Extended triple collocation: estimating errors and correlation coefficients with respect to an unknown target

Calibration and validation of geophysical measurement systems typically require knowledge of the true value of the target variable. However, the data considered to represent the true values often include their own measurement errors, biasing calibration, and validation results. Triple collocation (TC) can be used to estimate the root-mean-square-error (RMSE), using observations from three mutually independent, error-prone measurement systems. Here, we introduce Extended Triple Collocation (ETC): using exactly the same assumptions as TC, we derive an additional performance metric, the correlation coefficient of the measurement system with respect to the unknown target, rho(t,Xi). We demonstrate that rho(2)(t,Xi) is the scaled, unbiased signal-to-noise ratio and provides a complementary perspective compared to the RMSE. We apply it to three collocated wind data sets. Since ETC is as easy to implement as TC, requires no additional assumptions, and provides an extra performance metric, it may be of interest in a wide range of geophysical disciplines.Peer ReviewedPostprint (published version

On the Accuracy and Consistency of Quintuple Collocation Analysis of In Situ, Scatterometer, and NWP Winds

The accuracy and consistency of a quintuple collocation analysis of ocean surface vector winds from buoys, scatterometers, and NWP forecasts is established. A new solution method is introduced for the general multiple collocation problem formulated in terms of covariance equations. By a logarithmic transformation, the covariance equations reduce to ordinary linear equations that can be handled using standard methods. The method can be applied to each determined or overdetermined subset of the covariance equations. Representativeness errors are estimated from differences in spatial variances. The results are in good agreement with those from quadruple collocation analyses reported elsewhere. The geometric mean of all solutions from determined subsets of the covariance equations equals the least-squares solution of all equations. The accuracy of the solutions is estimated from synthetic data sets with random Gaussian errors that are constructed from the buoy data using the values of the calibration coefficients and error variances from the quintuple collocation analysis. For the calibration coefficients, the spread in the models is smaller than the accuracy, but for the observation error variances, the spread and the accuracy are about equal only for representativeness errors evaluated at a scale of 200 km for u and 100 km for v. Some average error covariances differ significantly from zero, indicating weak inconsistencies in the underlying error model. Possible causes for this are discussed. With a data set of 2454 collocations, the accuracy in the observation error standard deviation is 0.02 to 0.03 m/s at the one-sigma level for all observing systems

On the Accuracy and Consistency of Quintuple Collocation Analysis of In Situ, Scatterometer, and NWP Winds

The accuracy and consistency of a quintuple collocation analysis of ocean surface vector winds from buoys, scatterometers, and NWP forecasts is established. A new solution method is introduced for the general multiple collocation problem formulated in terms of covariance equations. By a logarithmic transformation, the covariance equations reduce to ordinary linear equations that can be handled using standard methods. The method can be applied to each determined or overdetermined subset of the covariance equations. Representativeness errors are estimated from differences in spatial variances. The results are in good agreement with those from quadruple collocation analyses reported elsewhere. The geometric mean of all solutions from determined subsets of the covariance equations equals the least-squares solution of all equations. The accuracy of the solutions is estimated from synthetic data sets with random Gaussian errors that are constructed from the buoy data using the values of the calibration coefficients and error variances from the quintuple collocation analysis. For the calibration coefficients, the spread in the models is smaller than the accuracy, but for the observation error variances, the spread and the accuracy are about equal only for representativeness errors evaluated at a scale of 200 km for u and 100 km for v. Some average error covariances differ significantly from zero, indicating weak inconsistencies in the underlying error model. Possible causes for this are discussed. With a data set of 2454 collocations, the accuracy in the observation error standard deviation is 0.02 to 0.03 m/s at the one-sigma level for all observing systems

Visiting Scientist mission report Second-order structure function analysis of scatterometer winds over the tropical Pacific: Part 2. Rainy and dry regions Second-order structure function analysis of scatterometer winds over the tropical Pacific: Part 2. R

