Quarterly Journal of the Royal Meteorological Society
1477-870X
0035-9009
Mỹ
Cơ quản chủ quản: Wiley-Blackwell , WILEY
Lĩnh vực:
Atmospheric Science
Các bài báo tiêu biểu
Evaporation from sparse crops‐an energy combination theory Abstract A one‐dimensional model is adopted to describe the energy partition of sparse crops. Theoretical development of this model yields a combination equation which describes evaporation in terms of controlling resistances associated with the plants, and with the soil or water in which they are growing. the equation provides a simple but physically plausible description of the transition between bare substrate and a closed canopy. Although the aerodynamic transfer resistances for incomplete canopies have, as yet, no experimental justification, typical values, appropriate to a specimen agricultural crop and soil, are shown to have limited sensitivity in the model. Processes which require further study if the equation is to be used to calculate evaporation throughout a crop season are also discussed.
Tập 111 Số 469 - Trang 839-855 - 1985
Improving the quality of simulated soil moisture with a multi‐model ensemble approach Abstract Multi‐model ensembles have been found to perform significantly better than a single‐model system in weather and seasonal climate forecasts. This paper explores the possibility of applying the multi‐model ensemble approach to the land surface component in order to improve the quality of simulated soil moisture. The simple average of 17 multiyear global soil moisture products is validated with long‐term in situ data in five regions (Illinois, USA; China; India; Mongolia and the former Soviet Union). The results show that in all regions the multi‐model analysis is clearly better than most individual products in simulating the phasing of the annual cycle, interannual variability, and magnitudes in observed soil moisture. The sensitivity of the performance of the multi‐model analysis to ensemble member size and composition is also examined. It is found that there is usually a clear improvement when a product of higher correlation to observations or lower error is included in the multi‐model ensemble, while there is no apparent degradation when a product with relatively poor skill is included. Copyright © 2007 Royal Meteorological Society
Tập 133 Số 624 - Trang 731-747 - 2007
Convergence properties of the primal and dual forms of variational data assimilation Abstract The variational data assimilation problem can be solved in either its primal (3D/4D‐Var) or dual (3D/4D‐PSAS) form. The methods are equivalent at convergence but the dual method exhibits a spurious behaviour at the beginning of the minimization which leads to less probable states than the background state. This is a serious concern when using the dual method in operational implementations when only a finite number of iterations can be afforded. Two classes of minimization algorithms are examined in this article: the conjugate gradient (CG) and the minimum residual (MINRES) methods. While the CG algorithms ensure a monotonic reduction of the cost function, those based on the MINRES enforce instead a monotonic decrease of the norm of the gradient. In this article, it is shown that when applied to the minimization of the dual problem, the MINRES algorithms also lead to iterates for which their ‘image’ in physical space leads to a monotonic decrease of the primal cost function. A relationship is established showing that the primal objective function is related to the value of the dual cost function and the norm of its gradient. This holds for the incremental forms of both the three‐ and four‐dimensional cases. A new convergence criterion is introduced based on the error norm in model space to make sure that, for the dual problem, the same accuracy is obtained in the analysis when only a finite number of iterations is completed. Copyright © 2010 Royal Meteorological Society
Tập 136 Số 646 - Trang 107-115 - 2010
Guaranteeing the convergence of the saddle formulation for weakly constrained 4D‐Var data assimilation This paper discusses convergence issues for the saddle variational formulation of the weakly constrained 4D‐Var method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationally coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.
Tập 144 Số 717 - Trang 2592-2602 - 2018
<b>B</b>‐preconditioned minimization algorithms for variational data assimilation with the dual formulation Abstract Variational data assimilation problems in meteorology and oceanography require the solution of a regularized nonlinear least‐squares problem. Practical solution algorithms are based on the incremental (truncated Gauss–Newton) approach, which involves the iterative solution of a sequence of linear least‐squares (quadratic minimization) sub‐problems. Each sub‐problem can be solved using a primal approach, where the minimization is performed in a space spanned by vectors of the size of the model control vector, or a dual approach, where the minimization is performed in a space spanned by vectors of the size of the observation vector. The dual formulation can be advantageous for two reasons. First, the dimension of the minimization problem with the dual formulation does not increase when additional control variables are considered, such as those accounting for model error in a weak‐constraint formulation. Second, whenever the dimension of observation space is significantly smaller than that of the model control space, the dual formulation can reduce both memory usage and computational cost. In this article, a new dual‐based algorithm called RestrictedB ‐preconditioned Lanczos (RBLanczos) is introduced, whereB denotes the background‐error covariance matrix. RBLanczos is the Lanczos formulation of the RestrictedB ‐preconditioned Conjugate Gradient (RBCG) method. RBLanczos generates mathematically equivalent iterates to those of RBCG and the correspondingB ‐preconditioned Conjugate Gradient and Lanczos algorithms used in the primal approach. All these algorithms can be implemented without the need for a square‐root factorization ofB . RBCG and RBLanczos, as well as the corresponding primal algorithms, are implemented in two operational ocean data assimilation systems and numerical results are presented. Practical diagnostic formulae for monitoring the convergence properties of the minimization are also presented.
