Optimal Interpolation Research Articles

Equation‐Free Surrogate Modeling of Geophysical Flows at the Intersection of Machine Learning and Data Assimilation

AbstractThere is a growing interest in developing data‐driven reduced‐order models for atmospheric and oceanic flows that are trained on data obtained either from high‐resolution simulations or satellite observations. The data‐driven models are non‐intrusive in nature and offer significant computational savings compared to large‐scale numerical models. These low‐dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation (DA) to produce accurate state estimates. This paper aims at exploring an equation‐free surrogate modeling approach at the intersection of machine learning and DA in Earth system modeling. With this objective, we introduce an end‐to‐end non‐intrusive reduced‐order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential DA. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short‐term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 data set. Our results indicate that the NIROM is stable for long‐term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by almost one order of magnitude by the DEnKF algorithm.

Comparison of spatial interpolation methods for distribution map an unmanned surface vehicle data for chlorophyll-a monitoring in the stream

This study aims to comparatively evaluate the interpolation methods to estimate the chlorophyll-a concentrations in a spatial distribution map using the unmanned surface vehicle (USV). We targeted 0.0231 km 2 of the N stream, installed and operated a Chlorophyll-a sensor on a USV, and collected a significant amount of data. These data were extracted via data pre-processing using the data exploration and linear interpolation methods and subsequently utilized for spatial distribution analysis. The inverse distance weighted (IDW) and Kriging interpolation methods were compared to express the chlorophyll-a in a spatial distribution map. With the IDW method, R 2 was 0.81, and the root mean square error (RMSE) was 4.45, and with the Kriging method, R 2 was 0.61, and the RMSE was 6.39. We selected IDW as the optimal interpolation method and manually classified the chlorophyll-a concentrations based on the Korean lake water-quality standard. The analysis of the chlorophyll-a distribution indicated the following: Type Ia (chlorophyll-a 5 μ g / L or less) was 2.6%; Type Ib (chlorophyll-a 9 μ g / L or less) was 9.9%; Type II (chlorophyll-a 14 μ g / L or less) was 19.1%; Type III (chlorophyll-a 20 μ g /L or less) was 27.9%; Type IV (chlorophyll-a 35 μ g /L or less) was 33.2%; and Type V (chlorophyll-a 70 μ g /L or less) was 7.4%. The chlorophyll-a concentrations determined using the USV were successfully represented in the spatial distribution map. • The unmanned surface vehicle (USV) was conducted to monitor the chlorophyll-a concentration distribution in river. • The inverse distance weighted (IDW) was applied for the spatial interpolation method. • The spatial distribution map exhibited considerable potential for the commercialization of remote monitoring technology development using USV.

Diagnosing Frontal Dynamics From Observations Using a Variational Approach

AbstractIntensive hydrographic and horizontal velocity measurements collected in the Alboran Sea enabled us to diagnose the three‐dimensional dynamics of a frontal system. The sampled domain was characterized by a 40 km diameter anticyclonic eddy, with an intense front on its eastern side, separating the Atlantic and Mediterranean waters. Here, we implemented a multi‐variate variational analysis (VA) to reconstruct the hydrographic fields, combining the 1‐km horizontal resolution of the Underway Conductivity‐Temperature‐Depth (CTD) system with information on the flow shape from the Acoustic Doppler Current Profiler velocities. One advantage of the VA is given by the physical constraint, which preserves fine‐scale gradients better than the classical optimal interpolation (OI). A comparison between real drifter trajectories and virtual particles advected in the mapping quantified the improvements in the VA over the OI, with a 15% larger skill score. Quasi‐geostrophic (QG) and semi‐geostrophic (SG) omega equations enabled us to estimate the vertical velocity (w) which reached 40 m/day on the dense side of the front. How nutrients and other passive tracers leave the mixed‐layer and subduct is estimated with 3D advection from the VA, which agreed with biological sampling from traditional CTD casts at two eddy locations. Downwelling warm filaments are further evidence of subduction, in line with the w from SG, but not with QG. SG better accounted for the along‐isopycnal component of w in agreement with another analysis made on isopycnal coordinates. The multi‐platform approach of this work and the use of variational methods improved the characterization and understanding of (sub)‐mesoscale frontal dynamics.

Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms

In this work we extend some ideas about greedy algorithms, which are well-established tools for, e.g., kernel bases, and exponential-polynomial splines whose main drawback consists in possible overfitting and consequent oscillations of the approximant. To partially overcome this issue, we develop some results on theoretically optimal interpolation points. Moreover, we introduce two algorithms which perform an adaptive selection of the spline interpolation points based on the minimization either of the sample residuals (f-greedy), or of an upper bound for the approximation error based on the spline Lebesgue function (lambda-greedy). Both methods allow us to obtain an adaptive selection of the sampling points, i.e., the spline nodes. While the f-greedy selection is tailored to one specific target function, the lambda-greedy algorithm enables us to define target-data-independent interpolation nodes.

Interannual, Seasonal, and Monthly Variability of Sea Surface Temperature Fronts in Offshore China from 1982–2021

The offshore China (OC) region is a significant sea area in the Western Pacific and many researchers have been interested in the distribution of sea surface temperature (SST) fronts in this area. In this study, the Cayula and Cornillon single image edge detection algorithm was used to detect SST fronts using the Daily Optimum Interpolation Sea Surface Temperature data from 1982 to 2021. The results revealed that there are eighteen SST fronts in OC— three in the Bohai Sea, seven in the Yellow Sea, two in the East China Sea, five in the South China Sea, one in the Pacific Ocean east of Taiwan province, China—and among them a new front was detected in the Yellow Sea and named the Yellow Sea Ring Front. The frequency of most fronts showed a tendency of initially increasing and then decreasing from January to September, followed by a trend of growing steadily from October to December. The frequency of a few fronts showed a decreasing tendency from January to September and an increasing tendency from October to December. The frequency of most fronts is highest in winter and lowest in summer. In spring and autumn, the frequency of most fronts is lower than that in winter and higher than that in summer. The annual average frontal probability of five-ninths of the fronts showed an upward trend, and the annual average frontal probability value of one-third of the fronts showed a downward trend. The rest of the fronts showed a stable trend. The results of this paper also showed that the Liaodong Bay Front and the Bohai-Laizhou Bay Front did not form a complete front, as previously reported. In addition, the frontal probability of the Bohai Front to the north of 39° N was in the tendency of decreasing.

Assessing Sea Surface Temperatures Estimated from Fused Infrared and Microwave Data

Sea surface temperature (SST), a critical parameter of the global ocean–atmosphere system, is an essential element in the study and in the application of marine science. Satellite–infrared observations currently represent the only available method for continuous, large-scale observation of SST. Although passive microwave observations are not blocked by clouds, allowing for data collection in all weather conditions, this technological tool is characterized by low spatial resolution. Conversely, infrared observations offer high resolution but are susceptible to cloud obscuration. Accordingly, a technique that effectively fuses microwave and infrared satellite observations into a high-resolution SST field with global coverage close to the actual distribution is of practical significance. This paper describes fusing MODIS infrared remote sensing and AMSR-2 microwave remote sensing SST data with an optimal interpolation (OI) approach to produce a high-resolution SST data. The study chose the coastal Kuroshio region of China to establish an appropriate scale for examining the spatial structure of SST and attaining a more realistic picture of SST observations and impacts. The included discussion of the sources of error in the fusion process provides a reference for improving the accuracy of fused marine remote sensing data. The study also compared the fused SST results and the current international mainstream multi-temporal resolution of the three using the OI algorithm. We compared the fusion product with ARGO data with and without typhoon impact to explore and practice the OI in SST fusion when evaluating the accuracy of different data in the case of external disturbance being present. The research results have great significance for improving regional SST forecast accuracy while ensuring the applicability of various approaches to fusing SST data by incorporating the influence of typhoons in the offshore region of the East China Sea (ECS). Implications for the future development of SST fusion data are also included in the discussion.

