# Fetch Effect on Flux-Variance Estimations of Sensible and Latent Heat Fluxes of Camellia Sinensis

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{n}) and soil heat flux (G) allow the derivation of latent heat flux (LE) as the residual of the energy balance equation. In this study, the Flux Variance method was investigated, and the results were compared against eddy covariance measurements. The specific goal of the present study was to assess the performance of the FV method for the estimation of surface fluxes along a variable fetch. Experiment was carried out in a tea garden; an EC system measured latent and sensible heat fluxes and five fine-wire thermocouples were installed towards the wind dominant direction at different distances (fetch) of TC

_{1}= 170 m, TC

_{2}= 165 m, TC

_{3}= 160 m, TC

_{4}= 155 m and TC

_{5}= 150 m from the field edge. Footprint analysis was employed to examine the effect of temperature measurement position on the ratio between 90% footprint and measurement height. Results showed a good agreement between FV and EC measurements of sensible heat flux, with all regression coefficients (R

^{2}) larger than 0.6; the sensor at 170 m (TC

_{1}), nearest to the EC system, had highest R

^{2}= 0.86 and lowest root mean square error (RMSE = 25 Wm

^{−2}). The estimation of LE at TC

_{1}was also in best agreement with eddy covariance, with the highest R

^{2}= 0.90. The FV similarity constant varied along the fetch within the range 2.2–2.4.

## 1. Introduction

## 2. Theory

#### 2.1. Flux Variance (FV) Method

^{−3}), c

_{p}is air specific heat capacity (J kg

^{−1}K

^{−1}), σ

_{T}is standard deviation of air temperature (K), C

_{T}is similarity constant, k is von Karman’s constant (k ≈ 0.41), g is gravitational acceleration (g = 9.81 m s

^{−2}), z is measurement height (m), d is zero-plane displacement (m) and $\overline{T}$ is mean air temperature (K).

#### 2.2. Footprint Analysis

_{a}), displacement height (d), mean wind speed (ms

^{−1}), Obukhov length (L), standard deviation of horizontal wind speed (ms

^{−1}), friction velocity (u

_{*}), and wind direction (°) [24,25,26,27]. The footprint model used for the estimation of the distance from which 90% of the measured flux originated or the ratio of this distance to measurement height is expressed as Equation (5) [28]:

_{a}is the measurement height, and x

_{peak}is the peak location of the footprint distribution function, expressed as Equation (6):

_{u}is calculated as Equation (7):

_{o}is surface roughness length.

## 3. Materials and Methods

#### 3.1. Study Site and Climate Features

^{−1}. The mean air temperature (T

_{a}) was varied from 10 to 23 °C (Figure 1). The mean daily relative humidity (RH) for the whole duration was ranging from 30 to 70 % (Figure 1). The mean precipitation for the experiment period was 2.73 mm day

^{−1}.

#### 3.2. The Field Experiments

_{v}), were sampled and half-hourly averages were recorded on a CR3000 data logger.

_{1}= 170 m, TC

_{2}= 165 m, TC

_{3}= 160 m, TC

_{4}= 155 m and TC

_{5}= 150 m) from the field boundary (Figure 2a). A CR3000 data logger sampled thermocouples signals at 10 Hz.

_{n}) (W m

^{−2}). Soil heat flux (G) was measured using two soil heat flux plates installed at a depth of 0.08 m in the soil and four soil temperature sensors, placed in the soil layer, two above each plate, at depths of 0.02 and 0.06 m respectively [33]. Half-hourly averages of measured variables (R

_{n}, G, and soil temperature) were sampled and recorded on the CR3000 data logger. Dry batteries, charged by solar panels, were used as a power source.

#### 3.3. Evaluation Criteria

^{2}) Equation (8) [34], (b) the root mean square error (RMSE) Equation (9) [35] (c) Relative error (RE) Equation (10) [36]:

_{max}and Y

_{min}are the maximum and minimum estimated values from the FV method respectively.

#### 3.4. Possible Error Sources

## 4. Results and Discussion

#### 4.1. The Footprint of EC Flux Measurements

#### 4.2. Energy Balance Closure Analysis

_{n}− G), as shown in (Figure 5). The linear regression is Equation (11):

^{2}= 0.83 which supports the reasonable quality of flux data measured by the EC and used for the further analysis against the FV estimations. Although the energy balance closure is low, this result is in good agreement with previous studies, as in most of the literature the slope is ranged between (0.55–0.99) for open fields [38,39]. These results support the use of H

_{EC}measured by the EC system to calibrate the similarity constant (C

_{T}) of the FV method using Equation (1).

#### 4.3. Sensible Heat Flux Comparison

_{T}) that was adjusted to give the best agreement between H

_{FV}and H

_{EC}for each position separately.

