Suitable region of dynamic optimal interpolation for efficiently altimetry sea surface height mapping

The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).

Assimilating the along-track sea level anomaly into the regional ocean modeling system using the ensemble optimal interpolation

The ensemble optimal interpolation （EnOI） is applied to the regional ocean modeling system （ROMS） with the ability to assimilate the along-track sea level anomaly （TSLA）. This system is tested with an eddy-resolving system of the South China Sea （SCS）. Background errors are derived from a running seasonal ensemble to account for the seasonal variability within the SCS. A fifth-order localization function with a 250 km localization radius is chosen to reduce the negative effects of sampling errors. The data assimilation system is tested from January 2004 to December 2006. The results show that the root mean square deviation （RMSD） of the sea level anomaly decreased from 10.57 to 6.70 cm, which represents a 36.6% reduction of error. The data assimilation reduces error for temperature within the upper 800 m and for salinity within the upper 200 m, although error degrades slightly at deeper depths. Surface currents are in better agreement with trajectories of surface drifters after data assimilation. The variance of sea level improves significantly in terms of both the amplitude and position of the strong and weak variance regions after assimilating TSLA. Results with AGE error （AGE） perform better than no AGE error （NoAGE） when considering the improvements of the temperature and the salinity. Furthermore, reasons for the extremely strong variability in the northern SCS in high resolution models are investigated. The results demonstrate that the strong variability of sea level in the high resolution model is caused by an extremely strong Kuroshio intrusion. Therefore, it is demonstrated that it is necessary to assimilate the TSLA in order to better simulate the SCS with high resolution models.

Fishery analysis using gradient-dependent optimal interpolation

The current lack of high-precision information on subsurface seawater is a constraint in fishery research.Based on Argo temperature and salinity profiles,this study applied the gradient-dependent optimal interpolation to reconstruct daily subsurface oceanic environmental information according to fishery dates and locations.The relationship between subsurface information and matching yellowfin tuna(YFT)in the western and central Pacific Ocean(WCPO)was examined using catch data from January 1,2008 to August 31,2017.The seawater temperature and salinity results showed differences of less than±0.5°C and±0.01 compared with the truth observations respectively.Statistical analysis revealed that the most suitable temperature for YFT fishery was 28–29°C at the near-surface.The most suitable salinity range for YFT fishery was 34.5–36.0 at depths shallower than 300 m.The suitable upper and lower bounds on the depths of the thermocline were 90–100 m and 300–350 m,respectively.The thermocline characteristics were prominent,with a mean temperature gradient exceeding 0.08°C/m.These results indicate that the profiles constructed by gradient-dependent optimal interpolation were more accurate than those of the nearest profiles adopted.

Altimeter significant wave height data assimilation in the South China Sea using Ensemble Optimal Interpolation

The application of ensemble optimal interpolation in wave data assimilation in the South China Sea is presented. A sampling strategy for a stationary ensemble is first discussed. The stationary ensemble is constructed by sampling from 24-h-interval significant wave height differences of model outputs over a long period,and is validated with altimeter significant wave height data,indicating that the ensemble errors have nearly the same probability distribution function. The background error covariance fields expressed by the ensemble sampled are anisotropic. Updating the static samples by season,the seasonal characteristics of the correlation coefficient distribution are reflected. Hindcast experiments including assimilation and control runs are conducted for the summer of 2010 in the South China Sea. The effect of ensemble optimal interpolation assimilation on wave hindcasts is validated using different satellite altimeter data(Jason-1 and 2 and ENVISAT) and buoy observations. It is found that the ensemble-optimal-interpolation-based wave assimilation scheme for the South China Sea achieves improvements similar to those of the previous optimal-interpolation-based scheme,indicating that the practical application of this computationally cheap ensemble method is feasible.

