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Article Relabelling Symme- Tation Activity Index for Different Seasons and Utilising the Try and the Energy-Vorticity Theory of fluid Mechanics, Meteorol

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Article Relabelling Symme- Tation Activity Index for Different Seasons and Utilising the Try and the Energy-Vorticity Theory of fluid Mechanics, Meteorol Adv. Geosci., 16, 33–41, 2008 www.adv-geosci.net/16/33/2008/ Advances in © Author(s) 2008. This work is distributed under Geosciences the Creative Commons Attribution 3.0 License. Process-oriented statistical-dynamical evaluation of LM precipitation forecasts A. Claußnitzer, I. Langer, P. Nevir,´ E. Reimer, and U. Cubasch Institut fur¨ Meteorologie, Freie Universitat¨ Berlin Carl-Heinrich-Becker-Weg 6-10, D-12165 Berlin, Germany Received: 1 August 2007 – Revised: 10 January 2008 – Accepted: 29 February 2008 – Published: 9 April 2008 Abstract. The objective of this study is the scale dependent Lin, 2003). Alternatively, the ageostrophic horizontal diver- evaluation of precipitation forecasts of the Lokal-Modell gence weighted with the specific humidity is used to esti- (LM) from the German Weather Service in relation to dy- mate diagnostic precipitation rates (Spar, 1953; Palmen´ and namical and cloud parameters. For this purpose the newly de- Holopainen, 1962; Banacos and Schultz, 2005). Other re- signed Dynamic State Index (DSI) is correlated with clouds search groups deal with the statistical analysis of precipita- and precipitation. The DSI quantitatively describes the devi- tion processes to investigate a multifractal (e.g. Olsson et al. , ation and relative distance from a stationary and adiabatic so- 1993; Tessier et al., 1993; Lovejoy and Schertzer, 1995) and lution of the primitive equations. A case study and statistical a chaotic behaviour (Rodriguez-Iturbe et al., 1989; Sivaku- analysis of clouds and precipitation demonstrates the avail- mar, 2001). In particular, there is an indication that convec- ability of the DSI as a dynamical threshold parameter. This tive precipitation is linked to self-organised critical phenom- confirms the importance of imbalances of the atmospheric ena, with the saturation of water vapour as the dynamical flow field, which dynamically induce the generation of rain- threshold (Peters and Christensen, 2006). A previous study fall. from Langer and Reimer (2007) shows an improvement by considering the clouds types derived from Meteosat-7 for an independent numerical interpolation procedure to build up 1 Introduction an observational precipitation analysis in a resolution corre- sponding to the LM grid (Reimer and Scherer, 1992). In the last years the development of numerical weather pre- diction (NWP) models there has been great progress in the short-term and middle-term forecast of temperature, wind speed or direction and cloud coverage, but only minor suc- cess in the quantitative precipitation forecast (QPF). In order to improve the NWP models, it is necessary to understand The aim of this paper is to present a connection between the precipitation processes. In general, rainfall is a very dis- the Dynamic State Index (DSI), which skillfully combines continuous variable in space and time. It is difficult to obtain the above-mentioned imbalances of the flow fields, and pre- spatial-temporal information about precipitation on the ob- cipitation as well as clouds. The paper is divided into the servational as well as on the modelled basis. following parts: Sect. 2 gives a short description of the DSI Physically, in the mid-latitudes rainfall develops via the and Sect. 3 specifies the Meteosat-8 channels and the derived ice phase in the clouds, the so-called Bergeron-Findeisen- cloud types. The data sets used as well as the calculation of Process. In synoptic meteorology, precipitation is linked to the DSI and cloud types are presented in Sect. 4. The results upward vertical motion in large-scale baroclinic systems. In of this study are given in Sect. 5, organised in three themes. particular, in the mid-latitudes high correlations of precip- First the correlation between the DSI and the precipitation itation rates and vertical velocity can be found (Rose and derived from the LM data is presented, then a case study shows the exceeding agreement in space. In the last subsec- tion Meteosat-8 data are used and with a new approach the Correspondence to: A. Claußnitzer precipitation activity of different cloud types is calculated. ([email protected]) Finally Sect. 6 gives a summary. Published by Copernicus Publications on behalf of the European Geosciences Union. 