Data assimilation with a barotropically unstable shallow water system using representer algorithms

The cycling representer algorithm of Xu and Daley (2000) is a weak constraint four-dimensional variational data assimilation algorithm. It was successfully applied to a one-dimensional transport problem and was able to successfully extract the signal from noisy and sparse observations. The algorithm, however, has not previously been applied to a multivariate, multidimensional system with dynamic instability. The algorithm is also very computationally demanding and awaits considerable enhancement in computer power before being practical for operational forecast models. We have two objectives in this paper. The first is to apply the cycling representer algorithm to a two-dimensional, multivariate barotropically unstable linear shallow water system. The second objective is to formulate and test an accelerated representer algorithm that is much more computationally tractable than the cycling representer algorithm itself. A linear shallow water system with a barotropically unstable basic state was used as a test bed to conduct data assimilation experiments. The evolution of a 'neutral' eastward-propagating singular vector was selected as the 'truth', against which all data assimilation experiments were to be evaluated. The results indicated that the cycling representer algorithm was capable of providing satisfying state estimates for a multivariate, multidimensional system. The results from the accelerated representer algorithm were very encouraging because it is sufficiently computationally tractable to be used on present day multi-processor machines for operational applications.     

Data assimilation with inequality constraints

If values of variables in a numerical model are limited to specified ranges, these restrictions should be enforced when data are assimilated. The simplest option is to assimilate without regard for constraints and then to correct any violations without worrying about additional corrections implied by correlated errors. This paper addresses the incorporation of inequality constraints into the standard variational framework of optimal interpolation with emphasis on our limited knowledge of the underlying probability distributions. Simple examples involving only two or three variables are used to illustrate graphically how active constraints can be treated as error-free data when background errors obey a truncated multi-normal distribution. Using Lagrange multipliers, the formalism is expanded to encompass the active constraints. Two algorithms are presented, both relying on a solution ignoring the inequality constraints to discover violations to be enforced. While explicitly enforcing a subset can, via correlations, correct the others, pragmatism based on our poor knowledge of the underlying probability distributions suggests the expedient of enforcing them all explicitly to avoid the computationally expensive task of determining the minimum active set. If additional violations are encountered with these solutions, the process can be repeated. Simple examples are used to illustrate the algorithms and to examine the nature of the corrections implied by correlated errors.     

Data assimilation for a coastal area morphodynamic model: Morecambe Bay

This paper investigates the use of data assimilation in coastal area morphodynamic modelling using Morecambe Bay as a study site. A simple model of the bay has been enhanced with a data assimilation scheme to better predict large-scale changes in bathymetry observed in the bay over a 3-year period. The 2DH decoupled morphodynamic model developed for the work is described, as is the optimal interpolation scheme used to assimilate waterline observations into the model run. Each waterline was acquired from a SAR satellite image and is essentially a contour of the bathymetry at some level within the inter-tidal zone of the bay. For model parameters calibrated against validation observations, model performance is good, even without data assimilation. However the use of data assimilation successfully compensates for a particular failing of the model, and helps to keep the model bathymetry on track. It also improves the ability of the model to predict future bathymetry. Although the benefits of data assimilation are demonstrated using waterline observations, any observations of morphology could potentially be used. These results suggest that data assimilation should be considered for use in future coastal area morphodynamic models.     

Effectiveness of data assimilation using probabilistic techniques in a model for synoptic velocity field evolution

The results of numerical experiments involving data assimilation by linear and non-linear models for synoptic ocean dynamics are presented. This paper considers the model's response to data assimilation at diverse values of the relative error in the determination of the initial fields and space-time discreteness of data assimilation. The data obtained using the optimal filtering are compared with those provided by the optimal interpolation (OI). A qualitative difference in the response of the linear and non-linear models to data assimilation is noted. The limiting values of the time-space discreteness of observations assimilation are determined, which allow correct application of OI.Translated by Vladimir A. Puchkin.     