Optimal Interpolation and Kriging Mapping of Soil Characters in Glacial Moraine Landscapes

The objective of this research is to analyze optimal interpolation and Kriging mapping of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The survey method was detailed using maps with scales of 1：5,000. Soil sampling was performed by soil pits and borings and completely analyzed in laboratory. Collected data were evaluated by Geostatistics program for spatial soil variability analyses. All maps （produced by Kriging interpolation） picture redistribution of soil nutrients and soil fractions and all map isolines run in similar directions according to landscape nets. The position in the landscape is responsible for increased soil variability. Soil variability becomes higher with decreasing elevation; this means it increases from hilltops to lower slopes. All observed soil characters show relationships to the soil variability. This variability system is caused by convex depressions and hedgerows （Knicks） function as barriers for the redistribution of transported material and offsite sedimentation. Therefore fluxes can be assessed by soil gain and loss balances.

OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES

This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

An effective method for improving the accuracy of Argo objective analysis

Based on the optimal interpolation objective analysis of the Argo data, improvements are made to the em- pirical formula of a background error covariance matrix widely used in data assimilation and objective anal- ysis systems. Specifically, an estimation of correlation scales that can improve effectively the accuracy of Ar- go objective analysis has been developed. This method can automatically adapt to the gradient change of a variable and is referred to as ＂gradient-dependent correlation scale method＂. Its effect on the Argo objective analysis is verified theoretically with Gaussian pulse and spectrum analysis. The results of one-dimensional simulation experiment show that the gradient-dependent correlation scales can improve the adaptability of the objective analysis system, making it possible for the analysis scheme to fully absorb the shortwave information of observation in areas with larger oceanographic gradients. The new scheme is applied to the Argo data obiective analysis system in the Pacific Ocean. The results are obviously improved.

Assimilating operational SST and sea ice analysis data into an operational circulation model for the coastal seas of China

The prediction of sea surface temperature （SST） is an essential task for an operational ocean circulation model. A sea surface heat flux, an initial temperature field, and boundary conditions directly affect the accuracy of a SST simulation. Here two quick and convenient data assimilation methods are employed to improve the SST simulation in the domain of the Bohai Sea, the Yellow Sea and the East China Sea （BYECS）. One is based on a surface net heat flux correction, named as Qcorrection （QC）, which nudges the flux correction to the model equation; the other is ensemble optimal interpolation （EnOI）, which optimizes the model initial field. Based on such two methods, the SST data obtained from the operational SST and sea ice analysis （OSTIA） system are assimilated into an operational circulation model for the coastal seas of China. The results of the simulated SST based on four experiments, in 2011, have been analyzed. By comparing with the OSTIA SST, the domain averaged root mean square error （RMSE） of the four experiments is 1.74, 1.16, 1.30 and 0.91~C, respectively; the improvements of assimilation experiments Exps 2, 3 and 4 are about 33.3%, 25.3%, and 47.7%, respectively. Although both two methods are effective in assimilating the SST, the EnOI shows more advantages than the QC, and the best result is achieved when the two methods are combined. Comparing with the observational data from coastal buoy stations, show that assimilating the high-resolution satellite SST products can effectively improve the SST prediction skill in coastal regions.

An Ocean Reanalysis System for the Joining Area of Asia and Indian-Pacific Ocean

An ocean reanalysis system for the joining area of Asia and Indian-Pacific Ocean (AIPO) has been developed and is currently delivering reanalysis data sets for study on the air-sea interaction over AIPO and its climate variation over China in the inter-annual time scale.This system consists of a nested ocean model forced by atmospheric reanalysis,an ensemble-based multivariate ocean data assimilation system and various ocean observations.The following report describes the main components of the data assimilation system in detail.The system adopts an ensemble optimal interpolation scheme that uses a seasonal update from a free running model to estimate the background error covariance matrix.In view of the systematic biases in some observation systems,some treatments were performed on the observations before the assimilation.A coarse resolution reanalysis dataset from the system is preliminarily evaluated to demonstrate the performance of the system for the period 1992 to 2006 by comparing this dataset with other observations or reanalysis data.

