SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Aggregation formulas are given for production estimation of a crop type for a zone, a region, and a country, and methods for estimating yield prediction errors for the three areas are described. A procedure is included for obtaining a combined yield prediction and its mean-squared error estimate for a mixed wheat pseudozone.
Aerosol optical depth (AOD), an indirect estimate of particle matter using satellite observations, has shown great promise in improving estimates of PM 2.5 air quality surface. Currently, few studies have been conducted to explore the optimal way to apply AOD data to improve the model accuracy of PM 2.5 surface estimation in a real-time air quality system. We believe that two major aspects may be worthy of consideration in that area: 1) the approach to integrate satellite measurements with ground measurements in the pollution estimation, and 2) identification of an optimal temporal scale to calculate the correlation of AOD and ground measurements. This paper is focused on the second aspect on the identifying the optimal temporal scale to correlate AOD with PM2.5. Five following different temporal scales were chosen to evaluate their impact on the model performance: 1) within the last 3 days, 2) within the last 10 days, 3) within the last 30 days, 4) within the last 90 days, and 5) the time period with the highest correlation in a year. The model performance is evaluated for its accuracy, bias, and errors based on the following selected statistics: the Mean Bias, the Normalized Mean Bias, the Root Mean Square Error, Normalized Mean Error, and the Index of Agreement. This research shows that the model with the temporal scale of within the last 30 days displays the best model performance in this study area using 2004 and 2005 data sets.
Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEP fixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEP uncertain( X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEP uncertain (X) can be estimated using a random effects ANOVA. It is argued that MSEP uncertain (X) is the more informative uncertainty criterion, because it is specific to each prediction situation.
In this paper both a microwave attenuation measurement along a horizontal line and multiple point gauge measurements are analyzed as possible ground-truth designs to validate satellite precipitation retrieval algorithms at the field of view spatial level (typically about 20 km). The design consists of comparing a sequence of pairs of contemporaneous measurements taken from the ground and from space. The authors examine theoretically the variance of expected differences between the two systems. The line average measurement leads to a smaller mean-square error compared to the case of a single point gauge, since some of the small-scale variability of the rain field is smoothed away by the line integration. The multiple point gauge measurements also give smaller mean-square error than that of a single point gauge. The centroid of the line and point gauge configurations are considered to be located randomly inside the field of view for different overpasses. A space-time spectral formalism is used with a noise-forced diffusive rain field to find the mean-square error. By considering instantaneous ground and satellite measurement pairs over about 50 visits when raining, we can reduce the expected error to approximately 10% of the standard deviation of climatological variability. This is considered to be a useful level of tolerance for identifying biases in the retrieval algorithms. It is found that the multiple point gauges (especially two gauges) are the economical ground-truth design compared to the microwave attenuation based on the mean-square error comparison. The major finding of this study is that a significant improvement over the point gauge is obtained by adding a single additional piece of information; adding more gauges or extending the line of attenuation is not an important improvement.
Aerosol optical depth (AOD) has become a crucial metric for assessing global climate change. Although global and regional AOD trends have been studied extensively, it remains unclear what factors are driving the inter-decadal variations in regional AOD and how to quantify the relative contribution of each dominant factor. This study used a long-term (1980–2016) aerosol dataset from the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2) reanalysis, along with two satellite-based AOD datasets (MODIS/Terra and MISR) from 2001 to 2016, to investigate the long-term trends in global and regional aerosol loading. Statistical models based on emission factors and meteorological parameters were developed to identify the main factors driving the inter-decadal changes of regional AOD and to quantify their contribution. Evaluation of the MERRA-2 AOD with the ground-based measurements of AERONET indicated significant spatial agreement on the global scale (r= 0.85, root-mean-square error = 0.12, mean fractional error = 38.7 %, fractional gross error = 9.86 % and index of agreement = 0.94). However, when AOD observations from the China Aerosol Remote Sensing Network (CARSNET) were employed for independent verification, the results showed that MERRA-2 AODs generally underestimated CARSNET AODs in China (relative mean bias = 0.72 and fractional gross error =−34.3 %). In general, MERRA-2 was able to quantitatively reproduce the annual and seasonal AOD trends on both regional and global scales, as observed by MODIS/Terra, although some differences were found when compared to MISR. Over the 37-year period in this study, significant decreasing trends were observed over Europe and the eastern United States. In contrast, eastern China and southern Asia showed AOD increases, but the increasing trend of the former reversed sharply in the most recent decade. The statistical analyses suggested that the meteorological parameters explained a larger proportion of the AOD variability (20.4 %–72.8 %) over almost all regions of interest (ROIs) during 1980–2014 when compared with emission factors (0 %–56 %). Further analysis also showed that SO2 was the dominant emission factor, explaining 12.7 %–32.6 % of the variation in AOD over anthropogenic-aerosol-dominant regions, while black carbon or organic carbon was the leading factor over the biomass-burning-dominant (BBD) regions, contributing 24.0 %–27.7 % of the variation. Additionally, wind speed was found to be the leading meteorological parameter, explaining 11.8 %–30.3 % of the variance over the mineral-dust-dominant regions, while ambient humidity (including soil moisture and relative humidity) was the top meteorological parameter over the BBD regions, accounting for 11.7 %–35.5 % of the variation. The results of this study indicate that the variation in meteorological parameters is a key factor in determining the inter-decadal change in regional AOD.
