Mesoscale Meteorological Modeling Overview

Mesoscale Meteorological Modeling (ATMO 558) HARMONIE HIRLAM ALADIN Research on Mesoscale Operation NWP in Europe Xiaojian Zheng Feb 26,2018

Development of HIRLAM Established in 1985 in Nordic countries and extended to 20+ members. Aim to provide a operational short and very short range numerical weather prediction system, with particular emphasis on the detection and forecasting of severe weather. code cooperation with M t o-France HARMONIE (Mesoscale) HIRLAM GLAMEPS HIRLAM-ALADIN collaboration (High Resolution Limited Area Model) (Grant Limited Area Ensemble Prediction System) Engage in a close code cooperation with the ALADIN consortium to develop and maintain a common, state-of-the-art mesoscale LAM model code for short-range numerical weather prediction, with in the code framework of the ECWMF/Arpege Integrated Forecasting System (IFS). Hydrostatic grid-point model, with hybrid coordinate in the vertical HIRLAM (Synoptic Scale) No longer under active development but still operational for many services.

Development of HIRLAM HARMONIE (HIRLAM ALADIN Research on Mesoscale Operation NWP in Europe) HIRLAM research collaboration has been focusing on the convection-permitting scale, and on adapting the AROME (Application of Research to Operations at Mesoscale, canonical model configurations of ALADIN) since 2005. A scripting system which facilitates data-assimilation and observation handling, climate generation, lateral boundary coupling and post-processing required to run AROME operationally within the HIRLAM countries. Uses non-hydrostatic (NH) dynamical core same as AROME-France Uses the updates in physical parameterizations of clouds (mixed phase) and land surfaces especially in northern latitude conditions. The horizontal resolution is 2.5km, and 65 levels (from 12m upto 10hpa) are used in vertical. Model time step is 75 seconds.

Dynamical Kernel General Description Fully elastic set of Euler Equations (non-hydrostatic & non-anelastic) All types of dynamical waves in atmosphere can be modelled with the EE system, including acoustic waves Using Semi-Implicit or Iterative-Centred-Implicit time-scheme combined with Semi-Lagrangian transport scheme to efficiently alleviate the wave-CFL limitations due to the propagation of fast waves. Spectral (bi-Fourier) transform method for horizontal directions Mass-based hybrid terrain-following vertical coordinate Spherical-geopotential Approximation: Intensity of Gravity g must be uniform Neglect the Centrifugal effect Associated coordinates (longitude , latitude , geocentric radius r) Shallow Atmosphere Approximation on top of the SGA r is replaced by the (spherical) Earth s radius a in the approximated metric factors ( ?= ?????, ?= ?, ?= 1) Coriolis terms involving ???? is neglected Used prognostic variable ?,? ??? ( ?,? ) instead of (?,?)

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Continuous Euler Equations in pure mass-based coordinates Hydrostatic pressure : defined at each point by the weight of the unit-area air column above this point. (e.g. pressure P is dramatically weak in area just above a montaneous ridge due to dynamical depressurization but not the hydrostatic- pressure ) + (x, y, z , t)g dz in local Hence, geographical Cartesian Coordinate. / z= g, (x, y, z, t) = ? Domain limits: ?(?,?,?,?) [??, ??(?,?,?)] Material boundary conditions: (mass flux is zero through the limits of the domain) ??=??=??? ??=??=??? ??+ ?? ??? ; ??+ ?? ???

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Euler Equations system in ? coordinate Momentum ?? ??+?? ?? ??+ ? 1 ?? ?? ?? ?? ?? ??+?? ?? ? +? ? ?? ??= ?? ; ???? +?? ????? = ? Vertical momentum = ? ?? ?? ??=? 1 ? Thermodynamic ?? ????3=?? ?? Continuity Diagnostic relation(valid whether hydrostatic or not) ??? Mass continuity ??= 0 ?? ??= ?? State law ? Where is lagrangian derivative; is ture 3-dimensional divergence of the wind ?,?,? : physical components of the forcing (? includes Coriolis term)

