Spatial Interpolation Scheme Research Articles

Reconstruction of directional sources using physics-informed neural networks

In the context of augmented/virtual reality applications, replicating the directivity of sound sources is a critical step to ensure a high-quality immersive experience. However, accurate directivity measurements require complex experimental procedures involving a high number of microphones. In these scenarios, spatial interpolation allows to reconstruct the sound field with fewer sensors, which can be sparsely distributed around the source. The literature offers several interpolation schemes for sound field reconstruction, although they exhibit limited accuracy due to the lack of knowledge on the underlying physics. Recently, Physics-Informed Neural Networks (PINN) have been used to directly solve partial differential equations and thus better predict the evolution of dynamical systems. In this manuscript, we propose a spatial interpolation scheme based on PINN for the reconstruction of sound source directivity. PINN are used to solve the Helmholtz equation starting from acquisitions of the directivity over a limited set of sparsely distributed points. Results are compared with the outcomes of well-established methods based on Spherical Harmonics Decomposition (SH), Thin Plate Pseudo-Splines Interpolation (SPLI) and Piece-wise Linear Spherical Triangular Interpolation (TRI). PINN prove to provide better reconstruction of the directivity with respect to the proposed comparison methods, even when dealing with highly sparse sampling grids.

A second-order particle Fokker-Planck model for rarefied gas flows

The direct simulation Monte Carlo (DSMC) method has become a powerful tool for studying rarefied gas flows. However, for the DSMC method to be effective, the cell size must be smaller than the mean free path, and the time step smaller than the mean collision time. These constraints make it difficult to use the DSMC method in multiscale rarefied gas flows. Over the past decade, the particle Fokker-Planck (FP) method has been studied to address computational cost issues in the near-continuum regime. To capture the main features of the Boltzmann equation, various FP models have been proposed, such as the quadratic entropic FP (Quad-EFP) and the ellipsoidal statistical FP (ESFP). Nevertheless, few studies have clearly demonstrated that the FP method offers a computational advantage over the DSMC method without sacrificing accuracy. This is because conventional particle FP methods have employed first-order accuracy schemes. The present study proposes a unified stochastic particle ESFP (USP-ESFP) model. This model improves the accuracy of shear stress and heat flux predictions. Additionally, a spatial interpolation scheme is introduced to the particle FP method. The numerical test cases include relaxation problem, Couette flows, Poiseuille flows, velocity perturbation, and hypersonic flows around a cylinder. The results show that the USP-ESFP model agrees well with both analytical and DSMC results. Furthermore, the USP-ESFP model is found to be less sensitive to cell size and time step than the DSMC method, resulting in a factor of four speed-up for the considered hypersonic flow around a cylinder.

A spatially adaptive multi-resolution generative algorithm: Application to simulating flood wave propagation

We propose a statistical model suitable for large spatio-temporal data sets exhibiting complex patterns such as simulated by physics-based hydraulic models over high resolution (HR) 2D meshes. Although necessary for impact studies such as urban flood hazard assessment, their long computation times limit their applicability leading to the development of statistical models that may emulate them quickly. Our model draws from the strengths of multi-resolution analysis and relies on an extension of the lifting scheme, a flexible implementation of discrete wavelet transforms, for spatio-temporal data. The extended lifting scheme exploits the idea that dominant spatial features, that may be identified with clustering, remain present through time. An easily interpretable non-parametric representation can be derived from the lifting scheme by combining a smoothed version of the data (obtained by simple averaging) with details (given by local regression residuals). A generative algorithm is built by introducing the information provided by a low resolution model, whose computation times are orders of magnitude smaller, yielding a downscaling model. This downscaling model assumes that sufficiently representative HR spatial patterns can be inferred from the training set. Our model is applied to a 2D dam break experiment using a synthetic urban configuration and to a field-scale test case simulating the propagation of a dike break flood wave into a Sacramento urban area. A comparison, carried out with spatial interpolation schemes and with a variant of our model based on principal component analysis, shows that the spatio-temporal lifting scheme based model is better at reproducing extreme events.

