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## Abstract

Random errors (uncertainties) in COSMIC radio occultation (RO) soundings, ERA-Interim (ERAi) reanalyses, and high-resolution radiosondes (RS) are estimated in the northeast Pacific Ocean during the MAGIC campaign in 2012 and 2013 using the three-cornered hat method. Estimated refractivity and bending angle errors peak at ∼2 km, and have a secondary peak at ∼15 km. They are related to vertical and horizontal gradients of temperature and water vapor and associated atmospheric variability at these two levels. MAGIC RS refractivity and bending angles obtained from forward models have the largest uncertainties, followed by COSMIC RO soundings. ERAi has the smallest uncertainties. The large RS uncertainties can be primarily attributed to representativeness errors (differences). Differences in space and time of the RO and model datasets from the RS observations, error correlations among datasets, and the small sample size are other possible reasons contributing to these differences of estimated error statistics. RO temperature and humidity are retrieved from refractivity using a one-dimensional variational (1D-Var) method from the COSMIC Data Analysis and Archive Center (CDAAC). The estimated errors for COSMIC temperature are comparable to those of the MAGIC RS except near 1 km, where they are much higher. The estimated errors for COSMIC specific humidity are similar to the MAGIC specific humidity errors below ∼5 km and much smaller above this level. Estimates of COSMIC random errors based on ERAi, JRA-55, and MERRA-2 reanalyses in the same region, as well as comparison with estimates from other studies, support the reliability of our estimates.

## Abstract

Random errors (uncertainties) in COSMIC radio occultation (RO) soundings, ERA-Interim (ERAi) reanalyses, and high-resolution radiosondes (RS) are estimated in the northeast Pacific Ocean during the MAGIC campaign in 2012 and 2013 using the three-cornered hat method. Estimated refractivity and bending angle errors peak at ∼2 km, and have a secondary peak at ∼15 km. They are related to vertical and horizontal gradients of temperature and water vapor and associated atmospheric variability at these two levels. MAGIC RS refractivity and bending angles obtained from forward models have the largest uncertainties, followed by COSMIC RO soundings. ERAi has the smallest uncertainties. The large RS uncertainties can be primarily attributed to representativeness errors (differences). Differences in space and time of the RO and model datasets from the RS observations, error correlations among datasets, and the small sample size are other possible reasons contributing to these differences of estimated error statistics. RO temperature and humidity are retrieved from refractivity using a one-dimensional variational (1D-Var) method from the COSMIC Data Analysis and Archive Center (CDAAC). The estimated errors for COSMIC temperature are comparable to those of the MAGIC RS except near 1 km, where they are much higher. The estimated errors for COSMIC specific humidity are similar to the MAGIC specific humidity errors below ∼5 km and much smaller above this level. Estimates of COSMIC random errors based on ERAi, JRA-55, and MERRA-2 reanalyses in the same region, as well as comparison with estimates from other studies, support the reliability of our estimates.

## Abstract

The dual-frequency ratio of radar reflectivity factors (DFR) has been shown to be a useful quantity as it is independent of the number concentration of the particle size distribution and primarily a function of the mass-weighted particle diameter *D _{m}
*. A drawback of DFR-related methods for rain estimation, however, is the nonunique relationship between

*D*and DFR. At Ku- and Ka-band frequencies, two solutions for

_{m}*D*exist when DFR is less than zero. This ambiguity generates multiple solutions for the range profiles of the particle size parameters. We investigate characteristics of these solutions for both the initial-value (forward) and final-value (backward) forms of the equations. To choose one among many possible range profiles of

_{m}*D*, number concentration, and rain rate

_{m}*R*, independently measured path attenuations are used. For the backward approach, the possibility exists of dispensing with externally measured path attenuations by achieving consistency between the input and output path attenuations. The methods are tested by means of a simulation based on disdrometer-measured raindrop size distributions and the results are compared with a simplified version of the operational

*R*–

*D*method.

_{m}## Abstract

The dual-frequency ratio of radar reflectivity factors (DFR) has been shown to be a useful quantity as it is independent of the number concentration of the particle size distribution and primarily a function of the mass-weighted particle diameter *D _{m}
*. A drawback of DFR-related methods for rain estimation, however, is the nonunique relationship between

*D*and DFR. At Ku- and Ka-band frequencies, two solutions for

_{m}*D*exist when DFR is less than zero. This ambiguity generates multiple solutions for the range profiles of the particle size parameters. We investigate characteristics of these solutions for both the initial-value (forward) and final-value (backward) forms of the equations. To choose one among many possible range profiles of

_{m}*D*, number concentration, and rain rate

_{m}*R*, independently measured path attenuations are used. For the backward approach, the possibility exists of dispensing with externally measured path attenuations by achieving consistency between the input and output path attenuations. The methods are tested by means of a simulation based on disdrometer-measured raindrop size distributions and the results are compared with a simplified version of the operational

*R*–

*D*method.

