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We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
This study examines whether cloud inhomogeneity influences the view angle dependence of MODIS cloud optical thickness (tau) retrieval results. The degree of cloud inhomogeneity is characterized through the local gradient in 11 microns brightness temperature. The analysis of liquid phase clouds in a one year long global dataset of Collection 4 MODIS data reveals that while optical thickness retrievals give remarkably consistent results for all view directions if clouds are homogeneous, they give much higher tau-values for oblique views than for overhead views if clouds are inhomogeneous and the sun is fairly oblique. For solar zenith angles larger than 55deg, the mean optical thickness retrieved for the most inhomogeneous third of cloudy pixels is more than 30% higher for oblique views than for overhead views. After considering a variety of possible scenarios, the paper concludes that the most likely reason for the increase lies in three-dimensional radiative interactions that are not considered in current, one-dimensional retrieval algorithms. Namely, the radiative effect of cloud sides viewed at oblique angles seems to contribute most to the enhanced tau-values. The results presented here will help understand cloud retrieval uncertainties related to cloud inhomogeneity. They complement the uncertainty estimates that will start accompanying MODIS cloud products in Collection 5 and may eventually help correct for the observed view angle dependent biases.
Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash-Sutcliffe metric approx. 0.84, annual volume bias <3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002-2006 period is estimated to be 29.7+/-2.9% (which includes 4.2+/-0.9% from snowfall that promptly melts), whereas 70.3+/-2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000-5500m range contributes the most to basin runoff, averaging 56.9+/-3.6% of all snowmelt input and 28.9+/-1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree-day melting model. Lastly, we demonstrate that the data assimilation approach is useful for quantifying and reducing uncertainty related to model parameters and thus provides uncertainty bounds on snowmelt and rainfall contributions in such mountainous watersheds.
A detailed computerized sensitivity analysis of the triple hot-wire equations has been performed in order to delineate the uncertainties associated with measurements of the velocity components. Absolute and relative uncertainties for the instantaneous hot-wire outputs are calculated as functions of roll and pitch angles, based on a constant probability combination of the uncertainties in the inputs. From the results, it is concluded that the small inherent difficulties associated with the triple hot-wire data do not reflect artifacts introduced by the data processing. Fixed errors present in the V and W channels of the output are due to the nonzero measuring volume of the triple wire probe, and are entirely predictable.
Salt marshes have highly variable spatial and temporal fluxes of hydrogen sulfide, carbonyl sulfide, methane thiol, dimethyl sulfide, and carbon disulfide (H2S, COS, MeSH, DMS, and CS2, respectively). This variability was tested at nine emission sites in a New Hampshire, USA salt marsh: three replicates in each of three vegetation zones, Spartina alterniflora, S. patens, and a transition zone. Three sites were sampled simultaneously, either within or across vegetation zones, using a dynamic flux chamber technique. Difficulties with calibration and field equipment resulted in fluxes with maximum absolute uncertainties of greater than plus or minus 200 percent. However, the relative uncertainty between subsequent samples was closer to plus or minus 20 percent. Chambers are expected to affect the natural flux of gases by altering the humidity, temperature, and composition of the gas inside the chamber. Summertime fluxes are highest for all gases except COS which demonstrated evidence of a springtime peak. A summertime background flux of 5 to 100 x 10(exp -9) g S/m(sup -2) min was observed for all gases, while S alternifora fluxes of MeSH and DMS were approximately 8 fold and approximately 100 fold higher than S. patens, respectively. DMS and MeSH fluxes were higher during the day than at night. Evidence of COS uptake by plants was observed. CS2 appeared to be the quantitatively least important sulfur gas emitted. Improved laboratory and sample collection techniques and further data collection in the field will yield information on the details of salt marsh variability, will improve estimates of the error associated with single flux measurements, and will allow a more accurate estimation of sulfur fluxes from salt marshes based on vegetation and area coverage data. Inability to control the temperature and humidity inside of the chamber remain significant problems with the chamber design.
Typical aircraft trajectory predictors use wind forecasts but do not account for the forecast uncertainty. A method for generating estimates of wind prediction uncertainty is described and its effect on aircraft trajectory prediction uncertainty is investigated. The procedure for estimating the wind prediction uncertainty relies uses a time-lagged ensemble of weather model forecasts from the hourly updated Rapid Update Cycle (RUC) weather prediction system. Forecast uncertainty is estimated using measures of the spread amongst various RUC time-lagged ensemble forecasts. This proof of concept study illustrates the estimated uncertainty and the actual wind errors, and documents the validity of the assumed ensemble-forecast accuracy relationship. Aircraft trajectory predictions are made using RUC winds with provision for the estimated uncertainty. Results for a set of simulated flights indicate this simple approach effectively translates the wind uncertainty estimate into an aircraft trajectory uncertainty. A key strength of the method is the ability to relate uncertainty to specific weather phenomena (contained in the various ensemble members) allowing identification of regional variations in uncertainty.
