Engineering topics

Bell, Thomas L.

Publications and source records attributed to Bell, Thomas L..

34 records · Page 2

NASA NTRS2002

Comparing Satellite Rainfall Estimates with Rain-Gauge Data: Optimal Strategies Suggested by a Spectral Model

Validation of satellite remote-sensing methods for estimating rainfall against rain-gauge data is attractive because of the direct nature of the rain-gauge measurements. Comparisons of satellite estimates to rain-gauge data are difficult, however, because of the extreme variability of rain and the fact that satellites view large areas over a short time while rain gauges monitor small areas continuously. In this paper, a statistical model of rainfall variability developed for studies of sampling error in averages of satellite data is used to examine the impact of spatial and temporal averaging of satellite and gauge data on intercomparison results. The model parameters were derived from radar observations of rain, but the model appears to capture many of the characteristics of rain-gauge data as well. The model predicts that many months of data from areas containing a few gauges are required to validate satellite estimates over the areas, and that the areas should be of the order of several hundred km in diameter. Over gauge arrays of sufficiently high density, the optimal areas and averaging times are reduced. The possibility of using time-weighted averages of gauge data is explored.

Bell, Thomas L.↗

NASA NTRS2002

A Stochastic Model of Space-Time Variability of Tropical Rainfall: I. Statistics of Spatial Averages

Global maps of rainfall are of great importance in connection with modeling of the earth s climate. Comparison between the maps of rainfall predicted by computer-generated climate models with observation provides a sensitive test for these models. To make such a comparison, one typically needs the total precipitation amount over a large area, which could be hundreds of kilometers in size over extended periods of time of order days or months. This presents a difficult problem since rain varies greatly from place to place as well as in time. Remote sensing methods using ground radar or satellites detect rain over a large area by essentially taking a series of snapshots at infrequent intervals and indirectly deriving the average rain intensity within a collection of pixels , usually several kilometers in size. They measure area average of rain at a particular instant. Rain gauges, on the other hand, record rain accumulation continuously in time but only over a very small area tens of centimeters across, say, the size of a dinner plate. They measure only a time average at a single location. In making use of either method one needs to fill in the gaps in the observation - either the gaps in the area covered or the gaps in time of observation. This involves using statistical models to obtain information about the rain that is missed from what is actually detected. This paper investigates such a statistical model and validates it with rain data collected over the tropical Western Pacific from ship borne radars during TOGA COARE (Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment). The model incorporates a number of commonly observed features of rain. While rain varies rapidly with location and time, the variability diminishes when averaged over larger areas or longer periods of time. Moreover, rain is patchy in nature - at any instant on the average only a certain fraction of the observed pixels contain rain. The fraction of area covered by rain decreases, as the size of a pixel becomes smaller. This means that within what looks like a patch of rainy area in a coarse resolution view with larger pixel size, one finds clusters of rainy and dry patches when viewed on a finer scale. The model makes definite predictions about how these and other related statistics depend on the pixel size. These predictions were found to agree well with data. In a subsequent second part of the work we plan to test the model with rain gauge data collected during the TRMM (Tropical Rainfall Measuring Mission) ground validation campaign.

Kundu, Prasun K.↗

NASA NTRS2001

Response to Comment on "Does the Earth Have an Adaptive Infrared IRIS?"

Harrison's (2001) Comment on the Methodology in Lindzen et al (2001) has prompted re-examination of several aspects of study. Probably the most significant disagreement in our conclusions is due to our different approaches to minimizing the influence of long-time-scale variations in the variables A and T on the results. Given the strength of the annual cycle and the 20-month period covered by the data, we believe that removing monthly means is a better approach to minimizing the long-time-scale behavior of the data than removal of the linear trend, which might actually add spurious long- time- scale variability into the modified data. We have also indicated how our statistical methods of establishing statistical significance differ. More definitive conclusions may only possible after more data have been analyzed, but we feel that our results are robust enough to encourage further study of this phenomenon.

