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Abstract
Ground-based sensing of wind profiles by sodars and lidars is becoming the standard for wind energy and other applications. However, there remain difficulties in complex terrain since the instruments sense wind components in spatially separated volumes, and systematic spatial variations of the wind components can lead to systematic bias in wind estimation. The errors are typically less than 6%, so corrections do not need to be very sophisticated.
Analytic potential flow models are developed for the flow over a bell-shaped hill and over an escarpment. These models are then used to find the radial Doppler shift from sampling volumes in typical sodar and lidar beam geometries, thereby allowing spatial variation bias to be removed. Since the models are straightforward, bias removal is readily achieved, and also lends itself to an understanding of the significant parameters affecting wind errors.
The bell model is tested against field data from sodars and lidars in both moderately complex and in very complex terrain. It is found that corrected winds are to within approximately 1% of those measured by mast instruments. Much more complex models do not correct wind errors better than these simple models.
Abstract
Ground-based sensing of wind profiles by sodars and lidars is becoming the standard for wind energy and other applications. However, there remain difficulties in complex terrain since the instruments sense wind components in spatially separated volumes, and systematic spatial variations of the wind components can lead to systematic bias in wind estimation. The errors are typically less than 6%, so corrections do not need to be very sophisticated.
Analytic potential flow models are developed for the flow over a bell-shaped hill and over an escarpment. These models are then used to find the radial Doppler shift from sampling volumes in typical sodar and lidar beam geometries, thereby allowing spatial variation bias to be removed. Since the models are straightforward, bias removal is readily achieved, and also lends itself to an understanding of the significant parameters affecting wind errors.
The bell model is tested against field data from sodars and lidars in both moderately complex and in very complex terrain. It is found that corrected winds are to within approximately 1% of those measured by mast instruments. Much more complex models do not correct wind errors better than these simple models.
Abstract
On a uniform terrain site, differences between a sodar and a mast-mounted cup anemometer will arise because of turbulent fluctuations and wind components being measured in different spaces, and because of the inherent difference between scalar and vector averaging. This paper develops theories for turbulence-related random fluctuations resulting from finite sampling rates and sampling from spatially distributed volumes. Coefficients of determination (R 2) are predicted comparable to those obtained in practice. It is shown that more than two-thirds of the reduction in R 2 arises from differences in the winds measured by mast instruments and by sodars, rather than by sodar errors: both instruments are measuring accurately, but just not in the same place or at the same time. The result is that sodars being used operationally should be able to measure winds to a root-mean-square accuracy of around 2%.
Abstract
On a uniform terrain site, differences between a sodar and a mast-mounted cup anemometer will arise because of turbulent fluctuations and wind components being measured in different spaces, and because of the inherent difference between scalar and vector averaging. This paper develops theories for turbulence-related random fluctuations resulting from finite sampling rates and sampling from spatially distributed volumes. Coefficients of determination (R 2) are predicted comparable to those obtained in practice. It is shown that more than two-thirds of the reduction in R 2 arises from differences in the winds measured by mast instruments and by sodars, rather than by sodar errors: both instruments are measuring accurately, but just not in the same place or at the same time. The result is that sodars being used operationally should be able to measure winds to a root-mean-square accuracy of around 2%.
Abstract
The differential absorption of sound (DIAS) depends on frequency, temperature, and humidity in a known fashion. By obtaining turbulent reflections at two or more frequencies from the same target air mass, it is possible to resolve other frequency-dependent factors and obtain estimates of the absorption coefficient at the sounding frequencies. Over a restricted range of frequency and humidity, it is shown that the differential absorption is essentially a function of temperature but not of humidity. This method therefore provides the potential for temperature sounding using conventional sodars.
The theory of this method is outlined, and sensitivity is estimated based on actual sodar data. As part of the Tekapo Field Experiment in the Southern Alps, two sodars were operated side by side at a range of frequencies, allowing estimates to be made of signal-to-noise ratio. Temperature retrievals using this method are discussed.
