scholarly journals Elimination of hidden a priori information from remotely sensed profile data

2006 ◽  
Vol 6 (4) ◽  
pp. 6723-6751 ◽  
Author(s):  
T. von Clarmann ◽  
U. Grabowski
Keyword(s):  
Degrees Of Freedom ◽  
A Priori ◽  
Michelson Interferometer ◽  
A Priori Information ◽  
Loss Of Information ◽  
Use Of Data ◽  
Remote Measurements ◽  
Ill Posed ◽  
Priori Information ◽  
Additional Loss

Abstract. Profiles of atmospheric state parameters retrieved from remote measurements often contain a priori information which causes complication in the use of data for validation, comparison with models, or data assimilation. For such applications it often is desirable to remove the a priori information from the data product. If the retrieval involves an ill-posed inversion problem, formal removal of the a priori information requires resampling of the data on a coarser grid, which, however, is a prior constraint in itself. The fact that the trace of the averaging kernel matrix of a retrieval is equivalent to the number of degrees of freedom of the retrieval is used to define an appropriate information-centered representation of the data where each data point represents one degree of freedom. Since regridding implies further degradation of the data and thus causes additional loss of information, a re-regularization scheme has been developed which allows resampling without additional loss of information. For a typical ClONO2 profile retrieved from spectra as measured by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), the constrained retrieval has 9.7 degrees of freedom. After application of the proposed transformation to a coarser information-centered altitude grid, there are exactly 9 degrees of freedom left, and the averaging kernel on the coarse grid is unity. Pure resampling on the information-centered grid without re-regularization would reduce the degrees of freedom to 7.1.

scholarly journals Elimination of hidden a priori information from remotely sensed profile data

2007 ◽  
Vol 7 (2) ◽  
pp. 397-408 ◽  
Author(s):  
T. von Clarmann ◽  
U. Grabowski
Keyword(s):  
Degrees Of Freedom ◽  
A Priori ◽  
Michelson Interferometer ◽  
State Variables ◽  
A Priori Information ◽  
Loss Of Information ◽  
Remote Measurements ◽  
Priori Information ◽  
Representation Scheme ◽  
Additional Loss

Abstract. Profiles of atmospheric state variables retrieved from remote measurements often contain a priori information which causes complication in the statistical use of data and in the comparison with other measured or modeled data. For such applications it often is desirable to remove the a priori information from the data product. If the retrieval involves an ill-posed inversion problem, formal removal of the a priori information requires resampling of the data on a coarser grid, which in some sense, however, is a prior constraint in itself. The fact that the trace of the averaging kernel matrix of a retrieval is equivalent to the number of degrees of freedom of the retrieval is used to define an appropriate information-centered representation of the data where each data point represents one degree of freedom. Since regridding implies further degradation of the data and thus causes additional loss of information, a re-regularization scheme has been developed which allows resampling without additional loss of information. For a typical ClONO2 profile retrieved from spectra as measured by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), the constrained retrieval has 9.7 degrees of freedom. After application of the proposed transformation to a coarser information-centered altitude grid, there are exactly 9 degrees of freedom left, and the averaging kernel on the coarse grid is unity. Pure resampling on the information-centered grid without re-regularization would reduce the degrees of freedom to 7.1 (6.7) for a staircase (triangular) representation scheme.

scholarly journals Retrieval of temperature profiles from CHAMP for climate monitoring: intercomparison with Envisat MIPAS and GOMOS and different atmospheric analyses

2007 ◽  
Vol 7 (13) ◽  
pp. 3519-3536 ◽  
Author(s):  
A. Gobiet ◽  
G. Kirchengast ◽  
G. L. Manney ◽  
M. Borsche ◽  
C. Retscher ◽  
...  
Keyword(s):  
High Altitude ◽  
Weather Prediction ◽  
A Priori ◽  
Michelson Interferometer ◽  
Altitude Range ◽  
A Priori Information ◽  
Climate Monitoring ◽  
Retrieval Scheme ◽  
Priori Information ◽  
Upper Boundary

Abstract. This study describes and evaluates a Global Navigation Satellite System (GNSS) radio occultation (RO) retrieval scheme particularly aimed at delivering bias-free atmospheric parameters for climate monitoring and research. The focus of the retrieval is on the sensible use of a priori information for careful high-altitude initialisation in order to maximise the usable altitude range. The RO retrieval scheme has been meanwhile applied to more than five years of data (September 2001 to present) from the German CHAllenging Minisatellite Payload for geoscientific research (CHAMP) satellite. In this study it was validated against various correlative datasets including the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) and the Global Ozone Monitoring for Occultation of Stars (GOMOS) sensors on Envisat, five different atmospheric analyses, and the operational CHAMP retrieval product from GeoForschungsZentrum (GFZ) Potsdam. In the global mean within 10 to 30 km altitude we find that the present validation observationally constrains the potential RO temperature bias to be <0.2 K. Latitudinally resolved analyses show biases to be observationally constrained to <0.2–0.5 K up to 35 km in most cases, and up to 30 km in any case, even if severely biased (about 10 K or more) a priori information is used in the high altitude initialisation of the retrieval. No evidence is found for the 10–35 km altitude range of residual RO bias sources other than those potentially propagated downward from initialisation, indicating that the widely quoted RO promise of "unbiasedness and long-term stability due to intrinsic self-calibration" can indeed be realised given care in the data processing to strictly limit structural uncertainty. The results thus reinforce that adequate high-altitude initialisation is crucial for accurate stratospheric RO retrievals. The common method of initialising, at some altitude in the upper stratosphere, the hydrostatic integral with an upper boundary temperature or pressure value derived from meteorological analyses is prone to introduce biases from the upper boundary down to below 25 km. Also above 30 to 35 km, GNSS RO delivers a considerable amount of observed information up to around 40 km, which is particularly interesting for numerical weather prediction (NWP) systems, where direct assimilation of non-initialised observed RO bending angles (free of a priori) is thus the method of choice. The results underline the value of RO for climate applications.