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Euler Equations system in hybrid mass-based coordinate Hybrid vertical coordinate ? ? ?,?,?,? = ? ? + ? ? ??(?,?,?) where ??is the ground hydrostatic pressure with the vertical metric factor ? =?? ? Elaboration: If A and B are two arbitrary functions, they must satisfy: Variation Domain: [??,?T] with boundaries ??= 1 ;??= 0 ?? d?+ (??)??? value of S in the domain and through all the duration of the forecast. ?? ??> 0; where (??)??? is a number smaller that the smallest likeky

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Upper domain limit: (? = 0 ??? ? = ??) Lower domain limit: (? = 1 ??? ? = ??(?,?,?)) A(1)=0; B(1)=1 ? 0 = ??;? 0 = 0 (?? ?? ???? ????????) Material boundary conditions: ? 1 = 0; ? 0 = 0 Transformation rules from ? toward ?: ? 1 ? ? ?? ??= ??= ?? ??? 1 ? ? ?? Which yields: ? =?? ?? ?? ??+ ?? ??? = ?????= ????????

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??)

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Euler Equations system in hybrid coordinate ? Momentum ?? ??+?? ?? ??+ ? 1 1 ?? ?? ?? ?? ??+?? ?? ??+ ? ?? + ?? ??= ?? ; ??? +1 ?? ???? = ? ?? ?? ?? ??=? ?? ??3=?? ??? ? ?? ?? ??= m?? ? Vertical momentum = ? ? Thermodynamic 1 ? ?? ?? ? ? = 0 Mass continuity State law ? 1 ? ???? ?? ? ? ? ? ?w ?? (3 ??????????? ??????????) Where: ?3= ? ? + ?? ??

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Integrate the Continuity equation on the vertical through the whole depth of the atmosphere leads to Surface hydrostatic pressure tendency equation: In the same way, integrating from the top to the current level gives the pseudo-vertical velocity in coordinate: the Lagrangian derivative of hydrostatic pressure ?(classically named ) can be obtained from the two previous equations, and leads to the following diagnostic relation: The horizontal gradient of geopotential is given by vertically integrating

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Introducing ? (reduced non-hydrostatic pressure departure) Traditionally, the problem of big cancelling terms in vertical momentum equation is alleviated by using the non-hydrostatic pressure departure p = p as a prognostic variable instead of the true pressure p. To avoid some instability in the semi-implicit scheme, this departure ? is rescaled by the hydrostatic pressure , and the resulting variable is put under the form of a logarithm. Therefore, the reduced non-hydrostatic pressure departure ? = ln(?/?) From derived the evolution equation:

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Introducing ? (reduced vertical divergence) In a similar way as inducing ?, the stability of the semi-implicit scheme calls for a change towards a pseudo vertical divergence in replacement of original vertical velocity w: Noted: Density is given by Necessity Using vertical velocity w as prognostic variable cause vertical staggering of the vertical momentum prognostic variables. Staggering result in two sets of origin points in semi-Lagrangian scheme needed (one for non-staggered and one for staggering variable) Replaced by ? make the model more simplified and efficient.

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Therefore, the origin vertical velocity can be diagnosed from ? through Take the logarithmic derivation obtains: states the evolution for ? Using ( ?,?) to rewrite Euler Equation system

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Final Form of Dynamical Model Equations (variables ?,? ) Prognostic equations: Momentum ?? ??+?? ??? +1 ?? ???? = ? ? ?? ??+ ?2 ? ? ?? 1 ? ? ? ? ?? ? ?? ?? ?? ? ? ? ?3 = ? ? ?? ?? ? ???? ???? ???? ?? ??+?? ?3=? Thermodynamic Energy ?? ?? Prognostic equation for ? ? ? ??+?? ? ?= ? ?3+ ?? ??? 1 Mass continuity ??? ??+ Surface hydrostatic- pressure tendency ? ?? ?? = 0 0

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Final Form of Dynamical Model Equations (variables ?,? ) ?????????? ?????????: ? =?? Horizontal gradient of geopotential ?? ? = ?? ? 1??? ? = ??+ ?? ? ? ?3= ? ? +?? ?? +1 ? ???? ?? ? ? ???? ? ?? Quantity 1 Pseudo-vertical velocity diagnostical of ?? ? ? = ? ? ???? 0 0 ? ? ???? ? = ? ?? 0 1???? ? 1 ?? ? ?? ?? + ??? = ????+ ???? ?? ? ?

