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)     

Effects of sample density on the assimilation performance of an explicit four-dimensional variational data assimilation method

The concepts of sample sphere radius and sample density are proposed in this paper to help illustrate that different vector transformations result in diverse sample density with the same sample ensemble, which finally affects their assimilation performance. Several numerical experiments using a one-dimensional (1-D) soil water equation and synthetic observations are conducted to evaluate this new theory in land data assimilation.     

利用GRACE数据联合新型尺度因子校正法提高陆地水储量变化准确性

本文围绕GRACE数据在信号处理过程中存在泄露误差开展了探索性研究.第一,在传统尺度因子法的基础上,根据模型与CSR-SHc数据的均方根误差和相关性赋予权重,构建了新型尺度因子校正法.第二,以长江流域为例,评估该方法的校正效果,研究结果表明:新型尺度因子校正法校正结果综合GLDAS(Global Land Data A...     

基于多层感知机重建GRACE与GRACE-FO之间数据缺失的黄河流域陆地水储量变化

GRACE重力卫星于2017年6月结束,GRACE-Follow On (GRACE-FO)任务于2018年5月启动,导致了约一年的数据缺失.为了研究长时间序列陆地水储量的变化情况,需要重建这两代重力卫星之间的数据.本文基于多层感知机的神经网络模型,通过将GLDAS、CPC土壤湿度、土壤温度、蒸散量以及降水量等数据作为输入参数,GRACE等效水高作为输出参数来训练神经网络,以黄河流域为研究区域,得到缺失等效水高.通过分析黄河流域等效水高时间序列,得出在2002-2020年间研究区域水储量整体上呈现以-0.51±0.03 cm·a^-1速率减少的趋势.GRACE反演的等效水高相对于降水、蒸散量以及土壤温度滞后时间达2~3个月.通过小波分析验证了GRACE与GLDAS、CPC计算的等效水高具有较强的相关性,且均具有明显的周年共振周期.

     

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.     

Initial ensemble generation and validation for ocean data assimilation using HYCOM in the Pacific

A method to initialize an ensemble, introduced by Evensen (Physica, D 77:108–129, 1994a; J Geophys Res 99(C5):10143–10162, 1994b; Ocean Dynamics 53:343–367, 2003), was applied to the Ocean General Circulation Model (OGCM) HYbrid Coordinate Ocean Model (HYCOM) for the Pacific Ocean. Taking advantage of the hybrid coordinates, an initial ensemble is created by first perturbing the layer interfaces and then running the model for a spin-up period of 1 month forced by randomly perturbed atmospheric forcing fields. In addition to the perturbations of layer interfaces, we implemented perturbations of the mixed layer temperatures. In this paper, we investigate the quality of the initial ensemble generated by this scheme and the influence of the horizontal decorrelation scale and vertical correlation on the statistics of the resulting ensemble. We performed six ensemble generation experiments with different combinations of horizontal decorrelation scales and with/without perturbations in the mixed layer. The resulting six sets of initial ensembles are then analyzed in terms of sustainability of the ensemble spread and realism of the correlation patterns. The ensemble spreads are validated against the difference between model and observations after 20 years of free run. The correlation patterns of six sets of ensemble are compared to each other. This study shows that the ensemble generation scheme can effectively generate an initial ensemble whose spread is consistent with the observed errors. The correlation pattern of the ensemble also exhibits realistic features. The addition of mixed layer perturbations improves both the spread and correlation. Some limitations of the ensemble generation scheme are also discussed. We found that the vertical shift of isopycnal coordinates provokes unrealistically large deviations in shallow layers near the islands of the West Pacific. A simple correction circumvents the problem.

Adjoint free four-dimensional variational data assimilation for a storm surge model of the German North Sea

In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.     

