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NASA NTRS1987

Empirical prediction of the summer monsoon rainfall over India

Forty-six years (1939-1984) of observed data were examined to study synoptic and statistical relationships between the summer monsoon rainfall over India, the Southern Oscillation, and the midtropospheric circulation over India. The change in Darwin pressure from January to April and the latitudinal position of the April 500-mb ridge along 75 deg E are taken as two quasi-independent predictor parameters to develop a regression equation to predict the summer monsoon rainfall. Verification of predictions on independent data shows that the root-mean-square error for predicted rainfall is 36 mm, which is less than half of the standard deviation and only about 4 percent of the mean rainfall (857 mm).

Shukla, J.↗

NASA NTRS1995

Error modeling for differential GPS

Differential Global Positioning System (DGPS) positioning is used to accurately locate a GPS receiver based upon the well-known position of a reference site. In utilizing this technique, several error sources contribute to position inaccuracy. This thesis investigates the error in DGPS operation and attempts to develop a statistical model for the behavior of this error. The model for DGPS error is developed using GPS data collected by Draper Laboratory. The Marquardt method for nonlinear curve-fitting is used to find the parameters of a first order Markov process that models the average errors from the collected data. The results show that a first order Markov process can be used to model the DGPS error as a function of baseline distance and time delay. The model's time correlation constant is 3847.1 seconds (1.07 hours) for the mean square error. The distance correlation constant is 122.8 kilometers. The total process variance for the DGPS model is 3.73 sq meters.

Blerman, Gregory S.↗

NASA NTRS2021

Quantifying the Observational Requirements of a Space-borne LiDAR Snow Mission

This study quantifies the level of observational accuracy required from a spaceborne light detection and ranging (LiDAR) snow depth retrieval mission for enabling beneficial impacts for snow estimation. The study is conducted over a region in Western Colorado using a suite of observing system simulation experiments(OSSEs).The Joint UK Land Environment Simulator, version 5.0 (JULES v5.0) is employed to simulate a suite of idealized LiDAR observations, considering a range of LiDAR snow depth retrieval errors, different hypothetical sensor swath widths, and the impact of cloud cover on observability. These simulated observations are then assimilated into the Noah land surface modelwith multi-parameterization options, version 3.6 (Noah-MP v3.6) model. This data assimilation setup is used to systematically evaluate the potential utility of LiDAR observations for improving modeled snow water equivalent (SWE)estimates and water budget variables such as runoff. Results from the OSSE runsshow that, in general, assimilation of synthetic LiDAR observations provide beneficial impacts when theLiDAR snow depth retrieval error standard deviation (σerror) is below 60 cm.Based on comparisons between the realistic (i.e., swath-limited and cloud-attenuated) case and the idealized (i.e., infinite swath width in the absence of cloud cover) case,this study concludes that observations with a conservative error standard deviation threshold of 40 cm (i.e., upper limit of the snow depth retrieval error that adds value to the SWE estimates viaassimilation) are needed for improving modeled snow estimates. More than a 33% reduction in SWEroot mean square errors and more than a 15% increase in correlation coefficientsare achieved when σ error ≤ 40 cmusing a 170-km sensor swath width in the presence of cloud attenuation effects. Further, the integrated hydrologic response, as represented by total (surface and subsurface) runoff estimates during the snow ablation season, are also enhanced when assimilating synthetic LiDAR snow depth retrievals with errors below this level.

Yonghwan Kwon↗

NASA NTRS2016

Performance Metrics, Error Modeling, and Uncertainty Quantification

A common set of statistical metrics has been used to summarize the performance of models or measurements- the most widely used ones being bias, mean square error, and linear correlation coefficient. They assume linear, additive, Gaussian errors, and they are interdependent, incomplete, and incapable of directly quantifying uncertainty. The authors demonstrate that these metrics can be directly derived from the parameters of the simple linear error model. Since a correct error model captures the full error information, it is argued that the specification of a parametric error model should be an alternative to the metrics-based approach. The error-modeling methodology is applicable to both linear and nonlinear errors, while the metrics are only meaningful for linear errors. In addition, the error model expresses the error structure more naturally, and directly quantifies uncertainty. This argument is further explained by highlighting the intrinsic connections between the performance metrics, the error model, and the joint distribution between the data and the reference.

