An explicit four-dimensional variational data assimilation method based on the proper orthogonal decomposition: Theoretics and evaluation

The proper orthogonal decomposition (POD) method is used to construct a set of basis functions for spanning the ensemble of data in a certain least squares optimal sense. Compared with the singular value decomposition (SVD), the POD basis functions can capture more energy in the forecast ensemble space and can represent its spatial structure and temporal evolution more effectively. After the analysis variables are expressed by a truncated expansion of the POD basis vectors in the ensemble space, the control variables appear explicitly in the cost function, so that the adjoint model, which is used to derive the gradient of the cost function with respect to the control variables, is no longer needed. The application of this new technique significantly simplifies the data assimilation process. Several assimilation experiments show that this POD-based explicit four-dimensional variational data assimilation method performs much better than the usual ensemble Kalman filter method on both enhancing the assimilation precision and reducing the computation cost. It is also better than the SVD-based explicit four-dimensional assimilation method, especially when the forecast model is not perfect and the forecast error comes from both the noise of the initial filed and the uncertainty of the forecast model. Supported by the National Natural Science Foundation of China (Grant No. 40705035), National High Technology Research and Development Program of China (Grant No. 2007AA12Z144), Knowledge Innovation Project of Chinese Academy of Sciences (Grant Nos. KZCX2-YW-217 and KZCX2-YW-126-2), and National Basic Research Program of China (Grant No. 2005CB321704)     

中国电离层TEC同化现报系统

数据同化是在基于物理机制的背景模型上,融合时空不规则分布的观测数据的一种现报方法.同化能够有效弥补数据的时空局限和模型的精度偏差,使二者相互匹配从而获得更加合理可信的模拟效果.本研究利用电离层数据同化方法,针对中国及周边区域（15°N—55°N,70°E—140°E）构建了电离层总电子含量（TEC）同化现报系统.系统使用国际参考电离层（IRI）作为背景场,利用中国科学院空间环境监测网和国际GNSS服务组织（IGS）的部分地基GNSS台站数据作为观测值,并采用三维变分与Gauss-Markov卡尔曼滤波相结合的算法进行背景场和观测值的数据同化,生成覆盖中国及周边区域的电离层TEC和GPS单频接收机延迟误差的格点化准实时现报地图,并在中国科学院空间环境预报中心（http://sepc.ac.cn/TEC_chn.php）网上发布,每15 min进行更新.该系统是我国基于同化算法的电离层现报系统之一,已用于中国及周边区域的电离层环境实时监测,可为卫星导航、雷达成像、短波通信等科学研究和工程应用提供相对及时、准确、有效的电离层TEC和误差修正信息.     

Nonlinear balance constraints in 3DVAR data assimilation

Consideration of the so-called balance properties/ constraints is of great importance in the data assimila- tion. First, it is desirable to separate the slow modes (e.g., Rossby waves) from the fast modes (e.g., gravity waves and deep convection). Second, consideration of the balance constraints enables us to infer information about all variables that are balanced with the observed variable and hereby improve the quality of the analy- sis. The balance properties are usually represented by some…     

Toward a global ocean data assimilation system based on ensemble optimum interpolation: altimetry data assimilation experiment

A global ocean data assimilation system based on the ensemble optimum interpolation (EnOI) has been under development as the Chinese contribution to the Global Ocean Data Assimilation Experiment. The system uses a global ocean general circulation model, which is eddy permitting, developed by the Institute of Atmospheric Physics of the Chinese Academy of Sciences. In this paper, the implementation of the system is described in detail. We describe the sampling strategy to generate the stationary ensembles for EnOI. In addition, technical methods are introduced to deal with the requirement of massive memory space to hold the stationary ensembles of the global ocean. The system can assimilate observations such as satellite altimetry, sea surface temperature (SST), in situ temperature and salinity from Argo, XBT, Tropical Atmosphere Ocean (TAO), and other sources in a straightforward way. As a first step, an assimilation experiment from 1997 to 2001 is carried out by assimilating the sea level anomaly (SLA) data from TOPEX/Poseidon. We evaluate the performance of the system by comparing the results with various types of observations. We find that SLA assimilation shows very positive impact on the modeled fields. The SST and sea surface height fields are clearly improved in terms of both the standard deviation and the root mean square difference. In addition, the assimilation produces some improvements in regions where mesoscale processes cannot be resolved with the horizontal resolution of this model. Comparisons with TAO profiles in the Pacific show that the temperature and salinity fields have been improved to varying degrees in the upper ocean. The biases with respect to the independent TAO profiles are reduced with a maximum magnitude of about 0.25°C and 0.1 psu for the time-averaged temperature and salinity. The improvements on temperature and salinity also lead to positive impact on the subsurface currents. The equatorial under current is enhanced in the Pacific although it is still underestimated after the assimilation.     

