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- Author or Editor: Owen E. Thompson x
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Abstract
A new method is derived for retrieving atmospheric temperature profiles from satellite-measured spectral radiance that appears, in first tests, to effectively circumvent certain difficulties of other well-known and implemented methods. In particular, the new method provides an elective way to avoid numerical instability without having to force the algorithm toward adherence to a priori statistics not dependent on the radiance measurements. This provides the opportunity to extract more information from satellite sounding instruments, without encountering instabilities owing to overlapping weighting functions. BY implication, this means that retrievals can be obtained without the typically strong external constraints of smoothing or cohesion to historical characteristics of the thermal or moisture structure.
The new retrieval method is derived from a singular-value decomposition (SVD) of the radiative transfer physics governing the satellite measurements. The basis is an orthogonal one depending only on the characteristics of the sounding radiometer and not on a priori statistics. The SVD procedure allows one to efficiently structure and extract the information content of satellite observations and to rationally control the numerical, algorithmic instability. This is accomplished by discarding those singular vectors that adversely transform small radiometer errors into large retrieval errors, while retaining those vectors that transform radiance information reliably and unproblematically into thermal information.
It is hoped that this new SVD methodology will find useful application for improving the impact of satellite observations on satellite retrievals and thereby improve the impact of retrievals on meteorological problems varying from short-range forecasting to long-range assessment of global change.
Abstract
A new method is derived for retrieving atmospheric temperature profiles from satellite-measured spectral radiance that appears, in first tests, to effectively circumvent certain difficulties of other well-known and implemented methods. In particular, the new method provides an elective way to avoid numerical instability without having to force the algorithm toward adherence to a priori statistics not dependent on the radiance measurements. This provides the opportunity to extract more information from satellite sounding instruments, without encountering instabilities owing to overlapping weighting functions. BY implication, this means that retrievals can be obtained without the typically strong external constraints of smoothing or cohesion to historical characteristics of the thermal or moisture structure.
The new retrieval method is derived from a singular-value decomposition (SVD) of the radiative transfer physics governing the satellite measurements. The basis is an orthogonal one depending only on the characteristics of the sounding radiometer and not on a priori statistics. The SVD procedure allows one to efficiently structure and extract the information content of satellite observations and to rationally control the numerical, algorithmic instability. This is accomplished by discarding those singular vectors that adversely transform small radiometer errors into large retrieval errors, while retaining those vectors that transform radiance information reliably and unproblematically into thermal information.
It is hoped that this new SVD methodology will find useful application for improving the impact of satellite observations on satellite retrievals and thereby improve the impact of retrievals on meteorological problems varying from short-range forecasting to long-range assessment of global change.
Abstract
Theoretical and empirical analyses of the vertical resolving power of the High resolution Infrared Radiation Sounder (HIRS) and the Advanced Moisture and Temperature Sounder (AMTS) is carried out. First, the infrared transmittance weighting functions, and associated radiative transfer kernels, are analyzed through singular value decomposition. The AMTS is found to contain several more pieces of independent information than HIRS when the transmittances are considered, but the two instruments appear to be much more similar when the temperature-sensitive radiative transfer kernels are analyzed.
The instruments are also subjected to a theoretical analysis using the methods of Backus and Gilbert. From this analysis, it is found that the two instruments should have very similar vertical resolving power below 500 mb but that AMTS should have superior resolving power above 200 mb. In the layer 200–500 mb, the AMTS shows a badly degraded spread function which may or may not be a realistic assessment of vertical resolving power there.
An empirical method for assessing vertical resolving power is also developed and compared with theory. This method involves a measure of vertical resolving length determined from retrievals carried out with minimum information and Backus-Gilbert inverse solutions. This test shows that the Backus-Gilbert spread function does not represent the minimum separation of resolvable signals in an atmospheric temperature profile. By the empirical evaluation, the HIRS and AMTS should have similar vertical resolution in the troposphere with vertical resolving length around 2–3 km, quite consistent with theory. The AMTS exhibits a slight advantage over the HIRS above 200 mb, a result which is also qualitatively consistent with theory. In the layer 200–500 mb, the two instruments appear to have very similar resolution with AMTS showing a slight advantage over HIRS. This is totally contrary to theoretical results which indicate that AMTS is very poor in this layer.
