Modifying Covariance Localization to Mitigate Sampling Errors from the Ensemble Data Assimilation

Algorithm 1

Analysis step for CL.

(i)	Require: A statistical sample of state estimates . is the ensemble matrix, that is, , where column are the ensemble number. is the model component. . Observation vector (input). is a multiplicative inflation factor (parameter). represents the vector with all elements being 1. is the identity matrix. is the localizing function .
(1)	for
(2)	and
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)	return analysis ensemble
(12)	end for