An improved CIP-based numerical model for simulating free-surface flow with adaptive mesh

In this paper, an improved CIP (constrained interpolation profile)-based numerical model, which combines with Afivo (Adaptive Finite Volume quadtree/Octree mesh, an adaptive mesh framework), has been presented to simulate free-surface flow. In the CIP-based model, the constrained interpolation profile (CIP) method, a high-order finite difference method, is employed as the base flow solver and THINC/SW (Tangent of Hyperbola for Interface Capturing with Slope Weighting) method, a volume of fluid method, is applied to capture the flow interface. In this present model, an adaptive mesh technique is introduced to reduce the computational cost and multigrid technique is used to improve the solution efficiency. In the adaptive mesh system, new spatial interpolation schemes are provided, which have better performance in mass conservation compared with schemes provided in Afivo. Lid-driven cavity flow test was carried out to validate the accuracy of the flow solver with adaptive mesh and two/three-dimensional interface benchmark tests were performed to test the reliability of the interface capturing scheme and spatial interpolation schemes. Then two/three-dimensional applications (dam-break flow case, tank sloshing case and dam-break flow over a rectangular obstacle case) were investigated to demonstrate the model accuracy. The numerical results were compared with the previous experimental and numerical results, and good agreements were observed. It is demonstrated that the present numerical model has good applicability in modeling the free-surface flow.

An Efficient Hybrid Machine Learning Classifier for Rainfall Prediction

The most leading applications of Artificial Intelligence that seems to witness an immense Progression in the digital era are the Machine Learning (ML) Techniques. It learns itself from the past experiences and attempts at the best prediction of future instances or trends. Such progressive learning does not demand any explicit programming structures. Machine learning finds a wide range of application areas, and out of which accurate real time weather prediction gains importance. An interactive neural network based classification model for better prediction of rainfall has been put forth in this paper; we have proposed an interactive model for predicting rainfall using neural classification. The model is premeditated in a way, that it fetches feature extraction from a database including information about previous rainfalls in a specific area. The features were then pre-processed and further segmented by employing the random forest. The segmented outputs are then classified using neural networks. A comparison of spatial interpolation scheme is done with existing systems by deploying the hybrid classifier. The efficiency of the proposed model is evaluated and is compared with the traditional Deep Learning process and it is observed that the Random forest based interactive model provides better performance. Results of the model seem to be more accurate as the model uses an iterative approach for feature extraction.

High-resolution mapping of urban air quality with heterogeneous observations: a new methodology and its application to Amsterdam

Abstract. In many cities around the world people are exposed to elevated levels of air pollution. Often local air quality is not well known due to the sparseness of official monitoring networks or unrealistic assumptions being made in urban-air-quality models. Low-cost sensor technology, which has become available in recent years, has the potential to provide complementary information. Unfortunately, an integrated interpretation of urban air pollution based on different sources is not straightforward because of the localized nature of air pollution and the large uncertainties associated with measurements of low-cost sensors. This study presents a practical approach to producing high-spatiotemporal-resolution maps of urban air pollution capable of assimilating air quality data from heterogeneous data streams. It offers a two-step solution: (1) building a versatile air quality model, driven by an open-source atmospheric-dispersion model and emission proxies from open-data sources, and (2) a practical spatial-interpolation scheme, capable of assimilating observations with different accuracies. The methodology, called Retina, has been applied and evaluated for nitrogen dioxide (NO2) in Amsterdam, the Netherlands, during the summer of 2016. The assimilation of reference measurements results in hourly maps with a typical accuracy (defined as the ratio between the root mean square error and the mean of the observations) of 39 % within 2 km of an observation location and 53 % at larger distances. When low-cost measurements of the Urban AirQ campaign are included, the maps reveal more detailed concentration patterns in areas which are undersampled by the official network. It is shown that during the summer holiday period, NO2 concentrations drop about 10 %. The reduction is less in the historic city centre, while strongest reductions are found around the access ways to the tunnel connecting the northern and the southern part of the city, which was closed for maintenance. The changing concentration patterns indicate how traffic flow is redirected to other main roads. Overall, it is shown that Retina can be applied for an enhanced understanding of reference measurements and as a framework to integrate low-cost measurements next to reference measurements in order to get better localized information in urban areas.