利用GPS垂直位移反演区域陆地水储量变化的TSVD-Tikhonov正则化方法

利用GPS垂直位移反演区域陆地水储量变化（TWSC）属于典型的病态问题,其关键是如何进行稳定求解并提高反演结果的精度和可靠性.本文引入TSVD-Tikhonov组合正则化方法对利用GPS垂直位移反演区域TWSC的病态问题进行求解,并以四川省TWSC反演为例进行分析与验证.首先,通过数值模拟对TSVD、Tikhonov和TSVD-Tikhonov正则化方法采用不同正则化参数选取策略（RMSE最小准则、GCV法和L-curve法）进行反演,结果显示基于TSVD-Tikhonov正则化反演的TWSC比单独使用TSVD或Tikhonov正则化反演结果的精度和可靠性更高,这三种正则化方法反演2005年1月至12月的TWSC差值的平均STD分别为14.97 mm、7.03 mm和5.04 mm.其次,利用中国地壳运动观测网络（CMONOC）的72个GPS测站的垂直位移数据,基于TSVD-Tikhonov正则化反演了四川省2010年12月至2021年2月的TWSC时间序列,结果表明GPS反演的TWSC与GRACE/GFO Mascon模型（JPL、CSR和GSFC）的空间分布特征及季节性变化符合较好,但其TWSC信号的振幅比GRACE/GFO Mascon模型更强.最后,采用广义三角帽方法（GTCH）融合不同类型的降水、蒸散发和径流数据,并根据水量平衡方程计算的dTWSC/dt序列（PER-dS/dt）对GPS反演的dTWSC/dt序列（GPS-dS/dt）和GRACE/GFO Mascon模型融合的dTWSC/dt序列（GRACE/GFO-dS/dt）进行验证,结果表明这三类dTWSC/dt序列的季节性变化符合较好,平滑后GPS-dS/dt和GRACE/GFO-dS/dt序列与PER-dS/dt序列的相关系数分别为0.78和0.87,但GPS相比GRACE/GFO对降水变化的响应更为敏感.本文研究证明了TSVD-Tikhonov组合正则化方法能够提高GPS垂直位移反演区域TWSC的精度和可靠性,同时也表明GPS观测数据对局部水质量负荷变化更为敏感,可作为GRACE/GFO反演区域TWSC的有益补充.

     

改进的GRACE约束正演法及其在尼皮贡湖陆地水储量变化估计中的应用

准确估计北美尼皮贡湖的陆地水储量(Terrestrial Water Storage,TWS)变化对该区域水资源调控具有重要意义.GRACE和GRACE-FO时变重力场被广泛用于定量估计TWS变化,然而截断与滤波处理会削弱信号幅度,造成信号泄漏.对于小区域尺度的研究,该现象尤为显著.约束正演法能减小泄漏误差,但是面对多质量块,传统迭代策略的收敛性能受初值影响大.为此,本文采用多个质量块分批迭代的策略,改进约束正演法在尼皮贡湖的收敛性能.模拟实验结果表明,在无偏差空间约束下,本文方法与逐格网点同时迭代和多个质量块同时迭代的策略相比,在尼皮贡湖区域绝对偏差的均方根分别降低了2.27 mm·a^-1和1.77 mm·a^-1.进一步,利用改进方法估计尼皮贡湖TWS变化,并与卫星测高数据进行对比.研究结果表明,本文方法显著降低了尼皮贡湖TWS的信号泄漏影响,恢复后的TWS信号幅度约为逐格网点同时迭代和多个质量块同时迭代策略的1.2倍.经泄漏改正后,GRACE/GRACE-FO反演的尼皮贡湖TWS与卫星测高水位变化时间序列的长期趋势相吻合.本文可为研究其他小尺度区域TWS提供一定参考.

