# A Review of Techniques for Diagnosing the Atmospheric Boundary Layer Height (ABLH) Using Aerosol Lidar Data

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## Abstract

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## 1. Introduction

## 2. Classical Methodologies for Lidar Measurement of ABLH

#### 2.1. Visual Inspection (or Ocular Estimate)

#### 2.2. Thereshold Method

#### 2.3. Gradient Method (GMs)

#### 2.4. Ideal Profile Fitting (Curve Fitting) (FIT)

#### 2.5. Wavelet Covariance Transform (WCT)

#### 2.6. Variance (or Standard Deviation) Analysis (VAR or STD)

## 3. Improvement of Some Classical Methodologies

#### 3.1. The Combination of GM and VAR

- For RSCS profile with time resolution of 60 s, the single $G{S}_{i}$ and $Va{r}_{i}$ profiles provide single evaluations of the MLH (for 1.5 h measurement, $i$ goes from 1 to 90), the moving variance analysis is applied to each $i$-profile within the temporal interval $\left[i-N/2,i+N/2\right]$,$N=10$.
- An average signal gradient profile and a variance profile are calculated over a time interval of 30 min, named $\overline{GS}$ and $\overline{Var}$. The reference height (${h}_{ref}$) is defined as the middle position of the heights of the $\overline{GS}$ minimum and the $\overline{Var}$ maximum, the related error is ${\sigma}_{ref}=\sqrt{{\sigma}_{\overline{GS}}^{2}+{\sigma}_{\overline{Var}}^{2}}$, where the standard deviations of $\overline{GS}$ and $\overline{Var}$ are calculated over the 30 min average at ${h}_{ref}$.
- For $i=1$, within a vertical range ${h}_{j}\in \left[0.85\left({h}_{ref}-{\sigma}_{ref}\right)-1.15\left({h}_{ref}+{\sigma}_{ref}\right)\right]$, $CBL{H}_{1}$ is determined as the middle position of the local minimum of $G{S}_{1}$ and local maximum of the $Va{r}_{1}$.
- For $i=2,30$, within the vertical range ${h}_{j}\in \left[0.85\left(CBL{H}_{i-1}-{\sigma}_{CBL{H}_{i-1}}\right)-1.15\left(CBL{H}_{i-1}-{\sigma}_{CBL{H}_{i-1}}\right)\right]$, the $CBL{H}_{i}$ is determined as the middle position of the local minimum of $G{S}_{i}$ and local maximum of the $Va{r}_{i}$. For next time window ($i=31,60$), procedures 2 to–4 are repeated, a simple scheme for THT algorithm is shown as Figure 10.

#### 3.2. The Combination of Thereshold Method and WCT

#### 3.3. The Combination of FIT and WCT

#### 3.4. 2D Version of Structure of the Atmosphere (STRAT-2D)

_{large}, MLH

_{second}) and the lowest gradient height (MLH

_{low}). The MLH is defined as one of the determined three minimum gradient heights at which the signal gradient is larger than a fixed threshold or it has neighbor value larger than the threshold (for details see Haeffelin et al. [116]).

#### 3.5. Height Restriction for Some Classical Methodologies

## 4. New Techniques Developed Recently

#### 4.1. New Techniques Based on Single-Wavelength Lidar

#### 4.2. ABLH Determination from Multi-Walelength Lidar

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A simplified scheme of diurnal cycle of atmospheric boundary layer (ABL) in clear-sky situations (adapted from Stull [1]). Solid line marks the height of ABL (ABLH), the dashed line marks the top of residual layer (RL). The entrainment process near the top of ABL is marked by the dashed arrows. SBL, stable boundary layer; CBL, convective boundary layer; EZ, entrainment zone; RL, residual layer; EMT, early morning transition; EET, early evening transition.

**Figure 2.**Principle vertical profiles of some variables for the well mixed boundary layer during daytime (

**left**), and the more stable nocturnal boundary layer with shallow surface mixing layer, residual aerosol layer and the above free atmosphere layer (

**right**) (adapted from Stull [1]).

**Figure 3.**A case at 12:00 UTC on 10 September 2010 over SACOL (Semi-Arid Climate Observatory and Laboratory, in China). (

**a**) the profiles of lidar range-squared-corrected signal (RSCS, black solid line), first derivative (red solid line), second derivative (blue solid line), the logarithm gradient (orange solid line) and the cubic root gradient (green solid line) of RSCS provided by a micro-pulse lidar (MPL), the respectively determined ABLH are named as h(GM), h(IPM), h(LGM), h(CRGM), (

**b**) the profiles of potential temperature (red profile) and the specific humidity (black profile) at a nearby radiosonde site with the CBLH determined by the theta-gradient method (h(PT)).