Abstract
Theoretical and empirical analyses of the vertical resolving power of the High resolution Infrared Radiation Sounder (HIRS) and the Advanced Moisture and Temperature Sounder (AMTS) is carried out. First, the infrared transmittance weighting functions, and associated radiative transfer kernels, are analyzed through singular value decomposition. The AMTS is found to contain several more pieces of independent information than HIRS when the transmittances are considered, but the two instruments appear to be much more similar when the temperature-sensitive radiative transfer kernels are analyzed.
The instruments are also subjected to a theoretical analysis using the methods of Backus and Gilbert. From this analysis, it is found that the two instruments should have very similar vertical resolving power below 500 mb but that AMTS should have superior resolving power above 200 mb. In the layer 200–500 mb, the AMTS shows a badly degraded spread function which may or may not be a realistic assessment of vertical resolving power there.
An empirical method for assessing vertical resolving power is also developed and compared with theory. This method involves a measure of vertical resolving length determined from retrievals carried out with minimum information and Backus-Gilbert inverse solutions. This test shows that the Backus-Gilbert spread function does not represent the minimum separation of resolvable signals in an atmospheric temperature profile. By the empirical evaluation, the HIRS and AMTS should have similar vertical resolution in the troposphere with vertical resolving length around 2–3 km, quite consistent with theory. The AMTS exhibits a slight advantage over the HIRS above 200 mb, a result which is also qualitatively consistent with theory. In the layer 200–500 mb, the two instruments appear to have very similar resolution with AMTS showing a slight advantage over HIRS. This is totally contrary to theoretical results which indicate that AMTS is very poor in this layer.
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Abstract
This study deals with atmospheric tropopause detection by satellite. It is found that incorrect forecasting of the tropopause height yields a systematic bias in temperature profile estimates which use an algorithm (specifically, the “minimum information” method) operating on satellite-measured spectral infrared radiances and forecast temperature profiles as first guess fields. This bias follows from the general inability of linear satellite-based temperature retrieval schemes to substantially correct “shape” errors in the first guess field, owing to the rather low vertical resolving power of such schemes. A non-linear approach to tropopause detection which makes use of certain selected ratios of measured spectral radiances is shown to have some power for correcting these biases.
Abstract
This study deals with atmospheric tropopause detection by satellite. It is found that incorrect forecasting of the tropopause height yields a systematic bias in temperature profile estimates which use an algorithm (specifically, the “minimum information” method) operating on satellite-measured spectral infrared radiances and forecast temperature profiles as first guess fields. This bias follows from the general inability of linear satellite-based temperature retrieval schemes to substantially correct “shape” errors in the first guess field, owing to the rather low vertical resolving power of such schemes. A non-linear approach to tropopause detection which makes use of certain selected ratios of measured spectral radiances is shown to have some power for correcting these biases.
Abstract
Satellite sensor optical systems now provide scan spots that are reasonably small and closely spaced compared with the horizontal scales of atmospheric variability that meteorologists might like to infer. Furthermore, geo-synchronous deployment of meteorological satellites provides the opportunity for almost arbitrarily frequent observational thus apparently increasing the temporal resolving power to almost an arbitrary degree. It is known, however, that the vertical resolving power of satellite sounding technology is poor compared with RAOBs. That is, finer scales of vertical atmospheric structure that can he resolved by radiosonde observations may not be detectable or resolvable by satellite radiance observations. In all retrieval methods, some external information or estimates of the ambient vertical structure must be included so that the apparent vertical resolution of the retrieval system is increased.
In this study we show that horizontal and temporal resolving power of satellite soundings is closely coupled to the vertical resolving power. This is demonstrated both empirically and theoretically. Moreover, we show that improving the horizontal or temporal resolving power is not a simple matter of improving scan spot optics or increasing the frequency of observation. Either the “vertical resolving power” of the satellite instrument itself must be improved, or the a priori external information must be extended to include correct horizontal and temporal structure. The vertical resolution limitation of satellite sounders has a direct effect on filtering out, or distorting, horizontal and temporal structural information.
