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- Author or Editor: RICHARD A. ANTHES x
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Estimating Error Variances of a Microwave Sensor and Dropsondes aboard the Global Hawk in Hurricanes Using the Three-Cornered Hat MethodAbstract
This study estimates the random error variances and standard deviations (STDs) for four datasets: Global Hawk (GH) dropsondes (DROP), the High-Altitude Monolithic Microwave Integrated Circuit Sounding Radiometer (HAMSR) aboard the GH, the fifth European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5), and the Hurricane Weather Research and Forecasting (HWRF) Model, using the three-cornered hat (3CH) method. These estimates are made during the 2016 Sensing Hazards with Operational Unmanned Technology (SHOUT) season in the environment of four tropical cyclones from August to October. For temperature and specific and relative humidity, the ERA5, HWRF, and DROP datasets all have similar magnitudes of errors, with ERA5 having the smallest. The error STDs of temperature and specific humidity are less than 0.8 K and 1.0 g kg−1 over most of the troposphere, while relative humidity error STDs increase from less than 5% near the surface to between 10% and 20% in the upper troposphere. The HAMSR bias-corrected data have larger errors, with estimated error STDs of temperature and specific humidity in the lower troposphere between 1.5 and 2.0 K and between 1.5 and 2.5 g kg−1. HAMSR’s relative humidity error STD increases from approximately 10% in the lower troposphere to 30% in the upper troposphere. The 3CH method error estimates are generally consistent with prior independent estimates of errors and uncertainties for the HAMSR and dropsonde datasets, although they are somewhat larger, likely due to the inclusion of representativeness errors (differences associated with different spatial and temporal scales represented by the data).
Abstract
This study estimates the random error variances and standard deviations (STDs) for four datasets: Global Hawk (GH) dropsondes (DROP), the High-Altitude Monolithic Microwave Integrated Circuit Sounding Radiometer (HAMSR) aboard the GH, the fifth European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5), and the Hurricane Weather Research and Forecasting (HWRF) Model, using the three-cornered hat (3CH) method. These estimates are made during the 2016 Sensing Hazards with Operational Unmanned Technology (SHOUT) season in the environment of four tropical cyclones from August to October. For temperature and specific and relative humidity, the ERA5, HWRF, and DROP datasets all have similar magnitudes of errors, with ERA5 having the smallest. The error STDs of temperature and specific humidity are less than 0.8 K and 1.0 g kg−1 over most of the troposphere, while relative humidity error STDs increase from less than 5% near the surface to between 10% and 20% in the upper troposphere. The HAMSR bias-corrected data have larger errors, with estimated error STDs of temperature and specific humidity in the lower troposphere between 1.5 and 2.0 K and between 1.5 and 2.5 g kg−1. HAMSR’s relative humidity error STD increases from approximately 10% in the lower troposphere to 30% in the upper troposphere. The 3CH method error estimates are generally consistent with prior independent estimates of errors and uncertainties for the HAMSR and dropsonde datasets, although they are somewhat larger, likely due to the inclusion of representativeness errors (differences associated with different spatial and temporal scales represented by the data).
Abstract
Observing systems simulation experiments were carried out to estimate the accuracy of temperatures diagnosed from the divergence equation when an army of nearly continuous (in time) wind observations is available. It was found that a useful estimate of temperature can be derived from high-resolution wind observations such as those obtainable from a network of wind profiling systems. Adding the divergence and vertical motion terms to the balance equation to form the complete divergence equation reduces the errors in derived temperatures and geopotential heights. Observations on an irregularly spaced grid lead to greater errors than those on a regularly spaced grid. Moderate errors are also introduced when large-scale errors in geopotential occur in the lateral boundary conditions. This suggests the need for some independent observations of temperature (from rawinsonde or temperature profiler) to prescribe the boundary conditions for the retrieval technique.
