NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL V. Bkhnov, O. Kryvook, B. Dormn Ukrinin Hydrometeorologicl Reserch Institute, Avenue of Science 37, 38 Kyiv, Ukrine ABSTRACT This pper presents some results of consecutive numericl simultion of the stellite signl (SS, cloud reflectnce in visile nd ner-infrred prt of spectrum) for frontl mixed clouds with severl forms of crystls. The simultion is sed on the next models: ) the microphysicl model of clouds, ) models of computtion of light scttering chrcteristics y drop nd crystl systems, c) the simultion of rditive trnsfer in non-uniform thick mixed clouds. Simultions hve shown tht the min contriution to the integrl opticl thickness mkes the liquid wter content. SS t λ =. µm nd λ 3 = 3. µm re very different in gret liquid wter content region ut ecome close in region of significnt crystlliztion nd precipittion. Considered in the next tle is the lock-digrm of the stellite signl simultion: Initil nd oundry conditions for the numericl cloud model. Thermodynmicl nd microphysicl prmeters of tmosphere Numericl microphysicl model of mixed strtiform cloud with severl forms of crystls Evolution of thermodynmicl, geometricl nd microphysicl chrcteristics of model clouds (including size spectr of droplets nd crystls of severl forms Wvelenth, complex index of refrction Clcultions of light scttering chrcteristics for droplets nd crystls Phse functions, extinction coefficients Geometry of oservtions, surfce reflectnce Simultion of stellite signl Reflectnce of model clouds
. NUMERICAL MICROPHYSICAL MODEL OF FRONTAL CLOUDS The numericl D time-dependent microphysicl model of strtiform mixed cloud with severl crystl forms (needles, columns, pltes) ws descried in our previous ppers (Bkhnov et l. 99,99). Here we will give only rief description of our model. The model eqution system consists of equtions of het nd vpor trnsfer nd kinetic equtions for size distriutions of drops nd crystls f j ( r j, t, z) (j = for drops, j = for needles, j = 3 for pltes, j = for columns; r j the chrcteristic dimension of prticles; t time; z height). Functions f j re normlised on n j concentrtion of prticles (in ir mss unit).the cloud dynmics is prmeterized: the updrft velocity w = w (z) depends on z proliclly in n intervl z < z with the mximum velocity w m t z 3 = ( z + z )/ (z, z, w m were vried). We will consider in this presenttion so clled sortion ( condenstion freezing ) ice nuclei (IN) which re ctivted if the supersturtion over wter is reched. Distriution of the IN concentrtion y overcooling hs the next form ( the pproximtion of empiric dt): -(dn j /dt)= µ j A S exp[ B s (T o T)], ( ) where T temperture, T o = o C, B s =. ( o C), A s ws vried in the rnge..5(g o C).Temperture intervls for nucletion of different crystl forms re different: for needles - < T < -5 o C, for columns T < - 5 o C, for pltes 5 < T < - o C. In these intervls µ j =, outside µ j =.Since the shre of needles in totl concentrtion of crystls elow.% we will not discuss chrcteristics of needles. Needles nd columns were pproximted y prolte spheroids with the minor nd mjor xes equls nd r respectively, pltes were pproximted y cylinders with rdius r 3. Numericl simultion hs een shown tht the dynmicl structure of front under study (especilly heights nd thicknesses of updrft cells) determines the phse composition, crystl form spectr nd efficiency of precipittion formtion.the predominte form in snowflls is plte if the top cloud oundry height less thn.8 5. km. These clouds hve very lrge totl liquid wter content (TLWC) to mm. If the top oundry hs height s isotherm - 3-35 o C the predominte crystl form is column, these clouds hve the high efficiency of precipittion formtion nd high ice content (IC). We will consider in this presenttion in detil only one exmple of the mixed cloud evolution ( w m = 5 cm/s, z =.3 km, z = 5.7 km, A S =.5 (g o C) ). Figure depicts the time-sptil sections of LWC liquid wter content, (IC) 3 ice content for pltes, (IC) ice content for columns. All vlues re given in g/kg (of ir). 5 5 5 5 Figure. Evolution of the model mixed cloud : LWC, ( IC ) 3 for pltes, c ( IC ) for columns. All in g/kg. It is seen tht the thick mixed cloud hs een formed in 3-5 hours of evolution, mxim LWC re more thn. g/kg t 5 h. The further crystlliztion process leds to rupt decrese of LWC, increse of (IC) 3 nd especilly (IC) t t > h (ner. g/kg). Averge sizes of pltes re more thn 8 µm (see Figure ) nd fter 8- h the precipittion rte mounts to.-.5 mm/h (see Figure 3). c 5 5 t. h
5 5 5 5 Figure. Averge sizes (in µm) of pltes ( ) nd columns ( )..5. PR, mm/h.3.. 3 5 5 time, h Figure 3. Dependence of precipittion rte on cloud evolution time. PR of pltes, columns, 3 totl PR.. LIGHT SCATTERING CHARACTERISTICS OF MIXED CLOUDS Simultions of scttering chrcteristics of liquid drops re sed on the Mie theory (Deirmendjin,99). Simultions of scttering properties for rndomly oriented ice crystls re sed on the geometric optics nd the fr-field diffrction pproximtion ( Mcke et l., 99). We will depict further some opticl chrcteristics of cloud mixture of drops nd crystls in our model cloud.. The expressions of the scttering coefficient β, the extinction coefficient β, the single scttering ledo ϖ,the symmetry fctor g hve so forms: s ( j ) β, () = β S S j= = ( j ) β e e j= β, (3) ϖ = β S β, e () ( j ) ( j ) g = β g, S β j= (5) S e