     

利用广义三角帽方法评估GRACE反演中国大陆地区水储量变化的不确定性

在无真实观测值的情况下,本文利用广义三角帽方法评估了五种GRACE时变重力场模型（CSR、GFZ、GRGS、HUST发布的球谐系数解和JPL发布的Mascon解）反演中国大陆地区2003-2013年水储量变化的不确定性.研究结果表明,CSR、GFZ、JPL、HUST和GRGS反演月水储量变化不确定性的区域平均RMS分别为14.4 mm、26.3 mm、25.3 mm、26.6 mm和56.1 mm,其中GRGS的结果未恢复泄漏信号;在季和年尺度上,模型的不确定性均小于月尺度;扣除周期和趋势信号后,各模型反演结果更为一致.除长江流域外,CSR在13个流域的不确定性均小于其他模型,GRGS反演各流域水储量变化的不确定性通常较大,且可能高估了温带大陆性气候地区水储量的波动;CSR和JPL的不确定性受流域周边水文特征、气候类型、流域面积和形状的影响相对较小,不确定性变化范围分别为2.3~17.1 mm和5.6~22.5 mm,GFZ和HUST受影响较大,不确定性变化范围分别为5.5~35.1 mm和4.0~40.6 mm.本文的研究结果为GRACE产品不确定性评估提供了新的途径,为GRACE时变重力场模型的选取提供参考.

     

基于四维变分同化法的巢湖流域南淝河水质模拟

针对河流模拟中未知不确定性源对模拟精度的影响,以巢湖流域南淝河为研究对象,建立了基于四维变分同化方法的南淝河干流水质模型,研究了含未知污染源的南淝河水质过程模拟.模型以未知污染负荷的动态变化过程为控制变量,通过同化沿河不同断面的逐日水质监测数据,识别不同河段的逐日入河污染负荷过程来实现水质过程的模拟,改变了常规模型模拟...     

GRACE/GRACE-FO空窗期的陆地水储量变化数据间断补偿:以全球典型流域为例

陆地水储量异常(TWSA)的长期可持续监测对研究水循环过程、合理配置水资源等具有重要的科学意义,针对GRACE与GRACE-FO数据之间存在空窗期问题,本文引入了奇异谱分析(SSA)与ARMA模型的组合方法对TWSA的间断进行补偿.为比较SSA+ARMA方法在典型流域的适用性,将GRACE球谐系数(SH)反演的2003...     

Projection of droughts and their socioeconomic exposures based on terrestrial water storage anomaly over China

Science China Earth Sciences - Global warming has altered the thermodynamic and dynamic environments of the climate system, thus affecting the energy budget and water cycle process of the...     

Contributions of terrestrial and GRACE data to the study of the secular geoid changes in North America

This paper tests and discusses different statistical methods for modelling secular rates of change of the geoid in North America. In particular, we use the method of principal component/empirical orthogonal functions (PC/EOF) analysis to model the geoid rates from Gravity Recovery and Climate Experiment (GRACE) satellite data. As demonstrated, the PC/EOF analysis is useful for studying the contributions from different signals (mainly residual hydrology signals and leakage effects) to the GRACE-derived geoid rates. The PC/EOF analysis leads to smaller geoid rates compared to the conventional least-squares fitting of a trend and annual and semi-annual cycles to the time series of the spherical harmonic coefficients. This is because we filter out particular spatiotemporal modes of the regional geoid changes.We apply the method of least-squares collocation with parameters to combine terrestrial data (GPS vertical velocities from the Canadian Base Network and terrestrial gravity rates from the Canadian Gravity Standardization Net) with the GRACE-derived vertical motion to obtain again the geoid rates. The combined model has a peak geoid rate of 1.4 mm/year in the southeastern area of Hudson Bay contrary to the GRACE-derived geoid rates that show a large peak of 1.6–1.7 mm/year west of Hudson Bay. We demonstrate that the terrestrial data, which have a longer time span than the GRACE data, are important for constraining the GRACE-derived secular signal in the areas that are well sampled by the data.     

