# Project Summary

High impact weather is often associated with small-scale substructures in larger-scale weather systems. Heavy precipitation or intense wind gusts associated with convection or frontal cyclones will be partially controlled by the synoptic flow, and partly by local orographic features or small-scale dynamical processes. Predictability, or forecast uncertainty, of these events will be influenced by all scales, but in different ways in different meteorological situations. The goal of the project is to develop an adaptive, multi-scale ensemble forecasting system, that represents the various sources of uncertainty through a hierarchy of models with different resolutions. It will include more or fewer members of each resolution and parametrization in order to more optimally sample that uncertainty that is likely to be present in the current environment.

The first part (WP1) is the development of stochastic physical parametrizations for cumulus convection and boundary layer variability and their implementation into DWDs local area model COSMO. In the second part (WP2) the time evolution of this small-scale variability and thier future impact is investigated. In cooperation with other members of the group, case studies of different weather systems are examined to identify the primary sources of uncertainty as a function of the meteorological situation.

# WP1: Stochastic parametrizations

Kirstin Kober, Pieter Groenemeijer, George Craig

Meteorologisches Institut, Ludwig-Maximilians-Universität München

### Stochastic convection scheme (Plant-Craig)

Traditional convective schemes produce just as much convection in each model grid column as to compensate for some kind of forcing mechanism for the convection (the closure). The Kain-Fritsch scheme, for example, uses a scheme that destroys the CAPE present at a given time within a certain time interval, the convective timescale (usually, 1800-3600 s). It does so by generating an upward mass flux within a small region within the gridbox and compensating subsidence elsewhere. This causes heating of the mid- and upper-troposphere, which destroys the CAPE. Another scheme, the Tiedtke scheme, uses moisture flux convergence as its forcing function. In both cases, the intensity of the convection, and hence precipitation, within a grid column is directly related to the forcing function.

A stochastic scheme uses a different approach. That is, in such a scheme, the probability of a convective plume with a certain intensity (mass flux) occurring is related to the forcing function. Given a forcing of magnitude X, a conventional scheme will produce convection of intensity X, even if X is a very low number. In contrast, the Plant-Craig scheme first calculates a probability density function of the probability p(r)*dr that gives the probability p(r) of a convective plume with diameter r to occur. Subsequently the scheme determines if such a plume is indeed lauched by drawing plumes from this probability density function.

The new scheme shows a more realistic-looking spatial distribution of precipitation than deterministic convective schemes such as the Tiedtke scheme (see Figure 1): instead of large areas with weak convective precipitation, the scheme produces a few intense convective showers. The scheme still needs some more tuning, though. In this particaular case, the total convective precipitation was too low, and some grid-scale convection occurred in addition to the parameterized convection.

**Figure 1:** 15-minute accumulated convective precipitation of the new Plant-Craig scheme (upper left), the standard Tiedke scheme (upper right) and the radar reflectivity (bottom).

### Stochastic boundary layer parametrization

Apart from convection the boundary layer is an important source for variability in the atmosphere, especially in situations with both a large convective potential energy and a large convective inhibition. In such cases, boundary layer fluctuation are able to initiate huge convective clouds with heavey precipitation. After the stochastic convection scheme of Plant and Craig has been implemented in Phase 1, a stochastic boundary layer scheme is being added to the COSMO model to account for such variabilities.

