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Noureddine Semane, Richard Anthes, Jeremiah Sjoberg, Sean Healy, and Benjamin Ruston

Abstract

We compare two seemingly different methods of estimating random error statistics (uncertainties) of observations, the three-cornered hat (3CH) method and Desroziers method, and show several examples of estimated uncertainties of COSMIC-2 (C2) radio occultation (RO) observations. The two methods yield similar results, attesting to the validity of both. The small differences provide insight into the sensitivity of the methods to the assumptions and computational details. These estimates of RO error statistics differ considerably from several RO error models used by operational weather forecast centers, suggesting that the impact of RO observations on forecasts can be improved by adjusting the RO error models to agree more closely with the RO error statistics. Both methods show RO uncertainty estimates that vary with latitude. In the troposphere, uncertainties are higher in the tropics than in the subtropics and middle latitudes. In the upper stratosphere–lower mesosphere, we find the reverse, with tropical uncertainties slightly less than in the subtropics and higher latitudes. The uncertainty estimates from the two techniques also show similar variations between a 31-day period during Northern Hemisphere tropical cyclone season (16 August–15 September 2020) and a month near the vernal equinox (April 2021). Finally, we find a relationship between the vertical variation of the C2 estimated uncertainties and atmospheric variability, as measured by the standard deviation of the C2 sample. The convergence of the error estimates and the standard deviations above 40 km indicates a lessening impact of assimilating RO above this level.

Significance Statement

Uncertainties of observations are of general interest and their knowledge is important for assimilation in numerical weather prediction models. This paper compares two methods of estimating these uncertainties and shows that they give nearly identical results under certain conditions. The estimation of the COSMIC-2 bending angle uncertainties and how they compare to the assumed bending angle error models in several operational weather centers suggests that there is an opportunity for obtaining improved impact of RO observations in numerical model forecasts. Finally, the relationship between the COSMIC-2 bending angle errors and atmospheric variability provides insight into the sources of RO observational uncertainties.

Open access
Zhijin Qiu, Tong Hu, Bo Wang, Jing Zou, and Zhiqian Li

Abstract

The evaporation duct is an abnormal refractive phenomenon with wide distribution and frequency occurrence at the boundary between the atmosphere and the ocean, which directly affects electromagnetic wave propagation. In recent years, the use of meteorological and hydrological data to predict the evaporation duct height has become an emerging and promising approach. There are some evaporation duct models that have been proposed based on the Monin–Obukhov similarity theory. However, each model adopts different stability functions and roughness length parameterization methods, so the prediction accuracies are different under different environmental conditions. To improve the prediction accuracy of the evaporation duct under different environmental conditions, a model selection optimization method (MSOM) of the evaporation duct model is proposed based on sensitivity analysis. According to the sensitivity of each model to input parameters analyzed by the sensor observation accuracy, curve graph, and Sobol sensitivity, the model input parameters are divided into several intervals. Then the optimization model is selected in different intervals. The model was established using numerical simulation data from local areas in the South China Sea, and its accuracy was verified by the observational data from the offshore observation platform located in the South China Sea. The results show that the MSOM can effectively improve the prediction accuracy of the evaporation duct height. Under unstable conditions, the maximum relative error is reduced by 7.1%, and under stable conditions, the relative error is reduced by 10.7%.

Significance Statement

The evaporation duct height has a significant effect on marine radar or wireless apparatus applications. To obtain the evaporation duct height, there are some evaporation duct models that have been proposed. However, different evaporation duct models are applicable to different meteorological and hydrological environments. A single model cannot achieve accurate evaporation duct height predictions in all environments. We propose a model selection optimization method of the evaporation duct model based on sensitivity analysis. This method can dynamically select the optimal model according to different meteorological and hydrological environment, and improve the prediction accuracy of the evaporation duct height. Under unstable conditions, the maximum relative error is reduced by 7.1%, and under stable conditions, the relative error is reduced by 10.7%.

Open access
Beth Reid and Tom Swanson

Abstract

Loon LLC collected 794 000 h of corona current observations between 15 and ∼20 km above sea level with time resolution between 1 and 30 min. We are publicly releasing this dataset to enable the research community’s understanding of electrical activity in the stratosphere. We validate the reliability of these measurements by aligning our flight data with both nearby Geostationary Lightning Mapper (GLM) events and the Convective Diagnostic Oceanic (CDO) indicator. Corona current observations that exceeded the sensor maximum of 10 μA were associated with high GLM optical flux accumulations along the flight trajectory. Using the CDO indicator as a persistence forecast for future electrical activity was effective at predicting corona current events, and so we highly recommend this data source for real-time stratospheric navigation for vehicles sensitive to the harsh electrical environment of the stratosphere.

