Research Article Adjusting of Wind Input Source Term in ...downloads.hindawi.com/journals/amete/2016/8539127.pdf · WAVEWATCH III Model for the Middle-Sized Water Body on the Basis

Research ArticleAdjusting of Wind Input Source Term inWAVEWATCH III Model for the Middle-Sized WaterBody on the Basis of the Field Experiment

Alexandra Kuznetsova12 Georgy Baydakov12 Vladislav Papko1 Alexander Kandaurov12

Maxim Vdovin12 Daniil Sergeev12 and Yuliya Troitskaya12

1 Institute of Applied Physics of the Russian Academy of Sciences 46 Ulyanov Street Nizhny Novgorod 603950 Russia2Nizhny Novgorod State University 23 Gagarina Avenue Nizhny Novgorod 603950 Russia

Correspondence should be addressed to Alexandra Kuznetsova alexandrahydroapplsci-nnovru

Received 20 August 2015 Accepted 18 November 2015

Academic Editor Alan Blumberg

Copyright copy 2016 Alexandra Kuznetsova et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Adjusting of wind input source term in numerical model WAVEWATCH III for the middle-sized water body is reported For thispurpose the field experiment on Gorky Reservoir is carried out Surface waves are measured along with the parameters of theairflow The measurement of wind speed in close proximity to the water surface is performed On the basis of the experimentalresults the parameterization of the drag coefficient depending on the 10m wind speed is proposed This parameterization is usedinWAVEWATCH III for the adjusting of the wind input source term within WAM 3 and Tolman and Chalikov parameterizationsThe simulation of the surface wind waves within tuned to the conditions of the middle-sized water body WAVEWATCH III isperformed using three built-in parameterizations (WAM 3 Tolman and Chalikov and WAM 4) and adjusted wind input sourceterm parameterizations Verification of the applicability of the model to the middle-sized reservoir is performed by comparing thesimulated data with the results of the field experiment It is shown that the use of the proposed parameterization 119862

119863(11988010) improves

the agreement in the significant wave height119867119878from the field experiment and from the numerical simulation

1 Introduction

Prediction of surfacewindwaves on the inlandwater bodies isrecognized as an important problem involvingmany environ-mental applications such as safety of the inland navigationand protection from the banks erosion Lake waves alsostrongly affect the processes of exchange of momentum heatand moisture in the low atmosphere and thus determinemicroclimate of the adjacent areas which should be takeninto account in planning structure of recreation zones [1]

The major physical problem of numerical wave modelingin inland water bodies is associated with short fetches whenparameters of wave excitation and development are stronglydifferent from long-fetch condition typical for the open ocean[2] Typically in these conditions the numerical descriptionof waves in lakes and reservoirs is based on empirical models

(see eg [3 4]) But the empirical relationships are based onthe averaged characteristics that cannot predict the extremesimportant for many tasks of operational meteorology (stormconditions such as Great Lakes storm discussed in [5])and numerical wave models are required Now there area number of examples of application of third generationmodels for waves forecast in large lakes So WAVEWATCHIII [2] is used successfully for the wave forecasts on theGreat Lakes in the USA [6 7] The data for a current wavesituation is presented on the open website and is updatedevery three hours [8] Furthermore WAVEWATCH III andSWAN [9] are applied to Caspian Sea and Ladoga Laketo analyze the wind and waves climate hindcasting [10]Nevertheless lakes and reservoirs of smaller sizes (less than100 km linear size the so-called middle-sized reservoirs) alsohave examples of hurricane-force wind and severe surface

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016 Article ID 8539127 13 pageshttpdxdoiorg10115520168539127

2 Advances in Meteorology

wave states conditions The first attempt of application of aglobal wave model WAM [11] for the wave forecasting on amiddle-sized reservoir was reported recently in [12]

Among the peculiarities of the low-fetch waves at themiddle-sized reservoirs is the stronger wind input which isproportional to the ratio of wind friction velocity (or 10mwind speed) to the wave phase velocity [2] Another featureis the enhanced nonlinearity caused by higher steepness ofthe waves Then the tuning of the ocean wave model to theinland water conditions should be twofold adjusting of thewind source and ldquocollision integralrdquo Dissipation due to wavebreaking can be expected to be similar towave conditions dueto their universal nature

One more problem of tuning of numerical models tothe conditions of middle-sized reservoirs and lakes is thesmall amount of experimental data that can be used for itsverification Rare examples of such experiments are studied[13 14] which show the specificity of wind-wave interactionin the indicated circumstances In this paper we present atuning of the wind input term inWAVEWATCH III model tothe conditions of the middle-sized reservoir on an exampleof Gorky Reservoir belonging to the Volga Cascade Thetuning is based on the data of the field experiment held byour groupThe methods of the experiment are different fromthose used in [13 14] and they focus on the study of airflowin close proximity to water surfaceThe comparison of resultsof the numerical experiments with the results of the fieldexperiments on Gorky Reservoir is presented

The paper has the following structure In Section 2 thebasic parameterizations of wind and wave interactions inWAVEWATCH III v314 are presented In Section 3 thestudied reservoir and the field experiment setup with itsinstrumentation andmethods are described In Section 4 thefield data processing and the results of the field experimentare presented In Section 5 numerical experiment withintuned to the conditions of the middle-sized reservoirWAVE-WATCH III is set out In Section 6 the adjustment of windinput source term in tunedWAVEWATCH III and the resultsof numerical experiments within tuned WAVEWATCH IIIandwithin a tunedWAVEWATCH III with the adjusted windinput are presented

2 Wind Input Parameterizationsin WAVEWATCH III

WAVEWATCH III [2 15 16] is based on the numericalsolution of the equation for the spectral density ofwave action119873 in the approximation of phase averaging

120597119873

120597119905+ nabla119909119873 +

120597

120597120590119873 +

120597

120597120579

120579119873 =1

120590(119878in + 119878dis + 119878nl) (1)

The lefthand side of (1) describes the kinematics ofwaves120590 is the radian frequency and 120579 is the wave direction In theright hand side there are terms that describe the wind-wavegrowth 119878in dissipation mainly due to wave breaking 119878dis and4-wave nonlinear interaction of waves 119878nl

