11A.1 MOISTURE FLUX CONVERGENCE: ITS HISTORY AND APPLICATION IN CONVECTIVE INITIATION FORECASTING Peter C. Banacos* NOAA/NWS/NCEP/Storm Prediction Center Norman, Oklahoma 73069 David M. Schultz Cooperative Institute for Mesoscale Meteorological Studies, Univ. of Oklahoma, and NOAA/National Severe Storms Laboratory, Norman, Oklahoma 73069 1. INTRODUCTION Convective initiation (CI) remains a difficult forecast condensation rate into the air parcel. Many studies that challenge (e.g., Ziegler and Rasmussen 1998; Moller employ (1) make the assumption that all the condensed 2001). Predicting the precise timing and location of water immediately precipitates out (P), so that S=E–P deep moist convection, even along well-defined surface (e.g., Palmén and Holopainen 1962). Using the boundaries (e.g., fronts, drylines), remains a hurdle to continuity equation, ∂ u ∂ x +∂v ∂ y +∂ω ∂ p = 0 , improved short-range forecasts of severe weather and (1) can be expanded and rewritten in flux form, which has been the subject of recent field work such as 2002’s conserves the total mass of moisture: International H2O Project (IHOP) (Weckwerth et al. 2004). ∂ ∂ ∂ ∂ ∂ ∂ ∂ω q + q + q + ω q + u + v + = − (2) u v q E P In view of imperfect scientific knowledge concerning ∂t ∂x ∂y ∂p ∂x ∂y ∂p processes related to CI, as well as inadequacies in numerical guidance concerning, in particular, warm ∂ ∂ , (3) season convective storm evolution (Fritsch and Carbone q + ∇ ⋅()+ ()ω = − qVh q E P 2004), forecasters have necessarily sought out a variety ∂t 14243 ∂p 123 { of diagnostic measures to aid in forecasting CI using local rate – horizontal 14243 sources MFC – vertical and sinks derived parameters from both observations and of change MFC numerical model output. One such diagnostic measure of q is moisture flux convergence (MFC). Reviews of the ∂ ∂ where ∇=ˆi + jˆ and Vh= (u,v). Specifically (3) strengths and limitations of surface MFC have appeared ∂ ∂ in Doswell (1982), Bothwell (1988), and Waldstreicher x y (1989). This preprint provides some additional expresses the moisture budget for an air parcel, where information; it traces the historical usage of MFC as a the terms consist of the local rate of change of q, forecast tool to understand the physical rationale behind horizontal moisture flux divergence (the negative of its origin, compares MFC to convergence through a horizontal MFC), the negative of vertical moisture flux scale analysis, and provides an example of elevated convergence, and source and sink terms of moisture severe thunderstorm development (e.g. convective (specifically, evaporation and precipitation rates). By updrafts not rooted in the local boundary layer), a vector identity, horizontal MFC can be written as: problem we feel deserves additional treatment of in the = ∇ ⋅ ()= ⋅ ∇ ∇ ⋅ , (4) research community with the goal of improving forecast MFC – qVh – Vh q – q Vh skill. ∂ ∂ ∂ ∂ q q u v (5) 2. PHYSICAL EXPRESSION OF MFC MFC = – u – v – q + . ∂x ∂y ∂x ∂y 1 44 2 4 43 1 44 2 4 43 The expression for MFC arises from the conservation advection convergence term term of water vapor in pressure (p) coordinates: dq = S , (1) In (5), the advection term represents the horizontal dt advection of specific humidity. The convergence term d ∂ ∂ ∂ ∂ denotes the product of the specific humidity and where = + u + v + ω , dt ∂t ∂x ∂y ∂p horizontal mass convergence. 3. FORECAST UTILITY ω V= (u,v, ), and q is the specific humidity. S represents the storage of water vapor, which is the difference The application of MFC in weather prediction has between the sources and sinks of water vapor following focused on three general topics: (1) calculation of large- an air parcel. S typically takes the form E–C, where E is scale precipitation fields within extratropical cyclones the evaporation rate into the air parcel and C is the during the 1950s through mid 1960s, (2) as in integral _____________________________________________ * Corresponding author address: Peter C. Banacos, Storm Prediction Center, 1313 Halley Circle, Norman, OK 73069; e-mail: [email protected] component in the Kuo convective parameterization p s = 1 ∇ ⋅ + . (9) scheme developed in the 1960s, and, (3) severe local M t – ( q V h ) dp F qs g ∫ 0 storm prediction beginning in 1970 as a direct result of (2). A more detailed treatment of the history of each of Moisture accession is the sum of a vertically integrated these areas is included in the following subsections. MFC and F , the vertical molecular flux of water vapor qs from the surface. Kuo (1965) assumed that all the 3.1 Calculations of precipitation in midlatitude moisture accession goes into making clouds (i.e. b=0), a cyclones good assumption where tropical cumulus form in Equation (3) can be solved for P–E, divided