Quantification↗

NASA NTRS1993

A survey of quality measures for gray-scale image compression

Although a variety of techniques are available today for gray-scale image compression, a complete evaluation of these techniques cannot be made as there is no single reliable objective criterion for measuring the error in compressed images. The traditional subjective criteria are burdensome, and usually inaccurate or inconsistent. On the other hand, being the most common objective criterion, the mean square error (MSE) does not have a good correlation with the viewer's response. It is now understood that in order to have a reliable quality measure, a representative model of the complex human visual system is required. In this paper, we survey and give a classification of the criteria for the evaluation of monochrome image quality.

Eskicioglu, Ahmet M.↗

NASA NTRS2016

Crop Model Improvement Reduces the Uncertainty of the Response to Temperature of Multi-Model Ensembles

To improve climate change impact estimates and to quantify their uncertainty, multi-model ensembles (MMEs) have been suggested. Model improvements can improve the accuracy of simulations and reduce the uncertainty of climate change impact assessments. Furthermore, they can reduce the number of models needed in a MME. Herein, 15 wheat growth models of a larger MME were improved through re-parameterization and/or incorporating or modifying heat stress effects on phenology, leaf growth and senescence, biomass growth, and grain number and size using detailed field experimental data from the USDA Hot Serial Cereal experiment (calibration data set). Simulation results from before and after model improvement were then evaluated with independent field experiments from a CIMMYT worldwide field trial network (evaluation data set). Model improvements decreased the variation (10th to 90th model ensemble percentile range) of grain yields simulated by the MME on average by 39% in the calibration data set and by 26% in the independent evaluation data set for crops grown in mean seasonal temperatures greater than 24 C. MME mean squared error in simulating grain yield decreased by 37%. A reduction in MME uncertainty range by 27% increased MME prediction skills by 47%. Results suggest that the mean level of variation observed in field experiments and used as a benchmark can be reached with half the number of models in the MME. Improving crop models is therefore important to increase the certainty of model-based impact assessments and allow more practical, i.e. smaller MMEs to be used effectively.

damage assessment↗

NASA NTRS2017

Comparison of Commonly-Used Microwave Radiative Transfer Models for Snow Remote Sensing

This paper reviews four commonly-used microwave radiative transfer models that take different electromagnetic approaches to simulate snow brightness temperature (T(sub B)): the Dense Media Radiative Transfer - Multi-Layer model (DMRT-ML), the Dense Media Radiative Transfer - Quasi-Crystalline Approximation Mie scattering of Sticky spheres (DMRT-QMS), the Helsinki University of Technology n-Layers model (HUT-nlayers) and the Microwave Emission Model of Layered Snowpacks (MEMLS). Using the same extensively measured physical snowpack properties, we compared the simulated T(sub B) at 11, 19 and 37 GHz from these four models. The analysis focuses on the impact of using different types of measured snow microstructure metrics in the simulations. In addition to density, snow microstructure is defined for each snow layer by grain optical diameter (Do) and stickiness for DMRT-ML and DMRT-QMS, mean grain geometrical maximum extent (D(sub max)) for HUT n-layers and the exponential correlation length for MEMLS. These metrics were derived from either in-situ measurements of snow specific surface area (SSA) or macrophotos of grain sizes (D(sub max)), assuming non-sticky spheres for the DMRT models. Simulated T(sub B) sensitivity analysis using the same inputs shows relatively consistent T(sub B) behavior as a function of Do and density variations for the vertical polarization (maximum deviation of 18 K and 27 K, respectively), while some divergences appear in simulated variations for the polarization ratio (PR). Comparisons with ground based radiometric measurements show that the simulations based on snow SSA measurements have to be scaled with a model-specific factor of Do in order to minimize the root mean square error (RMSE) between measured and simulated T(sub B). Results using in-situ grain size measurements (SSA or D(sub max), depending on the model) give a mean T(sub B) RMSE (19 and 37 GHz) of the order of 16-26 K, which is similar for all models when the snow microstructure metrics are scaled. However, the MEMLS model converges to better results when driven by the correlation length estimated from in-situ SSA measurements rather than D(sub max) measurements. On a practical level, this paper shows that the SSA parameter, a snow property that is easy to retrieve in-situ, appears to be the most relevant parameter for characterizing snow microstructure, despite the need for a scaling factor.