Abstract Kolmogorov second-order structure functions (second moment of velocity differences) are used to characterize and compare the small scale information contained in five scatterometer wind products: three were derived from the SeaWinds-on-QuikSCAT scatterometer and two from the ASCAT-on-MetOp-A scatterometer. An important difference in these products is the method used to remove ambiguities. A median filter method was used to produce two of the SeaWinds products, while a variational method (known as 2DVAR) was used to produce both ASCAT and one of the SeaWinds products. The analysis is carried out for rainy and dry regions in the tropical Pacific (nine regions between latitudes 10 • S and 10 • N and longitudes 140 • and 260 • E) for the period November 2008 -October 2009. Both longitudinal and transverse structure functions, calculated using separations in the along-track (meridional) direction, are calculated from monthly and regionally averaged velocity differences. Structure functions were characterized by estimating noise levels (the extrapolated value at zero separation), turbulent kinetic energy (structure function magnitude at 300 km), and structure function slope from fits in log-log space over the range 50 -250 km. The five wind products show good qualitative agreement, but instrument and processing differences reveal important differences. Estimates of noise level are sensitive to the method used. Fits to a symmetric quadratic yield noise levels that correlate well with rain-rate. These noise levels also show that SeaWinds median filter products have larger noise in the transverse component, while ASCAT products have larger noise in the longitudinal component. Fits to an asymmetric quadratic yields information about the strength of the filtering used to reduce noise 1 ASCAT and SeaWinds second-order structure functions Part 2: Rainy and dry regions NWPSAF-KN-VS-012 in Level 1 processing; results imply that ASCAT products are over filtered. Estimates of the turbulent kinetic energy show that ASCAT is greater than (less than) or equal to SeaWinds in the divergent (shear) component. Ratios of the shear to divergent turbulent kinetic energy shows that the greatest differences between SeaWinds median filtered and ASCAT winds occur in the convectively active months of each region. Longitudinal (transverse) structure function slopes are steeper (shallower) for SeaWinds than for ASCAT. Slope ratios in most regions show that SeaWinds median filtered winds have steeper longitudinal structure functions, while AS-CAT has steeper transverse structure functions. Results for the SeaWinds 2DVAR winds vary, sometimes closer to ASCAT and sometimes closer to the other SeaWinds products

The Effect of Error Non-Orthogonality on Triple Collocation Analyses

Triple collocation analysis is an established technique for calculating the relative linear intercalibration coefficients and observation error variances for physical quantities measured simultaneously in space and time by three different observation systems. A simple parameterized error model is used. It relies on a few assumptions, one of which is that the observation errors are independent of the magnitude of the observed quantities. This is referred to as error orthogonality. Using an ocean surface vector winds data set of 44,948 collocations, this study shows that the violation of error orthogonality does affect the calibration coefficients but has only a small second-order effect on the observation error variances of the calibrated data

Retrieving QuikSCAT winds closer to the coast

Living Planet Symposium, 23-27 May 2022, Bonn, GermanyHigh resolution accurate coastal winds are of paramount importance for a variety of applications, both civil and scientific. For example, they are important for monitoring some coastal phenomena such as orographic winds, coastal currents and the dispersion of atmospheric pollutants, or for the deployment of off-shore wind farms. In addition, they are fundamental for improving the forcing of regional ocean models and, consequently, the forecasting of some extreme events such as the Acqua Alta often occurring in the Venice lagoon. Scatterometer-derived winds represent the golden standard. However, their use in coastal areas is limited by the land contamination of the backscatter Normalized Radar Cross Section (NRCS) measurements. Nonetheless, the coastal sampling may be improved if the Spatial Response Function (SRF) orientation and the land contamination are properly considered in the wind retrieval processing chain. This study focuses on improving the coastal processing of the Seawinds scatterometer onboard QuikSCAT as part of a EUMETSAT study in the framework of the Ocean Sea Ice Satellite Application Facilities (OSI-SAF). In particular, the analytical model of the SRF is implemented with the aim of computing the so-called Land Contribution Ratio (LCR), which is, by definition, the portion of the footprint area covered by land. This index is then used for a double purpose: a) removing the excessively contaminated measurements; b) implementing a LCR-based NRCS correction scheme for the relatively low contaminated measurements. A second SRF estimate is obtained from a pre-computed Look-Up Table (LUT) of SRFs that are parameterized with respect to (w.r.t.) the orbit time, the latitude of the measurement centroid and the azimuth antenna angle. Finally, the useful measurements (including those LCR-based corrected) are averaged in order to obtain integrated measurements by beam or view, which are then input in the wind field retrieval processor. Two different averaging procedures, i.e., a box car and a noise-weighted averaging, are implemented A detailed comparison between the anaytical and the LUT-based SRF models is shown and the consistency of the derived LCR indices is verified against the coastline. A sensitivity analysis of the LCR-based NRCS correction scheme w.r.t. the LCR threshold is carried out. The effects of both averaging procedures on the retrieved winds are carefully analyzed. Finally, the retrieved winds are validated against some coastal buoys and their accuracy is assessed. Preliminary results will be presented and discussed at the conferencePeer reviewe