The initialization of nonlinear water waves in a numerical wave flume

This study investigates the initialization of nonlinear free-surface simulations in a numerical wave flume.Due to the mismatch between the linear input wavemaker motion and the kinematics of fully nonlinear waves,direct numerical simulations of progressive waves,generated by a sinusoidally moving wavemaker,are prone to suffering from high-frequency wave instability unless the flow is given sufficient time to adjust.A time ramp is superimposed on the wavemaker motion at the start that allows nonlinear free-surface simulations to be initialized with linear input.The duration of the ramp is adjusted to test its efficiency for short waves and long waves.Numerical results show that the time ramp scheme is effiective to stabilize the wave instability at the start of the simulation in a wave flume.     

Model initialization in a tidally energetic regime: A dynamically adjusted objective analysis

A simple improvement to objective analysis of hydrographic data is proposed to eliminate spatial aliasing effects in tidally energetic regions. The proposed method consists of the evaluation of anomalies from observations with respect to circulation model fields. The procedure is run iteratively to achieve convergence. The method is applied in the Bay of Fundy and compared with traditional objective analysis procedures and dynamically adjusted climatological fields. The hydrographic skill (difference between observed and model temperature and salinity) of the dynamically adjusted objective analysis is significantly improved by reducing bias and correcting the vertical structure. Representation of the observed velocities is also improved. The resulting flow is consistent with the known circulation in the Bay.     

Improving strategies with constraints regarding non-Gaussian statistics in a three-dimensional variational assimilation method

We assess validity of a Gaussian error assumption, the basic assumption in data assimilation theory, and propose two kinds of constraints regarding non-Gaussian statistics. In the mixed water region (MWR) off the east coast of Japan exhibiting complicated frontal structures, a probability density function (PDF) of subsurface temperature shows double peaks corresponding to the Kuroshio and Oyashio waters. The complicated frontal structures characterized by the temperature PDF sometimes cause large innovations, bringing about a non-Gaussianity of errors. It is also revealed that assimilated results with a standard three-dimensional variational (3DVAR) scheme have some issues in MWR, arising from the non-Gaussianity of errors. The Oyashio water sometimes becomes unrealistically cold. The double peaks seen in the observed temperature PDF are too smoothed. To improve the assimilated field in MWR, we introduce two kinds of constraints, J _c1 and J _c2, which model the observed temperature PDF. The constraint J _c1 prevents the unrealistically cold Oyashio water, and J _c2 intends to reproduce the double peaks. The assimilated fields are significantly improved by using these constraints. The constraint J _c1 effectively reduces the unrealistically cold Oyashio water. The double peaks in the observed temperature PDF are successfully reproduced by J _c2. In addition, not only subsurface temperature but also whole level temperature and salinity (T–S) fields are improved by adopting J _c1 and J _c2 to a multivariate 3DVAR scheme with vertical coupled T–S empirical orthogonal function modes.     

基于集合最优插值方法的南海北部海区的数据同化试验

基于ROMS(Regional Ocean Modeling System)模式建立一个南海北部集合最优插值的同化系统,并且利用2008年夏季SCOPE(Northern South China Sea Coastal Oceanographic Process Experiment)航次的温盐数据以及航次期间逐日OS...     

Co-management and “consciousness”: Fishers’ assimilation of management principles in Chile

Chile's new Management Area system delegates management responsibility to organizations of artisanal shell-fishers on the condition that they team with professionally trained marine biologists. A survey of participating fishers in Chile's Fourth and Fifth regions examined four social benefits predicted to result from this type of co-management: (1) improved rapport between fishers and the state, (2) greater awareness among fishers of ecology and the benefits of management, (3) cooperation between fishers and scientists, and (4) unity between fishers. A discussion analyzes the principal benefit encountered—fishers’ newfound “consciousness” of the value of management—within the context of co-management and territorial use rights.     

A baroclinic typhoon model with a moving multi-nested grid and variational adjustment initialization Ⅱ. Forecast experiments

INTRODUCTIONBeingoneofthemestdisastrousweathersystemsinfluencingthesoutheaStcoastofChinainsurnmerandautumn,typhoonsalsocausestrongstormsUrgeSandseawavesI'eSultinginsevereoceandisasters,whichthreaten~theasternChina'sagriculture,navigation,offshoreoila...     