_{m}## Abstract

This study develops a new thin cirrus detection algorithm applicable to overland scenes. The methodology builds from a previously developed overwater algorithm, which makes use of the *Geostationary Operational Environmental Satellite 16* (*GOES-16*) Advanced Baseline Imager (ABI) channel 4 radiance (1.378-*μ*m “cirrus” band). Calibration of this algorithm is based on coincident Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) cloud profiles. Emphasis is placed on rejection of false detections that are more common in overland scenes. Clear-sky false alarm rates over land are examined as a function of precipitable water vapor (PWV), showing that nearly all pixels having a PWV of <0.4 cm produce false alarms. Enforcing an above-cloud PWV minimum threshold of ∼1 cm ensures that most low-/midlevel clouds are not misclassified as cirrus by the algorithm. Pixel-filtering based on the total column PWV and the PWV for a layer between the top of the atmosphere (TOA) and a predetermined altitude *H* removes significant land surface and low-/midlevel cloud false alarms from the overall sample while preserving over 80% of valid cirrus pixels. Additionally, the use of an aggressive PWV layer threshold preferentially removes noncirrus pixels such that the remaining sample is composed of nearly 70% cirrus pixels, at the cost of a much-reduced overall sample size. This study shows that lower-tropospheric clouds are a much more significant source of uncertainty in cirrus detection than the land surface.

## Abstract

This study develops a new thin cirrus detection algorithm applicable to overland scenes. The methodology builds from a previously developed overwater algorithm, which makes use of the *Geostationary Operational Environmental Satellite 16* (*GOES-16*) Advanced Baseline Imager (ABI) channel 4 radiance (1.378-*μ*m “cirrus” band). Calibration of this algorithm is based on coincident Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) cloud profiles. Emphasis is placed on rejection of false detections that are more common in overland scenes. Clear-sky false alarm rates over land are examined as a function of precipitable water vapor (PWV), showing that nearly all pixels having a PWV of <0.4 cm produce false alarms. Enforcing an above-cloud PWV minimum threshold of ∼1 cm ensures that most low-/midlevel clouds are not misclassified as cirrus by the algorithm. Pixel-filtering based on the total column PWV and the PWV for a layer between the top of the atmosphere (TOA) and a predetermined altitude *H* removes significant land surface and low-/midlevel cloud false alarms from the overall sample while preserving over 80% of valid cirrus pixels. Additionally, the use of an aggressive PWV layer threshold preferentially removes noncirrus pixels such that the remaining sample is composed of nearly 70% cirrus pixels, at the cost of a much-reduced overall sample size. This study shows that lower-tropospheric clouds are a much more significant source of uncertainty in cirrus detection than the land surface.

## Abstract

Observing thermodynamic profiles within the planetary boundary layer is essential to understanding and predicting atmospheric phenomena because of the significant exchange of sensible and latent heat between the land and atmosphere within that layer. The Atmospheric Emitted Radiance Interferometer (AERI) is a ground-based infrared spectrometer used to obtain the vertical profiles of temperature and water vapor mixing ratio. Most AERIs are only capable of zenith views, although the Marine AERI (M-AERI) has a design that allows it to view various elevation angles. In this study, we quantify the improvement in the information content and accuracy of the retrieved profiles when nonzenith angles are included, as is common with microwave radiometer profilers. The impacts of the additional scan angles are quantified through both a synthetic study and with M-AERI observations from the ARM Cloud Aerosol Precipitation Experiment (ACAPEX) campaign. The simulation study shows that low elevation angles contain more information content for temperature whereas high elevation angles have more information content for water vapor. Outside of very humid environments, the addition of low elevation angles also results in lower root-mean-square errors when compared with high angles for both temperature and water vapor mixing ratio, although this is primarily a result of averaging multiple observations together to reduce instrument noise. Real-world results from the ACAPEX dataset indicate similar results as were found for the simulation study, although not all predicted benefits are realized because of the small sample size and observational uncertainties.