Abstract
Satellite sensor optical systems now provide scan spots that are reasonably small and closely spaced compared with the horizontal scales of atmospheric variability that meteorologists might like to infer. Furthermore, geo-synchronous deployment of meteorological satellites provides the opportunity for almost arbitrarily frequent observational thus apparently increasing the temporal resolving power to almost an arbitrary degree. It is known, however, that the vertical resolving power of satellite sounding technology is poor compared with RAOBs. That is, finer scales of vertical atmospheric structure that can he resolved by radiosonde observations may not be detectable or resolvable by satellite radiance observations. In all retrieval methods, some external information or estimates of the ambient vertical structure must be included so that the apparent vertical resolution of the retrieval system is increased.
In this study we show that horizontal and temporal resolving power of satellite soundings is closely coupled to the vertical resolving power. This is demonstrated both empirically and theoretically. Moreover, we show that improving the horizontal or temporal resolving power is not a simple matter of improving scan spot optics or increasing the frequency of observation. Either the “vertical resolving power” of the satellite instrument itself must be improved, or the a priori external information must be extended to include correct horizontal and temporal structure. The vertical resolution limitation of satellite sounders has a direct effect on filtering out, or distorting, horizontal and temporal structural information.
Abstract
An hypothesis is given for the cause of the observed diurnal oscillations in the mid- and upper-tropospheric wind field that occur in association with oscillations of the boundary layer wind field and low-level, nocturnal jet occurrences. A simple mathematical model of the middle and upper troposphere is solved using perturbation techniques subject to the condition that the three-dimensional velocity is continuous at a plane separating the boundary layer from the atmosphere above, and the vertical motion is zero at the tropopause height. Theoretical results are presented which show good agreement with previously published wind data from the surface to the region of the tropopause.
Abstract
An hypothesis is given for the cause of the observed diurnal oscillations in the mid- and upper-tropospheric wind field that occur in association with oscillations of the boundary layer wind field and low-level, nocturnal jet occurrences. A simple mathematical model of the middle and upper troposphere is solved using perturbation techniques subject to the condition that the three-dimensional velocity is continuous at a plane separating the boundary layer from the atmosphere above, and the vertical motion is zero at the tropopause height. Theoretical results are presented which show good agreement with previously published wind data from the surface to the region of the tropopause.
Abstract
Several research groups have announced plans to merge satellite profile retrieval methods and numerical weather prediction methods into “interactive” satellite retrieval approaches for both weather and climate-scale endeavors. Satellite profile retrievals, produced from algorithms that depend on hydrodynamic weather prediction models for first-guess and conditioning data, may be expected to contain some influence of the numerical weather prediction (NWP) model quite distinct from any influence of the satellite measurements. Research is described in this paper in which possible adverse impacts of NWP-produced first-guess information on temperature profile retrievals appear to signal danger for interactive methodologies. Deep-layer, synoptically correlated NWP forecast errors influence satellite retrieval errors in such a way that systematic distortions of the hydrostatic and baroclinic character of the resulting fields could lead to degradations of a subsequent forecast cycle rather than improvements.
Two related temperature retrieval algorithms are examined and compared using initializing and conditioning data derived from NMC T80 spectral model forecasts. The algorithms are the well-known statistical regularization method, also called the “minimum variance method,” and a method derived from a singular value decomposition (SVD) of the radiative transfer operator with regularization accomplished by truncation rather than a priori statistics. The two algorithms allow for a rational distinction between the effects of “statistics” and “physics” on the results. The SVD method provides an opportunity to explicitly examine the adverse effects of retrieval matrix instability and to infer how that may he influencing the statistical regularization algorithm for which matrix instability is an implicit property of both the physics and statistics incorporated into that algorithm.
Finally, the effect of linearization of the retrieval problem on retrieval errors is examined. For systematic first-guess error fields such as those encountered in this study, the contribution to retrieval error attributable to linearization is substantial. The retrieval algorithm based on SVD can he unambiguously iterated to reduce this source of error.