Comparison of methods to estimate areal means of short duration rainfalls in small catchments, using rain gauge and radar data

Flood forecasting for early alerts is a challenging task for hydrologists. This is particularly the case in small catchments due to a lack of upstream gauges and their flashy response. In such catchments, estimating areal mean rainfall at short intervals by applying spatial interpolation schemes based on rain gauge data in short time scales is a significant work for accurate flood forecasting. In this study, we compare and evaluate four commonly used spatial interpolation methods in small catchments, which have small numbers of rain gauges in South Korea. We investigate the impacts of catchment area on different spatial interpolation schemes. Then a simulation is done with hypothetical storms to illustrate the limitation of the Thiessen method. Local heavy rainfall events have been selected for case studies and 10-minute rain gauge rainfall data are used, since short time scales of rainfall data are generally needed for flash flood forecasting and alerts. Furthermore, we analyse the characteristics of different spatial interpolation techniques by comparing the results with weather radar rainfall. The results revealed that mean absolute percentage discrepancy (MAPD) of areal mean rainfall between the Thiessen polygon method and the other three interpolation schemes (Inverse distance weighting, Multiquadric interpolation, Kriging) increases rapidly as the catchment area becomes smaller, especially when the catchment area is less than 500km2. In addition, regarding the number of rain gauges in a catchment, the smaller the number of rain gauges used in calculating areal mean rainfall, the larger the MAPD becomes, as expected. Furthermore, the number of rainfall events with outliers increased as correlation among rain gauge locations increased, which implies that outliers are more likely to happen when the gauges are located in a linear format rather than in a cluster. Finally, the temporal distributions of areal mean rainfall obtained from rain gauge and weather radar data are different depending on the direction of rainfall movement, especially in sparsely gauged catchments. This study provides a possible guideline for rain gauge number and placement to estimate areal mean rainfall accurately at small catchments.

Spatial Interpolation of Gauge Measured Rainfall Using Compressed Sensing

In this work, we suggest new spatial precipitation interpolation schemes using compressed sensing (CS), which is a new framework for signal acquisition and smart sensor design. Using CS, the precipitation maps are recovered in high resolution by obtaining sparse coefficients of radial basis functions(RBFs). Two types of methods are designed according to the construction methods of CS matrix. In the first type, the CS matrix is derived as the product of an m × n (n ≫ m) weights matrix of inverse distance weighting (IDW) and an n × n radial basis function (RBF) matrix. The second type of CS matrix consists of an m × n RBF matrix that depends on a few observation vectors and a number of n unknown vectors. The advantage of the proposed CS methods is that it can be represented at a high resolution because it is interpolated based on a large number of bases (or degrees of freedom). This prevents the variance value from being much smaller than the actual value due to interpolation using a few observation scales. To test our CS interpolation schemes, interpolation results were compared with IDW, Ordinary Kriging (OK) and RBF interpolation methods for analytic test function and some actual rainfall data. In the case of an analytic test function, when the proposed method is compared at high resolution, the error from the true value is the smallest. In real rainfall data, comparison with real values is not possible at high resolutions, but the error with the observed data is the smallest in terms of ‘spatial variogram’. In addition, the proposed CS method generates hight resolution data from rainfall cases, showing promising results when identifying peaks.

A novel hybrid algorithm based on FDTD and WCS‐FDTD methods

In this article, a hybrid algorithm based on traditional finite-difference time-domain (FDTD) and weakly conditionally stable finite-difference time-domain (WCS-FDTD) algorithm is proposed. In this algorithm, the calculation domain is divided into fine-grid region and coarse-grid region. The traditional FDTD method is used to calculate the field value in the coarse-grid region, while the WCS-FDTD method is used in the fine-grid region. The spatial interpolation scheme is applied to the interface of the coarse grid region and fine grid region to insure the stability and precision of the presented hybrid algorithm. As a result, a relatively large time step size, which is only determined by the spatial cell sizes in the coarse grid region, is applied to the entire calculation domain. This scheme yields a significant reduction both of computation time and memory requirement in comparison with the conventional FDTD method and WCS-FDTD method, which are validated by using numerical results.

Learning the Structured Sparsity: 3-D Massive MIMO Channel Estimation and Adaptive Spatial Interpolation

This paper addresses the channel estimation problem for three-dimensional (3-D) massive multiple-input multiple-output (MIMO) systems, where the base station (BS) is equipped with a two-dimensional uniform planar array (UPA) to serve a number of user equipments (UEs). To implement with low hardware complexity, the number of available radio-frequency (RF) chains at BS is constrained to be much smaller than the number of antennas. The theoretical analysis of sparse property for 3-D massive MIMO channel reveals that there exists two kinds of sparse structures in beam-domain channel vector, namely the common sparsity structure among sub-arrays of UPA and block sparsity structure per sub-array. Based on this property, a novel structured sparse Bayesian learning framework is proposed to estimate the channel between BS and UE reliably. Moreover, an adaptive spatial interpolation scheme is proposed to further reduce the number of required RF chains at BS while maintaining the estimation performance. The simulation results show that the proposed scheme provides stable estimation performance for a variety of scenarios with different numbers of RF chains, transmit signal-to-noise ratios, Rician factors, and angular spreads, and outperforms the reference schemes significantly.

