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At least 73 records · Page 4

Linear and nonlinear trending and prediction for AVHRR time series data

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

Smid, J.↗

Airborne Observations of the Spatial and Temporal Variability of Tropospheric Carbon Dioxide during the INTEX-B Campaign

The Intercontinental Chemical Transport Experiment-North America (INTEX-NA) is an international field campaign envisioned to investigate the transport and transformation of gases and aerosols on transcontinental/intercontinental scales and assess their impact on air quality and climate. Phase B (INTEX-B) of the mission was conducted during a 10- week period from March 1 to May 15, 2006 and focused initially on pollution outflow from the Mexico City Metropolitan Area, later addressing the transport of pollution from Asia to North America during springtime meteorological conditions. During the deployment, fast-response (1-s resolution) CO2 measurements were recorded aboard the NASA DC-8 providing valuable regional-scale information on carbon sources and sinks over sparsely sampled areas of North America and adjacent ocean basins. When coupled with the enormously sophisticated chemistry payload on the DC-8, these measurements collectively afford extremely powerful multi-tracer constraints for carbon source/sink attribution. Preliminary examination of the two data sets from the INTEX-B campaign, acquired one month apart, reveals not only the influence of the CO2 seasonal cycle, but also the preponderance of human population and industrial activity in the northern hemisphere. In this presentation, a synergy of the ensemble of airborne and surface observations, bottomup emission inventories, as well as transport history are invoked in a GIS framework to elucidate the source/sink processes reflected in the observations. The airborne CO2 data, along with simultaneous surface measurements (e.g. NOAA ESRL), are examined to establish the vertical distribution and variability of CO2 as a function of location. The role of localized sources, long-range transport, the biosphere, stratospheric exchange, and dynamical processes on the CO2 spatial variability observed throughout the tropospheric column will be discussed.

Vay, Stephanie A.↗

Upper-Stratospheric Ozone Trends 1979-1998

Extensive analyses of ozone observations between 1978 and 1998 measured by Dobson Umkehr, Stratospheric Aerosol and Gas Experiment (SAGE) I and II, and Solar Backscattered Ultraviolet (SBUV) and (SBUV)/2 indicate continued significant ozone decline throughout the extratropical upper stratosphere from 30-45 km altitude. The maximum annual linear decline of -0.8 +/- 0.2 %/yr(2sigma) occurs at 40 km and is well described in terms of a linear decline modulated by the 11-year solar variation. The minimum decline of -0.110.1% yr-1(2o) occurs at 25 km in midlatitudes, with remarkable symmetry between the Northern and Southern Hemispheres at 40 km altitude. Midlatitude upper-stratospheric zonal trends exhibit significant seasonal variation (+/- 30% in the Northern Hemisphere, +/- 40% in the Southern Hemisphere) with the most negative trends of -1.2%/yr occurring in the winter. Significant seasonal trends of -0.7 to -0.9%/yr occur at 40 km in the tropics between April and September. Subjecting the statistical models used to calculate the ozone trends to intercomparison tests on a variety of common data sets yields results that indicate the standard deviation between trends estimated by 10 different statistical models is less than 0.1%/yr in the annual-mean trend for SAGE data and less than 0.2%/yr in the most demanding conditions (seasons with irregular, sparse data) [World Meteorological Organization (WMO), 1998]. These consistent trend results between statistical models together with extensive consistency between the independent measurement-system trend observations by Dobson Umkehr, SAGE I and II, and SBUV and SBUV/2 provide a high degree of confidence in the accuracy of the declining ozone amounts reported here. Additional details of ozone trend results from 1978 to 1996 (2 years shorter than reported here) along with lower-stratospheric and tropospheric ozone trends, extensive intercomparisons to assess relative instrument drifts, and retrieval algorithm details are given by WMO [1998].