Using a hybrid optimal interpolation–ensemble Kalman filter for the Canadian Precipitation Analysis

Abstract. Several data assimilation (DA) approaches exist to generate consistent and continuous precipitation fields valuable for hydrometeorological applications and land data assimilation. Usually, DA is based on either static or dynamic approaches. Static methods rely on deterministic forecasts to estimate background error covariance matrices, whereas dynamic approaches use ensemble forecasts. Associating the two methods is known as hybrid DA, and it has proven beneficial for different applications as it combines the advantages of both approaches. The present study intends to explore hybrid DA for the 6 h Canadian Precipitation Analysis (CaPA). Based on optimal interpolation (OI), CaPA blends forecasts and observations from surface stations and ground-based radar datasets to provide precipitation fields over the North American domain. The application of hybrid DA to CaPA consisted of finding the optimal linear combination between (i) an OI based on the Regional Deterministic Prediction System (RDPS) and (ii) an ensemble Kalman filter (EnKF) based on the 20-member Regional Ensemble Prediction System (REPS). The results confirmed the known effectiveness of the hybrid approach when low-density observation networks are assimilated. Indeed, the experiments conducted for the summer without radar datasets and for the winter (characterized by very few observations in CaPA) showed that attributing a relatively high weight to the EnKF (50 % and 70 % for summer and winter, respectively) resulted in better analysis skill and a reduction in false alarms compared with the OI method. A deterioration in the moderate- to high-intensity precipitation bias was, however, observed during summer. Reducing the weight attributed to the EnKF to 30 % alleviated the bias deterioration while improving skill compared with the OI-based CaPA.

3D morphology reconstruction of rock joints from 2D profile measurement by a profilograph

Rock mass stability is closely related to the shear strength of rock joints. Measuring the joint surface morphology is of vital importance for evaluating the shear strength of rock joints. Although non-contact measurement methods such as laser scanning are advantageous in high precision, the characteristics of high purchase cost or rental fees and being susceptible to the operating environment have weakened their practicability for in-situ batch measurement of the three-dimensional (3D) morphology of joints. To facilitate the possibility of utilizing cost-effective contact-based devices to replace the non-contact ones, we proposed a methodology to reconstruct the 3D morphology of rock joints using two-dimensional (2D) joint profiles measured by contact measurement methods (e.g., a profilograph). First, through a comprehensive comparison of commonly used spatial interpolation methods, the V4 method from the Griddata function is determined as the optimal one for the proposed methodology. Then, based on the optimal spatial interpolation method, the appropriate profile interval is determined through a referential band derived in this study. Finally, the performance of the proposed methodology was validated from experimental and theoretical perspectives. Results show that the relative errors of the test cases are within the engineering permissible error range, and more than 92% of the test cases are associated with an error less than 5%. In addition, the influences of the joint mechanical parameters, joint roughness level, and joint size on the appropriate profile interval are investigated. This methodology offers a cost-effective alternative for in-situ batch measurement of joint 3D morphology in the field survey of rock joints.

Global Trends in Marine Heatwaves and Cold Spells: The Impacts of Fixed Versus Changing Baselines

AbstractMarine heatwaves (MHW) and cold spells (MCS) are considered to be anomalously warm or cool events in sea surface temperature that are commonly defined relative to a long‐term fixed baseline. As a result, because of climate warming, it is often concluded that MHW will become stronger, longer, and more frequent in the future, whereas MCS will become weaker, shorter, and less frequent. Here, it is argued that in order to understand the physics of MHW/MCS, it is important to remove the climate signal when detecting events. The 1982–2021 National Oceanic and Atmospheric Administration optimum interpolation sea surface temperature data set (NOAA OISST V2) is used to show that using a fixed baseline leads on average to overestimating MHW and underestimating MCS strengths between 1982 and 2021 compared to using a linear trend to remove the climate signal. If a linear trend is used to remove the climate signal, global trends over the 40‐year record indicate a shift to weaker MHW and MCS in the tropics, especially in the eastern Pacific Ocean, and a shift to stronger MHW and MCS in the northern Pacific and Atlantic Oceans. The trends in the tropics are likely related to El Niño conditions predominating during the first half of the record and La Niña conditions predominating during the second half of the record. The trends at higher latitudes are consistent with changes in the North Atlantic and Atlantic Multidecadal Oscillations.