Variability of spatial patterns of autocorrelation and heterogeneity embedded in precipitation

Abstract Spatial interpolation of precipitation data is an essential input for hydrological modelling. At present, the most frequently used spatial interpolation methods for precipitation are based on the assumption of stationary in spatial autocorrelation and spatial heterogeneity. As climate change is altering the precipitation, stationary in spatial autocorrelation and spatial heterogeneity should be first analysed before spatial interpolation methods are applied. This study aims to propose a framework to understand the spatial patterns of autocorrelation and heterogeneity embedded in precipitation using Moran's I, Getis–Ord test, and semivariogram. Variations in autocorrelation and heterogeneity are analysed by the Mann–Kendall test. The indexes and test methods are applied to the 7-day precipitation series which are corresponding to the annual maximum 7-day flood volume (P-AM7FV) upstream of the Changjiang river basin. The spatial autocorrelation of the P-AM7FV showed a statistically significant increasing trend over the whole study area. Spatial interpolation schemes for precipitation may lead to better estimation and lower error for the spatial distribution of the areal precipitation. However, owing to the changing summer monsoons, random variation in the spatial heterogeneity analysis shows a significant increasing trend, which reduces the reliability of the distributed hydrological model with the input of local or microscales.

SeNorge2 daily precipitation, an observational gridded dataset over Norway from 1957 to the present day

Abstract. The conventional climate gridded datasets based on observations only are widely used in atmospheric sciences; our focus in this paper is on climate and hydrology. On the Norwegian mainland, seNorge2 provides high-resolution fields of daily total precipitation for applications requiring long-term datasets at regional or national level, where the challenge is to simulate small-scale processes often taking place in complex terrain. The dataset constitutes a valuable meteorological input for snow and hydrological simulations; it is updated daily and presented on a high-resolution grid (1 km of grid spacing). The climate archive goes back to 1957. The spatial interpolation scheme builds upon classical methods, such as optimal interpolation and successive-correction schemes. An original approach based on (spatial) scale-separation concepts has been implemented which uses geographical coordinates and elevation as complementary information in the interpolation. seNorge2 daily precipitation fields represent local precipitation features at spatial scales of a few kilometers, depending on the station network density. In the surroundings of a station or in dense station areas, the predictions are quite accurate even for intense precipitation. For most of the grid points, the performances are comparable to or better than a state-of-the-art pan-European dataset (E-OBS), because of the higher effective resolution of seNorge2. However, in very data-sparse areas, such as in the mountainous region of southern Norway, seNorge2 underestimates precipitation because it does not make use of enough geographical information to compensate for the lack of observations. The evaluation of seNorge2 as the meteorological forcing for the seNorge snow model and the DDD (Distance Distribution Dynamics) rainfall–runoff model shows that both models have been able to make profitable use of seNorge2, partly because of the automatic calibration procedure they incorporate for precipitation. The seNorge2 dataset 1957–2015 is available at https://doi.org/10.5281/zenodo.845733. Daily updates from 2015 onwards are available at http://thredds.met.no/thredds/catalog/metusers/senorge2/seNorge2/provisional_archive/PREC1d/gridded_dataset/catalog.html.

A rank-based approach for correcting systematic biases in spatial disaggregation of coarse-scale climate simulations

Use of General Circulation Model (GCM) precipitation and evapotranspiration sequences for hydrologic modelling can result in unrealistic simulations due to the coarse scales at which GCMs operate and the systematic biases they contain. The Bias Correction Spatial Disaggregation (BCSD) method is a popular statistical downscaling and bias correction method developed to address this issue. The advantage of BCSD is its ability to reduce biases in the distribution of precipitation totals at the GCM scale and then introduce more realistic variability at finer scales than simpler spatial interpolation schemes. Although BCSD corrects biases at the GCM scale before disaggregation; at finer spatial scales biases are re-introduced by the assumptions made in the spatial disaggregation process. Our study focuses on this limitation of BCSD and proposes a rank-based approach that aims to reduce the spatial disaggregation bias especially for both low and high precipitation extremes.BCSD requires the specification of a multiplicative bias correction anomaly field that represents the ratio of the fine scale precipitation to the disaggregated precipitation. It is shown that there is significant temporal variation in the anomalies, which is masked when a mean anomaly field is used. This can be improved by modelling the anomalies in rank-space. Results from the application of the rank-BCSD procedure improve the match between the distributions of observed and downscaled precipitation at the fine scale compared to the original BCSD approach. Further improvements in the distribution are identified when a scaling correction to preserve mass in the disaggregation process is implemented. An assessment of the approach using a single GCM over Australia shows clear advantages especially in the simulation of particularly low and high downscaled precipitation amounts.

