# Assessing Peak-To-Mean Ratios of Odour Intensity in the Atmosphere near Swine Operations

^{*}

## Abstract

**:**

## 1. Introduction

_{p}) during a short time interval (t

_{p}) from the mean concentration (C

_{m}) over a long time interval (t

_{m}):

_{p}= peak concentration;

_{m}= mean concentration;

_{p}= averaging time for peak concentration (short-term);

_{m}= averaging time for mean concentration (long-term);

_{x}= peak-to-mean ratio of concentration at distance x from source;

_{l}= γ/g;

_{p}= peak odour intensity;

_{m}= mean odour intensity.

## 2. Experiment

#### 2.1. Description of Study Sites

#### 2.2. Odour Measurement Grid

#### 2.3. Selection and Training of Field Human Odour Sniffers

#### 2.4. Field Odour Intensity Measurement Procedure

#### 2.5. Meteorological Condition Monitoring

#### 2.6. Data Analysis

_{m}). In the context of odour dispersion modelling, the peak value is estimated from a long-term average value by using empirical equations, such as Equation (1). This estimated peak value is commonly used to define the acceptable odour level. However, researchers are still debating the definition of the peak value [8]. In the current study, the peak intensity value (I

_{p}) was defined as the 90th percentile of measured odour intensity values during the time period of interest [8], which was calculated to be I

_{p}= 4.0 in this example. Therefore, the PMR_OI in this example was calculated to be PMR_OI = I

_{p}/I

_{m}= 4.0/1.6 = 2.5. In addition, 14 zero values (no odour) were reported, based on which the intermittency was calculated to be η = (1 − 14/31) = 0.548 (or 54.8%). The conditioned mean odour intensity, defined as the mean of the non-zero readings [4], was calculated to be 2.9 and the 90th percentile 5.0. Therefore, the corresponding conditioned peak-to-mean ratio (CPMR_OI) was determined to be 5.0/2.9 = 1.7.

## 3. Results and Discussion

#### 3.1. Preliminary Test

#### 3.2. Intermittency

#### 3.3. Peak-To-Mean Ratio of Odour Intensity

#### 3.3.1. PMR_OI versus CPMR_OI

#### 3.3.2. Variation of PMR_OI with Distance to the Odour Source

^{*}= peak-to-mean ratio of odour intensity as a function of intermittency;

_{i}= a reading of odour intensity at a time point;

^{*}, all zero I

_{i}values are included in the calculation. If the zeros are excluded, the conditioned mean I

_{m,c}is obtained. Given that the difference between the “true” odour intensity mean I

_{m}and the conditioned mean I

_{m,c}is due to the intermittency, it is reasonable to assume that the mean was proportional to the intermittency and the conditioned mean, that is, I

_{m}= ληI

_{m,c}. The PMR_OI

^{*}is now calculated as

_{m,c}= conditioned mean intensity (the mean of non-zero readings);

_{p}and I

_{m,c}are independent of intermittency, it was further assumed that they both follow a similar exponential decay pattern in the atmosphere as the distance to the source increases (due to dilution):

^{*}increases as the intermittency decreases. The intermittency η decreases with distance x (Table 3), and therefore, PMR_OI

^{*}increases with distance. It should be noted that at longer distances, the actual odour levels were much lower even though the PMR_OI was higher. Taking the measurement session of August 5 as an example (the measurements of other dates had similar patterns), the PMR_OI was 1.8, 3.1, and 6.1 for 100, 500, and 1000 m, respectively, while the measured peak odour intensity was 6.0, 2.0, and 1.0 at the three distances, respectively (Figure 8).

#### 3.3.3. Effect of Wind Direction on PMR_OI

#### 3.3.4. Effect of Atmospheric Stability on PMR_OI

#### 3.3.5. Effect of Averaging Time on PMR_OI

_{m}/t

_{p})

^{q}, was used to predict the PMR_OI from the time ratio (t

_{m}/t

_{p}). To evaluate the exponent q in the equation, the PMR_OI was plotted against (t

_{m}/t

_{p}) in the log–log scale and the exponent q was determined as the slope of the regression line (Table 4). The exponent q decreased from 0.33 for stability class B (unstable) to 0.19 for E (slightly stable). The measured exponent values were lower than those reported in the literature for unstable atmosphere conditions. Smith [13] gave the following q-values for three stability classes: 0.65 (stability class B), 0.52 (C), and 0.35 (D). Duffee et al. [27] reported values of q being 0.50 for stability class A or B, 0.33 for C, 0.20 for D, and 0.17 for E and F.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Grid for odour measurement in the field, with the positions of 15 human assessors denoted as 1–1 to 3–5 at 0°, 30°, and 45° from the wind direction at 100, 500, and 1000 m from the odour source.