An Ocean Data Assimilation System in the Indian Ocean and West Pacific Ocean

The development and application of a regional ocean data assimilation system are among the aims of the Global Ocean Data Assimilation Experiment. The ocean data assimilation system in the regions including the Indian and West Pacific oceans is an endeavor motivated by this goal. In this study, we describe the system in detail. Moreover, the reanalysis in the joint area of Asia, the Indian Ocean, and the western Pacific Ocean （hereafter AIPOcean） constructed using multi-year model integration with data assimilation is used to test the performance of this system. The ocean model is an eddy-resolving, hybrid coordinate ocean model. Various types of observations including in-situ temperature and salinity profiles （mechanical bathythermograph, expendable bathythermograph, Array for Real-time Geostrophic Oceanography, Tropical Atmosphere Ocean Array, conductivity-temperature-depth, station data）, remotely-sensed sea surface temperature, and altimetry sea level anomalies, are assimilated into the reanalysis via the ensemble optimal interpolation method. An ensemble of model states sampled from a long-term integration is allowed to change with season, rather than remaining stationary. The estimated background error covariance matrix may reasonably reflect the seasonality and anisotropy. We evaluate the performance of AIPOcean during the period 1993-2006 by comparisons with independent observations, and some reanalysis products. We show that AIPOcean reduces the errors of subsurface temperature and salinity, and reproduces mesoscale eddies. In contrast to ECCO and SODA products, AIPOcean captures the interannual variability and linear trend of sea level anomalies very well. AIPOcean also shows a good consistency with tide gauges.

Evaluation of Ocean Data Assimilation in CAS-ESM-C:Constraining the SST Field

A weakly coupled assimilation system, in which SST observations are assimilated into a coupled climate model （CAS- ESM-C） through an ensemble optimal interpolation scheme, was established. This system is a useful tool for historical climate simulation, showing substantial advantages, including maintaining the atmospheric feedback, and keeping the oceanic tields from drifting far away from the observation, among others. During the coupled model integration, the bias of both surface and subsurface oceanic fields in the analysis can be reduced compared to unassimilated fields. Based on 30 model years of ot.tput fiom the system, the climatology and imerannual variability of the climate system were evaluated. The results showed that the system can reasonably reproduce the climatological global precipitation and SLP, bul it still sutters from the double ITCZ problem. Besides, the ENSO footprint, which is revealed by ENSO-related surface air temperature, geopotential height and precipitation during El Nifio evolution, is basically reproduced by the system. The system can also simulate the observed SST-rainfall relationships well on both interannual and intraseasonal timescales in the western North Pacific region, in which atmospheric feedback is crucial for climate simulation.

Reconstruction of eddies by assimilating satellite altimeter data into Princeton Ocean Model

An optimal interpolation assimilation model for satellite altimetry data is developed based on Princeton Ocean Model （POM）, which is applied in a quasi-global domain, by the method of isotropic correlation between sea level anomaly （SLA） and sea temperature anomaly. The performance of this assimilation model is validated by the modeled results of SLA and the current patterns. Comparisons between modeling and satellite data show that both the magnitudes and distribution patterns of the sinmlated SLA are improved by assimilation. The most significant improvement is that meso-scale systems, e.g., eddies, are well reconstructed. The evolution of an eddy located in the northwest Pacific Ocean is traced by using the assimilation model. Model results show that during three months the eddy migrated southwestward for about 6 degrees before merging into the Kuroshio. The three dimensional structure of this eddy on 12 August 2001 is further analyzed. The strength of this warm, cyclonic eddy decreases with the increase of depth. The eddy shows different horizontal patterns at different layers, and the SLA and temperature fields agree with each other well. This study suggests that this kind of data assimilation is economic and reliable for eddy reconstruction, and can be used as a promising technique in further studies of ocean eddies as well as other fine circulation structures.