Comparison of Spatial Interpolation Schemes for Rainfall Data and Application in Hydrological Modeling

The spatial distribution of precipitation is an important aspect of water-related research. The use of different interpolation schemes in the same catchment may cause large differences and deviations from the actual spatial distribution of rainfall. Our study analyzes different methods of spatial rainfall interpolation at annual, daily, and hourly time scales to provide a comprehensive evaluation. An improved regression-based scheme is proposed using principal component regression with residual correction (PCRR) and is compared with inverse distance weighting (IDW) and multiple linear regression (MLR) interpolation methods. In this study, the meso-scale catchment of the Fuhe River in southeastern China was selected as a typical region. Furthermore, a hydrological model HEC-HMS was used to calculate streamflow and to evaluate the impact of rainfall interpolation methods on the results of the hydrological model. Results show that the PCRR method performed better than the other methods tested in the study and can effectively eliminate the interpolation anomalies caused by terrain differences between observation points and surrounding areas. Simulated streamflow showed different characteristics based on the mean, maximum, minimum, and peak flows. The results simulated by PCRR exhibited the lowest streamflow error and highest correlation with measured values at the daily time scale. The application of the PCRR method is found to be promising because it considers multicollinearity among variables.

A neural network approach to efficient valuation of large portfolios of variable annuities

Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, especially for intraday valuations, insurance companies need more efficient valuation techniques. Recently, a framework based on traditional spatial interpolation techniques has been proposed that can significantly decrease the computational complexity of MC simulation (Gan and Lin, 2015). However, traditional interpolation techniques require the definition of a distance function that can significantly impact their accuracy. Moreover, none of the traditional spatial interpolation techniques provide all of the key properties of accuracy, efficiency, and granularity (Hejazi et al., 2015). In this paper, we present a neural network approach for the spatial interpolation framework that affords an efficient way to find an effective distance function. The proposed approach is accurate, efficient, and provides an accurate granular view of the input portfolio. Our numerical experiments illustrate the superiority of the performance of the proposed neural network approach compared to the traditional spatial interpolation schemes.

New gridded daily climatology of Finland: Permutation‐based uncertainty estimates and temporal trends in climate

AbstractLong‐term time series of key climate variables with a relevant spatiotemporal resolution are essential for environmental science. Moreover, such spatially continuous data, based on weather observations, are commonly used in, e.g., downscaling and bias correcting of climate model simulations. Here we conducted a comprehensive spatial interpolation scheme where seven climate variables (daily mean, maximum, and minimum surface air temperatures, daily precipitation sum, relative humidity, sea level air pressure, and snow depth) were interpolated over Finland at the spatial resolution of 10 × 10 km2. More precisely, (1) we produced daily gridded time series (FMI_ClimGrid) of the variables covering the period of 1961–2010, with a special focus on evaluation and permutation‐based uncertainty estimates, and (2) we investigated temporal trends in the climate variables based on the gridded data. National climate station observations were supplemented by records from the surrounding countries, and kriging interpolation was applied to account for topography and water bodies. For daily precipitation sum and snow depth, a two‐stage interpolation with a binary classifier was deployed for an accurate delineation of areas with no precipitation or snow. A robust cross‐validation indicated a good agreement between the observed and interpolated values especially for the temperature variables and air pressure, although the effect of seasons was evident. Permutation‐based analysis suggested increased uncertainty toward northern areas, thus identifying regions with suboptimal station density. Finally, several variables had a statistically significant trend indicating a clear but locally varying signal of climate change during the last five decades.

Efficient and versatile surface integral approach to light scattering in stratified media.

