# Integrating Latent Heat Flux Products from MODIS and Landsat Data Using Multi-Resolution Kalman Filter Method in the Midstream of Heihe River Basin of Northwest China

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## Abstract

**:**

## 1. Introduction

^{2}and highest R

^{2}of 0.84 through the validation of 22 eddy covariance (EC) sites, compared with original datasets. However, these methods are generally used at the same spatial resolutions, and the scaling issues across different resolutions are rarely considered.

## 2. Study Area and Data

#### 2.1. Study Area and Ground Observations

^{2}in the arid region of northwestern China [19,27].

#### 2.2. Remotely Sensed Data

#### 2.2.1. MODIS LE Product

#### 2.2.2. Landsat-Based LE Product

## 3. Methodology

#### 3.1. The MKF Method

_{s}is the estimated value at the scale s, and y

_{pa}

_{(s)}is the variable at the parent node. A

_{s}estimates the state transition from the parent to children. W

_{s}controls the scale variability and follows a normal distribution N (0, Q(s)). Accordingly, there is an equation describing the variable at node s from its children node ch(s) [47].

_{s}is the measurement variable at node s with white noise ${\epsilon}_{s}$ which has a normal distribution N (0, R(s)). C

_{s}is a measurement matrix and is set to the identity matrix because both satellite measurement and the variable are LE and cover the same area in this study.

#### 3.2. Assessment Metrics

_{obs}and X

_{est}describe the observed values and estimated values, respectively.

## 4. Results and Discussion

#### 4.1. Integration of Satellite-Derived LE Products

#### 4.2. Comparison before and after MKF

#### 4.2.1. Spatial Assessment of the MKF Integration Performance

^{2}in most cases. The outliers with absolute difference larger than 20 W/m

^{2}were more than approximately 14% of the total, whereas the numbers of those outliers dropped to less than 1% after the integration. This hints that the two LE products were made more consistent across different resolutions through the MKF method.

#### 4.2.2. Evaluation of the MKF Performance Using Ground Observations

^{2}to 21.22 W/m

^{2}, a fall in bias from 9.33 W/m

^{2}to 9.27 W/m

^{2}, and an increase in R

^{2}from 0.46 to 0.58. Likewise, the RMSE% of the integrated Landsat data decreased from 42.98% to 40.42%, the RMSE fell from 34.15 W/m

^{2}to 32.5 W/m

^{2}, the bias decreased from 4.33 W/m

^{2}to 4.3 W/m

^{2}, and the R

^{2}improved from 0.63 to 0.67. The slight improvement illustrates that the coarse-to-fine sweep of the MKF method offered few updates for Landsat, and the uncertainty of the original LE products might be further propagated to the integrated LE data.

^{2}, the bias was 7.82 W/m

^{2}, and the R

^{2}was 0.57. Note that there is obvious underestimation of MOD16, which mainly comes from cropland, and was actually introduced by Landsat data that underestimated cropland during the fine-to-coarse sweep of the MKF method.

#### 4.3. Discussion

#### 4.3.1. Uncertainty Analysis

^{2}varied from 0.4 to 0.7 and the RMSE varied from approximately 37.5 W/m

^{2}to 44.4 W/m

^{2}for cropland and wetland. This is consistent with our validation results (i.e., R

^{2}is 0.67 and RMSE is 32.5 W/m

^{2}). Neglecting the differences in parameters from different biome types and complex terrain may cause the errors [55], and such findings are in accordance with previous studies over northeast China [44]. The errors could be reduced by 5–25% if calibrating the Priestley–Taylor coefficients controlled by the ground observations towards different biome types and climatic zones [56]. For MOD16, underestimation also exists because the soil moisture constraint in MOD16 applied relatively humidity (RH) and vapor pressure deficit (VPD) as indicators of water stress [44]. During the irrigation period, the soil water content in the surface and root layers is generally high and the overestimation of water stress, parameterized by RH and atmospheric VPD, brought about the underestimation of the soil evaporation in the arid and semi-arid midstream of the HRB [57]. Researchers drew similar conclusions in China [58], the United States [59], eastern Asia [60], and Brazil [61] when evaluating MOD16. Large errors and uncertainty may be introduced by these approximations and assumptions. Moreover, the integration evaluation greatly relies on the accuracy of EC ground observations, which were considered as true LE values in this study. However, Wang et al. (2015) [62] reported 16% uncertainty in LE observations derived from the HiWATER–MUSOEXE flux matrix. Even though we corrected the energy imbalance, errors that were caused by complexity in wind variation, footprint representation, and sampling variability are still unclear [23,63]. These corrections still cause large errors of EC ground observations in results [64].

#### 4.3.2. Superiority and Recommendation for the MKF integration

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Details of the MKF Method

#### Appendix A.1. Initialization

#### Appendix A.2. Fine-to Coarse Sweep

_{s}is the measurement matrix and K(s) is Kalman gain given by Ref. [66]:

#### Appendix A.3. Coarse-to-Fine Sweep

## Appendix B. Details of the MS-PT Algorithm Logic

_{ds}), the saturated wet soil surface evaporation (LE

_{ws}), the canopy transpiration (LE

_{c}), and the canopy interception evaporation (LE

_{ic}). Each part can be calculated by:

_{wet}is the wet surface fraction; f

_{sm}is the soil moisture constraint; f

_{T}is the plant temperature constraint; R

_{ns}and R

_{nc}are the net radiation into soil and vegetation, respectively; G is the soil heat flux; DT represents the diurnal air temperature range and DT

_{max}describes the maximum DT (40 °C); f

_{c}is the vegetation cover fraction; and NDVI

_{max}and NDVI

_{min}are the maximum and the minimum NDVI, with the values of 0.95 and 0.05, respectively in this algorithm [67].