This paper focuses on the wind input parameterizationswhose parameters can be adjusted on the basis of the field

measurements data Generally the term describing the windinput is determined as

119878in = 120573 (119896 120579)119873 (119896 120579) 120590 (2)

where 120573(119896 120579) is the dimensionless wind-wave growth rateparameter approximated in WAVEWATCH III v314 bydifferent parameterizations (WAM 3 Tolman and Chalikovand WAM 4) Among them the WAM 3 parameterization[17ndash19] is defined by two empirical formulas The first one isfor the wind-wave growth rate

120573 (119896 120579) = 119862in120588119886

120588119908

max[0 (28119906lowast

119888phcos (120579 minus 120579

119908) minus 1)] (3)

where 119862in = 025 is a constant 120588119886120588119908is the ratio of the

densities of air and water 119906lowastis the friction velocity 119888ph

is the phase velocity and 120579119908is the main wind direction

The second one is a relation between the 10m wind speed11988010

and a friction velocity 119906lowast

= 11988010radic119862119863provided by the

empirical formula of the parameterization of the surface dragcoefficient 119862

119863 proposed in [19]

119862119863= 0001 times (08 + 065119880

10) (4)

In the Tolman and Chalikov parameterization [20] thedimensionless coefficient depends on the drag coefficientand on the dimensionless frequency of the spectral com-ponents In the WAM 4 parameterization [21] the wind-waves interaction parameter 120573 is presented by the adjustedMiles formula To calculate the roughness parameter thefeedback of the wind-waves spectra is taken into account aswell So in the considered parameterizations the wind inputis determined by the wind-wave interaction parameter 120573 andby the dependence 119906

lowast(11988010) which is defined by 119862

119863

3 Field Experiment

The tuning of WAVEWATCH III to the conditions of themiddle-sized reservoir was performed for conditions ofGorky Reservoir on the basis of field experiment

Measurements were carried out in 2012ndash2014 from Mayto October in the waters of Gorky Reservoir It has anelongated shape (Figure 1) which allows studyingwindwavesof different fetch depending on the wind direction GorkyReservoir is an artificial lake in the central part of the VolgaRiver formed by the dam of Nizhny Novgorod HydroelectricStation Its lake part is 85 km long and up to 15 km wideThe mean depth of the reservoir varies in the range of4ndash20 meters and the depth in the area of measurementsis 9ndash12 meters depending on the season and the point ofmeasurement

31 Instrumentation Instrumentation was placed on a buoystation with the original design based on the oceanographicFroude buoy Froude buoy is a mast submerged in water andheld in a vertical position by the float close to the surfaceand by the load on the depth (Figures 2(a) and 2(b)) Buoyrsquostotal length is 12m and the length of the part above the water

Advances in Meteorology 3

(a)

Point ofmeasurements

1km

(b)

Figure 1 (a) Gorky Reservoir (Google Earth data) (b) Zoom view of the measurements area

(a)

Balanceweight

Float

Wirewave gauge

Ultrasonicwind sensors

Separate float

Water surface

12m

53

m

227

m

13

m

085

m

01

m

(b)

Figure 2 Froude buoy (a) real view of the operating state and (b) scheme

is 53m The resonant frequency of the vertical oscillationsis 025Hz which corresponds to a wavelength of 25m Onthe buoy mast 4 ultrasonic speed sensors (WindSonic GillInstruments Production) are located at heights of 085m13m 227m and 526m over the mean water surface A fifthsensor is located on the float tracking waveform that allowsmeasuring the wind speed in close proximity to the watersurface The distance from the float to the buoy mast is 1mthe height of thewind speedmeasuring zone is 10 cm from thewater surfaceThe buoy is also equipped with air temperaturesensors (at heights of 01m (float) 085m and 13m) watertemperature sensors and three-channel wire wave gauge thatallows us to retrieve the wave space-time spectra

WindSonic is two-component ultrasonic sensor with 4measurement accuracy and velocity resolution of 001msOperating range of wind speed measurements 0ndash60msincludesmeasurements in calm conditions Resistive temper-ature sensors measure the environmental temperature with

resolution of 001∘C and 3 measurement accuracy Wavegauge consists of three pairs of resistive wire sensors locatedat the vertices of an equilateral triangle with a side of 62mmand the data sampling rate is 100Hz

32 Surface Wave Spectra Three-dimensional frequency-wavenumber spectra were retrieved from wave gauge databy the algorithm similar to the wavelet directional method(WDM) suggested in [22] The details of the applied methodare described in [23] Time series of water elevation from eachpair of wire sensors were processed by the window FFT withthe windowwidth 2119873 (119873 is an integer) with 50 overlappingThe complex amplitudes of harmonics at each frequency120596 119860120596(119909119899 119910119899) exp(119894120601

120596(119909119899 119910119899))were calculated here119860

120596is the

wave magnitude 120601120596is the wave phase 119899 = 1 2 3 is

the number of the wave sensors and (119909119899 119910119899) are the 119899-

sensorrsquos Cartesian coordinates Suppose that the wave fieldis a superposition of harmonic waves with the wavenumbers


01 1

00001

0001

001

01

simfminus506

simfminus511

E(f

)(m

minus2 s)

1E minus 005

f (Hz)

(a)

0001 001 01

00001

0001

simkminus309

simkminus313

1E minus 005

1E minus 006

1E minus 007

E(k)

(m3 )

k (cmminus1)

(b)

Figure 3 Wave spectra for 11988010= 6-7ms averaged over 60 minutes (a) 1D frequency spectrum and (b) 1D wavenumber spectrum

= (119896119909 119896119910) and one harmonic wave dominates in each

interrogation window and then their phases are

120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)

Thus the wavenumber components can be calculated bythe phase difference at different wave sensors To obtain thedirectional spectra the Cartesian coordinates (119896

119909 119896119910) were

transformed to the polar coordinates (119896 120579) and then 3Dspectrum 119864(120590 119896 120579) was obtained similar to [22] by binningthe amplitudes squared into calculated bins in 119896 and 120579Integration of119864(120590 119896 120579) overwavenumber or frequency yieldsfrequency 119864(120590 120579) or wavenumber 119864(119896 120579) directional spec-tra respectively Integrating over 120579 gives the 1D frequencyand wavenumber spectra correspondingly (examples are inFigure 3)The system allows estimating the parameters of thewave whose length exceeds the double distance 119889 betweenthe sensors