QuikSCAT radar cross section correction for improved coastal winds retrieval

International Ocean Vector Winds Science Team Meeting (IOVWST), 12 April - 3 May 2022- Development of pencil-beam scatterometer coastal wind processor - Development of a QuikSCAT coastal wind climatologyPeer reviewe

Towards SeaWinds-derived coastal winds improvement

Oceans form Space V Symposium, 24-28 october 2022, Venice, Italy.-- 2 pages, 2 figuresThis paper presents a new methodology to correct the land-contaminated normalized radar crosssection (σ0) measurements acquired by the scatterometer SeaWinds, which flew aboard the QuikSCAT satellite platform from 1999 to 2009, operated by the National Aeronautics and Space Administration (NASA). This method is based on the hypothesis that contaminated σ0s are linearly dependent on the Land Contribution Ratio (LCR) index, which is defined as the ratio of the footprint area contaminated by the presence of land to the total footprint area. Furthermore, the σ0 deviations from the expected contaminated σ0 values are “regularized” by homogenizing their distribution, making them independent of land contamination. The preliminary results show that this methodology is effective up to few kilometers to the coast. In addition, it prevents the presence of negative corrected σ0sThis work has been carried out in the context of the Visiting Scientist Activity ”Coastal PenWP”, (OSI VSA 21 03) issued by the Ocean Sea Ice Satellite Application Facilities (OSI-SAF) of the European Agency for the Exploitation of Meteorological Satellites (EUMETSAT)Peer reviewe

SeaWinds-derived winds in coastal areas

IEEE International Workshop on Metrology for the Sea; Learning to Measure Sea Health Parameters, 4-6 October 2023, La Valletta, Malta.-- 5 pages, 7 figures.-- © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper presents a new methodology to improve the sampling of coastal winds derived from the SeaWinds scatterometer, which flew onboard the polar orbiting satellite platform Quick Scatterometer (QuikSCAT) from 1999 until 2009. The coastal SeaWinds Normalized Radar Cross Sections (σ 0 s) are corrected for land contamination using the so-called "noise-regularization" procedure. The results show that this methodology is effective in filling the typical coastal scatterometer gap of ≈ 30 km. From a visual check on a coastal test area, the distribution of the newly derived winds seems to be consistent with that of the offshore winds. However, proper validation is needed. This is left for the futureThis work has been funded by the Ocean and Sea Ice Satellite Application Facility (OSI-SAF) of the European Agency for the Exploitation of the Meteorological Satellites (EUMETSAT) with the projects “Set-up of PenWP for SeaWinds-derived coastal winds” (OSI VSA 22 02) and “Coastal PenWP”, (OSI VSA 21 03)With the institutional support of the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000928-S)Peer reviewe

SAR and ASCAT Tropical Cyclone Wind Speed Reconciliation

Wind speed reconciliation across different wind sources is critically needed for extending available satellite wind records in Tropical Cyclones. The deviations between wind references of extremes, such as the moored buoy data and dropsonde wind estimates for guidance on geophysical model function development, are one of the main causes of wind speed differences for wind products, for instance, the overestimation of Synthetic Aperture Radars (SARs) relative to ASCAT winds. The study proposes a new wind speed adjustment to achieve mutual adjustment between ASCAT CMOD7 winds and simultaneous SAR wind speeds. The so-called CMOD7D-v2 adjustment is constructed based on the statistical analysis of SAR and ASCAT Tropical Cyclone acquisitions between 2016 and 2021, showing a satisfactory performance in wind speed reconciliation for winds with speeds higher than 14 m/s. Furthermore, the error characteristics of the CMOD7D-v2 adjustment for Tropical Cyclone winds are analyzed using the Triple Collocation analysis technique. The analysis results show that the proposed wind adjustment can reduce ASCAT wind errors by around 16.0% when adjusting ASCAT winds to SAR wind speeds. In particular, when downscaling SAR winds, the improvement in ASCAT wind errors can be up to 42.3%, effectively alleviating wind speed differences across wind sources. Furthermore, to avoid the impacts of large footprints by ASCAT sensors, wind speeds retrieved from SAR VV signals (acting as a substitute for ASCAT winds) are adjusted accordingly and compared against SAR dual-polarized winds and collocated Stepped Frequency Microwave Radiometer (SFMR) observations. We find that the bias values of adjusted winds are lower than products from other adjustment schemes by around 5 m/s at the most extreme values. These promising results verify the plausibility of the CMOD7D-v2 adjustment, which is conducive to SAR and ASCAT wind speed comparisons and extreme wind analysis in Tropical Cyclone cases