Citizen scientists’ dive computers resolve seasonal and interannual temperature variations in the Red Sea

Dive computers have the potential to provide depth resolved temperature data that is often lacking especially in close to shore, but spatiotemporal assessment of the robustness of this citizen science approach has not been done. In this study, we provide this assessment for the Red Sea, one of the most dived areas in the world. A comparison was conducted between 17 years of minimum water temperatures collected from SCUBA dive computers in the northern Red Sea (23–30° N, 32–39.4° E), satellite-derived sea surface temperatures from the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) optimal interpolation product, and depth-banded monthly mean in-situ temperature from the TEMPERSEA dataset, which incorporates data originating from several in-situ recording platforms (including Argo floats, ships and gliders). We show that dive computer temperature data clearly resolve seasonal patterns, which are in good agreement in both phase and amplitude with OSTIA and TEMPERSEA. On average, dive computer temperatures had an overall negative bias of (–0.5 ± 1.1) °C compared with OSTIA and (–0.2 ± 1.4) °C compared with TEMPERSEA. As may be expected, increased depth-related biases were found to be associated with stratified periods and shallower mixed layer depths, i.e., stronger vertical temperature gradients. A south-north temperature gradient consistent with values reported in the literature was also identifiable. Bias remains consistent even when subsampling just 1% of the total 9310 dive computer datapoints. We conclude that dive computers offer potential as an alternative source of depth-resolved temperatures to complement existing in situ and satellite SST data sources.

A Frequency-Dependent Assimilation Algorithm: Ensemble Optimal Smoothing

Motivated by the need for a simple and effective assimilation scheme that could be used in a relocatable ocean model, a new assimilation algorithm called ensemble optimal smoothing (EnOS) was developed. This scheme was a straightforward extension of the ensemble optimal interpolation (EnOI) by involving time correlation information in the Kalman gain. The main advantage of this scheme was the ability to estimate the present state from the time history of observation. We first examined the new scheme in an ideal ocean model using simulated observations. Further applying these two assimilation schemes to the Chinese offshore and adjacent waters, the root-mean-square error (RMSE) of the EnOS scheme was reduced by 6.4% relative to EnOI. The results showed that the EnOS was more efficient and effective in eliminating model errors when compared to the EnOI scheme.

A new Level 4 multi-sensor ice surface temperature product for the Greenland Ice Sheet

Abstract. The Greenland Ice Sheet (GIS) is subject to amplified impacts of climate change and its monitoring is essential for understanding and improving scenarios of future climate conditions. Surface temperature over the GIS is an important variable, regulating processes related to the exchange of energy and water between the surface and the atmosphere. Few local observation sites exist; thus spaceborne platforms carrying thermal infrared instruments offer an alternative for surface temperature observations and are the basis for deriving ice surface temperature (IST) products. In this study several satellite IST products for the GIS were compared, and the first multi-sensor, gap-free (Level 4, L4) product was developed and validated for 2012. High-resolution Level 2 (L2) products from the European Space Agency (ESA) Land Surface Temperature Climate Change Initiative (LST_cci) project and the Arctic and Antarctic Ice Surface Temperatures from Thermal Infrared Satellite Sensors (AASTI) dataset were assessed using observations from the PROMICE (Programme for Monitoring of the Greenland Ice Sheet) stations and IceBridge flight campaigns. AASTI showed overall better performance compared to LST_cci data, which had superior spatial coverage and availability. Both datasets were utilised to construct a daily, gap-free L4 IST product using the optimal interpolation (OI) method. The resulting product performed satisfactorily when compared to surface temperature observations from PROMICE and IceBridge. Combining the advantages of satellite datasets, the L4 product allowed for the analysis of IST over the GIS during 2012, when a significant melt event occurred. Mean summer (June–August) IST was −5.5 ± 4.5 ∘C, with an annual mean of −22.1 ± 5.4 ∘C. Mean IST during the melt season (May–August) ranged from −15 to −1 ∘C, while almost the entire GIS experienced at least between 1 and 5 melt days when temperatures were −1 ∘C or higher. Finally, this study assessed the potential for using the satellite L4 IST product to improve model simulations of the GIS surface mass balance (SMB). The L4 IST product was assimilated into an SMB model of snow and firn processes during 2012, when extreme melting occurred, to assess the impact of including a high-resolution IST product on the SMB model. Compared with independent observations from PROMICE and IceBridge, inclusion of the L4 IST dataset improved the SMB model simulated IST during the key onset of the melt season, where model biases are typically large and can impact the amount of simulated melt.