34 A. Claußnitzer et al.: Process-oriented statistical-dynamical evaluation of LM precipitation forecasts of the functional dependence of the Bernoulli-stream func- tion and the PV in the stationary energy-vorticity basic state the index in this state is exactly zero (DSI=0). The oscil- lation around the basic state is visualised by spatial dipole structures in the horizontal plane. In this way the DSI is used as a dynamical threshold parameter for precipitation processes. An application of the DSI with respect to the visualisation of storm tracks and the evolution of severe win- S ter storms and hurricanes can be found in Weber and Nevir´ (2008). N 2.1 Physical and geometrical interpretation of the DSI In this section it will be shown that the DSI in the non- balanced state is proportional to the advection of the squared 5. Rewriting the definition of the DSI (Eq. 2) as scalar triple product [a · (b × c)] and using the stationary velocity S vst (Eq. 1), the DSI can be rewritten in the following way: ! 1 52 DSI = ∇5(ρ5v ) = v · ∇ . (3) Fig. 1. Isolines of 5 and Bernoulli-stream function on two different ρ st st 2 isentropic levels θ1 and θ2. The red lines indicate angles between Bernoulli streamfunctions and PV isolines with 54 > 51. Under general conditions the atmospheric flow is certainly not in the energy-vorticity equilibrium, so the stationary wind becomes the real, non-balanced wind. Therefore two 2 Dynamic State Index DSI cases have to be distinguished: 2 ! Usually, precipitation is a parameter, which is linked to 5 vst · ∇ = 0 changes in the atmospheric circulation, e.g. growth of baro- 2 clinic waves and frontogenesis on the synoptic scale. It DSI = . (4) is also coupled with the mesoscale convective system (e.g. ! 52 Houze, 2004). These meteorological phenomena can be at- v · ∇ 6= 0 tributed to non-balanced processes. The newly designed 2 Dynamic State Index (DSI) describes the deviation from the stationary solution of the adiabatic primitive equations In addition to the mathematical derivation a geometrical (Nevir´ , 2004) and is in this way a measure of non-balanced interpretation together with a discussion of the sign of the properties of atmospheric flow fields. The above-mentioned DSI is given in Fig. 1. Here the isolines of the Bernoulli solution describes a generalised geostrophic equilibrium, stream function and the PV are shown on two isentropic which can be expressed in terms of a three-dimensional sta- surfaces. In the case of vanishing DSI the isolines of the Bernoulli stream function and the PV are parallel. On the θ1- tionary velocity vector vst: surface, an angle between 0–90◦ denotes a DSI>0. Accord- ing to Eq. 4 this implies a negative advection of the squared 1 ◦ vst = ∇θ × ∇B· (1) PV. On the θ -surface, an angle between 90–180 denotes a ρ5 2 DSI<0, which implies a positive advection of the squared Here θ denotes the potential temperature, 5 is Ertel’s poten- PV. tial vorticity (PV), B the Bernoulli-stream function and ρ the density of air. For a classical derivation in terms of the gov- erning equations see Schar¨ (1993). The DSI is defined as a 3 Cloud types derived from satellite data Jacobian determinant: The products “cloud classes” and “cloud coverage” derived 1 ∂(θ, 5, B) from Meteosat-8 data are uses with a temporal resolution of DSI := , (2) 15 min. The original resolution of the Meteosat infrared ρ ∂(x, y, z) data is 3×3 km2. Meteosat-8 data are transformed into a which locally includes the information about entropy, en- geographic projection with an effective spatial resolution of ergy and potential vorticity and describes diabatic and non- 0.01◦. For the correction of the sun’s elevation, the cosine stationary processes of the atmospheric flow field. Because of the zenith distance was used. In order to determine the Adv. Geosci., 16, 33–41, 2008 www.adv-geosci.net/16/33/2008/ A. Claußnitzer et al.: Process-oriented statistical-dynamical evaluation of LM precipitation forecasts 35 cloud classes and the cloud cover, the near-infrared channels grid-scale snowfall, convective snowfall and the total precip- at 0.6 and 0.8 µm, called VIS06 and VIS08, and the ther- itation. The cumulus parametrization scheme according to mal infrared channel at 10 µm (VIS10) from Meteosat-8 be- Tiedtke (1989) uses a mass-flux approach to represent moist tween 06:00UTC and 18:00UTC were selected. The cloud convection in the LM. In the LM cumulus convection is a classification from satellite data is based on the distribution sub scaled process in the LM, which is not resolved from of clouds in different heights (i.e. with different cloud top the grid and can therefore not be simulated explicitly. To temperatures) and with different optical thicknesses in a bi- obtain the whole grid scale (stratiform) and convective pre- spectral histogram (Berger, 1992; Langer and Reimer, 2007). cipitation, the parts of rain and snow were added to the total One extreme case is the cloudless surface which should be stratiform precipitation (TG) and the total convective precip- the warmest and darkest area in the satellite image and the itation (TC). The total precipitation (TP) is the sum of total other extreme case is the cloud top of a cumulonimbus as convective and total stratiform precipitation. the coldest and brightest area. The automated classification scheme tries to find those areas and builds test classes for 4.2 Input data for DSI calculation other cloud types and calculates the arithmetic mean and the covariance for each class (Berger, 1992).
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