Estimating Model Parameters with Ensemble-Based Data Assimilation: A Review

In this work, various methods for the estimation of the parameter uncertainty and the covariance between the parameters and the state variables are investigated using the local ensemble transform Kalman filter (LETKF). Two methods are compared for the estimation of the covariances between the state variables and the parameters: one using a single ensemble for the simultaneous estimation of model state and parameters, and the other using two separate ensembles; for the initial conditions and for the parameters. It is found that the method which uses two ensembles produces a more accurate representation of the covariances between observed variables and parameters, although this does not produce an improvement of the parameter or state estimation. The experiments show that the former method with a single ensemble is more efficient and produces results as accurate as the ones obtained with the two separate ensembles method. The impact of parameter ensemble spread upon the parameter estimation and its associated analysis is also investigated. A new approach to the optimization of the estimated parameter ensemble spread (EPES) is proposed in this work. This approach preserves the structure of the analysis error covariance matrix of the augmented state vector. Results indicate that the new approach determines the value of the parameter ensemble spread that produces the lowest errors in the analysis and in the estimated parameters. A simple low-resolution atmospheric general circulation model known as SPEEDY is used for the evaluation of the different parameter estimation techniques.Fil: Ruiz, Juan Jose. Universidad Nacional del Nordeste; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pulido, Manuel Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Miyoshi, Takemasa. University of Maryland; Estados Unidos de América

EFSO at different geographical locations verified with observing-system experiments

ひとつひとつの観測データが気象予測に与える影響を簡易に評価する手法を確認 --北極の観測データは7日先の北米気象予測の改善に貢献することも明らかに--. 京都大学プレスリリース. 2021-04-30.An ensemble-based forecast sensitivity to observations (EFSO) diagnosis has been implemented in an atmospheric general circulation model–ensemble Kalman filter data assimilation system to estimate the impacts of specific observations from the quasi-operational global observing system on weekly short-range forecasts. It was examined whether EFSO reasonably approximates the impacts of a subset of observations from specific geographical locations for 6-hour forecasts, and how long the 6-hour observation impacts can be retained during the 7-day forecast period. The reference for these forecasts was obtained from 12 data denial experiments in each of which a subset of three radiosonde observations launched from a geographical location was excluded. The 12 locations were selected from three latitudinal bands comprising (i) four Arctic regions, (ii) four midlatitude regions in the Northern Hemisphere, and (iii) four tropical regions during the Northern Hemisphere winter of 2015/16. The estimated winter-averaged EFSO-derived observation impacts well corresponded to the 6-hour observation impacts obtained by the data denials and EFSO could reasonably estimate the observation impacts by the data denials on short-range (6-hour to 2-day) forecasts. Furthermore, during the medium-range (4-day to 7-day) forecasts, it was found that the Arctic observations tend to seed the broadest impacts and their short-range observation impacts could be projected to beneficial impacts in Arctic and midlatitude North American areas. The midlatitude area located just downstream of dynamical propagation from the Arctic toward the midlatitudes. Results obtained by repeated Arctic data-denial experiments were found to be generally common to those from the non-repeated experiments

Reduced non-Gaussianity by 30s rapid update in convective-scale numerical weather prediction

Non-Gaussian forecast error is a challenge for ensemble-based data assimilation (DA), particularly for more nonlinear convective dynamics. In this study, we investigate the degree of the non-Gaussianity of forecast error distributions at 1km resolution using a 1000-member ensemble Kalman filter, and how it is affected by the DA update frequency and observation number. Regional numerical weather prediction experiments are performed with the SCALE (Scalable Computing for Advanced Library and Environment) model and the LETKF (local ensemble transform Kalman filter) assimilating phased array radar observations every 30s. The results show that non-Gaussianity develops rapidly within convective clouds and is sensitive to the DA frequency and the number of assimilated observations. The non-Gaussianity is reduced by up to 40% when the assimilation window is shortened from 5min to 30s, particularly for vertical velocity and radar reflectivity.Fil: Ruiz, Juan Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina. Rikagaku Kenkyujo; JapónFil: Lien, Guo-Yuan. Central Weather Bureau, Taiwan; ArgentinaFil: Kondo, Keiichi. Meteorological Research Institute; JapónFil: Otsuka, Shigenori. Rikagaku Kenkyujo; JapónFil: Miyoshi, Takemasa. Rikagaku Kenkyujo; Japón. University of Maryland; Estados Unidos. Japan Agency for Marine-Earth Science and Technology; Japó

