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NASA NTRSDate not supplied

CERES ERBE-like Monthly Geographical Averages (ES-4) in HDF (CER_ES4_Terra-FM1_Edition1-CV)

The ERBE-like Monthly Geographical Averages (ES-4) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-4 is also produced for combinations of scanner instruments. For each observed 2.5-degree spatial region, the daily average, the hourly average over the month, and the overall monthly average of shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-9 product are spatially nested up from 2.5-degree regions to 5- and 10-degree regions, to 2.5-, 5-, and 10-degree zonal averages, and to global monthly averages. For each nested area, the albedo and net flux are given. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The following CERES ES4 data sets are currently available: CER_ES4_FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition2 CER_ES4_PFM+FM1_Edition1 CER_ES4_PFM+FM2_Edition1 CER_ES4_TRMM-PFM_Edition1 CER_ES4_TRMM-PFM_Edition2 CER_ES4_Terra-FM1_Edition1 CER_ES4_Terra-FM2_Edition1 CER_ES4_FM1+FM2_Edition2 CER_ES4_Terra-FM1_Edition2 CER_ES4_Terra-FM2_Edition2 CER_ES4_Aqua-FM3_Edition1 CER_ES4_Aqua-FM4_Edition1 CER_ES4_FM1+FM2+FM3+FM4_Edition1 CER_ES4_Aqua-FM3_Edition2 CER_ES4_Aqua-FM4_Edition2 CER_ES4_FM1+FM3_Edition2 CER_ES4_FM1+FM4_Edition2 CER_ES4_PFM+FM1_Edition2 CER_ES4_PFM+FM2_Edition2 CER_ES4_Aqua-FM3_Edition1-CV CER_ES4_Aqua-FM4_Edition1-CV CER_ES4_Terra-FM1_Edition1-CV CER_ES4_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2006-09-30] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].

GEOGRAPHIC SCENE TYPE↗
NASA NTRSDate not supplied

CERES ERBE-like Monthly Geographical Averages (ES-4) in HDF (CER_ES4_Terra-FM2_Edition1-CV)

The ERBE-like Monthly Geographical Averages (ES-4) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-4 is also produced for combinations of scanner instruments. For each observed 2.5-degree spatial region, the daily average, the hourly average over the month, and the overall monthly average of shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-9 product are spatially nested up from 2.5-degree regions to 5- and 10-degree regions, to 2.5-, 5-, and 10-degree zonal averages, and to global monthly averages. For each nested area, the albedo and net flux are given. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The following CERES ES4 data sets are currently available: CER_ES4_FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition2 CER_ES4_PFM+FM1_Edition1 CER_ES4_PFM+FM2_Edition1 CER_ES4_TRMM-PFM_Edition1 CER_ES4_TRMM-PFM_Edition2 CER_ES4_Terra-FM1_Edition1 CER_ES4_Terra-FM2_Edition1 CER_ES4_FM1+FM2_Edition2 CER_ES4_Terra-FM1_Edition2 CER_ES4_Terra-FM2_Edition2 CER_ES4_Aqua-FM3_Edition1 CER_ES4_Aqua-FM4_Edition1 CER_ES4_FM1+FM2+FM3+FM4_Edition1 CER_ES4_Aqua-FM3_Edition2 CER_ES4_Aqua-FM4_Edition2 CER_ES4_FM1+FM3_Edition2 CER_ES4_FM1+FM4_Edition2 CER_ES4_PFM+FM1_Edition2 CER_ES4_PFM+FM2_Edition2 CER_ES4_Aqua-FM3_Edition1-CV CER_ES4_Aqua-FM4_Edition1-CV CER_ES4_Terra-FM1_Edition1-CV CER_ES4_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2006-10-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].

