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- Author or Editor: Chong-Jian Qiu x
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Abstract
A least squares (LS) method is developed for retrieving low-altitude winds from single-Doppler radar scans. The method is tested with Denver airport microburst data and the results compared with the previously developed simple adjoint (SA) method. It is found that the LS method is slightly superior to the SA method for the microburst data obtained with fast radar scans (Δτ ≈ 60 s) but will become inferior to the SA method if the radar scans are twice as long (Δτ ≈ 120 s). Four previously developed detailed techniques for the SA method are used to improve the LS retrievals, and these include (i) using multiple-time-level data, (ii) imposing the weak divergence and weak vorticity constraints, (iii) retrieving the eddy coefficient and time-mean forcing term, and (iv) using the, observed time-mean radial wind as a weak constraint. Because the control equation is used as a weak constraint in a finite-difference form, the LS method depends more on the smoothness constraints but is less sensitive to equation error and is computationally much more efficient than the SA method. An objective way for the selections of weights is also proposed and tested in this paper.
Abstract
A least squares (LS) method is developed for retrieving low-altitude winds from single-Doppler radar scans. The method is tested with Denver airport microburst data and the results compared with the previously developed simple adjoint (SA) method. It is found that the LS method is slightly superior to the SA method for the microburst data obtained with fast radar scans (Δτ ≈ 60 s) but will become inferior to the SA method if the radar scans are twice as long (Δτ ≈ 120 s). Four previously developed detailed techniques for the SA method are used to improve the LS retrievals, and these include (i) using multiple-time-level data, (ii) imposing the weak divergence and weak vorticity constraints, (iii) retrieving the eddy coefficient and time-mean forcing term, and (iv) using the, observed time-mean radial wind as a weak constraint. Because the control equation is used as a weak constraint in a finite-difference form, the LS method depends more on the smoothness constraints but is less sensitive to equation error and is computationally much more efficient than the SA method. An objective way for the selections of weights is also proposed and tested in this paper.
Abstract
A variational method is developed to compute surface fluxes of sensible and latent heat from observed wind, temperature, humidity, and surface energy and radiation budget by the surface energy and radiation balance systems (SERBS). In comparison with the conventional Bowen ratio energy balance method and profile method, the new method makes better and more complete use of the information provided by the SERBS measurements, and by the surface energy balance equation and the similarity profile equations. Tested with the data collected at the Oklahoma Atmospheric Radiation Measurement Cloud and Radiation Testbed central station, the method is found to be more reliable and accurate than the two conventional methods.
Abstract
A variational method is developed to compute surface fluxes of sensible and latent heat from observed wind, temperature, humidity, and surface energy and radiation budget by the surface energy and radiation balance systems (SERBS). In comparison with the conventional Bowen ratio energy balance method and profile method, the new method makes better and more complete use of the information provided by the SERBS measurements, and by the surface energy balance equation and the similarity profile equations. Tested with the data collected at the Oklahoma Atmospheric Radiation Measurement Cloud and Radiation Testbed central station, the method is found to be more reliable and accurate than the two conventional methods.
Abstract
A simple adjoint method is developed for retrieving the time-mean winds from a number of consecutive single-Doppler measurements. The method assumes the Lagrangian conservation of reflectivity. Previous methods based on the same advection equation have to deal with problems of nonuniqueness, singularities, or both. These two problems are eliminated by using observations over multiple time levels. The method is tested on artificial data and the results show that using data over multiple time levels not only provides more information and increases the accuracy of the retrieval but also makes the method less sensitive to errors in the observed reflectivity field and errors in the model equation due to the assumed Lagrangian conservation of reflectivity. Because the control equation and its adjoint equation are very simple, the computational cost is very small. It is also found that incorporating the constraint of mass conservation into the method can significantly increase the accuracy of the retrieved winds and reduce the required frequency of observations for retrieving.
Abstract
A simple adjoint method is developed for retrieving the time-mean winds from a number of consecutive single-Doppler measurements. The method assumes the Lagrangian conservation of reflectivity. Previous methods based on the same advection equation have to deal with problems of nonuniqueness, singularities, or both. These two problems are eliminated by using observations over multiple time levels. The method is tested on artificial data and the results show that using data over multiple time levels not only provides more information and increases the accuracy of the retrieval but also makes the method less sensitive to errors in the observed reflectivity field and errors in the model equation due to the assumed Lagrangian conservation of reflectivity. Because the control equation and its adjoint equation are very simple, the computational cost is very small. It is also found that incorporating the constraint of mass conservation into the method can significantly increase the accuracy of the retrieved winds and reduce the required frequency of observations for retrieving.