Establishment and tests of EnOI assimilation module for WAVEWATCH Ⅲ

In this paper, we propose a parallel data assimilation module based on ensemble optimal interpolation （EnOI）. We embedded the method into the full-spectral third-generation wind-wave model, WAVEWATCH III Version 3.14, producing a wave data assimilation system. We present our preliminary experiments assimilating altimeter significant wave heights （SWH） using the EnOI-based wave assimilation system. Waters north of 15°S in the Indian Ocean and South China Sea were chosen as the target computational domain, which was two-way nested into the global implementation of the WAVEWATCH III. The wave model was forced by six-hourly ocean surface wind velocities from the cross-calibrated multi-platform wind vector dataset. The assimilation used along-track SWH data from the Jason-2 altimeter. We evaluated the effect of the assimilation on the analyses and hindcasts, and found that our technique was effective. Although there was a considerable mean bias in the control SWHs, a month-long consecutive assimilation reduced the bias by approximately 84% and the root mean-square error （RMSE） by approximately 65%. Improvements in the SWH RMSE for both the analysis and hindcast periods were more significant in July than January, because of the monsoon climate. The improvement in model skill persisted for up to 48 h in July. Furthermore, the SWH data assimilation had the greatest impact in areas and seasons where and when the sea-states were dominated by swells.

Anti-aliasing wavelet packet method for harmonic detection

A novel anti-aliasing wavelet packet transform method for harmonic detection is proposed. Aiming at the low measurement precision and poor robustness which exists in the former traditional wavelet methods for lack of the aliasing_reduction scheme, an optimal interpolation wavelet packet filter is designed according to new optimal criteria. First, the limitation of anti-aliasing on the traditional wavelet filter bank is analyzed. Second, the designed optimal interpolation filters axe denoted, and then the solution algorithm is given. This devised wavelet packet filter can seek a reasonable balance between signal preservation and aliasing reduction; it overcomes the inherent bug of traditional wavelet transforms, which rooted from just only concerning total aliasing cancellation but not aliasing-reduction in decomposition. Simulation and several comparative results indicate that the proposed method can effectively eliminate aliasing and precisely extract harmonic information.

The Impact of "Bad" Argo Profiles on Ocean Data Assimilation

Recent studies have found cold biases in a fraction of Argo profiles (hereinafter referred to as bad Array for Real-time Geostrophic Oceanography (Argo) profiles) due to the pressure drifts during 2003 and 2006. These bad Argo profiles have had an important impact on in situ observation-based global ocean heat content esti- mates. This study investigated the impact of bad Argo profiles on ocean data assimilation results that were based on observations from diverse ocean observation systems, such as in situ profiles (e.g., Argo, expendable bathy- thermograph (XBT), and Tropical Atmosphere Ocean (TAO), remote-sensing sea surface temperature products and satellite altimetry between 2004 and 2006. Results from this work show that the upper ocean heat content analysis is vulnerable to bad Argo profiles and demon- strate a cooling trend in the studied period despite the multiple independent data types that were assimilated. When the bad Argo profiles were excluded from the as- similation, the decreased heat content disappeared and a warming occurred. Combination of satellite altimetry and mass variation data from gravity satellite demonstrated an increase, which agrees well with the increased heat con- tent. Additionally, when an additional Argo profile quality control procedure was utilized that simply removed the profiles that presented static unstable water columns, the results were very similar to those obtained when the bad Argo profiles were excluded from the assimilation. This indicates that an ocean data assimilation that uses multiple data sources with improved quality control could be less vulnerable to a major observation system failure, such as a bad Argo event.

Ice concentration assimilation in a regional ice-ocean coupled model and its application in sea ice forecasting

A reasonable initial state of ice concentration is essential for accurate short-term forecasts of sea ice using ice-ocean coupled models. In this study, sea ice concentration data are assimilated into an operational ice forecast system based on a com- bined optimal interpolation and nudging scheme. The scheme produces a modeled sea ice concentration at every time step, based on the difference between observational and forecast data and on the ratio of observational error to modeled error. The impact and the effectiveness of data assimilation are investigated. Significant improvements to predictions of sea ice extent were obtained through the assimilation of ice concentration, and minor improvements through the adjustment of the upper ocean properties. The assimilation of ice thickness data did not significantly improve predictions. Forecast experiments show that the forecast accuracy is higher in summer, and that the errors on five-day forecasts occur mainly around the marginal ice zone.

