g. Exercise 1. Generator polynomials of a convolutional code, given in binary form, are g. Solution 1. Exerise Genertor polynomils of onvolutionl ode, given in binry form, re g, g j g. ) Sketh the enoding iruit. b) Sketh the stte digrm. ) Find the trnsfer funtion T. d) Wht is the minimum free distne of

More information

#A42 INTEGERS 11 (2011) ON THE CONDITIONED BINOMIAL COEFFICIENTS

#A42 INTEGERS 11 (2011) ON THE CONDITIONED BINOMIAL COEFFICIENTS #A42 INTEGERS 11 (2011 ON THE CONDITIONED BINOMIAL COEFFICIENTS Liqun To Shool of Mthemtil Sienes, Luoyng Norml University, Luoyng, Chin lqto@lynuedun Reeived: 12/24/10, Revised: 5/11/11, Aepted: 5/16/11,

More information

(a) A partition P of [a, b] is a finite subset of [a, b] containing a and b. If Q is another partition and P Q, then Q is a refinement of P.

(a) A partition P of [a, b] is a finite subset of [a, b] containing a and b. If Q is another partition and P Q, then Q is a refinement of P. Chpter 7: The Riemnn Integrl When the derivtive is introdued, it is not hrd to see tht the it of the differene quotient should be equl to the slope of the tngent line, or when the horizontl xis is time

More information

Descriptional Complexity of Non-Unary Self-Verifying Symmetric Difference Automata

Descriptional Complexity of Non-Unary Self-Verifying Symmetric Difference Automata Desriptionl Complexity of Non-Unry Self-Verifying Symmetri Differene Automt Lurette Mris 1,2 nd Lynette vn Zijl 1 1 Deprtment of Computer Siene, Stellenosh University, South Afri 2 Merk Institute, CSIR,

More information

H 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3.

H 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3. . Spetrosopy Mss spetrosopy igh resolution mss spetrometry n e used to determine the moleulr formul of ompound from the urte mss of the moleulr ion For exmple, the following moleulr formuls ll hve rough

More information

Chapter 4 State-Space Planning

Chapter 4 State-Space Planning Leture slides for Automted Plnning: Theory nd Prtie Chpter 4 Stte-Spe Plnning Dn S. Nu CMSC 722, AI Plnning University of Mrylnd, Spring 2008 1 Motivtion Nerly ll plnning proedures re serh proedures Different

More information

LAMEPS Limited area ensemble forecasting in Norway, using targeted EPS

LAMEPS Limited area ensemble forecasting in Norway, using targeted EPS Limited re ensemle forecsting in Norwy, using trgeted Mrit H. Jensen, Inger-Lise Frogner* nd Ole Vignes, Norwegin Meteorologicl Institute, (*held the presenttion) At the Norwegin Meteorologicl Institute

More information

Roughness Coefficients for Selected Residue Materials

Roughness Coefficients for Selected Residue Materials University of Nersk - Linoln DigitlCommons@University of Nersk - Linoln Biologil Systems Engineering: Ppers nd Pulitions Biologil Systems Engineering 8-1991 Roughness Coeffiients for Seleted Residue Mterils

More information

Solutions to Assignment 1

Solutions to Assignment 1 MTHE 237 Fll 2015 Solutions to Assignment 1 Problem 1 Find the order of the differentil eqution: t d3 y dt 3 +t2 y = os(t. Is the differentil eqution liner? Is the eqution homogeneous? b Repet the bove

More information

Overview of 10 years of GABLS

Overview of 10 years of GABLS Overview of 10 years of GABLS Bert Holtslag (Wageningen Univ, www.maq.wur.nl ) Thanks to Sukanta Basu (NC State Univ), Bob Beare (Exeter Univ), Fred Bosveld (KNMI), Joan Cuxart (Univ. Balearic Islands)

More information

QUADRATIC EQUATION. Contents

QUADRATIC EQUATION. Contents QUADRATIC EQUATION Contents Topi Pge No. Theory 0-04 Exerise - 05-09 Exerise - 09-3 Exerise - 3 4-5 Exerise - 4 6 Answer Key 7-8 Syllus Qudrti equtions with rel oeffiients, reltions etween roots nd oeffiients,

More information

Vectors. a Write down the vector AB as a column vector ( x y ). A (3, 2) x point C such that BC = 3. . Go to a OA = a

Vectors. a Write down the vector AB as a column vector ( x y ). A (3, 2) x point C such that BC = 3. . Go to a OA = a Streth lesson: Vetors Streth ojetives efore you strt this hpter, mrk how onfident you feel out eh of the sttements elow: I n lulte using olumn vetors nd represent the sum nd differene of two vetors grphilly.