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**Figure 1.**Land cover types (IGBP classification) of the study area and the location of EC sites. LEA: large experimental area, KEA: kernel experimental area.

**Figure 2.**Multi-resolution Kalman filter (MKF) data structure [25].

**Figure 4.**The integration comparison before and after MKF for DOY (day of year) 225, DOY 233, DOY 241, and DOY 249 in 2012. The order, from left to right, is the LE from original MODIS, MKF-integrated MODIS, original Landsat, and MKF-integrated Landsat. Dark blue color means no data.

**Figure 5.**Comparison of the integration difference between the aggregated Landsat and MOD16 before and after MKF on time series. (

**a**) DOY 177; (

**b**) DOY 185; (

**c**) DOY 193; (

**d**) DOY 217; (

**e**) DOY 225; (

**f**) DOY 233; (

**g**) DOY 241; (

**h**) DOY 249.

**Figure 6.**Validations of LE products versus ground observations before and after MKF. (

**a**) MOD16 before MKF; (

**b**) MOD16 after MKF; (

**c**) Landsat-based LE before MKF; (

**d**) Landsat-based LE after MKF.

**Table 1.**Summary of EC Sites in the midstream of the Heihe River Basin [11].

Observed Sites | Longitude | Latitude | Land Cover | Duration ^{1} |
---|---|---|---|---|

Zhangye wetland | 100.45° | 38.98° | wetland | 6/2012–12/2016 |

Shenshawo sandy desert | 100.49° | 38.79° | barren land | 6/2012–4/2015 |

Huazhaizi desert steppe | 100.32° | 38.77° | barren land | 6/2012–12/2016 |

Bajitan Gobi | 100.30° | 38.92° | barren land | 6/2012–4/2015 |

1 | 100.36° | 38.89° | cropland | 6/10/2012–9/17/2012 |

2 | 100.35° | 38.89° | cropland | 5/3/2012–9/21/2012 |

3 | 100.38° | 38.89° | cropland | 6/3/2012–9/18/2012 |

4 | 100.36° | 38.88° | cropland | 5/10/2012–9/17/2012 |

5 | 100.35° | 38.88° | cropland | 6/4/2012–9/18/2012 |

6 | 100.36° | 38.87° | cropland | 5/9/2012–9/21/2012 |

7 | 100.37° | 38.88° | cropland | 5/28/2012–9/18/2012 |

8 | 100.38° | 38.87° | cropland | 5/14/2012–9/21/2012 |

9 | 100.39° | 38.87° | cropland | 6/4/2012–9/17/2012 |

10 | 100.40° | 38.88° | cropland | 6/1/2012–9/17/2012 |

11 | 100.34° | 38.87° | cropland | 6/2/2012–9/18/2012 |

12 | 100.37° | 38.87° | cropland | 5/10/2012–9/21/2012 |

13 | 100.38° | 38.86° | cropland | 5/6/2012–9/20/2012 |

14 | 100.35° | 38.86° | cropland | 5/6/2012–9/21/2012 |

Daman (15) | 100.37° | 38.86° | cropland | 9/2012–12/2016 |

16 | 100.36° | 38.85° | cropland | 6/1/2012–9/17/2012 |

17 | 100.37° | 38.85° | cropland | 5/12/2012–9/17/2012 |

DOY | MOD16 VS Aggregated Landsat | |||||
---|---|---|---|---|---|---|

Before MKF | After MKF | |||||

Bias | RMSE | RMSE (%) | Bias | RMSE | RMSE (%) | |

177 | 1.13 | 32.99 | 38.60 | −1.22 | 5.37 | 6.29 |

185 | −4.83 | 28.57 | 39.53 | −7.49 | 11.35 | 15.70 |

193 | −11.06 | 24.05 | 35.18 | −13.12 | 16.25 | 23.77 |

217 | −8.42 | 24.77 | 28.09 | −11.52 | 17.17 | 19.48 |

225 | −8.20 | 29.64 | 31.97 | −10.51 | 13.50 | 14.57 |

233 | −11.93 | 35.58 | 49.92 | −13.10 | 17.60 | 24.69 |

241 | −10.32 | 35.92 | 49.81 | −11.30 | 17.16 | 23.79 |

249 | −9.16 | 24.56 | 52.83 | −10.33 | 14.46 | 31.11 |

^{2}.

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## Share and Cite

**MDPI and ACS Style**

Xu, J.; Yao, Y.; Tan, K.; Li, Y.; Liu, S.; Shang, K.; Jia, K.; Zhang, X.; Chen, X.; Bei, X.
Integrating Latent Heat Flux Products from MODIS and Landsat Data Using Multi-Resolution Kalman Filter Method in the Midstream of Heihe River Basin of Northwest China. *Remote Sens.* **2019**, *11*, 1787.
https://doi.org/10.3390/rs11151787

**AMA Style**

Xu J, Yao Y, Tan K, Li Y, Liu S, Shang K, Jia K, Zhang X, Chen X, Bei X.
Integrating Latent Heat Flux Products from MODIS and Landsat Data Using Multi-Resolution Kalman Filter Method in the Midstream of Heihe River Basin of Northwest China. *Remote Sensing*. 2019; 11(15):1787.
https://doi.org/10.3390/rs11151787

**Chicago/Turabian Style**

Xu, Jia, Yunjun Yao, Kanran Tan, Yufu Li, Shaomin Liu, Ke Shang, Kun Jia, Xiaotong Zhang, Xiaowei Chen, and Xiangyi Bei.
2019. "Integrating Latent Heat Flux Products from MODIS and Landsat Data Using Multi-Resolution Kalman Filter Method in the Midstream of Heihe River Basin of Northwest China" *Remote Sensing* 11, no. 15: 1787.
https://doi.org/10.3390/rs11151787