An Analysis of Meteorological Conditions in Relation to Occurrence of the Mucilage Outbreaks in Sea of Marmara, March-June 2021

A severe mucilage problem appeared as a major environmental disaster in the Marmara Sea, Turkey, during March-May 2021 period, imposing significant implications for the fishing industry, marine life and tourism. This study aimed to provide an insight into the mucilage outbreak observed in the Marmara Sea during March-May 2021 period by establishing some links between meteorological factors including SST anomalies and changes in wind speed and mucilage occurrence and puts some emphasis on the importance of monitoring variability of such parameters to assess mucilage outbreaks. For this purpose, mean and maximum SSTs and wind speed variability at a number of locations along the shores of Marmara and Black Seas are analysed for the April-June period, when the mucilage problem peaked. Both surface and satellite data are used to identify the spatial and temporal extent of the SST anomalies. Furthermore, the relationship between turbidity in the Marmara Sea and the SSTs is sought as a contributing factor to mucilage formation and enhancement. The findings indicate that most of the stations are characterized by warming trends and positive SST anomalies, with a few stations indicating periodic warming and cooling. Moreover, the NOAA NCEP Optimum Interpolation SST (OISST) data supported the warming event especially in central and eastern parts of the Marmara Sea. The wind observations at different locations along the shores of Marmara and Black Seas indicate decreasing trends in the mean wind speed. It is the view taken in this paper that both the increased SSTs and reduced wind speed generate a favourable environment both for the formation and enhancement of the mucilage episode over the Marmara Sea during the March-June 2021 period. Therefore, analysis of such meteorological parameters can provide a better understanding of mucilage aggregation in addition to other causative factors involved. The study also concluded that the modest turbidity conditions caused to increase in the SSTs to some extent in addition to the climate change-related warming.

A new operational Mediterranean diurnal optimally interpolated sea surface temperature product within the Copernicus Marine Service