A soil moisture assimilation scheme based on the ensemble Kalman filter using microwave brightness temperature

This study presents a soil moisture assimilation scheme, which could assimilate microwave brightness temperature directly, based on the ensemble Kalman filter and the shuffled complex evolution method (SCE-UA). It uses the soil water model of the land surface model CLM3.0 as the forecast operator, and a radiative transfer model (RTM) as the observation operator in the assimilation system. The assimilation scheme is implemented in two phases: the parameter calibration phase and the pure soil moisture assimilation phase. The vegetation optical thickness and surface roughness parameters in the RTM are calibrated by SCE-UA method and the optimal parameters are used as the final model parameters of the observation operator in the assimilation phase. The ideal experiments with synthetic data indicate that this scheme could significantly improve the simulation of soil moisture at the surface layer. Furthermore, the estimation of soil moisture in the deeper layers could also be improved to a certain extent. The real assimilation experiments with AMSR-E brightness temperature at 10.65 GHz (vertical polarization) show that the root mean square error (RMSE) of soil moisture in the top layer (0–10 cm) by assimilation is 0.03355 m³ · m⁻³, which is reduced by 33.6% compared with that by simulation (0.05052 m³ · m⁻³). The mean RMSE by assimilation for the deeper layers (10–50 cm) is also reduced by 20.9%. All these experiments demonstrate the reasonability of the assimilation scheme developed in this study.     

An effective method based on dynamic sampling for data assimilation in a global wave model

The ensemble Kalman filter (EnKF) performs well because that the covariance of background error is varying along time. It provides a dynamic estimate of background error and represents the reasonable statistic characters of background error. However, high computational cost due to model ensemble in EnKF is employed. In this study, two methods referred as static and dynamic sampling methods are proposed to obtain a good performance and reduce the computation cost. Ensemble adjustment Kalman filter (EAKF) method is used in a global surface wave model to examine the performance of EnKF. The 24-h interval difference of simulated significant wave height (SWH) within 1 year is used to compose the static samples for ensemble errors, and these errors are used to construct the ensemble states at each time the observations are available. And then, the same method of updating the model states in the EAKF is applied for the ensemble states constructed by a static sampling method. The dynamic sampling method employs a similar method to construct the ensemble states, but the period of the simulated SWH is changing with time. Here, 7 days before and after the observation time is used as this period. To examine the performance of three schemes, EAKF, static, or dynamic sampling method, observations from satellite Jason-2 in 2014 are assimilated into a global wave model, and observations from satellite Saral are used for validation. The results indicate that the EAKF performs best, while the static sampling method is relatively worse. The dynamic sampling method improves an assimilation effect dramatically compared to the static sampling method, and its overall performance is closed to the EAKF. In low latitudes, the dynamic sampling method has a slight advantage over the EAKF. In the dynamic or static sampling methods, only one wave model is required to run and their computational cost is reduced sharply. According to the performance of these three methods, the dynamic sampling method can treated as an effective alternative of EnKF, which could reduce the computational cost and provide a good performance of data assimilation.     

Analysis and partitioning of terrestrial water storage in the Yellow River source region

In order to increase the capability to understand and quantify the spatial differences in terrestrial water storage (TWS), and to reflect the unique energy balance processes and soil freeze–thaw mechanisms in the Qinghai-Tibet Plateau (QTP), this study improved the energy balance processes of the water and energy transfer processes model, including its surface radiation calculations and snowmelt module. By integrating these improvements, a water and energy transfer processes model in Qinghai-Tibet Plateau (WEP-QTP) for the Yellow River source region (YRSR) is developed. Using the improved WEP-QTP model to perform simulations, we assessed the daily changes in snow cover, soil moisture (SM), permafrost (PM), and groundwater storage (GWS) in the YRSR. Our analysis revealed an increase in TWS of 0.24 mm/yr from 1961 to 2020. Snow water equivalent (SWE), SM, PM, and GWS have proportional contributions of 8.33%, 216.67%, −154.17%, and 29.17% to the increased TWS, respectively. SM is the primary component of TWS. Temperature (T), precipitation (P), evapotranspiration (E), and solar radiation (Rs) influence the spatiotemporal variations in TWS, as well as those of its components. The increase in P is the primary cause for the rise in TWS, SWE, and SM, while the increase in T predominantly contributes to the decrease in PM. Furthermore, permafrost degradation and climate-induced warming and humidification lead to increased infiltration, resulting in elevated GWS.     

