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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Estimating local noise power spectrum from a few FBP-reconstructed CT scans

Purpose: Traditional ways to estimate 2D CT noise power spectrum (NPS) involve an ensemble average of the power spectrums of many noisy scans. When only a few scans are available, regions of interest are often extracted from different locations to obtain sufficient samples to estimate the NPS. Using image samples from different locations ignores the nonstationarity of CT noise and thus cannot accurately characterize its local properties. The purpose of this work is to develop a method to estimate local NPS using only a few fan-beam CT scans. Methods: As a result of FBP reconstruction, the CT NPS has the same radial profile shape for all projection angles, with the magnitude varying with the noise level in the raw data measurement. This allows a 2D CT NPS to be factored into products of a 1D angular and a 1D radial function in polar coordinates. The polar separability of CT NPS greatly reduces the data requirement for estimating the NPS. The authors use this property and derive a radial NPS estimation method: in brief, the radial profile shape is estimated from a traditional NPS based on image samples extracted at multiple locations. The amplitudes are estimated by fitting the traditional local NPS to the estimated radial profile shape. The estimated radial profile shape and amplitudes are then combined to form a final estimate of the local NPS. We evaluate the accuracy of the radial NPS method and compared it to traditional NPS methods in terms of normalized mean squared error (NMSE) and signal detectability index. Results: For both simulated and real CT data sets, the local NPS estimated with no more than six scans using the radial NPS method was very close to the reference NPS, according to the metrics of NMSE and detectability index. Even with only two scans, the radial NPS method was able to achieve a fairly good accuracy. Compared to those estimated using traditional NPS methods, the accuracy improvement was substantial when a few scans were available. Conclusions: The radial NPS method was shown to be accurate and efficient in estimating the local NPS of FBP-reconstructed 2D CT images. It presents strong advantages over traditional NPS methods when the number of scans is limited and can be extended to estimate the in-plane NPS of cone-beam CT and multislice helical CT scans.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS1992

A model for the cost of doing a cost estimate

A model for estimating the cost required to do a cost estimate for Deep Space Network (DSN) projects that range from $0.1 to $100 million is presented. The cost of the cost estimate in thousands of dollars, C(sub E), is found to be approximately given by C(sub E) = K((C(sub p))(sup 0.35)) where C(sub p) is the cost of the project being estimated in millions of dollars and K is a constant depending on the accuracy of the estimate. For an order-of-magnitude estimate, K = 24; for a budget estimate, K = 60; and for a definitive estimate, K = 115. That is, for a specific project, the cost of doing a budget estimate is about 2.5 times as much as that for an order-of-magnitude estimate, and a definitive estimate costs about twice as much as a budget estimate. Use of this model should help provide the level of resources required for doing cost estimates and, as a result, provide insights towards more accurate estimates with less potential for cost overruns.

Remer, D. S.↗
NASA NTRS1993

The cost of doing a cost estimate

A model for estimating the cost required to do a cost estimate for Deep Space Network (DSN) projects that range from $0.1 to $100 million is presented. The cost of the cost estimate in thousands of dollars, C(sub E), is found to be approximately given by C(sub E) = K(/C(sub p)/(sup 0.35)) where C(sub p) is the cost of the project being estimated in millions of dollars and K is a constant depending on the accuracy of the estimate. For an order-of-magnitude estimate, K = 24; for a budget estimate, K = 60; and for a definitive estimate, K = 115. That is, for a specific project, the cost of doing a budget estimate is about 2.5 times as much as that for an order-of-magnitude estimate, and a definitive estimate costs about twice as much as a budget estimate. Use of this model should help provide the level of resources required for doing cost estimates and, as a result, provide insights towards more accurate estimates with less potential for cost overruns.