Abstract. Within the Copernicus Marine Service, a new operational MEDiterranean diurnal optimally interpolated sea surface temperature (MED DOISST) product has been developed. This product provides hourly mean maps (level 4) of subskin SST at 1/16∘ horizontal resolution over the Mediterranean Sea from January 2019 to the present. Subskin is the temperature at ∼1 mm depth of the ocean surface and then potentially subjected to a large diurnal cycle. The product is built by combining hourly SST data from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) on board the Meteosat Second Generation and model analyses from the Mediterranean Forecasting System (MedFS) through optimal interpolation. SEVIRI and MedFS (first layer) SST data are respectively used as the observation source and first guess. The choice of using a model output as first guess represents an innovative alternative to the commonly adopted climatologies or previous day analyses, providing physically consistent estimates of hourly SSTs. The accuracy of the MED DOISST product is assessed here by comparison against surface drifting buoy measurements covering the years 2019 and 2020. The diurnal cycle reconstructed from DOISST is in good agreement with the one observed by independent drifter data, with a mean bias of 0.041±0.001 K and root mean square difference (RMSD) of 0.412±0.001 K. The new SST product is more accurate than the input MedFS SST during the central warming hours, when the model, on average, underestimates drifter SST by 1/10 of a degree. The capability of DOISST to reconstruct diurnal warming events, which may reach intense amplitudes larger than 5 K in the Mediterranean Sea, is also analyzed. Specifically, a comparison with the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) diurnal skin SST product, SEVIRI, MedFS, and drifter data shows that the DOISST product is able to reproduce more accurately diurnal warming events larger than 1 K. This product can contribute to improving the prediction capability of numerical models that assimilate or correct the heat fluxes starting from level 4 SST data and the monitoring of surface heat budget estimates and temperature extremes which can have significant impacts on the marine ecosystem. The full MED DOISST product (released on 4 May 2021) is available upon free registration at https://doi.org/10.48670/moi-00170 (CNR, 2021). The reduced subset used here for validation and review purposes is openly available at https://doi.org/10.5281/zenodo.5807729 (Pisano, 2021).

Determinantal Point Processes Implicitly Regularize Semiparametric Regression Problems

Semiparametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics and nonlinear time series problems, where the system includes a linear and nonlinear component. We discuss here the use of a finite determinantal point process (DPP) for approximating semiparametric models. Recently, Barthelmé, Tremblay, Usevich, and Amblard introduced a novel representation of finite DPPs. These authors formulated extended L-ensembles that can conveniently represent partial-projection DPPs and suggest their use for optimal interpolation. With the help of this formalism, we derive a key identity illustrating the implicit regularization effect of determinantal sampling for semiparametric regression and interpolation. Also, a novel projected Nyström approximation is defined and used to derive a bound on the expected in-sample prediction error for the corresponding approximation of semiparametric regression. This work naturally extends similar results obtained for kernel ridge regression.

Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements

AbstractAn error analysis of a mixed discontinuous Galerkin (DG) method with lifting operators as numerical fluxes for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method is that due to the low regularity the tangential trace of the exact solution is not well defined on the faces of the computational mesh. This difficulty is addressed by adopting the face-to-cell lifting introduced by Ern & Guermond (2021, Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and $H^{1+r}$, $r>0$, regularity. Found. Comput. Math., 1–36). To obtain optimal local interpolation estimates, we introduce Scott–Zhang-type interpolations that are well defined for $H(\textrm {curl})$ and $H(\textrm {div})$ functions with minimal regularity requirements. As a by-product of penalizing the lifting of the tangential jumps, an explicit and easily computable stabilization parameter is given.

End-to-End Neural Interpolation of Satellite-Derived Sea Surface Suspended Sediment Concentrations

The characterization of suspended sediment dynamics in the coastal ocean provides key information for both scientific studies and operational challenges regarding, among others, turbidity, water transparency and the development of micro-organisms using photosynthesis, which is critical to primary production. Due to the complex interplay between natural and anthropogenic forcings, the understanding and monitoring of the dynamics of suspended sediments remain highly challenging. Numerical models still lack the capabilities to account for the variability depicted by in situ and satellite-derived datasets. Through the ever increasing availability of both in situ and satellite-derived observation data, data-driven schemes have naturally become relevant approaches to complement model-driven ones. Our previous work has stressed this potential within an observing system simulation experiment. Here, we further explore their application to the interpolation of sea surface sediment concentration fields from real gappy satellite-derived observation datasets. We demonstrate that end-to-end deep learning schemes—namely 4DVarNet, which relies on variational data assimilation formulation—apply to the considered real dataset where the training phase cannot rely on gap-free references but only on the available gappy data. 4DVarNet significantly outperforms other data-driven schemes such as optimal interpolation and DINEOF with a relative gain greater than 20% in terms of RMSLE and improves the high spatial resolution of patterns in the reconstruction process. Interestingly, 4DVarNet also shows a better agreement between the interpolation performance assessed for an OSSE and for real data. This result emphasizes the relevance of OSSE settings for future development calibration phases before the applications to real datasets.