**Figure 5.**(

**a**) RSCS profile with the shapes of HAAR wavelet (HAAR) and the Mexican-Hat wavelet (MHAT), the resulting covariance transform for (

**b**) HAAR and (

**c**) MHAT at various values of the dilation at 06:00 UTC on 10 September 2010 over SACOL.

**Figure 6.**The wavelet variance, ${D}^{2}\left(a\right)$, of HAAR (

**a**) and MHAT (

**b**) as described in Equation (13), for the RSCS profile in Figure 5.

**Figure 7.**(

**a**) 31 vertical RSCS profiles between 05:15-05:45 UTC (1 min interval) on 10 September 2010 over SACOL, (

**b**) vertical profile of temporal variance (VAR).

**Figure 8.**Time-height cross-section of the RSCS provided by the MPL over SACOL, with height directly determined from first-order gradient method (GM), HAAR/MHAT wavelet covariance transform, and ideal profile fitting (CFM) on 28 July 2007 and on 12 June 2007.

**Figure 9.**Flowchart for the combination of the VAR and GM in Hennemuth and Lammert [42].

**Figure 10.**Synopsis of the temporal-height tracking (THT) algorithm in Martucci et al. [119]. The profiles of the $\overline{GS}$ and $\overline{Var}$ are averaged over the interval 30 min, for $i=1,30$, profile of the $G{S}_{i}$ is the single signal gradient profile at $i$ step, $Va{r}_{i}$ is calculated by the moving variance within the temporal interval $\left[i-N/2,i+N/2\right]$, $N=10$.

**Figure 11.**Flowchart for the combination of the STRAT-2D (structure of the atmosphere, 2D version) and VAR in Pal et al. [7].

**Table 1.**Some Measurements for ABLH (ABLH, atmospheric boundary layer height; CBL, convective boundary layer; SNR, signal-to-noise ratio).

Measurements | Observations | Advantages | Shortcomings | Examples of References |
---|---|---|---|---|

Radiosoundings | ||||

Radiosonde | Temperature Pressure Humidity Wind | - widely distributed all over the world
- long observation history, suited for ABLH climatology studying
- providing the most accurate information of the troposphere
| - infrequently, only 2–4 times per day
- in-situ observation, sparse spatial coverage
| Norton and Hoidale (1976) Cooper et al. (1994) Seidel et al. (2010) Guo et al. (2016) |

Tethered balloons | Turbulence Trace gas concentration | - turbulence measurements possible
- the ascent velocity can be controlled according to the desired resolution
| - high cost
- limited to field campaigns with manned operation
- limited measurement range
- inapplicable in case of high wind speed or strong convection
| Moores et al. (1979) Vernekar et al. (1991) Holden et al. (2000) |

Aircraft | Turbulence Temperature Humidity Wind | - simultaneous measurements of mean and turbulent quantities
- high sampling rate
| - high cost
- limited to field campaigns
- the lowest observation height (or flight level) is restricted (security)
| Galmarini and Attié (2000) Dai et al. (2011) Dai et al. (2014) |

Remote sensing | ||||

Sodar | Heat flux Temperature Mean Wind Vertical velocity Velocity-variance | - a simple and less expensive remote sensing system
- continuously operated in an unattended mode
- high temporal and vertical resolutions
- to define the height of any elevated temperature inversion layer
| - limited vertical observation range, a few hundred meters to 1 km
- reduced data availability in special weather situations (near-perfectly adiabatically stratified CBL in the afternoon)
- interpretation of the remotely-sensed structures sometimes ambiguous
| Beyrich and Weill (1993) Beyrich (1997) Lokoshchenko (2002) Emeis et al. (2004) Helmis et al. (2012) |

Microwave radiometer | Brightness temperature | - providing good estimate of temperature and humidity in the lower troposphere with high temporal resolution
| - the vertical resolution decreases with altitude
- poor data quality in cloudy and rainy conditions
| Crewell et al. (2007) Cimini et al. (2013) Saeed et al. (2015) Liu et al. (2015) |

Wind profiling radar | Humidity Turbulence | - continuous operation
- high temporal and vertical resolutions
- high sampling rate
| - expensive
- invalid data at the lowest range, unable to resolve shallow ABL
- limited vertical resolution
- the SNR easily influenced by several factors such as birds and insects.
- inapplicable when the signal is dominated by rain or snow
| White et al. (1991) Angevine (2000) Bianco et al. (2002) |

