scholarly journals A note on preconditioning weighted linear least-squares, with consequences for weakly constrained variational data assimilation

2018 ◽  
Vol 144 (712) ◽  
pp. 934-940
Author(s):  
Serge Gratton ◽  
Selime Gürol ◽  
Ehouarn Simon ◽  
Philippe L. Toint
Keyword(s):  
Data Assimilation ◽  
Least Squares ◽  
Variational Data Assimilation ◽  
Linear Least Squares

The Optimality of Potential Rescaling Approaches in Land Data Assimilation

2013 ◽  
Vol 14 (2) ◽  
pp. 650-660 ◽  
Author(s):  
M. Tugrul Yilmaz ◽  
Wade T. Crow
Keyword(s):  
Soil Moisture ◽  
Data Assimilation ◽  
Least Squares ◽  
Optimal Solution ◽  
Least Squares Regression ◽  
Linear Least Squares ◽  
Optimal Analysis ◽  
Land Data Assimilation ◽  
Temporal Statistics ◽  
Hydrological Variables

Abstract It is well known that systematic differences exist between modeled and observed realizations of hydrological variables like soil moisture. Prior to data assimilation, these differences must be removed in order to obtain an optimal analysis. A number of rescaling approaches have been proposed for this purpose. These methods include rescaling techniques based on matching sampled temporal statistics, minimizing the least squares distance between observations and models, and the application of triple collocation. Here, the authors evaluate the optimality and relative performances of these rescaling methods both analytically and numerically and find that a triple collocation–based rescaling method results in an optimal solution, whereas variance matching and linear least squares regression approaches result in only approximations to this optimal solution.

scholarly journals The conditioning of least-squares problems in variational data assimilation

2018 ◽  
Vol 25 (5) ◽  
pp. e2165 ◽  
Author(s):  
Jemima M. Tabeart ◽  
Sarah L. Dance ◽  
Stephen A. Haben ◽  
Amos S. Lawless ◽  
Nancy K. Nichols ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Least Squares ◽  
Variational Data Assimilation ◽  
Least Squares Problems
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