Assimilating OSTIA SST into regional modeling systems for the Yellow Sea using ensemble methods

The effects of sea surface temperature（SST） data assimilation in two regional ocean modeling systems were examined for the Yellow Sea（YS）. The SST data from the Operational Sea Surface Temperature and Sea Ice Analysis（OSTIA） were assimilated. The National Marine Environmental Forecasting Center（NMEFC） modeling system uses the ensemble optimal interpolation method for ocean data assimilation and the Kunsan National University（KNU） modeling system uses the ensemble Kalman filter. Without data assimilation, the NMEFC modeling system was better in simulating the subsurface temperature while the KNU modeling system was better in simulating SST. The disparity between both modeling systems might be related to differences in calculating the surface heat flux, horizontal grid spacing, and atmospheric forcing data. The data assimilation reduced the root mean square error（RMSE） of the SST from 1.78°C（1.46°C） to 1.30°C（1.21°C） for the NMEFC（KNU） modeling system when the simulated temperature was compared to Optimum Interpolation Sea Surface Temperature（OISST） SST dataset. A comparison with the buoy SST data indicated a 41%（31%） decrease in the SST error for the NMEFC（KNU） modeling system by the data assimilation. In both data assimilative systems, the RMSE of the temperature was less than 1.5°C in the upper 20 m and approximately 3.1°C in the lower layer in October. In contrast, it was less than 1.0°C throughout the water column in February. This study suggests that assimilations of the observed temperature profiles are necessary in order to correct the lower layer temperature during the stratified season and an ocean modeling system with small grid spacing and optimal data assimilation method is preferable to ensure accurate predictions of the coastal ocean in the YS.

Sample Numbers and Optimal Lagrange Interpolation of Sobolev Spaces W_(1)^(r)

This paper investigates the optimal recovery of Sobolev spaces W_(1)^(r)[-1,1],r∈N in the space L_(1)[-1,1].They obtain the values of the sampling numbers of W_(1)^(r)[-1,1]in L_(1)[-1,1]and show that the Lagrange interpolation algorithms based on the extreme points of Chebyshev polynomials are optimal algorithms.Meanwhile,they prove that the extreme points of Chebyshev polynomials are optimal Lagrange interpolation nodes.

The Warming and Wetting Ecological Environment Changes over the Qinghai-Tibetan Plateau and the Driving Effect of the Asian Summer Monsoon

The impact of warming and wetting on the ecological environment of the Qinghai-Tibet Plateau(TP)under the background of climate change has been a concern of the global scientific community.In this paper,the optimized interpolation variational correction approach is adopted for the analysis of monthly high-resolution satellite precipitation products and observations from meteorological stations during the past 20 years.As a result,the corrected precipitation products can not only supplement the“blank area”of precipitation observation stations on the TP,but also improve the accuracy of the original satellite precipitation products.The precipitation over the TP shows different spatial changes in the vegetation growing season,known as the time from May to September.The precipitation in the vegetation growing season and leaf area index(LAI)in the following month show a similar change pattern,indicating a“one-month lag”response of LAI to precipitation on the TP.Further analysis illustrates the influence of water vapor transport driven by the Asian summer monsoon.Water vapor derived from trans-equatorial air flows across the Indian Ocean and Arabian Sea is strengthened,leading to the increase of precipitation in the central and northern TP,where the trend of warming and wetting and the increase of vegetation tend to be more obvious.By contrast,as a result of the weakening trend of water vapor transport in the middle and low levels in southern TP,the precipitation decreases,and the LAI shows a downtrend,which inhibits the warming and wetting ecological environment in this area.