Abstract
The differential absorption of sound (DIAS) depends on frequency, temperature, and humidity in a known fashion. By obtaining turbulent reflections at two or more frequencies from the same target air mass, it is possible to resolve other frequency-dependent factors and obtain estimates of the absorption coefficient at the sounding frequencies. Over a restricted range of frequency and humidity, it is shown that the differential absorption is essentially a function of temperature but not of humidity. This method therefore provides the potential for temperature sounding using conventional sodars.
The theory of this method is outlined, and sensitivity is estimated based on actual sodar data. As part of the Tekapo Field Experiment in the Southern Alps, two sodars were operated side by side at a range of frequencies, allowing estimates to be made of signal-to-noise ratio. Temperature retrievals using this method are discussed.
Abstract
The design of a sodar that uses ultrasound to remotely sense drop size distributions in rainfall is described. The Doppler shift is proportional to a drop's terminal velocity and gives a measure of the drop diameter, whereas the intensity of scatter gives a measure of the number of drops of each diameter. Since rain drops cause Rayleigh scattering in the usable range of sound frequencies, the intensity of this scattering is proportional to the fourth power of the frequency. Because attenuation rises with frequency, a 40-kHz operating frequency was found to maximize the power reflected back from rain drops.
Verification of design factors was undertaken in an anechoic chamber. Field tests showed that Doppler frequency spectra and drop size concentrations matched expected profiles. Rainfall intensities inferred from the Doppler spectrum over time were within 20% of the values obtained by conventional rain gauges. The instrument was found to be useful for obtaining information in the lowest 10 m of the atmosphere, which makes it an attractive alternative to ground-based sensors.
Abstract
The design of a sodar that uses ultrasound to remotely sense drop size distributions in rainfall is described. The Doppler shift is proportional to a drop's terminal velocity and gives a measure of the drop diameter, whereas the intensity of scatter gives a measure of the number of drops of each diameter. Since rain drops cause Rayleigh scattering in the usable range of sound frequencies, the intensity of this scattering is proportional to the fourth power of the frequency. Because attenuation rises with frequency, a 40-kHz operating frequency was found to maximize the power reflected back from rain drops.
Verification of design factors was undertaken in an anechoic chamber. Field tests showed that Doppler frequency spectra and drop size concentrations matched expected profiles. Rainfall intensities inferred from the Doppler spectrum over time were within 20% of the values obtained by conventional rain gauges. The instrument was found to be useful for obtaining information in the lowest 10 m of the atmosphere, which makes it an attractive alternative to ground-based sensors.
Abstract
Ensemble prediction systems produce forecasts that represent the probability distribution of a continuous forecast variable. Most often, the verification problem is simplified by transforming the ensemble forecast into probability forecasts for discrete events, where the events are defined by one or more threshold values. Then, skill is evaluated using the mean-square error (MSE; i.e., Brier) skill score for binary events, or the ranked probability skill score (RPSS) for multicategory events. A framework is introduced that generalizes this approach, by describing the forecast quality of ensemble forecasts as a continuous function of the threshold value. Viewing ensemble forecast quality this way leads to the interpretation of the RPSS and the continuous ranked probability skill score (CRPSS) as measures of the weighted-average skill over the threshold values. It also motivates additional measures, derived to summarize other features of a continuous forecast quality function, which can be interpreted as descriptions of the function’s geometric shape. The measures can be computed not only for skill, but also for skill score decompositions, which characterize the resolution, reliability, discrimination, and other aspects of forecast quality. Collectively, they provide convenient metrics for comparing the performance of an ensemble prediction system at different locations, lead times, or issuance times, or for comparing alternative forecasting systems.