119896max =120587

119889= 05 cmminus1 (6)

The developed algorithm is based on the supposition thatthe dominatingwave field within the interrogationwindow ata given frequency 120590 is a harmonic wave which is correct for arather short time interval due to grouping of the surface wavefield Several periods of the energy-wave should fit into theinterrogationwindow For typical values of the observed peakfrequency 119891

119901= 035ndash08Hz (or the observed peak period 119879

119901

= 125ndash280 s) the size of interrogation window is selected tobe 2048 s (2048 points)

Frequency and wavenumber spectra shown in Figure 3are obtained by processing of two consecutive recordings 60minutes long It should be noted that the asymptotic behaviorof frequency spectrum and wavenumber spectrum (120590minus5 119896minus3)correspond to Philips saturation spectrum (see eg [24])but they do not correspond to Toba spectrum (see eg [25])which is typical for the ocean conditions

For the comparison with the numerical modeling resultsthe values of significant wave height119867

119878are estimated as four-

standard deviation of the water surface elevation which arecalculated as the integral of the frequency spectrum

119867119878= 4 (int119864 (120590) 119889120590)

12

(7)

33 Parameters of Low Atmosphere over the Inland WaterBody The location of wind velocity sensors corresponds tothe structure of the airflow It is well known (see eg [26])that the velocity profile in the constant flux layer (wherethe turbulent momentum flux 120591turb = 120588air⟨119906

1015840

1199091199061015840

119911⟩ does not

depend on the vertical coordinate 119911 here 120588air is the air densityand 119906

1015840

119909and 119906

1015840

119911are the fluctuations of horizontal and vertical

components of the wind velocity resp) has a logarithmicform

119880 (119911) =119906lowast

120581ln( 119911

1199110

) (8)

where 119906lowast

= radic120591turb120588air = radic⟨11990610158401199091199061015840119911⟩ is the friction velocity

determined by the turbulentmomentumflux 1199110is the surface

roughness parameter and 120581 is the von Karman constant In[27] a distortion of the velocity field in the presence of arough surface is considered and it is shown that in case ofa monochromatic wave propagating along the wind for thestream function 120593 averaged over the turbulent fluctuationsan equation can be written as

(119880 minus 119888) (1198892120593

1198891205782minus 1198962120593) minus

1198892119880

1198891205782120593 = 0 (9)

where119880(120578) is the dependence of wind speed on height abovethe surface (in curvilinear coordinates) 119888 is phase velocityof the wave and 119896 is wavenumber When the magnitude


119880101584010158401198962(119880 minus 119888) is much greater or much less than 1 an

approximate solution is the function 120593 = 119860(119880minus119888)119890minus119896120578 where

119860 is wave amplitude In the case of the logarithmic velocityprofile this condition takes the form (see [27])

119906lowast120581

(119896120578)2

|119880 minus 119888|

≪ 1

or 119906lowast120581

(119896120578)2

|119880 minus 119888|

≫ 1

(10)

and it is performed well enough at the height of the orderof the wave amplitude and higher Thus the perturbationis the bending of the flow lines along the rough surfaceand it decreases exponentially with altitude Therefore to fixspeed sensor relatively to the mean streamlines the speed ata distance from surface must be measured at a fixed horizonand the measurements close to the surface should be carriedout using a tracking waveform sensor located on the float

It is important that the lower sensor should not be locatedin the wave boundary layer The magnitude of the waveboundary layer 120576 can be estimated in accordance with [28]

(lowast

120581ln( 119911

1199110

) minus 119888)

10038161003816100381610038161003816100381610038161003816119911=120576

=120581lowast119911

1205762

10038161003816100381610038161003816100381610038161003816119911=120576

(11)

where 119888 and lowastdenote typical values of the mentioned

above variables In the conditions of the Gorky Reservoir (= 2-3mminus1

lowast= 01ndash04ms) the evaluation of the height

of the wave boundary layer gives a value 120576 sim 1mm thatis significantly less than the height of the lower sensormeasuring wind speed location

It should be noted that the buoy is connected to thevessel by the cable and is located at a fixed distance of30 meters the cross section of the vessel is approximatelyequal to 3 times 3m Thus the buoy is located at a distanceof about 10 characteristic dimensions from the obstacleAccording to the recommendations of Gill Instruments [29]it is enough to consider the airflow to be unperturbed but themeasurements show the presence of small (3ndash6) deviationsof the measured profile from the logarithmic form evenin a steady wind and neutral stratification (Figure 4) Thisdeviation consists of the speed increasing at a height of 526mon 3ndash6 compared with the logarithmic approximationApparently this is due to the effect of the vessel shielding onthe 4 lower sensors

To estimate the perturbations introduced by vessel theformulas of the defect rate attenuation in the turbulent wakeare used It is known [30] that the perturbation introduced bythe body in the unlimited turbulent flow decreases in propor-tion (119909119863)

minus23 along the flow and in proportion exp(minus119903222)along the cross sectionHere119863 is the characteristic size of thebody 119909 and 119903 are the cylindrical coordinates is a width ofthe Gaussian function and

119863sim (

119909

119863)

13

(12)

the coefficients of the proportionality are determined empiri-cally In the case of airflow vessel shielding in a semibounded

01 1 10Height (m)

2

3

4

5

6

7

8

9

Win

d ve

loci

ty (m

s)

U10 = 86msU10 = 72msU10 = 64ms

U10 = 55msU10 = 41ms

Figure 4 Examples of the deviation of the wind velocity profile(5 minutes averaging) from the logarithmic form under differentconditions

space it is fair to expect that the nature of the turbulentwake is the same but the appropriate factors must be chosenSince the top speed sensor is located outside the vesselshielding zone and the lower four are well approximated bya logarithmic dependence the value should be between theheights of the fourth and fifth sensors The linear coefficientis selected so that the velocity profiles are well approximatedby a logarithmic dependence in average Finally to determinethemagnitude of the perturbation introduced by the vessel inthe airflow the dependence