scholarly journals IASI-METOP and MIPAS-ENVISAT data fusion

2010 ◽  
Vol 10 (1) ◽  
pp. 183-211 ◽  
Author(s):  
S. Ceccherini ◽  
U. Cortesi ◽  
S. Del Bianco ◽  
P. Raspollini ◽  
B. Carli
Keyword(s):  
Data Fusion ◽  
Degrees Of Freedom ◽  
Solution Method ◽  
Information Gain ◽  
A Priori ◽  
A Priori Information ◽  
Priori Information ◽  
Single Instrument ◽  
Fusion Products ◽  
Temporal Coverage

Abstract. The combination of data obtained with different sensors (data fusion) is a powerful technique that can provide target products of the best quality in terms of precision and accuracy, as well as spatial and temporal coverage and resolution. In this paper the results are presented of the data fusion of measurements of ozone vertical profile performed by two space-borne interferometers (IASI on METOP and MIPAS on ENVISAT) using the new measurement-space-solution method. With this method both the loss of information due to interpolation and the propagation of possible biases (caused by a priori information) are avoided. The data fusion products are characterized by means of retrieval errors, information gain, averaging kernels and number of degrees of freedom. The analysis is performed both on simulated and real measurements and the results demonstrate and quantify the improvement of data fusion products with respect to measurements of a single instrument.

An optimal regularization method for convolution equations on the sourcewise represented set

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Ye Zhang ◽  
Dmitry V. Lukyanenko ◽  
Anatoly G. Yagola
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
A Priori ◽  
Noisy Data ◽  
Optimal Recovery ◽  
Multidimensional Case ◽  
A Priori Information ◽  
Ill Posed ◽  
Priori Information ◽  
Convolution Equations

AbstractIn this article, we consider an inverse problem for the integral equation of the convolution type in a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a priori information (sourcewise representation) based on optimal recovery theory we propose a new method. The regularization and optimization properties of this method are proved. An optimal minimal a priori error of the problem is found. Moreover, a so-called optimal regularized approximate solution and its corresponding error estimation are considered. Efficiency and applicability of this method are demonstrated in a numerical example of the image deblurring problem with noisy data.

scholarly journals Retrieval of temperature profiles from CHAMP for climate monitoring: intercomparison with Envisat MIPAS and GOMOS and different atmospheric analyses

2007 ◽  
Vol 7 (1) ◽  
pp. 3229-3268 ◽  
Author(s):  
A. Gobiet ◽  
G. Kirchengast ◽  
G. L. Manney ◽  
M. Borsche ◽  
C. Retscher ◽  
...  
Keyword(s):  
High Altitude ◽  
Weather Prediction ◽  
A Priori ◽  
Michelson Interferometer ◽  
Satellite System ◽  
Altitude Range ◽  
A Priori Information ◽  
Climate Monitoring ◽  
Retrieval Scheme ◽  
Priori Information

Abstract. This study describes and evaluates a Global Navigation Satellite System (GNSS) radio occultation (RO) retrieval scheme particularly aimed at delivering bias-free atmospheric parameters for climate monitoring and research. The focus of the retrieval is on the sensible use of a priori information for careful high-altitude initialisation in order to maximise the usable altitude range. The RO retrieval scheme has been meanwhile applied to more than five years of data (September 2001 to November 2006) from the German CHAllenging Minisatellite Payload for geoscientific research (CHAMP) satellite. In this study it was validated against various correlative datasets including the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) and the Global Ozone Monitoring for Occultation of Stars (GOMOS) sensors on Envisat, five different atmospheric analyses, and the operational CHAMP retrieval product from GeoForschungsZentrum (GFZ) Potsdam. In the global mean within 10 to 30 km altitude we find that the present validation observationally constrains the potential RO temperature bias to be <0.2 K. Latitudinally resolved analyses show biases to be observationally constrained to <0.2–0.5 K up to 35 km in most cases, and up to 30 km in any case, even if severely biased (about 10 K or more) a priori information is used in the high altitude initialisation of the retrieval. No evidence is found for the 10–35 km altitude range of RO bias sources other than those potentially propagated downward from initialisation, indicating that the widely quoted RO promise of "unbiasedness and long-term stability due to intrinsic self-calibration" can indeed be realized given care in the data processing to strictly limit structural uncertainty. The results demonstrate that an adequate high-altitude initialisation technique is crucial for accurate stratospheric RO retrievals and that still common methods of initialising the involved hydrostatic integral with an upper boundary temperature or pressure value derived from meteorological analyses is prone to introduce biases from the initialisation data to the retrieved temperatures down to below 25 km. Above 30 to 35 km, GNSS RO delivers a considerable amount of observed information up to around 40 km, which is particularly interesting for numerical weather prediction (NWP) systems, where direct assimilation of non-initialized (a priori-free) observed RO bending angles is thus the method of choice. The results underline the value of RO for climate applications.

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