Remer, Donald S.↗
DOE OSTI2016

Unbiased Ratio Estimator for k-Eigenvalue in Monte Carlo Criticality Calculations

In criticality calculations, the effective multiplication factor (k{sub eff}) is an important parameter for reactor analysis. It can be interpreted as the ratio of the neutron production rate to the loss rate in a reactor core. In Monte Carlo (MC) criticality calculations, k{sub eff} is obtained for each active cycle i as: k-i = P{sub i}/L{sub i} for I = 1 to I where P{sub i} and L{sub i} are the production rate and the loss rate at cycle i, respectively, and they are normalized by the nominal source size for cycle. Since all neutron particles in a cycle will be absorbed or leaks out at the end, the loss rate, L{sub i}, can be set as the source rate, which is the unity. Thus, in MCNP5, k{sub i} is simply calculated with P{sub i} by using three conventional estimators; collision, absorption, and track-length estimators. In domain decomposed MC criticality calculations based on the fission and surface source (FSS) iteration method, k{sub i} is calculated by a ratio of P{sub i} and L{sub i}, where both P{sub i} and L{sub i} are random variables, sampled by using the same particle histories. When the numerator and the denominator are correlated, the variance of the ratio can be smaller than that of the numerator. Then, the final estimate of k{sub eff} is provided as the sample mean of k{sub i}, which will be referred as 'simple' ratio estimator in this paper. In Ref., it is shown that this ratio estimator converges faster and fluctuates less than the conventional estimator. A similar ratio estimator is also used in Serpent 2, as an implicit estimate of k{sub eff}. However, this type of 'simple' ratio estimator is biased, which means that the expectation of the ratio is different from the ratio of the expectation of the numerator and that of the denominator. In this paper, an unbiased ratio estimator which was originally derived in the cytometry analysis is introduced to estimate k{sub eff} and is tested on a continuous-energy UO{sub 2} pin-cell problem. In this test problem, it is shown that the variance of the unbiased ratio estimator is smaller than those of the conventional estimators provided by MCNP5, while the simple ratio estimator can be significantly biased when the number of histories per cycle is too small. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2014

Estimated stocks of circumpolar permafrost carbon with quantified uncertainty ranges and identified data gaps

Soils and other unconsolidated deposits in the northern circumpolar permafrost region store large amounts of soil organic carbon (SOC). This SOC is potentially vulnerable to remobilization following soil warming and permafrost thaw, but SOC stock estimates were poorly constrained and quantitative error estimates were lacking. This study presents revised estimates of permafrost SOC stocks, including quantitative uncertainty estimates, in the 0–3 m depth range in soils as well as for sediments deeper than 3 m in deltaic deposits of major rivers and in the Yedoma region of Siberia and Alaska. Revised estimates are based on significantly larger databases compared to previous studies. Despite this there is evidence of significant remaining regional data gaps. Estimates remain particularly poorly constrained for soils in the High Arctic region and physiographic regions with thin sedimentary overburden (mountains, highlands and plateaus) as well as for deposits below 3 m depth in deltas and the Yedoma region. While some components of the revised SOC stocks are similar in magnitude to those previously reported for this region, there are substantial differences in other components, including the fraction of perennially frozen SOC. Upscaled based on regional soil maps, estimated permafrost region SOC stocks are 217 ± 12 and 472 ± 27 Pg for the 0–0.3 and 0–1 m soil depths, respectively (±95% confidence intervals). Storage of SOC in 0–3 m of soils is estimated to 1035 ± 150 Pg. Of this, 34 ± 16 Pg C is stored in poorly developed soils of the High Arctic. Based on generalized calculations, storage of SOC below 3 m of surface soils in deltaic alluvium of major Arctic rivers is estimated as 91 ± 52 Pg. In the Yedoma region, estimated SOC stocks below 3 m depth are 181 ± 54 Pg, of which 74 ± 20 Pg is stored in intact Yedoma (late Pleistocene ice- and organic-rich silty sediments) with the remainder in refrozen thermokarst deposits. Total estimated SOC storage for the permafrost region is ∼1300 Pg with an uncertainty range of ∼1100 to 1500 Pg. Of this, ∼500 Pg is in non-permafrost soils, seasonally thawed in the active layer or in deeper taliks, while ∼800 Pg is perennially frozen. In conclusion, this represents a substantial ∼300 Pg lowering of the estimated perennially frozen SOC stock compared to previous estimates.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

A novel multistage estimation of the signal parameters of a possibly data-modulated sinusoid under very high dynamics