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Introducing ? (modified vertical divergence) For the purpose of a more robust scheme in presence of orography. The new variable ? is defined by: The cross-term ? ? is traditionally called the X-term with the notation The 3-D divergence: From the prognostic equation for ? can derive:

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Final Form of Dynamical Model Equations (variables ?,? ) Prognostic equations: Momentum ?? ??+?? ??? +1 ?? ???? = ? ? ?? ??+ ?2 ? ? ?? 1 ? ? ? ? ?? ? ?V ?? ?? ? ? ?? ?? + 1 ?? ? ?? ?? ? ? = ? ? ???? ???? ? ???? ?? ??+?? ?3=? ?? ?? Thermodynamic Energy ? ? ??+?? ? ?= ? Prognostic equation for ? ?3+ ?? ??? 1 ??? ??+ ? ???? = 0 Mass continuity Surface hydrostatic- pressure tendency 0

Toward the Non-Hydrostatic prognostic variable ?,? ??? ( ?,??) Final Form of Dynamical Model Equations (variables ?,? ) ?????????? ?????????: ? =?? ?? ? = ?? ? 1??? ? = ??+ ?? ? ? ?3= ? ? +?? ?? + 1 ?? ? ? 1 ? ? ???? ? ? = ? ? ???? 0 0 ? ? ???? ? = ? ?? 0 1???? ? 1 ?? ? ?(? ?) ?? + ??? = ????+ (? ?)? ?? ? ? ????? ?V ? ? = ??

Vertical grid 3D prognostic variables are defined inside layers on so called full levels 1, . . . , L fluxes and vertical velocities are defined on layer interfaces or half levels 0, . . . , ? half level 0 is the top boundary, half level is the earth surface schematically, vertical grid looks like this:

Associated Linear Continuous System (perturbation) atmosphere in a given state (noted symbolically ? ), the instantaneous evolution of small amplitude disturbances around this state ? can be deduced from the analysis of the linearized set of equations around ? (noted symbolically ? ) Definition of the deviation

Associated Linear Continuous System (perturbation) Basic state Equation of state for the basic state Vertical profile of pressure in basic state

Associated Linear Continuous System (perturbation) Linearized system surface pressure tendency Vertical divergence Thermodynamic equation Omega equation ? ???????? State Equation Divergence equation

Parameterization Radiation: The default shortwave (SW) radiation parametrization in AROME-France and HARMONIE-AROME is the Morcrette radiation scheme from ECMWF, IFS cycle 25R1, and contains six spectral intervals(0.185-0.25-0.44-0.69-1.1-2.38-4.00 mm). The default longwave (LW) radiation scheme contains 16 spectral bands between 3:33 and 1000mm. This uses the Rapid Radiative Transfer Model (RRTM) of Mlawer et al. (1997). Clouds and Cloud Microphysics The microphysics scheme used in AROME-France and HARMONIE-AROME is a one-moment bulk scheme, which uses a three-class ice parametrization, referred to as ICE3, originally developed for meso-NH (Pinty and Jabouille 1998; Lascaux et al. 2006).

Parameterization Turbulence: HARATU (HARMONIE with RACMO Turbulence), which has a larger cloud top entrainment, has been implemented in HARMONIE-AROME cycle 40h1.1. HARATU is based on a scheme that was originally developed for use in the regional climate model RACMO (Van Meijgaard et al. 2012; Lenderink and Holtslag 2004). Convection: HARMONIE-AROME uses a different scheme for shallow convection than AROME- France (Seity et al. 2011), called EDMFm. Siebesma and Teixeira (2000), Soares et al. (2004), Siebesma et al. (2007) and Rio and Hourdin (2008) Surface: The surface physics in AROME-France and HARMONIE-AROME is simulated by the surface scheme named SURFEX . SURFEX (Surface Externalise e, Masson et al. (2013)) is a surface modelling platform developed mainly by Me te o-France in cooperation with the scientific community.

Spectral