Assimilation of climatic data in a model of circulation of waters in the Black Sea with regard for the space and time behavior of the variances and cross-covariance functions of forecast errors

We propose an improvement of the algorithm of joint assimilation of the data on climatic temperature, salinity, and altimetric sea level in a model of circulation. Unlike the previous works, the variances of the forecast errors of temperature and salinity and the cross-covariance functions of of the forecast errors of salinity-level and temperature-level depend on the dynamics of waters. It is shown that the structure of the fields of cross-covariance functions in the upper mixed layer is formed by the vertical turbulent diffusion of the variances of forecast errors of temperature and salinity. At greater depths, these statistical characteristics are mainly determined by the vertical advection. We compared the results of calculations with and without taking into account the dynamics of the statistical characteristics. The analysis of the influence of the dynamics of these characteristics makes it possible to reconstruct the mutually adapted climatic fields of temperature, salinity, and horizontal and vertical current velocities in the Black Sea with the assimilation of data in the numerical model in each time step. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 18–31, July–August, 2008.     

Analysis of the Black-Sea climatic fields below the main pycnocline obtained on the basis of assimilation of the archival data on temperature and salinity in the numerical hydrodynamic model

We study model climatic temperature and salinity fields and the fields of currents in the 350–1000-m layer. The following specific features are revealed: Colder waters are observed in the regions with anticyclonic vorticity. At the same time, warmer waters are detected in the regions with cyclonic vorticity. This temperature effect can be explained by the elevation of temperature with depth below the main pycnocline. In the region of the Sevastopol anticyclone, at depths greater than 500 m, we observe a zone of cyclonic rotation of waters. Near the Caucasian coast, in the region of Gelendzhik, we reveal a narrow jet current existing at a depth of 350 m from March till July. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp.3–15, January–February, 2009.     

Assimilation of hydrological observation data for calculating currents in seas and oceans

This paper considers the main steps in improving the methods for calculating the ocean (sea) dynamics on the basis of observational data on sea-water temperature and salinity. The results of diagnostic and adaptation calculations for the near-equatorial area of the West Atlantic in the area of the Lomonosov countercurrent formation are presented. We consider the problem of the complex use of measurements of temperature, salinity, and current velocity in the POLYMODE polygons with their assimilation into the model using a Kalman filter. The results of calculations of the coordinated fields with the mechanism of geostrophic adaptation and using asynchronous measurements obtained by the Razrezy program are given. We discuss further modifications of the assimilation algorithms for hydrological observation data in models of sea dynamics and the principles of adaptation of hydrophysical fields that made it possible to reconstruct the climate fields of the Black Sea and to reproduce the basin dynamics for 23 years.     

Assimilation of the data of observations and adaptive prediction of the natural processes

We propose a dynamical model for the prediction of random components of natural processes. The model is based on the system concept of adaptive balance of causes (ABC-model) and contains dynamic equations for the coefficients of influence adapted to the correlations existing in the predicted processes. To improve the accuracy of predictions, we consider two possible schemes of assimilation of the data of observations in the equations of the ABC-model, namely, the Kolmogorov and Kalman schemes. Both schemes are oriented toward the application of sample correlation coefficients for the prediction of time series of measurements and, hence, take into account the nonstationarity of actual natural processes. We present some examples of prediction of the simulated time series clarifying the algorithms of assimilation of the data of observations. A conclusion is made that the methods of systems modeling and adaptive prediction of random processes by the ABC-method are quite promising.     

Estimation of the long-term variability of hydrophysical characteristics of the Black Sea based on the assimilation of the climatic hydrological fields L and altimetry data

To study the long-term variability of the thermohaline and dynamic characteristics of the Black Sea, we use three versions of climatic fields, namely, the fields reconstructed in the model according to the old (1903–1982) and new (1903–2003) hydrological climatic data arrays of temperature and salinity and according to the data of satellite altimetry. The analysis of the altimetry-based climatic fields confirms the distinctions (established earlier according to the old and new data arrays) in the seasonal variability of the integral characteristics of temperature and salinity and in the structures of hydrophysical fields in the sea. It is shown that, in the winter-spring season, the thermohaline fields reconstructed according to the new and altimetry data arrays are characterized by a small elevation of the halocline (pycnocline) and the upper boundary of the cold intermediate layer. In all seasons, the altimetry-based surface geostrophic currents contain numerous mesoscale eddies with different signs of rotation. Moreover, in all seasons, the Rim Current reconstructed according to the altimetry data is characterized by a narrower jet almost along the entire its length. This jet is especially intense near the coasts of West Anatolia. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 3–17, July–August, 2006.     