A long-term global XCO2 dataset: Ensemble of satellite products

Many satellites such as SCIAMACHY (scanning imaging absorption spectrometer for atmospheric cartography), GOSAT-1/2 (greenhouse gases observing satellite), OCO-2/3 (orbiting carbon observatory) and TanSat (CarbonSat, Tan means “carbon” in Chinese) provide key observations of atmospheric CO2 concentration and different XCO2 retrieval algorithms have been developed for these satellite measurements. However, limited by the revisit period and scanning swath of the satellites, the effective daily observation coverage of satellites mentioned above is very small (<1%), which is a great challenge for high-resolution mapping of global XCO2. In this paper, we re-evaluated the uncertainty of each XCO2 pixel with 0.5° × 0.5° spatial resolution in the global based on season, AOD (aerosol optical depth), surface albedo, uncertainty parameters of SCIAMACHY, GOSAT-1/2, OCO-2/3 and TanSat XCO2 products by TCCON (Total Carbon Column Observing Network) data. Then, a 30-day time window was used to smooth XCO2 datasets from satellite observations and filled in the missing values according to CarbonTracker. Finally, we ensembled global XCO2 datasets using maximum likelihood estimation (MLE) method and optimal interpolation (OI) based on the re-evaluated uncertainty. The ensemble XCO2 dataset at 0.5° × 0.5° spatial resolution for every three hours from January 2003 to August 2020 was generated. Compared to TCCON and WDCGG (World Data Centre for Greenhouse Gases) measurements separately on the global scale, we obtained the correlation coefficient R = 0.96, the Root Mean Square Error (RMSE) of 2.62 ppm for TCCON and R = 0.82, the RMSE of 6.75 ppm for WDCGG, respectively. The RMSE of the ensemble dataset was 6 ppm lower than that of the satellites' XCO2 used for fusion compared with WDCGG and the coverage is greatly improved at a higher spatial and temporal resolution, proving the feasibility and high precision of the method.

Adaptive Transition Gait Planning of Snake Robot Based on Polynomial Interpolation Method

This paper mainly studies the transition gait planning by updating the parameters of snack robot motion control function through ROS nodes, including a straight running gait into a turning gait. In the practical scenario, when changing the control parameters, the joint angle of the snake robot will increase or decrease sharply, and the angular velocity and angular acceleration of the driving joints will also change, which results in oscillation and sideslip of the body. In the turning scene, the visual tracking will loss if the head joint of the snake robot causes the lateral movement and oscillation. To solve those problems, firstly, the dynamic model of the snake robot’s gait of serpentine movement is established. Then, we propose a method based on polynomial interpolation compensation to solve the body oscillation and sideslip caused by nodes updating. To further improve the efficiency of snake robot’s gait switching, an optimal dichotomy interpolation time search is proposed to realize the snake robot’s adaptive transition gait. Finally, some simulation experiments are verified the effectiveness of the proposed method.

Operational Assimilation of Spectral Wave Data From the Sofar Spotter Network

AbstractHistorically, the sparseness of in situ open‐ocean wave and weather observations has severely limited the forecast skill of weather over the ocean with major social and economic consequences for coastal communities and maritime industries. Ocean surface waves, specifically, are important for the interaction between atmosphere and ocean, and thus key in modeling weather and climate processes. Here, we investigate the improvements achievable from a large distributed sensor network combined with advances in assimilation strategies. Wave spectra from a global network of over 600 Sofar Spotter buoys are assimilated into an operational global wave forecast via optimal interpolation to update model spectra to best fit observations. We demonstrate end‐to‐end improvements in forecast skill of significant wave height of 38%, and up to 45% for other bulk parameters. This shows distributed observations of the air‐sea interface, with advances in assimilation strategies, can reduce uncertainty in forecasts to dramatically improve earth system modeling.