Snow↗

NASA NTRS1978

A note on obtaining an approximate value for the period of a periodic solution of x-double prime = -V prime /x/

The first integral of x-double prime = - V prime (x) yields an integral for the period of a periodic solution, if such exists. In general, this integral cannot be evaluated. By means of an approximate solution along with the minimization of a mean-square error, one can obtain an approximate value for the period in terms of the amplitude of the motion. The calculated period agrees very well with the period obtained by means of numerical integration for the case of orbit-orbit resonance involving the motion of two satellites of a planet. The same method is applied to obtain an alternative derivation of the first Krylov-Bogoliuboff averaging method in nonlinear mechanics.

Lass, H.↗

NASA NTRS1973

Automatic equalization using the discrete frequency domain.

A new mean-square-error automatic equalizer for synchronous data transmission is developed. It utilizes Rosen's gradient-projection method to optimize parameters in the discrete frequency domain. The algorithm converges (in the mean) for any channel even in the presence of noise. It is shown that for the channels considered, convergence is faster (in a bounded sense) than for comparable time-domain equalizers.

Walzman, T.↗

NASA NTRS2020

Scaling Observation Error for Optimal Assimilation of CCI SST Data into a Regional HYCOM EnOI System

South Africa currently possesses no operational ocean forecasting system for the purpose of predicting ocean state variables including temperature,salinity and velocity. Substantial initial efforts towards this goal have been made and resulted in a system using a regional Hybrid Coordinate Ocean Model (HYCOM) along with the Ensemble Optimal Interpolation (EnOI)assimilation scheme. Assimilating only sea surface temperature (SST) observations from the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) product into the system resulted in a degraded forecast. Aiming to address this, Climate Change Initiative (CCI) SSTs are assimilated into the system in an effort to improve the forecast skill. Observation errors in the assimilated product are used in the EnOI to determine whether more confidence should be placed in the model or observations in producing the analysis, but overconfidence in observations can shock the model and result in failure. To tweak the impact of the assimilation, a scaling factor is applied in the assimilation code. A scaling factor of 25 was found to produce a favourable result with lowest mean root mean square error (RMSE;1.098°C) between the model and observations over time. Postulating the error to be overconfident, a floor value is introduced in order to set a minimum value for the observation error thereby reducing confidence in the observations. These experiments fared less favourably with a floor value of 0.5 and a scaling factor of 15 producing the best mean RMSE (1.118°C).

Luyt, Hermann↗

NASA NTRS1980

Evaluation of Bayesian Sequential Proportion Estimation Using Analyst Labels

The author has identified the following significant results. A total of ten Large Area Crop Inventory Experiment Phase 3 blind sites and analyst-interpreter labels were used in a study to compare proportional estimates obtained by the Bayes sequential procedure with estimates obtained from simple random sampling and from Procedure 1. The analyst error rate using the Bayes technique was shown to be no greater than that for the simple random sampling. Also, the segment proportion estimates produced using this technique had smaller bias and mean squared errors than the estimates produced using either simple random sampling or Procedure 1.