SOLAR INCIDENCE↗
NASA NTRSDate not supplied

CERES ERBE-like Monthly Geographical Averages (ES-4) in HDF (CER_ES4_Aqua-FM3_Edition1-CV)

The ERBE-like Monthly Geographical Averages (ES-4) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-4 is also produced for combinations of scanner instruments. For each observed 2.5-degree spatial region, the daily average, the hourly average over the month, and the overall monthly average of shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-9 product are spatially nested up from 2.5-degree regions to 5- and 10-degree regions, to 2.5-, 5-, and 10-degree zonal averages, and to global monthly averages. For each nested area, the albedo and net flux are given. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The following CERES ES4 data sets are currently available: CER_ES4_FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition2 CER_ES4_PFM+FM1_Edition1 CER_ES4_PFM+FM2_Edition1 CER_ES4_TRMM-PFM_Edition1 CER_ES4_TRMM-PFM_Edition2 CER_ES4_Terra-FM1_Edition1 CER_ES4_Terra-FM2_Edition1 CER_ES4_FM1+FM2_Edition2 CER_ES4_Terra-FM1_Edition2 CER_ES4_Terra-FM2_Edition2 CER_ES4_Aqua-FM3_Edition1 CER_ES4_Aqua-FM4_Edition1 CER_ES4_FM1+FM2+FM3+FM4_Edition1 CER_ES4_Aqua-FM3_Edition2 CER_ES4_Aqua-FM4_Edition2 CER_ES4_FM1+FM3_Edition2 CER_ES4_FM1+FM4_Edition2 CER_ES4_PFM+FM1_Edition2 CER_ES4_PFM+FM2_Edition2 CER_ES4_Aqua-FM3_Edition1-CV CER_ES4_Aqua-FM4_Edition1-CV CER_ES4_Terra-FM1_Edition1-CV CER_ES4_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2006-10-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].

NET FLUX↗
NASA NTRSDate not supplied

CERES ERBE-like Monthly Geographical Averages (ES-4) in HDF (CER_ES4_Aqua-FM4_Edition1-CV)

The ERBE-like Monthly Geographical Averages (ES-4) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-4 is also produced for combinations of scanner instruments. For each observed 2.5-degree spatial region, the daily average, the hourly average over the month, and the overall monthly average of shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-9 product are spatially nested up from 2.5-degree regions to 5- and 10-degree regions, to 2.5-, 5-, and 10-degree zonal averages, and to global monthly averages. For each nested area, the albedo and net flux are given. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The following CERES ES4 data sets are currently available: CER_ES4_FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition2 CER_ES4_PFM+FM1_Edition1 CER_ES4_PFM+FM2_Edition1 CER_ES4_TRMM-PFM_Edition1 CER_ES4_TRMM-PFM_Edition2 CER_ES4_Terra-FM1_Edition1 CER_ES4_Terra-FM2_Edition1 CER_ES4_FM1+FM2_Edition2 CER_ES4_Terra-FM1_Edition2 CER_ES4_Terra-FM2_Edition2 CER_ES4_Aqua-FM3_Edition1 CER_ES4_Aqua-FM4_Edition1 CER_ES4_FM1+FM2+FM3+FM4_Edition1 CER_ES4_Aqua-FM3_Edition2 CER_ES4_Aqua-FM4_Edition2 CER_ES4_FM1+FM3_Edition2 CER_ES4_FM1+FM4_Edition2 CER_ES4_PFM+FM1_Edition2 CER_ES4_PFM+FM2_Edition2 CER_ES4_Aqua-FM3_Edition1-CV CER_ES4_Aqua-FM4_Edition1-CV CER_ES4_Terra-FM1_Edition1-CV CER_ES4_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2005-03-29] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].

CLEAR-SKY SHORTWAVE FLUX↗
NASA NTRS2009

Hybrid Reynolds-Averaged/Large-Eddy Simulations of a Co-Axial Supersonic Free-Jet Experiment

Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment utilized either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Mach 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state-of-the-art for each modeling approach, and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The baseline value chosen for this parameter resulted in an over-prediction of the mixing layer spreading rate for the helium case, but the opposite trend was noted when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid simulation results showed the same trends as the baseline Reynolds-averaged predictions. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds-averaged state to one with resolved turbulent content. Improvements to the inflow conditions are suggested as a remedy to this dilemma. Comparisons between resolved second-order turbulence statistics and their modeled Reynolds-averaged counterparts were also performed.