Bell, Thomas L.↗

NASA NTRS2001

Response to Comment on "Does the Earth Have an Adaptive Infrared Iris?"

In his comment on Lindzen et al., Harrison found that the amount of high-level clouds, A, and the sea-surface temperature beneath clouds, T, averaged over a large oceanic domain in the western Pacific have secular linear trends of opposite signs over a period of 20 months. He found that when the linear trends are subtracted from the data, the correlation between the residual A and T is much reduced. His estimates of the confidence levels for the correlation indicate, moreover, that this correlation is not statistically significant. The domain-averaged A and, to a lesser degree, T, have distinct intra-seasonal and seasonal variations. These variations are influenced by the large-scale wind and temperature distributions and by the seasonal variation of insolation. To separate the local effect from the effect of slowly changing large-scale conditions, rather than subtracting 20-month linear trends from the series, which has the potential to spuriously extrapolate intra-seasonal and seasonal variations to even longer time scales, we subtracted 30-day running means of A and T from each time series; in effect, the data were high-pass filtered. The number of points (days), N, is reduced by this process from the original value of 510 to 480.

Bell, Thomas L.↗

NASA NTRS2001

Sampling of the Diurnal Cycle of Precipitation using TRMM

We examine the temporal sampling of tropical regions using observations from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Precipitation Radar (PR). We conclude that PR estimates at any one hour, even using three years of data, are inadequate to describe the diurnal cycle of precipitation over regions smaller than 12 degrees, due to high spatial variability in sampling. We show that the optimum period of accumulation is four hours. Diurnal signatures display half as much sampling error when averaged over four hours of local time. A similar pattern of sampling variability is found in the TMI data, despite the TMI's wider swath and increased sampling. These results are verified using an orbital model. The sensitivity of the sampling to satellite altitude is presented, as well as sampling patterns at the new TRMM altitude of 402.5 km.

Negri, Andrew J.↗

NASA NTRS2000

Sampling Errors of SSM/I and TRMM Rainfall Averages: Comparison with Error Estimates from Surface Data and a Sample Model

Quantitative use of satellite-derived maps of monthly rainfall requires some measure of the accuracy of the satellite estimates. The rainfall estimate for a given map grid box is subject to both remote-sensing error and, in the case of low-orbiting satellites, sampling error due to the limited number of observations of the grid box provided by the satellite. A simple model of rain behavior predicts that Root-mean-square (RMS) random error in grid-box averages should depend in a simple way on the local average rain rate, and the predicted behavior has been seen in simulations using surface rain-gauge and radar data. This relationship was examined using satellite SSM/I data obtained over the western equatorial Pacific during TOGA COARE. RMS error inferred directly from SSM/I rainfall estimates was found to be larger than predicted from surface data, and to depend less on local rain rate than was predicted. Preliminary examination of TRMM microwave estimates shows better agreement with surface data. A simple method of estimating rms error in satellite rainfall estimates is suggested, based on quantities that can be directly computed from the satellite data.

Bell, Thomas L.↗

NASA NTRS2000

Sampling Errors in Monthly Rainfall Totals for TRMM and SSM/I, Based on Statistics of Retrieved Rain Rates and Simple Models

Estimates from TRMM satellite data of monthly total rainfall over an area are subject to substantial sampling errors due to the limited number of visits to the area by the satellite during the month. Quantitative comparisons of TRMM averages with data collected by other satellites and by ground-based systems require some estimate of the size of this sampling error. A method of estimating this sampling error based on the actual statistics of the TRMM observations and on some modeling work has been developed. "Sampling error" in TRMM monthly averages is defined here relative to the monthly total a hypothetical satellite permanently stationed above the area would have reported. "Sampling error" therefore includes contributions from the random and systematic errors introduced by the satellite remote sensing system. As part of our long-term goal of providing error estimates for each grid point accessible to the TRMM instruments, sampling error estimates for TRMM based on rain retrievals from TRMM microwave (TMI) data are compared for different times of the year and different oceanic areas (to minimize changes in the statistics due to algorithmic differences over land and ocean). Changes in sampling error estimates due to changes in rain statistics due 1) to evolution of the official algorithms used to process the data, and 2) differences from other remote sensing systems such as the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I), are analyzed.