120574 =1198801015840

1198800

= 03 (119909

119863)

minus23

exp(minus 1199032

22) (13)

is used where 119863 = 04(119909119863)13 1198800is the estimated wind

speed in the unperturbed flow and 1198801015840 is the magnitude

of the perturbation Note that the selected coefficients aresimilar to those obtained in [31] for the wake behind thesphere To determine the wind velocity in the unperturbedflow the wind speed measured by sensors is multiplied bythe coefficient 120572 = (1 minus 120574)

minus1 The coefficients 120572 for thevarious sensors are equal to 1069 1065 1061 1047 and 1009respectively from the bottom up to the top

4 Field Data Processing and Results

Investigation of the wind flow parameters is carried outby profiling General recording of wind speed is up to 5-hour duration and is divided into 5-minute sections (300measuring points) with a 50 of overlap As a result of


0 1 2 3 4 5 6 7 8 9 10 11 120

000050001

000150002

000250003

000350004

000450005

00055

Binning Gorky Reservoir sensors 2 3 4 and 5Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30

U10 (ms)

CD

Figure 5 Comparison of the retrieved dependence 119862119863(11988010) with

and without the lower sensor gray diamonds denote the binning ofdatawith the lower sensor (the standard deviation as the error gates)black solid circles are the binning of the data without the lowersensor (the standard deviation as the error gates) gray circles arethe results of field experiment [13] gray crosses are the results of fieldexperiment [14] dashed line is the empiric oceanic parameterizationCOARE 30

the averaging 5 values of wind speed corresponding to fivehorizons of measurements are received for each sectionThe resulting averaged profile is approximated by function(8) with the parameters of the approximation 119906

lowast(friction

velocity) and 1199110(surface roughness) The values of the 10m

wind speed 11988010

and of the drag coefficient 119862119863are retrieved

from the resulting approximationThe impact of data obtained from different horizons

on the resulting approximation of the wind velocity profileis analyzed Figure 5 shows a comparison of the retrieveddependence 119862

119863(11988010) for two combinations of speed sensors

with and without the lower sensor The points on the plot arethe result of the binning of the wind speed data within a cellwith size of Δ119880

10= 05ms The error gates correspond to

the standard deviation Also the results of field experiments[13 14] and empiric oceanic parameterization COARE 30[32] are shown in Figure 5 It is evident that without thelower sensor data the values 119862

119863(11988010) are characterized by

a slightly greater spread and are located higher and moreclose to the results of [13 14 32] while taking the lowersensor into account shows lower values of the drag coefficientIn [13] the sensors are located at the heights of 089m upto 10m from the mean water level in [14] the sensors arelocated at heights from 05m up to 4m In both cases all thesensors are firmly fixed on the masts and the approximationis performed throughout the wind speed profile

Figure 6 shows a comparison of the retrieved dependence119862119863(11988010) using two lower sensors only and using all five

sensors The use of two sensors only reveals significant dif-ferences in the wind parameters recovery in the weak windsarea the scatter and absolute value of 119862

119863(11988010) decreases In

the field of moderate and strong winds the retrieved values

0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025

0003

Binning Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30

U10 (ms)

CD

Figure 6 Comparison of retrieved dependence 119862119863(11988010) using two

and five sensors gray solid circles are the binning of the five-sensordata (the standard deviation as the error gates) black diamonds arethe binning of the two-sensor data (the standard deviation as theerror gates) gray circles are the results of the field experiment [13]gray crosses are the results of the field experiment [14] dashed lineis the empiric oceanic parameterization COARE 30

of drag coefficient differ slightly despite the small increase inthe measurement error

These results can be explained by the deviation of windvelocity profile from the logarithmic form It may be causedby the stratification of the surface layer of the atmosphereand impact of the coastline as well as gustiness of thewind because the lower part of the profile adapts morequickly to the changing conditions of waves and the airflowparameters determine themomentum transfer from thewindto the waves exactly at the water-air boundary Consequentlyfurther analysis of the dependence 119862

119863(11988010) was based on the

measured data from sensors 1 and 2Throughout the 2012ndash2014 years the dataset consisting of

approximately 100 hours of recordings in the range of windvelocities 1ndash12ms for different fetch values (119871 fetch = 1ndash50 km)and stratification conditions (119879air minus 119879water = (minus5) minus 15

∘C) isobtainedThe resulting dependence119862

119863(11988010) using two lower

sensors is received and shown in Figure 7The approximationof the obtained data is made by a function

119862119863= 000124119880

minus1

10+ 000034 + 0000049119880

10 (14)

The result of binning of the wind speed data within a cellwith size Δ119880

10= 05ms and the standard deviation as the

error gates are shown in Figure 7The dependence (14) is usedbelow to adjust the wind input in WAVEWATCH III

5 Tuning of WAVEWATCH IIINumerical Experiment

The tuning of WAVEWATCH III to the conditions of theGorky Reservoir consists of the following factors In the opencode the minimum value of a significant wave height 119867

119878is

adjusted in a number of blocks where the lowest value of


0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025

Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30

U10 (ms)

CD

Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds

denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862

119863= 000124 sdot

119880minus1

10+ 000034 + 0000049 sdot 119880

10 black circles denote binning of the

two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30

119867119878is directly indicated For a description of the reservoir

the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken

The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth

120590119873= (120575)119873minus1

1205901 (15)

where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this

GrADS COLAIGES 2014-04-24-2047

4345∘ E

434∘ E

4335∘ E

433∘ E

4325∘ E

432∘ E

4315∘ E

431∘ E

4305∘ E

43∘ E

4295∘ E

429∘ E

566∘N

567∘N

568∘N

569∘N

57∘N

571∘N

572∘N

573∘N

574∘N

cellComputational

Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown

assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment

As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment

6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III

For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862

119863and 120573) are displayed at each step of

the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of

numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-

ization 119862119863(11988010) obtained as a result of field measurements

(14) It can be seen that different parameterization of120573 and119862119863

used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906

lowast119892 = 01ndash015 119880

10


01 1

WAM 3Tolman and ChalikovWAM 4

120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025

WAM 3Tolman and Chalikov

WAM 4Experimental

U10 (ms)

