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Christoph Schär
and
Nico Kröner

sciences, in addition to the classical use of theory and laboratory experiments. Since the beginning of numerical models, they have widely been used to disentangle the complexity of nonlinear, multiscale, and chaotic physical systems considered. In numerical models, highly sophisticated experimentation is possible, as individual factors of the modeling systems can be switched on and off at discretion. There are numerous studies that have used this approach and made progress in this way. While sometimes

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Ning Wang
and
Chungu Lu

with small absolute values, we get a denoised field ( Fig. 4 , right). The formula we use for this particular case is t ( x , s ) = t 1 ( x ) t 2 ( s ), where x and s denote coefficient and scale: T = 0.03, and The formula is adapted from a similar formula by Kingsbury (1999) . 4. Application to meteorological data analyses In this section, a two-dimensional wavelet analysis algorithm is applied to a meteorological dataset. We are given a set of modeled horizontal velocity

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Chih-Chieh Young
,
Yu-Chiao Liang
,
Yu-Heng Tseng
, and
Chun-Hoe Chow

characteristics of the RAW filter and its spatial dependency, which is essential before further implementation into any oceanic (or atmospheric) general circulation models. a. Classical model problem-oscillation equation Consider the classical benchmark test in numerical analysis: , where the complex constant λ = λ R + iλ I determines the amplification ( λ R > 0)/damping ( λ R < 0) and frequency (arbitrary λ I ) of the oscillation ( Durran 1991 ). Discretizing the above equation by the RAW

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Alan Shapiro
,
Stefan Rahimi
,
Corey K. Potvin
, and
Leigh Orf

unstaggered horizontal ( x , y ) Cartesian analysis grid using low-altitude u and υ (but not w ) data. Experiments focus on the temporal resolution of the input data and on variations of implementing the advection correction. In each experiment, the trajectories are compared with a set of reference (verification) trajectories obtained using the linear time interpolation procedure with very-high-temporal-resolution input data from the numerical model. However, since w data are not used in any of

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E. Adam Paxton
,
Matthew Chantry
,
Milan Klöwer
,
Leo Saffin
, and
Tim Palmer

ways to avoid stagnation, such as increasing the time step, which is extremely small in this example and well below what is necessary for stability, or implementing a compensated summation for the time-stepping. Rather, this section aims to illustrate an interesting advantage of SR in mitigating stagnation by means of a clear and visual example. For more analysis of SR in the numerical solution of the heat equation see Croci and Giles (2020) . 5. A global atmospheric model Finally, we

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Eun-Gyeong Yang
and
Hyun Mee Kim

1. Introduction A reanalysis is a high-quality climate-data product produced by assimilating long time series of observations with a consistent and state-of-the-art numerical weather prediction (NWP) model and data assimilation (DA) system to represent the best estimate of the state of the atmosphere. Reanalysis is used for a variety of applications, such as climatic variability, chemical transport, and parameterization studies ( Rood and Bosilovich 2010 ). Before the production of reanalyses

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Abdelaziz Beljadid
,
Abdolmajid Mohammadian
,
Martin Charron
, and
Claude Girard

1. Introduction Semi-Lagrangian (SL) semi-implicit integration methods, first proposed by Robert (1981) , have been extensively studied and widely incorporated into atmospheric numerical models. A comprehensive review of the applications of SL methods in atmospheric problems was given by Staniforth and Côté (1991) . Other extensive studies have also been conducted to examine SL methods (e.g., Bonaventura 2000 ; White and Dongarra 2011 ). A three-time-level SL method was implemented

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Tomasz J. Glowacki
,
Yi Xiao
, and
Peter Steinle

the numerical model first guess. The impacts of temperature and dewpoint observations over ocean sites (ships, reef stations) are retained in the analysis over land near the coast. The use of a persistence first guess in MSAS is an option for the infrequent situations when a model first guess is not available. However, the inhomogeneous observation network does not support the use of persistence for a prolonged period. The value of persistence as a first guess in data-dense regions was discussed

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Brett T. Hoover
,
Jason A. Otkin
,
Eugene M. Petrescu
, and
Emily Niebuhr

efficiency in windy conditions, evaporation, or sublimation of precipitation before measurement ( Rasmussen et al. 2012 ), depending on the method of measurement and design of the gauge. Fig . 1. (a) Map of gauge observation stations. The QPE analysis domain, based on the domain of the HRRR-AK model, is shaded in gray. Stars represent Anchorage (cyan), Fairbanks (green), and Juneau (yellow). (b) Map of QPF domains covered by each member of the QPE first guess. (c) Map of Alaska’s NWS NEXRAD stations

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Emily L. Kang
and
John Harlim

the pseudo-observations and their corresponding variances and step 5 for performing the microscopic analysis step. In practice, we first use the offline training dataset to obtain the estimates, and , and always substitute them into (12) to implement the filtering strategy. The step-by-step algorithm of this MMF procedure in the context of the L96 model is described in appendix B . Before we show the numerical results of implementing the filtering strategies described above, MF and MMF

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