Baurle, R. A.↗
NASA NTRS2010

Hybrid Reynolds-Averaged/Large-Eddy Simulations of a Coaxial Supersonic Free-Jet Experiment

Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment was designed to study compressible mixing flow phenomenon under conditions that are representative of those encountered in scramjet combustors. The experiment utilized either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Mach 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state-of-the-art for each modeling approach, and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The initial value chosen for this parameter resulted in an over-prediction of the mixing layer spreading rate for the helium case, but the opposite trend was observed when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid Reynolds-averaged/large-eddy simulations also over-predicted the mixing layer spreading rate for the helium case, while under-predicting the rate of mixing when argon was used as the injectant. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds-averaged state to one with resolved turbulent content. Improvements to the inflow conditions were suggested as a remedy to this dilemma. Second-order turbulence statistics were also compared to their modeled Reynolds-averaged counterparts to evaluate the effectiveness of common turbulence closure assumptions.

Baurle, Robert A.↗
NASA NTRS2012

Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows

In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.

Shih, Tsan-Hsing↗
NASA NTRS2015

Hybrid Reynolds-Averaged/Large Eddy Simulation of a Cavity Flameholder; Assessment of Modeling Sensitivities

Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. The cases simulated corresponded to those used to examine this flowfield experimentally using particle image velocimetry. A variety of turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged / large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This effort was undertaken to formally assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community. The numerical errors were quantified for both the steady-state and scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results showed a high degree of variability when comparing the predictions obtained from each turbulence model, with the non-linear eddy viscosity model (an explicit algebraic stress model) providing the most accurate prediction of the measured values. The hybrid Reynolds-averaged/large eddy simulation results were carefully scrutinized to ensure that even the coarsest grid had an acceptable level of resolution for large eddy simulation, and that the time-averaged statistics were acceptably accurate. The autocorrelation and its Fourier transform were the primary tools used for this assessment. The statistics extracted from the hybrid simulation strategy proved to be more accurate than the Reynolds-averaged results obtained using the linear eddy viscosity models. However, there was no predictive improvement noted over the results obtained from the explicit Reynolds stress model. Fortunately, the numerical error assessment at most of the axial stations used to compare with measurements clearly indicated that the scale-resolving simulations were improving (i.e. approaching the measured values) as the grid was refined. Hence, unlike a Reynolds-averaged simulation, the hybrid approach provides a mechanism to the end-user for reducing model-form errors.

Baurle, R. A.↗
NASA NTRS1991

Estimation of time averages from irregularly spaced observations - With application to coastal zone color scanner estimates of chlorophyll concentration

The sampling error of an arbitrary linear estimate of a time-averaged quantity constructed from a time series of irregularly spaced observations at a fixed located is quantified through a formalism. The method is applied to satellite observations of chlorophyll from the coastal zone color scanner. The two specific linear estimates under consideration are the composite average formed from the simple average of all observations within the averaging period and the optimal estimate formed by minimizing the mean squared error of the temporal average based on all the observations in the time series. The resulting suboptimal estimates are shown to be more accurate than composite averages. Suboptimal estimates are also found to be nearly as accurate as optimal estimates using the correct signal and measurement error variances and correlation functions for realistic ranges of these parameters, which makes it a viable practical alternative to the composite average method generally employed at present.

Chelton, Dudley B.↗
NASA NTRS1993

Programmable noise bandwidth reduction by means of digital averaging

Predetection noise bandwidth reduction is effected by a pre-averager capable of digitally averaging the samples of an input data signal over two or more symbols, the averaging interval being defined by the input sampling rate divided by the output sampling rate. As the averaged sample is clocked to a suitable detector at a much slower rate than the input signal sampling rate the noise bandwidth at the input to the detector is reduced, the input to the detector having an improved signal to noise ratio as a result of the averaging process, and the rate at which such subsequent processing must operate is correspondingly reduced. The pre-averager forms a data filter having an output sampling rate of one sample per symbol of received data. More specifically, selected ones of a plurality of samples accumulated over two or more symbol intervals are output in response to clock signals at a rate of one sample per symbol interval. The pre-averager includes circuitry for weighting digitized signal samples using stored finite impulse response (FIR) filter coefficients. A method according to the present invention is also disclosed.