Abstract
Ensemble prediction systems produce forecasts that represent the probability distribution of a continuous forecast variable. Most often, the verification problem is simplified by transforming the ensemble forecast into probability forecasts for discrete events, where the events are defined by one or more threshold values. Then, skill is evaluated using the mean-square error (MSE; i.e., Brier) skill score for binary events, or the ranked probability skill score (RPSS) for multicategory events. A framework is introduced that generalizes this approach, by describing the forecast quality of ensemble forecasts as a continuous function of the threshold value. Viewing ensemble forecast quality this way leads to the interpretation of the RPSS and the continuous ranked probability skill score (CRPSS) as measures of the weighted-average skill over the threshold values. It also motivates additional measures, derived to summarize other features of a continuous forecast quality function, which can be interpreted as descriptions of the function’s geometric shape. The measures can be computed not only for skill, but also for skill score decompositions, which characterize the resolution, reliability, discrimination, and other aspects of forecast quality. Collectively, they provide convenient metrics for comparing the performance of an ensemble prediction system at different locations, lead times, or issuance times, or for comparing alternative forecasting systems.
Abstract
A new method for calibration of sodar wind speed measurements is described. The method makes no assumptions whatsoever about the sodar operation and its hardware and software, other than the assumption that only one beam is transmitted at a time. Regardless of the complexity of the actual beam shape, the effective beam zenith angle is accurately estimated: this is the angle that must be used in estimations of velocity components. In a very simple experiment, the effective beam zenith angle has been found to within around 0.2°, which is as good as is required in the most stringent sodar calibration procedures. It has been found, even for such a short data run, that the estimated beam angle is very close to that calculated from the sodar array geometry. The main limitation is the requirement for horizontally homogeneous flow, since the regression methods use both a tilted beam and a vertical beam. Note that this is also a fundamental limiting assumption in the normal operation of ground-based wind lidars and sodars.
Abstract
A new method for calibration of sodar wind speed measurements is described. The method makes no assumptions whatsoever about the sodar operation and its hardware and software, other than the assumption that only one beam is transmitted at a time. Regardless of the complexity of the actual beam shape, the effective beam zenith angle is accurately estimated: this is the angle that must be used in estimations of velocity components. In a very simple experiment, the effective beam zenith angle has been found to within around 0.2°, which is as good as is required in the most stringent sodar calibration procedures. It has been found, even for such a short data run, that the estimated beam angle is very close to that calculated from the sodar array geometry. The main limitation is the requirement for horizontally homogeneous flow, since the regression methods use both a tilted beam and a vertical beam. Note that this is also a fundamental limiting assumption in the normal operation of ground-based wind lidars and sodars.
Abstract
A new ground-based wind profiling technology—a scanned bistatic sodar—is described. The motivation for this design is to obtain a “mastlike” wind vector profile in a single atmospheric column extending from the ground to heights of more than 200 m. The need for this columnar profiling arises from difficulties experienced by all existing lidars and sodars in the presence of nonhorizontally uniform wind fields, such as found generically in complex terrain. Other advantages are described, including improved signal strength from turbulent velocity fluctuations, improved data availability in neutral atmospheric temperature profiles, improved rejection of rain echoes, and improved rejection of echoes from fixed (nonatmospheric) objects. Initial brief field tests indicate that the scattered intensity profile agrees with theoretical expectations, and bistatic sodar winds are consistent with winds from standard mast-mounted instruments.
Abstract
A new ground-based wind profiling technology—a scanned bistatic sodar—is described. The motivation for this design is to obtain a “mastlike” wind vector profile in a single atmospheric column extending from the ground to heights of more than 200 m. The need for this columnar profiling arises from difficulties experienced by all existing lidars and sodars in the presence of nonhorizontally uniform wind fields, such as found generically in complex terrain. Other advantages are described, including improved signal strength from turbulent velocity fluctuations, improved data availability in neutral atmospheric temperature profiles, improved rejection of rain echoes, and improved rejection of echoes from fixed (nonatmospheric) objects. Initial brief field tests indicate that the scattered intensity profile agrees with theoretical expectations, and bistatic sodar winds are consistent with winds from standard mast-mounted instruments.