by the regions of deep conditional instability and large-scale acceleration due to gravity g, and vertically integrated surface convergence. Kuo (1974) found that b was over the depth of the atmosphere from the surface p=p s much smaller than 1 in most situations and could be to p=0 (Väisänen 1961; Palmén and Holopainen 1962), neglected in (9), leading to a direct relationship between yielding the moisture accession and the condensation. Consequently, he argued that cumulus convection in the s ∂ s s − = 1 p q 1 p ⋅∇ 1 p ∇ ⋅ , (6) P E – dp – Vh qdp – q V dp Tropics would be driven by the large-scale vertically ∫0 ∂ ∫0 ∫0 h g t g g integrated MFC. It is important to note that the Kuo scheme was where the overbar represents a vertical integrated developed initially for tropical cyclone simulations, quantity. If one assumes that evaporation E is small in where the important question is “how much” latent heat areas of intense precipitation and saturation, and that will be released, not “will” latent heat be released. In local changes in water vapor content are primarily those contrast, the latter is often of central concern to owing to advection in synoptic-scale systems (such that convective forecasters in mid-latitudes, particularly in the first two terms on the right-hand side are in balance, thermodynamic environments possessing an elevated see references above), then mixed-layer (Carlson et al. 1983) and some degree of convective inhibition (CIN) through most (if not all) of the ≈ 1 p s ∇ ⋅ . (7) diurnal cycle. More formally, the Kuo formulation P – q V h dp g ∫ 0 assumes convection processes moisture at the rate supplied by the environment (i.e. statistical equilibrium Thus, the precipitation amount is proportional to the exists, Type I convection (Emanuel 1994)). Conversely, vertically integrated product of specific humidity and the sudden release of a finite, and typically large, mass convergence through the depth of the amount of CAPE that has been built over time is a atmosphere. binary episode (“triggered” or Type II convection The earliest synoptic application of (7) was from (Emanuel 1994)) in which the timing, and even the moisture budgets to estimate the large-scale occurrence of the convection itself, remains a difficult precipitation in mid latitude cyclones using rawinsonde and important forecast problem. This dilemma holds observations (Spar 1953; Bradbury 1957; Väisänen true for both forecasters and numerical simulations, as 1961; Palmén and Holopainen 1962; Fankhauser 1965). was alluded to in the introduction. These imperfections However, advances in numerical weather prediction in applicability of MFC endured by forecasters help to almost certainly resulted in the phasing out of these explain “false-alarm” events in which well-defined axes attempts beginning in the 1960s, although the concept of MFC exist but capping inversions preclude deep was theoretically sound (but also quite laborious). The convective development in otherwise favorable case studies referenced above over the United States environments. and the United Kingdom showed that precipitation calculated from (7) reproduced well the observed spatial 3.3 Application of MFC to Mid Latitude Convection pattern of precipitation and the maximum precipitation Hudson (1970, 1971) was the first to compute amount associated with mid latitude cyclones. vertically integrated MFC and to compare it to the 3.2 The Kuo Convective Parameterization Scheme amount of moisture required for cloud development in Kuo (1965, 1974) wished to quantify the latent heat the midlatitudes for nine severe-weather events, release during condensation in tropical cumulonimbus, interpreting the ratio between these two quantities as the main source of energy in tropical cyclones. He the fraction of convective cloud cover. He computed surmised that quantification of the water vapor budget vertically integrated MFC over a depth from the surface might reveal the magnitude of the vertical motion and to 10 000 ft (3048 m) MSL because “most of the water latent heat release indirectly. He derived the vertically vapor is in this layer and because loss of wind data becomes significant above this level” (Hudson 1971, p. integrated condensation minus evaporation C – E as 759). Similarly, Kuo (1974) employed the top of his integration at 400 mb because of the perceived poor − = − C E (1 b ) gM t , (8) quality of the upper-air data above this level. Newman (1971), however, argued for using surface hourly where b represents the storage of moisture and Mt is observations to compute MFC because of their higher termed the moisture accession: temporal and spatial resolution. As a result, he became the first to document the calculation of surface MFC. The majority of studies since