Bell, Thomas L.↗

NASA NTRS1999

Optimal Scales for Comparing Satellite and Rain-Gauge Rainfall Estimates for Verification Purposes

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. The comparison of the two requires that some quantitative measure be supplied for the amount of disagreement that can be tolerated due to the differences in sampling. As part of an effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed and its parameters fit to radar data from a field experiment conducted near the Inter-Tropical Convergence Zone (ITCZ) in the eastern Atlantic (GATE). Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. It can therefore be used to study some of the issues involved with comparing rain-gauge averages to satellite averages. Its implications for the best time and space scales for comparing the two will be discussed.

Bell, Thomas L.↗

NASA NTRS1994

Principal modes of variation of rain-rate probability distributions

Radar or satellite observations of an area generate sequences of rain-rate maps. From a gridded map a histogram of rain rates can be obtained representing the relative areas occupied by rain rates of various strengths. The histograms vary with time as precipitating systems in the area evolve and decay and amounts of convective and stratiform rain in the area change. A method of decomposing the histograms into linear combinations of a few empirical distributions with time-dependent coefficients is developed, using principal component analysis as a starting point. When applied to a tropical Atlantic dataset (GATE), two distributions emerge naturally from the analysis, resembling stratiform and convective rain-rate distributions in that they peak at low and high rain rates, respectively. The two 'modes' have different timescales and only the high-rain-rate mode has a statistically significant diurnal cycle. The ability of just two modes to describe rain variabiltiy over an area can explain why methods of estimating area-averaged rain rate from the area covered by rain rates above a certain threshold are so successful.

Bell, Thomas L.↗

NASA NTRS1994

The albedo of fractal stratocumulus clouds

An increase in the planetary albedo of the earth-atmosphere system by only 10% can decrease the equilibrium surface temperature to that of the last ice age. Nevertheless, albedo biases of 10% or greater would be introduced into large regions of current climate models if clouds were given their observed liquid water amounts, because of the treatment of clouds as plane parallel. The focus on marine stratocumulus clouds is due to their important role in cloud radiative forcing and also that, of the wide variety of earth's cloud types, they are most nearly plane parallel, so that they have the least albedo bias. The fractal model employed here reproduces both the probability distribution and the wavenumber spectrum of the stratocumulus liquid water path, as observed during the First ISCCP Regional Experiment (FIRE). A single new fractal parameter 0 less than or equal to f less than or equal to 1, is introduced and determined empirically by the variance of the logarithm of the vertically integrated liquid water. The reduced reflectivity of fractal stratocumulus clouds is approximately given by the plane-parallel reflectivity evaluated at a reduced 'effective optical thickness,' which when f = 0.5 is tau(sub eff) approximately equal to 10. Study of the diurnal cycle of stratocumulus liquid water during FIRE leads to a key unexpected result: the plane-parallel albedo bias is largest when the cloud fraction reaches 100%, that is, when any bias associated with the cloud fraction vanishes. This is primarily due to the variability increase with cloud fraction. Thus, the within-cloud fractal structure of stratocumulus has a more significant impact on estimates of its mesoscale-average albedo than does the cloud fraction.