A novel multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data, and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity, acceleration and jerk of the GPS receiver. In the proposed multistage scheme, the first stage estimator operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second state of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first stage algorithm is selected to be a modified least squares algorithm operating upon the differential signal model and referred to as differential least squares. This estimation stage provides relatively coarse estimates of the frequency and its derivatives. The second algorithm is simply an extended Kalman filter which also yields the estimate of the phase along with a more refined estimate of frequency as well. A major advantage of the proposed algorithm is a reduction in the threshold on received carrier power-to-noise power spectral density ratio as compared to the threshold achievable by either of these algorithms alone. In fact, it appears from the simulations that for the case of an unmodulated carrier, the proposed scheme achieves the same threshold as for an almost exact and computationally intensive implementation of the maximum likelihood estimator.

Kumar, Rajendra↗
NASA NTRS1996

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system.

Keel, Byron M.↗
DOE OSTI2025

Comparison of removal and spatial mark‐resight models for estimating wild pig density

Density estimation is critical to effectively manage invasive species and elucidate areas of highest concern. For wild pigs (Sus scrofa), the ability to estimate density is complicated because of their variable home range sizes and social structure. Common methods for estimating density (e.g., mark-recapture) may be unsuitable in management applications because additional data needs to be collected before and after management. Removal models offer a suitable alternative to estimate density changes following management and can be applied broadly across areas where management of wild pigs is ongoing. We collected wild pig removal and camera trap data from 25 private properties ranging in size from approximately 0.5 km 2 to 95 km 2 across 3 ecoregions in South Carolina, USA, from 2020–2023. We compared factors affecting consistency and precision of property-level density estimates between removal and spatial mark-resight (SMR) models. In general, excluding 1 large outlier, density estimates from removal models were between 0.60 and 15.85 wild pigs/km 2 (median = 5.34) with a median coefficient of variation (CV) of 0.76 and 95% confidence intervals for the CV between 0.70 and 0.94. Similarly, excluding 1 large outlier, density estimates from SMR were between 0.22 and 30.97 wild pigs/km 2 (median = 5.48) with a median CV of 0.39 and 95% confidence intervals for the CV between 0.38 and 1.20. We found the precision of removal models was affected primarily by the number of wild pigs dispatched in the removal period (3 months) and the ecoregion in which they were removed. None of the covariates, including the number of recaptures (a corresponding measure of sample size), influenced precision of the SMR models, although recaptures did influence the density estimates. At the individual property level, density estimates from our 2 estimators were dissimilar from each other in approximately 80% of instances, although none of the covariates we examined influenced dissimilarity. Our results provide unique insight into how sample size affects density estimates using 2 common methods and into novel SMR models that incorporate both marked and unmarked detections. In addition, the density estimates in this study can be used as a reference for wild pig densities in common land cover types throughout the southeastern United States.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Kumaraswamy distribution: different methods of estimation

This paper addresses different methods of estimation of the unknown parameters of a two-parameter Kumaraswamy distribution from a frequentist point of view. We briefly describe ten different frequentist approaches, namely, maximum likelihood estimators, moments estimators, L-moments estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, Cramér–von-Mises estimators, Anderson–Darling estimators and right tailed Anderson–Darling estimators. Monte Carlo simulations and two real data applications are performed to compare the performances of the estimators for both small and large samples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Monte Carlo volumetric-ray-casting estimator for global fluence tallies on GPUs

A Monte Carlo fluence estimator has been designed to take advantage of the computational power of graphical processing units (GPUs). This new estimator, termed the volumetric-ray-casting estimator, is an extension of the expectation estimator. It can be used as a replacement of the track-length estimator for the estimation of global fluence. Calculations for this estimator are performed on the GPU while the Monte Carlo random walk is performed on the central processing unit (CPU). This method lowers the implementation cost for GPU acceleration of existing Monte Carlo particle transport codes as there is little modification of the particle history logic flow. Three test problems have been evaluated to assess the performance of the volumetric-ray-casting estimator for neutron transport on GPU hardware in comparison to the standard track-length estimator on CPU hardware. Evaluation of neutron transport through air in a criticality accident scenario showed that the volumetric-ray-casting estimator achieved 23 times the performance of the track-length estimator using a single core CPU paired with a GPU and 15 times the performance of the track-length estimator using an eight core CPU paired with a GPU. Finally, simulation of a pressurized water reactor fuel assembly showed that the performance improvement was 6 times within the fuel and 7 times within the control rods using an eight core CPU paired with a single GPU.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Evaluation of top-down and bottom-up global terrestrial respiration estimates and their mismatch with model simulations