## WP2: Error growth experiments

Tobias Selz, George Craig

Meteorologisches Institut, Ludwig-Maximilians-Universität München

Beside a direct effect that the different sources of variability have on the forecast there might also be indirect effects: Small scale uncertainties from convection or boundary layer processes move upscale and alter the balanced motions after some time. Theoretical background on this topic is provided by Zhang et al. (2007) who suggested a three-stage error growth model based on idealized simulations of a convection permitting model. We took this study as a starting point and first tried to reproduce those results, but for a real weather event and with a state of the art limited area cloud resolving model (the COSMO in 2.8km resolution). We therefore selected a weather event (20th July, 2007) which is well known from the COPS field campaign, where an almost stationary low pressure system over Great Britten caused several days of synoptically forced convection and a cold front passage over central Europe. For this case we performed an unperturbed control run (Ctl) and two runs (P15 and P27), where we put in uncorrelated grid-scale noise on the temperature field 15h and 27h after forecast start, respectively. The perturbations have an amplitude of 0.01K and are not meant to represent uncertainties from observations but should cause the model to simulate a different realization of the convection within the exact same meteorological situation. We have chosen to run two perturbed runs 12h apart because this enables us to average out the diurnal cycle which turned out to have a large impact.

To study upscale error growth and possible effects on the balanced motions we had to use a domain size which at least covers the Rossby radius of deformation. Furthermore, the unperturbed boundary conditions which comes from IFS forecast limit the error growth in the domain. A bigger domain reduces this limitation. According to our computational resources we chose a domain which is about 7.000km in longitude and 4.250km in latitude, resulting in 2400 times 1500 gridpoints (see figure 2a). The three model runs (Ctl, P15, P27) of a slightly modified version of the COSMO model (version 4.21) were performed at the ECMWF computer. With this data we were able to confirm the basic ideas of Zhang et al. three-stage error growth model: In the first stage, right after the perturbations were put in, there is very rapid error growth on small scales associated with convective instability. Consequentially, the errors are almost confined to the precipitating areas (see figure 2a). This rapid initial error growth then slows down and saturates after about six hours due to a compete displacement of the individual convective cells, while the overall amount of convection is controlled by the large-scale motions and hasn't changed

much yet.

**Figure 2a:** Early stage of the error growth. The small black lines show v windspeed difference between P15 and Ctl. Thick black lines are 500hPa geoptential of Ctl. Blueish shading shows precipitation, white shading cloud cover and yellow shading high CAPE values of Ctl.

**Figure 2b:** Late stage of the error growth. The thick colored lines show the large-scale 500hPa geopotential difference between Ctl and P15.

In stage two, the gravity waves that are spreading out from the convection distribute the errors all over the domain and geostrophic adjustment processes projects them onto the balanced motions. In stage three finally, this balanced perturbation growth further in time and scale together with the baroclinic wave. Figure 2b shows the final large-scale perturbation that developed in 60 hours out of the grid-scale noise (thick coloured lines).

A more quantitative measure to describe the error growth is Difference Total Energy (DTE). By applying a fourier filter to the fields we selected three different scales (S: <200km, M: 200-1000km, L:>1000km). Figure 3 shows the time development of DTE for these three scales. We have averaged over both perturbed simulations (P15 and P27) to average out the diurnal cycle. This figure is in good agreement with a similar analysis from Zhang et al. (2007). It shows the small scales growing fast initially and then saturating while the large-scale DTE is still growing at the end of the simulation: Initially S and L have been four orders of magnitude apart, at the end this difference scaled down to less than one order of magnitude. In addition, we developed a mathematical function which describes the observed DTE development and is related to the error growth stages. The function is as follows:

DTE ( t ) =d_{0}⋅exp ( r/s⋅(1−exp [ −s⋅t ]) ) ⋅exp [ g⋅t ]

It describes initially exponential error growth at rate r, which then exponentially decays at rate s towards a final exponential growth at rate g. The dotted lines in figure 3 show a least-square fit to this equation. For all scales 1/r turns out to be about half an hour. This is of the order of the convection turn-over time and indicates the dominant role of convection and moist processes during the first phase of the error growth. The final growth rate g is very different for the different scales: 1/g equals 42h for small scales and 9h for large scales, meaning that the small scales are (almost) saturated while the large scales are still growing at the end of the simulation.

**Figure 3:** Time development of Difference Total Energy (DTE) by scale (solid lines). The dotted lines show a least-square fit with the equation above.