Abstract
Several research groups have announced plans to merge satellite profile retrieval methods and numerical weather prediction methods into “interactive” satellite retrieval approaches for both weather and climate-scale endeavors. Satellite profile retrievals, produced from algorithms that depend on hydrodynamic weather prediction models for first-guess and conditioning data, may be expected to contain some influence of the numerical weather prediction (NWP) model quite distinct from any influence of the satellite measurements. Research is described in this paper in which possible adverse impacts of NWP-produced first-guess information on temperature profile retrievals appear to signal danger for interactive methodologies. Deep-layer, synoptically correlated NWP forecast errors influence satellite retrieval errors in such a way that systematic distortions of the hydrostatic and baroclinic character of the resulting fields could lead to degradations of a subsequent forecast cycle rather than improvements.
Two related temperature retrieval algorithms are examined and compared using initializing and conditioning data derived from NMC T80 spectral model forecasts. The algorithms are the well-known statistical regularization method, also called the “minimum variance method,” and a method derived from a singular value decomposition (SVD) of the radiative transfer operator with regularization accomplished by truncation rather than a priori statistics. The two algorithms allow for a rational distinction between the effects of “statistics” and “physics” on the results. The SVD method provides an opportunity to explicitly examine the adverse effects of retrieval matrix instability and to infer how that may he influencing the statistical regularization algorithm for which matrix instability is an implicit property of both the physics and statistics incorporated into that algorithm.
Finally, the effect of linearization of the retrieval problem on retrieval errors is examined. For systematic first-guess error fields such as those encountered in this study, the contribution to retrieval error attributable to linearization is substantial. The retrieval algorithm based on SVD can he unambiguously iterated to reduce this source of error.
Abstract
An integrating device for totalizing the output of various transducers with respect to time is described. The device is battery operated and costs less than $150. The input span is adjustable from 6 to 100 millivolts and the zero point can be set anywhere in the span. The unit can detect changes in input voltage as low as 25 microvolts. An overall accuracy of 1% to 2% for sufficiently slowly varying inputs and from 3% to 5% for input variations with a period of the order of 1 minute or less is claimed.
Abstract
An integrating device for totalizing the output of various transducers with respect to time is described. The device is battery operated and costs less than $150. The input span is adjustable from 6 to 100 millivolts and the zero point can be set anywhere in the span. The unit can detect changes in input voltage as low as 25 microvolts. An overall accuracy of 1% to 2% for sufficiently slowly varying inputs and from 3% to 5% for input variations with a period of the order of 1 minute or less is claimed.
Abstract
A comprehensive summary of diurnal wind variations in the midwestern region of the United States is presented. Analyses are based on seven summers of four per day soundings at Fort Worth, Tex., Topeka, Kan., and International Falls, Minn. It is found that the diurnal oscillations are most prominent at Fort Worth, of significant amplitude at Topeka, and, although of lesser amplitude, still detectable at International Falls. An analysis is made of the forcing required to account for that part of the wind oscillation which cannot be attributed to Coriolis effects. This analysis indicates that the forcing is comparatively small at Fort Worth when the wind oscillations are largest owing to a resonance there with natural inertial oscillations. Significant forcing is present at higher latitude stations even though the manifestation of the forcing in the wind field is somewhat smaller in amplitude. The data suggest that forcing mechanisms at low and high attitudes may propagate to cause wind oscillations in the middle levels.
Abstract
A comprehensive summary of diurnal wind variations in the midwestern region of the United States is presented. Analyses are based on seven summers of four per day soundings at Fort Worth, Tex., Topeka, Kan., and International Falls, Minn. It is found that the diurnal oscillations are most prominent at Fort Worth, of significant amplitude at Topeka, and, although of lesser amplitude, still detectable at International Falls. An analysis is made of the forcing required to account for that part of the wind oscillation which cannot be attributed to Coriolis effects. This analysis indicates that the forcing is comparatively small at Fort Worth when the wind oscillations are largest owing to a resonance there with natural inertial oscillations. Significant forcing is present at higher latitude stations even though the manifestation of the forcing in the wind field is somewhat smaller in amplitude. The data suggest that forcing mechanisms at low and high attitudes may propagate to cause wind oscillations in the middle levels.