Terrestrial respiration is one of the most poorly understood processes in the global carbon cycle, making respiration predictions uncertain. However, expanding observations and machine learning approaches have led to a proliferation of estimates. We compiled total ecosystem and heterotrophic respiration estimates derived from top-down atmospheric inversions and bottom-up upscaling of ecosystem observations and compared them with dynamic vegetation models (DGVM) simulations over the 1980-2020 period. Our analysis revealed a convergence in mean annual global total ecosystem respiration estimates between top-down 97.1 (± SD 6.8) PgC yr-1 and bottom-up 98.5 (+/-13.4) PgC yr-1, which were both significantly lower than the ensemble mean from DGVMs estimates 133.7 (±4.7) PgC yr-1. We also found similar temporal trends between top-down estimates with a mean of 0.075 (±0.05) PgC yr-2, and bottom-up estimates of 0.05 (±0.05) PgC yr-2, which were 5 to 7 times smaller than the ensemble mean trend of 0.34 PgC yr-2 simulated by DGVMs. Global heterotrophic respiration showed much less agreement, ranging from top-down estimates of 42.7 (±4.0) PgC yr-1 to bottom-up estimates of 51.5 (±4.0) PgC yr-1 and a significantly larger ensemble model mean estimate of 60.8 PgC yr-1 (±1.9). The temporal trends in observation-based bottom-up estimates of heterotrophic respiration of 0.03 PgC yr-2 were five times lower than the model ensemble mean 0.15 PgC yr-2. Large regional disagreements in heterotrophic respiration estimates and simulations were evident in tropical and boreal latitudes. Therefore, improved regional and heterotrophic respiration estimates are necessary to reduce uncertainties regarding the future vulnerability of soil carbon.

Ballantyne, Ashley↗
DOE OSTI2019

Comparison of Local Recurrence Risk Estimates After Breast-Conserving Surgery for DCIS: DCIS Nomogram Versus Refined Oncotype DX Breast DCIS Score

Background: A ductal carcinoma in situ (DCIS) Nomogram integrating 10 clinicopathologic/treatment factors and a Refined DCIS Score (RDS) that incorporates a genomic assay and three clinicopathologic factors (Oncotype DX DCIS Score) are available to estimate DCIS 10-year local recurrence risk (LRR). This study compared these estimates. Methods: Patients 50 years of age or older with DCIS size 2.5 cm or smaller and a genomic assay available were identified. An RDS within 1–2% of the range of Nomogram LRR estimates obtained by assuming use and non-use of endocrine therapy (Nomogram ± ET) was defined as concordant. Assuming a 10-year risk threshold of 10% for recommending radiation, Nomogram ± ET and RDS estimates were compared, and threshold concordance was determined. Results: For 54 (92%) of 59 patients, the RDS and Nomogram ± ET LRR estimates were concordant. For the remaining 5 (8%) of the 59 patients, the RDS LRR estimates were lower than the Nomogram + ET estimates, with an absolute difference of 3–8%, and thus were discordant. For these five patients, the RDS estimates of 10-year LRR were lower than 10% (range 5–8%) and the Nomogram + ET estimates were 10% or higher (range 11–14%). These five patients with both discordant and threshold-discordant estimates all had close margins (≤ 2 mm). Conclusions: Among 92% of women 50 years of age or older with DCIS size 2.5 cm or smaller, free-of-charge online Nomogram 10-year LRR estimates were concordant with those obtained using the commercially available RDS (> $4600). Among the 8% with discordant risk estimates, the RDS appeared to underestimate the LRR and may lead to inappropriate omission of radiotherapy. Unless other data show a clinically significant advantage of the RDS (Oncotype DX DCIS Score), the study data suggest that for women 50 years of age or older with DCIS size 2.5 cm or smaller, its use is not warranted.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Quantifying Uncertainty in All-to-All Estimates of Space Object Conjunction Probabilities using U-Statistics

