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Last modified
7/28/2009 2:33:55 PM
Creation date
4/11/2008 3:44:13 PM
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Weather Modification
Title
Bulk Parameterization of the Snow Field in a Cloud Model
Date
6/6/1983
Weather Modification - Doc Type
Report
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<br />JUNE 1983 <br /> <br />UN, FARLEY AND ORVILLE <br /> <br />1077 <br /> <br />I <br />i <br />for temperatures below Oo~. The equation is given <br />by (45). i <br />In the temperature regidn T ~ To, the melting of <br />snow and hail contribute t6 the rain content. These <br />rates, PSMLT and PGMLT, have already been shown in <br />(32) and (47). ' <br /> <br />4) Ev APORA nON <br /> <br />The evaporation rate o( rain is according to the <br />concepts of diffusional grqwth originally developed <br />by Byers (1965) and is described in Orville and Kopp <br />(1977): : <br /> <br />PREVP = 21[(8 - l)noR[ 0.7~^1? + 0.318~/3 <br /> <br />r[(b + 5)/2~a 1/2v-i/2(:o f\li[(b+5J/2l] <br /> <br />(1)~: L~ 1 )-1 <br />X - ! + - (52) <br />p :KaRwT2 p~~ ' <br /> <br />where Rw is the gas consta6t for water vapor, rs the <br />saturation mixing ratio ofi water vapor, and 8 the <br />saturation ratio rlrs (here :<1). The evaporation of <br />. rain is applied only in the subsaturated air. <br /> <br />f Non-precipitating fields I <br />I <br />The non-precipitating fields, water vapor, cloud <br />water and cloud ice, are treated as a single combined <br />quantity in the conservation equation given by (14). <br />The production terms involving the various types of <br />precipitating particles and: the water vapor, cloud <br />water and cloud ice fields: have. been presented in <br />previous sections. Several 6f these terms cancel out <br />if total production terms FR, Ps and PG in (14) are <br />expanded to the individual !terms, leaving only those <br />terms with impact on thei non-precipitating fields. <br />This results in water vapo~ being depleted by PSDEP <br />(31) and created by PSSUB (~1), PGSUB (46) and PREVP <br />(52). Cloud water is depleted by PSACW (24), PSFW (33), <br />PGACW (40), PRAUT (50) and PRACW (51), while cloud <br />ice is depleted by PSAUT (2l), PSAC1 (22), PRAC1 (25), <br />PSFI (34) and PGACI (4\). : <br />Saturation is diagnosed: following the treatment <br />given by Orville and Kopp (1977). In addition, the <br />interactions between cloud ~ater and cloud ice which <br />are allowed in the model ~ave yet to be described. <br />These are explained in greater detail in Hsie et al. <br />(1980), and only a brief sUlrtmary will be given here. <br />If the temperature is colder than -40oC, homo- <br />geneous nucleation (denofed as PIHOM) will occur <br />naturally. Saunders' (1957) bquation of isobaric freez- <br />ing for cloud water into clo~d ice is used to calculate <br />the temperature change ass~ciated with this process. <br />Between 0 and -40oC, clo~d water and cloud ice can <br />coexist. The transformationl between cloud water and <br />I <br />I <br />I <br />! <br />I <br /> <br />! <br />I <br />~J'L""",i1". <br /> <br />cloud ice in this temperature regime (denoted as <br />PlOW) is based on deposition nucleation of natural ice <br />nuclei and depositional grO'Yih of cloud ice at the <br />expense of cloud water [Bergeron process, based on <br />Koenig (1971 )]. The number concentration of active <br />natural ice nuclei is given by Fletcher (1962) as <br /> <br />Nn(!1T) = no exp({j!1T), <br /> <br />where !1T is the supercooling and no and {j are pa- <br />rameters with values of {j ranging between 0.4 and <br />0.8; no can vary by several orders of magnitude. The <br />typical values of no = 10-8 m-3 and (j = 0.5 K-1 are <br />used in this study. If the temperature is warmer than <br />OOC, the cloud ice is assumed to instantaneously melt <br />back to cloud water (P1MLT). <br /> <br />g. Dynamics and thermodynamics <br /> <br />1) DYNAMICS <br /> <br />Applying Newton's second law of motion in the <br />2DTD model yields equations of motion in the hor- <br />izontal and vertical directions (Orville and Kopp, <br />1977). The non-hydrostatic, anelastic equations of <br />motion include buoyancy effects due to loading of <br />hydrometeors and turbulent mixing. All hydrome- <br />teors are assumed to fall at their mass-weighted mean <br />terminal velocities. <br />Combining the two equations of motion and the <br />continuity equation, we can derive a vorticity equa- <br />tion which is then used to obtain the velocity field <br />(see Chen and Orville, 1980). <br /> <br />2) THERMODYNAMICS <br /> <br />The thermodynamics energy equation is based on <br />Orville and Kopp ( 1977) with the effects of the snow <br />field added. The equation is <br /> <br />acp' L <br />- = -V. VA.' + V.K VA.' + ----L- (P' + P') <br />at 'I' h 'I' CpT 00 G s <br /> <br />CwTc <br />+ CpToo (PGMLT + PSMLT) <br /> <br />- ~ [lcwV . VT + IR(V - kUR). VT] <br />CpToo <br />C <br />- -C I o[lcN. VT + ld'v - kUG). VT <br />pToo <br />+ Is(V - kUs). VT, (53) <br /> <br />with <br /> <br />()' Lr <br />cp' = e + CpT 00 (unsaturated), (54a) <br /> <br />(J' Lr <br />cp' = e + Cp;oo (saturated), (54b) <br />
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