Abstract
The simple adjoint (SA) method is extended to use both the reflectivity equation and the radial-wind equation to retrieve the low-altitude horizontal wind field from single-Doppler reflectivity and radial-wind data. Three extended methods are proposed. The extended method A uses the reflectivity equation and radial-wind equation simultaneously. The extended method B (or method C) uses the reflectivity equation and radial-wind equation alternately with the velocity retrieved from the reflectivity (or radial wind) data first. The first-step retrieved wind is then used to estimate the time-mean residual forcing (or source) term in the radial-wind (or reflectivity) equation, and this estimated forcing (or source) is used as a weak constraint in the second-step retrieval from the radial-wind (or reflectivity) data. The retrieval is expected to be maximally improved when the procedure goes to the third step (and beyond). Tested with the Doppler radar data measured during the Phoenix II field experiment, all three extended methods are found to be better than the previous SA method based on a single (reflectivity or radial wind) equation. Among the three extended methods, method C is found to be slightly better than method A, but slightly worse than method B.
Abstract
The simple adjoint (SA) method is extended to use both the reflectivity equation and the radial-wind equation to retrieve the low-altitude horizontal wind field from single-Doppler reflectivity and radial-wind data. Three extended methods are proposed. The extended method A uses the reflectivity equation and radial-wind equation simultaneously. The extended method B (or method C) uses the reflectivity equation and radial-wind equation alternately with the velocity retrieved from the reflectivity (or radial wind) data first. The first-step retrieved wind is then used to estimate the time-mean residual forcing (or source) term in the radial-wind (or reflectivity) equation, and this estimated forcing (or source) is used as a weak constraint in the second-step retrieval from the radial-wind (or reflectivity) data. The retrieval is expected to be maximally improved when the procedure goes to the third step (and beyond). Tested with the Doppler radar data measured during the Phoenix II field experiment, all three extended methods are found to be better than the previous SA method based on a single (reflectivity or radial wind) equation. Among the three extended methods, method C is found to be slightly better than method A, but slightly worse than method B.
Abstract
Three schemes are developed to incorporate a strong constraint of (incompressible) mass conservation into the basic scheme (scheme B) of the simple adjoint method of Qiu and Xu for retrieving the time-mean wind field from a sequence of single-Doppler scans. In the first scheme (S1), the two-dimensional wind field on a surface normal to the radar beam is partitioned into an irrotational component expressed by the velocity potential and a nondivergent component expressed by the streamfunction. The velocity potential can be obtained directly from single-Doppler observations, and the streamfunction is retrieved by the adjoint method. In this way, the retrieved wind field satisfies the mass conservation equation precisely. The second scheme (S2) is the same as scheme S1 except that a spectral expression is used to replace the grid representation of the streamfunction. The third scheme (S3) imposes a strong mass conservation constraint through a postadjustment after the wind field is retrieved by scheme B with a weak mass conservation constraint. These schemes are tested with artificial data. Their relative merits and disadvantages are examined and compared in terms of accuracy, convergence rate, sensitivity to errors, and computational efficiency.
Abstract
Three schemes are developed to incorporate a strong constraint of (incompressible) mass conservation into the basic scheme (scheme B) of the simple adjoint method of Qiu and Xu for retrieving the time-mean wind field from a sequence of single-Doppler scans. In the first scheme (S1), the two-dimensional wind field on a surface normal to the radar beam is partitioned into an irrotational component expressed by the velocity potential and a nondivergent component expressed by the streamfunction. The velocity potential can be obtained directly from single-Doppler observations, and the streamfunction is retrieved by the adjoint method. In this way, the retrieved wind field satisfies the mass conservation equation precisely. The second scheme (S2) is the same as scheme S1 except that a spectral expression is used to replace the grid representation of the streamfunction. The third scheme (S3) imposes a strong mass conservation constraint through a postadjustment after the wind field is retrieved by scheme B with a weak mass conservation constraint. These schemes are tested with artificial data. Their relative merits and disadvantages are examined and compared in terms of accuracy, convergence rate, sensitivity to errors, and computational efficiency.
Abstract
A spectral simple adjoint (SSA) method for retrieving, low-attitude time-mean horizontal winds from single-Doppler wind measurements is developed and tested with the Phoenix II held experimental data. The SSA method is similar to the previous grid simple adjoint (GSA) methods of Qiu and Xu and Xu et al., except that a truncated spectral expression is used to replace the grid representation of the wind field. In the previous GSA methods the retrieved lime-mean winds were resolved on the same full spatial grid as the data. This full spatial resolution was often excessive and unnecessary as the time-mean wind field was quite smooth. When a truncated spectral expression is used to reduce the excessive and unnecessary spatial resolution, the SSA method not only gains temporal resolution (e.g., the retrieving period can be reduced to 130 s—a single time interval of radar scan) but also improves the accuracy of the retrieved winds (because short-wave noise is filtered). The merits and limitations of the SSA method are also examined with idealized examples.