Physical and biological modeling in the Gulf Stream region:: I. Data assimilation methodology

Physical and biological data are assimilated into a time-evolving, mesoscale-resolution three-dimensional (3-D) ocean model using optimal interpolation. Simulations are conducted in the Gulf Stream region during the BIOSYNOP/Anatomy of a Meander Experiment in September–October of 1988. Physical data assimilation only or biological data assimilation only resulted in misalignment of the physical and biological fronts, causing spurious cross-frontal fluxes of biological quantities. Assimilation of both physical and compatible biological fields was necessary for adequate equilibration of the simulated fields. The resulting combined 4-D fields substantially extend the value of the observations alone. A technique is presented for deriving the necessary, dynamically consistent 3-D physical and biological field estimates from data for initialization and assimilation into time-evolving model simulations.     

El Niño phenomenon in simple ocean data assimilation data

[1]Battisti D S. 1988. The dynamics and     

同化技术在渤海溢油应急预报系统中的应用

溢油应急预报对溢油事故现场处理具有重要指导意义。国内外已开展大量溢油数值预报技术研究,但由于各类误差的引入(尤其风和流数值预报误差的引入)以及模型本身的不完善等各种原因导致溢油数值预报无法满足日益提高的溢油预报精度需求。随着现场观测技术和监测水平的提高,如何充分利用实时观测数据提高业务化溢油应急预报精度,并满足应急预报迅速快捷的要求,成为目前业务化溢油应急预报的首要问题。国家海洋环境预报中心于2008年实现了渤海溢油业务化预报系统的建立和业务化应用,本文针对当前渤海溢油业务化应急预报中存在的现实问题,利用已有渤海海上5个石油平台从2010年1月至2011年2月的风场观测数据,初步开展最优插值方法(optimal interpolation assimilation method,OI)同化技术在国家海洋环境预报中心渤海溢油应急预报系统风场订正的应用研究。本文采用交错订正方法,确定了OI同化技术中相关尺度因子的选取,从而实现在这5个观测站地理分布情况下,OI同化技术应用中参数的最优化,之后在理想实验和实际案例的应用中,该同化方法明显提高渤海溢油预报精度。本文为如何进一步利用同化方法迅速快捷地实现溢油应急预报精度的提高提供了一定研究基础。     

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.     

Phytoplankton production in two east coast estuaries: Photosynthesis-light functions and patterns of carbon assimilation in Chesapeake and Delaware Bays

Chesapeake Bay is a large and productive estuary that has received close scrutiny in recent years because of indications that its water quality and biota have been damaged by man's activities. Data on primary production for the estuary as a whole, however, are surprisingly sparse. We describe here the distribution of photosynthetic carbon assimilation by phytoplankton in Chesapeake Bay, and relate productivity patterns to hydrographic characteristics of the estuary. Between March 1982 and April 1983, a series of four cruises was conducted on Chesapeake Bay, and two cruises on the urbanized Delaware Bay for comparison. The upper Chesapeake and Delaware were highly turbid with high concentrations of suspended particulate matter and dissolved inorganic nutrients. Low chlorophyll concentrations were usually found in these areas of high turbidity, despite the abundance of nutrients, suggesting light limitation. Application of Wofsy's (1983) model of phytoplanton growth confirmed this suggestion. Chlorophyll and productivity maxima usually occurred seaward of the turbidity maxima where light penetration increased and suffient nutrients were present to support active phytoplankton growth. Further seaward of the chlorophyll maxima in the Chesapeake, the photic zone depth increased, concentrations of nutrients decreased, and phytoplankton biomass decreased, suggesting that nutrient availability, rather than light, controlled phytoplankton growth in the lower portion of the estuary. In contrast to the Chesapeake, Delaware Bay was more turbid, had generally higher nutrient concentrations, and was lower in phytoplankton productivity. The chlorophyll maxima and region of rapid phytoplankton growth occurred further toward the lower estuary and shelf regions in Delaware Bay because the high turbidity extended further seaward. Nutrients were never depleted at the shelf end of the estuary sufficiently to retard phytoplankton growth. Photosynthesis-irradiance (P-I) curves from simulated in situ and constant intensity incubations showed a strong correlation of the light-limited slope (a^B) with the light-saturated rate ( ) on each cruise. Spatial variations in corresponded to patterns of phytoplankton abundance, as did integral production (PP) and carbon-based growth rates (μ_C, μ_m), and photosynthetic parameters varied significantly with temperature.     

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.