# Spatial Characteristics of Deep-Developed Boundary Layers and Numerical Simulation Applicability over Arid and Semi-Arid Regions in Northwest China

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Method for Determining Boundary Layer Height

_{v}is potential temperature, u and v are component wind speeds, b is constant, ${u}_{*}$ is surface friction velocity. Since ${u}_{*}$ cannot be obtained from the reanalysis data, set b = 0 and thus ignore the effects of surface friction, and its effect is much less than the bulk shear term in the denominator [28]. The ground wind speed is set to 0 and the critical value of Ri is defined as 0.25 (Ri0.25); that is, the height z when Ri(z) is greater than 0.25 for the first time is the boundary layer height [13].

#### 2.3. Scope of Research and Representative Regions

#### 2.4. Numerical Model

## 3. Characteristics of Atmospheric Boundary Layer Height in Arid and Semi-Arid Regions

#### 3.1. Monthly Variation of Atmospheric Boundary Layer Height

#### 3.2. Deep-Developed Boundary Layer Height in Daytime

## 4. Spatial Distribution and Weather Influence

#### 4.1. Spatial Distribution of Atmospheric Boundary Layer Height

#### 4.2. Weather Influence on Atmospheric Boundary Layer Development

## 5. Numerical Simulation on Deep-Developed Boundary Layer Height

#### 5.1. Experimental Design

#### 5.2. Simulation Results

_{s}is the appropriate temperature near the surface, θ

_{va}is the virtual potential temperature at the lowest model level, U(h) is the horizontal wind speed at h, and θ

_{v}(h) is the virtual potential temperature at h. When Ri

_{b}= Ri

_{cri}(critical bulk Richardson number), the corresponding h is the boundary layer height, Ri

_{cri}= 0.25 in stable conditions and Ri

_{cri}= 0 in unstable conditions. The temperature near the surface is defined as θ

_{s}= θ

_{va}+ θ

_{T},

_{T}is the virtual temperature excess near the surface and w

_{s}is the mixed-layer velocity scale. The virtual heat flux from the surface is ${(\overline{{w}^{\prime}{\theta}_{v}^{\prime}})}_{0}$ and the proportionality factor b is set as 7.8. First, h is estimated by the bulk Richardson number without considering the thermal excess θ

_{T}(θ

_{s}= θ

_{va}). This estimated h is utilized to compute w

_{s}and θ

_{T}. Using ws and θ

_{T}, h is enhanced. Ri

_{cri}= 0 eliminates the excessive boundary layer height calculated when there is a certain large wind speed. The ACM2 scheme [35] also uses the Richardson number to compute the boundary layer height. For stable conditions:

_{v}(h) is the virtual potential temperature, z

_{1}is the height of the lowest model level, and ${\overline{\theta}}_{v}$ is the average virtual potential temperature between the layer 1 and h. For unstable conditions, first the top of the convectively unstable layer (z

_{mix}) is found as the height at which

_{v}(z

_{1}) is the potential temperature at the lowest model level, ${(\overline{{w}^{\prime}{\theta}_{v}^{\prime}})}_{0}$ is the sensible heat fluxes from the surface, w

_{m}is the scale of convective velocity. Second, calculation of the boundary layer height is based on the Richardson number:

_{v}is the potential temperature, θ

_{s}is the potential temperature at the surface, and U is the horizontal wind speed. The corresponding h is the boundary layer height when Ri

_{b}= Ri

_{cri}= 0.25. Due to the different value of Ri

_{cri}in the unstable layer between the YSU scheme and the ACM2 scheme, the result of the ACM2 scheme is slightly higher than the YSU scheme. The MYJ scheme [36] defines the height at which the turbulence intensity drops to a critical value of 0.001 m

^{2}s

^{−2}as the boundary layer height. The MYJ scheme is more suitable for stabilizing the boundary layer and the weak and unstable boundary layer, so the simulation effect on the deep convective boundary layer is poor.

_{3}, CO

_{2}, O

_{2}, cloud and aerosols. The radiation reaching the ground directly determines the near-surface energy conditions and the release of surface sensible heat and latent heat [46]. The absorbed energy at the surface is not only dependent on solar radiation transmission, but also closely related to CO

_{2}, water vapor, and O

_{3}in the atmosphere. Strong absorption of radiation by CO

_{2}and O3 is also an important source of atmospheric energy and power [47]. The Goddard scheme deals more with CO

_{2}than the Dudhia scheme. The flux reduction caused by CO

_{2}can be obtained from the pre-calculated table, which also considers O

_{3}which is not considered in the Dudhia scheme. This makes the energy obtained from the low-level atmosphere simulated by the Dudhia scheme slightly smaller than that of the Goddard scheme. The simulated boundary layer height is also slightly lower than that of the Goddrad scheme.