It is shown that high-resolution low-uncertainty temperature-height profiles cannot be deduced from pressure-height data alone because the relative uncertainty in pressure data cannot be expected to be smaller than 1% or 2% in present-day practical instrumentation. The basic equations relating temperature to pressure-height or density-height data are subjected to error analysis to determine the uncertainty introduced into computed temperature-height values by observed data. The results show that the use of density data is much more preferable than the use of pressure data if atmospheric temperature is to be determined as a function of height with a fine height resolution and a small uncertainty from the height profiles of pressure or density and if pressures and densities can be measured with comparable accuracies.
The Voyager II flyby of Uranus in January 1986 was the most distant planetary encounter ever attempted, and presented unique challenges to the process of orbit determination. Long light-times and spacecraft receiver difficulties hampered the collection of two-way radiometric data and helped bring about the maturation of a Very Long Baseline Interferometry navigational data type during the long cruise from Saturn. Planet and satellite ephemeris uncertainties necessitated the use of the onboard spacecraft optical system for Uranus-relative navigation. During the close approach phase, these optical data were combined with radiometric data to drive the Uranus system-relative uncertainties down to the level of a few tens of kilometers. This paper contains qualitative and quantitative results and conclusions based on orbit determination experience during Uranus cruise and encounter. Topics include an overview of the navigation-related mission events and requirements, and a review of the salient orbit determination results.
MODIS dark-target (DT) algorithm retrieves aerosol optical depth (AOD) using a Look Up Table (LUT) approach. Global comparison of AOD (Collection 6 ) with ground-based sun photometer gives an Estimated Error (EE) of +/-(0.04 + 10%) over ocean. However, EE does not represent per-retrieval uncertainty. For retrievals that are biased high compared to AERONET, here we aim to closely examine the contribution of biases due to presence of clouds and per-pixel retrieval uncertainty. We have characterized AOD uncertainty at 550 nm, due to standard deviation of reflectance in 10 km retrieval region, uncertainty related to gas (H2O, O3) absorption, surface albedo, and aerosol models. The uncertainty in retrieved AOD seems to lie within the estimated over ocean error envelope of +/-(0.03+10%). Regions between broken clouds tend to have higher uncertainty. Compared to C6 AOD, a retrieval omitting observations in the vicinity of clouds (< or = 1 km) is biased by about +/- 0.05. For homogeneous aerosol distribution, clear sky retrievals show near zero bias. Close look at per-pixel reflectance histograms suggests retrieval possibility using median reflectance values.
The method of saturated fluorescence for measuring species concentrations in flames is usually performed with laser beams that do not provide a constant intensity distribution across the focal volume. Because of the intensity distribution across the beam, the fluorescence signal does not depend on laser power or intensity in the same manner as for uniform illumination. This leads to anomolous apparent saturation intensities. In the following, the effect is considered for atomic fluorescence. Relations for the fluorescence signal under two common excitation geometries are derived and uncertainty relations used to consider the benefits of high laser intensity.
In the last decade, the Electric Arc Shock Tube (EAST) facility has been widely used to provide experimental data aiming to validate radiative heating models used for atmospheric entry, mostly at velocities above 9km/s in air. In more recent years, another experimental campaign aimed to look at velocity below 9 km/s and its analysis resulted in a significant improvement of the air kinetic model using new rates found in the literature but discrepancies were still observed, especially for the N2 second positive system. Despite these previous studies, the overall uncertainties related to surface heating for lunar return remain around 50% To reduce these uncertainties, the last experimental campaign at EAST, named test 62, was conducted in pure nitrogen at velocity ranging from 6 to 11 km/s at a freestream pressure of 0.2 Torr to provide more fundamental data on nitrogen. A previous study analyzed the data obtained at a velocity of 10.3 km/s, where atomic radiation is dominant, and provided spatially resolved density measurements of different states of nitrogen. This study will focus on experimental data obtained at shock velocity of 6.88 and 7.15 km/s where molecular nitrogen is expected to be the dominant source of radiation.
The NASA SMAP (Soil Moisture Active Passive) mission provides a global coverage of soil moisture measurements based on its L-band microwave radiometer every 2-3 days at about 40 km resolution. The soil moisture retrieval algorithms model the brightness temperature as a function of soil moisture, surface conditions and vegetation. External data sources inform the algorithms about the surface conditions and vegetation, which enable the retrieval of soil moisture. The inversion process contains uncertainties related to radiometer measurements, forward model assumptions and ancillary data sources. This study focuses on the uncertainties that depend on the seasonal evolution of the surface conditions and vegetation. This study compares the SMAP and core validation site (CVS) soil moisture values over a period of three years to extract the evolution of performance metrics over time. The analysis showed that most CVS that include managed agriculture exhibit significant time-dependent seasonal bias. This bias was linked to seasonal temperature cycle, which is a proxy to several features that can cause seasonally dependent errors in the SMAP product.