A classification of hydrological climatic seasons in the China seas

By using a method of boundary temperature index of seasons, a classification of hydrological climatic seasons in the China seas is made on the basis statistics of the sea surface air and water temperatures over the years. The results indicate that the assignment of hydrological seasons in the China seas differs with various sea areas. It may be divided into three climatic belts. In the temperate zone area, four seasons are clearly distinct with very long winter. While in the subtropical zone area, there is no winter throughout the year. The autumn is linked together with the spring, and the summer is unusually long. As for the tropical zone area, it is summer all the year round without any other seasons. In addition , the regular pattern of transformation of the four seasons and the regional characteristics of the length of each season are analyzed in greater detail. The results are in agreement with the continental seasonal classification and it is also shown that the results are reasonable and reliabl     

Assimilation of simulated altimeter data in a two-layer linear Rossby wave model using the variational method

The variational assimilation method has been examined for ability of reconstructing mesoscale features in altimeter data using a simple dynamic model. A one-dimensional, two-layer Rossby wave model in a cross-track channel has been chosen. The simulated data are constructed from a theoretical solution, which is composed of any combination of two normal vertical (barotropic and baroclinic) modes. The data are collected along tracks and with repeat periods similar to those of the Geosat altimeter. The phase space of control variables is composed of initial and boundary conditions. A cost function is defined to measure differences between the simulated data and the model solution. Regularization (smoothing) terms are also included in the cost function in the form of secon-order spatial and time derivatives of the solution. In this paper, two potential problems existing in the altimeter data assimilation are addressed: one is low cross-track resolution, and the other is vertical projection of the data measured at the sea surface. A succesful metho is developed for reconstructing Rossby waves with wavelengths as short as twice the track intervals for any combination of two vertical modes. A key component to efficient assimilation is a preparation step prior to the actual variational assimilation: a uniform ratio of pressure amplitudes in the two layers is included as an optimization parameter. Starting with the first guess from the preparation step, the variational method is carried out based on adjoint equations without such constraint. Separation of the control variables into the two subsets of the initial and the boundary conditions is found useful. Characteristics of the Hessian matrix are related to the performance of this technique. The method developed for the linear system implies steps to be included in data assimilation for nonlinear meanders and eddies in a major current system as well.     

基于Cressman客观分析的南海北部海区数据同化实验

利用POM模式和空间插值法构造的同化方案对南海北部的航次观测资料进行了数据同化模拟.结果表明,数据同化有效兼顾了模式模拟和航次观测,在一定程度上纠正了模式模拟值相对于真实数据的误差;同化结果与模拟结果相比更接近观测值,在航次断面及其附近海域同化结果误差较小;另一方面,由于航次资料站点相对较少,在无观测数据的海域模式同化不是很理想,有待改进.此方法可为南海大型航次及其他资料同化提供一个再分析资料的实验性参考.     

Assimilation of altimeter wave height data into a spectral wave model using statistical interpolation

A scheme for the assimilation of altimeter wave height data into a second generation wave prediction model is developed. The scheme modifies the model wave spectrum so as to be consistent with the satellite observed values of significant wave height. This modification is achieved, however, so that the adjusted wave field is consistent with the model physics and the forcing wind field. In this manner the modifications to the wave field persist in the model, thus yielding long term improvements in model performance. In addition, a statistical interpolation scheme is used to ensure that maximum use is made of the point observations made by the satellite. In this manner, not only points directly beneath the satellite track are updated. Points adjacent to the track are also modified, the extent of this modification depending on the spatial correlation of the wave field. The scheme is applied to a computationally efficient second generation wave model. The improvement in performance is significant, demonstrating that assimilation may be a very efficient alternative to proceeding to more sophisticated and expensive third generation models. This is particularly true where the forcing wind field may be of poor quality. The results also demonstrate that with the addition of assimilation, relatively small computational grids can be utilized. Swell generated external to the grid will be included through the assimilation cycle.     