Predicting space object conjunctions is inherently probabilistic due to initial state and orbit model uncertainty. A commonly considered Monte Carlo estimator of the conjunction probability is the ’all-to-all’ estimator. Given independent random samples of the trajectories of both objects, the estimator is the percentage of all pairs of trajectories that result in a conjunction. Intuitively, the all-to-all estimator is the best possible estimator of the conjunction probability since it considers all pairs of Monte Carlo samples. However, its distribution is not available in closed-form, which limits its use in practice and makes this intuition difficult to make rigorous. In this paper, the all-to-all estimator is identified as a U-statistic, which implies that it has several favorable properties. Specifically, the estimator is the minimum variance unbiased estimator of the conjunction probability and is asymptotically Gaussian distributed. An approximate confidence interval for the conjunction probability is obtained from an estimate of the asymptotic Gaussian distribution. We show how to efficiently compute the confidence interval and demonstrate that the interval has the nominal coverage level. The confidence intervals are also seen to be narrower than those based on the commonly-used each-to-each estimator. Furthermore, the all-to-all estimator is shown to allow different Monte Carlo sample sizes, whereas the each-to-each estimator requires equal sample sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate these five estimators using a groundwater transport model selection problem. SS and MOSS give the least biased BME estimation at an efficient computational cost. If the estimated BME has a bias that covariates with the true BME, this would not be a problem because we are interested in BME ratios and not their absolute values. On the contrary, the results show that BME estimation bias can be a function of model complexity. Thus, biased BME estimation results in inaccurate penalization of more complex models, which changes the model ranking. This was less observed with SS and MOSS as with the three other methods.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2002

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.↗
NASA NTRS2004

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry: Evaluation of Estimates Using Independent Data - Part 2

Rainfall rate estimates from space-borne k&ents are generally accepted as reliable by a majority of the atmospheric science commu&y. One-of the Tropical Rainfall Measuring Mission (TRh4M) facility rain rate algorithms is based upon passive microwave observations fiom the TRMM Microwave Imager (TMI). Part I of this study describes improvements in the TMI algorithm that are required to introduce cloud latent heating and drying as additional algorithm products. Here, estimates of surface rain rate, convective proportion, and latent heating are evaluated using independent ground-based estimates and satellite products. Instantaneous, OP5resolution estimates of surface rain rate over ocean fiom the improved TMI algorithm are well correlated with independent radar estimates (r approx. 0.88 over the Tropics), but bias reduction is the most significant improvement over forerunning algorithms. The bias reduction is attributed to the greater breadth of cloud-resolving model simulations that support the improved algorithm, and the more consistent and specific convective/stratiform rain separation method utilized. The bias of monthly, 2.5 deg. -resolution estimates is similarly reduced, with comparable correlations to radar estimates. Although the amount of independent latent heating data are limited, TMI estimated latent heating profiles compare favorably with instantaneous estimates based upon dual-Doppler radar observations, and time series of surface rain rate and heating profiles are generally consistent with those derived from rawinsonde analyses. Still, some biases in profile shape are evident, and these may be resolved with: (a) additional contextual information brought to the estimation problem, and/or; (b) physically-consistent and representative databases supporting the algorithm. A model of the random error in instantaneous, 0.5 deg-resolution rain rate estimates appears to be consistent with the levels of error determined from TMI comparisons to collocated radar. Error model modifications for non-raining situations will be required, however. Sampling error appears to represent only a fraction of the total error in monthly, 2S0-resolution TMI estimates; the remaining error is attributed to physical inconsistency or non-representativeness of cloud-resolving model simulated profiles supporting the algorithm.

