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Prognostic mesoscale Model PROWIMO

Introduction

PROWIMO is a prognostic mesoscale model. With respect to the physical content this model is comparable to METRAS-PC und FITNAH, which are well known in Germany.

PROWIMO is evaluated (Flassak 2016, 2018) according to the guidline VDI 3783 page 7.

The model PROWIMO is based on Flassak (1990) and was lately completely recoded and extended at our office. For example the Predicted Mean Vote (PMV) or the "perceived temperature" according to VDI 3787 page 2 (2008) has been added in order to be capable to provide climatological assessments. PROWIMO is suited to simulate the local wind and temperature distribution. The model can be adapted individually to site-specific conditions.

In addition to the scientifically recognized and reliable model METRAS-PC we now can deal at our office with another prognostic mesoscale model which we apply for example for climatological assessments of land use changes in the meso scale. 

Model description

The model PROWIMO is based on the conservation equations for momentum, mass and energy, which are solved numerically in 3D in the flux formulation in terrain flollowing co-ordinates. Prognostic variables are the 3 velocity components u, v and w, the potential temperature, the humidity, the surface temperature and the surface humidity. The non-hydrostatic pressure is computed by solving an elliptic differential equation. The elliptic solver is based on a Fast Fourier Transformation algorithm in conjunction with a generalized Conjugate Gradient Method. 

The model applies the anelastic approximation as well as the Boussinesq approximation. The subgridscaled turbulent fluxes are parametrised with a first order closure. 

The complete documentation of the model PROWIMO (physical background, approximations, numerical methods, boundary and initial conditions, parametrisations) are given in Flassak (1990, in German).

Application example "Simulation of the Nocturnal Drainage Flow within the Greater Stuttgart area"

For the simulation of nocturnal drainage flows for many years two-dimensional models have been available and in operational use. Those 2d models solve the so-called shallow water equations, e.g. model KALM (Schädler, 1994).  In the case of a nocturnal drainage flow in conjunction with an overlying regional wind, instead of such a 2d shallow water equations model a fully 3d prognostic mesoscale model has to be applied.    

In 1996/1997 in Stuttgart a field experiment took place with the aim to measure nocturnal drainage flow (Vogt et al., 1999). The results of this field experiment are best suited as a validation data set for 3d prognostic mesoscale models.

During the measuring night from April 1st to 2nd, 1997 in the Stuttgart basin (= Stuttgarter Talkessel in Fig. 3) the flow was decoupled in a lower regime and an upper regime. The lower regime is the nocturnal drainage flow, the upper regime the overlying regional wind.

At measuring station "Planetarium" (cf. Fig. 1 left) at 22h from surface up to a height of 100m the wind direction ranges from south to south west. This flow system is the nocturnal drainage flow from the Nesenbachtal via the Stuttgarter Talkessel to the Neckartal.   Above approx. 100m above ground the wind direction turns rapidly within a zone less than 30m to easterly directions which is the overlying regional wind direction. In the upper wind regime the wind velocity increases up to approx. 5 m/s above 300m above ground.

At measuring station "Höhenpark" (located approx. 100 m higher than the measuring station "Planetarium", cf. Fig. 2 left) the wind direction near ground was westsouthwest and turned with increasing height over north to east. The lower flow system has a thickness of approx 50m.

Both measuring stations "Planetarium" and "Höhenpark" are depicted in Fig. 3.

Fig. 1: Measured (left) and simulated (right) vertical wind profile at April 1, 1997, 22.00 h at measuring station "Planetarium"

Fig. 2Measured (left) and simulated (right) vertical wind profile at April 1, 1997, 23.00 h at measuring station "Höhenpark"

In the following simulation results of the prognostic mesoscale model PROWIMO are shown. The simulation domain has a horizontal extent of  30 km x 30 km. The horizontal grid size within an inner domain of  20 km x 20 km is 100m, outside of that inner domain the horizontal grid size increases with a factor of 1.2. A vertical grid size of 10m has been chosen from surface up to a height of 120m, above the vertical grid size increases with a factor of 1.2.  

Fig. 3 shows the simulated wind field at 22h at a height of 10 m above ground. The simulation reveals the observed nocturnal drainage flows from the Nesenbachtal via the Stuttgarter Talkessel to the Neckartal. At higher altitudes the simulated wind direction is from east. The simulated vertical wind profile at measuring station "Planetarium" is depicted in Fig. 1 right and at measuring station "Höhenpark" in Fig. 2 right.   

Qualitatively the observed and the simulated wind profiles fit quite well. Especially the simulated height of the wind shear i.e. separation height between the lower and the upper wind regime is in good agreement with the observation. In summary PROWIMO is capable to simulate those decoupled flow systems in complex terrain quite satisfactorily.  

Fig. 3: Simulated wind field at 10m above ground at April 1, 1997, 22.00 h and location of measuring stations "Planetarium" and "Höhenpark"

When the minimum in the vertical velocity profile is defined as the thickness of the nocturnal drainage flow, the simulated thickness of the nocturnal drainage flow at measuring location "Planetarium" ("Höhenpark") is slightly higher than the measured thickness. On the other hand the simulated velocities in the nocturnal drainage flow layer are lower than the measured values.  

An integral measure for the comparsion of simulation and measurement is the co-called volume stream density. This quantity is the nocturnal drainage volume flow through an 1m wide area from the surface up to the thickness of the nocturnal drainage flow [unit: m³/(sm)]. 

From the measurements a value of  172 m³/(sm) has been determined for the ascent of the tethered balloon and 146 m³/(sm) for the desent at measuring location "Planetarium" at 22h. The simulation gives a value of 146 m³/(sm), i.e. a value inside the bandwidth of both measured values.

At measuring location "Höhenpark" the measured volume stream density at 23h is 51 m³/(sm) for the ascent and 52 m³/(sm) for the desent of the tethered balloon. The simulation yields 63 m³/(sm), i.e. a slightly higher value than the measured volume stream density.

A visualisation of the daily cycle of the flow field can be found at: http://youtu.be/deGpuvRPXTs. The visualisation has been done with the software ParaView, siehe: http://www.paraview.org/

Literature