P2M.11 Disdrometer and Radar Observation-Based Microphysical Parameterization to Improve Weather Forecast Guifu Zhang+, Juanzhen Sun*, Edward Brandes*, Jimy Dudhia*, and Wei Wang* +: School of Meteorology, University of Oklahoma, Norman, OK 73019 *: National Center for Atmospheric Research, Boulder, CO 80307-3000 1. Introduction The gamma distribution has been used to improve the characterization of rain DSDs over the exponential The fundamental characterization of rain microphysics is distribution (Ulbrich, 1983). Recent disdrometer observations through the raindrop size distribution (DSD). Microphysical indicate that rain DSDs can be represented by a constrained- processes of evaporation, accretion, and precipitation rate are gamma (C-G) distribution model (Zhang et al. 2001). The C- all related by the DSD. Most parameterization schemes used G model was developed for retrieving rain DSDs from in numerical weather prediction were developed (Kessler, polarization radar observations. The procedure is to 1969) on the assumption of an exponential distribution of determine the three parameters of the gamma distribution raindrops, written as from radar reflectivity, differential reflectivity, and a constraining relation between the shape and slope of the N(D) = N exp(!"D) , (1) distribution. It has been shown that the C-G model 0 characterizes natural DSDs better and leads to more accurate retrievals than that with a two parameter exponential model where the slope parameter Λ relates to a characteristic size of and with a variable N (Brandes et al. 2003). The C-G rain the raindrops such as the mean diameter (<D>) or median 0 DSD model allows accurate rainfall estimation and detailed volume diameter (D ). N is an intercept parameter, which 0 0 study of storm microphysics (Brandes et al., 2005; Zhang et was fixed at 10000 m−3 mm−1 by Kessler. When N = 8000 0 al., 2005). m−3 mm−1, Eq. (1) becomes the Marshall−Palmer (M-P) drop size distribution (Marshall and Palmer, 1948). For the M-P In this paper, we apply the constrained-gamma DSD model to DSD model and Kessler’s parameterization scheme, the microphysical parameterization in a cloud model and microphysical processes for evaporation rate (R in g m-3 s-1) e evaluate the impact of the parameterization scheme on the for a unit water vapor saturation deficit, accretion rate (R in c initialization and forecasting of storms g m-3 s-1) for a unit cloud water content, and mass-weighted terminal velocity (V in m s-1) can be represented in terms of tm 2. Parameterization of rain microphysics based on rain water content (W in g m-3) as follows constrained-gamma DSD model !4 13/ 20 (2) Re = 5.03"10 W The constrained-gamma DSD model consists of a gamma !3 7 /8 (3) distribution in the form (Ulbrich, 1983) Rc = 5.08"10 W 1/8 . (4) Vtm = 5.32W µ (6) N(D) = N0 D exp(!"D) The radar reflectivity factor at horizontal polarization (ZH in –1–µ –3 mm6 m-3) is related to water content by [where N0 (mm m ) is a concentration parameter, µ is a shape parameter, and (mm–1) is a slope parameter] and a Λ 4 7 / 4 . (5) constraining relation between µ and Λ given by ZH = 2.04!10 W 2 . (7) Although there have been some modifications, e.g., Klemp ! = 0.0365µ + 0.735µ +1.935 and Wilhelmson (1978), and Lin et al. (1983), this simple approach to model parameterization, called a Kessler-type Relation (7) was derived from 2-D video-disdrometer scheme, is still widely used in mesoscale models. The measurements made in Florida (Zhang et al. 2001) and has problem with fixed-intercept parameterizations is that the rain been verified by data collected in Oklahoma (Brandes et al. water gets redistributed into smaller drop categories as the 2003). It has been shown that (7) characterizes natural rain drop spectra slope parameter increases, thus accelerating the DSD variations quite well and applies to both convective and process of rain water removal through evaporation. Rainfall stratiform DSDs except for that at leading edges of rate cannot be accurately estimated with a R-Z relation convective storms and drizzle rains. Fine tuning for derived from the M-P DSD model (Wilson and Brandes geographical locations/climatology with further observations 1979), having estimation error of 50%. Another issue with may improve the model results. the M-P model is the convergence problem which occurs in a four-dimensional data assimilation (4D-Var) system, due to The constrained-gamma DSD model represented by (6) and the highly nonlinear nature of expressions such as Eqs (2) (7) is essentially a two-parameter model much like the and (4), the minimization of the cost function