# Convective Shower Characteristics Simulated with the Convection-Permitting Climate Model COSMO-CLM

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Model Setup

#### 2.2. Radar Data

#### 2.3. Tracking Algorithm

- Contiguous precipitation areas with precipitation intensity above a threshold of 8.5 mm/h (within 5 min), potential convective objects, are identified in the current and the subsequent time step. Contiguous areas are defined as pixels that share a common edge.
- Wind information is used to predict the position of the object at the subsequent time step. To this end, a “cone of detection” is set up for each pixel of every object, and the cone is swept for precipitation objects from the subsequent time step. The axis of the cone is defined by the wind direction; the length of the cone is calculated as twice the wind speed. The opening angle of the cone is 45°. If a new cell is present in the cone, a probability value is assigned to the origin pixel of the cone, which links this pixel to the new cell. The probability value is highest in the center of the cone and drops off exponentially in all directions. As an example, Figure 2a shows the probability values for a single pixel in the case of purely westward wind. In this case, the probability is calculated according to the following formula:$$\mathit{P}\mathit{r}\mathit{o}\mathit{b}\left(\mathbf{0},\mathbf{0}\right)=\mathit{e}\mathit{x}\mathit{p}\left(-\sqrt{{\left({\mathit{Y}}_{\mathit{c}\mathit{e}\mathit{n}\mathit{t}}-\mathit{y}\right)}^{\mathbf{2}}+{\left(\frac{{\mathit{X}}_{\mathit{m}\mathit{a}\mathit{x}}}{\mathbf{2}}-\mathit{x}\right)}^{\mathbf{2}}}\right)$$
_{cent}denotes the centerline of the cone, and X_{max}is the length of the cone, as determined by the wind data. This procedure is repeated for wind information in three height levels (500, 700, and 850 hPa). Afterward, the height dependent probability values are averaged to obtain the final probability value. - In the next step, the probabilities of all pixels are summed up for each cell. If one single object is present in the cone, the corresponding objects from the current and the subsequent time step are connected. If multiple cells are present, the current cell is associated with the cell with the highest probability in the subsequent time step.

## 3. Results and Discussion

#### 3.1. Precipitation Statistics

#### 3.2. Frequency and Characteristics of Convective Cells

^{2}) to be unrealistically large and discard those cells, then the underestimation of convective activity is only slightly reduced to 28%.

^{2}for cells living 195 to 210 min, the median is only 25 km

^{2}for cells living 15 to 30 min. The observed median values of mean intensity of cells in the same lifetime classes are 21 mm/h for long-living and 12 mm/h for short-living cells. These relationships indicate that the detected short-living cells can either be single-cell storms or individual cells of a multicell storm. The long-living, large, and intense cells are organized forms of convective systems like squall lines, supercells, and mesoscale convective systems. The simulation systematically underestimates the increase in mean intensity with lifetime. The increase in maximum area is well matched.

#### 3.3. Spatial Distribution of Cell Characteristics

#### 3.4. Diurnal Cycle

#### 3.5. Temperature Scaling of Cell Characteristics

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Visualization of the tracking algorithm: (

**a**) detection probabilities for a cone with X

_{max}= 8 and Y

_{cent}= 0 (assuming a grid size of 1 km × 1 km and a time step of 5 min, this is equal to a westward wind of ca. 13.3 m/s), and (

**b**) radar snapshot of a cell (shown is the 5-min precipitation intensity on 30 May 2008 at 21:40 (UTC) in colors and the detected cell track as red line).

**Figure 3.**Mean precipitation intensities and differences in the period 2001–2015; (

**a**–

**c**) full year; (

**d**–

**f**) summer half-year (April–September).

**Figure 4.**Frequency distribution of (

**a**) hourly and of (

**b**) 5-min precipitation intensities from radar observations (black) and CCLM simulation (red).

**Figure 5.**Frequency distributions of the cell characteristics (

**a**) lifetime, (

**b**) total precipitation, (

**c**) maximum area, and (

**d**) mean cell intensity as observed by the radar (black), by radar remapped to the model grid (blue) and simulated (red).

**Figure 6.**Dependence of (

**a**) cell mean intensity and (

**b**) cell maximum area on cell lifetime for radar observation and CCLM simulation. The boxes denote the 25th, 50th, and 75th percentiles. The whiskers denote the 5th and 95th percentile.

**Figure 7.**Spatial distribution of the number of convective cells; (

**a**) observation, (

**b**) simulation, (

**c**) relative difference CCLM—radar.

**Figure 8.**Diurnal cycle of convection; (

**a**) cell number at cell initiation (every cell is counted once), (

**b**) cell number at each individual time step (cells are counted multiple times, according to their lifetime), and (

**c**) mean intensity of all cells at a certain point in time.

**Figure 9.**Dependence of the diurnal cycle of cell initiation. (

**a**) Cells originating over terrain with an elevation <400 m. (

**b**) Cells originating over terrain with an elevation >400 m.

**Figure 10.**Temperature scaling of cell characteristics. (

**a**) Spatial and temporal mean intensity of cells, (

**b**) total precipitation, (

**c**) lifetime, and (

**d**) maximum area. Shaded areas denote the uncertainty range estimated by repeatedly calculating the respective quantile using bootstrapping. Note the logarithmic y-axis in all panels.

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**MDPI and ACS Style**

Purr, C.; Brisson, E.; Ahrens, B. Convective Shower Characteristics Simulated with the Convection-Permitting Climate Model COSMO-CLM. *Atmosphere* **2019**, *10*, 810.
https://doi.org/10.3390/atmos10120810

**AMA Style**

Purr C, Brisson E, Ahrens B. Convective Shower Characteristics Simulated with the Convection-Permitting Climate Model COSMO-CLM. *Atmosphere*. 2019; 10(12):810.
https://doi.org/10.3390/atmos10120810

**Chicago/Turabian Style**

Purr, Christopher, Erwan Brisson, and Bodo Ahrens. 2019. "Convective Shower Characteristics Simulated with the Convection-Permitting Climate Model COSMO-CLM" *Atmosphere* 10, no. 12: 810.
https://doi.org/10.3390/atmos10120810