Abstract
A 21:1 scaled sodar, operating at 40 kHz, has been built and tested in the laboratory. Sodars, which use sound scattered by turbulence to profile the lowest few hundred meters of the atmosphere, need good acoustic shielding to diminish annoyance and to reduce unwanted reflections from nearby objects. Design of the acoustic shielding is generally inhibited by the difficulty of testing on full-scale systems and uncertainty as to accuracy of models. In contrast, the scale model approach described allows for “bench testing” of many designs under controlled conditions, and efficient comparison with models. Measured beam patterns from the scale model were compared with those from a numerical model based on the Kirchhoff integral theorem. Satisfactory agreement has allowed using the numerical model to optimize the acoustic shield design, both for the gross acoustic baffle geometry and for the geometry of rim modulations known as thnadners. Optimization was performed in the specific case of a scaled model of a commercial phased array sodar.
Abstract
A 21:1 scaled sodar, operating at 40 kHz, has been built and tested in the laboratory. Sodars, which use sound scattered by turbulence to profile the lowest few hundred meters of the atmosphere, need good acoustic shielding to diminish annoyance and to reduce unwanted reflections from nearby objects. Design of the acoustic shielding is generally inhibited by the difficulty of testing on full-scale systems and uncertainty as to accuracy of models. In contrast, the scale model approach described allows for “bench testing” of many designs under controlled conditions, and efficient comparison with models. Measured beam patterns from the scale model were compared with those from a numerical model based on the Kirchhoff integral theorem. Satisfactory agreement has allowed using the numerical model to optimize the acoustic shield design, both for the gross acoustic baffle geometry and for the geometry of rim modulations known as thnadners. Optimization was performed in the specific case of a scaled model of a commercial phased array sodar.
Abstract
The distributions-oriented approach to forecast verification uses an estimate of the joint distribution of forecasts and observations to evaluate forecast quality. However, small verification data samples can produce unreliable estimates of forecast quality due to sampling variability and biases. In this paper, new techniques for verification of probability forecasts of dichotomous events are presented. For forecasts of this type, simplified expressions for forecast quality measures can be derived from the joint distribution. Although traditional approaches assume that forecasts are discrete variables, the simplified expressions apply to either discrete or continuous forecasts. With the derived expressions, most of the forecast quality measures can be estimated analytically using sample moments of forecasts and observations from the verification data sample. Other measures require a statistical modeling approach for estimation. Results from Monte Carlo experiments for two forecasting examples show that the statistical modeling approach can significantly improve estimates of these measures in many situations. The improvement is achieved mostly by reducing the bias of forecast quality estimates and, for very small sample sizes, by slightly reducing the sampling variability. The statistical modeling techniques are most useful when the verification data sample is small (a few hundred forecast–observation pairs or less), and for verification of rare events, where the sampling variability of forecast quality measures is inherently large.
Abstract
The distributions-oriented approach to forecast verification uses an estimate of the joint distribution of forecasts and observations to evaluate forecast quality. However, small verification data samples can produce unreliable estimates of forecast quality due to sampling variability and biases. In this paper, new techniques for verification of probability forecasts of dichotomous events are presented. For forecasts of this type, simplified expressions for forecast quality measures can be derived from the joint distribution. Although traditional approaches assume that forecasts are discrete variables, the simplified expressions apply to either discrete or continuous forecasts. With the derived expressions, most of the forecast quality measures can be estimated analytically using sample moments of forecasts and observations from the verification data sample. Other measures require a statistical modeling approach for estimation. Results from Monte Carlo experiments for two forecasting examples show that the statistical modeling approach can significantly improve estimates of these measures in many situations. The improvement is achieved mostly by reducing the bias of forecast quality estimates and, for very small sample sizes, by slightly reducing the sampling variability. The statistical modeling techniques are most useful when the verification data sample is small (a few hundred forecast–observation pairs or less), and for verification of rare events, where the sampling variability of forecast quality measures is inherently large.
