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1. Introduction Knowledge regarding the three-dimensional variability of precipitation is essential in the development of precipitation retrieval algorithms from satellite radiometer observations. This is because satellite radiometer observations cannot be uniquely associated with precipitation, and statistical information is required to determine optimal precipitation estimates. Spaceborne radar observations may be used to derive such information. For example, it is anticipated that in the
1. Introduction Knowledge regarding the three-dimensional variability of precipitation is essential in the development of precipitation retrieval algorithms from satellite radiometer observations. This is because satellite radiometer observations cannot be uniquely associated with precipitation, and statistical information is required to determine optimal precipitation estimates. Spaceborne radar observations may be used to derive such information. For example, it is anticipated that in the
1. Introduction Algorithms that can extract properties of storm cells 1 and track those properties over time provide information that is important to forecasters in assessing storm intensity, growth, and decay ( Wilson et al. 1998 ). However, associating storm cells across frames of remotely sensed images poses a difficult problem because storms evolve, split, and merge. Because storm-tracking algorithms are a key component of nowcasting systems, the problem of how to track storms has received
1. Introduction Algorithms that can extract properties of storm cells 1 and track those properties over time provide information that is important to forecasters in assessing storm intensity, growth, and decay ( Wilson et al. 1998 ). However, associating storm cells across frames of remotely sensed images poses a difficult problem because storms evolve, split, and merge. Because storm-tracking algorithms are a key component of nowcasting systems, the problem of how to track storms has received
The GPM Combined Algorithmuniformly calibrated rain algorithms for all radiometers in the GPM constellation ( Kummerow et al. 2011 ). The constellation of radiometers provides the temporal sampling necessary to achieve the mission objective. During the Tropical Rainfall Measuring Mission (TRMM) era, several algorithms for estimating precipitation from a combination of radar and microwave radiometer observations were developed. The TRMM observatory included a single-frequency (Ku band) cross-track scanning radar and a
uniformly calibrated rain algorithms for all radiometers in the GPM constellation ( Kummerow et al. 2011 ). The constellation of radiometers provides the temporal sampling necessary to achieve the mission objective. During the Tropical Rainfall Measuring Mission (TRMM) era, several algorithms for estimating precipitation from a combination of radar and microwave radiometer observations were developed. The TRMM observatory included a single-frequency (Ku band) cross-track scanning radar and a
budgets, verification and data assimilation in general circulation model simulations, and hydrologic applications. The accumulated rainfall estimations are required for precipitation climatological research ( Huffman et al. 1997 ; Kidd 2001 ; Mark et al. 2001 ). The methods for estimating precipitation from satellite observations have been evolving and improving for decades. The early rain retrieval algorithms with satellite visible (VIS) and infrared (IR) measurements applied statistical regression
budgets, verification and data assimilation in general circulation model simulations, and hydrologic applications. The accumulated rainfall estimations are required for precipitation climatological research ( Huffman et al. 1997 ; Kidd 2001 ; Mark et al. 2001 ). The methods for estimating precipitation from satellite observations have been evolving and improving for decades. The early rain retrieval algorithms with satellite visible (VIS) and infrared (IR) measurements applied statistical regression
least squares framework for implementing most variants of ensemble filters that have been described in the literature. In this framework, it is possible to completely describe an ensemble filter by discussing only the impact of a single scalar observation on a single state variable. Several filters have been implemented using this framework in both idealized and large models ( Zhang et al. 2005 ). However, the sequential nature of the algorithm has led to concerns that it cannot be practically
least squares framework for implementing most variants of ensemble filters that have been described in the literature. In this framework, it is possible to completely describe an ensemble filter by discussing only the impact of a single scalar observation on a single state variable. Several filters have been implemented using this framework in both idealized and large models ( Zhang et al. 2005 ). However, the sequential nature of the algorithm has led to concerns that it cannot be practically
