Evaluation of the Weak Constraint Data Assimilation Approach for Estimating Turbulent Heat Fluxes at Six Sites

Abstract

A number of studies have estimated turbulent heat fluxes by assimilating sequences of land surface temperature (LST) observations into the strong constraint-variational data assimilation (SC-VDA) approaches. The SC-VDA approaches do not account for the structural model errors and uncertainties in the micrometeorological variables. In contrast to the SC-VDA approaches, the WC-VDA approach (the so-called weak constraint-VDA) accounts for the effects of structural and model errors by adding a model error term. In this study, the WC-VDA approach is tested at six study sites with different climatic and vegetative conditions. Its performance is also compared with that of SC-VDA at the six study sites. The results show that the WC-VDA produces 10.16% and 10.15% lower root mean square errors (RMSEs) for sensible and latent heat flux estimates compared with the SC-VDA approach. The model error term can capture errors in the turbulent heat flux estimates due to errors in LST and micrometeorological measurements, as well as structural model errors, and does not allow those errors to adversely affect the turbulent heat flux estimates. The findings also indicate that the estimated model error term varies reasonably well, so as to capture the misfit between predicted and observed net radiation in different hydrological and vegetative conditions. Finally, synthetically generated positive (negative) noises are added to the hydrological input variables (e.g., LST, air temperature, air humidity, incoming solar radiation, and wind speed) to examine whether the WC-VDA approach can capture those errors. It was found that the WC-VDA approach accounts for the errors in the input data and reduces their effect on the turbulent heat flux estimates.

Impact of satellite and in situ data assimilation on hydrological predictions

“…In this work, we applied the EnKF method to assimilate the MODIS accumulated 8-day actual and potential evapotranspiration (AET and PET, respectively); and the daily CRYOLAND optical satellite FSC and passive microwave snow water equivalent (SWE); and river discharge and local inflows into hydropower reservoirs with the aim of improving the estimates for the latter two variables. Most previous studies e.g., Li et al [37,38], He et al [39], Pimentel et al [40], De Lannoy et al [41] assimilated one variable. Few studies assimilated two variables, e.g., Liu et al [42] assimilated satellite FSC and snow depth; Rasmussen et al [43] assimilated groundwater heads and stream discharge; while Ines et al [44] assimilated satellite SM and Leaf Area Index.…”

Estimating Turbulent Fluxes in the Tropical Andes

“…However, the eddy covariance method has some restrictions that limit its applicability: (i) it requires constant supervision and maintenance, (ii) measurements in complex terrain are challenging because of the theoretical assumptions to transform the high-frequency measurements to turbulent fluxes [5], and (iii) because of extensive data quality requisites, gaps are inevitable, particularly under low turbulence mixing conditions [6,7]. Because of these difficulties, efforts have been made to parameterise them based on more commonly measured variables [8][9][10][11][12][13] and to compare among different methods to estimate and measure these fluxes [14][15][16][17][18]. One of the most frequently used approaches is to follow the work of [19] and [20], which relates the average temperature, humidity, and wind speed profiles in the boundary layer to the turbulent fluxes.…”

Mapping Regional Turbulent Heat Fluxes via Assimilation of MODIS Land Surface Temperature Data into an Ensemble Kalman Smoother Framework

“…Hence, a number of methods have been developed to estimates turbulent heat fluxes from remotely sensed land surface temperature (LST) data. Broadly speaking, these approaches fall into two main categories: retrieval-based (e.g., Anderson et al, 1997;Bastiaanssen, Menenti, et al, 1998;Bastiaanssen, Pelgrum, et al, 1998;Carlson, 2007;Jia et al, 2009;Jiang & Islam, 2003;Kustas et al, 2012;Liang et al, 2010;Liu et al, 2007;Ma et al, 2018;Mallick et al, 2013Mallick et al, , 2014Moran et al, 1994;Norman et al, 1995;Song et al, 2018;Su 2002;Sun et al, 2013;Tang et al, 2010;Wang et al, 2006;Yao et al, 2013;Zhu et al, 2017), and data assimilation approaches (e.g., Abdolghafoorian et al, 2017;Bateni, Entekhabi, & Jeng, 2013;Bateni, Entekhabi, & Castelli, 2013;Bateni et al, 2014;Bateni & Liang, 2012;Boni et al, 2001;Castelli et al, 1999;Caparrini et al, 2003Caparrini et al, , 2004aCaparrini et al, , 2004bCarrera et al, 2015;Farhadi et al, 2014Farhadi et al, , 2016He et al, 2018;Lu et al, 2016Lu et al, , 2017Xu, et al, 2014;Xu, Bateni, et al, 2015;…”

“…Variational data assimilation (VDA) methods estimate the key unknowns of the surface energy balance (SEB) equations (i.e., neutral bulk heat transfer coefficient, C HN , and evaporative fraction, EF) by assimilating LST observations into the heat diffusion or force-restore equations (Abdolghafoorian et al, 2017;Bateni, Entekhabi, & Jeng, 2013;Bateni, Entekhabi, & Castelli, 2013;Bateni et al, 2014;Bateni & Entekhabi, 2012a;Bateni & Liang, 2012;Crow & Kustas, 2005;He et al, 2018;Qin et al, 2007;Sini et al, 2008;Xu et al, 2014Xu et al, , 2016Xu, Bateni, et al, 2015;Xu, He, et al, 2019). The unknown parameters of the VDA approaches (i.e., C HN and EF) are obtained by minimizing the misfit between the LST observations and estimations from the force-restore or heat diffusion equation.…”

“…Monthly C HN estimates from the EnKS approach (first row), and LAI values (second row) over the HRB.corresponding EF estimates are chosen as optimum values, Herein, C HN is varied from 0.001 to 0.05 with an increment of 0.001He et al, 2018;Xu, Bateni, et al, 2018;Xu, He, et al, 2019).…”