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- Author or Editor: Stuart Bradley x
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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.
Abstract
Ensemble streamflow prediction systems produce forecasts in the form of a conditional probability distribution for a continuous forecast variable. A distributions-oriented approach is presented for verification of these probability distribution forecasts. First, a flow threshold is used to transform the ensemble forecast into a probability forecast for a dichotomous event. The event is said to occur if the observed flow is less than or equal to the threshold; the probability forecast is the probability that the event occurs. The distributions-oriented approach, which has been developed for meteorological forecast verification, is then applied to estimate forecast quality measures for a verification dataset. The results are summarized for thresholds chosen to cover the range of possible flow outcomes. To aid in the comparison for different thresholds, relative measures are used to assess forecast quality. An application with experimental forecasts for the Des Moines River basin illustrates the approach. The application demonstrates the added insights on forecast quality gained through this approach, as compared to more traditional ensemble verification approaches. By examining aspects of forecast quality over the range of possible flow outcomes, the distributions-oriented approach facilitates a diagnostic evaluation of ensemble forecasting systems.
Abstract
Ensemble streamflow prediction systems produce forecasts in the form of a conditional probability distribution for a continuous forecast variable. A distributions-oriented approach is presented for verification of these probability distribution forecasts. First, a flow threshold is used to transform the ensemble forecast into a probability forecast for a dichotomous event. The event is said to occur if the observed flow is less than or equal to the threshold; the probability forecast is the probability that the event occurs. The distributions-oriented approach, which has been developed for meteorological forecast verification, is then applied to estimate forecast quality measures for a verification dataset. The results are summarized for thresholds chosen to cover the range of possible flow outcomes. To aid in the comparison for different thresholds, relative measures are used to assess forecast quality. An application with experimental forecasts for the Des Moines River basin illustrates the approach. The application demonstrates the added insights on forecast quality gained through this approach, as compared to more traditional ensemble verification approaches. By examining aspects of forecast quality over the range of possible flow outcomes, the distributions-oriented approach facilitates a diagnostic evaluation of ensemble forecasting systems.
Abstract
For probability forecasts, the Brier score and Brier skill score are commonly used verification measures of forecast accuracy and skill. Using sampling theory, analytical expressions are derived to estimate their sampling uncertainties. The Brier score is an unbiased estimator of the accuracy, and an exact expression defines its sampling variance. The Brier skill score (with climatology as a reference forecast) is a biased estimator, and approximations are needed to estimate its bias and sampling variance. The uncertainty estimators depend only on the moments of the forecasts and observations, so it is easy to routinely compute them at the same time as the Brier score and skill score. The resulting uncertainty estimates can be used to construct error bars or confidence intervals for the verification measures, or perform hypothesis testing.
Monte Carlo experiments using synthetic forecasting examples illustrate the performance of the expressions. In general, the estimates provide very reliable information on uncertainty. However, the quality of an estimate depends on both the sample size and the occurrence frequency of the forecast event. The examples also illustrate that with infrequently occurring events, verification sample sizes of a few hundred forecast–observation pairs are needed to establish that a forecast is skillful because of the large uncertainties that exist.
Abstract
For probability forecasts, the Brier score and Brier skill score are commonly used verification measures of forecast accuracy and skill. Using sampling theory, analytical expressions are derived to estimate their sampling uncertainties. The Brier score is an unbiased estimator of the accuracy, and an exact expression defines its sampling variance. The Brier skill score (with climatology as a reference forecast) is a biased estimator, and approximations are needed to estimate its bias and sampling variance. The uncertainty estimators depend only on the moments of the forecasts and observations, so it is easy to routinely compute them at the same time as the Brier score and skill score. The resulting uncertainty estimates can be used to construct error bars or confidence intervals for the verification measures, or perform hypothesis testing.
Monte Carlo experiments using synthetic forecasting examples illustrate the performance of the expressions. In general, the estimates provide very reliable information on uncertainty. However, the quality of an estimate depends on both the sample size and the occurrence frequency of the forecast event. The examples also illustrate that with infrequently occurring events, verification sample sizes of a few hundred forecast–observation pairs are needed to establish that a forecast is skillful because of the large uncertainties that exist.
Abstract
A spectrometer allowing size-fractional chemical analysis of raindrops has been described previously by the authors. Modifications to this raindrop chemistry spectrometer now allow improved performance in windy conditions. Instrument verifications show that drop-size distribution parameters can be estimated to 2%, and pH versus drop-size spectra can be obtained to 0.02 pH units in wind speeds up to 3 m s−1. Improved resolution will allow trace chemical analysis for comparison with detailed rain chemistry models.
Abstract
A spectrometer allowing size-fractional chemical analysis of raindrops has been described previously by the authors. Modifications to this raindrop chemistry spectrometer now allow improved performance in windy conditions. Instrument verifications show that drop-size distribution parameters can be estimated to 2%, and pH versus drop-size spectra can be obtained to 0.02 pH units in wind speeds up to 3 m s−1. Improved resolution will allow trace chemical analysis for comparison with detailed rain chemistry models.
Abstract
A rain gauge is described that quantizes rainwater collected by a funnel into equal-sized drops. Using a funnel of 150-mm diameter, the quantization corresponds to 1/160 mm of rainfall, enabling the measurement of low rainfall rates and the attainment of a fine temporal resolution on the order of 15 s without unduly large sampling errors. Two drop-producing units are compared and an operational rain gauge design is presented. Field comparisons with conventional rain gauges are made, showing excellent correlations for daily rain totals, and intercomparisons between clusters of dropper gauges are also given. Examples of highly resolved rainfall events are shown demonstrating the ability to measure low rainfall accumulations and also coherent high intensity events of short duration, which are not detectable with conventional rain gauges.
Abstract
A rain gauge is described that quantizes rainwater collected by a funnel into equal-sized drops. Using a funnel of 150-mm diameter, the quantization corresponds to 1/160 mm of rainfall, enabling the measurement of low rainfall rates and the attainment of a fine temporal resolution on the order of 15 s without unduly large sampling errors. Two drop-producing units are compared and an operational rain gauge design is presented. Field comparisons with conventional rain gauges are made, showing excellent correlations for daily rain totals, and intercomparisons between clusters of dropper gauges are also given. Examples of highly resolved rainfall events are shown demonstrating the ability to measure low rainfall accumulations and also coherent high intensity events of short duration, which are not detectable with conventional rain gauges.