satisfied a suitable fluctuation–dissipation theorem (FDT), then climate response to small external forcing could be calculated by estimating suitable statistics in the present climate. For the general FDT, see Deker and Haake (1975) , Risken (1989) , and Majda et al. (2005 , hereafter MAG05) . The topic of this paper is the use of a new algorithm ( Abramov and Majda 2007 , 2008 , hereafter AM07 , AM08 ) for calculating the FDT response to address the above issues in a prototype setting for the
satisfied a suitable fluctuation–dissipation theorem (FDT), then climate response to small external forcing could be calculated by estimating suitable statistics in the present climate. For the general FDT, see Deker and Haake (1975) , Risken (1989) , and Majda et al. (2005 , hereafter MAG05) . The topic of this paper is the use of a new algorithm ( Abramov and Majda 2007 , 2008 , hereafter AM07 , AM08 ) for calculating the FDT response to address the above issues in a prototype setting for the
) measurements of reflected and earth-emitted radiation in three broadband channels: a shortwave (SW) channel (0.2–5.0 μ m), a total channel (from 0.2 to >100 μ m), and a thermal infrared (IR) window channel (8–12 μ m). An extensive modeling effort is subsequently used with TOA measurements for deriving surface SW and longwave (LW) fluxes and corresponding flux profiles at multiple levels in the atmosphere. The three LW algorithms discussed in this study are part of the surface-only flux algorithms (SOFA
) measurements of reflected and earth-emitted radiation in three broadband channels: a shortwave (SW) channel (0.2–5.0 μ m), a total channel (from 0.2 to >100 μ m), and a thermal infrared (IR) window channel (8–12 μ m). An extensive modeling effort is subsequently used with TOA measurements for deriving surface SW and longwave (LW) fluxes and corresponding flux profiles at multiple levels in the atmosphere. The three LW algorithms discussed in this study are part of the surface-only flux algorithms (SOFA
maximum wind (RMW), and the center location of a TC from Doppler radar data, and could be applied in an operational environment. However, it was highly affected by the asymmetry of circulations and strong mean flows across the vortex. Marks et al. (1992) used the “simplex” algorithm ( Nelder and Mead 1965 ) to find the center that maximizes the tangential circulations encompassing the observed RMW at different altitudes. They found that the center was 3–6 km to the right of that determined
maximum wind (RMW), and the center location of a TC from Doppler radar data, and could be applied in an operational environment. However, it was highly affected by the asymmetry of circulations and strong mean flows across the vortex. Marks et al. (1992) used the “simplex” algorithm ( Nelder and Mead 1965 ) to find the center that maximizes the tangential circulations encompassing the observed RMW at different altitudes. They found that the center was 3–6 km to the right of that determined
the global community, but to the authors’ best knowledge, no detailed information about the algorithm has been published in English. The major weakness of algorithms that use a combination of visual and IR channels for snow detection is that they can be used only during daytime and in cloud-free conditions. The high temporal resolution of the instruments on board a geostationary satellite helps to mitigate this to some extent, as it is much more likely that, for a certain area during one day, at
the global community, but to the authors’ best knowledge, no detailed information about the algorithm has been published in English. The major weakness of algorithms that use a combination of visual and IR channels for snow detection is that they can be used only during daytime and in cloud-free conditions. The high temporal resolution of the instruments on board a geostationary satellite helps to mitigate this to some extent, as it is much more likely that, for a certain area during one day, at
summarized first in section 2 with the state-of-the-art Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) algorithm as an example. Then, the new estimator is described in section 3 to deal with wrapped phases, and an adaptive algorithm for its implementation is developed in section 4 . Its application to radar observations from CSU–CHILL S-band radar and the Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) Integrated Project 1 (IP1) X
summarized first in section 2 with the state-of-the-art Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) algorithm as an example. Then, the new estimator is described in section 3 to deal with wrapped phases, and an adaptive algorithm for its implementation is developed in section 4 . Its application to radar observations from CSU–CHILL S-band radar and the Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) Integrated Project 1 (IP1) X