This second paper of the two-part series focuses on demonstrating the impact of assimilating satellite-based snow cover and freeze/thaw observations into the hyper-resolution, offline terrestrial modeling system used for the High Mountain Asia (HMA) region from 2003 to 2016. To this end, this study systematically evaluates a total of six sets of 0.01° (∼1 km) model simulations forced by different precipitation forcings, with and without the dual assimilation scheme enabled, at point-scale, basin-scale, and domain-scale. The key variables of interest include surface net shortwave radiation, surface net longwave radiation, skin temperature, near-surface soil temperature, snow depth, snow water equivalent (SWE), and total runoff. First, the point-scale assessment is mainly conducted via evaluating against ground-based measurements. In general, the assimilation enabled estimates are better than no-assimilation counterparts. Second, the basin-scale runoff assessment demonstrates that across three snow-dominated basins, the assimilation enabled experiment yields systematic improvements in all goodness-of-fit statistics through mitigating the negative effects brought by the fixed long-term precipitation correction factors. For example, when forced by the bias-corrected precipitation, the assimilation-enabled experiment improves the bias by 69%, the root-mean-squared error by 30%, and the unbiased root-mean-squared error by 18% (relative to the no-assimilation counterpart). Finally, the domainscale assessment is conducted via evaluating against satellite-based SWE and skin temperature products. Both sets of domain-scale analysis further corroborate the findings in the point-scale evaluations. Overall, this study suggests the benefits of the proposed multi-variate assimilation system in improving the cryospherichydrological process within a land surface model for use in HMA.
This second paper of the two-part series focuses on demonstrating the impact of assimilating satellite-based snow cover and freeze/thaw observations into the hyper-resolution, offline terrestrial modeling system used for the High Mountain Asia (HMA) region from 2003 to 2016. To this end, this study systematically evaluates a total of six sets of 0.01° (∼1 km) model simulations forced by different precipitation forcings, with and without the dual assimilation scheme enabled, at point-scale, basin-scale, and domain-scale. The key variables of interest include surface net shortwave radiation, surface net longwave radiation, skin temperature, near-surface soil temperature, snow depth, snow water equivalent (SWE), and total runoff. First, the point-scale assessment is mainly conducted via evaluating against ground-based measurements. In general, the assimilation enabled estimates are better than no-assimilation counterparts. Second, the basin-scale runoff assessment demonstrates that across three snow-dominated basins, the assimilation enabled experiment yields systematic improvements in all goodness-of-fit statistics through mitigating the negative effects brought by the fixed long-term precipitation correction factors. For example, when forced by the bias-corrected precipitation, the assimilation-enabled experiment improves the bias by 69%, the root-mean-squared error by 30%, and the unbiased root-mean-squared error by 18% (relative to the no-assimilation counterpart). Finally, the domain-scale assessment is conducted via evaluating against satellite-based SWE and skin temperature products. Both sets of domain-scale analysis further corroborate the findings in the point-scale evaluations. Overall, this study suggests the benefits of the proposed multi-variate assimilation system in improving the cryospheric-hydrological process within a land surface model for use in HMA.
Performance assessment of ocean color satellite data has generally relied on statistical metrics chosen for their common usage and the rationale for selecting certain metrics is infrequently explained. Commonly reported statistics based on mean squared errors, such as the coefficient of determination (r2), root mean square error, and regression slopes, are most appropriate for Gaussian distributions without outliers and, therefore, are often not ideal for ocean color algorithm performance assessment, which is often limited by sample availability. In contrast, metrics based on simple deviations, such as bias and mean absolute error, as well as pair-wise comparisons, often provide more robust and straightforward quantities for evaluating ocean color algorithms with non-Gaussian distributions and outliers. This study uses a SeaWiFS chlorophyll-a validation data set to demonstrate a framework for satellite data product assessment and recommends a multimetric and user-dependent approach that can be applied within science, modeling, and resource management communities.
Methods developed for image quality metrics are reviewed with focus on basic interpretation or recognition elements including: tone or color; shape; pattern; size; shadow; texture; site; association or context; and resolution. Seven metrics are believed to show promise as a way of characterizing the quality of an image: (1) the dynamic range of intensities in the displayed image; (2) the system signal-to-noise ratio; (3) the system spatial bandwidth or bandpass; (4) the system resolution or acutance; (5) the normalized-mean-square-error as a measure of geometric fidelity; (6) the perceptual mean square error; and (7) the radar threshold quality factor. Selective levels of degradation are being applied to simulated synthetic radar images to test the validity of these metrics.