Significance Statement

Loon LLC operated a fleet of balloons in the stratosphere, between 15 and 20 km above sea level. The balloons were instrumented with a sensor that measured the current flowing through a wire dangling from the flight vehicle. The observed currents were caused by the motion of nearby charged particles that are often associated with thunderstorms and lightning activity. In this paper we show that Loon’s sensor registered current at the same time lightning was recorded near the balloon by other instruments like the Geostationary Lightning Mapper satellite. This is the first dataset of its kind and size, reaching 794 000 flight hours. We are publicly releasing these data in hopes of aiding scientific discovery by researchers and to help future stratospheric vehicle operators better understand and plan for the electrical environment.

Open access
C. O. Collins III and R. E. Jensen

Abstract

We identify and characterize an error in the National Data Buoy Center (NDBC) wave records due to the sustained tilt of a buoy under high winds. We use a standard, operational 3-m aluminum discus buoy from NDBC with two wave systems, one gimballed, and the other strapped down but uncorrected. By comparing the two, we find that the most extreme significant wave heights are systematically overestimated. The overestimation is shown to be confined to a region around the peak frequency in the spectra: 0.05–0.15 Hz. Wave direction and directional spread are unaffected. A bias due to tilt error can be observed starting at winds of 10 m s−1 or wave heights of 4 m. The bias increases as a function of wind speed and wave height, i.e., the bias is +10% when winds are 20 m s−1. Very high waves and winds are relatively rare, so while the tilt error does not affect overall statistics and basic analyses it could potentially affect analysis sensitive to the extremes. A correction is derived for significant wave height, which is a quadratic function of wind speed. The correction is shown to reduce wave heights in uncorrected records, but is found inadequate for general use. There is evidence of tilt error at other NDBC stations, but the full extent of prevalence in the record is not known at this time.

Open access
Dudley B. Chelton, Roger M. Samelson, and J. Thomas Farrar

Abstract

The Ka-band Radar Interferometer on the Surface Water and Ocean Topography (SWOT) satellite will revolutionize satellite altimetry by measuring sea surface height (SSH) with unprecedented accuracy and resolution across two 50-km swaths separated by a 20-km gap. The original plan to provide an SSH product with a footprint diameter of 1 km has changed to providing two SSH data products with footprint diameters of 0.5 km and 2 km. The swathaveraged standard deviations and wavenumber spectra of the uncorrelated measurement errors for these footprints are derived from the SWOT science requirements that are expressed in terms of the wavenumber spectrum of SSH after smoothing with a filter cutoff wavelength of 15 km. The availability of 2-dimensional fields of SSH within the measurement swaths will provide the first spaceborne estimates of instantaneous surface velocity and vorticity through the geostrophic equations. The swath-averaged standard deviations of the noise in estimates of velocity and vorticity derived by propagation of the uncorrelated SSH measurement noise through the finite difference approximations of the derivatives are shown to be too large for the SWOT data products to be used directly in most applications, even with the footprint diameter of 2 km. It is shown from wavenumber spectra and maps constructed from simulated SWOT data that additional smoothing will be required for most applications of SWOT estimates of velocity and vorticity. Equations are presented for the swath-averaged standard deviations and wavenumber spectra of residual noise in SSH and geostrophically computed velocity and vorticity after isotropic 2-dimensional smoothing for any user-defined filter cutoff wavelength of the smoothing.

Open access
Rolf G. Lueck

Abstract

This manuscript provides (i) the statistical uncertainty of a shear spectrum and (ii) a new universal shear spectrum, and (iii) shows how these are combined to quantify the quality of a shear spectrum. The data from four co-located shear probes, described in Part 1 (Lueck 2022) are used to estimate the spectra of shear, Ψ(k), for wavenumbers k ≥ 2 cpm, from data lengths of 1.0 to 50.5 m, using Fourier transform (FT) segments of 0.5 m length. The differences of the logarithm of pairs of simultaneous shear spectra are stationary, distributed normally, independent of the rate of dissipation, and only weakly dependent on wavenumber. The variance of the logarithm of an individual spectrum, σ 2 lnΨ, equals one-half of the variance of these differences and is σ 2 lnΨ = 1.25N −7/9 ƒ, where is the number of FT segments used to estimate the spectrum. σlnΨ provides the statistical basis for constructing the confidence interval of the logarithm of spectrum, and thus, the spectrum itself.

A universal spectrum of turbulence shear is derived from the nondimensionalization of 14600 spectra estimated from 5 m segments of data. This spectrum differs from the Nasmyth spectrum (Oakey 1982) and from the spectrum of Panchev and Kesich (1969) by 8% near its peak, and is approximated to within 1% by a new analytic equation.