_{FV}and H

_{EC}at 170 m from the field edge, with a slope of 0.94, a relatively high R

^{2}= 0.86, low RMSE = 25 Wm

^{−2}and relative error RE = 9.25%. All estimations at the other positions were also in good agreement with the measurements of the EC method, with R

^{2}always larger than 0.6. Some data points, especially in Figure 6b–e show a relatively high estimation of H

_{FV}as compared to H

_{EC}. The analysis showed that this occurred mainly in the later part of the day, from 15:00 to 16:00. The parameters of regressions between H

_{FV}and H

_{EC}flux estimates at the five positions are presented in Table 4 and plotted in Figure 7. Figure 7 clearly shows that R

^{2}increases, whereas RMSE decreases with increasing fetch. Hence, a larger fetch provides a better agreement between FV and EC sensible heat flux. This is presumably because with a larger fetch the surface layer becomes more developed and the FV approach, which is based on MOST, is more valid.

_{T}), estimated from the regression analysis between H measurements of the EC system and that estimated by the FV method using Equation (1). In the present study, the estimated C

_{T}was ranging between 2.2 and 2.4 (Table 4) with an average value of 2.3 [40]. Overall, it was observed from the study that the similarity constant was independent of the fetch.

^{2}and C

_{T}with fetch (Table 4) are qualitatively similar to those by Tanny et al [14] who studied the FV method in a screenhouse in which pepper was grown. In both studies, R

^{2}of the regression between H

_{EC}and H

_{FV}increased with fetch, indicating the spatial development process of the surface layer and the increasing validity of MOST with distance. The similarity constant obtained in the screenhouse by Tanny et al. [14] was about 3.8, significantly larger than the value obtained here of 2.3. This could be explained by the presence of the screened roof in Tanny et al.’s experiment, which presumably inhibited the development of the turbulence as compared to the open field studied here [14].

#### 4.4. Latent Heat Flux Estimation

_{FV}and measured LE

_{EC}, are presented in (Figure 8a–e).

^{2}varied from TC

_{1}to TC

_{5}along the fetch. The LE

_{FV}gave a good estimate of LE

_{EC}for all thermocouples and all the slopes were close to unity with RMSE always less than 45 Wm

^{−2}. The FV latent heat flux at TC

_{1}which was closest to the EC system and had the longest fetch yielded best results with a slope 0.95, lowest RMSE of 25.11 Wm

^{−2}, lowest RE of 4.73 %, and largest R

^{2}= 0.90, as compared to all other thermocouples. The performance of the LE

_{FV}, as indicated by RMSE, was improved as position changed and became closer to the EC system and with longer fetch. The overall estimates of LE

_{FV}, at all positions, were in good agreement with the measurements of the EC system.

## 5. Conclusions and Outlook

_{T}), estimated from the regression analysis between the H estimates of the FV and the measurements by the EC method, changed along the fetch, but a consistent trend was not observed, and it was concluded that the C

_{T}has a mean value of 2.3, and is independent of the fetch. The regression between the H

_{FV}and H

_{EC}for the TC

_{1}which is very close to the EC system and far from the field edge provided higher R

^{2}= 0.86 and lower RMSE = 25 Wm

^{−2}relative to the other thermocouples. In summary, the FV method proved to be a reliable method for the monitoring of surface fluxes at low cost as compared to the EC method.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Mean daily values of air temperature and relative humidity for the whole experimental period.

**Figure 2.**The experimental setup (

**a**) Schematic top view of the tea field with thermocouples positions (TC

_{1}…TC

_{5}) and EC system (Pic from google earth). (

**b**) Photo of the TC sensors distributed in the tea field along the prevailing wind direction. (

**c**) The EC system (Campbell Scientific, USA).

**Figure 3.**The wind rose presentation of wind direction and wind speed (m s

^{−1}) during the experiment period of Sept–Nov 2018. The prevailing wind direction of West-North-West is clearly observed.

**Figure 4.**Variation of half-hourly 90% footprint to measurement height ratio Equation (5) for two days one partly cloudy (27/11/2018) and the other with a clear sky (sunny day) (18/10/2018) [28].

**Figure 5.**Linear regression between the components of the energy balance closure based on the EC flux measurements.

**Figure 6.**(

**a**) Fetch of 170 m from field boundary; (

**b**) Fetch 165 m from the field boundary; (

**c**) Fetch of 160 m from field boundary; (

**d**) Fetch of 155 m from field boundary; (

**e**) Fetch of 150 m from field boundary. Regression analysis between the estimated H

_{FV}and measured H

_{EC}at five different positions along the fetch.

**Figure 8.**(

**a**) Fetch of 170 m from field boundary; (

**b**) Fetch of 165 m from field boundary; (

**c**) Fetch of 160 m from field boundary; (

**d**) Fetch of 155 m from field boundary; (

**e**) Fetch of 150 m from field boundary. Half-hourly LE

_{FV}derived by using Equation (12) plotted against LE

_{EC}for unstable conditions during Sep–Nov 2018.