L-band brightness temperature (T(sub b)) is one of the key remotely-sensed variables that provides information regarding surface soil moisture conditions. In order to harness the information in T(sub b) observations, a radiative transfer model (RTM) is investigated for eventual inclusion into a data assimilation framework. In this study, T(sub b) estimates from the RTM implemented in the NASA Goddard Earth Observing System (GEOS) were evaluated against the nearly four-year record of daily T(sub b) observations collected by L-band radiometers onboard the Aquarius satellite. Statistics between the modeled and observed T(sub b) were computed over North America as a function of soil hydraulic properties and vegetation types. Overall, statistics showed good agreement between the modeled and observed T(sub b) with a relatively low, domain-average bias (0.79 K (ascending) and -2.79 K (descending)), root mean squared error (11.0 K (ascending) and 11.7 K (descending)), and unbiased root mean squared error (8.14 K (ascending) and 8.28 K (descending)). In terms of soil hydraulic parameters, large porosity and large wilting point both lead to high uncertainty in modeled T(sub b) due to the large variability in dielectric constant and surface roughness used by the RTM. The performance of the RTM as a function of vegetation type suggests better agreement in regions with broadleaf deciduous and needleleaf forests while grassland regions exhibited the worst accuracy amongst the five different vegetation types.
The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.
A multi channel physical approach for retrieving rainfall and its vertical structure from Special Sensor Microwave/Imager (SSM/I) observations is examined. While a companion paper was devoted exclusively to the description of the algorithm, its strengths, and its limitations, the main focus of this paper is to report on the results, applicability, and expected accuraciesfrom this algorithm. Some examples are given that compare retrieved results with ground-based radar data from different geographical regions to illustrate the performance and utility of the algorithm under distinct rainfall conditions. More quantitative validation is accomplished using two months of radar data from Darwin, Australia, and the radar network over Japan. Instantaneous comparisons at Darwin indicate that root-mean-square errors for 1.25 deg areas over water are 0.09 mm/h compared to the mean rainfall value of 0.224 mm/h while the correlation exceeds 0.9. Similar results are obtained over the Japanese validation site with rms errors of 0.615 mm/h compared to the mean of 0.0880 mm/h and a correlation of 0.9. Results are less encouraging over land with root-mean-square errors somewhat larger than the mean rain rates and correlations of only 0.71 and 0.62 for Darwin and Japan, respectively. These validation studies are further used in combination with the theoretical treatment of expected accuracies developed in the companion paper to define error estimates on a broader scale than individual radar sites from which the errors may be analyzed. Comparisons with simpler techniques that are based on either emission or scattering measurements are used to illustrate the fact that the current algorithm, while better correlated with the emission methods over water, cannot be reduced to either of these simpler methods.
This report describes an optimal ensemble forecasting model for seasonal precipitation and its error estimation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. This new CCA model includes the following features: (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States precipitation field. The predictor is the sea surface temperature.
A formula permitting calculation of the mean-square error of the mean value of a random variable due to periodic sampling is derived and applied to estimating the sampling error for satellite observation of the mean rainfall during the GARP Atlantic Tropical Experiment (GATE). The effects of both spatial resolution and frequency of observation on the sampling error are summarized in graphs. It is found that four observations per day are sufficient to determine the monthly mean rainfall over an area of 2.5 deg square (280km x 280km) to within a standard deviation of 5 percent of its mean value; two samples per day would yield an error with a standard deviation slightly less than 10 percent of the mean. A satellite instrument with less frequent sampling may produce significantly greater error in the estimate of monthly mean rainfall.
The frame to frame correlation properties of the video process are utilized to reduce the mean squared error of the demodulated video where zero mean noise is a factor. An interpolative estimator is used for continuous estimation with the output process delayed in time by one frame. Theoretical development shows that for the model herein developed reduction of the mean squared error by 1.0 to 4.0 db possible for parameter ranges of interest. Interpolative estimation using inter-frame correlation properties of a video process is then applied to the Apollo 17 parameters to yield a model for application on that mission.
This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.
Rate distortion functions for two-dimensional homogeneous isotropic images are compared with the performance of 5 source encoders designed for such images. Both unweighted and frequency weighted mean square error distortion measures are considered. The coders considered are differential PCM (DPCM) using six previous samples in the prediction, herein called 6 pel (picutre element) DPCM; simple DPCM using single sample prediction; 6 pel DPCM followed by entropy coding; 8 x 8 discrete cosine transform coder, and 4 x 4 Hadamard transform coder. Other transform coders were studied and found to have about the same performance as the two transform coders above. With the mean square error distortion measure DPCM with entropy coding performed best. The relative performance of the coders changes slightly when the distortion measure is frequency weighted mean square error. The performance of all the coders was separated by only about 4 dB.
We consider optimum uniform data quantization for noisy channels. We present a general formulation for natural encoding that results in simple expressions for the mean-square error. Specifically, we show that the optimum location of the center of the quantizer is at the mean of the distribution for all error rates. The optimum levels for quantization and the corresponding mean-square error are presented for Gaussian and uniform data. For the latter the width of the optimum quantizer for noisy channels is shown to be smaller than the entire range of probability distribution.