Physical and hydrological characteristics of climatic frontal zones in the Tropical Atlantic

Climatic frontal zones are selected in the thermohaline fields of the Tropical Atlantic by analyzing the many-year-average seasonal database reduced to the nodes of a one-degree grid. We determine physical characteristics of the frontal zones, study their spatial and temporal variability, and reveal basic regularities of the appearance of frontal zones in the fields of thermohaline characteristics. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Assimilation of altimetry data in the numerical model of the circulation in the Black Sea: The model numerical experiments

The numerical algorithm of the Kalman optimum filtration generalized for the case of three-dimensional fields and a multicomponent vector of the ocean state, with level measurements discrete over space and time being available, is given. The results of model numerical experiments on the assimilation of data on the Black Sea level are given. An attempt to estimate the effect of the time interval of data input on the results of field reconstruction was made.Translated by Mikhail M. Trufanov.     

水文资料插值计算方法探讨

本文利用5种常用的插值计算方法,对海洋实测资料序列中的某些固定节点进行插值计算,然后根据均方误差和图形拟合相结合的方法,探讨插值计算方法的适用性及应用条件并得出结论:阿基玛插值和三点拉格朗日插值效果拟合性最好,具有普遍应用性,多点拉格朗日和线性插值较为中性,在插值步长不大的条件下,插值效果较好,而牛顿插值不稳定,应用条件相对苛刻.     

Optimization of the data assimilation algorithm in a model for synoptic dynamics of the velocity field

The results of numerical experiments involving data assimilation by a non-linear model for synoptic dynamics of the ocean are given. The results of application of simplified optimal filtration algorithms (with the correlation error function being parametrized for both linear and non-linear variants) and of the optimal interpolation are intercompared. The use of a non-linear equation to predict average values and a linear one to predict dispersion in the filtration algorithm is suggested as most appropriate for the cases, when anisotropy of the correlation function is to be included. In other cases, it is considered worth-while to apply optimal interpolation.Translated by V. Puchkin.     

Analysis of the response of a non-linear data assimilation algorithm in a one-dimensional model of the upper ocean

A one-dimensional (1D) integral dynamico-stochastic model of the upper ocean with a non-linear assimilation algorithm is considered. The accuracy of computing the characteristics of the upper layer depends essentially on the values of the empirical coefficients. A numerical experiment was carried out which verified the efficiency of the model's adaptive mechanism operation when different values of the empirical coefficients and their variances were preset. Recommendations on assigment of the model's initial parameters are derived.Translated by Mikhail M. Trufanov.     

Calculation of adapted black sea fields on the basis of assimilation of climatic temperature and salinity data into the model

A scheme of a periodic assimilation of climatic temperature and salinity data into a model is proposed. In accordance with the criteria chosen on the basis of numerical experiments, an optimum assimilation period of three hours is set. The proposed method allows a hydrodynamic adaptation of the fields of temperature, salinity, and flow velocity that are close to the climatic ones within the framework of the proposed criteria. The main feature of the adapted fields of vertical flows in the layer 0–700 m is their smooth character and an almost complete absence of small-scale noise. The extreme values of vertical velocity in this layer decrease by almost an order of magnitude as compared to analogous values calculated for the variant of data assimilation with a weak adjustment of fields.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

Method and results of assimilation of climatic data on temperature,salinity, and sea level into a numerical model of the Black Sea

A method for combined assimilation of climatic hydrologic fields of temperature, salinity, and the climatic dynamic level of the Black Sea into a model of sea dynamics is proposed. The monthly mean fields of the dynamic sea level were obtained from the results of assimilation of satellite altimetry data into the model. The statistical characteristics of errors in the forecasts of the level, salinity, and temperature were assumed to be proportional to the statistical characteristics of the differences between monthly mean climatic fields of temperature, salinity, and sea level calculated by means of assimilating altimetry observations of the sea level and analogous climatic hydrologic fields. The climatic fields of currents are reconstructed and analyzed. The assimilation of the climatic altimetry level allows the reproduction (in current fields) of quasi-stationary synoptic anticyclonic eddies located along the periphery of the Black Sea Rim Current.