CD

(b)

Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862

119863on the wind speed 119880

10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles

and WAM 4 by crosses

= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate

and strong wind speeds 11988010

gt 4msThen wind-waves regime is studied for built-in param-

eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862

119863within parameterizations

WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program

code Thus instead of built-in parameterizations of 119862119863in

the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867

119878 obtained both from the field

experiment and from the numerical experiments In themodel calculation119867

119878is based on a formula

119867119878= 4radic119864 (16)

The same value gives the calculation of119867119878in the experi-

ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862

119863(11988010) improves

the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time

interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5

the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required

Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867

119878

compared with the experimental data for both dates whereasthe use of the proposed new119862

119863improves the accordance very

wellAt the same time Tolman and Chalikov parameterization

underestimates the part of the values for 130613 but theuse of new 119862

119863improves the total standard deviation (STD)

for all the day of 130613 For 200614 the use of new 119862119863

makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862

119863lies

lower than 119862119863in Tolman and Chalikov as it is shown in

Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862

119863for 200614 It should be mentioned that

built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863

on 11988010

in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880

10lt

3ms) and overestimates it at higher wind speeds (11988010

gt

4ms) in comparison with the proposed new 119862119863

in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867

119878

Nevertheless new 119862119863is applied in the framework of this

parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all


Table 1 Standard deviation of119867119878

WAM 3 + new 119862119863

WAM 3 Tolman and Chalikov + new 119862119863

Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020

0 60 120 180 240 300Internal time (min)


004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)

ExperimentTolman and Chalikov + new CD

WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD

WAM 3 + new CD

(a)

Internal time (min)0 60 120 180 240 300


01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)

Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867

119878for

parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)

Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field

experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614

the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))

The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))

Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862

119863(11988010) as in formula

(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862

119863(11988010) for the

biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to

the situation in Figure 10 where the experimental valuesexceed the estimated values of119867

119878 are shown in Figure 11(b)

However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867

119878are overestimated compared with the

experimental values this situation is reflected in the spectrain Figure 11(c)

For all of the considered experiments a comparison of theintegral characteristics (119867

119878and the mean wave period 119879

119898) is

performed The mean wave period 119879119898is simulated using the

following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)

WAM 3Tolman and ChalikovWAM 4Experiment

WAM 3 + new CD

Tolman and Chalikov + new CD

(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)

Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862

119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman

and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with

the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are

higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment


0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04

Tolman and ChalikovHS

experiment (m)

HS

Tolm

anan

dCh

alik

ov(m

)Tolman and Chalikov + new CD

06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)

Figure 12 119867119878(top graph) and 119879

119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3

(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov

with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)

On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867

119878in the output of

the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879

119898

For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867

119878forWAM3 is 52

for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867

119878for

WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862

119863 the

wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately

However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862

119863(11988010) does not make sufficient changes Perhaps

this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies


downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867

119878 which indicates the amount of energy

received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments

7 Conclusions

The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments

Field experiments in the Gorky Reservoir show that thevalues of 119862

119863in moderate and strong winds are on asymp50

lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862

119863in moderate

and strong winds are on asymp50 lower than those typical forthe ocean conditions

The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867

119878

comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the

new parameterization119862119863(11988010) based on field measurements

on the reservoir reduces the values of 119906lowastand hence wind

increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical

simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879

119898as well At the same time the

adjustment of the wind input does not affect significantly theagreement of119879

119898values in the results of numerical simulation

and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir

Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient

experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)

References

[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984

[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014

[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002

[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011

[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014

[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011

[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014

[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-


[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006

[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004

[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992

[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013

[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008

[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999

[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991

[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009

[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981

[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984

[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982

[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996

[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004

[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996

[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012

[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985

[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004

[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953

[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959

[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993

[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013

[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991

[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997

[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003

[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985

[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of


OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


MineralogyInternational Journal of


MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


wave states conditions The first attempt of application of aglobal wave model WAM [11] for the wave forecasting on amiddle-sized reservoir was reported recently in [12]

Among the peculiarities of the low-fetch waves at themiddle-sized reservoirs is the stronger wind input which isproportional to the ratio of wind friction velocity (or 10mwind speed) to the wave phase velocity [2] Another featureis the enhanced nonlinearity caused by higher steepness ofthe waves Then the tuning of the ocean wave model to theinland water conditions should be twofold adjusting of thewind source and ldquocollision integralrdquo Dissipation due to wavebreaking can be expected to be similar towave conditions dueto their universal nature

One more problem of tuning of numerical models tothe conditions of middle-sized reservoirs and lakes is thesmall amount of experimental data that can be used for itsverification Rare examples of such experiments are studied[13 14] which show the specificity of wind-wave interactionin the indicated circumstances In this paper we present atuning of the wind input term inWAVEWATCH III model tothe conditions of the middle-sized reservoir on an exampleof Gorky Reservoir belonging to the Volga Cascade Thetuning is based on the data of the field experiment held byour groupThe methods of the experiment are different fromthose used in [13 14] and they focus on the study of airflowin close proximity to water surfaceThe comparison of resultsof the numerical experiments with the results of the fieldexperiments on Gorky Reservoir is presented

The paper has the following structure In Section 2 thebasic parameterizations of wind and wave interactions inWAVEWATCH III v314 are presented In Section 3 thestudied reservoir and the field experiment setup with itsinstrumentation andmethods are described In Section 4 thefield data processing and the results of the field experimentare presented In Section 5 numerical experiment withintuned to the conditions of the middle-sized reservoirWAVE-WATCH III is set out In Section 6 the adjustment of windinput source term in tunedWAVEWATCH III and the resultsof numerical experiments within tuned WAVEWATCH IIIandwithin a tunedWAVEWATCH III with the adjusted windinput are presented

2 Wind Input Parameterizationsin WAVEWATCH III

WAVEWATCH III [2 15 16] is based on the numericalsolution of the equation for the spectral density ofwave action119873 in the approximation of phase averaging

120597119873

120597119905+ nabla119909119873 +

120597

120597120590119873 +

120597

120597120579

120579119873 =1

120590(119878in + 119878dis + 119878nl) (1)