More information

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS IN-SITU PROBING OF DOMAIN POLING IN Bi 4 Ti 3 O 12 THIN FILMS BY OPTICAL SECOND HARMONIC GENERATION YANIV BARAD, VENKATRAMAN GOPALAN Mterils Reserh Lortory

More information

MA10207B: ANALYSIS SECOND SEMESTER OUTLINE NOTES

MA10207B: ANALYSIS SECOND SEMESTER OUTLINE NOTES MA10207B: ANALYSIS SECOND SEMESTER OUTLINE NOTES CHARLIE COLLIER UNIVERSITY OF BATH These notes hve been typeset by Chrlie Collier nd re bsed on the leture notes by Adrin Hill nd Thoms Cottrell. These

More information

WRF/NMM-CMAQ derived planetary boundary layer heights and vertical diffusivity for transport of trace species

WRF/NMM-CMAQ derived planetary boundary layer heights and vertical diffusivity for transport of trace species WRF/NMM-CMAQ derived plnetry oundry lyer heights nd verticl diffusivity for trnsport of trce species Pius Lee *, Mrin Tsidulko, You-Hu Tng, nd Ho-Chun Hung Scientific Applictions Interntionl Corportion,

More information

Appendix A: HVAC Equipment Efficiency Tables

Appendix A: HVAC Equipment Efficiency Tables Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER

More information

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions MEP: Demonstrtion Projet UNIT 4: Trigonometry UNIT 4 Trigonometry tivities tivities 4. Pythgors' Theorem 4.2 Spirls 4.3 linometers 4.4 Rdr 4.5 Posting Prels 4.6 Interloking Pipes 4.7 Sine Rule Notes nd

More information

where the box contains a finite number of gates from the given collection. Examples of gates that are commonly used are the following: a b

where the box contains a finite number of gates from the given collection. Examples of gates that are commonly used are the following: a b CS 294-2 9/11/04 Quntum Ciruit Model, Solovy-Kitev Theorem, BQP Fll 2004 Leture 4 1 Quntum Ciruit Model 1.1 Clssil Ciruits - Universl Gte Sets A lssil iruit implements multi-output oolen funtion f : {0,1}

More information

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx Fill in the Blnks for the Big Topis in Chpter 5: The Definite Integrl Estimting n integrl using Riemnn sum:. The Left rule uses the left endpoint of eh suintervl.. The Right rule uses the right endpoint

More information

7.6 A RE-EXAMINATION OF DENSITY EFFECTS IN EDDY COVARIANCE MEASUREMENTS OF CO 2 FLUXES. Heping Liu Jackson State University, Jackson, MS, USA

7.6 A RE-EXAMINATION OF DENSITY EFFECTS IN EDDY COVARIANCE MEASUREMENTS OF CO 2 FLUXES. Heping Liu Jackson State University, Jackson, MS, USA . A RE-EXAMINATION OF DENSITY EFFECTS IN EDDY COVARIANCE MEASUREMENTS OF CO FLUXES Heping Liu Jkson Stte University, Jkson, MS, USA INTRODUCTION Corretions of the density effets resulting from ir-prel

More information

INTEGRATION. 1 Integrals of Complex Valued functions of a REAL variable

INTEGRATION. 1 Integrals of Complex Valued functions of a REAL variable INTEGRATION NOTE: These notes re supposed to supplement Chpter 4 of the online textbook. 1 Integrls of Complex Vlued funtions of REAL vrible If I is n intervl in R (for exmple I = [, b] or I = (, b)) nd

More information

Research Article Comparative Studies of Different Switching Patterns for Direct and Indirect Space Vector Modulated Matrix Converter

Research Article Comparative Studies of Different Switching Patterns for Direct and Indirect Space Vector Modulated Matrix Converter dvnes in Power Eletronis Volume, rtile ID 854, 8 pges doi:.55//854 Reserh rtile omprtive Studies of Different Swithing Ptterns for Diret nd Indiret Spe Vetor Modulted Mtrix onverter min Shnpour, Ssn Gholmi,

More information

Lecture 6. CMOS Static & Dynamic Logic Gates. Static CMOS Circuit. PMOS Transistors in Series/Parallel Connection

Lecture 6. CMOS Static & Dynamic Logic Gates. Static CMOS Circuit. PMOS Transistors in Series/Parallel Connection NMOS Trnsistors in Series/Prllel onnetion Leture 6 MOS Stti & ynmi Logi Gtes Trnsistors n e thought s swith ontrolled y its gte signl NMOS swith loses when swith ontrol input is high Peter heung eprtment

More information