Vincent and Reid (1983) proposed a technique to measure gravity-wave momentum fluxes in the atmosphere by mesosphere-stratosphere-troposphere (MST) radars using two or more radar beams. Since the vertical momentum fluxes are assumed to be due to gravity waves, it appears possible to make use of the dispersion and polarization relations for gravity waves in extracting useful information from the radar data. In particular, for an oblique radar beam, information about both the vertical and the horizontal velocities associated with the waves are contained in the measured Doppler data. Therefore, it should be possible to extract both V sub Z and V sub h from a single beam observational configuration. A procedure is proposed to perform such an analysis. The basic assumptions are: the measured velocity fluctuations are due to gravity waves and a separable model gravity-wave spectrum of the Garrett-Munk type that is statistically homogeneous in the horizontal plane. Analytical expressions can be derived that relate the observed velocity fluctuations to the wave momentum flux at each range gate. In practice, the uncertainties related to the model parameters and measurement accuracy will affect the results. A MST radar configuration is considered.
A review is presented of remote sensing techniques which measure the electric field component transverse to the line of sight and achieve a sensitivity range of 5-10 V/cm. Three models are shown to predict quasistatic, macroscopic values of E(parallel), the electric field component parallel to the magnetic vector, beyond the sensitivity range considered. These processes are: the discharge model of flares; the models of return currents related to flare particle beams; and the models of neutral sheets related to two-ribbon flares and postflare loops. Time dependent electric fields related to MHD and plasma waves, and to plasma disturbance, may allow the detection of both E components (parallel and perpendicular). The uncertainty relating to the emission measures, time scales, volumes, and plasma conditions of these flares and electrified plasma volumes is emphasized. It is pointed out, however, that important information can be obtained by observing electric fields at existing sensitivity levels. By measuring these E-fields, the understanding of flares and related dynamic events can be improved.
The paper summarizes several studies to develop aerodynamic technology for high performance VSTOL aircraft anticipated after 1990. A contracted study jointly sponsored by NASA-Ames and David Taylor Naval Ship Research and Development Center is emphasized. Four contractors analyzed two vertical-attitude and three horizontal-attitude takeoff and landing concepts with gross weights ranging from about 10433 kg (23,000 lb) to 17236 kg (38,000 lb). The aircraft have supersonic capability, high maneuver performance (sustained load factor 6.2 at Mach 0.6, 3048 m (10,000 ft)) and a 4536 kg (10,000-lb) STO overload capability. The contractors have estimated the aerodynamics and identified aerodynamic uncertainties associated with their concept. Example uncertainties relate to propulsion-induced flows, canard-wing interactions, and top inlets. Wind-tunnel research programs were proposed to investigate these uncertainties.
The process of secondary-particle emission in hadron-hadron collisions is analytically studied using a simple model of hadron structure. The model neglects the 'size' of the hadron constituents, considering a hadron as a continuous distribution of matter according to a step function of radius R. A version of the eikonal approximation is applied to derive the relative probability for interaction and emission of secondaries when the impact parameter b is smaller than 2R. On the basis of these assumptions, and using the uncertainty relation, an empirical parameterization is obtained for the dependence of the transverse momentum of charged secondaries on their multiplicity in the case of high-energy proton-proton collisions. Comparison with experimental data at 28 GeV/c yields agreement to within about 3%. The analysis shows that at a fixed beam momentum, the transverse momentum decreases with increasing multiplicity, and that for a given multiplicity, the transverse momentum exhibits a slow increase with beam momentum.
The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantity: there are always quantum mechanical fluctuations. The amplitude, having both a magnitude and a phase, is a complex number and is described by the mode annihilation operator a. It is also possible to characterize the amplitude by its real and imaginary parts which correspond to the Hermitian and anti-Hermitian parts of a, X sub 1 = 1/2(a(sup +) + a) and X sub 2 = i/2(a(sup +) - a), respectively. These operators do not commute and, as a result, obey the uncertainty relation (h = 1) delta X sub 1(delta X sub 2) greater than or = 1/4. From this relation we see that the amplitude fluctuates within an 'error box' in the complex plane whose area is at least 1/4. Coherent states, among them the vacuum state, are minimum uncertainty states with delta X sub 1 = delta X sub 2 = 1/2. A squeezed state, squeezed in the X sub 1 direction, has the property that delta X sub 1 is less than 1/2. A squeezed state need not be a minimum uncertainty state, but those that are can be obtained by applying the squeeze operator.
The statistical uncertainty in the flux densities reported in the IRAS Serendipitous Survey Catalog (1986) is analyzed by examining differences in the measurements of sources in two independent observations. An assessment of the statistical uncertainty as a function of flux density in the Catalog has been made by accumulating these differences for over 4000 sources spanning a brightness range from 0.05 to over 20 Jy. The functional forms of the relative uncertainties at 12, 25, 60, and 100 microns are presented.