An explicit four-dimensional variational data assimilation method

A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost func-tion with respect to the control variables, is no longer needed. The new technique significantly simpli-fies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.     

Theoretical analyses and numerical experiments of variational assimilation for one-dimensional ocean temperature model with techniques in inverse problems

There is an international focus on the develop-ments of data assimilation systems for meteorology and physical oceanography models. Data assimilation and inverse methods are normally used for optimal control of poorly known initial boundary conditions and model parameters by taking into account both the information about dynamics of a model and the infor-mation about the true state which is constrained by a set of measurements. The research methodology of parameter estimation in meteorology ca…     

A land surface data assimilation framework using the land information system: Description and applications

The Land Information System (LIS) is an established land surface modeling framework that integrates various community land surface models, ground measurements, satellite-based observations, high performance computing and data management tools. The use of advanced software engineering principles in LIS allows interoperability of individual system components and thus enables assessment and prediction of hydrologic conditions at various spatial and temporal scales. In this work, we describe a sequential data assimilation extension of LIS that incorporates multiple observational sources, land surface models and assimilation algorithms. These capabilities are demonstrated here in a suite of experiments that use the ensemble Kalman filter (EnKF) and assimilation through direct insertion. In a soil moisture experiment, we discuss the impact of differences in modeling approaches on assimilation performance. Provided careful choice of model error parameters, we find that two entirely different hydrological modeling approaches offer comparable assimilation results. In a snow assimilation experiment, we investigate the relative merits of assimilating different types of observations (snow cover area and snow water equivalent). The experiments show that data assimilation enhancements in LIS are uniquely suited to compare the assimilation of various data types into different land surface models within a single framework. The high performance infrastructure provides adequate support for efficient data assimilation integrations of high computational granularity.     

Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean

This paper presents a comparison of two reduced-order, sequential, and variational data assimilation methods: the singular evolutive extended Kalman filter (SEEK) and the reduced 4D-Var (R-4D-Var). A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasilinear regime, both methods produce similarly good results. However, the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more nonlinear regime, when tropical instability waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error.     

A data assimilation approach to discharge estimation from space

River discharge is currently monitored by a diminishing network of gauges, which provide a spatially incomplete picture of global discharges. This study assimilated water level information derived from a fused satellite Synthetic Aperture Radar (SAR) image and digital terrain model (DTM) with simulations from a coupled hydrological and hydrodynamic model to estimate discharge in an un‐gauged basin scenario. Assimilating water level measurements led to a 79% reduction in ensemble discharge uncertainty over the coupled hydrological hydrodynamic model alone. Measurement bias was evident, but the method still provided a means of improving estimates of discharge for high flows. The study demonstrates the potential of currently available synthetic aperture radar imagery to reduce discharge uncertainty in un‐gauged basins when combined with model simulations in a data assimilation framework, where sufficient topographic data are available. The work is timely because in the near future the launch of satellite radar missions will lead to a significant increase in the volume of data available for space‐borne discharge estimation. Copyright © 2009 John Wiley & Sons, Ltd.     

Utilization of satellite data in land surface hydrology: sensitivity and assimilation

This paper investigates the sensitivity of potential evapotranspiration to input meteorological variables, i.e. surface air temperature and surface vapor pressure. The sensitivity studies have been carried out for a wide range of land surface variables such as wind speed, leaf area index and surface temperatures. Errors in the surface air temperature and surface vapor pressure result in errors of different signs in the computed potential evapotranspiration. This result has implications for use of estimated values from satellite data or analysis of surface air temperature and surface vapor pressure in large‐scale hydrological modeling. The comparison of cumulative potential evapotranspiration estimates using ground observations and satellite observations over Manhattan, Kansas for a period of several months shows a variable difference between the two estimates. The use of satellite estimates of surface skin temperature in hydrological modeling to update the soil moisture using a physical adjustment concept is studied in detail, including the extent of changes in soil moisture resulting from the assimilation of surface skin temperature. The soil moisture of the 1 cm surface layer was adjusted by 0·9 mm over a 10‐day period as a result of a 3 K difference between the predicted and the observed surface temperature. This is a considerable amount given the fact that the top layer can hold only 5 mm of moisture. Copyright © 2001 John Wiley & Sons, Ltd.     

