# Scaling Flux Tower Observations of Sensible Heat Flux Using Weighted Area-to-Area Regression Kriging

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Description

#### 2.2. Weighted Area-to-Area Regression Kriging

**Figure 1.**Yingke-Daman irrigation district in the Heihe River Basin, China (modified from [20], footprint in 2012/6/24).

#### 2.2.1. Spatial Trend Extraction

#### 2.2.2. Weighted Area-to-Area Kriging

#### 2.2.3. Point-to-Point Variogram Reconstruction

## 3. Results and Discussion

**Figure 3.**YComparison of estimations and observations for LAS H. (

**a**) Estimated by regression; (

**b**) estimated by WATA regression kriging.

^{2}of 0.89. The discrepancy is considered to be caused mainly by the heterogeneity of the surface. An improved aggregation method might enable higher correlation and R

^{2}coefficients. The discrepancies in measurements of LAS and EC are more obvious for heterogeneous surfaces. This might be the result of an energy imbalance phenomenon in response to the different source areas of the LAS and EC measurements [3]. The energy imbalance of EC was found in almost all the experiments around the world, and the reasons leading to the imbalance were still under-debated [33]. Previous studies usually considered H from EC was correct in the energy budget when compared with models [34]. The energy balance closures at ASTER passing time were around 0.8 in our study area.

Model | LAS 1 | LAS 2 | LAS 3 | LAS 4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Slope | RMSE | MBE | Slope | RMSE | MBE | Slope | RMSE | MBE | Slope | RMSE | MBE | |

Area-weighted [31] | 0.965 | 23.7 | −13.3 | 0.923 | 27.0 | −18.5 | 0.704 | 59.7 | −56.6 | 0.910 | 25.5 | −13.5 |

Footprint-weighted [31] | 0.996 | 30.0 | −12.2 | 0.924 | 27.9 | −18.6 | 0.726 | 54.4 | −51.6 | 0.917 | 26.6 | −13.5 |

Multiple linear regression | 0.991 | 17.5 | −7.7 | 1.097 | 23.6 | −4.6 | 0.776 | 43.0 | −33.4 | 1.110 | 25.7 | 8.0 |

ATA RK [20] | 0.961 | 17.6 | −11.2 | 1.006 | 23.5 | −6.3 | 0.784 | 48.0 | −40.4 | 1.040 | 20.7 | 1.6 |

WATA RK | 1.001 | 21.0 | −6.8 | 1.004 | 21.1 | −6.4 | 0.805 | 44.5 | −30.6 | 1.056 | 23.4 | 4.4 |

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Hu, M.; Wang, J.; Ge, Y.; Liu, M.; Liu, S.; Xu, Z.; Xu, T.
Scaling Flux Tower Observations of Sensible Heat Flux Using Weighted Area-to-Area Regression Kriging. *Atmosphere* **2015**, *6*, 1032-1044.
https://doi.org/10.3390/atmos6081032

**AMA Style**

Hu M, Wang J, Ge Y, Liu M, Liu S, Xu Z, Xu T.
Scaling Flux Tower Observations of Sensible Heat Flux Using Weighted Area-to-Area Regression Kriging. *Atmosphere*. 2015; 6(8):1032-1044.
https://doi.org/10.3390/atmos6081032

**Chicago/Turabian Style**

Hu, Maogui, Jianghao Wang, Yong Ge, Mengxiao Liu, Shaomin Liu, Ziwei Xu, and Tongren Xu.
2015. "Scaling Flux Tower Observations of Sensible Heat Flux Using Weighted Area-to-Area Regression Kriging" *Atmosphere* 6, no. 8: 1032-1044.
https://doi.org/10.3390/atmos6081032