The lefthand side of (1) describes the kinematics ofwaves120590 is the radian frequency and 120579 is the wave direction In theright hand side there are terms that describe the wind-wavegrowth 119878in dissipation mainly due to wave breaking 119878dis and4-wave nonlinear interaction of waves 119878nl

This paper focuses on the wind input parameterizationswhose parameters can be adjusted on the basis of the field

measurements data Generally the term describing the windinput is determined as

119878in = 120573 (119896 120579)119873 (119896 120579) 120590 (2)

where 120573(119896 120579) is the dimensionless wind-wave growth rateparameter approximated in WAVEWATCH III v314 bydifferent parameterizations (WAM 3 Tolman and Chalikovand WAM 4) Among them the WAM 3 parameterization[17ndash19] is defined by two empirical formulas The first one isfor the wind-wave growth rate

120573 (119896 120579) = 119862in120588119886

120588119908

max[0 (28119906lowast

119888phcos (120579 minus 120579

119908) minus 1)] (3)

where 119862in = 025 is a constant 120588119886120588119908is the ratio of the

densities of air and water 119906lowastis the friction velocity 119888ph

is the phase velocity and 120579119908is the main wind direction

The second one is a relation between the 10m wind speed11988010

and a friction velocity 119906lowast

= 11988010radic119862119863provided by the

empirical formula of the parameterization of the surface dragcoefficient 119862

119863 proposed in [19]

119862119863= 0001 times (08 + 065119880

10) (4)

In the Tolman and Chalikov parameterization [20] thedimensionless coefficient depends on the drag coefficientand on the dimensionless frequency of the spectral com-ponents In the WAM 4 parameterization [21] the wind-waves interaction parameter 120573 is presented by the adjustedMiles formula To calculate the roughness parameter thefeedback of the wind-waves spectra is taken into account aswell So in the considered parameterizations the wind inputis determined by the wind-wave interaction parameter 120573 andby the dependence 119906

lowast(11988010) which is defined by 119862

119863

3 Field Experiment

The tuning of WAVEWATCH III to the conditions of themiddle-sized reservoir was performed for conditions ofGorky Reservoir on the basis of field experiment

Measurements were carried out in 2012ndash2014 from Mayto October in the waters of Gorky Reservoir It has anelongated shape (Figure 1) which allows studyingwindwavesof different fetch depending on the wind direction GorkyReservoir is an artificial lake in the central part of the VolgaRiver formed by the dam of Nizhny Novgorod HydroelectricStation Its lake part is 85 km long and up to 15 km wideThe mean depth of the reservoir varies in the range of4ndash20 meters and the depth in the area of measurementsis 9ndash12 meters depending on the season and the point ofmeasurement

31 Instrumentation Instrumentation was placed on a buoystation with the original design based on the oceanographicFroude buoy Froude buoy is a mast submerged in water andheld in a vertical position by the float close to the surfaceand by the load on the depth (Figures 2(a) and 2(b)) Buoyrsquostotal length is 12m and the length of the part above the water


(a)


1km

(b)


(a)

Balanceweight

Float

Wirewave gauge


Separate float

Water surface

12m

53

m

227

m

13

m

085

m

01

m

(b)







120596is the





01 1

00001

0001

001

01

simfminus506

simfminus511

E(f

)(m

minus2 s)

1E minus 005

f (Hz)

(a)

0001 001 01

00001

0001

simkminus309

simkminus313

1E minus 005

1E minus 006

1E minus 007

E(k)

(m3 )

k (cmminus1)

(b)




120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)


119909 119896119910) were


119896max =120587

119889= 05 cmminus1 (6)



119901






119867119878= 4 (int119864 (120590) 119889120590)

12

(7)


1015840

1199091199061015840

119911⟩ does not


1015840

119909and 119906

1015840



119880 (119911) =119906lowast

120581ln( 119911

1199110

) (8)

where 119906lowast




(119880 minus 119888) (1198892120593

1198891205782minus 1198962120593) minus

1198892119880

1198891205782120593 = 0 (9)






119906lowast120581

(119896120578)2

|119880 minus 119888|

≪ 1

or 119906lowast120581

(119896120578)2

|119880 minus 119888|

≫ 1

(10)



(lowast

120581ln( 119911

1199110

) minus 119888)

10038161003816100381610038161003816100381610038161003816119911=120576

=120581lowast119911

1205762

10038161003816100381610038161003816100381610038161003816119911=120576

(11)








119863sim (

119909

119863)

13

(12)


01 1 10Height (m)

2

3

4

5

6

7

8

9

Win

d ve

loci

ty (m

s)

U10 = 86msU10 = 72msU10 = 64ms

U10 = 55msU10 = 41ms



120574 =1198801015840

1198800

= 03 (119909

119863)

minus23

exp(minus 1199032

22) (13)








0 1 2 3 4 5 6 7 8 9 10 11 120

000050001

000150002

000250003

000350004

000450005

00055


U10 (ms)

CD




lowast(friction


wind speed 11988010












119863(11988010) decreases In


0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025

0003


U10 (ms)

CD





119863(11988010) was based on the






119862119863= 000124119880

minus1

10+ 000034 + 0000049119880

10 (14)






119878is



0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025


U10 (ms)

CD



119863= 000124 sdot

119880minus1

10+ 000034 + 0000049 sdot 119880






120590119873= (120575)119873minus1

1205901 (15)



4345∘ E

434∘ E

4335∘ E

433∘ E

4325∘ E

432∘ E

4315∘ E

431∘ E

4305∘ E

43∘ E

4295∘ E

429∘ E

566∘N

567∘N

568∘N

569∘N

57∘N

571∘N

572∘N

573∘N

574∘N

cellComputational












lowast119892 = 01ndash015 119880

10


01 1


120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025


WAM 4Experimental

U10 (ms)

CD

(b)
















119867119878= 4radic119864 (16)



119863(11988010) improves





119878








119863lies





on 11988010


10lt


gt



119878





WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


(a)


1km

(b)


(a)

Balanceweight

Float

Wirewave gauge


Separate float

Water surface

12m

53

m

227

m

13

m

085

m

01

m

(b)