## Abstract

Observing thermodynamic profiles within the planetary boundary layer is essential to understanding and predicting atmospheric phenomena because of the significant exchange of sensible and latent heat between the land and atmosphere within that layer. The Atmospheric Emitted Radiance Interferometer (AERI) is a ground-based infrared spectrometer used to obtain the vertical profiles of temperature and water vapor mixing ratio. Most AERIs are only capable of zenith views, although the Marine AERI (M-AERI) has a design that allows it to view various elevation angles. In this study, we quantify the improvement in the information content and accuracy of the retrieved profiles when nonzenith angles are included, as is common with microwave radiometer profilers. The impacts of the additional scan angles are quantified through both a synthetic study and with M-AERI observations from the ARM Cloud Aerosol Precipitation Experiment (ACAPEX) campaign. The simulation study shows that low elevation angles contain more information content for temperature whereas high elevation angles have more information content for water vapor. Outside of very humid environments, the addition of low elevation angles also results in lower root-mean-square errors when compared with high angles for both temperature and water vapor mixing ratio, although this is primarily a result of averaging multiple observations together to reduce instrument noise. Real-world results from the ACAPEX dataset indicate similar results as were found for the simulation study, although not all predicted benefits are realized because of the small sample size and observational uncertainties.

## Abstract

Historical in situ ocean temperature profile measurements are important for a wide range of ocean and climate research activities. A large proportion of the profile observations have been recorded using expendable bathythermographs (XBTs), and required bias corrections for use in climate change studies. It is generally accepted that the bias, and therefore bias correction, depends on the type of XBT used. However, poor historical metadata collection practices mean the XBT probe type information is often missing, for 59% of profiles between 1967 and 2000, limiting the development of reliable bias corrections. We develop a process of estimating missing instrument type metadata (the combination of both model and manufacturer) systematically, constructing a machine learning pipeline based on thorough data exploration to inform these choices. The predicted instrument type, where missing, will facilitate improved XBT bias corrections. The new approach improves the accuracy of the XBT type classification compared to previous approaches from a recall value of 0.75–0.94. We also develop an approach to account for the uncertainty associated with metadata assignments using ensembles of decision trees, which could feed into an ensemble approach to creating ocean temperature datasets. We describe the challenges arising from the nature of the dataset in applying standard machine learning techniques to the problem. We have implemented this in a portable, reproducible way using standard data science tools, with a view to these techniques being applied to other similar problems in climate science.

## Abstract

Historical in situ ocean temperature profile measurements are important for a wide range of ocean and climate research activities. A large proportion of the profile observations have been recorded using expendable bathythermographs (XBTs), and required bias corrections for use in climate change studies. It is generally accepted that the bias, and therefore bias correction, depends on the type of XBT used. However, poor historical metadata collection practices mean the XBT probe type information is often missing, for 59% of profiles between 1967 and 2000, limiting the development of reliable bias corrections. We develop a process of estimating missing instrument type metadata (the combination of both model and manufacturer) systematically, constructing a machine learning pipeline based on thorough data exploration to inform these choices. The predicted instrument type, where missing, will facilitate improved XBT bias corrections. The new approach improves the accuracy of the XBT type classification compared to previous approaches from a recall value of 0.75–0.94. We also develop an approach to account for the uncertainty associated with metadata assignments using ensembles of decision trees, which could feed into an ensemble approach to creating ocean temperature datasets. We describe the challenges arising from the nature of the dataset in applying standard machine learning techniques to the problem. We have implemented this in a portable, reproducible way using standard data science tools, with a view to these techniques being applied to other similar problems in climate science.

## 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.

## 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.

## Abstract

Marine heatwaves (MHWs) exert devastating impacts on ecosystems. Understanding their responses to anthropogenic forcing has attracted rapidly growing scientific interest. Given the disparate adaptation capacity and mobility among marine species, it is crucial to disentangle changes of MHWs related to the rising mean temperature from those to the changing temperature variability. It has been suggested that the latter’s effects could be isolated by replacing a fixed baseline with a moving one for calculating the climatological mean and percentile metrics in MHW analysis. In this study, the effects of a moving baseline on MHW statistics (annual MHW days and cumulative intensity) changes in a warming climate are systematically evaluated based on simulations from simple stochastic climate models and a set of coupled general circulation models in the Community Earth System Model Large Ensemble project. On the one hand, a moving baseline does not necessarily remove the influences of rising mean temperature on MHW changes and will artificially cause negative trends in MHW statistics when the ocean exhibits an accelerated warming rate as in the RCP8.5 scenario. On the other hand, it always underestimates the effects of changing temperature variability on MHW changes. We propose a new model that adopts a “partial” moving baseline combined with a local linear detrending to isolate MHW changes caused by changing temperature variability.