Abstract
A spectral simple adjoint (SSA) method for retrieving, low-attitude time-mean horizontal winds from single-Doppler wind measurements is developed and tested with the Phoenix II held experimental data. The SSA method is similar to the previous grid simple adjoint (GSA) methods of Qiu and Xu and Xu et al., except that a truncated spectral expression is used to replace the grid representation of the wind field. In the previous GSA methods the retrieved lime-mean winds were resolved on the same full spatial grid as the data. This full spatial resolution was often excessive and unnecessary as the time-mean wind field was quite smooth. When a truncated spectral expression is used to reduce the excessive and unnecessary spatial resolution, the SSA method not only gains temporal resolution (e.g., the retrieving period can be reduced to 130 s—a single time interval of radar scan) but also improves the accuracy of the retrieved winds (because short-wave noise is filtered). The merits and limitations of the SSA method are also examined with idealized examples.
Abstract
The significance of mass sinks (or sources) due to precipitation (or evaporation) is examined using numerical experiments performed with the Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model. The results show that the effect of mass sinks (or sources) can have a significant impact on numerical simulations of heavy precipitation. When this effect is ignored, as is commonly done in most global and regional weather prediction models, precipitation is reduced in the model.
Abstract
The significance of mass sinks (or sources) due to precipitation (or evaporation) is examined using numerical experiments performed with the Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model. The results show that the effect of mass sinks (or sources) can have a significant impact on numerical simulations of heavy precipitation. When this effect is ignored, as is commonly done in most global and regional weather prediction models, precipitation is reduced in the model.
Abstract
A simple soil heat transfer model is used together with an adaptive Kalman filter to estimate the daily averaged soil volumetric water contents from diurnal variations of the soil temperatures measured at different depths. In this method, the soil water contents are estimated as control variables that regulate the variations of soil temperatures at different depths and make the model nonbiased, while the model system noise covariance matrix is estimated by the covariance-matching technique. The method is tested with soil temperature data collected during 1–31 July 2000 from the Soil Water and Temperature System (SWATS) within the Oklahoma Atmospheric Radiation Measurement (ARM) central facilities at Lamont. The estimated soil water contents are verified against the observed values, and the rms differences are found to be small. Sensitivity tests are performed, showing that the method is reliable and stable.
Abstract
A simple soil heat transfer model is used together with an adaptive Kalman filter to estimate the daily averaged soil volumetric water contents from diurnal variations of the soil temperatures measured at different depths. In this method, the soil water contents are estimated as control variables that regulate the variations of soil temperatures at different depths and make the model nonbiased, while the model system noise covariance matrix is estimated by the covariance-matching technique. The method is tested with soil temperature data collected during 1–31 July 2000 from the Soil Water and Temperature System (SWATS) within the Oklahoma Atmospheric Radiation Measurement (ARM) central facilities at Lamont. The estimated soil water contents are verified against the observed values, and the rms differences are found to be small. Sensitivity tests are performed, showing that the method is reliable and stable.
Abstract
The simple adjoint method of Qiu and Xu is upgraded and tested with the Phoenix II data for retrieving the low-altitude winds from the movements of reflectivity patterns measured by a single-Doppler radar. The upgraded method uses an improved reflectivity advection equation that contains not only the advection terms but also the eddy diffusion terms. The test results show that (i) utilizing multiple-time-level data provides more information and, thus, increases the accuracy of the retrieval; (ii) the adjoint method can retrieve not only the time-mean (or running mean) velocity field but also the coefficients of horizontal and vertical eddy diffusion (retrieving the eddy coefficients improves the velocity retrieval); (iii) the retrieval is improved by judiciously setting the weights in the cost function and by spatial noise-filtering and temporal interpolation of the data; (iv) the retrieval is further improved when the observed radial wind (along the radar beam) is used.
Abstract
The simple adjoint method of Qiu and Xu is upgraded and tested with the Phoenix II data for retrieving the low-altitude winds from the movements of reflectivity patterns measured by a single-Doppler radar. The upgraded method uses an improved reflectivity advection equation that contains not only the advection terms but also the eddy diffusion terms. The test results show that (i) utilizing multiple-time-level data provides more information and, thus, increases the accuracy of the retrieval; (ii) the adjoint method can retrieve not only the time-mean (or running mean) velocity field but also the coefficients of horizontal and vertical eddy diffusion (retrieving the eddy coefficients improves the velocity retrieval); (iii) the retrieval is improved by judiciously setting the weights in the cost function and by spatial noise-filtering and temporal interpolation of the data; (iv) the retrieval is further improved when the observed radial wind (along the radar beam) is used.