120596is the





01 1

00001

0001

001

01

simfminus506

simfminus511

E(f

)(m

minus2 s)

1E minus 005

f (Hz)

(a)

0001 001 01

00001

0001

simkminus309

simkminus313

1E minus 005

1E minus 006

1E minus 007

E(k)

(m3 )

k (cmminus1)

(b)




120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)


119909 119896119910) were


119896max =120587

119889= 05 cmminus1 (6)



119901






119867119878= 4 (int119864 (120590) 119889120590)

12

(7)


1015840

1199091199061015840

119911⟩ does not


1015840

119909and 119906

1015840



119880 (119911) =119906lowast

120581ln( 119911

1199110

) (8)

where 119906lowast




(119880 minus 119888) (1198892120593

1198891205782minus 1198962120593) minus

1198892119880

1198891205782120593 = 0 (9)






119906lowast120581

(119896120578)2

|119880 minus 119888|

≪ 1

or 119906lowast120581

(119896120578)2

|119880 minus 119888|

≫ 1

(10)



(lowast

120581ln( 119911

1199110

) minus 119888)

10038161003816100381610038161003816100381610038161003816119911=120576

=120581lowast119911

1205762

10038161003816100381610038161003816100381610038161003816119911=120576

(11)








119863sim (

119909

119863)

13

(12)


01 1 10Height (m)

2

3

4

5

6

7

8

9

Win

d ve

loci

ty (m

s)

U10 = 86msU10 = 72msU10 = 64ms

U10 = 55msU10 = 41ms



120574 =1198801015840

1198800

= 03 (119909

119863)

minus23

exp(minus 1199032

22) (13)








0 1 2 3 4 5 6 7 8 9 10 11 120

000050001

000150002

000250003

000350004

000450005

00055


U10 (ms)

CD




lowast(friction


wind speed 11988010












119863(11988010) decreases In


0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025

0003


U10 (ms)

CD





119863(11988010) was based on the






119862119863= 000124119880

minus1

10+ 000034 + 0000049119880

10 (14)






119878is



0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025


U10 (ms)

CD



119863= 000124 sdot

119880minus1

10+ 000034 + 0000049 sdot 119880






120590119873= (120575)119873minus1

1205901 (15)



4345∘ E

434∘ E

4335∘ E

433∘ E

4325∘ E

432∘ E

4315∘ E

431∘ E

4305∘ E

43∘ E

4295∘ E

429∘ E

566∘N

567∘N

568∘N

569∘N

57∘N

571∘N

572∘N

573∘N

574∘N

cellComputational












lowast119892 = 01ndash015 119880

10


01 1


120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025


WAM 4Experimental

U10 (ms)

CD

(b)
















119867119878= 4radic119864 (16)



119863(11988010) improves





119878








119863lies





on 11988010


10lt


gt



119878





WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


01 1

00001

0001

001

01

simfminus506

simfminus511

E(f

)(m

minus2 s)

1E minus 005

f (Hz)

(a)

0001 001 01

00001

0001

simkminus309

simkminus313

1E minus 005

1E minus 006

1E minus 007

E(k)

(m3 )

k (cmminus1)

(b)




120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)


119909 119896119910) were


119896max =120587

119889= 05 cmminus1 (6)



119901






119867119878= 4 (int119864 (120590) 119889120590)

12

(7)


1015840

1199091199061015840

119911⟩ does not


1015840

119909and 119906

1015840



119880 (119911) =119906lowast

120581ln( 119911

1199110

) (8)

where 119906lowast




(119880 minus 119888) (1198892120593

1198891205782minus 1198962120593) minus

1198892119880

1198891205782120593 = 0 (9)






119906lowast120581

(119896120578)2

|119880 minus 119888|

≪ 1

or 119906lowast120581

(119896120578)2

|119880 minus 119888|

≫ 1

(10)



(lowast

120581ln( 119911

1199110

) minus 119888)

10038161003816100381610038161003816100381610038161003816119911=120576

=120581lowast119911

1205762

10038161003816100381610038161003816100381610038161003816119911=120576

(11)








119863sim (

119909

119863)

13

(12)


01 1 10Height (m)

2

3

4

5

6

7

8

9

Win

d ve

loci

ty (m

s)

U10 = 86msU10 = 72msU10 = 64ms

U10 = 55msU10 = 41ms



120574 =1198801015840

1198800

= 03 (119909

119863)

minus23

exp(minus 1199032

22) (13)








0 1 2 3 4 5 6 7 8 9 10 11 120

000050001

000150002

000250003

000350004

000450005

00055


U10 (ms)

CD




lowast(friction


wind speed 11988010












119863(11988010) decreases In


0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025

0003


U10 (ms)

CD





119863(11988010) was based on the






119862119863= 000124119880

minus1

10+ 000034 + 0000049119880

10 (14)






119878is



0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025


U10 (ms)

CD



119863= 000124 sdot

119880minus1

10+ 000034 + 0000049 sdot 119880






120590119873= (120575)119873minus1

1205901 (15)



4345∘ E

434∘ E

4335∘ E

433∘ E

4325∘ E

432∘ E

4315∘ E

431∘ E

4305∘ E

43∘ E

4295∘ E

429∘ E

566∘N

567∘N

568∘N

569∘N

57∘N

571∘N

572∘N

573∘N

574∘N

cellComputational












lowast119892 = 01ndash015 119880

10


01 1


120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025


WAM 4Experimental

U10 (ms)

CD

(b)
















119867119878= 4radic119864 (16)



119863(11988010) improves





119878








119863lies





on 11988010


10lt


gt



119878





WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





119906lowast120581

(119896120578)2

|119880 minus 119888|

≪ 1

or 119906lowast120581

(119896120578)2

|119880 minus 119888|

≫ 1

(10)



(lowast

120581ln( 119911

1199110

) minus 119888)

10038161003816100381610038161003816100381610038161003816119911=120576

=120581lowast119911

1205762

10038161003816100381610038161003816100381610038161003816119911=120576

(11)








119863sim (

119909

119863)

13

(12)


01 1 10Height (m)

2

3

4

5

6

7

8

9

Win

d ve

loci

ty (m

s)