Yang, Song↗
NASA NTRS2006

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry. Part II: Evaluation of Estimates Using Independent Data

Rainfall rate estimates from spaceborne microwave radiometers are generally accepted as reliable by a majority of the atmospheric science community. One of the Tropical Rainfall Measuring Mission (TRMM) facility rain-rate algorithms is based upon passive microwave observations from the TRMM Microwave Imager (TMI). In Part I of this series, improvements of the TMI algorithm that are required to introduce latent heating as an additional algorithm product are described. Here, estimates of surface rain rate, convective proportion, and latent heating are evaluated using independent ground-based estimates and satellite products. Instantaneous, 0.5 deg. -resolution estimates of surface rain rate over ocean from the improved TMI algorithm are well correlated with independent radar estimates (r approx. 0.88 over the Tropics), but bias reduction is the most significant improvement over earlier algorithms. The bias reduction is attributed to the greater breadth of cloud-resolving model simulations that support the improved algorithm and the more consistent and specific convective/stratiform rain separation method utilized. The bias of monthly 2.5 -resolution estimates is similarly reduced, with comparable correlations to radar estimates. Although the amount of independent latent heating data is limited, TMI-estimated latent heating profiles compare favorably with instantaneous estimates based upon dual-Doppler radar observations, and time series of surface rain-rate and heating profiles are generally consistent with those derived from rawinsonde analyses. Still, some biases in profile shape are evident, and these may be resolved with (a) additional contextual information brought to the estimation problem and/or (b) physically consistent and representative databases supporting the algorithm. A model of the random error in instantaneous 0.5 deg. -resolution rain-rate estimates appears to be consistent with the levels of error determined from TMI comparisons with collocated radar. Error model modifications for nonraining situations will be required, however. Sampling error represents only a portion of the total error in monthly 2.5 -resolution TMI estimates; the remaining error is attributed to random and systematic algorithm errors arising from the physical inconsistency and/or nonrepresentativeness of cloud-resolving-model-simulated profiles that support the algorithm.

Yang, Song↗
NASA NTRS2006

Bayesian Estimation of Precipitation from Satellite Passive Microwave Observations Using Combined Radar-Radiometer Retrievals

Precipitation estimation from satellite passive microwave radiometer observations is a problem that does not have a unique solution that is insensitive to errors in the input data. Traditionally, to make this problem well posed, a priori information derived from physical models or independent, high-quality observations is incorporated into the solution. In the present study, a database of precipitation profiles and associated brightness temperatures is constructed to serve as a priori information in a passive microwave radiometer algorithm. The precipitation profiles are derived from a Tropical Rainfall Measuring Mission (TRMM) combined radar radiometer algorithm, and the brightness temperatures are TRMM Microwave Imager (TMI) observed. Because the observed brightness temperatures are consistent with those derived from a radiative transfer model embedded in the combined algorithm, the precipitation brightness temperature database is considered to be physically consistent. The database examined here is derived from the analysis of a month-long record of TRMM data that yields more than a million profiles of precipitation and associated brightness temperatures. These profiles are clustered into a tractable number of classes based on the local sea surface temperature, a radiometer-based estimate of the echo-top height (the height beyond which the reflectivity drops below 17 dBZ), and brightness temperature principal components. For each class, the mean precipitation profile, brightness temperature principal components, and probability of occurrence are determined. The precipitation brightness temperature database supports a radiometer-only algorithm that incorporates a Bayesian estimation methodology. In the Bayesian framework, precipitation estimates are weighted averages of the mean precipitation values corresponding to the classes in the database, with the weights being determined according to the similarity between the observed brightness temperature principal components and the brightness temperature principal components of the classes. Because the classes are stratified by the sea surface temperature and the echo-top-height estimator, the number of classes that are considered for retrieval is significantly smaller than the total number of classes, making the algorithm computationally efficient. The radiometer-only algorithm is applied to TMI observations, and precipitation estimates are compared with combined TRMM precipitation radar (PR) TMI reference estimates. The TMI-only algorithm, supported by the empirically derived database, produces estimates that are more consistent with the reference values than the precipitation estimates from the version-6 TRMM facility TMI algorithm. Cloud-resolving model simulations are used to assign a latent heating profile to each precipitation profile in the empirically derived database, making it possible to estimate latent heating using the radiometer-only algorithm. Although the evaluation of latent heating estimates in this study is preliminary, because realistic conditional probability distribution functions are attached to latent heating structures in the algorithm s database, a generally positive impact on latent heating estimation from passive microwave observations is expected.

Grecu, Mircea↗