The difference between the logarithms of a measured and a universal spectrum, together with the confidence interval of a spectrum, provides the statistical basis for quantifying the quality of a measured shear (and velocity) spectrum, and the quality of a dissipation estimate that is derived from the spectrum.

Open access
T. Tanaka, D. Hasegawa, T. Okunishi, I. Yasuda, and T. P. Welch

Abstract

The angle of attack (AOA) is the difference between the underwater glider’s path and pitch angle and is necessary to accurately estimate dead-reckoned position and depth-averaged velocity. The AOA is also important for any sensor measurements that are affected by the glider’s velocity through water, such as ocean turbulence measurement. A glider flight model is generally used to accurately estimate AOA and glider’s actual velocity based on the knowledge of lift and drag coefficients optimized for each glider. This paper examines the AOA of a Slocum glider using an acoustic Doppler current profiler (ADCP) to demonstrate a regression method to estimate these coefficients. Since the current shear was sufficiently small on average, it was reasonable to assume that the ADCP velocity at the nearest bin could capture the glider’s motion during flight and was used to calculate AOA. The lift and drag coefficients were optimized so the flight model estimated the observed pitch – AOA relationship derived from the ADCP and the glider’s pitch observations. The resultant coefficients also satisfied the vertical and horizontal constraints of glider motion and gave unbiased estimates of turbulence intensity derived from the flight model and ADCP. Our method was also applied to a SeaExplorer glider to derive the lift and drag coefficients for the first time. The observed pitch – AOA relationship was reasonably captured by the flight model with the resultant coefficients, suggesting that our method to estimate the lift and drag coefficient of underwater gliders can be applied to any type of underwater glider equipped with an ADCP.

Open access
Shinta Seto, Toshio Iguchi, and Robert Meneghini

Abstract

Spaceborne precipitation radars, including the Tropical Rainfall Measuring Mission’s Precipitation Radar (PR) and the Global Precipitation Measurement Mission’s Dual-Frequency Precipitation Radar (DPR), measure not only precipitation echoes but surface echoes as well, the latter of which are used to estimate the path-integrated attenuation (PIA) in the surface reference technique (SRT). In our previous study based on analyzing PR measurements, we found that attenuation-free surface backscattering cross sections (denoted by σe0) over land increased in the presence of precipitation. This behavior, called the soil moisture effect, causes an underestimate of the PIA by the SRT as the method does not explicitly consider this effect. In this study, measurements made by Ku-band Precipitation Radar (KuPR) and Ka-band Precipitation Radar (KaPR), which comprise the DPR, were analyzed to examine whether KuPR and KaPR exhibit similar dependencies on the soil moisture as does the PR. For both KuPR and KaPR, an increase in σe0 was observed for a large portion of the land area, except for forests and deserts. Results from the Hitschfeld–Bordan (HB) method suggest that σe0 increases with the surface precipitation rate for light precipitation events. Meanwhile, for heavy precipitation, owing to the degradation of the HB method, it is difficult to estimate σe0 quantitatively. Thus, a correction method for PIA that considers the soil moisture effect was developed and implemented into the DPR standard algorithm. With this correction, the surface precipitation rate estimates increased by approximately 18% for KuPR and 15% for the normal scan of KaPR over land.

Open access
Free access
Candice Hall, Robert E. Jensen, and David W. Wang

Abstract

The importance of quantifying the accuracy in wave measurements is critical to not only understand the complexities of wind-generated waves, but imperative for the interpretation of implied accuracy of the prediction systems that use these data for verification and validation. As wave measurement systems have unique collection and processing attributes that result in large accuracy ranges, this work quantifies bias that may be introduced into wave models from the newly operational NOAA National Data Buoy Center (NDBC) 2.1-m hull. Data quality consistency between the legacy NDBC 3-m aluminum hulls and the new 2.1-m hull is compared to a relative reference, and provides a standardized methodology and graphical representation template for future intrameasurement evaluations. Statistical analyses and wave spectral comparisons confirm that the wave measurements reported from the NDBC 2.1-m hulls show an increased accuracy from previously collected NDBC 3-m hull wave data for significant wave height and average wave period, while retaining consistent accuracy for directional results, purporting that hull size does not impact NDBC directional data estimates. Spectrally, the NDBC 2.1-m hulls show an improved signal-to-noise ratio, allowing for increase in energy retention in the lower-frequency spectral range, with an improved high-frequency spectral accuracy above 0.25 Hz within the short seas and wind chop wave component regions. These improvements in both NDBC bulk and spectral data accuracy provide confidence for the wave community’s use of NDBC wave data to drive wave model technologies, improvements, and validations.

Open access