### Significance Statement

A new model is proposed to isolate marine heatwave changes caused by changing temperature variability from those by rising mean temperature under greenhouse warming.

## Abstract

Marine heatwaves (MHWs) exert devastating impacts on ecosystems. Understanding their responses to anthropogenic forcing has attracted rapidly growing scientific interest. Given the disparate adaptation capacity and mobility among marine species, it is crucial to disentangle changes of MHWs related to the rising mean temperature from those to the changing temperature variability. It has been suggested that the latter’s effects could be isolated by replacing a fixed baseline with a moving one for calculating the climatological mean and percentile metrics in MHW analysis. In this study, the effects of a moving baseline on MHW statistics (annual MHW days and cumulative intensity) changes in a warming climate are systematically evaluated based on simulations from simple stochastic climate models and a set of coupled general circulation models in the Community Earth System Model Large Ensemble project. On the one hand, a moving baseline does not necessarily remove the influences of rising mean temperature on MHW changes and will artificially cause negative trends in MHW statistics when the ocean exhibits an accelerated warming rate as in the RCP8.5 scenario. On the other hand, it always underestimates the effects of changing temperature variability on MHW changes. We propose a new model that adopts a “partial” moving baseline combined with a local linear detrending to isolate MHW changes caused by changing temperature variability.

### Significance Statement

A new model is proposed to isolate marine heatwave changes caused by changing temperature variability from those by rising mean temperature under greenhouse warming.

## Abstract

An empirically derived statistic is used to estimate the confidence interval of a dissipation estimate that uses a finite amount of shear data. Four collocated shear probes, mounted on a bottom anchored float, are used to measure the rate of dissipation of turbulence kinetic energy *ϵ* at a height of 15 m above the bottom in a 55 m deep tidal channel. One pair of probes measures ∂*w*/∂*x* while the other measures ∂*υ*/∂*x*, where *w* and *υ* are the vertical and lateral velocity. The shear-probe signals are converted into a regularly resampled space series to permit the rate of dissipation to be estimated directly from the variance of the shear using *υ* component), for averaging lengths, *L* ranging from 1 to 10^{4} Kolmogorov lengths. While the rate of dissipation fluctuates by more than a factor of 100, the fluctuations of the differences of *L* = ∼30 to 10^{4} Kolmogorov lengths. The variance of the differences, *L*
^{−7/9}, independent of stratification for buoyancy Reynolds numbers larger than ∼600, and for dissipation rates from ∼10^{−10} to ∼10^{−5} W kg^{−1}. The variance decreases more slowly than *L*
^{−1} because the averaging is done in linear space while the variance is evaluated in logarithmic space. This statistic provides the confidence interval of an *ϵ* estimate such as the 95% interval *ϵ* estimates that are made by way of spectral integration, after *L* is adjusted for the truncation of the shear spectrum.

### Significance Statement

The results reported here can be used to estimate the statistical uncertainty of a dissipation estimate that is derived from a finite length of turbulence shear data.

## Abstract

An empirically derived statistic is used to estimate the confidence interval of a dissipation estimate that uses a finite amount of shear data. Four collocated shear probes, mounted on a bottom anchored float, are used to measure the rate of dissipation of turbulence kinetic energy *ϵ* at a height of 15 m above the bottom in a 55 m deep tidal channel. One pair of probes measures ∂*w*/∂*x* while the other measures ∂*υ*/∂*x*, where *w* and *υ* are the vertical and lateral velocity. The shear-probe signals are converted into a regularly resampled space series to permit the rate of dissipation to be estimated directly from the variance of the shear using *υ* component), for averaging lengths, *L* ranging from 1 to 10^{4} Kolmogorov lengths. While the rate of dissipation fluctuates by more than a factor of 100, the fluctuations of the differences of *L* = ∼30 to 10^{4} Kolmogorov lengths. The variance of the differences, *L*
^{−7/9}, independent of stratification for buoyancy Reynolds numbers larger than ∼600, and for dissipation rates from ∼10^{−10} to ∼10^{−5} W kg^{−1}. The variance decreases more slowly than *L*
^{−1} because the averaging is done in linear space while the variance is evaluated in logarithmic space. This statistic provides the confidence interval of an *ϵ* estimate such as the 95% interval *ϵ* estimates that are made by way of spectral integration, after *L* is adjusted for the truncation of the shear spectrum.

### Significance Statement

The results reported here can be used to estimate the statistical uncertainty of a dissipation estimate that is derived from a finite length of turbulence shear data.