Lennington, R. K.↗

NASA NTRS1981

Estimating cell populations

An important step in the diagnosis of a cervical cytology specimen is estimating the proportions of the various cell types present. This is usually done with a cell classifier, the error rates of which can be expressed as a confusion matrix. We show how to use the confusion matrix to obtain an unbiased estimate of the desired proportions. We show that the mean square error of this estimate depends on a 'befuddlement matrix' derived from the confusion matrix, and how this, in turn, leads to a figure of merit for cell classifiers. Finally, we work out the two-class problem in detail and present examples to illustrate the theory.

White, B. S.↗

NASA NTRS1996

Surface Turbulent Fluxes Over Pack Ice Inferred from TOVS Observations

A one-dimensional, atmospheric boundary layer model is coupled to a thermodynamic ice model to estimate the surface turbulent fluxes over thick sea ice. The principal forcing parameters in this time-dependent model are the air temperature, humidity, and wind speed at a specified level (either at 2 m or at 850 mb) and the downwelling surface radiative fluxes. The free parameters. are the air temperature, humidity, and wind speed profiles below the specified level, the surface skin temperature, the ice temperature profile, and the surface turbulent fluxes. The goal is to determine how well we can estimate the turbulent surface heat and momentum fluxes using forcing parameters from atmospheric temperatures and radiative fluxes retrieved from the TIROS-N Operational Vertical Sounder (TOVS) data. Meteorological observations from the Lead Experiment (LeadEx, April 1992) ice camp are used to validate turbulent fluxes computed with the surface observations and the results are used to compare with estimates based on radio-sonde observations or with estimates based on TOVS data. We find that the TOVS-based estimates of the stress are significantly more accurate than those found with a constant geostrophic drag coefficient, with a root-mean-square error about half as large. This improvement is due to stratification effects included in the boundary layer model. The errors in the sensible heat flux estimates, however, are large compared to the small mean values observed during the field experiment.

Lindsay, R. W.↗

NASA NTRS2010

Mini-TES Observations of Comanche Carbonate and Its Distribution

The discovery by the Spirit rover of outcrops rich in Mg-Fe carbonate [Morris et al., 2010] represents another manifestation of a diverse aqueous history in Gusev crater. In 2005, observations by the Moessbauer spectrometer (MB) on outcrops dubbed Comanche provided initial indication of Fe-Mg carbonate that was subsequently supported by analysis of elemental data from the Alpha Particle X-ray Spectrometer (APXS). The recognition of a carbonate component in thermal infrared spectra measured by the Miniature Thermal Emission Spectrometer (Mini-TES) was significantly delayed due to dust contamination of the instrument's optics. With the implementation of a viable dust correction, the Comanche spectra were revisited and presented clear and compelling evidence for a Mg-Fe carbonate component that could be as much as a third of the total mineral abundance. The data from all three instruments in combination are best matched by Mg-Fe carbonate with an abundance of 16-34 wt%. Mini-TES spectra were acquired for 12 targets at various locations on the Comanche (4-5 m long) and Comanche Spur (1-2 m long) outcrops, the latter being the location of the MB and APXS measurements. The two outcrops are spectrally comparable and share similar morphology and texture based on color images from the Panoramic Camera (Pancam). The highest quality Mini-TES spectrum comes from the larger Comanche outcrop on a target named Saupitty. Linear least squares modeling of the Saupitty spectrum employed a library of laboratory spectra tailored for consistency with the APXS and MB data and included spectra representing Martian dust, a slope spectrum to account for any temperature determination errors, and a blackbody spectrum to account for differences in spectral contrast between the laboratory and Mini-TES spectrum. Successful modeling of the Comanche Saupitty spectrum required one or more carbonate phases to obtain a good fit. Excluding all carbonates from the full starting library more than doubled the root-mean-squared error of the model fit (0.147% vs. 0.299%). Because Mg-Fe carbonate and Ca-Mg carbonate (dolomite) are so spectrally similar over the range used for modeling, both provide a comparable fit. However, Carich carbonates like dolomite are precluded based on APXS data and are inconsistent with MB results. The Comanche carbonate rocks are stratigraphically above a set of olivine-rich volcaniclastic rocks known as Algonquin class that mantle the Haskin Ridge feature of the Columbia Hills. Based on ~50 Mini-TES observations, the Comanche outcrops are the only rocks that host abundant carbonate. However, a target at the base of the larger Comanche outcrop appears spectrally transitional between the carbonate and olivine units. This transitional spectral character applies to additional outcrops a few 10s of meters away from Comanche that also appear stratigraphically transitional. Additional work will attempt to establish whether we are seeing an alteration horizon or depositional unit associated with the emplacement Comanche carbonate.