tends to have exponential distribution or a gamma distribution with a fixed convergence problems (Sun and Crook, 1997). µ. The difference, however, is that the constrained-gamma ________________________________________________ DSD model is capable of describing a variety of drop-size Corresponding author address: School of Meteorology, distributions with different spectral shapes: concave upward University of Oklahoma, Norman, OK 73019; shape for a broad distribution versus convex for a narrow Email: [email protected] distribution on a semi-logarithm plot. Because µ and Λ jointly describe the DSD shape, the characteristic size (e.g., 1 median volume diameter D0) and the spectrum width are where ZH is in dBZ and ZDR is in dB. related. This makes physical sense because, except at the leading edge of some convective storms, large raindrops are Based radar retrieval, the microphysical process parameters usually accompanied by small drops, which leads to a broad are expressed as function of rain water content as spectrum. On the other hand, small and medium size 4 3 2 raindrops are not necessarily accompanied by large drops, R =10[0.00679(logW ) +0.0557(logW ) +0.119(logW ) +0.937logW !3.369] (13) e.g., stratiform and light convective rain DSDs. A µ - Λ (or µ e [!0.0000603(logW )4 !0.00255(logW )3 !0.0212(logW )2 +0.933logW !2.294] (14) - D0) relation allows better characterization of the raindrop Rc =10 size/spectrum width dependence than a fixed distribution 4 4 3 2 V = !4.509"10! (logW ) + 0.0148(logW ) + 0.263(logW ) +1.410logW + 5.799 (15) shape without increasing the number of parameters. A fixed tm is a special - relation, e.g.; an exponential distribution µ µ Λ The simplified C-G (S-C-G) parameterization scheme of (µ = 0). (13)-(15) can be applied to any numerical weather model with microphysics characterized by a single parameter, that The µ - Λ relation facilitates the reliable retrieval of the is, by bulk water content or rain water mixing ratio. Rain gamma DSD parameters (N0, µ, and Λ) from polarization water estimates from radar reflectivity using the S-C-G radar measurements of radar reflectivity factor (ZH) and model with (8) and (12) and the M-P model (5) are compared differential reflectivity (ZDR). Once the rain DSD is known, in Fig. 2. Calculations with disdrometer data are also shown rain microphysical processes can be estimated. The for reference. It is seen that the two estimated water contents constrained- gamma DSD model with two independent agree for the medial radar reflectivity values at which most parameters can be used to derive rain physical parameter and rain falls, but the S-C-G DSD model allows a larger dynamic -3 microphysical processes: water content (W in g m ), range of water content and gives a smaller water content for -3 -1 -3 - evaporation rate (Re in g m s ), accretion rate (Rc in g m s weak radar reflectivity (stratiform rain) than the M-P model. 1 -1 ) and mass-weighted terminal velocity (Vtm in m s ) The S-C-G model results agree with disdrometer observations Following Kessler’s parameterization procedure, the better than the M-P model. microphysical process parameters are derived (Zhang et al., 2005) by integration of the gamma DSD (6). Figure 3 shows the spatial distributions of the rain microphysical process parameters estimated from NCAR’s For convenience, the C-G parameterization are expressed in Spol radar measurements using the C-G, S-C-G, and M-P terms of ZH and ZDR as models. The polarization radar is located at (-9km, -25km) from the origin. The radar measurements of reflectivity and 2 (0.229ZDR -1.212Z DR -3.232) differential reflectivity were collected at 0.5 degree of W = Z H "10 (8) 2 elevation. In general, the C-G model gives a larger dynamic (0.322ZDR -1.649Z DR -6.298) (9) Re = Z H "10 range, and more detailed features, and larger spatial 2 (0.238ZDR -1.293Z DR -5.448) variations for R and R than the M-P model. Results for the Rc = Z H "10 (10) e c 2 (11) S-C-G model are between that for the C-G and M-P models. ! Vtm = "0.592ZDR +2.870ZDR + 3.573 The M-P model overestimates evaporation by about three ! times for the stratiform rain in the upper-right corner of the Eqs. (8)-(11) are obtained by fitting W/Z , R /Z , R /Z and H e H c H images. The S-C-G model gives stratiform rain evaporation !V to polynomial functions of Z . The fitting results are tm DR close to that of the C-G model. s!h own in Fig. 1. The discrete points are calculations from disdrometer data collected in east-central Florida during the 4. Application of the S-C-G parameterization in model summer of 1998 field program (PRECIP98) (Zhang et al.