In a simulation of a possible operational system in which wind observations with random errors of 1 m s−1 are available on a 350 km grid and boundary values of geopotential height contain errors typical of a 12 h model forecast, the derived temperatures and heights on the interior of the grid contain root-mean-square errors of 1.55°C and 18.8 m, respectively.
Abstract
Observing systems simulation experiments were carried out to estimate the accuracy of temperatures diagnosed from the divergence equation when an army of nearly continuous (in time) wind observations is available. It was found that a useful estimate of temperature can be derived from high-resolution wind observations such as those obtainable from a network of wind profiling systems. Adding the divergence and vertical motion terms to the balance equation to form the complete divergence equation reduces the errors in derived temperatures and geopotential heights. Observations on an irregularly spaced grid lead to greater errors than those on a regularly spaced grid. Moderate errors are also introduced when large-scale errors in geopotential occur in the lateral boundary conditions. This suggests the need for some independent observations of temperature (from rawinsonde or temperature profiler) to prescribe the boundary conditions for the retrieval technique.
In a simulation of a possible operational system in which wind observations with random errors of 1 m s−1 are available on a 350 km grid and boundary values of geopotential height contain errors typical of a 12 h model forecast, the derived temperatures and heights on the interior of the grid contain root-mean-square errors of 1.55°C and 18.8 m, respectively.
The Three-Cornered Hat Method for Estimating Error Variances of Three or More Atmospheric Datasets. Part I: Overview and EvaluationAbstract
The three-cornered hat (3CH) method, which was originally developed to assess the random errors of atomic clocks, is a means for estimating the error variances of three different datasets. Here we give an overview of the historical development of the 3CH and select other methods for estimating error variances that use either two or three datasets. We discuss similarities and differences between these methods and the 3CH method. This study assesses the sensitivity of the 3CH method to the factors that limit its accuracy, including sample size, outliers, different magnitudes of errors between the datasets, biases, and unknown error correlations. Using simulated datasets for which the errors and their correlations among the datasets are known, this analysis shows the conditions under which the 3CH method provides the most and least accurate estimates. The effect of representativeness errors caused by differences in vertical resolution of datasets is investigated. These representativeness errors are generally small relative to the magnitude of the random errors in the datasets, and the impact of this source of errors can be reduced by appropriate filtering.
Abstract
The three-cornered hat (3CH) method, which was originally developed to assess the random errors of atomic clocks, is a means for estimating the error variances of three different datasets. Here we give an overview of the historical development of the 3CH and select other methods for estimating error variances that use either two or three datasets. We discuss similarities and differences between these methods and the 3CH method. This study assesses the sensitivity of the 3CH method to the factors that limit its accuracy, including sample size, outliers, different magnitudes of errors between the datasets, biases, and unknown error correlations. Using simulated datasets for which the errors and their correlations among the datasets are known, this analysis shows the conditions under which the 3CH method provides the most and least accurate estimates. The effect of representativeness errors caused by differences in vertical resolution of datasets is investigated. These representativeness errors are generally small relative to the magnitude of the random errors in the datasets, and the impact of this source of errors can be reduced by appropriate filtering.
Ducting and Biases of GPS Radio Occultation Bending Angle and Refractivity in the Moist Lower TroposphereAbstract
Radio occultation (RO) can provide high-vertical-resolution thermodynamic soundings of the planetary boundary layer (PBL). However, sharp moisture gradients and strong temperature inversion lead to large gradients in refractivity N and often cause ducting. Ducting results in systematically negative RO N biases resulting from a nonunique Abel inversion problem. Using 8 years (2006–13) of Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) RO soundings and collocated European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-I) data, we confirm that the large lower-tropospheric negative N biases are mainly located in the subtropical eastern oceans and we quantify the contribution of ducting for the first time. The ducting-contributed N biases in the northeast Pacific Ocean (160°–110°W; 15°–45°N) are isolated from other sources of N biases using a two-step geometric-optics simulation. Negative bending angle biases in this region are also observed in COSMIC RO soundings. Both the negative refractivity and bending angle biases in COSMIC soundings mainly lie below ~2 km. Such bending angle biases introduce N biases that are in addition to those caused by ducting. Following the increasing PBL height from the southern California coast westward to Hawaii, centers of maxima bending angles and N biases tilt southwestward. In areas where ducting conditions prevail, ducting is the major cause of the RO N biases. Ducting-induced N biases with reference to ERA-I compose over 70% of the total negative N biases near the southern California coast, where strongest ducting conditions prevail, and decrease southwestward to less than 20% near Hawaii.