## 6. Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scope of research and each representative region’s topography, and a grid point data range diagram. 1: Dunhuang, 2: Jiuquan (Suzhou District), 3: Minqin, 4: Yuzhong, and 5: Lanzhou (urban). The red dots indicate the location of the sounding station. The red boxes indicate the grid point data range of the ERA-Interim (ECMWF Reanalysis data, ECMWF: European Centre for Medium-Range Weather Forecasts) mode level product.

**Figure 2.**Monthly variation of the boundary layer height, four times per day, in the five representative areas: (

**a**) Dunhuang, (

**b**) Jiuquan (Suzhou District), (

**c**) Minqin, (

**d**) Yuzhong, and (

**e**) Lanzhou. For the low atmospheric boundary layer height (Pblh) at 08:00 and 02:00 BJT, a non-equidistant Y-axis is used in the figure).

**Figure 3.**Hourly variation of the boundary layer height over Dunhuang in monthly averages in April, July, October, 2016 and January, 2017.

**Figure 4.**The spatial distribution of the atmospheric boundary layer height at 14:00 BJT, over Gansu province in northwest China, in four seasons of 2016: (

**a**) spring, (

**b**) summer, (

**c**) autumn, and (

**d**) winter. The five rectangles labeled 1–5 stand for the area positions of Dunhuang, Jiuquan, Minqin, Yuzhong and Lanzhou, respectively.

**Figure 5.**The spatial distribution of the atmospheric boundary layer height at four times in the summer of 2016 over Gansu province in northwest China. (

**a**) 08:00 BJT, (

**b**) 14:00 BJT, (

**c**) 20:00 BJT, and (

**d**) 02:00 BJT. The five rectangles labeled 1–5 stand for the area position of Dunhuang, Jiuquan, Minqin, Yuzhong and Lanzhou, respectively.

**Figure 6.**Variation in the monthly average of maximum height differences four times per day (Unit: m).

**Figure 7.**Triple nesting of simulation area: (

**a**) Dunhuang, (

**b**) Jiuquan, (

**c**) Minqin, (

**d**) Yuzhong and Lanzhou. The simulation time is from 00:00 BJT on 3 June 2016, to 00:00 BJT on 4 June 2016. During the simulation period, there are relatively deep-developed boundary layers in all five regions. The height of the boundary layer at 14:00 BJT was 4291 m in Dunhuang, 3618 m in Jiuquan, 4355 m in Minqin, 3079 m in Yuzhong, and 3172 m in Lanzhou.

**Figure 8.**Numerical simulation of Dunhuang using different combinations of parameterization schemes and calculation of boundary layer heights with ERA-Interim model level data from 16:00 on 2 June 2016, to 16:00 on 3 June 2016.

**Figure 9.**Numerical simulation of Jiuquan using different combinations of parameterization schemes and calculation of boundary layer heights with ERA-Interim model level data from 16:00 on 2 June 2016, to 16:00 on 3 June 2016.

**Figure 10.**Numerical simulation of Minqin using different combinations of parameterization schemes and calculation of boundary layer heights with ERA-Interim model level data from 16:00 on 2 June 2016, to 16:00 on 3 June 2016.

**Figure 11.**Numerical simulation of Yuzhong using different combinations of parameterization schemes and calculation of boundary layer heights with ERA-Interim model level data from 16:00 on 2 June 2016, to 16:00 on 3 June 2016.

**Figure 12.**Numerical simulation of Lanzhou using different combinations of parameterization schemes and calculation of boundary layer heights with ERA-Interim model level data from 16:00 on 2 June 2016, to 16:00 on 3 June 2016.

**Table 1.**Correlation between daily boundary layer height and temperature in each representative region.

Temperature | Dunhuang | Jiuquan | Minqin | Yuzhong | Lanzhou |
---|---|---|---|---|---|

08:00 BJT | 0.193 ** | 0.24 ** | 0.325 ** | 0.247 ** | 0.213 ** |

14:00 BJT | 0.802 ** | 0.749 ** | 0.757 ** | 0.629 ** | 0.654 ** |

20:00 BJT | 0.762 ** | 0.658 ** | 0.535 ** | 0.5 ** | 0.531 ** |

02:00 BJT | 0.158 ** | −0.024 | 0.209 ** | 0.159 ** | 0.093 * |

≥4000 m | 3000–4000 m | 2000–3000 m | 1000–2000 m | <1000 m | ||
---|---|---|---|---|---|---|

