# A Gap Filling Model For Eddy Covariance Latent Heat Flux Estimating

**Topics:**Linear regression, Regression analysis, Principal component analysis

**Pages:**10 (7845 words)

**Published:**April 17, 2015

Contents lists available at SciVerse ScienceDirect

Journal of Hydrology

journal homepage: www.elsevier.com/locate/jhydrol

A gap-ﬁlling model for eddy covariance latent heat ﬂux: Estimating evapotranspiration of a subtropical seasonal evergreen broad-leaved forest as an example

Yi-Ying Chen a, Chia-Ren Chu b, Ming-Hsu Li a,⇑

a

b

Graduate Institute of Hydrological and Oceanic Sciences, National Central University, Taiwan Department of Civil Engineering, National Central University, Taiwan

a r t i c l e

i n f o

Article history:

Received 8 February 2012

Received in revised form 13 June 2012

Accepted 12 August 2012

Available online 25 August 2012

This manuscript was handled by A.

Bardossy, Editor-in-Chief, with the

assistance of K.P. Sudheer, Associate Editor

Keywords:

Gap-ﬁlling model

Principal component analysis

K-nearest neighbors

Multiple regressions

Evapotranspiration

s u m m a r y

In this paper we present a semi-parametric multivariate gap-ﬁlling model for tower-based measurement of latent heat ﬂux (LE). Two statistical techniques, the principal component analysis (PCA) and a nonlinear interpolation approach were integrated into this LE gap-ﬁlling model. The PCA was ﬁrst used to resolve the multicollinearity relationships among various environmental variables, including radiation, soil moisture deﬁcit, leaf area index, wind speed, etc. Two nonlinear interpolation methods, multiple regressions (MRS) and the K-nearest neighbors (KNNs) were examined with random selected ﬂux gaps for both clear sky and nighttime/cloudy data to incorporate into this LE gap-ﬁlling model. Experimental results indicated that the KNN interpolation approach is able to provide consistent LE estimations while MRS presents over estimations during nighttime/cloudy. Rather than using empirical regression parameters, the KNN approach resolves the nonlinear relationship between the gap-ﬁlled LE ﬂux and principal components with adaptive K values under different atmospheric states. The developed LE gap-ﬁlling model (PCA with KNN) works with a RMSE of 2.4 W mÀ2 ($0.09 mm dayÀ1) at a weekly time scale by adding 40% artiﬁcial ﬂux gaps into original dataset. Annual evapotranspiration at this study site were estimated at 736 mm (1803 MJ) and 728 mm (1785 MJ) for year 2008 and 2009, respectively. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction

The exchange of heat and water vapor between the atmosphere

and the biosphere plays an important role in regulating the thermal environment. For example, the energy partitioning among latent heat (LE), sensible heat (SH) and ground heat (G) has a strong inﬂuence on weather and climate (Pielke et al., 1998; Wilson et al., 2002), such as near surface convection (Juang et al., 2007), land–sea breeze (Seth and Giorgi, 1996), long range transport of pollutants (Zhang and Rao, 1999), and drought events (Dirmeyer, 1994). In order to understand the impact of temporal and spatial variability of these surface ﬂuxes on above issues, a global ﬂux network (FLUXNET) has been established to coordinate these surface ﬂuxes measured by the eddy covariance (EC) approach from regional networks (Aubinet et al., 2001; Baldocchi et al., 2001; Baldocchi, 2008). The EC approach directly computed these surface ﬂuxes by calculating covariance between vertical

⇑ Corresponding author. Address: Graduate Institute of Hydrological and Oceanic Sciences, National Central University, 300 Jhongda Road, Jhongli, Taoyuan 32001, Taiwan. Tel.: +886 3 4222964; fax: +886 3 4222874.

E-mail addresses: spancer@cc.ncu.edu.tw (Y.-Y. Chen), crchu@ncu.edu.tw (C.-R. Chu), mli@cc.ncu.edu.tw (M.-H. Li).

0022-1694/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2012.08.026

wind velocity and temperature and water vapor mixing ratio from a certain averaging period to obtain SH ﬂux and LE ﬂux, respectively. The spatial...

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