Tập 140 Số 679 - Trang 539-556 - 2014
Dual formulation of four‐dimensional variational assimilation Abstract A duality between two formulations of variational assimilation, three‐dimensionsal (3D‐Var) and the Physicalspace Statistical Analysis System (PSAS), is presented. It is shown that their conditioning is identical. the temporal extension of 3D‐Var leads to 4D‐Var. the temporal extension of PSAS, 4D‐PSAS, is achieved using an algorithm inspired by the representer technique but without the explicit computation of the representers. Assuming the model is perfect, both 4D‐Var and 4D‐PSAS are equivalent in terms of results produced and cost. Assuming the model is not perfect, the equivalence is preserved, but in 4D‐Var it is necessary to increase the size of the control variable while 4D‐PSAS remains almost unchanged. In duality, 4D‐Var remains almost unchanged by an increase in the number of observations used, whereas the size of the control variable in PSAS depends directly on this number.
Tập 123 Số 544 - Trang 2449-2461 - 1997
Accounting for an imperfect model in 4D‐Var Abstract In most operational implementations of four‐dimensional variational data assimilation (4D‐Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D‐Var. We present three approaches for the formulation of weak‐constraint 4D‐Var: estimating explicitly a model‐error forcing term, estimating a representation of model bias or, estimating a four‐dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D‐Var are discussed. We show that 4D‐Var with an additional model‐error representation as part of the control variable is essentially an initial‐value problem and that its characteristics are very similar to that of strong constraint 4D‐Var. Taking the four‐dimensional state as the control variable, however, leads to very different properties. In that case, weak‐constraint 4D‐Var can be interpreted as a coupling between successive strong‐constraint assimilation cycles. A possible extension towards long‐window 4D‐Var and possibilities for evolutions of the data assimilation system are presented. Copyright © 2006 Royal Meteorological Society
Tập 132 Số 621 - Trang 2483-2504 - 2006
Parallelization in the time dimension of four‐dimensional variational data assimilation The current evolution of computer architectures towards increasing parallelism requires a corresponding evolution towards more parallel data assimilation algorithms. In this article, we consider parallelization of weak‐constraint four‐dimensional variational data assimilation (4D‐Var) in the time dimension. We categorize algorithms according to whether or not they admit such parallelization and introduce a new, highly parallel weak‐constraint 4D‐Var algorithm based on a saddle‐point representation of the underlying optimization problem. The potential benefits of the new saddle‐point formulation are illustrated with a simple two‐level quasi‐geostrophic model.
Tập 143 Số 703 - Trang 1136-1147 - 2017
Randomised preconditioning for the forcing formulation of weak‐constraint 4D‐Var Abstract There is growing awareness that errors in the model equations cannot be ignored in data assimilation methods such as four‐dimensional variational assimilation (4D‐Var). If allowed for, more information can be extracted from observations, longer time windows are possible, and the minimisation process is easier, at least in principle. Weak‐constraint 4D‐Var estimates the model error and minimises a series of quadratic cost functions, which can be achieved using the conjugate gradient (CG) method; minimising each cost function is called an inner loop. CG needs preconditioning to improve its performance. In previous work, limited‐memory preconditioners (LMPs) have been constructed using approximations of the eigenvalues and eigenvectors of the Hessian in the previous inner loop. If the Hessian changes significantly in consecutive inner loops, the LMP may be of limited usefulness. To circumvent this, we propose using randomised methods for low‐rank eigenvalue decomposition and use these approximations to construct LMPs cheaply using information from the current inner loop. Three randomised methods are compared. Numerical experiments in idealized systems show that the resulting LMPs perform better than the existing LMPs. Using these methods may allow more efficient and robust implementations of incremental weak‐constraint 4D‐Var.
Tập 147 Số 740 - Trang 3719-3734 - 2021
Correlation modelling on the sphere using a generalized diffusion equation Abstract An important element of a data assimilation system is the statistical model used for representing the correlations of background error. This paper describes a practical algorithm that can be used to model a large class of two‐ and three‐dimensional, univariate correlation functions on the sphere. Application of the algorithm involves a numerical integration of a generalized diffusion‐type equation (GDE). The GDE is formed by replacing the Laplacian operator in the classical diffusion equation by a polynomial in the Laplacian. The integral solution of the GDE defines, after appropriate normalization, a correlation operator on the sphere. The kernel of the correlation operator is an isotropic correlation function. The free parameters controlling the shape and length‐scale of the correlation function are the products kpT, p = 1, 2, …, where (‐1)p kp is a weighting (‘diffusion’) coefficient (kp > 0) attached to the Laplacian with exponent p, and T is the total integration ‘time’. For the classical diffusion equation (a special case of the GDE with kp = 0 for all p > 1) the correlation function is shown to be well approximated by a Gaussian with length‐scale equal to (2k1T)1/2 . The Laplacian‐based correlation model is particularly well suited for ocean models as it can be easily generalized to account for complex boundaries imposed by coastlines. Furthermore, a one‐dimensional analogue of the GDE can be used to model a family of vertical correlation functions, which in combination with the two‐dimensional GDE forms the basis of a three‐dimensional, (generally) non‐separable correlation model. Generalizations to account for anisotropic correlations are also possible by stretching and/or rotating the computational coordinates via a ‘diffusion’ tensor. Examples are presented from a variational assimilation system currently under development for the OPA ocean general‐circulation model of the Laboratoire d'Oceanographie Dynamique et de Climatologie.
Tập 127 Số 575 - Trang 1815-1846 - 2001