A local particle filter and its Gaussian mixture extension implemented with minor modifications to the LETKF

A particle filter (PF) is an ensemble data assimilation method that does not assume Gaussian error distributions. Recent studies proposed local PFs (LPFs), which use localization, as in the ensemble Kalman filter, to apply the PF efficiently for high-dimensional dynamics. Among others, Penny and Miyoshi (2016) developed an LPF in the form of the ensemble transform matrix of the local ensemble transform Kalman filter (LETKF). The LETKF has been widely accepted for various geophysical systems, including numerical weather prediction (NWP) models. Therefore, implementing the LPF consistently with an existing LETKF code is useful. This study develops a software platform for the LPF and its Gaussian mixture extension (LPFGM) by making slight modifications to the LETKF code with a simplified global climate model known as Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY). A series of idealized twin experiments were accomplished under the ideal-model assumption. With large inflation by the relaxation to prior spread, the LPF showed stable filter performance with dense observations but became unstable with sparse observations. The LPFGM showed a more accurate and stable performance than the LPF with both dense and sparse observations. In addition to the relaxation parameter, regulating the resampling frequency and the amplitude of Gaussian kernels was important for the LPFGM. With a spatially inhomogeneous observing network, the LPFGM was superior to the LETKF in sparsely observed regions, where the background ensemble spread and non-Gaussianity were larger. The SPEEDY-based LETKF, LPF, and LPFGM systems are available as open-source software on GitHub (https://github.com/skotsuki/speedy-lpf, last access: 16 November 2022) and can be adapted to various models relatively easily, as in the case of the LETKF

A convective-scale 1,000-member ensemble simulation and potential applications

This study presents the first convective-scale 1,000-member ensemble simulation over central Europe, which provides a unique data set for various applications. A comparison with the operational regional 40-member ensemble of Deutscher Wetterdienst shows that the 1,000-member simulation exhibits realistic spread properties overall. Based on this, we discuss two potential applications. First, we quantify the sampling error of spatial covariances of smaller subsets compared with the 1,000-member simulation. Knowledge about sampling errors and their dependence on ensemble size is crucial for ensemble and hybrid data assimilation and for developing better approaches for localization in this context. Secondly, we present an approach for estimating the relative potential impact of different observable quantities using ensemble sensitivity analysis. This will provide the basis for consecutive studies developing future observation and data assimilation strategies. Sensitivity studies on the ensemble size indicate that about 200 ensemble members are required to estimate the potential impact of observable quantities with respect to precipitation forecasts.Fil: Necker, Tobias. Ludwig Maximilians Universitat; Alemania. Universidad de Viena; AustriaFil: Geiss, Stefan. Ludwig Maximilians Universitat; AlemaniaFil: Weissmann, Martin. Ludwig Maximilians Universitat; AlemaniaFil: Ruiz, Juan Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; ArgentinaFil: Miyoshi, Takemasa. RIKEN Center for Computational Science; JapónFil: Lien, Guo Yuan. RIKEN Center for Computational Science; Japó

Distributions and convergence of forecast variables in a 1,000-member convection-permitting ensemble