Poklemba, John J.↗
NASA NTRS2016

Hybrid Reynolds-Averaged/Large Eddy Simulation of the Flow in a Model SCRamjet Cavity Flameholder

Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. Experimental data available for this configuration include velocity statistics obtained from particle image velocimetry. Several turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged/large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This e ort was undertaken to not only assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community, but to also begin to understand how this capability can best be used to augment standard Reynolds-averaged simulations. The numerical errors were quantified for the steady-state simulations, and at least qualitatively assessed for the scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results displayed a high degree of variability when comparing the flameholder fuel distributions obtained from each turbulence model. This prompted the consideration of applying the higher-fidelity scale-resolving simulations as a surrogate "truth" model to calibrate the Reynolds-averaged closures in a non-reacting setting prior to their use for the combusting simulations. In general, the Reynolds-averaged velocity profile predictions at the lowest fueling level matched the particle imaging measurements almost as well as was observed for the non-reacting condition. However, the velocity field predictions proved to be more sensitive to the flameholder fueling rate than was indicated in the measurements.

Baurle, R. A.↗
NASA NTRS2020

Assessing the Impacts of Two Averaging Methods on AIRS Level 3 Monthly Products and Multi-Year Monthly Means

The Atmospheric Infrared Sounder (AIRS) onboard NASA’s Aqua satellite provides more than 16 years of data. Its monthly gridded (Level 3) product has been widely used for climate research and applications. Since counts of successful soundings in a grid cell are used to derive monthly averages, this “Averaged By Observations (ABO)” approach effectively gives equal importance to all participating soundings within a month. It is conceivable, then, that days with more observations due to day-to-day orbit shift and regimes with better retrieval skills, will contribute disproportionately to the monthly average within a cell. Alternatively, the AIRS Level 3 monthly product can be produced through an "Averaged By Days (ABD)” approach, where the monthly mean in a grid cell is a simple average of the daily means. The effects of these averaging methods on the AIRS version 6 monthly product are assessed quantitatively using temperature and water vapor at surface and 500hPa. The ABO method results in a warmer (slightly colder) global mean temperature at surface (500hPa) and a drier global mean water vapor than ABD method. The AIRS multi-year monthly mean temperature and water vapor from both methods are also compared with the Modern-Era Retrospective analysis for Research and Applications – 2 (MERRA-2) product and evaluated with a simulation experiment, indicating the ABD method has less error and is more closely correlated with MERRA-2. In summary, the ABD method is recommended for future versions of the AIRS Level 3 monthly product and more data services supporting Level 3 aggregation are needed.

AIRS↗
NASA NTRS1977

Instrument to average 100 data sets

An instrumentation system is currently under development which will measure many of the important parameters associated with the operation of an internal combustion engine. Some of these parameters include mass-fraction burn rate, ignition energy, and the indicated mean effective pressure. One of the characteristics of an internal combustion engine is the cycle-to-cycle variation of these parameters. A curve-averaging instrument has been produced which will generate the average curve, over 100 cycles, of any engine parameter. the average curve is described by 2048 discrete points which are displayed on an oscilloscope screen to facilitate recording and is available in real time. Input can be any parameter which is expressed as a + or - 10-volt signal. Operation of the curve-averaging instrument is defined between 100 and 6000 rpm. Provisions have also been made for averaging as many as four parameters simultaneously, with a subsequent decrease in resolution. This provides the means to correlate and perhaps interrelate the phenomena occurring in an internal combustion engine. This instrument has been used successfully on a 1975 Chevrolet V8 engine, and on a Continental 6-cylinder aircraft engine. While this instrument was designed for use on an internal combustion engine, with some modification it can be used to average any cyclically varying waveform.

