SEPTEMBER 2003 DOTZEK AND FEHR 1285 Relationship between Precipitation Rates at the Ground and AloftÐA Modeling Study NIKOLAI DOTZEK AND THORSTEN FEHR Institut fuÈr Physik der AtmosphaÈre, DLR, Oberpfaffenhofen, Germany (Manuscript received 17 June 2002, in ®nal form 1 January 2003) ABSTRACT Two cloud-resolving mesoscale models, the Karlsruhe Atmospheric Mesoscale Model (KAMM) and the ®fth- generation Pennsylvania State University±National Center for Atmospheric Research Mesoscale Model (MM5), were used to study re¯ectivity factor±rain-rate (Z±R) relationships and instantaneous and horizontally averaged pro®les of precipitation rate for convective storms of varying intensity. Simulations were conducted for idealized terrain. KAMM modeled a single shower cloud; MM5 was used to study split-storm supercell development. Both models consistently con®rm analytical results from earlier studies: convective drafts and strati®cation of air density signi®cantly alter the local rain rate and, therefore, also any Z±R relation relying on conditions of stagnant air and sea level air density. Air density effects can be almost completely corrected for by a recently proposed algorithm, but effects of convective drafts remain. They can lead to upward precipitation mass ¯uxes of signi®cant magnitude and subsequent horizontal displacement of precipitation. Applicability of simple Z±R relations over complex terrain with distinct watershed boundaries will be strongly degraded by such convection effects on precipitation mass ¯uxes. 1. Introduction r a R 5 w 1 w 00 rq, (3) As recently quanti®ed by Dotzek and Beheng (2001) []t,00 12r and brie¯y summarized here in the appendix, standard re¯ectivity±rainfall (Z±R) relations of the form Z 5 aRb with rq denoting hydrometeor mass per unit volume are signi®cantly altered in deep convective clouds by and w t,00 hydrometeor fall speed. The term f(r) from convection effects on precipitation rate R, de®ned as Eq. (2) was chosen in its most widely used form with vertical mass ¯ux density of hydrometeors with diam- its best-®t value of a 5 0.45 for terminal velocities, eter D and bulk density r , that is, after Beard (1985). Even though Beard proposed a 5 h 0.42 for direct rain-rate computations, we have to stay ` p with a 5 0.45, because it enters the equations from the R 5 r n(D)D3 w dD. (1) 6 h E s fall speed term. 0 By convention in radar meteorology, R is taken to be Not only is R subject to variations in particle number positive for precipitation falling to the ground, despite spectra n(D), but there is a much stronger dependence a negative w s. We will conform with that convention on the effective sedimentation velocity (Dotzek and Be- and show the negative of R de®ned in Eq. (3) in our heng 2001): graphs and Z±R and R±rq relations. wst(D, w, r) 5 w 1 w (D, r) 5 w 1 f (r)w t,00(D). (2) Lower air density aloft increases R because hydro- meteor fall speed depends on r in a way that lower- Here, w denotes ambient vertical air velocity, w (D) t,00 density air exerts a smaller friction force on the falling is terminal fall speed of hydrometeors at sea level con- hydrometeors, allowing them to fall faster than at sea ditions, and effects of air density r are covered by f(r). level air density (e.g., Foote and du Toit 1969; Battan Therefore, aside from n(D), variations of R may result 1973). Dotzek et al. (2002) were able to show that, from up- and downdrafts and, secondarily, from vertical although being a secondary effect on the precipitation density strati®cation from its sea level value to small- r 00 rate pro®le alone, this effect can have signi®cant con- er values aloft. After integration of Eq. (1), the precip- sequences for radar-based quantitative precipitation es- itation rate in bulk variables reads timation (QPE) at large radar ranges. Also, downdrafts increase R, whereas updrafts de- crease the precipitation rate. In the limit of updrafts Corresponding author address: Dr. Nikolai Dotzek, DLRÐInstitut fuÈr Physik der AtmosphaÈre, Oberpfaffenhofen, D-82234 Wessling, greater than the hydrometeor fall speed, R can become Germany. highly negative even for arbitrarily high hydrometeor E-mail: [email protected] contents by the action of strong updrafts. As noted by q 2003 American Meteorological Society Unauthenticated | Downloaded 09/29/21 02:43 AM UTC 1286 JOURNAL OF APPLIED METEOROLOGY VOLUME 42 FIG. 1. Conceptual view of precipitation with and without mean windV (z) plus convection. For a rain cell with R 5 0 at the ground, application of a Z±R relation implies accumulated precipitation Pac right below the cloud (graph ``a''). In reality, hydrometeor