Newchurch, M. J.↗

Imaging spectrometer measurement of water vapor in the 400 to 2500 nm spectral region

The Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) measures the total upwelling spectral radiance from 400 to 2500 nm sampled at 10 nm intervals. The instrument acquires spectral data at an altitude of 20 km above sea level, as images of 11 by up to 100 km at 17x17 meter spatial sampling. We have developed a nonlinear spectral fitting algorithm coupled with a radiative transfer code to derive the total path water vapor from the spectrum, measured for each spatial element in an AVIRIS image. The algorithm compensates for variation in the surface spectral reflectance and atmospheric aerosols. It uses water vapor absorption bands centered at 940 nm, 1040 nm, and 1380 nm. We analyze data sets with water vapor abundances ranging from 1 to 40 perceptible millimeters. In one data set, the total path water vapor varies from 7 to 21 mm over a distance of less than 10 km. We have analyzed a time series of five images acquired at 12 minute intervals; these show spatially heterogeneous changes of advocated water vapor of 25 percent over 1 hour. The algorithm determines water vapor for images with a range of ground covers, including bare rock and soil, sparse to dense vegetation, snow and ice, open water, and clouds. The precision of the water vapor determination approaches one percent. However, the precision is sensitive to the absolute abundance and the absorption strength of the atmospheric water vapor band analyzed. We have evaluated the accuracy of the algorithm by comparing several surface-based determinations of water vapor at the time of the AVIRIS data acquisition. The agreement between the AVIRIS measured water vapor and the in situ surface radiometer and surface interferometer measured water vapor is 5 to 10 percent.

Green, Robert O.↗

Validation and Development of the GPCP Experimental One-Degree Daily (1DD) Global Precipitation Product

The One-Degree Daily (1DD) precipitation dataset has been developed for the Global Precipitation Climatology Project (GPCP) and is currently in beta test preparatory to release as an official GPCP product. The 1DD provides a globally-complete, observation-only estimate of precipitation on a daily 1 deg. x 1 deg. grid for the period 1997 through early 2000 (by the time of the conference). In the latitude band 40N-40S the 1DD uses the Threshold-Matched Precipitation Index (TMPI), a GPI-like IR product with the pixel-level T(sub b) threshold and (single) conditional rain rate determined locally for each month by the frequency of precipitation in the GPROF SSM/I product and by, the precipitation amount in the GPCP monthly satellite-gauge (SG) combination. Outside 40N-40S the 1DD uses a scaled TOVS precipitation estimate that has month-by-month adjustments based on the TMPI and the SG. Early validation results are encouraging. The 1DD shows relatively large scatter about the daily validation values in individual grid boxes, as expected for a technique that depends on cloud-sensing schemes such as the TMPI and TOVS. On the other hand, the time series of 1DD shows good correlation with validation in individual boxes. For example, the 1997-1998 time series of 1DD and Oklahoma Mesonet values in a grid box in northeastern Oklahoma have the correlation coefficient = 0.73. Looking more carefully at these two time series, the number of raining days for the 1DD is within 7% of the Mesonet value, while the distribution of daily rain values is very similar. Other tests indicate that area- or time-averaging improve the error characteristics, making the data set highly attractive to users interested in stream flow, short-term regional climatology, and model comparisons. The second generation of the 1DD product is currently under development; it is designed to directly incorporate TRMM and other high-quality precipitation estimates. These data are generally sparse because they are observed by low-orbit satellites, so a fair amount of work must be devoted to analyzing the effect of data boundaries. This work is laying, the groundwork for effective use of the NASA Global Precipitation Mission, which will have full Global coverage by low-orbit passive microwave satellites every three hours.

Huffman, George J.↗

Real-time qualitative reasoning for telerobotic systems

This paper discusses the sensor-based telerobotic driving of a car in a-priori unknown environments using 'human-like' reasoning schemes implemented on custom-designed VLSI fuzzy inferencing boards. These boards use the Fuzzy Set theoretic framework to allow very vast (30 kHz) processing of full sets of information that are expressed in qualitative form using membership functions. The sensor-based and fuzzy inferencing system was incorporated on an outdoor test-bed platform to investigate two control modes for driving a car on the basis of very sparse and imprecise range data. In the first mode, the car navigates fully autonomously to a goal specified by the operator, while in the second mode, the system acts as a telerobotic driver's aid providing the driver with linguistic (fuzzy) commands to turn left or right, speed up, slow down, stop, or back up depending on the obstacles perceived by the sensors. Indoor and outdoor experiments with both modes of control are described in which the system uses only three acoustic range (sonar) sensor channels to perceive the environment. Sample results are presented that illustrate the feasibility of developing autonomous navigation modules and robust, safety-enhancing driver's aids for telerobotic systems using the new fuzzy inferencing VLSI hardware and 'human-like' reasoning schemes.