Stability Condition | Obukhov Length (L) |
---|---|

Stable | 0 < L < 200 |

Unstable | −200 < L < 0 |

Neutral | |L| > 200 |

**Table 2.**Similarity constants (D and P) for different stability conditions [29].

D | P | Stability Condition |
---|---|---|

0.28 | 0.59 | Unstable |

0.97 | 1 | Natural |

2.44 | 1.33 | Stable |

Notation | Units | Height (m) | Equipment | |
---|---|---|---|---|

3D-Wind velocity, Sonic temperature | u, v, w, T_{s} | m s^{−1}, °C | 2.3 | CSAT3, Sonic anemometer, Campbell Scientific, USA. |

H_{2}O and CO_{2} concentrations | - | µmol m^{−3} | 2.3 | EC150, Campbell Scientific., USA. |

Soil temperature | T_{soil} | °C | 0.02 and 0.06 (Depth) | TCAV-L, Campbell Scientific, USA. |

Air temperature for FV analysis | T_{a} | °C | 1.7 | Fine-wire thermocouple, COCO-002, Omega, Eng., UK. |

Relative humidity | RH | % | 2.1 | HC2S3-L, Campbell Scientific., USA. |

Soil heat flux | G | W m^{−2} | 0.08 | HFP01, Hukseflux plate sensor. |

Net radiation | R_{n} | W m^{−2} | 2.3 | CNR4-L, KIPP and ZENON. |

Liquid precipitation | - | mm | 2.1 | TE525MM, Campbell Scientific Inc., USA. |

Soil water content | ϴ_{v} | m^{3}m^{−3} | 0.04 (Depth) | CS655, Campbell Scientific Inc., USA. |

**Table 4.**Statistical parameters of the regressions between H

_{EC}and H

_{FV}at the different positions: R

^{2}, the similarity constant C

_{T}, RMSE, RE, and slope. n is the number of data points in each regression. Fetch is the distance from the field edge for the dominant wind direction.

Statistics | H_{FV} | ||||
---|---|---|---|---|---|

Sensors | TC_{1} | TC_{2} | TC_{3} | TC_{4} | TC_{5} |

Fetch (m) | 170 | 165 | 160 | 155 | 150 |

R^{2} | 0.86 | 0.80 | 0.72 | 0.68 | 0.64 |

C_{T} | 2.3 | 2.4 | 2.3 | 2.2 | 2.3 |

RMSE (Wm^{−2}) | 25.00 | 30.55 | 37.85 | 41.70 | 44.84 |

RE (%) | 9.25 | 10.74 | 14.33 | 14.44 | 12.57 |

Slope | 0.94 | 0.98 | 0.98 | 0.96 | 0.97 |

n | 291 | 289 | 294 | 291 | 293 |

**Table 5.**Regression statistics of half-hourly LE

_{FV}vs LE

_{EC}as indicated by R

^{2}, RMSE, RE and the slope of linear regression.

Statistics | LE_{FV} | ||||
---|---|---|---|---|---|

Sensors | TC_{1} | TC_{2} | TC_{3} | TC_{4} | TC_{5} |

Fetch (m) | 170 | 165 | 160 | 155 | 150 |

R^{2} | 0.90 | 0.87 | 0.78 | 0.75 | 0.71 |

RMSE (Wm^{−2}) | 25.11 | 29.22 | 37.79 | 41.74 | 44.77 |

RE (%) | 4.73 | 5.96 | 7.52 | 7.78 | 7.03 |

Slope | 0.95 | 0.87 | 0.97 | 0.97 | 0.96 |

n | 291 | 289 | 294 | 291 | 293 |

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## Share and Cite

**MDPI and ACS Style**

Buttar, N.A.; Yongguang, H.; Tanny, J.; Akram, M.W.; Shabbir, A.
Fetch Effect on Flux-Variance Estimations of Sensible and Latent Heat Fluxes of *Camellia Sinensis*. *Atmosphere* **2019**, *10*, 299.
https://doi.org/10.3390/atmos10060299

**AMA Style**

Buttar NA, Yongguang H, Tanny J, Akram MW, Shabbir A.
Fetch Effect on Flux-Variance Estimations of Sensible and Latent Heat Fluxes of *Camellia Sinensis*. *Atmosphere*. 2019; 10(6):299.
https://doi.org/10.3390/atmos10060299

**Chicago/Turabian Style**

Buttar, Noman Ali, Hu Yongguang, Josef Tanny, M Waqar Akram, and Abdul Shabbir.
2019. "Fetch Effect on Flux-Variance Estimations of Sensible and Latent Heat Fluxes of *Camellia Sinensis*" *Atmosphere* 10, no. 6: 299.
https://doi.org/10.3390/atmos10060299