Ruff, Steven W.↗

NASA NTRS1979

Simulations of the monthly mean atmosphere for February 1976 with the GISS model

Three monthly mean simulations of the global atmosphere were computed for February 1976 with the GISS model from observed initial conditions on the first day of the month. In a replication experiment, two of these computations generated slightly different monthly mean states, apparently due to the schedule of interruptions on the computer. The root-mean-square errors of replication over the Northern Hemisphere were found to be about 2 mb, 20 m and 1 K for sea level pressure, 500 mb height and 850 mb temperature, respectively. The monthly mean 500 mb forecast results for February 1976 over the Northern Hemisphere are consistent with those from earlier GISS model experiments and again indicate some predictive skill at that level. Use of the observed monthly mean sea surface temperature (SST) field for February 1976 in place of the climatological SST field for February resulted in slightly improved simulations over the globe and Northern Hemisphere,

Spar, J.↗

NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 3

The Always-Convergent Iterative Noise Removal and Deconvolution Method of Ioup is applied as a single-filter in the transform domain to deconvolution with both narrow and wide Gaussian impulse response functions. The wraparound error for both cases is also studied. A method is developed by which one can find the optimum iteration number for single-filter iterative deconvolution of sampled data. The method employs the mean square error (MSE), the square of the difference between the deconvolved result and the input, for optimization. The MSE decreases as the deconvolution iterations proceed, but at the optimum iteration number, the MSE starts to increase. This procedure is repeated for signal-to-noise ratio of 10 to 150. The optimum iteration number and the MSE are plotted vs SNR. By knowing the SNR for a particular experiment, one can find the optimum iteration number and MSE.

Ioup, George E.↗

NASA NTRS1978

Simulations of the monthly mean atmosphere for February 1976 with the GISS model

Monthly mean simulations of the global atmosphere were computed for February 1976 with the GISS model from observed initial conditions. In a replication experiment, two of these computations generated slightly different monthly mean states, apparently due to the schedule of interruptions on the computer. The root-mean-square errors of replication over the Northern Hemisphere were found to be about 2 mb, 20 m, and 1 K for sea-level pressure, 500 mb height, and 850 mb temperature, respectively. The monthly mean 500 mb forecast results for February 1976 over the Northern Hemisphere were consistent with those from earlier GISS model experiments.

Spar, J.↗

NASA NTRS1980

LACIE - An application of meteorology for United States and foreign wheat assessment

This paper describes the overall Large Area Crop Inventory Experiment technical approach utilizing the global weather-reporting network and the Landsat satellite to make a quasi-operational application of existing research results, and the accomplishments of this cooperative experiment in utilizing the weather information. Global weather data were utilized in preparing timely yield estimates for selected areas of the U.S. Great Plains, the U.S.S.R. and Canada. Additionally, wheat yield models were developed and pilot tested for Brazil, Australia, India and Argentina. The results of the work show that heading dates for wheat in North America can be predicted with an average absolute error of about 5 days for winter wheat and 4 days for spring wheat. Independent tests of wheat yield models over a 10-year period for the U.S. Great Plains produced a root-mean-square error of 1.12 quintals per hectare (q/ha) while similar tests in the U.S.S.R. produced an error of 1.31 q/ha. Research designed to improve the initial capability is described as is the rationale for further evolution of a capability to monitor global climate and assess its impact on world food supplies.

Hill, J. D.↗