Pin, Eancois G.↗

Random Variables with Moment-Matching Staircase Density Functions

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Luis G. Crespo↗

Characterization of the Crab Pulsar's Timing Noise

We present a power spectral analysis of the Crab pulsar's timing noise, mainly using radio measurements from Jodrell Bank taken over the period 1982-1989, an interval bounded by sparse data sampling and a large glitch. The power spectral analysis is complicated by nonuniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power 'leakage'. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of noninteger spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation onto a uniform time series is possible. A windowed power spectrum is computed revealing a periodic or nearly periodic component with a period of 568 +/- 10 days and a l/f(exp 3) power-law noise component in pulse phase with a noise strength S(sub infinity)=(1.24 +/- 0.067) x 10(exp 16) cycles(exp 2)/sec(exp 2) over the analysis frequency range f=0.003- 0.1 cycles/day. This result deviates from past analyses which characterized the pulse phase timing residuals as either l/f(sub 4) power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of nonuniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a mass function f(M) = (6.8 +/- 2.4) x 10(exp -16) solar mass and a companion mass, M(sub c) is greater than or equal to 3.2 solar mass assuming a Crab pulsar mass of 1.4 solar mass.

Scott, D. M.↗

Recognition of simple visual images using a sparse distributed memory: Some implementations and experiments

Previously, a method was described of representing a class of simple visual images so that they could be used with a Sparse Distributed Memory (SDM). Herein, two possible implementations are described of a SDM, for which these images, suitably encoded, will serve both as addresses to the memory and as data to be stored in the memory. A key feature of both implementations is that a pattern that is represented as an unordered set with a variable number of members can be used as an address to the memory. In the 1st model, an image is encoded as a 9072 bit string to be used as a read or write address; the bit string may also be used as data to be stored in the memory. Another representation, in which an image is encoded as a 256 bit string, may be used with either model as data to be stored in the memory, but not as an address. In the 2nd model, an image is not represented as a vector of fixed length to be used as an address. Instead, a rule is given for determining which memory locations are to be activated in response to an encoded image. This activation rule treats the pieces of an image as an unordered set. With this model, the memory can be simulated, based on a method of computing the approximate result of a read operation.

Jaeckel, Louis A.↗

Application of Spectral Analysis Techniques in the Intercomparison of Aerosol Data. Part II: Using Maximum Covariance Analysis to Effectively Compare Spatiotemporal Variability of Satellite and AERONET Measured Aerosol Optical Depth

Moderate Resolution Imaging SpectroRadiometer (MODIS) and Multi-angle Imaging Spectroradiomater (MISR) provide regular aerosol observations with global coverage. It is essential to examine the coherency between space- and ground-measured aerosol parameters in representing aerosol spatial and temporal variability, especially in the climate forcing and model validation context. In this paper, we introduce Maximum Covariance Analysis (MCA), also known as Singular Value Decomposition analysis as an effective way to compare correlated aerosol spatial and temporal patterns between satellite measurements and AERONET data. This technique not only successfully extracts the variability of major aerosol regimes but also allows the simultaneous examination of the aerosol variability both spatially and temporally. More importantly, it well accommodates the sparsely distributed AERONET data, for which other spectral decomposition methods, such as Principal Component Analysis, do not yield satisfactory results. The comparison shows overall good agreement between MODIS/MISR and AERONET AOD variability. The correlations between the first three modes of MCA results for both MODIS/AERONET and MISR/ AERONET are above 0.8 for the full data set and above 0.75 for the AOD anomaly data. The correlations between MODIS and MISR modes are also quite high (greater than 0.9). We also examine the extent of spatial agreement between satellite and AERONET AOD data at the selected stations. Some sites with disagreements in the MCA results, such as Kanpur, also have low spatial coherency. This should be associated partly with high AOD spatial variability and partly with uncertainties in satellite retrievals due to the seasonally varying aerosol types and surface properties.

aerosols↗

Analysis of airborne imaging spectrometer data for the Ruby Mountains, Montana, by use of absorption-band-depth images

Airborne Imaging Spectrometer-1 (AIS-1) data were obtained for an area of amphibolite grade metamorphic rocks that have moderate rangeland vegetation cover. Although rock exposures are sparse and patchy at this site, soils are visible through the vegetation and typically comprise 20 to 30 percent of the surface area. Channel averaged low band depth images for diagnostic soil rock absorption bands. Sets of three such images were combined to produce color composite band depth images. This relative simple approach did not require extensive calibration efforts and was effective for discerning a number of spectrally distinctive rocks and soils, including soils having high talc concentrations. The results show that the high spectral and spatial resolution of AIS-1 and future sensors hold considerable promise for mapping mineral variations in soil, even in moderately vegetated areas.