Estimation of model errors generated by atmospheric forcings for ocean data assimilation: experiments in a regional model of the Bay of Biscay

The characterization of model errors is an essential step for effective data assimilation into open-ocean and shelf-seas models. In this paper, we propose an experimental protocol to properly estimate the error statistics generated by imperfect atmospheric forcings in a regional model of the Bay of Biscay, nested in a basin-scale North Atlantic configuration. The model used is the Hybrid Coordinate Ocean Model (HYCOM), and the experimental protocol involves Monte Carlo (or ensemble) simulations. The spatial structure of the model error is analyzed using the representer technique, which allows us to anticipate the subsequent impact in data assimilation systems. The results show that the error is essentially anisotropic and inhomogeneous, affecting mainly the model layers close to the surface. Even when the forcings errors are centered around zero, a divergence is observed between the central forecast and the mean forecast of the Monte Carlo simulations as a result of nonlinearities. The 3D structure of the representers characterizes the capacity of different types of measurement (sea level, sea surface temperature, surface velocities, subsurface temperature, and salinity) to control the circulation. Finally, data assimilation experiments demonstrate the superiority of the proposed methodology for the implementation of reduced-order Kalman filters.     

Sea surface height and transport stream function of the South China Sea from a variable-grid global ocean circulation model

The study on the South China Sea (SCS) circulation has a history of more than 40 years. Nevertheless, the SCS circulation is not fully understood compared with the Bohai Sea, Yellow Sea and East China Sea (ECS). Many numerical studies on the SCS circulati…     

A three-dimensional variational data assimilation system for a size-resolved aerosol model: Implementation and application for particulate matter and gaseous pollutant forecasts across China

A three-dimensional variational(3DVAR) data assimilation(DA) system is presented here based on a size-resolved sectional aerosol model, the Model for Simulating Aerosol Interactions and Chemistry(MOSAIC) within the Weather Research and Forecasting model coupled to Chemistry(WRF-Chem) model. The use of this approach means that both gaseous pollutants such as SO_2, NO_2, CO, and O_3 as well as particulate matter(PM_(2.5), PM_(10)) observational data can be assimilated simultaneously.Two one-month parallel simulation experiments were conducted, one with the assimilation of surface hourly concentration observations of the above six pollutants released by the China National Environmental Monitoring Centre(CNEMC) and one without assimilation in order to verify the impact of assimilation on initial chemical fields and subsequent forecasts. Results show that, in the first place, use of the DA system can provide a more accurate model initial field. The root-mean-square error of PM_(2.5), PM_(10), SO_2, NO_2, CO, and O_3 mass concentrations in analysis field fell by 29.27 μg m~(-3)(53.5%), 34.5 μg m~(-3)(50.9%),30.36 μg m~(-3)(64.2%), 8.91 μg m~(-3)(39.5%), 0.46 mg m~(-3)(47.4%), and 15.11 μg m~(-3)(51.0%), respectively, compared to a background field without assimilation. At the same time, mean fraction error was reduced by 42.6%, 53.1%, 45.2%, 43.1%,69.9%, and 48.8%, respectively, while the correlation coefficient increased by 0.51, 0.55, 0.48, 0.38, 0.47, 0.65, respectively.Secondly, the results of this analysis reveal variable benefits from assimilation on different pollutants. DA significantly improves PM_(2.5), PM_(10), and CO forecasts leading to positive effects that last more than 48 h. The positive effects of DA on SO_2 and O_3 forecasts last up to 8 h but that remains relatively poor for NO_2 forecasts. Thirdly, the influence of assimilation varies in different areas. It is possible that the positive effects of DA on PM_(2.5) and PM_(10) forecasts can last more than 48 h across most regions of China. Indeed, DA significantly improves SO_2 forecasts within 48 h over north China, and much longer CO assimilation benefits(48 h) are found in most regions apart from north and east China and across the Sichuan Basin. DA is able to improve O_3 forecasts within 48 h across China with the exception of southwest and northwest regions and the O_3 DA benefits in southern China are more evident, while from a spatial distribution perspective, NO_2 DA benefits remain relatively poor.     