## 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 collocated shear probes, described in Part I, 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, *N _{f}
* is the number of FT segments used to estimate the spectrum. This term

*σ*

_{lnΨ}provides the statistical basis for constructing the confidence interval of the logarithm of a spectrum, and thus, the spectrum itself. A universal spectrum of turbulence shear is derived from the nondimensionalization of 14 600 spectra estimated from 5 m segments of data. This spectrum differs from the Nasmyth spectrum and from the spectrum of Panchev and Kesich 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.

### Significance Statement

The results reported here can be used to estimate the statistical uncertainty of a spectrum of turbulent shear or velocity that is derived from a finite number of discrete Fourier transform segments, and they can be used to quantify the quality of a spectrum.

## 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 collocated shear probes, described in Part I, 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, *N _{f}
* is the number of FT segments used to estimate the spectrum. This term

*σ*

_{lnΨ}provides the statistical basis for constructing the confidence interval of the logarithm of a spectrum, and thus, the spectrum itself. A universal spectrum of turbulence shear is derived from the nondimensionalization of 14 600 spectra estimated from 5 m segments of data. This spectrum differs from the Nasmyth spectrum and from the spectrum of Panchev and Kesich 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.

### Significance Statement

The results reported here can be used to estimate the statistical uncertainty of a spectrum of turbulent shear or velocity that is derived from a finite number of discrete Fourier transform segments, and they can be used to quantify the quality of a spectrum.

## Abstract

This paper investigates the limitation in calculating the vertical wavelength of downward phase propagating gravity waves from the vertical fluctuation of idealized radiosonde balloons in a homogeneous background environment. The wave signals are artificially observed by an idealized weather balloon with a constant ascent rate. The apparent vertical wavelengths obtained from the moving radiosonde balloon are compared to the true vertical wavelength obtained from the dispersion relation, both in the no-wind case and in the constant-zonal-flow case. The node method and FFT method are employed to calculate the apparent vertical wavelength from the sounding profile. The difference between the node apparent vertical wavelength and the true vertical wavelength is attributed to the fact that the ascent rate of the balloon and the downward phase speed induce a strong Doppler-shifting bias on the apparent vertical wavelength from the observation records. The difference between the FFT apparent vertical wavelength and the true vertical wavelength includes both the Doppler-shifting bias and the mathematical bias. The extent to which the apparent vertical wavelength is reliable is discussed. The Coriolis parameter has negligible effects on the comparison between the true vertical wavelength and the apparent one.

### Significance Statement

The purpose of this study is to discuss the Doppler-shifting bias induced by the ascent rate of radiosonde balloon when measuring the apparent vertical wavelengths of downward phase propagating gravity waves from the vertical fluctuation of idealized radiosonde balloons. This is an easily omitted problem. However, it can dramatically affect the gravity wave diagnosis when the ascent rate profile is treated as a quasi-instantaneous data. Further, such uncertainty could lead to remarkable errors in other derived wave propagating properties (e.g., phase velocity, which is the key input parameter in gravity wave parameterization).

## Abstract

This paper investigates the limitation in calculating the vertical wavelength of downward phase propagating gravity waves from the vertical fluctuation of idealized radiosonde balloons in a homogeneous background environment. The wave signals are artificially observed by an idealized weather balloon with a constant ascent rate. The apparent vertical wavelengths obtained from the moving radiosonde balloon are compared to the true vertical wavelength obtained from the dispersion relation, both in the no-wind case and in the constant-zonal-flow case. The node method and FFT method are employed to calculate the apparent vertical wavelength from the sounding profile. The difference between the node apparent vertical wavelength and the true vertical wavelength is attributed to the fact that the ascent rate of the balloon and the downward phase speed induce a strong Doppler-shifting bias on the apparent vertical wavelength from the observation records. The difference between the FFT apparent vertical wavelength and the true vertical wavelength includes both the Doppler-shifting bias and the mathematical bias. The extent to which the apparent vertical wavelength is reliable is discussed. The Coriolis parameter has negligible effects on the comparison between the true vertical wavelength and the apparent one.

### Significance Statement

The purpose of this study is to discuss the Doppler-shifting bias induced by the ascent rate of radiosonde balloon when measuring the apparent vertical wavelengths of downward phase propagating gravity waves from the vertical fluctuation of idealized radiosonde balloons. This is an easily omitted problem. However, it can dramatically affect the gravity wave diagnosis when the ascent rate profile is treated as a quasi-instantaneous data. Further, such uncertainty could lead to remarkable errors in other derived wave propagating properties (e.g., phase velocity, which is the key input parameter in gravity wave parameterization).