Brickey, David W.↗

The StarView intelligent query mechanism

The StarView interface is being developed to facilitate the retrieval of scientific and engineering data produced by the Hubble Space Telescope. While predefined screens in the interface can be used to specify many common requests, ad hoc requests require a dynamic query formulation capability. Unfortunately, logical level knowledge is too sparse to support this capability. In particular, essential formulation knowledge is lost when the domain of interest is mapped to a set of database relation schemas. Thus, a system known as QUICK has been developed that uses conceptual design knowledge to facilitate query formulation. By heuristically determining strongly associated objects at the conceptual level, QUICK is able to formulate semantically reasonable queries in response to high-level requests that specify only attributes of interest. Moreover, by exploiting constraint knowledge in the conceptual design, QUICK assures that queries are formulated quickly and will execute efficiently.

Semmel, R. D.↗

Towards an Automated Classification of Transient Events in Synoptic Sky Surveys

We describe the development of a system for an automated, iterative, real-time classification of transient events discovered in synoptic sky surveys. The system under development incorporates a number of Machine Learning techniques, mostly using Bayesian approaches, due to the sparse nature, heterogeneity, and variable incompleteness of the available data. The classifications are improved iteratively as the new measurements are obtained. One novel featrue is the development of an automated follow-up recommendation engine, that suggest those measruements that would be the most advantageous in terms of resolving classification ambiguities and/or characterization of the astrophysically most interesting objects, given a set of available follow-up assets and their cost funcations. This illustrates the symbiotic relationship of astronomy and applied computer science through the emerging disciplne of AstroInformatics.

classification↗

Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning

Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions.

Corbetta, Matteo↗

Comparison of GPCP Monthly and Daily Precipitation Estimates with High-Latitude Gauge Observations

It is very important to know how much rain and snow falls around the world for uses that range from crop forecasting to disaster response, drought monitoring to flood forecasting, and weather analysis to climate research. Precipitation is usually measured with rain gauges, but rain gauges don t exist in areas that are sparsely populated, which tends to be a good portion of the globe. To overcome this, meteorologists use satellite data to estimate global precipitation. However, it is difficult to estimate rain and especially snow in cold climates using most current satellites. The satellite sensors are often "confused" by a snowy or frozen surface and therefore cannot distinguish precipitation. One commonly used satellite-based precipitation data set, the Global Precipitation Climatology Project (GPCP) data, overcomes this frozen-surface problem through the innovative use of two sources of satellite data, the Television Infrared Observation Satellite Operational Vertical Sounder (TOVS) and the Atmospheric Infrared Sounder (AIRS). Though the GPCP estimates are generally considered a very reliable source of precipitation, it has been difficult to assess the quality of these estimates in cold climates due to the lack of gauges. Recently, the Finnish Meteorological Institute (FMI) has provided a 12-year span of high-quality daily rain gauge observations, covering all of Finland, that can be used to compare with the GPCP data to determine how well the satellites estimate cold-climate precipitation. Comparison of the monthly GPCP satellite-based estimates and the FMI gauge observations shows remarkably good agreement, with the GPCP estimates being 6% lower in the amount of precipitation than the FMI observations. Furthermore, the month-to-month correlation between the GPCP and FMI is very high at 0.95 (1.0 is perfect). The daily GPCP estimates replicate the FMI daily occurrences of precipitation with a correlation of 0.55 in the summer and 0.45 in the winter. The winter result indicates the GPCP estimates have skill in "seeing" snowfall, which is the most challenging situation. Thus, the GPCP data set successfully overcomes a current limitation in satellite meteorology, namely the estimation of cold-climate precipitation. The success of the GPCP data set bodes well for future missions, whose instrumentation is specifically designed to give even more information for addressing cold-climate precipitation.