Recent advances in nano-optics elicit a growing need for more efficient numerical treatments of light-matter interaction in stratified backgrounds. While being known for its many favorable properties, usage of the surface integral approach is hindered by numerical difficulties associated with layered-medium Green's functions. We present an efficient and robust implementation of this approach, addressing the limiting issues. The singularity extraction method is generalized to account for the occurring secondary-term singularities. The resulting scheme thus allows for arbitrary positioning of the scatterers. Further, the laborious matrix-filling process is dramatically accelerated through a simple and robustly-devised, spatial interpolation scheme, completely devoid of integral evaluations. The accuracy and versatility of the method are demonstrated by treating several representative plasmonic problems.

Comparing Spatial Interpolation Schemes for Constructing a Flow Duration Curve in an Ungauged Basin

This study aims to investigate the applicability of proposed ensemble interpolation technique based on both geographical and physiographical spaces, for prediction of flow duration curve (FDC) at ungauged site. The interpolation schemes were applied for selected 15 different percentiles of the FDC. Firstly, different FDC parametric models were tested to approximate FDCs at gauged sites. It was found that the suggested reliable ensemble averaging (REA) model outperformed the traditional deterministic models (linear, exponential, and logarithmic models). The REA model approximated the FDC with high consistency and small deviations from the observed percentiles. The results obtained by the REA model were further utilized to define homogeneity in the selected region. Secondly, based on the inverse distance weighting (IDW) concept, both geographical and physiographical spaces estimations were ensemble (using proposed estimated true value (ETV) method) to predict the hydrological information (FDC) at ungauged sites. It was noted that ETV based interpolation provided more efficient, reliable and consistent efficiency. Finally, to identify physical conditions that could favor the high predictability of the proposed methodology, we investigated the relationship between Nash-Sutcliffe efficiency (NASH) and catchments attributes. The results indicated that significance correlations were observed between NASH and catchments attributes even though no clear tends exist.

Comparison and evaluation of spatial interpolation schemes for daily rainfall in data scarce regions

Summary Accurate rainfall data are of prime importance for many environmental applications. To provide spatially distributed rainfall data, point measurements are interpolated. However, in low density measurement networks, the use of different interpolation methods may result in large differences and hence in deviations from the actual spatial distribution of rainfall. Our study aims at analyzing different rainfall interpolation schemes with regard to their suitability to produce spatial rainfall estimates in a monsoon dominated region with scarce rainfall measurements. The study was carried out in the meso-scale catchment of the Mula and the Mutha Rivers (2036 km 2 ) upstream of the city of Pune, India. Rainfall data from 16 rain gauges were spatially interpolated using seven different methods, including Thiessen polygons, statistical, and geostatistical approaches. The two most suitable covariates for rainfall interpolation were identified as (i) distance in wind direction from the main orographic barrier and as (ii) a 0.05° pattern of mean annual rainfall derived from satellite data acquired by the Tropical Rainfall Measuring Mission (TRMM). Consequently, these two covariates were used in the regression-based interpolation approaches. The quality of the different methods was assessed using a two step validation approach: (i) Cross-validation was used to evaluate the capability to reproduce measured data. (ii) Spatially integrated interpolation performance was assessed by using a hydrologic model to calculate runoff and compare modeled to measured runoff. By this assessment, the regression-based methods showed the best performance. We found that the choice of the covariate had a significant impact on precipitation and runoff amounts, as well as on the temporal course of runoff events. Our results show, that the decision on the suitable interpolation scheme should not only be based on the comparison with point measurements, but should also take the representativeness of the given measurement network as well as of the interpolated spatial rainfall distribution into account. The successful application of regression-based interpolation methods using a high resolution TRMM pattern as covariate is very promising as it is transferable to other data scarce regions.

Generation and validation of analysed wind vectors over the global oceans

Daily and 12 hourly gridded analysed wind vectors (AWVs) over global ocean were generated using the simple spatial interpolation scheme of ‘box averaging’, with a horizontal resolution of 0.5° × 0.5°. For daily analysed winds, observations only from Oceansat-2 Scatterometer (OSCAT) were used. The 12 hourly AWVs were generated by combining the data from both OSCAT and Advanced Scatterometer (ASCAT). Apart from ocean wind vectors, an effort was made also to produce analysed wind stress, divergence and curl of wind stress. The daily and 12 hourly analysed winds were validated using in situ observations from 97 global moored buoys and data from European Centre for Medium Range Weather Forecasting analyses for a period of 9 months. The validation result shows a good agreement between AWV products and the buoy and model analysis data, yielding a standard deviation of around 2 m s−1 in wind speed and around 20° in wind direction.