Tuma, G. B.↗
NASA NTRS1993

Average-cost based robust structural control

A method is presented for the synthesis of robust controllers for linear time invariant structural systems with parameterized uncertainty. The method involves minimizing quantities related to the quadratic cost (H2-norm) averaged over a set of systems described by real parameters such as natural frequencies and modal residues. Bounded average cost is shown to imply stability over the set of systems. Approximations for the exact average are derived and proposed as cost functionals. The properties of these approximate average cost functionals are established. The exact average and approximate average cost functionals are used to derive dynamic controllers which can provide stability robustness. The robustness properties of these controllers are demonstrated in illustrative numerical examples and tested in a simple SISO experiment on the MIT multi-point alignment testbed.

Hagood, Nesbitt W.↗
NASA NTRS2003

A Stochastic Model of Space-Time Variability of Mesoscale Rainfall: Statistics of Spatial Averages

A characteristic feature of rainfall statistics is that they depend on the space and time scales over which rain data are averaged. A previously developed spectral model of rain statistics that is designed to capture this property, predicts power law scaling behavior for the second moment statistics of area-averaged rain rate on the averaging length scale L as L right arrow 0. In the present work a more efficient method of estimating the model parameters is presented, and used to fit the model to the statistics of area-averaged rain rate derived from gridded radar precipitation data from TOGA COARE. Statistical properties of the data and the model predictions are compared over a wide range of averaging scales. An extension of the spectral model scaling relations to describe the dependence of the average fraction of grid boxes within an area containing nonzero rain (the "rainy area fraction") on the grid scale L is also explored.

Kundu, Prasun K.↗
NASA NTRSDate not supplied

CERES ERBE-like Monthly Regional Averages (ES-9) in HDF (CER_ES9_TRMM-PFM_Edition1)

The ERBE-like Monthly Regional Averages (ES-9) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-9 is also produced for combinations of scanner instruments. All instantaneous shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-8 product for a month are sorted by 2.5-degree spatial regions, by day number, and by the local hour of observation. The mean of the instantaneous fluxes for a given region-day-hour bin is determined and recorded on the ES-9 along with other flux statistics and scene information. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The ES-9 also contains hourly average fluxes for the month and an overall monthly average for each region. These average fluxes are given for both clear-sky and total-sky scenes. The following CERES ES9 data sets are currently available: CER_ES9_FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition2 CER_ES9_PFM+FM1_Edition1 CER_ES9_PFM+FM2_Edition1 CER_ES9_PFM+FM1_Edition2 CER_ES9_PFM+FM2_Edition2 CER_ES9_TRMM-PFM_Edition1 CER_ES9_TRMM-PFM_Edition2 CER_ES9_Terra-FM1_Edition1 CER_ES9_Terra-FM2_Edition1 CER_ES9_FM1+FM2_Edition2 CER_ES9_Terra-FM1_Edition2 CER_ES9_Terra-FM2_Edition2 CER_ES9_Aqua-FM3_Edition1 CER_ES9_Aqua-FM4_Edition1 CER_ES9_FM1+FM2+FM3+FM4_Edition1 CER_ES9_Aqua-FM3_Edition2 CER_ES9_Aqua-FM4_Edition2 CER_ES9_FM1+FM3_Edition2 CER_ES9_FM1+FM4_Edition2 CER_ES9_Aqua-FM3_Edition1-CV CER_ES9_Aqua-FM4_Edition1-CV CER_ES9_Terra-FM1_Edition1-CV CER_ES9_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=1998-08-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=hourly, daily, monthly; Temporal_Resolution_Range=Hourly - < Daily, Daily - < Weekly, Monthly - < Annual].