U10 = 86msU10 = 72msU10 = 64ms

U10 = 55msU10 = 41ms



120574 =1198801015840

1198800

= 03 (119909

119863)

minus23

exp(minus 1199032

22) (13)








0 1 2 3 4 5 6 7 8 9 10 11 120

000050001

000150002

000250003

000350004

000450005

00055


U10 (ms)

CD




lowast(friction


wind speed 11988010












119863(11988010) decreases In


0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025

0003


U10 (ms)

CD





119863(11988010) was based on the






119862119863= 000124119880

minus1

10+ 000034 + 0000049119880

10 (14)






119878is



0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025


U10 (ms)

CD



119863= 000124 sdot

119880minus1

10+ 000034 + 0000049 sdot 119880






120590119873= (120575)119873minus1

1205901 (15)



4345∘ E

434∘ E

4335∘ E

433∘ E

4325∘ E

432∘ E

4315∘ E

431∘ E

4305∘ E

43∘ E

4295∘ E

429∘ E

566∘N

567∘N

568∘N

569∘N

57∘N

571∘N

572∘N

573∘N

574∘N

cellComputational












lowast119892 = 01ndash015 119880

10


01 1


120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025


WAM 4Experimental

U10 (ms)

CD

(b)
















119867119878= 4radic119864 (16)



119863(11988010) improves





119878








119863lies





on 11988010


10lt


gt



119878





WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0 1 2 3 4 5 6 7 8 9 10 11 120

000050001

000150002

000250003

000350004

000450005

00055


U10 (ms)

CD




lowast(friction


wind speed 11988010












119863(11988010) decreases In


0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025

0003


U10 (ms)

CD





119863(11988010) was based on the






119862119863= 000124119880

minus1

10+ 000034 + 0000049119880

10 (14)






119878is



0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025


U10 (ms)

CD



119863= 000124 sdot

119880minus1

10+ 000034 + 0000049 sdot 119880






120590119873= (120575)119873minus1

1205901 (15)



4345∘ E

434∘ E

4335∘ E

433∘ E

4325∘ E

432∘ E

4315∘ E

431∘ E

4305∘ E

43∘ E

4295∘ E

429∘ E

566∘N

567∘N

568∘N

569∘N

57∘N

571∘N

572∘N

573∘N

574∘N

cellComputational












lowast119892 = 01ndash015 119880

10


01 1


120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025


WAM 4Experimental

U10 (ms)

CD

(b)
















119867119878= 4radic119864 (16)



119863(11988010) improves





119878








119863lies





on 11988010


10lt


gt



119878





WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0 1 2 3 4 5 6 7 8 9 10 11 120

00005

0001

00015

0002

00025


U10 (ms)

CD



119863= 000124 sdot

119880minus1

10+ 000034 + 0000049 sdot 119880






120590119873= (120575)119873minus1

1205901 (15)



4345∘ E

434∘ E

4335∘ E

433∘ E

4325∘ E

432∘ E

4315∘ E

431∘ E

4305∘ E

43∘ E

4295∘ E

429∘ E

566∘N

567∘N

568∘N

569∘N

57∘N

571∘N

572∘N

573∘N

574∘N

cellComputational












lowast119892 = 01ndash015 119880

10


01 1


120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025


WAM 4Experimental

U10 (ms)

CD

(b)
















119867119878= 4radic119864 (16)



119863(11988010) improves





119878








119863lies





on 11988010


10lt


gt



119878





WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


01 1


120590ulowastg

1E minus 005

00001

0001

001

01

120573

(a)

0 2 4 6 8 100

00005

0001

00015

0002

00025


WAM 4Experimental

U10 (ms)

CD

(b)
















119867119878= 4radic119864 (16)



119863(11988010) improves





119878








119863lies





on 11988010


10lt


gt



119878





WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



WAM 3 + new 119862119863





004

008

012

016

02

024

02468

10

Win

d ve

loci

ty (m

s)

130613

HS

(m)



WAM 3 + new CD

(a)



01

02

03

04

05

06

56789

10

Win

d ve

loci

ty (m

s)

200614

HS

(m)


WAM 3 + new CD


(b)


119878for







119863(11988010) as in formula


119863(11988010) for the









119898) is


following formula

119879119898= 1198791198980minus1

= (int

119891119903

119891min

119864 (119891) 119889119891)

minus1

int

119891119903

119891min

119864 (119891)119891minus1119889119891 (17)


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


1

0

0002

0004

0006

0008

001

f (Hz)

E(m

2 s)


WAM 3 + new CD


(a)

1

0

0004

0008

0012

0016

002

f (Hz)E

(m2 s)


WAM 3 + new CD


(b)


1

0

0004

0008

0012

0016

002

f (Hz)

E(m

2 s)

WAM 3 + new CD


(c)







0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0 01 02 03 04 05 060

01

02

03

04

05

06

WAM 3HS

experiment (m)

WAM 3 + new CD

08 1 12 14 16 18 2 22 2408

112141618

22224

Trexperiment (s)

WAM 3

WAM 3 + new CD

HS

WA

M3

(m)

Tr

WA

M3

(s)

STD = 052

STD = 039

STD = 019

STD = 025(a)

0 01 02 03 040

01

02

03

04


experiment (m)

HS

Tolm

anan

dCh

alik

ov(m


06 08 1 12 14 16 18 2 22 240608

112141618

22224

Tr

Tolm

anan

dCh

alik

ov(s

)

Trexperiment (s)

Tolman and Chalikov


STD = 040

STD = 037

STD = 026

STD = 028(b)

STD = 025

WAM 4

WAM 4

01 02 03 040HS

experiment (m)

0

01

02

03

04

081

12141618

22224

1 12 14 16 18 2 22 2408Tr

experiment (s)H

SW

AM

4(m

)Tr

WA

M4

(s)

STD = 046

(c)








119898


119878forWAM3 is 52


119878for


119863 the









7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





7 Conclusions





119863in moderate



119878














Acknowledgments


References













































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in










Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

Documents

Research Article Adjusting of Wind Input Source Term in ...downloads.hindawi.com/journals/amete/2016/8539127.pdf · WAVEWATCH III Model for the Middle-Sized Water Body on the Basis