The errors in numerical weather forecasts resulting from limited ensemble size are explored using 1,000-member forecasts of convective weather over Germany at 3-km resolution. A large number of forecast variables at different lead times were examined, and their distributions could be classified into three categories: quasi-normal (e.g., tropospheric temperature), highly skewed (e.g. precipitation), and mixtures (e.g., humidity). Dependence on ensemble size was examined in comparison to the asymptotic convergence law that the sampling error decreases proportional to N−1/2 for large enough ensemble size N, independent of the underlying distribution shape. The asymptotic convergence behavior was observed for the ensemble mean of all forecast variables, even for ensemble sizes less than 10. For the ensemble standard deviation, sizes of up to 100 were required for the convergence law to apply. In contrast, there was no clear sign of convergence for the 95th percentile even with 1,000 members. Methods such as neighborhood statistics or prediction of area-averaged quantities were found to improve accuracy, but only for variables with random small-scale variability, such as convective precipitation.Fil: Craig, George C.. Ludwig Maximilians Universitat; AlemaniaFil: Puh, Matjaž. Ludwig Maximilians Universitat; AlemaniaFil: Keil, Christian. Ludwig Maximilians Universitat; AlemaniaFil: Tempest, Kirsten. Ludwig Maximilians Universitat; AlemaniaFil: Necker, Tobias. Universidad de Viena; AustriaFil: Ruiz, Juan Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; ArgentinaFil: Weissmann, Martin. Universidad de Viena; AustriaFil: Miyoshi, Takemasa. Riken Center For Computational Science; Japó

On methods for assessment of the influence and impact of observations in convection-permitting numerical weather prediction

In numerical weather prediction (NWP), a large number of observations are used to create initial conditions for weather forecasting through a process known as data assimilation. An assessment of the value of these observations for NWP can guide us in the design of future observation networks, help us to identify problems with the assimilation system, and allow us to assess changes to the assimilation system. However, the assessment can be challenging in convection-permitting NWP. First, the strong nonlinearity in the forecast model limits the methods available for the assessment. Second, convection-permitting NWP typically uses a limited area model and provides short forecasts, giving problems with verification and our ability to gather sufficient statistics. Third, convection-permitting NWP often makes use of novel observations, which can be difficult to simulate in an observing system simulation experiment (OSSE). We compare methods that can be used to assess the value of observations in convection-permitting NWP and discuss operational considerations when using these methods. We focus on their applicability to ensemble forecasting systems, as these systems are becoming increasingly dominant for convection-permitting NWP. We also identify several future research directions: comparison of forecast validation using analyses and observations, the effect of ensemble size on assessing the value of observations, flow-dependent covariance localization, and generation and validation of the nature run in an OSSE.Comment: 35 page

Modeling sustainability : Population, inequality, consumption, and bidirectional coupling of the Earth and human systems

Over the last two centuries, the impact of the Human System has grown dramatically, becoming strongly dominant within the Earth System in many different ways. Consumption, inequality, and population have increased extremely fast, especially since about 1950, threatening to overwhelm the many critical functions and ecosystems of the Earth System. Changes in the Earth System, in turn, have important feedback effects on the Human System, with costly and potentially serious consequences. However, current models do not incorporate these critical feedbacks. We argue that in order to understand the dynamics of either system, Earth SystemModels must be coupled with Human SystemModels through bidirectional couplings representing the positive, negative, and delayed feedbacks that exist in the real systems. In particular, key Human System variables, such as demographics, inequality, economic growth, and migration, are not coupled with the Earth System but are instead driven by exogenous estimates, such as United Nations population projections.This makes current models likely to miss important feedbacks in the real Earth-Human system, especially those that may result in unexpected or counterintuitive outcomes, and thus requiring different policy interventions from current models.The importance and imminence of sustainability challenges, the dominant role of the Human System in the Earth System, and the essential roles the Earth System plays for the Human System, all call for collaboration of natural scientists, social scientists, and engineers in multidisciplinary research and modeling to develop coupled Earth-Human system models for devising effective science-based policies and measures to benefit current and future generations