Feed-forward vs recurrent neural network models for non-stationarity modelling using data assimilation and adaptivity

Abstract

Artificial neural networks (ANN) are nonlinear models widely investigated in hydrology due to their properties of universal approximation and parsimony. Their performance during the training phase is very good, and their ability to generalize can be improved by using regularization methods such as early stopping and cross-validation. In our research, two kinds of generic models are implemented: the feed-forward model and the recurrent model. At first glance, the feed-forward model would seem to be more effective than the recurrent one on non-stationary datasets, because measured information on the state of the system (measured discharge) is used as input, thereby implementing a kind of data assimilation. This study investigates the feasibility and effectiveness of data assimilation and adaptivity when implemented in both feed-forward and recurrent neural networks. Based on the IAHS Workshop held in Göteborg, Sweden (July 2013), the hydrological behaviour of two watersheds of different sizes and different kind of non-stationarity will be modelled: (a) the Fernow watershed (0.2 km²) in the USA, affected by significant modifications in land cover during the study period, and (b) the Durance watershed (2170 km²) in France, affected by an increase in temperature that is causing a decrease in the extent of glaciers. Two methods were applied to evaluate the ability of ANN to adapt on the test set: (i) adaptivity using observed data to adapt parameter values in real time; and (ii) data assimilation using observed data to modify inaccurate inputs in real time. The goal of the study is thus re-analysis and not forecasting. This study highlights how effective the feed-forward model is compared to the recurrent model for dealing with non-stationarity. It also shows that adaptivity and data assimilation improve the recurrent model considerably, whereas improvement is marginal for the feed-forward model in the same conditions. Finally, this study suggests that adaptivity is effective in the case of changing conditions of the watershed, whereas data assimilation is better in the case of climate change (inputs modification).     

Parameter estimation in ensemble based snow data assimilation: A synthetic study

Estimating erroneous parameters in ensemble based snow data assimilation system has been given little attention in the literature. Little is known about the related methods’ effectiveness, performance, and sensitivity to other error sources such as model structural error. This research tackles these questions by running synthetic one-dimensional snow data assimilation with the ensemble Kalman filter (EnKF), in which both state and parameter are simultaneously updated. The first part of the paper investigates the effectiveness of this parameter estimation approach in a perfect-model-structure scenario, and the second part focuses on its dependence on model structure error. The results from first part research demonstrate the advantages of this parameter estimation approach in reducing the systematic error of snow water equivalent (SWE) estimates, and retrieving the correct parameter value. The second part results indicate that, at least in our experiment, there is an evident dependence of parameter search convergence on model structural error. In the imperfect-model-structure run, the parameter search diverges, although it can simulate the state variable well. This result suggest that, good data assimilation performance in estimating state variables is not a sufficient indicator of reliable parameter retrieval in the presence of model structural error. The generality of this conclusion needs to be tested by data assimilation experiments with more complex structural error configurations.     

Numerical simulation and data assimilation of the water-energy cycle over semiarid northeastern China

The default fractional vegetation cover and terrain height were replaced by the estimated fractional vegetation cover, which was calculated by the Normalized Difference Vegetation Index(NDVI) of Earth Observing System Moderate-Resolution Imaging Spectroradiometer(EOS-MODIS) and the Digital Elevation Model of the Shuttle Radar Topography Mission(SRTM) system. The near-surface meteorological elements over northeastern China were assimilated into the three-dimensional variational data assimilation system(3DVar) module in the Weather Research and Forecasting(WRF) model. The structure and daily variations of air temperature, humidity, wind and energy fields over northeastern China were simulated using the WRF model. Four groups of numerical experiments were performed, and the simulation results were analyzed of latent heat flux, sensible heat flux, and their relationships with changes in the surface energy flux due to soil moisture and precipitation over different surfaces. The simulations were compared with observations of the stations Tongyu, Naiman, Jinzhou, and Miyun from June to August, 2009. The results showed that the WRF model achieves high-quality simulations of the diurnal characteristics of the surface layer temperature, wind direction, net radiation, sensible heat flux, and latent heat flux over semiarid northeastern China in the summer. The simulated near-surface temperature, relative humidity, and wind speed were improved in the data assimilation case(Case 2) compared with control case(Case 1). The simulated sensible heat fluxes and surface heat fluxes were improved by the land surface parameterization case(Case 3) and the combined case(Case 4). The simulated temporal variations in soil moisture over the northeastern arid areas agree well with observations in Case 4, but the simulated precipitation should be improved in the WRF model. This study could improve the land surface parameters by utilizing remote sensing data and could further improve atmospheric elements with a data assimilation system. This work provides an effective attempt at combining multi-source data with different spatial and temporal scales into numerical simulations. The assimilation datasets generated by this work can be applied to research on climate change and environmental monitoring of arid lands, as well as research on the formation and stability of climate over semiarid areas.     