利用GNSS垂直位移研究长江流域陆地水储量变化的时空分布特征

连续运行的GNSS参考站网络能够实时监测地表水文负荷变迁引起的弹性地壳垂直变形.因此,利用GNSS观测的水文负荷垂直位移估计区域陆地水储量变化是一种行之有效的方案.本文收集了长江流域98个GNSS台站2011—2020年的垂直位移时间序列,并采用Slepian基函数方法将其转化为相应的位移谱,基于质量负荷理论估算长江流域陆地水储量变化,然后联合GRACE、GLDAS和降水数据分析其时空分布特征及水文驱动机制.GNSS反演结果与GRACE、GLDAS水储量变化均表现出明显的季节特征,周年振幅的空间相关系数分别为0.79和0.91.三种结果均表现出年水储量变化东西部大、中部小的空间模式,但GNSS反演结果显示整个长江流域水储量变化的最大周年振幅为~214 mm,明显大于GRACE (~121 mm)和GLDAS (~107 mm)的结果.此外,本文深入调查了长江流域三个子区域(金沙江流域、传统上游及长江中下游)水储量变化的空间格局与时序特征,发现基于三个数据集的水储量变化周年振幅在金沙江流域均呈现出西南向东北递减的趋势,且GNSS与GRACE结果显示长江中下游水储量变化较为显著.GNSS时序结果与GRACE、GLDAS及降水数据在三个子区域的时间相关系数均在0.48~0.84之间,其中金沙江流域GNSS与GLDAS相关系数达到了0.84.研究同时发现GNSS结果与降水存在非规律性的时滞关系：在金沙江流域与传统上游,GNSS结果出现峰值时刻较降水滞后2月,而在长江中下游几乎没有时延现象. 利用长江中下游GNSS结果估算的水储量盈亏情况与历史极端水文事件有较好的对应,表明利用稀疏GNSS台站网络可以有效捕捉流域尺度极端水文情况,能够为研究区域尺度水储量时空变化提供新的解决方案.

     

A prototype upper-atmospheric data assimilation scheme based on optimal interpolation: 1. Theory

Introduced almost 40 years ago, the method of optimal interpolation (OI) has been successfully used in various forms for data analysis in meteorology and oceanography. At the same time upper-atmospheric applications of OI and other techniques based on optimal estimation have remained relatively limited. The theory of OI and related methods is reviewed. Properties of optimal estimation relevant to typical problems of data analysis in the upper atmosphere are highlighted. As a specific example, a simple one-dimensional scheme of OI in time is considered. The scheme is devised to address an important problem of the upper-atmospheric data analysis: extraction of periodic (tidal) components from observations covering a fraction of a day. Possible generalizations of the scheme are also briefly discussed. © 1999 Elsevier Science Ltd. All rights reserved.     

一种通过地形指数提取流域自由水蓄水容量空间分布的方法

对于分布式水文模型而言,如何获得参数的空间分布是模型应用的重点和难点问题.本文将分水源参数中的敏感参数——自由水蓄水容量为研究对象.建立地形指数与自由水蓄水容量的函数关系,以此提取流域内的自由水蓄水容量空间分布.最后利用本方法提取了陕西省陈河流域的自由水蓄水容量空间分布,并将之作为栅格型新安江模型的参数进行洪水模拟演算.应用结果表明本文提出的方法得到了理想的模拟结果.该方法以物理规律为基础能较为准确地计算出流域内自由水蓄水容量的空间分布,为分布式模型的发展奠定了坚实的基础.