Dunhuang | Spring | 6 | 22 | 35 | 29 | 0 |

Summer | 13 | 35 | 32 | 10 | 2 | |

Autumn | 2 | 10 | 18 | 51 | 10 | |

Winter | 0 | 0 | 3 | 33 | 54 | |

Jiuquan | Spring | 2 | 19 | 32 | 39 | 1 |

Summer | 6 | 30 | 30 | 20 | 6 | |

Autumn | 1 | 9 | 23 | 43 | 15 | |

Winter | 0 | 0 | 3 | 27 | 60 | |

Minqin | Spring | 7 | 21 | 32 | 29 | 3 |

Summer | 13 | 26 | 35 | 17 | 1 | |

Autumn | 2 | 10 | 16 | 48 | 15 | |

Winter | 0 | 1 | 2 | 33 | 54 | |

Yuzhong | Spring | 2 | 6 | 23 | 53 | 8 |

Summer | 2 | 9 | 34 | 37 | 10 | |

Autumn | 0 | 1 | 10 | 46 | 34 | |

Winter | 0 | 0 | 0 | 30 | 60 | |

Lanzhou | Spring | 2 | 5 | 22 | 56 | 7 |

Summer | 2 | 10 | 36 | 32 | 12 | |

Autumn | 0 | 0 | 11 | 47 | 33 | |

Winter | 0 | 0 | 0 | 31 | 59 |

**Table 3.**Statistics of days of different weather and total cloud cover (Unit: 1) in the three areas from June to September 2016.

June | July | August | September | ||
---|---|---|---|---|---|

Dunhuang | sunny days | 12 | 14 | 4 | 14 |

precipitation, cloudy and overcast days | 18 | 17 | 27 | 16 | |

monthly average of the total cloud amount | 4.81 | 4.76 | 6.36 | 3.89 | |

Jiuquan | sunny days | 10 | 16 | 4 | 15 |

precipitation, cloudy and overcast days | 20 | 15 | 27 | 15 | |

monthly average of the total cloud amount | 5.53 | 5.26 | 7.21 | 4.48 | |

Minqin | sunny days | 24 | 19 | 14 | 20 |

precipitation, cloudy and overcast days | 6 | 12 | 17 | 10 | |

monthly average of the total cloud amount | 6.28 | 5.38 | 7.12 | 5.51 |

**Table 4.**Combinations of parameterization schemes for simulation [33].

Serial Number | Shortwave Radiation Scheme | Land Surface Scheme | Atmospheric Boundary Layer Scheme/Surface Layer Scheme |
---|---|---|---|

01 | Dudhia | Noah | YSU/Monin–Obukhov |

02 | MYJ/MYJ Monin–Obukhov | ||

03 | ACM2/Monin–Obukhov | ||

04 | SLAB | YSU/Monin–Obukhov | |

05 | MYJ/MYJ Monin–Obukhov | ||

06 | ACM2/Monin–Obukhov | ||

07 | RUC | YSU/Monin–Obukhov | |

08 | MYJ/MYJ Monin–Obukhov | ||

09 | ACM2/Monin–Obukhov | ||

10 | Goddard | Noah | YSU/Monin–Obukhov |

11 | MYJ/MYJ Monin–Obukhov | ||

12 | ACM2/Monin–Obukhov | ||

13 | SLAB | YSU/Monin–Obukhov | |

14 | MYJ/MYJ Monin–Obukhov | ||

15 | ACM2/Monin–Obukhov | ||

16 | RUC | YSU/Monin–Obukhov | |

17 | MYJ/MYJ Monin–Obukhov | ||

18 | ACM2/Monin–Obukhov |

**Table 5.**The average value of the bias of the simulation results for each parametric scheme from 4:00 to 10:00 on 3 June (Unit: m).

Dunhuang | Jiuquan | Minqin | Yuzhong | Lanzhou | |
---|---|---|---|---|---|

shortwave radiation scheme | 543 | 564 | 205 | 213 | 377 |

atmospheric boundary layer scheme | 1255 | 972 | 1228 | 1202 | 1351 |

land surface scheme | 678 | 272 | 568 | 516 | 532 |

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**MDPI and ACS Style**

Ma, M.; Tan, Z.; Ding, F.; Chen, Y.; Yang, Y. Spatial Characteristics of Deep-Developed Boundary Layers and Numerical Simulation Applicability over Arid and Semi-Arid Regions in Northwest China. *Atmosphere* **2019**, *10*, 195.
https://doi.org/10.3390/atmos10040195

**AMA Style**

Ma M, Tan Z, Ding F, Chen Y, Yang Y. Spatial Characteristics of Deep-Developed Boundary Layers and Numerical Simulation Applicability over Arid and Semi-Arid Regions in Northwest China. *Atmosphere*. 2019; 10(4):195.
https://doi.org/10.3390/atmos10040195

**Chicago/Turabian Style**

Ma, Minjin, Ziyuan Tan, Fan Ding, Yue Chen, and Yi Yang. 2019. "Spatial Characteristics of Deep-Developed Boundary Layers and Numerical Simulation Applicability over Arid and Semi-Arid Regions in Northwest China" *Atmosphere* 10, no. 4: 195.
https://doi.org/10.3390/atmos10040195