CLEAR-SKY ALBEDO↗
NASA NTRSDate not supplied

CERES ERBE-like Monthly Regional Averages (ES-9) in HDF (CER_ES9_TRMM-PFM_Edition2)

The ERBE-like Monthly Regional Averages (ES-9) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-9 is also produced for combinations of scanner instruments. All instantaneous shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-8 product for a month are sorted by 2.5-degree spatial regions, by day number, and by the local hour of observation. The mean of the instantaneous fluxes for a given region-day-hour bin is determined and recorded on the ES-9 along with other flux statistics and scene information. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The ES-9 also contains hourly average fluxes for the month and an overall monthly average for each region. These average fluxes are given for both clear-sky and total-sky scenes. The following CERES ES9 data sets are currently available: CER_ES9_FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition2 CER_ES9_PFM+FM1_Edition1 CER_ES9_PFM+FM2_Edition1 CER_ES9_PFM+FM1_Edition2 CER_ES9_PFM+FM2_Edition2 CER_ES9_TRMM-PFM_Edition1 CER_ES9_TRMM-PFM_Edition2 CER_ES9_Terra-FM1_Edition1 CER_ES9_Terra-FM2_Edition1 CER_ES9_FM1+FM2_Edition2 CER_ES9_Terra-FM1_Edition2 CER_ES9_Terra-FM2_Edition2 CER_ES9_Aqua-FM3_Edition1 CER_ES9_Aqua-FM4_Edition1 CER_ES9_FM1+FM2+FM3+FM4_Edition1 CER_ES9_Aqua-FM3_Edition2 CER_ES9_Aqua-FM4_Edition2 CER_ES9_FM1+FM3_Edition2 CER_ES9_FM1+FM4_Edition2 CER_ES9_Aqua-FM3_Edition1-CV CER_ES9_Aqua-FM4_Edition1-CV CER_ES9_Terra-FM1_Edition1-CV CER_ES9_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2000-03-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=hourly, daily, monthly; Temporal_Resolution_Range=Hourly - < Daily, Daily - < Weekly, Monthly - < Annual].

CLEAR-SKY SHORTWAVE FLUX↗
NASA NTRSDate not supplied

CERES ERBE-like Monthly Regional Averages (ES-9) in HDF (CER_ES9_Terra-FM1_Edition1)

The ERBE-like Monthly Regional Averages (ES-9) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-9 is also produced for combinations of scanner instruments. All instantaneous shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-8 product for a month are sorted by 2.5-degree spatial regions, by day number, and by the local hour of observation. The mean of the instantaneous fluxes for a given region-day-hour bin is determined and recorded on the ES-9 along with other flux statistics and scene information. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The ES-9 also contains hourly average fluxes for the month and an overall monthly average for each region. These average fluxes are given for both clear-sky and total-sky scenes. The following CERES ES9 data sets are currently available: CER_ES9_FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition2 CER_ES9_PFM+FM1_Edition1 CER_ES9_PFM+FM2_Edition1 CER_ES9_PFM+FM1_Edition2 CER_ES9_PFM+FM2_Edition2 CER_ES9_TRMM-PFM_Edition1 CER_ES9_TRMM-PFM_Edition2 CER_ES9_Terra-FM1_Edition1 CER_ES9_Terra-FM2_Edition1 CER_ES9_FM1+FM2_Edition2 CER_ES9_Terra-FM1_Edition2 CER_ES9_Terra-FM2_Edition2 CER_ES9_Aqua-FM3_Edition1 CER_ES9_Aqua-FM4_Edition1 CER_ES9_FM1+FM2+FM3+FM4_Edition1 CER_ES9_Aqua-FM3_Edition2 CER_ES9_Aqua-FM4_Edition2 CER_ES9_FM1+FM3_Edition2 CER_ES9_FM1+FM4_Edition2 CER_ES9_Aqua-FM3_Edition1-CV CER_ES9_Aqua-FM4_Edition1-CV CER_ES9_Terra-FM1_Edition1-CV CER_ES9_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2005-10-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=hourly, daily, monthly; Temporal_Resolution_Range=Hourly - < Daily, Daily - < Weekly, Monthly - < Annual].

LONGWAVE FLUX↗