Cahalan, Robert F.↗

NASA NTRS1993

Detecting the diurnal cycle of rainfall using satellite observations

The diurnal cycle in rainfall varies considerably from region to region in the tropics. Determining this variability is important both for comparing predictions of atmospheric models to real atmospheric behavior and for making sure that estimates of total rainfall from low-altitude satellites are not biased because of their infrequent observations of a given region of the earth. Although there are no data from the proposed Tropical Rainfall Measuring Mission (TRMM) satellite to work with yet, we can ask how well the diurnal cycle in rainfall will be detected when the satellite is eventually collecting data, given the satellite's proposed sampling characteristics. Data analyses for the diurnal cycle are discussed, taking into account the fact that the satellite visits will be irregularly spaced in time. The amplitudes of the first few harmonics will be determined by least-squares fits to the satellite observations, and the tests needed to establish the statistical significance of the fitted amplitudes are discussed. The accuracy with which the first few harmonics of the diurnal cycle can be detected is estimated from several months of satellite data using rainfall statistics observed during the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment (GATE).

Bell, Thomas L.↗

NASA NTRS1992

The relation of radar to cloud area-time integrals and implications for rain measurements from space

The relationships between satellite-based and radar-measured area-time integrals (ATI) for convective storms are determined, and both are shown to depend on the climatological conditional mean rain rate and the ratio of the measured cloud area to the actual rain area of the storms. The GOES precipitation index of Arkin (1986) for convective storms, an area-time integral for satellite cloud areas, is shown to be related to the ATI for radar-observed rain areas. The quality of GPI-based rainfall estimates depends on how well the cloud area is related to the rain area and the size of the sampling domain. It is also noted that the use of a GOES cloud ATI in conjunction with the radar area-time integral will improve the accuracy of rainfall estimates and allow such estimates to be made in much smaller space-time domains than the 1-month and 5-deg boxes anticipated for the Tropical Rainfall Measuring Mission.

Atlas, David↗

NASA NTRS1990

Sampling errors for satellite-derived tropical rainfall - Monte Carlo study using a space-time stochastic model

Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.

Bell, Thomas L.↗

NASA NTRS1989

Detection of the diurnal cycle in rainfall from the TRMM satellite

Consideration is given to the process of detecting the diurnal cycle from data that will be collected by the Tropical Rainfall Measuring Mission satellite. The analysis of data for the diurnal cycle is discussed, accounting for the fact that satellite visits will be irregularly spaced in time. The accuracy with which the first few harmonics of the diurnal cycle can be detected from several months of satellite data is estimated using rainfall statistics observed during the GARP Atlantic Tropical Experiment.

Bell, Thomas L.↗

NASA NTRS1987

Latitude dependence of eddy variances

The eddy variance of a meteorological field must tend to zero at high latitudes due solely to the nature of spherical polar coordinates. The zonal averaging operator defines a length scale: the circumference of the latitude circle. When the circumference of the latitude circle is greater than the correlation length of the field, the eddy variance from transient eddies is the result of differences between statistically independent regions. When the circumference is less than the correlation length, the eddy variance is computed from points that are well correlated with each other, and so is reduced. The expansion of a field into zonal Fourier components is also influenced by the use of spherical coordinates. As is well known, a phenomenon of fixed wavelength will have different zonal wavenumbers at different latitudes. Simple analytical examples of these effects are presented along with an observational example from satellite ozone data. It is found that geometrical effects can be important even in middle latitudes.

Bowman, Kenneth P.↗

NASA NTRS1987

A space-time stochastic model of rainfall for satellite remote-sensing studies

A model of the spatial and temporal distribution of rainfall is described that produces random spatial rainfall patterns with these characteristics: (1) the model is defined on a grid with each grid point representing the average rain rate over the surrounding grid box, (2) rain occurs at any one grid point, on average, a specified percentage of the time and has a lognormal probability distribution, (3) spatial correlation of the rainfall can be arbitrarily prescribed, and (4) time stepping is carried out so that large-scale features persist longer than small-scale features. Rain is generated in the model from the portion of a correlated Gaussian random field that exceeds a threshold. The portion of the field above the threshold is rescaled to have a lognormal probability distribution. Sample output of the model designed to mimic radar observations of rainfall during the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE), is shown. The model is intended for use in evaluating sampling strategies for satellite remote-sensing of rainfall and for development of algorithms for converting radiant intensity received by an instrument from its field of view into rainfall amount.

Bell, Thomas L.↗