trajectories at later times will lead to Pac (graph ``b''). Dotzek and Beheng (2001) and many other researchers 2002). Here, with R at the ground (where w 5 0) being before (e.g., Battan 1976; Aniol et al. 1980; Wilson and derived from Z measured by low-elevation radar scans, Brandes 1979; Zawadzki 1984; Austin 1987; Joss and the problem arises as to how to relate Z at a few kilo- Waldvogel 1990; Atlas et al. 1995, 1999; DoÈlling et al. meters above radar to an instantaneous rain rate at (or 1998; Jordan et al. 2000), this effect makes application below) the radar level. Even in the case of stratiform of standard Z±R relations for deep convective clouds clouds, vertical drafts, density strati®cation, and the pro- dif®cult or even questionable. Various Z±R relations, ®le of the horizontal wind may introduce considerable however, have been publishedÐfor instance, by Battan error to this nonlocal approach. At least, the effect of (1973) and Sauvageot (1992). air density strati®cation on terminal fall velocity and, Besides, deep moist convection also induces hori- hence, on Z±R relations of the form Z 5 aRb can nearly zontal components and is usually superposed to strong be eliminated (Dotzek et al. 2002). vertically sheared mean horizontal air¯ow, as schemat- So, to supplement Dotzek and Beheng (2001) and ically outlined in Fig. 1. For a developing rain cell with- Dotzek et al. (2002), in our paper Z±R relations and in a radar scan volume but with no rain at the ground vertical pro®les of instantaneous (R) and horizontally yet (i.e., R 00 5 0), application of a Z±R relation would averaged (^R&) precipitation rate are studied in more erroneously diagnose R 00 . 0 and also a precipitation detail with a cloud-resolving-model analysis. Despite accumulation Pac on the ground. In reality, rain will only the cloud microphysical simpli®cations inherent to Kes- reach the ground at later times and with a horizontal sler-type bulk cloud models (Kessler 1969), they offer displacement due to a combination of convection and the unique opportunity to compare consistent ®elds of transport by the mean wind pro®le. Although it is a hydrometeor content, vertical drafts, and air density minor effect over large areas with homogeneous orog- strati®cation. From these ®elds, R and Z can be com- raphy, this horizontal shift can become important over puted at every grid point to conduct a study that re¯ects complex terrain with small distances between neigh- effects of deep convective motions in a strati®ed at- boring river catchments. It is evident that the rain rate mosphere alone, unbiased by microphysical processes for a given value of Z in convective clouds changes in hardly accessible for either models or observations. space and time and that no unique Z±R relation exists The paper is organized as follows. Section 2 brie¯y in general [see the discussion given by Battan (1976), presents the two model simulations applied for our study Atlas et al. (1995), and Dotzek and Beheng (2001)]. with their initialization and procedure. In section 3, Practical problems of this kind in the context of QPE Karlsruhe Atmospheric Mesoscale Model (KAMM) re- are usually addressed by combining data from one sults for a single-cell cumulonimbus are discussed; sec- (Dotzek et al. 2002) or several radars (Gourley et al. tion 4 addresses the ®fth-generation Pennsylvania State Unauthenticated | Downloaded 09/29/21 02:43 AM UTC SEPTEMBER 2003 DOTZEK AND FEHR 1287 University±National Center for Atmospheric Research TABLE 1. Vertical pro®les of virtual potential temperature Qy and Mesoscale Model (MM5) supercell and multicell storm RH up to 10 km AGL used for the KAMM simulation. simulations, respectively. Sections 5 and 6 present dis- z (km AGL) Qy (K) RH (%) cussion and conclusions. 10.0 333.19 4.89 9.5 326.34 6.60 9.0 320.47 8.23 2. Model setup 8.5 316.26 9.68 Two different three-dimensional nonhydrostatic me- 8.0 314.51 11.25 7.5 313.20 12.90 soscale models, KAMM (e.g., Adrian and Fiedler 1991; 7.0 311.81 13.51 Dotzek 1999) and MM5 (e.g., Grell et al. 1994), were 6.5 309.78 8.35 used to model individual storms over idealized orog- 6.0 307.58 23.28 raphy with 1-km horizontal grid size. Note that both 5.5 306.28 20.97 5.0 304.68 43.13 simulations were initially conducted to clarify scienti®c 4.5 303.96 39.57 problems other than the one considered here. Only after 4.5 302.43 57.73 the ®ndings by Dotzek and Beheng (2001), did it appear 3.5 300.11 73.75 fruitful to exploit the two simulations to determine the 3.0 298.11 93.06 in¯uence of deep convection on vertical pro®les of pre- 2.5 296.20 98.45 2.0 294.41 86.88 cipitation rate.