年代际预测和耦合资料同化研究综述

年代际预测是近年来气候变化研究的一个迅速发展的新兴热点领域,其首要步骤是进行初始化,目的是为年代际预测提供包含观测变率信息的初值.发展效果好且省时的初始化方法是年代际预测的重大挑战之一,目前国际上主流的初始化方法是耦合资料同化,即在耦合模式框架下进行同化.在年代际预测时,由于模式偏差和初始化方法性能的限制会产生初始冲击问题.目前国际上的各模式机构普遍对北大西洋、热带东西太平洋和印度洋海表温度的年代际预测水平高,而对全球平均近地面气温和北太平洋海表温度的年代际预测水平相对较差.本文主要从初始化方法和年代际预测这两方面的研究现状进行全面回顾,指出存在的问题并讨论未来的发展趋势和挑战.

     

地球电子外辐射带的数据同化建模与分析

地球电子外辐射带对太阳与地磁活动呈现高度动态变化的响应,了解外辐射带的全球动态变化过程对于近地空间粒子辐射环境的理解认知和预测预报具有重要意义.基于卡尔曼滤波数据同化方法,本文利用范阿伦A星、B星和GOES-13和GOES-15四颗卫星的辐射带电子观测数据,分别利用三种不同维度的辐射带物理模型,将观测结果与数值结果有机融合,对2013年3月地球外辐射带电子通量的径向分布与变化进行数据同化分析.结果表明,考虑了磁层波动与辐射带电子共振作用引起的径向扩散、投掷角扩散以及能量扩散过程的三维同化模型可有效、合理地重现外辐射带电子通量的径向分布.本文进一步利用该三维同化模型对2013年一整年外辐射带电子的相空间密度分布进行重构与分析,得到了不同绝热不变量和不同地磁活动条件下电子辐射带的时空演化过程,从而为深入理解外辐射带电子的变化过程和动力学机制提供了强有力信息.通过分析同化过程中的新息矢量以及度量同化过程中观测数据在多大程度上修改了物理模型结果,还有助于定量分析现有辐射带物理模型中的源项和损失项的相对贡献以及可能忽略的物理机制或过程.

     

Exploring the effect of data assimilation by WRF‐3DVar for numerical rainfall prediction with different types of storm events

The mesoscale Numerical Weather Prediction (NWP) model is gaining popularity among the hydrometeorological community in providing high‐resolution rainfall forecasts at the catchment scale. Although the performance of the model has been verified in capturing the physical processes of severe storm events, the modelling accuracy is negatively affected by significant errors in the initial conditions used to drive the model. Several meteorological investigations have shown that the assimilation of real‐time observations, especially the radar data can help improve the accuracy of the rainfall predictions given by mesoscale NWP models. The aim of this study is to investigate the effect of data assimilation for hydrological applications at the catchment scale. Radar reflectivity together with surface and upper‐air meteorological observations is assimilated into the Weather Research and Forecasting (WRF) model using the three‐dimensional variational data‐assimilation technique. Improvement of the rainfall accumulation and its temporal variation after data assimilation is examined for four storm events in the Brue catchment (135.2 km²) located in southwest England. The storm events are selected with different rainfall distributions in space and time. It is found that the rainfall improvement is most obvious for the events with one‐dimensional evenness in either space or time. The effect of data assimilation is even more significant in the innermost domain which has the finest spatial resolution. However, for the events with two‐dimensional unevenness of rainfall, i.e. the rainfall is concentrated in a small area and in a short time period, the effect of data assimilation is not ideal. WRF fails in capturing the whole process of the highly convective storm with densely concentrated rainfall in a small area and a short time period. A shortened assimilation time interval together with more efficient utilisation of the weather radar data might help improve the effectiveness of data assimilation in such cases. Copyright © 2012 John Wiley & Sons, Ltd.