Lidar | Aerosols Wind speed Humidity | - continuous operation in an almost automated status
- high temporal resolution and wide vertical spatial coverage
- a great number of aerosol lidars deployed and established networks all over the world
| - expensive
- limited data quality near surface because of the blind zone
- easily being interfered by multiple aerosol layers or cloud layers
| Steyn et al. (1999) Davis et al. (2000) Sawyer and Li (2013) Pal et al. (2013) Toledo et al. (2017) |

Methods | Advantages | Shortcomings | Examples of References |
---|---|---|---|

Visual inspection (Ocular estimate) | - simple
| - subjective
- visual error
- inability to process large volumes of lidar data automatically or efficiently
| Flamant et al. (1997) |

Threshold method | - simple
- less subjective than ocular estimate
| - difficult to define an appropriate and universal threshold
- interfered by multiple layers such as cloud layer and RL
- require subjective check
| Melfi et al. (1985) Dupont et al. (1994) Frioud et al. (2003) |

Gradient methods:
- First-order gradient
- inflection point(second derivative)
- logarithm gradient
- cubic root gradient
| - objective
- low computation cost
| - sensitive to noisy data
- interfered by multiple layers such as cloud layer and RL
- averaging may be required to improve signal-to-noise ratio
| Hayden et al. (1997) Sicard et al. (2006) Menut et al. (1999) Senff et al. (1996) |

Ideal profile fitting (curve fitting) | - using the entire vertical backscatter profile
- less sensitive to signal local structures
| - not suitable in cases of clean, near-surface air overlain by aerosol laden air
- relatively rich computation
| Steyn et al. (1999) Eresmaa et al. (2005) |

Wavelet covariance transform | - requires little prior information about the atmosphere or the lidar
- automated detection
| - interfered by multiple layers such as cloud layer and RL
- an appropriate dilation of the wavelet is critical
| Mallat et al. (1992) Gamage and Hagelberg (1993) Brooks et al. (2003) Cohn and Angevine (2000) Davis et al. (2000) Morille et al. (2007) Moreira et al. (2014) |

Variance (or Standard Deviation) analysis | - less sensitive to transient signal noise
| - sensitive to number of profiles for variance calculating
- only suitable for daytime CBL
- resulted ABLH with lower temporal resolution
| Piironen and Eloranta (1995) Menut et al. (1999) |

**Table 3.**Improved versions of some classical methodologies in Table 2 (GM, gradient method; VAR, variance analysis; WCT, wavelet covariance transform; FIT, ideal profile fitting).

Methods | Steps | Main Shortcomings | Examples of References |
---|---|---|---|

Combination of GM and VAR | - variance analysis providing average reference height
- gradient analysis on signal profile around the reference height
| - only suitable for daytime CBL
| Lammert (2004) Martucci et al. (2010) |

Combination of threshold method and WCT | - threshold definition
- finding the altitude where the wavelet covariance exceeds the threshold
| - universal lack of the determined thresholds
| Baars et al. (2008) |

Combination of FIT and WCT | - wavelet covariance analysis providing first guess of ABLH for curve fitting
- ABLH determination by the curve fitting
| - relatively high computation cost
| Sawyer and Li (2013) |

2-D structure of the atmosphere (START-2D) | - determination of the altitudes of 3 major aerosol gradients and the cloud base heights by START-2D
- define one of the determined aerosol gradient heights as the ABLH through considering the temporal continuity or variance analysis
| - other assistant methods such as threshold method is required
| Morille et al. (2007) Haeffelin et al. (2012) Pal et al. (2013) |

Height restriction for some classical methodologies | - determination of upper limit height
- ABLH determination below the height
| - the subjective or statistical height threshold lacks universality
| Yang et al. (2013) Li et al. (2017) Dang et al. (2019) |

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Dang, R.; Yang, Y.; Hu, X.-M.; Wang, Z.; Zhang, S.
A Review of Techniques for Diagnosing the Atmospheric Boundary Layer Height (ABLH) Using Aerosol Lidar Data. *Remote Sens.* **2019**, *11*, 1590.
https://doi.org/10.3390/rs11131590

**AMA Style**

Dang R, Yang Y, Hu X-M, Wang Z, Zhang S.
A Review of Techniques for Diagnosing the Atmospheric Boundary Layer Height (ABLH) Using Aerosol Lidar Data. *Remote Sensing*. 2019; 11(13):1590.
https://doi.org/10.3390/rs11131590

**Chicago/Turabian Style**

Dang, Ruijun, Yi Yang, Xiao-Ming Hu, Zhiting Wang, and Shuwen Zhang.
2019. "A Review of Techniques for Diagnosing the Atmospheric Boundary Layer Height (ABLH) Using Aerosol Lidar Data" *Remote Sensing* 11, no. 13: 1590.
https://doi.org/10.3390/rs11131590