Bolvin, David T.↗

Transfer of Satellite Rainfall Uncertainty from Gauged to Ungauged Regions at Regional and Seasonal Timescales

Hydrologists and other users need to know the uncertainty of the satellite rainfall data sets across the range of time/space scales over the whole domain of the data set. Here, uncertainty' refers to the general concept of the deviation' of an estimate from the reference (or ground truth) where the deviation may be defined in multiple ways. This uncertainty information can provide insight to the user on the realistic limits of utility, such as hydrologic predictability, that can be achieved with these satellite rainfall data sets. However, satellite rainfall uncertainty estimation requires ground validation (GV) precipitation data. On the other hand, satellite data will be most useful over regions that lack GV data, for example developing countries. This paper addresses the open issues for developing an appropriate uncertainty transfer scheme that can routinely estimate various uncertainty metrics across the globe by leveraging a combination of spatially-dense GV data and temporally sparse surrogate (or proxy) GV data, such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar and the Global Precipitation Measurement (GPM) mission Dual-Frequency Precipitation Radar. The TRMM Multi-satellite Precipitation Analysis (TMPA) products over the US spanning a record of 6 years are used as a representative example of satellite rainfall. It is shown that there exists a quantifiable spatial structure in the uncertainty of satellite data for spatial interpolation. Probabilistic analysis of sampling offered by the existing constellation of passive microwave sensors indicate that transfer of uncertainty for hydrologic applications may be effective at daily time scales or higher during the GPM era. Finally, a commonly used spatial interpolation technique (kriging), that leverages the spatial correlation of estimation uncertainty, is assessed at climatologic, seasonal, monthly and weekly timescales. It is found that the effectiveness of kriging is sensitive to the type of uncertainty metric, time scale of transfer and the density of GV data within the transfer domain. Transfer accuracy is lowest at weekly timescales with the error doubling from monthly to weekly.However, at very low GV data density (<20% of the domain), the transfer accuracy is too low to show any distinction as a function of the timescale of transfer.

Tang, Ling↗

A Study on the Potential Applications of Satellite Data in Air Quality Monitoring and Forecasting

In this study we explore the potential applications of MODIS (Moderate Resolution Imaging Spectroradiometer) -like satellite sensors in air quality research for some Asian regions. The MODIS aerosol optical thickness (AOT), NCEP global reanalysis meteorological data, and daily surface PM(sub 10) concentrations over China and Thailand from 2001 to 2009 were analyzed using simple and multiple regression models. The AOT-PM(sub 10) correlation demonstrates substantial seasonal and regional difference, likely reflecting variations in aerosol composition and atmospheric conditions, Meteorological factors, particularly relative humidity, were found to influence the AOT-PM(sub 10) relationship. Their inclusion in regression models leads to more accurate assessment of PM(sub 10) from space borne observations. We further introduced a simple method for employing the satellite data to empirically forecast surface particulate pollution, In general, AOT from the previous day (day 0) is used as a predicator variable, along with the forecasted meteorology for the following day (day 1), to predict the PM(sub 10) level for day 1. The contribution of regional transport is represented by backward trajectories combined with AOT. This method was evaluated through PM(sub 10) hindcasts for 2008-2009, using ohservations from 2005 to 2007 as a training data set to obtain model coefficients. For five big Chinese cities, over 50% of the hindcasts have percentage error less than or equal to 30%. Similar performance was achieved for cities in northern Thailand. The MODIS AOT data are responsible for at least part of the demonstrated forecasting skill. This method can be easily adapted for other regions, but is probably most useful for those having sparse ground monitoring networks or no access to sophisticated deterministic models. We also highlight several existing issues, including some inherent to a regression-based approach as exemplified by a case study for Beijing, Further studies will be necessa1Y before satellite data can see more extensive applications in the operational air quality monitoring and forecasting.

Li, Can↗

Performance Calculations for a Boundary-Layer-Ingesting Fan Stage from Sparse Measurements

A test of the Boundary Layer Ingesting-Inlet / Distortion-Tolerant Fan was completed in NASA Glenn's 8-Foot by 6-Foot supersonic wind tunnel. Inlet and fan performance were measured by surveys using a set of rotating rake arrays upstream and downstream of the fan stage. Surveys were conducted along the 100 percent speed line and a constant exit corrected flow line passing through the aerodynamic design point. These surveys represented only a small fraction of the data collected during the test. For other operating points, data was recorded as snapshots without rotating the rakes which resulted in a sparser set of recorded data. This paper will discuss analysis of these additional, lower measurement density data points to expand our coverage of the fan map. Several techniques will be used to supplement the snapshot data at test conditions where survey data also exists. The supplemented snapshot data will be compared with survey results to assess the quality of the approach. Effective methods will be used to analyze the data set for which only snapshots exist.

fan efficiency↗