**Figure 4.**A sample of field odour intensity measurements reported by human assessors in a 30 min sniffing session at: (

**a**) 100 m, (

**b**) 500 m, and (

**c**) 1000 m from odour source (August 5, Session 2).

**Figure 5.**Intermittency measured along the wind direction at 100, 500, and 1000 m from odour source (bar: standard deviation).

**Figure 6.**Frequency distribution of the peak-to-mean ratio of odour intensity along the wind direction at 100, 500, and 1000 m from the odour source. (

**a**) PMR_OI (true peak-to-mean ratio of odour intensity) and (

**b**) CPMR_OI (conditioned peak-to-mean ratio).

**Figure 7.**Comparison of measured PMR_OI (peak-to-mean ratio of odour intensity) and CPMR_OI (conditioned peak-to-mean ratio of odour intensity) (30 min averaging time) along the wind direction at 100, 500, and 1000 m from odour source (bar: standard deviation).

**Figure 8.**Variations of the PMR_OI (30 min averaging time) and odour intensity with distance from the odour source.

**Figure 9.**Comparison of measured PMR_OIs (30 min averaging time) between 0° (along the wind direction) and 45° from wind direction at 100, 500, and 1000 m from the odour source.

**Figure 10.**Measured PMR_OI for 30 min averaging time under different stability classes (B, C, D, and E) at 100, 500, and 1000 m from the odour source.

**Figure 11.**Variation of the PMR_OI with the time ratio (t

_{m}/t

_{p}) at 1000 m from the odour source under different atmospheric stability classes (B1, C1, D1, and E1 are curves predicted by the equation PMR_OI = (t

_{m}/t

_{p})

^{q}for stability classes B, C, D, and E, respectively).

**Table 1.**ASTM standard 8 point n-butanol odour intensity reference scale [18].

N-Butanol in Water (ppm) | 0 | 120 | 240 | 480 | 960 | 1940 | 3880 | 7750 | 15,500 |
---|---|---|---|---|---|---|---|---|---|

Intensity level | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Stability Class | Number of Sessions |
---|---|

A | 2 |

B | 25 |

C | 12 |

D | 6 |

E | 5 |

**Table 3.**Comparison of intermittency between the along-wind (0°) condition and 45° from the wind direction.

Distance from Source (m) | Direction from Wind (°) | Averaging Time (Minutes) | |||
---|---|---|---|---|---|

1 | 5 | 10 | 30 | ||

100 | 0° | 75% | 80% | 83% | 85% |

45° | 70% | 74% | 77% | 77% | |

500 | 0° | 42% | 61% | 83% | 87% |

45° | 35% | 51% | 65% | 74% | |

1000 | 0° | 17% | 33% | 50% | 57% |

45° | 13% | 21% | 35% | 42% |

**Table 4.**Results of the regression for log(PMR_OI) = q log(t

_{m}/t

_{p}) for different stability classes.

Stability Class | Slope (Exponent) q (SE *) | R^{2} |
---|---|---|

B | 0.33 (0.031) | 0.85 |

C | 0.28 (0.030) | 0.79 |

D | 0.27 (0.032) | 0.75 |

E | 0.19 (0.011) | 0.94 |

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Zhang, Q.; Zhou, X. Assessing Peak-To-Mean Ratios of Odour Intensity in the Atmosphere near Swine Operations. *Atmosphere* **2020**, *11*, 224.
https://doi.org/10.3390/atmos11030224

**AMA Style**

Zhang Q, Zhou X. Assessing Peak-To-Mean Ratios of Odour Intensity in the Atmosphere near Swine Operations. *Atmosphere*. 2020; 11(3):224.
https://doi.org/10.3390/atmos11030224

**Chicago/Turabian Style**

Zhang, Qiang, and Xiaojing Zhou. 2020. "Assessing Peak-To-Mean Ratios of Odour Intensity in the Atmosphere near Swine Operations" *Atmosphere* 11, no. 3: 224.
https://doi.org/10.3390/atmos11030224