where summtion (j =,,3,) is crried out ll prticle species. Figure nd depict correspondingly the time-sptil section of ϖ nd g in the cloud under study. In upper cloud lyers (droplets nd crystls re present) ϖ =.7-.8, g =.-.7. Vlues essentilly rise in lower cloud lyers where LWQ is nerly sent nd only pltes nd columns re present: ϖ >.9, g >.8). z, km 5 5 t, h Figure. Time-sptil sections of single scttering ledo ( ) nd symmetry fctor of cloud prticles (), λ 3 =3. µm. Figure 5 depicts the time-sptil section of locl opticl thicknesses (LOT) or else opticl thicknesses of thin 3 m lyers in our model cloud under study: z + z k ) e z k k τ = β ( ζ dζ. () k The section on Figure 5 corresponds to the wve length of stellite rdiometer λ 3 = 3. µm. Figure 5 depicts the dependence of the integrl opticl thickness of the whole model cloud under study on time (λ 3 = 3. µm lso). Dependences of IOT on time for three wve lengths ( λ =.55 µm, λ =. µm, λ 3 = 3. µm ) under study re close with ech other. 5 5 IOT 8 5 5 5 5 Figure 5. Time-sptil section of the locl opticl thicknesses (λ 3 = 3. µm), Dependence of the cloud integrl opticl thickness (IOT) on time (λ 3 =3. µm). It s esy to see from comprison Figure nd Figure 5 tht LWC determines LOT sufficiently. IOT runs up mximum vlue ~8 t t=5 h nd then decreses s result of crystlliztion of the cloud nd considerle decrese of LWC.
3. SIMULATION OF SATELLITE SIGNAL Discrete Ordinte Method (DOM, Liou, 973; Stmnes et ll., 988) ws used for simultion of solr rdition trnsfer in not uniform clouds nd clcultion of mesured reflected intensity on stellite. We hve used the two-strem pproximtion for rditive trnsfer. This method ws slightly modified y one of uthors (Kryvook, 988). Thick clouds were divided into thin lyers with constnt microphysicl nd opticl chrcteristics. The cosine of the solr ngle is equl.9, the erth surfce ledo is equl zero. We will determine SS (stellite signl) s cloud reflectnce of solr rdition in visile nd ner-infrred prt of spectrum. Figure 8 depicts results of SS simultion for the cloud under study in this presenttion..9 SS..3 3 3 7 5 9 t, h Figure. Stellite signl from the model cloud, - λ =.55 µm, λ =. µm, 3 λ 3 =3. µm. Comprison Figure 5 nd Figure shows tht reflectnces for stellite rdiometer chnnels λ =.55 µm nd λ =. µm chnge synchronously with IOT. The rupt decrese of IOT nd SS t t > 7h is connected with crystlliztion process nd LWC decrese. SS in the rdiometer chnnel λ 3 = 3. µm is less sensile to the opticl thickness (more sensile to microphysicl nd opticl chrcteristics of single scttering). The importnt result: SS λ nd SS λ 3 re very different in gret LWC region: ( SS λ / SS λ 3 ) ~ 3, ut these signls get close vlues in region of significnt crystlliztion nd precipittion.. CONCLUSIONS ) The numericl model of mixed frontl clouds with severl forms of crystls shows tht the phse composition, the crystl form spectr nd precipittion formtion efficiency re dependent on dynmicl structure of front nd ice nuclei properties. ) Simultions of stellite signl (cloud ledo) show tht SS λ nd SS λ chnge synchronously with the integrl opticl thickness of cloud. The min contriution to IOT mkes LWC. c) The chnnel λ 3 =3. µm is less sensile to the opticl thickness. SS t λ =. µm nd λ 3 = 3. µm re very different in gret LWC region ut ecome close in region of significnt crystlliztion nd precipittion. The preliminry conclusion: the comprison of SS λ, SS λ, SS λ3 gives the possiility to distinguish regions with thick LWC lyers nd regions of highly developed crystlliztion nd precipittion.
5. REFERENCES BAKHANOV, V. P., nd DORMAN, B. A., (99 ) Nturl nd seeded precipittion formtion in frontl strtiform clouds with severl crystl forms. Proceedings of the UHRI (Kyiv, in Russin), 3, pp 8-3 BAKHANOV, V.P., nd DORMAN, B.A., (99 ) Precipittion formtion in winter frontl strtiform clouds with severl crystl forms. Proceedings of the -th Intern. Conf. on Clouds nd Precipittion ( Zurich), pp 8-89 DEIRMENDJIAN, D., (99 ) Electromgnetic scttering on sphericl polydispersions. The Rnd Corportion (Snt Monic), Americn Elsevier Pulishing Compny (New York), 5 p. KRYVOBOK, O. A., (998) Atmospheric correction of multispectrl stellite dt. Proceedings of the UHRI (Kyiv, in Russin),, pp-5 LIOU, K.- N., (973 ) A numericl exepriment on Chndrsekr s discrete-ordinte for rditive trnsfer : Applictions to cloudy nd hzy tmospheres. J. Atm. Sci., 3, pp33-3 MAKE, A., MUELLER, J., nd RADKE, E., (99 ) Single scttering properties of tmospheric ice crystls. J. Atm. Sci., 53,pp 83-85 STAMNES, K., nd DALE, H., (98) A new look t the discrete-ordinte method for rditive trnsfer clcultions in nisotropiclly scttering tmospheres.. Intensity computtions. J. Atm. Sci., 38, pp 9-7