Abstract
Radio occultation (RO) can provide high-vertical-resolution thermodynamic soundings of the planetary boundary layer (PBL). However, sharp moisture gradients and strong temperature inversion lead to large gradients in refractivity N and often cause ducting. Ducting results in systematically negative RO N biases resulting from a nonunique Abel inversion problem. Using 8 years (2006–13) of Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) RO soundings and collocated European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-I) data, we confirm that the large lower-tropospheric negative N biases are mainly located in the subtropical eastern oceans and we quantify the contribution of ducting for the first time. The ducting-contributed N biases in the northeast Pacific Ocean (160°–110°W; 15°–45°N) are isolated from other sources of N biases using a two-step geometric-optics simulation. Negative bending angle biases in this region are also observed in COSMIC RO soundings. Both the negative refractivity and bending angle biases in COSMIC soundings mainly lie below ~2 km. Such bending angle biases introduce N biases that are in addition to those caused by ducting. Following the increasing PBL height from the southern California coast westward to Hawaii, centers of maxima bending angles and N biases tilt southwestward. In areas where ducting conditions prevail, ducting is the major cause of the RO N biases. Ducting-induced N biases with reference to ERA-I compose over 70% of the total negative N biases near the southern California coast, where strongest ducting conditions prevail, and decrease southwestward to less than 20% near Hawaii.
The Three-Cornered Hat Method for Estimating Error Variances of Three or More Atmospheric Datasets. Part II: Evaluating Radio Occultation and Radiosonde Observations, Global Model Forecasts, and ReanalysesAbstract
We apply the three-cornered hat (3CH) method to estimate refractivity, bending angle, and specific humidity error variances for a number of datasets widely used in research and/or operations: radiosondes, radio occultation (COSMIC, COSMIC-2), NCEP global forecasts, and nine reanalyses. We use a large number and combinations of datasets to obtain insights into the impact of the error correlations among different datasets that affect 3CH estimates. Error correlations may be caused by actual correlations of errors, representativeness differences, or imperfect collocation of the datasets. We show that the 3CH method discriminates among the datasets and how error statistics of observations compare to state-of-the-art reanalyses and forecasts, as well as reanalyses that do not assimilate satellite data. We explore results for October and November 2006 and 2019 over different latitudinal regions and show error growth of the NCEP forecasts with time. Because of the importance of tropospheric water vapor to weather and climate, we compare error estimates of refractivity for dry and moist atmospheric conditions.
Abstract
We apply the three-cornered hat (3CH) method to estimate refractivity, bending angle, and specific humidity error variances for a number of datasets widely used in research and/or operations: radiosondes, radio occultation (COSMIC, COSMIC-2), NCEP global forecasts, and nine reanalyses. We use a large number and combinations of datasets to obtain insights into the impact of the error correlations among different datasets that affect 3CH estimates. Error correlations may be caused by actual correlations of errors, representativeness differences, or imperfect collocation of the datasets. We show that the 3CH method discriminates among the datasets and how error statistics of observations compare to state-of-the-art reanalyses and forecasts, as well as reanalyses that do not assimilate satellite data. We explore results for October and November 2006 and 2019 over different latitudinal regions and show error growth of the NCEP forecasts with time. Because of the importance of tropospheric water vapor to weather and climate, we compare error estimates of refractivity for dry and moist atmospheric conditions.
